The Proceedings of the 5th International Conference on Energy Storage and Intelligent Vehicles (ICEIV 2022) 9819910269, 9789819910267
This book includes original, peer-reviewed research papers from the 5th International Conference on Energy Storage and I
290 52 157MB
English Pages 1343 [1344] Year 2023
Contents
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries Under Different Precooling Conditions
1 Introduction
2 Model Development
2.1 Battery Parameters
2.2 Electrochemical Model
2.3 3D Thermal Model
2.4 Side Reaction Model
2.5 Methodology
3 Results and Discussion
3.1 Model Validation
3.2 Impact of Pre-cooling
3.3 Resting Time
4 Conclusion
References
Research on Detection Method of Metal Foreign Objects in Electric Vehicle Wireless Power Transfer System
1 Introduction
2 Theoretical Analysis
2.1 Detection Sensitivity Analysis
2.2 Long Rectangular Detection Coils
3 Long Rectangular Interconnection Coil Group
3.1 Direct Connection and Reverse Connection of Detection Coil
3.2 Magnetic Field Distribution and Magnetic Line of Force Direction
3.3 Long Rectangular Interconnecting Coil Group
4 Experimental Result
5 Conclusion
References
An Adaptive Equivalent Heat Minimization Strategy for Hybrid Electric Trucks Braking Considering Brake Temperature Rise in Long Downhills
1 Introduction
2 Vehicle Models
2.1 Vehicle Models
2.2 Electric Drive System Model
2.3 Brake System Model
3 Adaptive Equivalent Heat Minimization Strategy
3.1 Braking Control Problem Description
3.2 The Optimal Solution Method
4 Simulation Results and Discussion
4.1 Results
4.2 Discussion
5 Conclusion
References
Field-Oriented Control Strategy Verification Based on Power Hardware in Loop Simulation Technology
1 Introduction
2 Induction Motor Mathematical Model
3 Indirect Field-Oriented Control
4 SVPWM Method in PWM Inverter
5 Typhoon Hil Real-Time Modeling
6 Test Bench Layout
7 Results
8 Conclusion
References
Hybrid Estimation of Residual Capacity for Retired LFP Batteries
1 Introduction
2 Estimation Model Establishment
2.1 Capacity Loss Mechanism Model
2.2 Support Vector Regression Method
2.3 SVR Parameters Optimized Using Improved Whale Optimization Algorithm
2.4 The Framework of Residual Capacity Estimation Method
3 Results Verification and Discussion
4 Conclusion
References
Design of a Full-Time Security Protection System for Energy Storage Stations Based on Digital Twin Technology
1 Introduction
2 Digital Twin Technology
2.1 Digital Twin Battery Energy Storage Stations
2.2 Features of the Digital Twin BESS
3 Digital Twin Technology
3.1 BESS Full-Time Security Protection Method
3.2 TR Early Warning Method Based on Multi-feature Parameter BESS
3.3 Full-Time Multi-level Security Protection System Design
4 Design of BESS Security Protection System Based on Digital Twin
4.1 Framework Design
4.2 Digital Twin Security Protection System Implementation Solution
5 Conclusion
References
Online Electrical Fault Diagnosis and Low-Cost State Estimation for Lithium-Ion Battery Pack Based Electric Drive System
1 Introduction
2 Workflow of Proposed Method
3 Data Preparation
4 Theory of Proposed Method
5 Experimental Validations and Discussion
6 Conclusion
References
Capacity Prediction of Lithium-Ion Battery Based on HGWO-SVR
1 Introduction
2 HGWO-SVR
2.1 DE
2.2 GWO
2.3 SVR
3 Simulation Result
3.1 Influence of HGWO Optimization Algorithm on Prediction Results
3.2 Influence of Different Neural Networks on Prediction Results
3.3 HGWO-SVR Algorithm Predicting Impact of Different Proportional Capacity Training Data
4 Conclusions
References
Life Cycle Carbon Footprint Assessment of Power Transmission Equipment
1 Introduction
2 Life Cycle Carbon Footprint of Power Transmission Equipment Definition and Calculation Process
2.1 Life Cycle Carbon Footprint Definition of Power Transmission Equipment
2.2 Life Cycle Carbon Footprint Calculation Process of Power Transmission Equipment
3 Carbon Footprint Assessment Model of Power Transmission Equipment Based on Life Cycle
3.1 Raw Material Acquisition Stage
3.2 Manufacturing and Assembly Stage
3.3 Transportation Stage
3.4 Operation and Maintenance Stage
3.5 Decommissioning and Scrapping Stage
4 Proposed Conversion Method for Life Cycle Carbon Footprint
5 Case Study
5.1 Parameter Setting
5.2 Numerical Results
6 Conclusion
References
Performance Optimization of Tesla Valve Microchannel Cold Plates for Li-Ion Battery
1 Introduction
2 Battery Microchannel Cooling Simulation
3 Battery Microchannel Cooling Experiments
4 Conclusions
References
Data-Driven Method Based Wind Power Characteristic Analysis and Climbing Identification
1 Introduction
2 Data-Driven based Wind Power Characteristic Analysis and Climbing Identification Method
2.1 Wind Power Output Characteristics
2.2 Extraction for Climbing Threshold
2.3 2D Convolutional Neural Network-Based Climbing Identification
3 Case Study
3.1 Analysis Results for Climbing Threshold Extraction
3.2 Analysis Results for Climbing Identification
4 Conclusion
References
Nonlinear-Drift-Driven Wiener Process–Markov Chain Switching Model for Predicting Lithium-Ion Battery Remaining Useful Life
1 Introduction
1.1 Motivation
1.2 Literature Review
1.3 Research Gaps and Contributions
1.4 Organization
2 Nonlinear-Drift-Driven Wiener Process–Markov Chain Switching Model
2.1 Collective Structure
2.2 Degradation Model Based on Nonlinear-Drift-Driven Wiener Process
2.3 Switching Model Based on Markov Chain
2.4 Combined Model Based on Fuzzy System
2.5 Parameter Identification
3 Algorithm Verification
3.1 Battery Degradation Data
3.2 RUL Prediction Results
4 Conclusion
References
Estimation of Battery State Based on Discharge Voltage Drop and AC Impedance at Full Charge
1 Introduction
2 Discharge Voltage Drop and AC Impedance of Lead-Acid Batteries Under Full Charge
2.1 The Coup De Fouet Phenomenon in Lead-Acid Batteries
2.2 Discharge Performance of Batteries in Different Health States
2.3 AC Impedance Characteristics of Lead-Acid Batteries
2.4 Estimation of the Dischargeable Capacity of a Battery by Combining Voltage Drop and AC Impedance
3 Analysis of Algorithms
4 Conclusion
References
Study on Ferromagnetic Noise of EMU Traction Transformer
1 Introduction
2 Ferromagnetic Noise Generation Mechanism of Traction Transformer
3 Principle of Four-Quadrant Rectifier
4 Analysis with Simulation
4.1 Modeling
4.2 Leakage Inductor and Secondary Side Resistor
4.3 DC Link Voltage
4.4 Switching Frequency of Four-Quadrant Rectifier
4.5 Switching off Four-Quadrant Rectifier
5 Conclusion
References
Research on Driving Cycle Recognition Strategy Based on Machine Learning
1 Introduction
2 Construction of Comprehensive Driving Cycle Database
2.1 Analysis of Driving Cycles Data
2.2 Principal Component Analysis (PCA)
2.3 K-means Clustering Analysis of Driving Cycles
3 Driving Cycles Identification Based on Machine Learning Intelligent Algorithm
3.1 Selection of Driving Cycles Identification Parameters
3.2 Analysis and Comparison of Driving Cycle Recognition Strategies Based on Machine Learning Algorithms
3.3 Analysis and Comparison of Different Driving Cycle Identification Strategies
4 Identify the Recognition Period
5 Summary
References
Research on Energy Management Strategy of Fuel Cell Buses In and Out of Bus Stop Based on Speed Optimization
1 Introduction
2 Construction of Traffic Simulation Environment
3 FCHEB Model
3.1 Drive Motor Model
3.2 Fuel Cell Hybrid Power System Model
4 Energy Management of FCHEB with Optimized Speed
4.1 Speed Optimization Based on DP
4.2 Energy Management Based on MPC
5 Simulation Results and Discussions
6 Conclusion
References
A DFT Study on Electronic and Optical Properties of La/Ce-Doped CaTiO3 Perovskite
1 Introduction
2 Computational Methods
3 Results and Discussion
3.1 Structural Phase Transformation and Defect Formation Energy
3.2 Electronic Structure
3.3 Optical Properties
4 Conclusion
References
Charging Pile Sharing Scheme Based on Blockchain Technology
1 Introduction
2 Introduction to Blockchain
2.1 The Origin of Blockchain
2.2 The Advantages of Blockchain Technology
2.3 The Application of Blockchain
3 Charging Pile Sharing Scheme Based on Blockchain Technology
3.1 The Solution of Blockchain
3.2 Shared Advantage
4 Blockchain Technology Charging Pile Sharing Solution Platform
5 Conclusions
References
An Electric Vehicle Charging Station Based on SiC MOSFETs and Si IGBTs Hybrid Cascaded Three-Level H-Bridge Converter
1 Introduction
2 Proposed Topology and Control Schemes
2.1 Proposed Topology
2.2 Modulation Scheme for Hybrid Cascaded Three-Level H-Bridge Converter
2.3 System-Level Control Schemes
3 Simulation Results
4 Conclusion
References
A Simulation Study on Magnetic Field Distribution of Two-Cells Proton Exchange Membrane Fuel Cell Stack
1 Introduction
2 Modeling and Simulation of PEMFC
2.1 Background Theory of Numerical Analysis
2.2 Modeling of PEMFC
3 Result and Discussion
3.1 The Polarization Curve and Power Curve of PEMFC Model
3.2 Magnetic Field Distribution of PEMFC Stack
3.3 Influence of Cell Distance on Magnetic Field
4 Conclusion
References
3D Modeling and Performance Analysis of a PEM Water Electrolyzer Based on Multiphysics Couplings
1 Introduction
2 Model Description
2.1 Basics of PEMWE and Geometric Model
2.2 Numerical Model
3 Results and Discussion
3.1 Operating Temperature
3.2 Operating Pressure
3.3 Membrane Thickness
4 Conclusion
References
State of Health Estimation of Lithium-Ion Battery Considering Random Charging
1 Introduction
2 Voltage Estimation of the CC Charging Phase
2.1 Voltage Estimation Method
2.2 Verification for Different Cycles
2.3 Verification for Different Cycles
3 SOH Estimation
3.1 Gaussian Process Regression Algorithm
3.2 SOH Estimation Based on Different Voltage Ranges
3.3 SOH Estimation in Random Charging Scenarios
4 Conclusion
References
Unified Control of Bidirectional H4 Bridge Converter in Single-Phase Energy Storage Inverter
1 Introduction
2 Rectification Operating Principle of Single-Phase H4 Bridge Converter
3 Control Method of Bidirectional H4 Bridge Converter
3.1 Modeling and Control of Current Inner Loop
3.2 Parameter Tuning of Voltage Outer Loop Controller Based on Power Balance
3.3 Control Method of Inverter State Voltage Outer Loop
3.4 Design of Phase Locked Loop Based on Second-Order Generalized Integrator (SOGI)
4 Analysis of Simulation and Experimental Results
4.1 Simulation of Rectifier and Grid Connected Inverter of Bidirectional H4 Bridge Converter
4.2 Grid Connected Inverter and Rectifier Experiment
5 Conclusion
References
Optimal Siting and Capacity Allocation of BESS Based on Improved Multi-objective Particle Swarm Algorithm
1 Introduction
2 Optimal Siting and Capacity Model for BESS
2.1 Target Function
2.2 Binding Conditions
2.3 Economic Analysis
3 Adaptive Multi-target Particle Swarm
3.1 Adaptive Inertia Weights
3.2 Crossover Variation
3.3 Non-disadvantageous Solution Set Update
3.4 Multi-attribute Decision Making Based on TOPSIS Method
3.5 Problem Solving
4 Analysis and Study of Algorithms
4.1 Simulation Analysis
4.2 Access to 2 Battery Energy Storage Systems Analysis
5 Conclusion
References
Coupling Forecasting of Short-Term Power Load and Renewable Energy Sources Generation Based on State-Space Equations
1 Introduction
2 Methodology
2.1 State-Space Equations
2.2 Error Correction Model
3 Result and Discussion
3.1 Coupling Relationship
3.2 Analysis of Forecast Results
4 Conclusion
References
Active Equalization of Lithium Battery Based on WOA and FLC Algorithm
1 Introduction
2 Equalizing Circuit Topology
3 Circuit Equilibrium Strategy and Algorithm
3.1 Energy Balance Path Optimization Based on Whale Algorithm
3.2 Fuzzy Logic Control Strategy
4 Simulation Results and Analysis
5 Conclusion
References
Bi-level Optimal Sizing and Scheduling of Hybrid Thermal Power-Energy Storage System for Peak Shaving
1 Introduction
2 System Configuration
3 Optimization Model
3.1 Objective Function of Lower-Layer Model
3.2 Constraints of Lower-Layer Model
3.3 Objective Function of Upper-Layer Model
3.4 Constraints of Upper-Layer Model
4 Results and Discussion
4.1 Data Descriptions
4.2 Optimization Results
4.3 Operation Analysis
4.4 Economic Sensitivity Analysis of Different Sizing
5 Conclusions
References
Economic Optimal Dispatch of Integrated Energy System Considering Market Plan
1 Introduction
2 Integrated Energy System Model
2.1 System Physical Model
2.2 Landscape Uncertainty
3 Economic Optimization Model of Integrated Energy System
3.1 Optimize the Target
3.2 Restrictions
4 Case Analysis
4.1 Example Introduction
4.2 Optimization Results and Analysis
5 Summarize
References
Analysis of Energy Loss and Heat Generation Characteristics of Supercapacitors
1 Introduction
2 Experimental Device and Method
3 Calibration of Measuring Devices
4 Results and Discussion
4.1 Electrical Analysis of SCs
4.2 Thermal Analysis of SCs
4.3 Energy Loss Analysis of SCs
5 Conclusions
References
Grid-Supported Modular Multi-level Energy Storage Power Conversion System
1 Introduction
2 Topology of MMC-ESS
3 Grid-Supported Control Strategy of MMC-ESS
3.1 The Principle of Grid-Supported Control
3.2 Grid-Supported Control Strategy
4 Simulation and Experiment of the System
4.1 Load Sudden Change
4.2 Frequency Sudden Change
5 Conclusion
References
On-line Monitoring and State of Health Estimation Technology of Lead-Acid Battery
1 Introduction
2 VRLA Battery Working Principle
2.1 VRLA Battery Electromotive Force (EMF)
2.2 VRLA Battery Voltage “steep drop and rise again” (Coup de fouet)
3 Battery SOH Estimation Method
3.1 Principal Component Analysis (PCA)
3.2 SOH Estimation Model
4 Experimental Validation
4.1 Online Monitoring Platform
4.2 SOH Estimation Results and Analysis
5 Conclusion
References
Distributed Optimal Allocation of Renewable Energy and Energy Storage Based on Alternating Direction Method of Multipliers
1 Introduction
2 Centralized Optimization Model
2.1 Objective Function
2.2 Constraints
3 ADMM-Based Distributed Cooperative Optimization Model
3.1 Decomposition of Synergistic Mechanisms
3.2 Distributed Collaborative Optimal Allocation Algorithm
4 Example Analysis
4.1 Distributed Collaborative Optimal Allocation Analysis
5 Conclusion
References
Optimization of Moisture Absorption of High Temperature Composite Phase Change Thermal Storage Materials
1 Introduction
2 High Temperature Composite Form-Stable Phase Change Material System Screening
2.1 Screening of Phase Change Materials and Their Hygroscopicity
2.2 Screening of Skeleton Materials
2.3 Screening of Thermally Conductive Materials
3 Experimental Materials and Methods
3.1 Sample Preparation Process
3.2 Measurement Method
4 Results and Discussion
4.1 Material Modification
4.2 Material Surface Treatment
5 Conclusion
References
Research Progress of Coordination Control Strategy for Flywheel Array Energy Storage System
1 Introduction
2 FAESS Topology
3 FAESS Power Coordination Control Strategy
3.1 DC Bus Parallel FAESS Power Coordination Control
3.2 AC Bus Parallel FAESS Power Coordination Control
4 FAESS Array Parallel Control Strategy
5 FAESS Coordinated Control Strategy Application Extension
6 Conclusion and Outlook
References
Lifetime Test Platform of Mica Paper Capacitors Under Microsecond Pulse
1 Introduction
2 Operation Principle
3 The Design of Subsystems
3.1 Air-Core Pulse Transformer
3.2 Low Jitter Triggered Gas Switch
4 Experimental Result
5 Conclusion
References
Simulation Study of External Short Circuit Characteristics for Lithium-Ion Battery Based on Electrochemical-Thermal Model
1 Introduction
2 Test Platform and Test Procedures
3 Modeling
3.1 Electrochemical Model
3.2 Thermal Model
3.3 Parameter Acquisition and Model Validation
4 Simulation Research on ESC Characteristics
4.1 Influence of Initial SOC on ESC Characteristics
4.2 Influence of Ambient Temperature on ESC Characteristics
4.3 Influence of Particle Radius on ESC Characteristics
4.4 Influence of Exchange Current Density on ESC Characteristics
5 Conclusion
References
Operation Analysis and Optimization Suggestions of User-Side Battery Energy Storage Systems
1 Introduction
2 Evaluation Indexes of Operation Performance
3 Evaluation Indexes of Charge-Discharge Performance
3.1 Evaluation Indexes of Energy Efficiency Performance
3.2 Evaluation Indexes of Safety Performance
3.3 Evaluation Indexes of Reliability Performance
3.4 Evaluation Indexes of Economic Performance
4 Operation Analysis and Evaluation of a Typical User-Side BESS for Peak-Load Shifting
4.1 Basic Information About the User-Side BESS
4.2 Calculation Results of the Operation Evaluation Indexes
4.3 Results Analysis and Optimization Suggestions
5 Conclusion
References
Discussion on Key Components Design for Off-Grid Photovoltaic Electrolysis Hydrogen Production System
1 Introduction
2 Design of Off-Grid Photovoltaic Electrolysis Hydrogen Production System
3 Power Supply System
3.1 Photovoltaic DC Power Supply Unit for Electrolyzers
3.2 AC Power Supply Unit for Hydrogen Production Auxiliary System
4 Control System Design
4.1 Hardware Design
4.2 Software Design of Auxiliary Power Supply Control System
5 Conclusions
References
Minimization Design of Energy Storage Capacitor of Electromagnetic Switch Control Module Based on Zero-Current Opening Strategy
1 Introduction
2 Zero-Current Opening Control Strategy
3 Capacity and Maintenance Operation Time
3.1 Iterative Model
3.2 Simulation Analysis
4 Experimental Verification
5 Conclusion
References
Analysis of Pulse and Alternating Current Low Temperature Charging Based on Optimal Charging Frequency
1 Introduction
2 AC Impedance Model and Data Introduction
2.1 AC Impedance Model and Optimal Frequency
2.2 Data Introduction and Basic Information of Cell
3 Battery Model
3.1 Equivalent Circuit Model
3.2 Thermal Model
4 Simulation and Discussion
5 Conclusions
References
Axial Magnetic Field Simulation and Structure Optimization of Contacts in Vacuum Interrupter with Iron Core
1 Introduction
2 Contact Model Establishment
3 Analysis of Simulation Results
4 Simulation Analysis of Transient Magnetic Field After Contact Optimization
4.1 AMF Distribution at Peak Current
4.2 AMF Distribution at Current Zero
4.3 AMF Lag Time Distribution
5 Conclusions
References
Balancing Topology Research of Lithium-Ion Battery Pack
1 Introduction
2 Battery Balance
2.1 Balanced Topology
2.2 Balancing Strategy
2.3 Passive Balancing
3 Active Balancing
3.1 Capacitor Based Battery Pack Balancing Topology
3.2 Inductance Based Battery Pack Balance Topology
3.3 Transformer Based Battery Pack Balancing Topology
3.4 Converter Based Battery Pack Balancing Topology
4 Balanced Topology Comparison
5 Conclusion
References
Coordinated Control Strategy of Secondary Ripple in DC Microgrid Based on Impedance Model
1 Introduction
2 DC Microgrid System Structure
3 Impedance Modeling of Conventionally Controlled DC/DC Converters
3.1 Modeling of Output Impedance of Energy Storage Bidirectional Buck/boost Converter
3.2 Modeling of Input Impedance of DC Load Buck Converter
4 Impedance Coordination Control Strategy
4.1 Improved Energy Storage Bidirectional Buck/boost Converter
4.2 Improved Active Capacitor Boost1 Converter
5 Simulation
6 Conclusion
References
Research on Coordinated Control Strategy for Islanded Operation of Household Photovoltaic-Storage Micro-grid
1 Introduction
2 The Topology of Household Photovoltaic-Storage Micro-grid
3 Control Strategy for Islanded Operation of Photovoltaic-Storage Micro-grid
3.1 Inner Loop Current Control Based on d-q Coordinate System
3.2 P-f and Q-V Droop Control Based on d-q Coordinate System
3.3 Constant Voltage Frequency Control Based on d-q Coordinate System
3.4 Coordinated Control of Islanded Operation of Photovoltaic-Storage Micro-grid
4 Simulation Analysis
4.1 Operating Condition 1 of Household Photovoltaic-Storage Micro-grid
4.2 Operating Condition 2 of Household Photovoltaic-Storage Micro-grid
4.3 Operating Condition 3 of Household Photovoltaic-Storage Micro-grid
5 Conclusion
References
Fuzzy Comprehensive Evaluation on Hydraulic High Voltage Circuit Breaker Mechanical Characteristics in Smart Substation
1 Introduction
2 Fuzzy Comprehensive Evaluation Principles
3 Establishment of Fuzzy Evaluation Model for Hydraulic High Voltage Circuit Breaker
3.1 Establishment of Evaluation Factor Set
3.2 Establishment of Evaluation Level
3.3 Determination of Weight
3.4 Establishment of Membership Function
4 Case Analysis
4.1 Normal Working Condition
4.2 Abnormal Working Condition
5 Conclusion
References
State of Charge Estimation for Lithium-Ion Battery Based on Particle Swarm Optimization Algorithm and Multi-Kernel Relevance Vector Machine
1 Introduction
2 SOC Estimation Model Based on PSO-MKRVM
2.1 Multicore Relevance Vector Machine Algorithm
2.2 Particle Swarm Optimization Algorithms
2.3 PSO-MKRVM Algorithm Steps
3 Experimental Results and Analysis
3.1 Data Pre-processing
3.2 Evaluation Indicators
3.3 Estimated Results from One Measurement
3.4 Estimated Results from Multiple Measurements
4 Conclusions
References
Research on Variation Rules of Characteristic Parameters and Early Warning Method of Thermal Runaway of Lithium Titanate Battery
1 Introduction
2 Development Process and Judging Method of Thermal Runaway of Lithium Battery
2.1 Thermal Runaway Development Process of Lithium Ion Batteries
2.2 Thermal Runaway Judging Criterias of Lithium Ion Batteries
3 Design of Experiment
3.1 Samples of the Battery
3.2 Experimental Facility and Design
4 Analysis of Characteristic Parameters of Thermal Runaway
4.1 Thermal Runaway Phenomenon
4.2 Analysis of Characteristic Parameters of Heating Thermal Runaway
4.3 Analysis of Characteristic Parameters of Overcharging Thermal Runaway
5 Conclusion
References
Study on Parameter Characteristics and Sensitivity of Equivalent Circuit Model of Lithium Iron Phosphate Battery in Decay Dimension
1 Introduction
2 Test Bench and Experimental Procedures
3 Battery Model
3.1 Difference Analysis
3.2 Change of Euclidean Distance Analysis Parameters
4 Simulation Verification
5 Conclusion
References
Research on Defect Simulation and Diagnosis Method of On-Load Tap Changer
1 Introduction
2 Experiment Preparation
2.1 Detection Platform Construction
2.2 Signal Processing Short Time Energy Method
3 Defect Simulation of OLTCs
4 Diagnosis Method of OLTCs
5 Conclusion
References
Internal Short Circuit Warning Method of Parallel Lithium-Ion Module Based on Loop Current Detection
1 Introduction
2 Internal Short Circuit Loop Current Characteristic Experiment
2.1 Acupuncture Simulation of Internal Short Circuit Experiments of Parallel Lithium-Ion Batteries
2.2 4-Series 2-Parallel Lithium-Ion Battery Pack Acupuncture to Simulate Internal Short Circuit Experiment
3 Conclusion
References
Prediction Method of Ohmic Resistance and Charge Transfer Resistance for Lithium-Ion Batteries Based on CSA-SVR
1 Introduction
2 Feature Extraction and Analysis
2.1 Experimental Data of Cycle Life Attenuation of Lithium Ion Battery
2.2 Feature Extraction Based on Charging Curve
2.3 Feature Extraction Based on Incremental Capacity Curve
2.4 Grey Relation Analysis of Features
3 CSA Optimized SVR Prediction Model
3.1 Cuckoo Search Algorithm
3.2 Support Vector Regression
3.3 CSA-SVR Method
4 Simulation Results and Analysis
5 Conclusions
References
Research on Experimental System of Magnetically Mediated Thermoacoustic Detecting Method
1 Introduction
2 Principle of MMTDM
3 Construction of Experimental System
4 Experimental Results and Analysis
5 Conclusion
References
Research on Mobile Energy Storage Vehicles Planning with Multi-scenario and Multi-objective Requirements
1 Introduction
2 Design of MESV
3 Models and Algorithms
3.1 MESV Target Model
3.2 MESV Constrained Boundary Model
3.3 Solving Algorithm
4 Case Analysis
5 Conclusion
References
A Novel Control Strategy of Air-Core Pulsed Alternators for Driving Electromagnetic Railgun
1 Introduction
2 Single-Phase Short-Circuit Discharge
3 Discharge with Inductive Load
4 Speed Control
5 Conclusion
References
Optimal Dispatch Strategy of a Flexible Energy Aggregator Considering Virtual Energy Storage
1 Introduction
2 Model
2.1 Data Center Model
2.2 Flexible Scheduling Model of Data Load in Data Center
2.3 Data Center Power Consumption Model Based on DVFS Technology
2.4 Data Center Model Based on the First Law of Thermodynamics
2.5 Residential Building Model
2.6 Demand-Side and Supply-Side Equilibrium Equations
2.7 Generalized Energy Storage Model
2.8 Battery Storage
2.9 Virtual Energy Storage
2.10 Aggregator Objective Function
3 Case Study
3.1 Comparison of Power Purchase, PV Output Curve and Load Curve
3.2 Thermal Characteristics and Power Consumption of Data Centers and Buildings Under Different Operation Models
3.3 Hourly SOC of Virtual Energy Storage
4 Conclusion
References
State of Charge Estimation of Lithium-Ion Battery Based on EKF with Adaptive Fading Factor
1 Introduction
2 Equivalent Model and Parameter Identification of Lithium-Ion Battery
2.1 Equivalent Circuit Model of Lithium-Ion Battery
2.2 SOC-OCV Relationship Curve of Battery
2.3 Parameter Identification of Battery Model
3 Extended Kalman Filter with Adaptive Fading Factor
3.1 Traditional Extended Kalman Filter
3.2 Analysis of EKF with Adaptive Fading Factor
4 Experiment and Simulation Analysis
5 Conclusion
References
On-Line Evaluation Method of Battery Bank Inconsistency for DC Power System
1 Introduction
2 Comprehensive Weighting Method and Grey Clustering
3 Establishment of Evaluation Model for Battery Bank
4 Conclusions
References
A Coordinated Control Strategy for PV-BESS Combined System and Optimal Configuration of Energy Storage System
1 Introduction
2 Coordinated Control Strategy of PV-BESS System
2.1 Definition of the Inertial Constant of PV-BESS System
2.2 Dynamic Control Strategy Based on VSG
3 Control Verification and Impacts Analysis of Different Control Parameters
3.1 Verification of Dynamic Control Scheme
3.2 Impact Analysis of Control Parameters
4 Conclusions
References
Multi-objective Optimal Scheduling Strategy of EVs Considering Customer Satisfaction and Demand Response
1 Introduction
2 Demand Response Model of Electric Vehicle
2.1 Overall Framework of the System
2.2 User Trip Characteristics
2.3 Period Shift Model and User Psychological Model
2.4 Customer Satisfaction Model of Electric Vehicle
3 Optimal Scheduling Model of Electric Vehicle
3.1 Objective Functions and Constraints
3.2 Solution Method
4 Case Study
4.1 Parameter Setting
4.2 Optimization Results
5 Conclusion
References
Deep-Learning Network-Based Method for SOH Estimation of Lithium-Ion Battery for Electric Vehicles
1 Introduction
2 Datasets For SOH Estimation.
3 Methodologies
3.1 Model Description
3.2 Full Architecture for SOH Estimation
4 Results and Discussions
4.1 Experimental Platform
4.2 Results on NASA Dataset
4.3 Results on Oxford Dataset
5 Conclusions
References
Research on Optimal Allocation of Energy Storage in Active Distribution Network Based on Differential Particle Swarm Algorithm
1 Introduction
2 Optimization Model of Energy Storage Location Based on Standard Deviation of Network Loss Sensitivity
3 Energy Storage Capacity Optimization Model
3.1 Objective Function
3.2 Binding Conditions
4 Model Solving Method Based on Differential Particle Swarm Algorithm
4.1 Differential Particle Swarm Algorithm
4.2 Algorithm Flow
5 Example Analysis
5.1 Test System
5.2 Energy Storage Location Optimization
5.3 Optimal Allocation of Capacity
6 Conclusion
References
Adjusting Energy Storage Performance of PMMA/P(VDF-HFP) Composites by Improving Compatibility Through Molecular Weight Regulation
1 Introduction
2 Experimental Section
2.1 Materials
2.2 Fabricating Process of Polymer Films
2.3 Characterization
3 Results
3.1 Microstructure and Compatibility
3.2 Dielectric and Energy Storage Performance
4 Conclusion
References
Composite Micro Energy System for Wireless Sensor Network Nodes
1 Introduction
2 Prototype Design and Fabrication of Hybrid Micro-energy System
2.1 General System Design
2.2 System Integration
2.3 Design and Fabrication of Vibration Generator
2.4 Circuit Design and Fabrication of Vibration Energy Collection Unit
2.5 Solar Collection Unit Design
3 Testing and Demonstration Verification of Hybrid Micro-energy System
3.1 Vibration Energy Collection Unit Test
3.2 Solar Energy Collection Unit Test
3.3 Demonstration and Verification of Power Supply for WSN Nodes
4 Conclusions
References
Research on Map Construction and Location Technology Based on Multi-line LiDAR
1 Introduction
2 Map Building
2.1 Point Cloud Preprocessing
2.2 Inter-Frame Point Cloud Matching
3 Location
4 Experiment and Analysis
4.1 Accuracy and Time Comparison
4.2 Positioning Experiment
5 Conclusion
References
Isolated ISOP Control of a Medium Voltage Lithium Battery Storage Converter for Railroad Engine Rooms
1 Introduction
2 Analysis of Output Voltage Equalization Performance of Boost Converter
2.1 Small-Signal Model of a Boost Converter
2.2 Output Voltage Equalization Characteristics of Three-Level Boost Converters
3 Full-Bridge LLC Output Current Performance Analysis
4 Co-occupancy Ratio Control Strategy for ISOP Systems
5 Conclusion
References
A Deep-Learning Based Method for Real-Time Insulator Detection in Power System
1 Introduction
2 Network Architecture
2.1 Overall Structure
2.2 Network Architecture
2.3 Aggregation
3 Experiments and Results
3.1 Experiments Setup
3.2 Results
4 Conclusion
References
Corrosion Defect Detection in Multi-color Space by Channel Exchanging
1 Introduction
2 Method
2.1 Backbone Networks with Channels Exchanging
2.2 Feature Pyramid Networks
2.3 Detection Head Networks
3 Experiments
3.1 Implementation Details
3.2 Experimental Results
4 Conclusion
References
Data-Efficient Matching for Object Detection with Transformer in Pin Defect Detection
1 Introduction
2 Method
2.1 Data-Efficient Hungarian Match
2.2 Group Object Query
3 Experiments
3.1 Dataset
3.2 Implement Details
3.3 Comparison Result
3.4 Ablation Study
4 Conclusion
References
Heterogeneous Parallel Computing Based Thermal Fault Detection Model for Substation Equipment Using Infrared and Visible Image
1 Introduction
2 Related Works
2.1 Infrared and Visible Image Fusion Methods
2.2 Target Detection Methods
3 Method
3.1 Architecture of Detection Method
3.2 Fusion Network
3.3 Faults Detection Network
3.4 Heterogeneous Parallel Computing Implement
3.5 Training and Network Deployment
4 Experiments and Results
4.1 Experiment Setup
4.2 Results
5 Conclusion
References
Research on Bullet Recognition Technology Based on Deep Learning
1 Introduction
2 Introduction to Bullet Recognition Algorithm Interface
2.1 Dark Channel Prior Algorithm
2.2 YOLO V3 Algorithm
3 Dataset and Model Training
4 Model Building
5 Experiments and Analyses
6 Summary
References
An Investigation of ASC Peak Current Suppression Method for Permanent Magnet Synchronous Motors
1 Introduction
2 ASC Analysis
2.1 Principles of ASC
2.2 Mathematical Model of PMSM After ASC
3 Experiment and Simulation
4 Conclusions
References
A Power Distribution Method for Multi-stack Fuel Cell Considering Operating Efficiency and Aging
1 Introduction
2 Object Description
2.1 System Introduction
2.2 Modeling of MFC
3 Design of Power Distribution Method
4 Results
5 Conclusion
References
A Hybrid Domain Adaptation-Based Method for State of Health Prediction of Lithium-Ion Batteries
1 Introduction
2 The Methodology
2.1 Overview of the Proposed Method
2.2 CNN-GRU Network
2.3 Domain Adaptation Method
2.4 Optimization Objective
3 Experiments
3.1 Degeneration Data
3.2 Experiment Details
4 Results and Discussions
4.1 SOH Estimation with Different Approaches
4.2 Ablation Experiment
5 Conclusions
References
Risk Assessment of Retired Power Battery Energy Storage System
1 Introduction
2 Comprehensive Evaluation Index
2.1 Battery Data Source
2.2 Evaluation Indicators
3 Comprehensive Security Assessment Model
3.1 Comprehensive Scoring Model
4 Comprehensive Scoring Model
4.1 Estimated Results of Evaluation Indicators
4.2 Subjective and Objective Weight Calculation Results
4.3 Comprehensive Evaluation Results Analysis
5 Conclusion
References
The Stability Improvement Method for Interline Power Flow Controller
1 Introduction
2 The Safety Boundary of IPFC’S Converter and Its Impact Factors
3 The IPFC and Virtual Impedance Method
4 Case Study
5 Conclusions
References
Annealing Effect on Thermal-Electrical Performance of XLPE Insulation from Retired Power Cables
1 Introduction
2 Experimental Details
2.1 Cable Preparation
2.2 Aging Test and Heat Treatment
2.3 Character Measurements
3 Results and Discussions
3.1 Differential Scanning Calorimetry
3.2 Electrical Conductivity
4 Conclusion
References
Modification Method for Guide Vane Opening and Speed Optimizer of Variable-Speed Pumped Storage Under Pump Condition
1 Introduction
2 Modeling of DFVSPS Under Pump Condition
3 Guide Vane Opening and Speed Optimization Modification
3.1 Pump Model Experiment
3.2 Guide Vane Opening and Speed Optimization Modification
4 Simulation
5 Conclusion
References
Energy Management Strategy of Hybrid Energy Storage System Based on Multi-objective Model Predictive Control
1 Introduction
2 Semi-active Hybrid Energy Storage System
3 Hybrid Energy Storage System Modeling and Model Predictive Control Strategy
3.1 Lithium-Ion Battery Model
3.2 DC/DC Converter Loss Model
3.3 DC Bus Voltage Model
3.4 Multi-objective Model Predictive Control of Hybrid Energy Storage System
4 Experiment and Result Analysis
5 Conclusion
References
Pressure Difference Control Between Cathode and Anode of Proton Exchange Membrane Fuel Cell Based on Fuzzy PID Controller
1 Introduction
2 Modeling and Control Method for PEMFC Systems
2.1 System Modeling
2.2 Control Target
2.3 PID Control
2.4 Adaptive Fuzzy PID Controller
3 Simulation and Results
4 Conclusions
References
Additional Charge Throughput Reduction Method Based on Circulating Current Injection for the MMC Battery Energy Storage System
1 Introduction
2 Analysis of Additional Charge Throughput for MMC-BESS
2.1 Topology of MMC-BESS
2.2 Principles of MMC-BESS
2.3 Analysis on Charge Throughput of MMC-BESS
3 Second-Order Circulating Current Injection Scheme
4 Experimental Verification
4.1 Experimental Parameters
4.2 Experimental Results
5 Conclusion
References
Rapid Impedance Spectroscopy Reconstruction Based on M Sequence for SOH Estimation of Lithium-Ion Battery
1 Introduction
2 Brief Description of M Sequence
3 Fast Impedance Spectroscopy Testing and Reconstruction
3.1 Fast Impedance Spectroscopy Testing
3.2 Impedance Spectroscopy Reconstruction and Validation Analysis
4 Fractional Order Model Building and SOH Estimation
4.1 Fractional Order Modeling Based on Impedance Spectroscopy
4.2 SOH Estimation Based on Equivalent Impedance Model
5 Conclusion
References
Monitoring Method of Multi-band Oscillation Based on Synchronous Wavelet Compression Transform and Gaussian Naive Bayes Algorithm
1 Introduction
2 Multi-band Oscillation Monitoring System Based on Two-Stage Gaussian Naive Bayes
2.1 Gaussian Naive Bayes
2.2 Online Monitoring System Operation Steps
3 Feature Extraction Based on Simulated PMU Data
3.1 The Feature Vectors of the First-Stage Classifier
3.2 The Feature Vectors of the Second-Stage Classifier
4 Simulation Verification of Four-Machine Two-Area System
4.1 Collection of Sample Data
4.2 Verification Result
5 Conclusion
References
Health Status Estimation with Hybrid Neural Network for Lithium-Ion Battery
1 Introduction
2 Health Features Sequence
2.1 Detail of Battery Datasets
2.2 Health Features Extraction
3 Hybrid Neural Network
3.1 Convolution Layer
3.2 Long Short-Term Memory Layer
4 Results and Discussion
References
Numerical Analysis on Thermal Management Performance of Lithium-Ion Battery Pack with Liquid Cooling
1 Introduction
2 Numerical Model Validation
2.1 Geometric Model
2.2 Govern Equations
2.3 Boundary Conditions
2.4 Numerical Model Validation
3 Results and Discussion
3.1 High-Speed Climbing Operational Condition
3.2 Overspeed Operational Condition
3.3 Driving Durability Operational Condition
3.4 Heating Operational Condition
4 Conclusions
References
Design and Optimization of a Novel Dual-Motor Coupling Propulsion System with Composite Transmission
1 Introduction
2 Architecture of the Propulsion System
2.1 Conventional Dual-Motor Transmission Architecture
2.2 A Novel Composite Transmission Architecture
3 Operating Principle
4 Parameter Optimization
5 Conclusion
References
Research on Marine Electrochemical Energy Storage System Under Ship-Shore Connected Cable Faults in Ship-Shore Power System
1 Introduction
2 Shore Power System
2.1 Structure Composition
2.2 Shore Power System Model
3 Marine Electric Power System Design
3.1 Diesel Generator Design
3.2 Ship Shore Power System Design
4 Simulation Results and Analysis
4.1 Diesel Generator as Standby Power Supply
4.2 Battery Energy Storage System as Standby Power Supply
5 Conclusion
References
Sodium-Ion Batteries State of Charge Estimation Based on Recurrent Deep Forest
1 Introduction
2 SoC of Sodium Battery Estimation Method Based on Recurrent Deep Forest
3 Experimental Data and Results
3.1 Experimental Data Background
3.2 Description of Experimental Data
3.3 Data Preprocessing, Training and Testing
3.4 Experimental Results and Analysis
4 Conclusion
References
Study on Ultrasonic Transmission Characteristics and Failure Modes of a Lithium-Ion Battery
1 Introduction
2 Ultrasonic Transmission Principle of Battery
3 Establishment of Finite Element Model of Battery
3.1 Battery Reference Model
3.2 Battery Comparison Model
4 Analysis of Simulation and Experimental Results
4.1 Influence of Battery Structure on Ultrasonic Signal
4.2 Influence of Process Problems on Ultrasonic Signals
4.3 Influence of Internal Faults of Battery on Ultrasonic Signal
4.4 Comparison and Analysis of Simulation and Experimental Results
5 Conclusions
References
Parameter Matching Optimization of All-Terrain Vehicle Battery System Considering Multi-objective Optimization
1 Introduction
2 Performance Requirements of the Target Vehicle
2.1 Power Demand Calculation
2.2 Energy Demand Calculation
2.3 Lithium Battery Pack Parameter Configuration
3 Parameter Matching and Optimization of Lithium Battery Pack
3.1 Optimization Model
3.2 Optimistic Algorithm
3.3 Result and Discussion
4 Conclusion
References
Study on Water Content and Water Saturation of Proton Exchange Membrane Fuel Cell Under Dynamic Conditions
1 Introduction
2 Three-Dimensional Non-isothermal Two-Phase Model
2.1 Theory of Model
2.2 Model Validation
2.3 Setting of Dynamic Conditions
3 Water Content and Water Saturation
3.1 Average Water Content and Average Water Saturation
3.2 Location of Lowest Water Content
3.3 Location of Highest Water Saturation
4 Conclusion
References
An Intelligent Loading Method of Air Containers for Air Express Transportation Based on Modular Assembling
1 Introduction
2 Intelligent Loading Method
2.1 Loading Object Analysis
2.2 Air Container Dimensional Analysis
2.3 Modularity of Express Packages
3 Experiment
4 Conclusion
References
A Passenger Safety Status Detection Method for Rail Transit Stations Based on Machine Learning
1 Background
2 Related Work
3 Introduction
3.1 Dataset
3.2 Human Post Estimation
3.3 Platform
4 Conclusion
References
Effect of the Clearance Between Corner Fittings and Locks on Longitudinal Acceleration of Freight
1 Introduction
1.1 Background
1.2 Research Status of Loading Reinforcement for Container Freight
2 Container Corner Fittings and Locks on Flat Car
3 Impact Test Simulation Modelling Based on SIMPACK
3.1 Modelling of MT-2 Buffer
3.2 Establishment of Vehicle Model
3.3 Establishment of Impact Test Model
4 Simulation Results and Analysis of Impact Test
4.1 Impact Test Results and Analysis
5 Conclusion
References
Research on Multimodal Transport Route Optimization of the New Western Land-Sea Corridor
1 Introduction
2 Analysis on Influencing Factors of Path Optimization
2.1 Transportation Time Analysis
2.2 Transportation Cost Analysis
2.3 Time Value of Goods Analysis
3 Model
3.1 Model Assumptions
3.2 Model Building
3.3 Model Solution
4 Case Analysis
4.1 Example Introduction
4.2 Data Processing
4.3 Example Calculation
4.4 Result Analysis
5 Conclusion
References
Active Vibration Control of Cylindrical Structures Using Piezoelectric Patches
1 Foreword
1.1 Design Research Background and Research Significance
1.2 Scheme Ideas
2 Piezoelectric Actuators and Controllability Gramian Method
2.1 Properties of Piezoelectric Materials
2.2 Controllable Gramian Method
3 Software Simulation
3.1 Cylinder Structure Modeling and Modal Analysis
3.2 Random Vibration Analysis of Cylindrical Structure
3.3 Simulation Analysis of Piezoelectric Effect of Piezoelectric Patch Actuator and Sensor
3.4 System Simulation Analysis
4 Summary
References
High-Speed Railway Express Collection and Distribution Scheme Design
1 Introduction
2 Design of Collection and Distribution Scheme for High-Speed Railway Express
2.1 Problem Description
2.2 Establishment of the Model
2.3 Numerical Experiment
2.4 Discussion
3 Conclusion
References
Analyzing the Air Dual-Hub Connectivity: A Case Study of Beijing Dual Airports
1 Introduction
2 Analysis of Flight Connection Between Dual Airports
2.1 Hub Connectivity Indicator Evaluation of the Dual Airport
3 Case Study—Evaluation of Flight Connection of Beijing Dual Airports
3.1 Operation Status of Beijing Double Airport
3.2 Evaluation of the Connecting Quality of Beijing Double Airports
4 Conclusions
References
Recognition of Remote and Small Intrusion Targets Around High-Speed Railway Based on Deep Learning Method
1 Foreword
1.1 Research Background and Significance
1.2 Research Status at Home and Abroad
1.3 Main Contents of This Article
2 Target Detection Algorithm Based on Deep Learning
2.1 Single State Target Detection Network
2.2 Two-Stage Target Detection Network
3 Experiment Data Set
3.1 Definition of Small Target
3.2 Data Set Construction
4 Analysis of Experimental Results
5 Remote and Small Intrusion Target Detection System for High Speed Railway Perimeter
6 Summary
References
Facial Expression Recognition Algorithm Based on Multi-source Information Fusion
1 Introduce
2 Related Works
2.1 Facial Expression Recognition
2.2 Multi-source Information Fusion
3 Methodology
3.1 Dataset
3.2 Data Preprocessing
3.3 Training
4 Experimental Results and Analysis
4.1 Single-Mode Expression Recognition Experiment
4.2 Single-Mode Expression Recognition Experiment
5 Conclusion
References
Optimization of Township Logistics Distribution Route Based on Simulated Annealing Algorithm
1 Introduction
2 Mathematical Model
2.1 Problem Description and Model Assumptions
2.2 Modeling
3 Solution Algorithm
3.1 Simulated Annealing Algorithm Theory
3.2 Encoding Method
3.3 Neighborhood Search
3.4 Cooling Function
3.5 Algorithm Termination Criterion
4 Case Analysis
4.1 Model Solving
4.2 Solution Result
5 Conclusions
References
Study and Experimental Verification of the Effect of Assembly Pressure on the Electrical Efficiency of PEM Fuel Cells
1 Introduction
2 Methodology
2.1 W-M Fractal Function
2.2 Electrical Efficiency Model
2.3 Experiment
3 Fuel Cell Model Construction
3.1 Model Assumptions
3.2 Simulation Model
3.3 Boundary Conditions
4 Results and Discussion
4.1 Interface Contact Characteristics
4.2 Effect of Clamping Pressure
5 Conclusions
References
Design of Non-intrusive Type Load-Monitor System for Smart Grid
1 Introduction
2 Ease of Use
2.1 System Requirements Analysis
2.2 System Technical Architecture Design
3 Overall System Design
3.1 Introduction to the Core Modules of the System
3.2 System Operation Process Analysis
4 System Function Module Design
4.1 Design of Data Acquisition Module
4.2 Main Control Module Design
4.3 Communication Module Design
5 System Test
5.1 System Performance Test
5.2 Cloud Platform Online Monitoring Test
6 Epilogue
References
Application of Digital Twin Model in Monitoring the Steady State Operation of DC Bus Capacitor Bank
1 Introduction
2 Digital Twin Model of DC Bus Capacitor Bank
3 Digital Twin Model of DC Bus Capacitor Bank and Its Application in Condition Monitoring
4 Verification
5 Conclusion
References
Improve the Temperature Stability of PVDF/PMMA Energy Storage Performance by Crosslinking
1 Introduction
2 Experimental
2.1 Materials
2.2 Preparation Principle and Process of Crosslinked PVDF/PMMA Film
2.3 Characterization
3 Results and Discussion
3.1 Surface Topography and Energy Spectroscopy Analysis
3.2 Thermal Properties
3.3 Crystal Structure Properties of Crosslinked Samples
3.4 Dielectric Properties of Crosslinked Samples
3.5 Variable Temperature Energy Storage Performance of Crosslinked Samples
4 Conclusion
References
Research on the Main Motor Pre- and Post-switchable Configuration Based on DCT Hybrid Vehicle
1 Introduction
2 Configuration Analysis of a DCT Hybrid Vehicle
2.1 Configuration Classification
2.2 Working Principle of Main Motor Pre- and Post-switchable Configuration
3 Model Building and Control Strategy Optimization
3.1 Development of the Vehicle Model Based on CRUISE
3.2 Rule Based Control Strategy Design
3.3 Transmission Parameter Optimization Based on Isight
4 Simulation Analysis and Optimization
4.1 Simulation Analysis
4.2 Optimization Analysis of Transmission Parameters
5 Conclusions
References
Application of Lane Detection Based on Point Instance Network in Autonomous Driving
1 Introduction
2 Methodology
2.1 Traditional Methods
2.2 Deep Learning Methods
2.3 Stacked Hourglass Network
2.4 Key Points Estimation
3 Model Evaluation
3.1 Confidence Loss
3.2 Offset Loss
3.3 Embedding Feature Loss
3.4 Distillation Loss
4 Experimental Results
4.1 Dataset
4.2 Results
5 Conclusion
References
Effect of Lithium Rich Manganese Based Materials Coated Carbon Nanotubes Graphene Hybrid
1 Introduction
2 Experiment
2.1 Preparation of Lithium Rich Manganese Based Materials
2.2 Preparation of LLOs Coated with Carbon Nanotube Graphene Hybrid
2.3 Preparation of LLOs Coated with Carbon Nanotube Graphene Hybrid
3 Results and Discussion
3.1 Effect of Carbon Nanotube Graphene Hybrid Coating on Material Structure
3.2 Effect of Carbon Nanotube Graphene Hybrid Coating on Material Structure
3.3 Effect of Carbon Nanotube Graphene Hybrid Coating on Capacity and Magnification Properties of Materials
4 Conclusions Summary and Prospect
References
State of Health Prediction of Lithium Battery Based on Extreme Learning Machine Optimized by Genetic Algorithm
1 Introduction
2 Correlation Coefficient
2.1 Pearson Correlation Coefficient
2.2 Establishment of Finite Element Model
2.3 Kendall Correlation Coefficient
3 Build SOH Prediction Model
3.1 Extreme Learning Machine Algorithm
3.2 ELM Optimized by Genetic Algorithm
3.3 The Prediction Model of SOH
3.4 Criteria for Assessment
4 Experiment and Analysis
5 Conclusion
References
Suppression Technology of Thrust Fluctuation for Long-Stroke Segmented Linear Motor
1 Introduction
2 The Thrust Fluctuation Characteristics of DSMPMLSM
2.1 Cogging Force Analysis
2.2 End Force Analysis
2.3 Detent Force Analysis for Between-Segment
3 Experimental Evaluation
3.1 Experimental Setup
3.2 Experimental Results
3.3 Thrust Fluctuation Suppression
4 Conclusion
References
A Uniformity Sorting Strategy for Lithium-Ion Batteries Based on Impedance Spectroscopy
1 Introduction
2 Impedance Spectrum Measurement of Lithium-Ion Battery
3 Feature Extraction and Analysis of Lithium-Ion Battery Sorting
4 Classification Method and Effect Verification
5 Conclusions
References
Integrated Dynamics Control for Path Tracking and Obstacle Avoidance of Four-Wheel Intelligent Distributed Drive Vehicles Based on Time-Varying Predictive Control
1 Introduction
2 Vehicle System Model
3 Integrated Dynamics Control
3.1 Time-Varying Predictive Model
3.2 Linear Adaptive Time-Varying Predictive Control
4 Simulation Results
5 Conclusion
References
Research on Communication Mechanism of Cloud-Edge-End Distributed Energy Storage System
1 Introduction
2 Distributed Energy Storage System Communication Networking Method
3 Distributed Energy Storage System Information Model
3.1 IEC61850-Based Virtual Logic Device Modeling
3.2 IOT Terminal Model
4 Cloud-Side Interaction Mechanism Based on MQTT Protocol
4.1 Distributed Energy Storage System Communication Model
4.2 IEC61850-MQTT Protocol Conversion
4.3 Cloud-Side Interaction Architecture
5 Example Analysis
6 Conclusion
References
Predictive Cruise Control Algorithm Design for Commercial Vehicle Energy Saving Based on Quadratic Programming
1 Introduction
2 Lower Layer Gear Optimization Controller Design
2.1 Gear Optimization Map Design
2.2 Fuel Consumption Model Fitting
3 Upper Layer PCC Controller Design
3.1 Vehicle Model Conversion
3.2 Optimized Problem Establishment
3.3 Optimization Problem Solving
4 Simulation
4.1 Simulation Results
4.2 Analysis of Simulation Results
5 Summary and Future Work
References
Charge Transport and Energy Accumulation Breakdown Probability Distribution Characteristics of Polyimide
1 Introduction
2 Experiment
2.1 The Sample Processing
2.2 Characterization and Performance Testing
2.3 A Subsection Sample
3 Modeling and Simulation of CTMD
3.1 Charge Transport and Molecular Chain Energy Accumulation Modulation Model
3.2 Parameter Extraction
3.3 Simulation and Results Analysis
3.4 Discussion on Simulation Results of Weibull Distribution
4 Conclution
References
State of Health Estimation for Lithium-Ion Batteries Using Random Charging Data
1 Introduction
2 Voltage Fitting and Feather Extraction
3 State of Health Estimation Framework
4 Validation and Discussion
4.1 Voltage Fitting Validation
4.2 SOH Estimation Results
5 Conclusion
References
Capacity Estimation of Lithium-Ion Batteries Based on an Optimal Voltage Section and LSTM Network
1 Introduction
2 Battery Dataset and Feasibility Analysis
2.1 Battery Dataset
2.2 Feasibility Analysis and HF Extraction
3 Proposed Method
3.1 Voltage Section Optimization with QPSO
3.2 Estimation Model Construction
4 Experimental Validation and Discussion
4.1 Validation for the Voltage Section Optimization
4.2 Validation for Capacity Estimation
5 Conclusions
References
Enhancing Specific Capacitance and Structural Durability of VO2 Through Rationally Constructed Core-Shell Heterostructures
1 Introduction
2 Experimental Section
3 Results and Discussion
4 Conclusions
References
Determination Method of Solid-State Diffusion Coefficient for Lithium-Ion Batteries Based on Electrochemical Impedance Model
1 Introduction
2 Model Development
2.1 Model Description
2.2 Model Parameter Identification
3 Experimental
3.1 Fabrication of Positive and Negative Half Cells
3.2 Electrochemical Performance Tests of Positive and Negative Half Cells
4 Results and Discussion
4.1 Analysis of Electrochemical Characteristics of Half Cells
4.2 Electrochemical Impedance Spectroscopy Analysis of Different Lithium Intercalation States
4.3 Identification of Lithium Ion Solid-Phase Diffusion Coefficient
5 Conclusions
References
Remaining Capacity Estimation for Lithium-Ion Batteries Based on Differential Temperature Curve and Hybrid Deep Learning Approach
1 Introduction
2 Battery Cycle Data
3 Health Features Generation
4 Remaining Capacity Estimation
5 Results and Discussion
6 Conclusion
References
Energy Management Strategy for Fuel Cell Hybrid Power System Considering Fuel Cell Recoverable Performance Loss
1 Introduction
2 Modeling of Fuel Cell Hybrid System
2.1 Fuel Cell Degradation Model
2.2 Hydrogen Consumption Model
2.3 PEMFC Recoverable Performance Loss Model
2.4 Battery Equivalent Hydrogen Consumption Model
3 Proposed EMS Approach
3.1 Description of Objective Function
3.2 Proposed DDPG Based EMS
4 Simulation Results
5 Conclusion
References
Collaborative Eco-Routing Optimization for Continuous Traffic Flow in a Road Network
1 Introduction
2 The Collaborative Eco-Routing Optimization Strategy
3 Simulation and Analysis
4 Conclusion
References
Lithium-Ion Battery SOC Estimation Based on OWA Operator Fusion Algorithm
1 Introduction
2 Battery Modeling and Parameter Identification
3 Kalman Filter
3.1 Adaptive Extended Kalman Filter
3.2 The Central Difference Filter
3.3 H-Infinity Filter
4 OWA Operator Fusion Algorithm
5 Results and Discussion
6 Conclusions
References
Model Predictive Control Based Frequency Regulation for Power Systems Containing Massive Energy Storage Clusters
1 Introduction
2 Methods
2.1 The Lower Layer
2.2 The Upper Layer
3 Experimental Validation and Results Comparison
3.1 Case 1: Dynamic Performance
3.2 Case 2: Control Scheme Comparisons
4 Conclusion
References
Analysis and Application of Energy-Saving Approaches for Mining Dump Trucks Based on the Reuse of Braking Energy
1 Introduction
2 Modeling of the Transmission System and Operating Conditions
2.1 Vehicle Longitudinal Dynamics Model
2.2 Engine-Generator Model
2.3 Drive Motor Model
2.4 Operating Case Model
3 Reuse of Braking Energy
3.1 Motor Light Overload
3.2 Electrification of Cooling Fans
3.3 Reverse Drag Engine
4 Theoretical Analysis and Comparison of Energy-Saving Effect
4.1 Comparative Analysis of Energy-Saving Solutions
4.2 Results Comparison
5 Conclusion
References
Optimal Scheduling of Integrated Energy System Considering Gas Pipeline Leakage Failure
1 Introduction
2 System Network Model
2.1 Gas Flow Model Considering the Small Hole Leakage Failure
2.2 The Optimal Scheduling Model for IES
2.3 Objective Function
2.4 Gas System Constraints
2.5 Power System Constraints
3 Case Studies
3.1 System Description and Data Sources
References
Multi-index Thermal Safety Warning Based on Real Vehicle Big Data
1 Introduction
2 Data Introduction and Cleaning
2.1 Data Introduction
2.2 Data Cleaning
3 Multi-index Selection
3.1 3Methodology
3.2 Voltage Polarity
3.3 Temperature Extremes
3.4 Voltage Entropy
3.5 Maximum Temperature
4 Potential Risk Cell Screening Strategy
5 Conclusion
References
A Fault Diagnosis Method for Lithium-Ion Battery Based on Kolmogorov Complexity
1 Introduction
2 Methodology
3 Kolmogorov Complexity Calculation Process
3.1 Symbol Sequence Conversion
3.2 Single Voltage Sequence Component Count Calculation
3.3 Complexity Calculation of Single Voltage Sequence
3.4 Complexity Calculation for Battery Life Cycle
4 Analysis of Fault Diagnosis Results
5 Conclusion
References
Power Capability Prediction and Energy Management Strategy of Hybrid Energy Storage System with Air-Cooled System
1 Introduction
2 System Model
2.1 Battery Model
2.2 SC Model
2.3 Battery Pack Electro-thermal Model
3 SOP Estimation Under Temperature Constraints
4 Energy Management Strategy
5 Simulation Results
6 Conclusion
References
Signaling Game Approach for Energy Scheduling in the Community Microgrid
1 Introduction
2 System Model of the Community Microgrid
2.1 Scheduling Structure for the Community Microgrid
2.2 Utility Model of the Shared Energy Storage Provider
2.3 Utility Model of Prosumers
3 Scheduling Strategy Based on a Signaling Game
3.1 Formulation of Signaling Game
3.2 Solution for Game Equilibrium
4 Performance Evaluation
5 Conclusion
References
Lithium-Ion Battery Fast Charging Strategy Based on Reinforcement Learning Algorithm in Electric Vehicles
1 Introduction
2 Introduction of the Fast Charging Strategy
2.1 Model Establishment
3 State Observer
4 Establishment of Target Function
5 DDPG Algorithm Battery Fast Charging
6 Conclusions
References
Differential Drive Based Cooperate Steering Control Strategy Considering Energy Efficiency for Multi-axle Distributed Vehicle
1 Introduction
2 Modeling of Vehicle System
2.1 2DOF Dynamic Model
2.2 Steering System Model
2.3 Tracking Error Model
3 Strategy of Cooperate Steering Control
3.1 MPC Based Path Tracking Control
3.2 Optimal Torque Allocation
4 Experiment
5 Conclusion
References
Hysteresis Characteristics Analysis and SOC Estimation of Lithium Iron Phosphate Batteries Under Energy Storage Frequency Regulation Conditions and Automotive Dynamic Conditions
1 Introduction
2 Battery Experiment
2.1 Standard Capacity Test
2.2 Hysteresis Experiment
2.3 HPPC Experiment
2.4 Energy Storage Frequency Regulation Working Condition and Vehicle Dynamic Working Condition Experiment
3 Battery Modeling and Parameter Identification
3.1 First-Order RC Equivalent Circuit Model
3.2 Hysteresis Voltage Reconstruction Model
3.3 Model Parameter Identification
4 Model Accuracy Validation and Analysis of Hysteresis Characteristics
4.1 Model Accuracy Comparison Analysis
4.2 Analysis of Hysteresis Characteristics
5 SOC Estimation Based on the EKF Algorithm
6 Conclusion
References
Using Frequency-Dependent Integer Order Models to Simulate Fractional Order Model for Battery Management
1 Introduction
2 Methodology
2.1 Integer Order Model
2.2 Fractional Order Model
2.3 Frequency-Dependent Model
3 Results
4 Conclusions
References
An Adaptive Load Baseline Prediction Method for Power Users as Virtual Energy Storage Elements
1 Introduction
2 The Relationship Between Multi-dimensional Factors and VESE Power
2.1 Temperature Factor
2.2 Date Attribute Factor
2.3 Electricity Price Factor
3 Adaptive VESE Baseline Prediction Method Considering Multi-dimensional Factors
3.1 BP Neural Network
3.2 SVR
3.3 LSTM Neural Network
3.4 Adaptive VESE Baseline Prediction Method
4 Case Study
4.1 Small Sample Range Case
4.2 Large Sample Range Case
5 Conclusion
References
Time Series Prediction of New Energy Battery SOC Based on LSTM Network
1 Introduction
2 Related Work
3 Method
3.1 Visualization
3.2 LSTM Network Algorithm
4 Experiments
4.1 Data Preparation and Processing
4.2 Analysis of Results
5 Conclusion
References
Fault Diagnosis for Lithium-Ion Batteries in Electric Vehicles Based on VMD and Edit Distance
1 Introduction
2 Principle of the Proposed Method
2.1 Variational Mode Decomposition
2.2 Edit Distance
3 Data Acquisition and Introduction
4 Results and Discussion
4.1 Results
4.2 Clustering with DBSCAN
4.3 Comparison
5 Conclusion
References
Joint Estimation of State-of-Charge and State-of-Health for Lithium-Ion Batteries Based on OLS-UKF Algorithm
1 Introduction
2 Joint SOC-SOH Estimation
2.1 SOH Estimation
2.2 SOC Estimation
3 Results
4 Conclusions
References
Author Index
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Lecture Notes in Electrical Engineering 1016
Fengchun Sun Qingxin Yang Erik Dahlquist Rui Xiong Editors
The Proceedings of the 5th International Conference on Energy Storage and Intelligent Vehicles (ICEIV 2022)
Lecture Notes in Electrical Engineering Volume 1016
Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Departamento de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Gebäude 07.21, University of Karlsruhe (TH) IAIM, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dipartimento di Ingegneria dell’Informazione, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Intrinsic Innovation, Mountain View, CA, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Subhas Mukhopadhyay, School of Engineering, Macquarie University, NSW, Australia Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Department of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Federica Pascucci, Department di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA
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Fengchun Sun · Qingxin Yang · Erik Dahlquist · Rui Xiong Editors
The Proceedings of the 5th International Conference on Energy Storage and Intelligent Vehicles (ICEIV 2022)
Editors Fengchun Sun Beijing Institute of Technology Beijing, China Erik Dahlquist Mälardalen University Västerås, Sweden
Qingxin Yang Tianjin University of Technology Tianjin, China Rui Xiong Department of Vehicle Engineering Beijing Institute of Technology Beijing, China
ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-1026-7 ISBN 978-981-99-1027-4 (eBook) https://doi.org/10.1007/978-981-99-1027-4 © Beijing Paike Culture Commu. Co., Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Contents
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries Under Different Precooling Conditions . . . . . . . . . . . . . . . . . . . . Jianbo Shi, Xueqiang Li, Yabo Wang, Zhiming Wang, Shengchun Liu, and Hailong Li
1
Research on Detection Method of Metal Foreign Objects in Electric Vehicle Wireless Power Transfer System . . . . . . . . . . . . . . . . . . Anjie Ran, Xiaobo Wu, Donglei Sha, Zhongping Yang, and Fei Lin
10
An Adaptive Equivalent Heat Minimization Strategy for Hybrid Electric Trucks Braking Considering Brake Temperature Rise in Long Downhills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liuquan Yang, Weida Wang, Chao Yang, Xuelong Du, and Bingquan Zhao
22
Field-Oriented Control Strategy Verification Based on Power Hardware in Loop Simulation Technology . . . . . . . . . . . . . . . . . . . . . . . . . . Menglong Xu, Abdul Hadi Hanan, Zhichuan Wei, Shaokun Wang, Jun Li, and Bin Chen Hybrid Estimation of Residual Capacity for Retired LFP Batteries . . . . Yulong Ni, Jianing Xu, He Zhang, Chunbo Zhu, and Kai Song Design of a Full-Time Security Protection System for Energy Storage Stations Based on Digital Twin Technology . . . . . . . . . . . . . . . . . . Yuhang Song, Xin Jiang, Jiabao Min, and Yang Jin Online Electrical Fault Diagnosis and Low-Cost State Estimation for Lithium-Ion Battery Pack Based Electric Drive System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qiao Wang, Min Ye, Meng Wei, Gaoqi Lian, and Yan Li
32
44
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61
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Contents
Capacity Prediction of Lithium-Ion Battery Based on HGWO-SVR . . . Qiang Liao, Kui Chen, Kai Liu, Yan Yang, Guoqiang Gao, and Guangning Wu Life Cycle Carbon Footprint Assessment of Power Transmission Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kaibin Sun, Changzheng Shao, Yue Sun, Chengrong Lin, Xin Cheng, Weizhan Li, Bo Hu, and Kaigui Xie
68
79
Performance Optimization of Tesla Valve Microchannel Cold Plates for Li-Ion Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fen Liu, Jianfeng Wang, and Yanbing Lu
92
Data-Driven Method Based Wind Power Characteristic Analysis and Climbing Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yanli Liu and Junyi Wang
100
Nonlinear-Drift-Driven Wiener Process–Markov Chain Switching Model for Predicting Lithium-Ion Battery Remaining Useful Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yixing Zhang, Fei Feng, Shunli Wang, Jinhao Meng, Jiale Xie, Hongpeng Yin, and Yi Chai
107
Estimation of Battery State Based on Discharge Voltage Drop and AC Impedance at Full Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shengli Kong, Xiaochuan Huang, Guangjin Zhao, Yu Chen, and Wei Han Study on Ferromagnetic Noise of EMU Traction Transformer . . . . . . . . Ande Zhou, Zewen Ren, Hongbing Xie, Libing Fan, and Jianshun Yu Research on Driving Cycle Recognition Strategy Based on Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin Ye, Jintao Lu, Shiming Tian, Zhichao Zhao, Qiang Lv, and Zhiyong Zhang Research on Energy Management Strategy of Fuel Cell Buses In and Out of Bus Stop Based on Speed Optimization . . . . . . . . . . . . . . . . Mei Yan, Hongyang Xu, Menglin Li, Haoran Liu, and Hongwen He A DFT Study on Electronic and Optical Properties of La/Ce-Doped CaTiO3 Perovskite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qiankai Zhang, Manqing Zhao, Qinghao Li, Jun Zhou, Jinghui Gao, Qingdong Zhu, and Yang Wang Charging Pile Sharing Scheme Based on Blockchain Technology . . . . . . Aihua Tang, Sha Zhan, Tingting Xu, and Xiaorui Hu
119
127
140
152
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Contents
An Electric Vehicle Charging Station Based on SiC MOSFETs and Si IGBTs Hybrid Cascaded Three-Level H-Bridge Converter . . . . . Qishan Liu, Shishun Wang, Sizhao Lu, and Siqi Li A Simulation Study on Magnetic Field Distribution of Two-Cells Proton Exchange Membrane Fuel Cell Stack . . . . . . . . . . . . . . . . . . . . . . . . Yuning Sun, Lei Mao, Kai He, Zhongyong Liu, Shouxiang Lu, and Lisa Jackson 3D Modeling and Performance Analysis of a PEM Water Electrolyzer Based on Multiphysics Couplings . . . . . . . . . . . . . . . . . . . . . . Jihua Wang, Xiaming Ye, Ruyi Qin, Haojin Qi, Fangyi Ying, Qi Li, Jiajie Yu, and Yueping Yang State of Health Estimation of Lithium-Ion Battery Considering Random Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wensai Ma, Jiangwei Shen, Chengzhi Gao, Zheng Chen, and Yonggang Liu
vii
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186
194
206
Unified Control of Bidirectional H4 Bridge Converter in Single-Phase Energy Storage Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuyan Ju, Yu Fang, Xiaofei Wang, and Li Zhang
216
Optimal Siting and Capacity Allocation of BESS Based on Improved Multi-objective Particle Swarm Algorithm . . . . . . . . . . . . . Jianlin Li, Jingyue Kang, Yaxin Li, and Haitao Liu
225
Coupling Forecasting of Short-Term Power Load and Renewable Energy Sources Generation Based on State-Space Equations . . . . . . . . . Jinzhong Li, Yuguang Xie, Hu Wang, and Lei Mao
234
Active Equalization of Lithium Battery Based on WOA and FLC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhongan Yu, Junling Zhang, and Zezhou Hu
242
Bi-level Optimal Sizing and Scheduling of Hybrid Thermal Power-Energy Storage System for Peak Shaving . . . . . . . . . . . . . . . . . . . . . Deng Yang, Guo Xu, Bao Yusheng, Chen Feixiang, Chen Xiaoxia, Zhou Sheng, Yan Shiye, and Ye Jilei
250
Economic Optimal Dispatch of Integrated Energy System Considering Market Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Jia, Wei Wang, Na Li, Xinyu Duan, and Zhenya Ji
262
Analysis of Energy Loss and Heat Generation Characteristics of Supercapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wentao Zhang, Jilin Liu, and Bing-Ang Mei
272
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Grid-Supported Modular Multi-level Energy Storage Power Conversion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ziqing Cao, Yichao Sun, and Kai Yang
281
On-line Monitoring and State of Health Estimation Technology of Lead-Acid Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Danyang Li, Gang Zhang, Zhaofeng Gong, and Xingyuan Ma
289
Distributed Optimal Allocation of Renewable Energy and Energy Storage Based on Alternating Direction Method of Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mingyu Ma, Jinpeng Shen, LiGao Junjie, Jun Yang, Song Ke, and Hongli Wang
300
Optimization of Moisture Absorption of High Temperature Composite Phase Change Thermal Storage Materials . . . . . . . . . . . . . . . . Qiao Geng, Chaomurilige, Jin Lu, Ma Hongkun, Deng Weiyu, Jiang Zhu, Huang Zibo, and Ding Yulong
310
Research Progress of Coordination Control Strategy for Flywheel Array Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . Yongming Zhao, Qingquan Qiu, and Zipan Nie
320
Lifetime Test Platform of Mica Paper Capacitors Under Microsecond Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shifei Liu, Jiande Zhang, Zicheng Zhang, Jilu Xia, and Teli Qi
330
Simulation Study of External Short Circuit Characteristics for Lithium-Ion Battery Based on Electrochemical-Thermal Model . . . Shichang Ma, Bingxiang Sun, Simin Ma, Xiaojia Su, and Xingzhen Zhou Operation Analysis and Optimization Suggestions of User-Side Battery Energy Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fu Rui, Liu Haitao, and Jiang Ling Discussion on Key Components Design for Off-Grid Photovoltaic Electrolysis Hydrogen Production System . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Zhao, Mingyu Lei, Yuanyuan Chen, Yanjiao Hou, Zhuo Chen, and Yibo Wang Minimization Design of Energy Storage Capacitor of Electromagnetic Switch Control Module Based on Zero-Current Opening Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changyi Hu, Changkun Zhang, and Zhihong Xu Analysis of Pulse and Alternating Current Low Temperature Charging Based on Optimal Charging Frequency . . . . . . . . . . . . . . . . . . . Tingting Xu, Xiaorui Hu, Aihua Tang, and Peng Gong
340
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Contents
Axial Magnetic Field Simulation and Structure Optimization of Contacts in Vacuum Interrupter with Iron Core . . . . . . . . . . . . . . . . . . Huajun Dong, Xingrui Lu, Zhaoyu Ku, and Xinying Chen Balancing Topology Research of Lithium-Ion Battery Pack . . . . . . . . . . . Lingying Tu and Yu Qin Coordinated Control Strategy of Secondary Ripple in DC Microgrid Based on Impedance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xuejin Li, Chunguang Ren, Fangyuan Pang, Haonan Deng, Yifan Wang, and Yue Qin
ix
389 398
408
Research on Coordinated Control Strategy for Islanded Operation of Household Photovoltaic-Storage Micro-grid . . . . . . . . . . . . Bowen Chen, Junhao Chang, Aoling Yang, Yu Tian, and Bowen Zhou
420
Fuzzy Comprehensive Evaluation on Hydraulic High Voltage Circuit Breaker Mechanical Characteristics in Smart Substation . . . . . Chengyou Wang, Meng Li, and Candong Liu
435
State of Charge Estimation for Lithium-Ion Battery Based on Particle Swarm Optimization Algorithm and Multi-Kernel Relevance Vector Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuyuan Zhou, Kui Chen, Kai Liu, Guoqiang Gao, and Guangning Wu Research on Variation Rules of Characteristic Parameters and Early Warning Method of Thermal Runaway of Lithium Titanate Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhilin Shan, Qixing Zhang, Yongmin Zhang, Shuping Wang, and Yifeng Chen Study on Parameter Characteristics and Sensitivity of Equivalent Circuit Model of Lithium Iron Phosphate Battery in Decay Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuan Zhang, Bingxiang Sun, Mao Li, Xiaojia Su, and Shichang Ma Research on Defect Simulation and Diagnosis Method of On-Load Tap Changer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiangang Bi, Jinpeng Jiang, Yuan Xu, Yanpeng Gong, Shuai Yuan, Guangzhen Wang, and Dehui Fu
448
459
471
479
Internal Short Circuit Warning Method of Parallel Lithium-Ion Module Based on Loop Current Detection . . . . . . . . . . . . . . . . . . . . . . . . . . Wenfei Zhang, Nawei Lyu, and Yang Jin
487
Prediction Method of Ohmic Resistance and Charge Transfer Resistance for Lithium-Ion Batteries Based on CSA-SVR . . . . . . . . . . . . Jiamin Zhu, Kui Chen, Kai Liu, Guoqiang Gao, and Guangning Wu
494
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Research on Experimental System of Magnetically Mediated Thermoacoustic Detecting Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yanju Yang, Shengming Zhang, Chunlei Cheng, Wenyao Yang, Chong Zeng, Yongchen Huo, and Yu Zhang Research on Mobile Energy Storage Vehicles Planning with Multi-scenario and Multi-objective Requirements . . . . . . . . . . . . . . . Yuanyuan Chen, Shaobing Yang, Zhuo Chen, Yong Zhao, and Yibo Wang A Novel Control Strategy of Air-Core Pulsed Alternators for Driving Electromagnetic Railgun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiasong Wang, Xianfei Xie, and Kexun Yu Optimal Dispatch Strategy of a Flexible Energy Aggregator Considering Virtual Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zeyu Liang, Zhengzheng Ge, Sheng Chen, Haohui Ding, Yiheng Liang, and Qinran Hu State of Charge Estimation of Lithium-Ion Battery Based on EKF with Adaptive Fading Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Na Li, Xusheng Yang, Shuangle Liao, Guangjun Liu, Shuai Cheng, Kai Kang, Yufeng Xia, Nian Shi, and Chaochong Pan
506
514
525
536
547
On-Line Evaluation Method of Battery Bank Inconsistency for DC Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haihong Huang, Chuangming Ma, and Haixin Wang
558
A Coordinated Control Strategy for PV-BESS Combined System and Optimal Configuration of Energy Storage System . . . . . . . . Chu Jin, Yan Yang, Zhengmin Zuo, Shuxin Luo, and Jinyu Wen
566
Multi-objective Optimal Scheduling Strategy of EVs Considering Customer Satisfaction and Demand Response . . . . . . . . . . . Zhihua Wang, Hui Hou, Tingting Hou, Rengcun Fang, Jinrui Tang, and Changjun Xie
579
Deep-Learning Network-Based Method for SOH Estimation of Lithium-Ion Battery for Electric Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . Zhengyi Bao, Huipin Lin, Chunxiang Zhu, and Mingyu Gao
588
Research on Optimal Allocation of Energy Storage in Active Distribution Network Based on Differential Particle Swarm Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sile Hu, Linfeng Cao, Yuan Wang, Ying Sun, Kaiyang Song, Yuchan Zhao, and Jiaqiang Yang
598
Contents
Adjusting Energy Storage Performance of PMMA/P(VDF-HFP) Composites by Improving Compatibility Through Molecular Weight Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jingbin Man, Yuetao Zhao, Yujiu Zhou, Hu Ye, Fujia Chen, Yajie Yang, Qifeng Pan, and Jianhua Xu Composite Micro Energy System for Wireless Sensor Network Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ze Wang, Nanjian Qi, Keren Dai, He Zhang, Xiaofeng Wang, and Zheng You Research on Map Construction and Location Technology Based on Multi-line LiDAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fang Liu, Yang Yang, and Weixing Su Isolated ISOP Control of a Medium Voltage Lithium Battery Storage Converter for Railroad Engine Rooms . . . . . . . . . . . . . . . . . . . . . . Guosheng Huang, Xuexiang Yan, Feng Huang, Keliang Tan, and Shuo Zhang
xi
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617
627
635
A Deep-Learning Based Method for Real-Time Insulator Detection in Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shengpu Gao and Yunxiang Zhang
644
Corrosion Defect Detection in Multi-color Space by Channel Exchanging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yunxiang Zhang and Yun Zheng
652
Data-Efficient Matching for Object Detection with Transformer in Pin Defect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ying Li and Zhuyi Rao
659
Heterogeneous Parallel Computing Based Thermal Fault Detection Model for Substation Equipment Using Infrared and Visible Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yun Dong, Jiacheng Fu, Xuhua Ai, Qi Meng, Zhaoli Chen, Yuan Yin, and Xixiang Zhang
667
Research on Bullet Recognition Technology Based on Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qunxian Qiu and Pengfei Li
678
An Investigation of ASC Peak Current Suppression Method for Permanent Magnet Synchronous Motors . . . . . . . . . . . . . . . . . . . . . . . . Fang Liu, Sai Tang, Kai Ma, and Yan Li
688
A Power Distribution Method for Multi-stack Fuel Cell Considering Operating Efficiency and Aging . . . . . . . . . . . . . . . . . . . . . . . . Xiaming Ye, Ruyi Qin, Ting He, Fangyi Ying, Jianqi Yao, Lijun Ma, Jiajie Yu, and Yueping Yang
696
xii
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A Hybrid Domain Adaptation-Based Method for State of Health Prediction of Lithium-Ion Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Baolei Liu, Jinli Xu, and Wei Xia Risk Assessment of Retired Power Battery Energy Storage System . . . . Yuan Cao, Yan Wu, Peigen Tian, Xi Xiao, and Lu Yu The Stability Improvement Method for Interline Power Flow Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuqiao Jia, Dajiang Wang, Zheng Li, Jingbo Zhao, and Xinyao Zhu Annealing Effect on Thermal-Electrical Performance of XLPE Insulation from Retired Power Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Runge Lu, Tao Xu, Chaochan Huang, Wenzhuo Xie, and Zhuobei Zhou
707 720
730
737
Modification Method for Guide Vane Opening and Speed Optimizer of Variable-Speed Pumped Storage Under Pump Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haoran Jing, Jia Li, Hongsheng Zhao, Wei Yao, Qiushi Xu, Bo Wang, and Jinyu Wen
745
Energy Management Strategy of Hybrid Energy Storage System Based on Multi-objective Model Predictive Control . . . . . . . . . . . . . . . . . . Yongpeng Shen, Songnan Sun, Yuanfeng Li, and Junchao Xie
754
Pressure Difference Control Between Cathode and Anode of Proton Exchange Membrane Fuel Cell Based on Fuzzy PID Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aihua Tang, Lin Yang, and Tao Zeng Additional Charge Throughput Reduction Method Based on Circulating Current Injection for the MMC Battery Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haolin Yu, Qian Xiao, Yu Jin, Yunfei Mu, Shiqian Ma, and Hongjie Jia Rapid Impedance Spectroscopy Reconstruction Based on M Sequence for SOH Estimation of Lithium-Ion Battery . . . . . . . . . . . . . . . Yanchao Liu, Jinfu Li, Lintao Hou, Xue Cai, and Caiping Zhang Monitoring Method of Multi-band Oscillation Based on Synchronous Wavelet Compression Transform and Gaussian Naive Bayes Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ming Yu, Dahu Li, Yifan Zhao, Wei Yao, Kan Cao, and Jinyu Wen Health Status Estimation with Hybrid Neural Network for Lithium-Ion Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aihua Tang, Yihan Jiang, Tingting Xu, and Xiaorui Hu
762
770
778
786
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Contents
Numerical Analysis on Thermal Management Performance of Lithium-Ion Battery Pack with Liquid Cooling . . . . . . . . . . . . . . . . . . . Junxiong Zeng, Hao Fu, Shuai Feng, Chenguang Lai, Jie Song, Lijuan Fu, Hu Chen, and Tieyu Gao Design and Optimization of a Novel Dual-Motor Coupling Propulsion System with Composite Transmission . . . . . . . . . . . . . . . . . . . . Mingjie Zhao, Junzhi Zhang, Cheng Lin, and Xiao Yu Research on Marine Electrochemical Energy Storage System Under Ship-Shore Connected Cable Faults in Ship-Shore Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaotian Lu, Jinrui Tang, Yongle Chang, and Lvquan Chen
xiii
809
824
833
Sodium-Ion Batteries State of Charge Estimation Based on Recurrent Deep Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bangyu Zhou, Zhile Yang, and Huan Xu
841
Study on Ultrasonic Transmission Characteristics and Failure Modes of a Lithium-Ion Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaoyu Li, Xintong Yu, Shanpi Zheng, Yong Tian, and Jindong Tian
850
Parameter Matching Optimization of All-Terrain Vehicle Battery System Considering Multi-objective Optimization . . . . . . . . . . . . Yixin Hu, Chun Wang, and Lei Fu
857
Study on Water Content and Water Saturation of Proton Exchange Membrane Fuel Cell Under Dynamic Conditions . . . . . . . . . . Xuanyu Wang, Kai Han, Xiaolong Li, Chang Ke, and Bao Lv
865
An Intelligent Loading Method of Air Containers for Air Express Transportation Based on Modular Assembling . . . . . . . . . . . . . . Luoyan Zhou, Xinzhu Hu, Yuexi Xie, and Li Wang
873
A Passenger Safety Status Detection Method for Rail Transit Stations Based on Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shengjia Yu, Sihan Tao, Jiayi Wang, Jiaxin Liao, and Zhengyu Xie
881
Effect of the Clearance Between Corner Fittings and Locks on Longitudinal Acceleration of Freight . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zecheng Wang, Li Wang, and Yuhang Xu
890
Research on Multimodal Transport Route Optimization of the New Western Land-Sea Corridor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuhang Xu, Li Wang, and Zecheng Wang
898
Active Vibration Control of Cylindrical Structures Using Piezoelectric Patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zengqing Wang, Haifeng Wang, and Zhengyu Xie
906
xiv
Contents
High-Speed Railway Express Collection and Distribution Scheme Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jinting Dong, Xiaoning Zhu, and Li Wang
918
Analyzing the Air Dual-Hub Connectivity: A Case Study of Beijing Dual Airports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuxin Chen, Xiaoning Zhu, and Li Wang
926
Recognition of Remote and Small Intrusion Targets Around High-Speed Railway Based on Deep Learning Method . . . . . . . . . . . . . . . Mengting Lu and Zhengyu Xie
935
Facial Expression Recognition Algorithm Based on Multi-source Information Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xun Xiao and Zhengyu Xie
946
Optimization of Township Logistics Distribution Route Based on Simulated Annealing Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dongying Li and Li Wang
959
Study and Experimental Verification of the Effect of Assembly Pressure on the Electrical Efficiency of PEM Fuel Cells . . . . . . . . . . . . . . Bao Lv, Kai Han, Xiaolong Li, and Xuanyu Wang
967
Design of Non-intrusive Type Load-Monitor System for Smart Grid . . . Sun Guofu, Guan Huashen, and Xin Haomiao
975
Application of Digital Twin Model in Monitoring the Steady State Operation of DC Bus Capacitor Bank . . . . . . . . . . . . . . . . . . . . . . . . . Mingshuo Zhu, Yi Liu, Meng Huang, and Xiaoming Zha
984
Improve the Temperature Stability of PVDF/PMMA Energy Storage Performance by Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhengwei Liu, Yongbin Liu, Jinghui Gao, and Lisheng Zhong
993
Research on the Main Motor Pre- and Post-switchable Configuration Based on DCT Hybrid Vehicle . . . . . . . . . . . . . . . . . . . . . . . . 1002 Zhengfeng Yan, Linzi Hou, Bingbing Wu, and Bo Zhang Application of Lane Detection Based on Point Instance Network in Autonomous Driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014 Jialin Liu, Quanqing Yu, and Pengyu Zhu Effect of Lithium Rich Manganese Based Materials Coated Carbon Nanotubes Graphene Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023 Chuangxin Ye, Weijing Yang, Haijuan Pei, and Jingying Xie State of Health Prediction of Lithium Battery Based on Extreme Learning Machine Optimized by Genetic Algorithm . . . . . . . . . . . . . . . . . 1029 Changshan Bai, Kui Chen, Kai Liu, Yan Yang, Guoqiang Gao, and Guangning Wu
Contents
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Suppression Technology of Thrust Fluctuation for Long-Stroke Segmented Linear Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1040 Mingyi Wang, Kai Kang, Chengming Zhang, and Liyi Li A Uniformity Sorting Strategy for Lithium-Ion Batteries Based on Impedance Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1050 Miao Bai, Chao Lyu, and Tong Liu Integrated Dynamics Control for Path Tracking and Obstacle Avoidance of Four-Wheel Intelligent Distributed Drive Vehicles Based on Time-Varying Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 Bowen Wang, Cheng Lin, Peiyuan Lyu, Xinle Gong, and Sheng Liang Research on Communication Mechanism of Cloud-Edge-End Distributed Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067 Jiabao Min, Yuhang Song, and Xin Jiang Predictive Cruise Control Algorithm Design for Commercial Vehicle Energy Saving Based on Quadratic Programming . . . . . . . . . . . . 1076 Xianning Li, Tingting Lv, Hanqi Yue, Shuangping Liu, Xiaoxiang Na, Hong Chen, and Bingzhao Gao Charge Transport and Energy Accumulation Breakdown Probability Distribution Characteristics of Polyimide . . . . . . . . . . . . . . . . 1089 Gao Ziwei, Min Daomin, Yang Lingyu, Duan Yanan, Wu Qingzhou, Zhu Shenlong, and Qin Shaorui State of Health Estimation for Lithium-Ion Batteries Using Random Charging Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108 Xing Shu, Zheng Chen, Hongqian Zhao, Jiangwei Shen, and Yongang Liu Capacity Estimation of Lithium-Ion Batteries Based on an Optimal Voltage Section and LSTM Network . . . . . . . . . . . . . . . . . . 1117 Qianyuan Dong, Xiaoyu Li, Jindong Tian, and Yong Tian Enhancing Specific Capacitance and Structural Durability of VO2 Through Rationally Constructed Core-Shell Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128 Minghua Chen, Nianbo Zhang, Jiawei Zhang, and Yu Li Determination Method of Solid-State Diffusion Coefficient for Lithium-Ion Batteries Based on Electrochemical Impedance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137 Linjing Zhang, Kefan Zhai, Xue Cai, Caiping Zhang, and Weige Zhang
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Remaining Capacity Estimation for Lithium-Ion Batteries Based on Differential Temperature Curve and Hybrid Deep Learning Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1151 Hongqian Zhao, Zheng Chen, Xing Shu, Jiangwei Shen, and Yongang Liu Energy Management Strategy for Fuel Cell Hybrid Power System Considering Fuel Cell Recoverable Performance Loss . . . . . . . . 1160 Kai He, Zhongyong Liu, Heng Zhang, and Lei Mao Collaborative Eco-Routing Optimization for Continuous Traffic Flow in a Road Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169 Qianyou Chen, Yitao Wu, Zhenzhen Lei, Zheng Chen, and Yonggang Liu Lithium-Ion Battery SOC Estimation Based on OWA Operator Fusion Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174 Aihua Tang, Jiajie Li, and Yukun Huang Model Predictive Control Based Frequency Regulation for Power Systems Containing Massive Energy Storage Clusters . . . . . . 1183 Yujun Lin, Qiufan Yang, Jianyu Zhou, Xia Chen, and Jinyu Wen Analysis and Application of Energy-Saving Approaches for Mining Dump Trucks Based on the Reuse of Braking Energy . . . . . . 1191 Yilin Wang and Weiwei Yang Optimal Scheduling of Integrated Energy System Considering Gas Pipeline Leakage Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1200 Maosen Cao, Bo Hu, Changzheng Shao, and Kaigui Xie Multi-index Thermal Safety Warning Based on Real Vehicle Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209 Xinyu Wu, Zheming Chen, Aihua Tang, Quanqing Yu, Manni Zou, and Shengwen Long A Fault Diagnosis Method for Lithium-Ion Battery Based on Kolmogorov Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217 Shengxu Huang, Ni Lin, Zhaosheng Zhang, and Jinghan Zhang Power Capability Prediction and Energy Management Strategy of Hybrid Energy Storage System with Air-Cooled System . . . . . . . . . . . 1224 Li Wang, Ji Wu, Ying Du, Yadong Liu, Xiuchen Jiang, and Duo Yang Signaling Game Approach for Energy Scheduling in the Community Microgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235 Ruilong Xu, Yujie Wang, and Zonghai Chen
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Lithium-Ion Battery Fast Charging Strategy Based on Reinforcement Learning Algorithm in Electric Vehicles . . . . . . . . . . . 1249 Aihua Tang, Jinyuan Shao, Tingting Xu, and Xiaorui Hu Differential Drive Based Cooperate Steering Control Strategy Considering Energy Efficiency for Multi-axle Distributed Vehicle . . . . . 1256 Yonghua Wu, Junqiu Li, and Weichen Wang Hysteresis Characteristics Analysis and SOC Estimation of Lithium Iron Phosphate Batteries Under Energy Storage Frequency Regulation Conditions and Automotive Dynamic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266 Zhihang Zhang, Yalun Li, Siqi Chen, Xuebing Han, Languang Lu, Hewu Wang, and Minggao Ouyang Using Frequency-Dependent Integer Order Models to Simulate Fractional Order Model for Battery Management . . . . . . . . . . . . . . . . . . . 1276 Xiaopeng Tang, Xin Lai, Yuanqiang Zhou, Ming Yuan, and Furong Gao An Adaptive Load Baseline Prediction Method for Power Users as Virtual Energy Storage Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285 Hong Xie, Yuming Zhao, Jing Wang, Lianwei Bao, Haiyue Yu, and Taoyi Qi Time Series Prediction of New Energy Battery SOC Based on LSTM Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296 Wenbo Ren, Xinran Bian, and Jiayuan Gong Fault Diagnosis for Lithium-Ion Batteries in Electric Vehicles Based on VMD and Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305 Xianglong Li, Qian Zhang, Yuan Jin, Huimin Chen, Hongqing Yang, Shaohua Du, Shuowei Li, and Caiping Zhang Joint Estimation of State-of-Charge and State-of-Health for Lithium-Ion Batteries Based on OLS-UKF Algorithm . . . . . . . . . . . . 1314 Xin Lai, Ming Yuan, Jiahui Weng, Yi Yao, and Yuejiu Zheng Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1321
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries Under Different Precooling Conditions Jianbo Shi1 , Xueqiang Li1 , Yabo Wang1 , Zhiming Wang1 , Shengchun Liu1 , and Hailong Li1,2(B) 1 Tianjin Key Laboratory of Refrigeration Technology, Tianjin University of Commerce,
Tianjin 300134, China [email protected] 2 School of Sustainable Development of Society and Technology, University of Mälardalen, 72123 Västerås, Sweden
Abstract. The capacity fading of lithium iron phosphate batteries is related to its internal temperature and the growth of solid electrolyte (SEI). It is an effective way by controlling its internal temperature to mitigate capacity fading. This paper discusses the impact of pre-cooling and resting time on capacity fading and the growth of SEI. Results showed that the battery capacity increased and the thickness of SEI decreased if the pre-cooling was employed. Compared to 25 °C of ambient temperature, the thickness of SEI under 5 °C of pre-cooling temperature decreased by 404 nm, 386 nm, and 502 nm for 2C, 3C, and 5C discharge rate, respectively. The internal temperature of battery could be better cooled and therefore capacity increased with the increase of resting time. At 15 °C of precooling temperature, the capacity increased by 3.8% if the resting time increased from 600 s to 2400 s. Therefore, the pre-cooling method could effectively mitigate capacity fading. The conclusion obtained in this paper could provide guidance for battery thermal management. Keyword: LiFePO4 battery · Capacity fade · Pre-cooling · Battery thermal management
1 Introduction As a rechargeable device, Lithium-ion batteries (LIBs) perform a vital function in energy storage systems in terms of high energy density, low self-discharge rate and no memory effect [1, 2]. With the development of energy and power density, LIBs are used in a variety of fields, especially in electric vehicles [4]. During operation, battery capacity, cycle life and safety performance are highly depended on temperature, which is in the range of 15–35 °C [4, 5]. The performance and stability of LIBs would rapidly decrease if the temperature beyond this range [6, 7]. Lithium plating and capacity fading would occur if the temperature is too low; whereas, side reaction and degradation [8], such as the growth of SEI film [9] and loss of active materials [10], would happen if the © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1–9, 2023. https://doi.org/10.1007/978-981-99-1027-4_1
2
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temperature is too high, leading to the aging of battery. Seriously, thermal runaway may be happened if the temperature is uncontrolled [11]. Therefore, an effectively functioning battery thermal management system (BTMs) is necessary for the performance of LIBS. The battery thermal management systems could be divided into air based cooling, liquid based cooling, phase change material (PCM) based cooling, and heat pipe based cooling [12]. Zhang et al. [13] changed the air distribution to improve the performance. Results showed that the modified structure could reduce the maximum temperature drop by 2.17 °C and the maximum temperature difference down by 4.49 °C compared to BTMs of Z-type. Sabbah et al. [14] compared the efficacy of PCM-based cooling and forcedair-based cooling. Results showed that PCM cooling was superior to forced air cooling at high discharge rate or ambient temperature. Though the surface temperature of battery could be controlled by using different BTMs, the temperature gradient between internal and external of battery is also existed, which leads to the aging of battery. Therefore, to better understand the battery aging and electrochemical behavior, a coupled model regarding one-dimensional electrochemical and three-dimensional thermal model is established. The impact of different pre-cooling conditions and resting time is discussed. The conclusion obtained in this paper could provide some guidance for battery aging studies and related thermal management initiatives.
2 Model Development The coupled model consists of three parts: a pseudo two-dimensional (P2D) electrochemical model based on Newman’s theory [15], a three-dimensional thermal model, and an electrochemical side reaction model. The model is established and coupled by COMSOL Multiphysics 5.6 platform and solved numerically using the finite element method. 2.1 Battery Parameters In this paper, the capacity fading characteristics are studied using a prismatic battery. Battery information is shown in Table 1. Table 1. Battery parameters Parameter
Unit
Value
Length × width × height
mm
135 × 30 × 80
Maximum voltage
V
3.6
Cut-off voltage
V
2
Nominal capacity
Ah
50
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries
3
2.2 Electrochemical Model On the basis of the theory of concentrated solution and the theory of porous electrodes, the electrochemical model includes mass (electron) conservation, charge conservation and electrode kinetic principles. During charging and discharging, lithium ions and electrons are de-embedded from one electrode and embedded in the other electrode with the following electrochemical reactions: Negative: Lix C6 Li1−x C6 + xLi+ + e− Positive: xLi+ + xe− + LI1−x FePO4 LiFePO4 In order to establish this electrochemical model, the following assumptions are made: (1) No gas generation during working process. (2) Positive and negative active material particles are homogenously distributed and in a ball shape. (3) The phenomenon of diffusion and migration is the cause of the migration of Li+ in the electrolyte. (4) Neglecting the generation of SEI film on the positive surface. (5) Volume and porosity of the material remain constant. 2.3 3D Thermal Model The thermal model in this paper consists of positive electrode, negative electrode, and cell. Thermal models ignore the hierarchical structure of the cell for simplifying the calculations, which is an anisotropic material with thermally conductive. The model as well regards the heat transfer between the cell and to the surroundings. In the 3D thermal model, the equation of energy conservation in terms of the heat transfer theory is as follows: ρCp = ∇(λ∇T) + q
(1)
q = qre + qohm + qact
(2)
where, q in the above equation is the rate of volumetric heat generation of the cell, which is thermodynamically comprised of reversible and irreversible heat.. The reversible heat is caused by the entropic change due to Li+ (de)embedding in the porous electrode. Irreversible heat comprises ohmic heat due to charge transport and polarization heat due to overpotential The cooling condition of the outer vessel surface is defined by Newton’s cooling equation as: −λ∇T = h(T − Tamb )
(3)
where, h is the convective heat transfer coefficient and Tamb is the external environmental temperature. The battery’s heat and physical parameters of the cell are shown in Table 2.
4
J. Shi et al. Table 2. The battery’s heat and physical parameters
Parameter
Unit
kT
W m−1 K− 1
Cu
Negative
Separator
Positive
Al
398
1.04
1.0
1.48
238
ρ
Kg m−3
8900
2500
1200
1500
2700
Cp
J Kg−1 K−1
385
1437
1269
1978
900
σ
S m−1
–
100
–
0.5
2.4 Side Reaction Model The primary capacity fading in this model is the reduction reaction occurring at the interface between the electrolyte and the anode, leading to the generation of SEI film and the loss of active Li+ . To describe the kinetics of the side reactions, the Tafel equation can be used. αSEI FηSEI (4) jloc,SEI = −FkSEI ce exp − RT where, jloc,SEI is the local current density of the side reactions generated by the SEI film; kSEI and αSEI are the SEI side reaction rate constant and charge transfer coefficient, respectively; and ηSEI represents the SEI side reaction overpotential, which is expressed as follows: ηSEI =ϕs −ϕe − Ueq,SEI − jloc,SEI Rfilm
(5)
where, Ueq,SEI is SEI film equilibrium potential, and Rfilm is the film resistance of the by-products deposited on the anode surface, which affects the overpotential: Rfilm =
δ SEI σSEI
(6)
where, δ SEI is SEI film thickness; σSEI is the SEI film conductivity. 2.5 Methodology 2.5.1 Model Coupling Method The volume average of the heat from the cell is obtained from the one-dimensional electrochemical model, which is used as an input to the three-dimensional thermal model. The temperature calculated from the thermal model is averaged over the entire domain and used as the temperature input to the electrochemical model. The side reaction model integrates the aging effect into the electrochemical model by changing the electrode kinetics of the negative electrode.
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries
5
2.5.2 Pre-cooling and Resting Time In this study, the pre-cooling temperature, means the ambient temperature, are assumed as 5 °C, 10 °C, and 15 °C, which is used to reduce the internal temperature of battery. To better understand the impact, 25 °C is considered as the normal ambient temperature. In order to reduce the polarization voltage and battery temperature, resting time is employed, during which the battery is without any operation after charge or discharge process. 600 s, 1200 s, 1800 s, and 2400 s, are considered in this paper.
3 Results and Discussion 3.1 Model Validation To validate the validity of the above model., the end voltage versus temperature variation of 50 Ah LiFePO4 discharged at 1C, 2C and 3C are obtained experimentally in this paper. The experimental steps are as follows: (1) Put the battery in 25 °C of ambient temperature for 30 min. (2) The cell is charged at a 25A constant current to 3.6V, then charged at a constant voltage until the current is less than 2.5A. (3) Put the battery in 25 °C of ambient temperature for 2 h. (3) The battery is discharged at 1C. (4) Repeat step 1–3 at 2C and 3C, respectively. The model validation is shown in Fig. 1. As is shown in the figure, the simulation results agree well with the experimental results in terms of both temperature and voltage. The largest error occurs at the stage where the cell SOC is less than 10%, with a maximum error of 6.2%, which may be caused by the difference in the open-circuit potential interpolation function associated with the SOC. Therefore, the model validation results were creditable and it can be used to do the following simulation. 44
1C Sim 2C Sim 3C Sim 1C Exp 2C Exp 3C Exp
42
38 36
3.4 3.2 3.0
Voltage (V)
Temperature (°C)
40
34 32 30
2.8 2.6 2.4
28
2.2
26 2.0
24 22 -500
0
500
1000
1500
2000
2500
3000
3500
1.8 -500
1C Sim 1C Exp 2C Sim 2C Exp 3C Sim 3C Exp 0
500
1000
1500
2000
2500
3000
3500
Discharge time (s)
Discharge time (s)
(a) Validation of temperature
(b) Validation of voltage
Fig. 1. Model validation
3.2 Impact of Pre-cooling Figure 2 shows the variation of SEI film thickness for various discharge rates. The thickness of SEI grows as the discharge rate increases, which was caused by the increasing
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polarization and side reaction overpotential and current density at high charge/discharge rate. In addition, the increasing rate of SEI slowed down as the number of cycles increased. This phenomenon was caused by the increase of diffusion resistance with the increase of cycle. For example, the thickness of SEI increased by 680 nm during 0–1000 cycles, while this value was only 300 nm during 1000–2500 cycles at 2C. Figure 3 depicts the variation of thickness of SEI at different pre-cooling temperatures. It was clear that the thickness decreased as the pre-cooling temperature decreased. The low pre-cooling temperature could mitigate the electrochemical reaction, reduce the activity of battery, and decrease polarization, leading to the decreasing thickness. For example, compared to 25 °C, 5 °C of pre-cooling temperature could decrease the thickness of SEI by 404 nm, 386 nm, and 502 nm for 2C, 3C, and 5C, respectively. Moreover, the effect of pre-cooling temperature became more obvious at high discharge rate. Also compared to 25 °C, the thickness of SEI would decrease by 387 nm, 353 nm, and 348 nm for 5 °C, 10 °C, and 15 °C, at 3C, respectively.
2C at 25°C 3C at 25°C 5C at 25°C
1200
SEI film thickness (nm)
1000 800 600 400 200 0 0
500
1000
1500
2000
2500
Number of cycles
Fig. 2. Variation of thickness of SEI at different discharge rates
5°C 15°C
1200
1.17E3 1.03E3
988
1000
SEI film thickness (nm)
10°C 25°C
791 793
800 648 654 600
644
677 683
668
584
400
200
0 2C
3C
5C
Discharge rate
Fig. 3. Variation of thickness of SEI at different pre-cooling temperatures
Figure 4 shows the variation of relative capacity at different discharge rate and precooling temperature. It was clear that the relative capacity almost linearly decreased with the increasing number of cycles, which was caused due to the increase of SEI thickness. In addition, the application of pre-cool could obviously mitigate the decrease of relative capacity, as shown in Fig. 4(a). Figure 4(b) compares the impact of pre-cooling
Capacity Fading Characteristics of Lithium Iron Phosphate Batteries
7
temperature on relative capacity of battery. The highest relative capacity of battery can be found when the pre-cooling temperature was 15 °C. This was because that, other side reactions occurred when the pre-cooling temperature was low, such as lithium deposition. In addition, pre-cooling temperature effects on relative capacity become more pronounced at high discharge rates. Under 2C discharge rate, the difference of relative capacity between 25 °C and 15 °C was 3.6%; while, the value was 4.1% at 5C of discharge rate. 0.90
2C at 25oC 3C at 25oC 5C at 25oC
1.00
2C at 5oC 3C at 5oC 5C at 5oC 0.85
0.90
5°C 10°C 15°C 25°C
0.866
0.83
Relative capacity
Relative capacity
0.95
0.861 0.851
0.8
0.80
0.85
0.80
0.807
0.79
0.785 0.776 0.769 0.765
0.75
0.744
0.75 0.70
0
500
1000
1500
2000
2C
2500
Number of cycle
(a) Impact of discharge rate on relative capacity
3C
Discharge rate
5C
(b) Impact of pre-cooling temperature on relative capacity
Fig. 4. Variation of relative capacity at different discharge rates and pre-cooling temperature
3.3 Resting Time Figure 5 shows the impact of resting time on internal temperature of battery. It was easy to find the internal temperature decreased with the increase of resting time. Figure 6 shows the impact of resting time on relative capacity. Since low internal temperature of battery could be obtained when resting time was long, the relative capacity was also increased. Compared to 600 s of resting time, the relative capacity would increase by 0.6%, 1.6%, and 3.8% for 1200 s, 1800 s, and 2400 s, respectively. 600s 1800s
1200s 2400s
Battery internal temperature (°C)
18.0 17.5 17.0 16.5 16.0 15.5 15.0 14.5 -200
0
200
400
600
800
1000 1200 1400 1600
Number of cycles
Fig. 5. Impact of resting time on internal temperature of battery
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J. Shi et al. 0.90
Relative capacity
0.85
0.844 0.822 0.806
0.812
0.80
0.75
0.70 600s
1200s
1800s
Resting time
2400s
Fig. 6. Impact of resting time on relative capacity
4 Conclusion In this paper, a coupled model, regarding electrochemical model, thermal model, and capacity fading model, was established to explore the characteristic of capacity fading and the variation of thickness of SEI. Through the results, it can be concluded: (1) Precooling was an effective way to mitigate capacity fading and the optimal temperature was 15 °C. (2) Pre-cooling could also mitigate the growth of SEI. (3) Long resting time was helpful to reduce the internal temperature and capacity fading of battery. Acknowledgments. This work was funded by Science and Technology Program of Tianjin, China (No. 2021ZD031).
References 1. Alfaro-Algaba, M., Javier Ramirez, F.: Techno-economic and environmental disassembly planning of lithium-ion electric vehicle battery packs for remanufacturing. Resour. Conserv. Recycl. 154 (2020) 2. Collath, N., Tepe, B., Englberger, S., Jossen, A., Hessem, H.: Aging aware operation of lithium-ion battery energy storage systems: a review. J. Energy Storage 55 (2022) 3. Yang, X., Leng, Y., et al.: Modeling of lithium plating induced aging of lithium-ion batteries: transition from linear to nonlinear aging. J. Power Sources 360, 28–40 (2017) 4. Lin, J., Liu, X. et al.: A review on recent progress, challenges and perspective of battery thermal management system. Int. J. Heat Mass Transf. 167 (2021) 5. Alipour, M., Ziebert, C. et al.: A review on temperature-dependent electrochemical properties, aging, and performance of lithium-ion cells. Batteries 6(3) (2020) 6. Zhang, G., Wei, X., Han, G., Dai, H. et al.: Lithium plating on the anode for lithium-ion batteries during long-term low temperature cycling. J. Power Sources 484 (2021) 7. Zhang, D., Tan, C., Ou, T., Zhang, S., Li, L., Ji, X.: Constructing advanced electrode materials for low-temperature lithium-ion batteries: a review. Energy Rep. 8, 4525–4534 (2022) 8. Pender, P., Jha, G., Youn, D., et al.: Electrode degradation in lithium-ion batteries. ACS Nano 14(2), 1243–1295 (2020) 9. Yan, C., Yao, Y., et al.: The influence of formation temperature on the solid electrolyte interphase of graphite in lithium ion batteries. J. Energy Chem. 49, 335–338 (2020)
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10. Wang, H., Whitacre, J.: Inhomogeneous aging of cathode materials in commercial 18650 lithium ion battery cells. J. Energy Storage 35 (2021) 11. Feng, X., Ren, D., et al.: Mitigating thermal runaway of lithium-ion batteries. Joule 4(4), 743–770 (2020) 12. Xia, G., Cao, L., et al.: A review on battery thermal management in electric vehicle application. J. Power Sources 367, 90–105 (2017) 13. Zhang, F., Liu, P. et al.: Cooling performance optimization of air cooling lithium-ion battery thermal management system based on multiple secondary outlets and baffle. J. Energy Storage 52 (2022) 14. Sabbah, R., Kizilel, R. et al.: Active (air-cooled) vs. passive (phase change material) thermal management of high power lithium-ion packs: limitation of temperature rise and uniformity of temperature distribution. J. Power Sources 182(2), 630–638 (2018) 15. Fuller, M.D.T., Newman, J.: Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. J. Electrochem. Soc. (1993)
Research on Detection Method of Metal Foreign Objects in Electric Vehicle Wireless Power Transfer System Anjie Ran1(B) , Xiaobo Wu2 , Donglei Sha2 , Zhongping Yang1 , and Fei Lin1 1 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China
[email protected], [email protected] 2 National Innovation Center of High Speed Train, Chengyang 266111, China
Abstract. The high frequency magnetic field area in the radio energy transmission system (WPT) is an important medium for electric energy transmission. As an open structure, the high frequency magnetic field often inevitably falls into metal foreign matters, leading to a decline in the transmission efficiency of the system, and the heating of the metal itself will also cause potential safety hazards. In this paper, based on the loose coupling model, the detection sensitivity formula of the detection coil method is established. On this basis, combined with the magnetic field characteristics of the square transmission coil surface, a long rectangular interconnection detection coil group and its layout are proposed. Compared with the traditional small coil independent detection method, this method has the advantages of less detection channels, high detection sensitivity, simple control and less blind area. Through electromagnetic field simulation, the advantages of the proposed structure are proved, and experimental verification is carried out on the WPT platform of the square transmission coil to achieve effective detection of ferrite, copper sheet, iron sheet and aluminum alloy sheet. Keywords: Wireless Power Transfer · Detection Sensitivity Formula · Metal Foreign Object Detection · Detection Coil Interconnection
1 Introduction Due to the non-contact open structure of the WPT system, metal foreign objects can easily invade the high-frequency AC magnetic field, which is an important medium for energy transmission in the air, resulting in a decrease in the transmission performance of the system and serious heating of the metal itself, cause damage to the coil or even fire, a complete WPT system must have the auxiliary function of metal foreign object detection. Regardless of whether the metal plate with the size of the transmission coil is located at the transmitting end, the receiving end, the middle of the two coils or the outside of the coil, the operating frequency of the system is changed and the output power of the system is reduced [1]. According to the eddy current loose coupling model, establish the equivalent circuit model between the metal foreign object and the coupling © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 10–21, 2023. https://doi.org/10.1007/978-981-99-1027-4_2
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coil, quantitatively analyze the impact of the metal foreign object on the system transmission performance, and provide the theoretical analysis basis for the metal foreign object invading the wireless charging system [2, 3]. Metal foreign object detection methods are divided into three categories: physical detection method, system parameter detection method and auxiliary coil method [4, 5]. The physical detection method is susceptible to environmental interference, the realization of the detection system is more complicated and costly. The system parameter detection method is to directly use the electrical parameters inside the WPT system as the detection index to complete the high-precision detection system design [6, 7], but it’s not suitable for high-power systems, the influence of metal foreign objects on the system parameters is often covered by the fluctuation of the circuit itself, and the system parameter detection method is completely invalid. Due to the limitations of the physical detection method and the system parameter detection method to deal with the intrusion of metal foreign objects in the high-power WPT system, the auxiliary coil method has become the only option. The detection coil method is divided into active excitation [8, 9] and passive excitation [10, 11] according to the different excitation sources. Compared with the active excitation method, the passive excitation method does not need an external excitation source, and depends on the magnetic field distribution of the primary coil, so the detection is more targeted. In this paper, the detection system is designed for the large-size transmission coil used in the high-power WPT system, and the passive excitation method is selected as the auxiliary coil method. First, according to the loose coupling model, analyze the relationship between the voltage change of the detection coil and the voltage change rate before and after the metal intrusion, and explain the advantages of the long rectangular detection coil. Based on the distribution of the magnetic field intensity of the square primary coil and the direction of the magnetic field lines, the long rectangular coils are interconnected, so that the number of detection channels is reduced, the detection sensitivity is improved, and the detection area is increased. Finally, the effectiveness of the detection system was verified on the 800 mm * 800 mm transmission coil platform.
2 Theoretical Analysis 2.1 Detection Sensitivity Analysis In the high-power WPT system, the air gap of the primary and secondary coil is about 20cm, and the coil itself is large in size, and small-sized foreign objects fall on the surface of the primary coil, which has minimal impact on the secondary coil. In order to simplify the analysis model, only the three circuits of the primary coil, the detection coil and the metal foreign object are analyzed here.As shown in Fig. 1, I p is the primary coil current, M kp is mutual inductance between primary coil and detection coil, M pm is the mutual inductance between the primary coil and metal foreign object, M km is the mutual inductance between detection coil and metal foreign object, I k is the detection coil current, Rk is the internal resistance of the detection coil, L k is self inductance of detection coil, I m is the equivalent induced current generated by metal foreign object, Rm is the equivalent internal resistance of metal foreign object, L m is the equivalent
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internal resistance of metal foreign object, R is the external resistance of detection coil, V k is detection coil induced voltage, ω is the resonant frequency of the system. Mkm
+
Vk -
R
Rk
Ik
Rm
Lm
Lk Mkp
Mpm
Ip
Im
Rp
Fig. 1. Modeling of primary coil, metal foreign body and detection coil
When there is no foreign object intervention, deduce the detection coil voltage: Vk =
Ip jωMkp R Rk + jωLk + R
(1)
The voltage difference caused by foreign objects is obtained: Vk =
Im jωMkm R Rk + jωLk + R
(2)
Substituting the expression of I m into (2), and the detection coil of passive excitation method can be regarded as open circuit treatment, and the detection coil current is very small, so I k ≈ 0, R jωL k + Rk . Finally, the voltage change rate is the sensitivity expression: M
M
km jω pm Vk Mkp = Vk Rm + jωLm
(3)
2.2 Long Rectangular Detection Coils As shown in Formula (3), the detection sensitivity is positively correlated with M M km . Taking the common single turn rectangular detection coil as an example, the foreign object can be equivalent to a sheet with a surface area of S, and the distance between the foreign object and the four sides of the rectangular detection coil is a1 , a2 , b1 and b2 , the relationship between these parameters and M km is derived (Fig. 2). The magnetic field generated by the rectangular detection coil in the plane is in the same direction, which can be superposed with each other to obtain the mutual inductance expression between the detection coil and foreign object. Similarly, formula (4) of N
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D
A
Detection coil Mental
b2
S
C
B
Fig. 2. Metal foreign object and detection coil
turn coil M is obtained. It can be seen that M km is related to a1 , a2 , b1 , and b2 . Mkm =
NBS I ⎛k
⎞ a1 ⎜ b a2 + b2 b1 a12 + b21 ⎟ ⎟ ⎜ 1 2 1 ⎟ ⎜ ⎟ ⎜ a a 1 ⎟ ⎜+ 2 + ⎟ ⎜ 2 2 ⎜ b2 a2 + b2 b2 a1 + b2 ⎟ 2 2 ⎟ μNS ⎜ ⎟ ⎜ = ⎟ ⎜ b b 2 1 4π ⎜ + ⎟ + ⎟ ⎜ 2 2 ⎜ a2 a22 + b22 a2 a2 + b1 ⎟ ⎟ ⎜ ⎟ ⎜ b1 b2 ⎟ ⎜ ⎠ ⎝+ + 2 2 2 2 a1 a1 + b1 a1 a1 + b2
a2
+
(4)
When a foreign object invades, the four parameters a1 , a2 , b1 , and b2 all tend to be extremely small, and the detection sensitivity is the highest. As shown in Fig. 3, when the metal foreign object moves inside the long rectangular detection coil, it can ensure that the two parameters in a1 , a2 , b1 , and b2 are close to zero. Therefore, the long rectangular detection coil has a higher detection sensitivity while ensuring a wider detection area, which is suitable for the detection of small metal foreign objects on a large platform. a1
Long rectangular detection coil
0
b2 Mental
a2
0
Fig. 3. Metal foreign object and detection coil.
3 Long Rectangular Interconnection Coil Group 3.1 Direct Connection and Reverse Connection of Detection Coil Reasonable coil interconnection can reduce M kp while increasing M km , which is finally manifested as a larger voltage difference V k generated by the detection coil caused
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by metal intrusion, so as to improve sensitivity. The difference in the connection of the two coils will lead to two results: the induced potentials superimpose each other after the positive connection, and the induced potentials cancel each other after the reverse connection. as shown in Fig. 4, increasing the number of turns and sequential connection can improve M km , and the latter can eliminate the blind area in adjacent areas. The voltage difference caused by the metal foreign object is increased, and the V kc after interconnection is close to the V ka when the metal foreign object is completely inside the coil, which realizes the elimination of the detection blind zone.
Fig. 4. Method of increasing detection coil M km . a Metal intrusion detection coil. b Increase turns. c Positive connection
However, the two methods mentioned above increase the mutual inductance M kp between the primary coil and the detection coil. It can be seen from Formula (3) that the increase of M leads to the decrease of detection sensitivity. Remote reverse connection is also required. As shown in Fig. 5, M km is increased by increasing the number of turns and adjacent sequential connection. Then, through the remote reverse connection of coil groups 1 and 2, the M kp is reduced. Because the 2 coil group is weakly coupled with A and B, the voltage change caused by A and B will not be affected by the 2 coil group The induced voltage of the final coil group drops from V 1 to V 1 − V 2 . Finally, the coil set not only increases M km , but also decreases M kp . While improving the sensitivity, the number of voltage to be processed is reduced, and the sampling circuit is simplified. 3.2 Magnetic Field Distribution and Magnetic Line of Force Direction For high-power WPT platform, this paper uses equivalent model to build square primary side transmission coil and ferrite core simulation model in Maxwell software. As shown in Fig. 6, the side length of primary side square transmission coil is 800 mm, the number of turns is 10, the wire diameter is 7.3 mm, the side length of square ferrite core is 900 mm, and the coil excitation current is selected as 85 kHz effective value 24A. The distribution of magnetic induction intensity is shown in Fig. 6. It can be seen that the distribution of magnetic field presents a downward trend from the coil to the outer ring. The stronger the magnetic induction intensity is, the greater the hysteresis loss and eddy current loss of metal are, and the more serious the heating is. The metal foreign matters in the weak magnetic field area have low coupling with the transmission coil, and the M pm is small and difficult to detect. However, the metal foreign matters in this area have
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Adjacent forward connection
Increase turns
A
B
V1
Long-distance reverse connection
V2
V1-V2
Fig. 5. Interconnect coil group after positive and reverse connection
little impact on the system, and there is no obvious heating itself, so the detection can be omitted. The magnetic field lines of the square transmission coil at a certain moment is shown in Fig. 6. The position where metal foreign objects may invade is divided into areas A and B with a dashed line. In the front view, the magnetic field lines of area B are perpendicular to the paper surface outward, the magnetic field lines of area A are perpendicular to the paper surface inward, and the magnetic field lines near the dotted line are approximately parallel to the paper surface. (a)
Primary transmission coil
(b)
(c) Primary transmission coil
Ferrite core
$
%
Current direction
Fig. 6. Simulation of Magnetic Induction Intensity Distribution of Square Coil. a Square transmission coil platform. b Magnetic field distribution. c Magnetic line of force distribution
The detection coil is arranged in area A or B, and the direction of the internal magnetic field line is consistent. When metal invades, the detection coil voltage changes. When the arrangement of the detection coil is at the dotted line position shown in Fig. 6, the direction of the internal magnetic line is different, and the voltage of the detection coil does not change when the metal invades the surface, the detection system fails. As shown in Fig. 7, when the detection coil is arranged at the dotted line, the left and right magnetic force lines on the coil surface are reversed. When the metal foreign matters invade the detection coil, they have the same effect on the magnetic force lines in the opposite direction. If it is arranged on both sides of the dotted line and the magnetic force lines inside the detection coil are in the same direction, this problem can be avoided. Therefore, when the detection coil is arranged above the transmission coil, the latter shall be located on both sides of the transmission coil as far as possible.
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Fig. 7. Distribution of metal foreign matters, detection coils and magnetic lines of force. a Double view of the detection coil arranged at the dotted line. b Double view of the detection coil arranged on both sides of the dotted line
3.3 Long Rectangular Interconnecting Coil Group Figure 6 shows that the center of the square transmission coil belongs to the weak magnetic field area. Since the harm of metal foreign matters invading this area is low, it can not be detected when unnecessary. In this paper, it is considered that the detection can be omitted when the magnetic field drops to 0.2 times of the strong magnetic field area. As shown in Fig. 8, the unnecessary detection area is determined to be a square area 120 mm away from the inner edge of the transmission coil, and the long rectangular detection coil structure is designed. Design principle: Unless necessary detection area, the transmission coil platform shall cover the detection coil; The detection coils shall be arranged on both sides of the transmission coil directly above the transmission coil, that is, the area where the magnetic line of force is reversed; On the inner and outer sides of the transmission coil, that is, the area where the magnetic lines of force are in the same direction, the detection coils are arranged side by side; If the detection coil part is located in the unnecessary detection area, the size can be adjusted as required to achieve the purpose of small M kp between the final interconnection coil group and the primary coil and save the coil consumption, while ensuring that the detection coil can be covered in the strong magnetic field area.
Fig. 8. Unnecessary detection area of square transmission coil
Taking the metal foreign object with a side length of 40 mm as the detection target, according to the design principles obtained from the previous analysis, the coil structure
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as shown in Fig. 9 is finally obtained. All long rectangular coils are coaxial and connected in sequence with the inner and outer rings. The 1 and 2 (A and B) detection coils are distributed on both sides of the primary coil, and the 3, 4, and 5 (C, D, E) detection coils are arranged close to each other. 4, 5 The part of (D, E) detection coil in the unnecessary detection area can be flexibly adjusted in size. In order to ensure that the strong magnetic field area covers the detection coil, the width of the outer loop coil is appropriately expanded to 100 mm, and the inner loop coil is also expanded to 60 mm. The inner and outer ring coils are connected in coaxial sequence to ensure that the coupling between the metal foreign matters inside the detection coil and the detection coil is high. 1, 2 (A, B) are connected in adjacent sequence, and 3, 4, 5 (C, D, E) are connected in adjacent sequence to ensure that the coupling between the metal foreign matters at the edge of the detection coil and the detection coil is high. Finally, 12 (AB) coil groups and CDE (345) coil groups are connected in reverse from a long distance to complete the design.
Fig. 9. Long rectangular interconnection coil group. a Structure of long rectangular detection coil group. b The long rectangular detection coil group is arranged on the surface of the square transmission coil
Combined with Maxwell software to verify the detection effect, take the thin iron sheet with side length of 40 mm as the simulation object, compare the three detection coil structures, and obtain the change rate of induced voltage at each point of the iron sheet intrusion detection area (Fig. 10).
Fig. 10. Comparison of three detection coil schemes. a Independent long rectangular detection coil. b Double layer interconnected long rectangular detection coil. c Inner and outer ring interconnected long rectangular detection coil
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The horizontal and vertical movement gradient of 40 mm square iron sheet is 40 mm, and the induced voltage change rate of the three cases is summarized. The results are shown in Fig. 11. The heat map shows the results. The darker the color, the higher the sensitivity. The detection sensitivity of the two schemes with interconnection is obviously higher than that of the scheme with non interconnection independent detection coil. In this paper, the sensitivity of structure detection is more than 5%. When metal invades the strong magnetic field area, the sensitivity basically reaches above 30%, and some weak magnetic field areas can also reach above 10%. To sum up, the designed rectangular interconnect coil group with long inner and outer rings has the best detection effect. (a)
(b)
(c)
Fig. 11. The sensitivity thermogram of the last three schemes when the sheet iron intrudes into each position in the dotted line frame coil. a Independent long rectangular detection coil. b Double layer interconnected long rectangular detection coil. c Inner and outer ring interconnected long rectangular detection coil
4 Experimental Result In order to verify the detection effect of the designed detection system, experimental verification is carried out. In this paper, PCB is used to make the interconnect detection coil to avoid errors that may be caused by manual winding. Place the long rectangular detection coil group on the surface of the primary coil, the effective value of the primary coil current is 5A, and the working frequency is 85 kHz. The final experimental platform is shown in Fig. 12. The final test results show that when the four metals shown in Fig. 13 are thrown into the strong magnetic field area, the output voltage of the detection circuit changes as shown in Fig. 14, and the smallest 50 mm thin iron sheet in the strong magnetic field area reaches 98% detection sensitivity.
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Primary Transmission coil platform
Detection circuit
Detecion coil
Fig. 12. Primary coil platform and detection system
Fig. 13. Four kinds of metal foreign bodies
5 Conclusion In this paper, the detection coil method is theoretically analyzed, and the advantages of the long rectangular detection coil are explained after the sensitivity formula is obtained. Then, taking the square transmission coil as an example, the magnetic field is analyzed, and a detection coil group with long rectangular interconnection structure is proposed. The effectiveness of the proposed structure is proved by comparative simulation, and is verified by experiments on the 800 mm * 800 mm wireless charging platform. The final detection system realizes the effective detection of aluminum alloy, ferrite, iron and copper. The minimum size of 50 mm iron sheet in the strong magnetic field area can cause a change rate of more than 90% of the induced voltage of the detection coil.
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Fig. 14. Variation of Induced Voltage of Coil Filter Rectifier Output When Four Metal Foreign Objects Intrude. a 100 mm Copper. b 100 mm Aluminium. c 50 mm Iron. d 50 mm Ferrite
Acknowledgment. This research was partially funded by National Innovation Center of High Speed Train.
References 1. Chen, C., Xueliang, H., Wenhui, S. et al.: The influence of metal obstacles on the magnetic coupling resonance wireless power transfer system. Trans. China Electrotech. Soc. 29(09), 22–26 (2014). (In Chinese) 2. Liang, H.W.R., Wang, H., Lee, C.-K. et al.: Analysis and performance enhancement of wireless power transfer systems with intended metallic objects. IEEE Trans. Power Electron. 36(2), 1388–1398 (2021) 3. Changsheng, L., Juan, C., He, Z.: Modeling and analysis of magnetic resonance coupled power transmission system under the influence of non ferromagnetic metals. Autom. Electr. Power Syst. (23), 152–157 (2015). (In Chinese) 4. Yugang, S., Xinyu, H., Xin, D.: Overview of foreign object detection technology in magnetic coupling wireless power transfer system. Chin. J. Electr. Eng. 41(02), 715–728 (2021). (In Chinese) 5. Xia, J., Yuan, X., Li, J., et al.: Foreign object detection for electric vehicle wireless charging. Electronics 9, 805 (2020) 6. Jafari, H., Moghaddami, M., Sarwat, A.I.: Foreign object detection in inductive charging systems based on primary side measurements. IEEE Trans. Ind. Appl. 55(6), 6466–6475 (2019)
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7. Fukuda, S., Nakano, H., Murayama, Y., et al.: A novel metal detector using the quality factor of the secondary coil for wireless power transfer systems. In: Proceedings of the 2012 IEEE MTT-S International Microwave Workshop Series on Innovative Wireless power transfer: Technologies, Systems, and Applications, Kyoto, Japan, 10–11 (May); pp. 241–244 (2012) 8. Jeong, S.Y., Thai, V.X., Park, J.H. et al.: Self-inductance-based metal object detection with mistuned resonant circuits and nullifying induced voltage for wireless EV chargers. IEEE Trans. Power Electron. 34(1), 748–758 (2019) 9. Ying, S., Tian, Z., Kai, S. et al.: High-order composite resonant topology for improving sensitivity of wireless charging foreign object detection system. Trans. China Electrotech. Soc. 1–12 (2022). (In Chinese) 10. Jeong, S.Y., Kwak, H.G., Jang, G.C.: Dual-purpose nonoverlapping coil sets as metal object and vehicle position detections for wireless stationary EV chargers. IEEE Trans. Power Electron. 33(9), 7387–7397 (2018) 11. Thai, V.X., Jang, G.C., Jeong, S.Y. et al.: Symmetric sensing coil design for the blind-zone free metal object detection of a stationary wireless electric vehicles charger. IEEE Trans. Power Electron. 35(4), 3466–3477 (2020)
An Adaptive Equivalent Heat Minimization Strategy for Hybrid Electric Trucks Braking Considering Brake Temperature Rise in Long Downhills Liuquan Yang1 , Weida Wang1,2 , Chao Yang1,2(B) , Xuelong Du1 , and Bingquan Zhao1 1 School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
{ylq,cyang}@bit.edu.cn, [email protected], [email protected], [email protected] 2 Chongqing Innovation Center, Beijing Institute of Technology, Chongqing 401122, China
Abstract. High temperature failure of truck brake is one of the main causes of truck accidents, which is an urgent problem to be solved for vehicle safety. Especially in long downhill, the problem is more pronounced due to the frequent braking. In this paper, a brake control strategy is proposed to be applied in hybrid electric trucks. Firstly, the model considering hybrid powertrain and brake temperature rise is established. Then, an optimal method based on Pontryagin’s minimum principle (PMP) is designed. To improve the adaptability of the proposed strategy to the road, a self-correcting law is designed adjust the costates in the optimization method based on road information and vehicle state. Finally, four test roads were fitted by reference to several typical highways with long downhills in China. The results that the proposed can significantly reduce the maximum braking temperature with a rule strategy in fitting long downhill. It is also found that the continuous long downhill is more disadvantageous to the brake than the staged downhill. Keywords: Hybrid Electric Trucks · Brake Control Strategy · Adaptive Optimal Control · Brake Temperature Rise Model · Energy Management
1 Introduction With the development of land transportation, truck technology has become the focus of research [1]. The transportation efficiency and safety of trucks are widely concerned. In particular, the frequent braking not only loses a lot of gravitational potential energy, but also causes the high temperature of the brake in long downhill. High temperatures will lead to a sharp decline in braking performance, resulting in braking failure [2]. In order to avoid braking failure accidents due to high temperature, many scholars have carried out relevant research. The acquired results can be divided into three categories, including material improvement, structure improvement and configuration improvement. The friction sheet material is one of the main factors that determine the performance of the brake, its research has attracted much attention. Sathishkumar et al. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 22–31, 2023. https://doi.org/10.1007/978-981-99-1027-4_3
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[3] study the characteristics of temperature dissipation and thermal expansion by using different materials. The suggestion on the use of various materials in brake parts is given. Material improvement is an expensive and lengthy study, and new materials require long development cycles. Habtamu et al. [4] study three-disc brakes with different profiles, the results show that the grooved type brake is efficient by far more magnitude than the solid type and the drilled type. This way is to slow down the rate of temperature rise of the brake by improving heat dissipation structure. In high velocity condition, the improvement effect is obvious. As the velocity decreases, the improvement effect will become worse. The configuration improvement is an effective scheme, such as the installation of retarder [5]. Although this method is effective for vehicle braking in long downhills, it also has two disadvantages. The single device increases the vehicle cost, and the huge gravitational potential energy is wasted. Hybrid electric vehicles (HEVs) have been widely used due to the higher fuel economy through regenerative braking energy recovery [6]. Ko et al. [7] present a regenerative braking cooperative control algorithm. The energy of the regenerative braking recovery is increased, by considering the characteristics of the brake system. The current research on HEVs mainly focuses on the problem of improving fuel efficiency [8], but its braking research in long downhill is still empty. In long downhill, the generation of the electric motor can not only recover the electric energy, but also reduce the working intensity of the brake. However, through analysis, it is found that the amount of energy recovered by batteries and torque of electric motor is limited. However, the limit of battery is still a difficult problem. Hence, the problem of how to use this limited battery power to minimize the brake temperature rise is a difficult but meaningful study. Motived by the above problem, the problem of braking for HEV is studied in this paper. An adaptive optimal braking control strategy is presented. Firstly, the model considering brake temperature rise is established. Then, an optimal method based on Pontryagin’s minimum principle (PMP) is designed. Considering the diversity of roads, a self-correcting law is designed to adjust the costates in the optimization method based on road information and vehicle state. Finally, four test roads were fitted by reference to several typical highways with long downhills in China. The effect of the proposed strategy is tested separately by the road based on the fitting roads.
2 Vehicle Models The vehicle considered in this paper is a parallel hybrid electric trucks (HETs) with drum brake, the braking of which can be achieved by the together powertrain and brake system. The powertrain of HET consists of an engine, the electric motor of which can work as motor and generator. A powered lithium battery that powers an electric motor, an automatic electric clutch to engage and disengage the engine in difference modes and an automatic mechanical transmission (AMT) with six gears. The brake system is controlled by the solenoid valve. Both the powertrain and the brake system receive instructions from the vehicle control unite (VCU). This architecture enables the HET to have coupling regeneration braking mode. The configuration of the HET is illustrated in Fig. 1.
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Fig. 1. The configuration of the HET.
2.1 Vehicle Models In this study, the energy conversion and dissipation is research, which is mainly influenced by the longitudinal states of vehicle, thus the longitudinal dynamic model of vehicle is considered as the analysis platform. The longitudinal dynamics of the HEV is expressed as follows: ⎧ CD ρa Af v2 dv ⎪ ⎪ + Mgf cos θ + Mg sin θ + δM ⎨ Ft + Fb = 2 dt (1) + T )i i (T ⎪ e m g f ⎪ ⎩ Ft = ηg ηf r where F t is the propulsion provided by powertrain, F b is the braking force provided by brake system, C D is the drag coefficient, ρ a is air density, Af is the frontal area, v is the vehicle velocity, M is the curb weight of the vehicle, g is the gravity coefficient, f is the rolling resistance coefficient, θ is the road slope, δ is the correction coefficient of rotating mass, T e and T m are the output torque of the engine and electric motor, respectively, ig and if are the ratio of the AMT and final drive, respectively. ηg and ηf are the efficiencies of the AMT and final drive, respectively. r is the radius of the wheel. Note that the F b is equal to zero when the vehicle accelerating or traveling at a constant velocity. 2.2 Electric Drive System Model A permanent magnet synchronous motor (PMSM) is used as electric motor, which has the function of motor and generator. And a lithium battery is used as a source of electricity. The change of the battery charge is influenced by electric motor, thus the battery and electric motor is as a whole component. The state of charge (SOC) of battery is commonly to describe the energy of battery. The rate of the SOC(t) can be described as ˙ S OC(t) =
˙ Q(t) Ibat (t) =− Qnc 3600Qnc
(2)
where Q(t) is the remain capacity of the battery, Qnc is the nominal capacity of battery, I bat (t) is the current at time t and is shown as 2 (t) − 4000P (t)R (t) Vbat (t) − Vbat bat bat Ibat (t) = (3) 2Rbat (t) where V bat (t) is the voltage of the battery, Rbat is the resistance of the battery.
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2.3 Brake System Model The drum brake is used to in the truck due to lower production cost and large braking force. However, the closed structure results in the poor performance in heat dissipation. Therefore, high temperature failure is one of the common faults of drum brake. The temperature model of drum brake can be expressed with: tf Ttf = Tt0 + t0
Pmec − Prh − Pch dt mdb cdb
(4)
where T tf and T t0 denote the temperature of drum brake at time t f and t 0 , respectively. M db and cdb are the weight and specific heat of drum brake, respectively. Pmec is the mechanical frictional heat power. Prh and Pch are the radiation heat transfer and convective heat transfer power. Note that the heat transfer power is ignored in drum brake system because its effects is very small. The mechanical friction is the main source of the heat, which is related to wheel speed and braking torque, as Eq. (5). Pmec = Tb · ωw
(5)
where T b is the braking torque, and ωw is the speed of wheel. The radiation hear transfer power can be express as follow. Prh =
σb Asur [T14 − T24 ] 1 ε1
+
Asur 1 Arim ( ε2
− 1)
(6)
where σ b is the black-body radiation constant, Asur is the area of the outer surface of drum brake, Arim is the area of the inner surface of the rim. T 1 and T 2 are the thermodynamic temperature of the drum brake surface and the air, respectively. ε1 and ε2 are the blackness of the drum brake and rim, respectively. The convective heat transfer power can be express as follow. Pch = hAsur (tw − tf )
(7)
where h is the convective coefficient. t w and t air are the temperature of the drum brake surface and the air. The convective coefficient h is given as [9], λdb uρldrum drum n h=C (8) ldrum ηair where λdb is conductivity coefficient, ρ is the air density, ldrum is the brake drum surface geometry, ηair is the viscosity of air, u is the fluid velocity which is seen as consistent with the vehicle velocity in this paper. C and n are the constant.
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3 Adaptive Equivalent Heat Minimization Strategy To avoid high temperature failure of brake due to long time high intensity work and improve energy efficiency, the electric motor and engine of the powertrain is used as an auxiliary brake device in this paper. One advantage is that the heat accumulation problem of the brake can be alleviated, and another advantage is that the energy can be recovered to improve the vehicle economy. A key problem is that the braking ability of electric motor will be lost when the battery is fully charged. Therefore, the height of the road is considered to evaluate the electrical energy that can be provided for the battery. Then an instantaneous optimization strategy is proposed to allocate the braking torque between the brake and the powertrain. The proposed strategy is shown in Fig. 2.
Fig. 2. The structure of the adaptive optimal brake control strategy.
3.1 Braking Control Problem Description In long downhills, most of the gravitational potential energy of the vehicle needs to be consumed by the braking system. When the battery can fully recover this energy, the braking force of the motor can be fully used to share the pressure of the brake. However, the battery of a hybrid vehicle is only used as part of the energy reserve, and it is difficult to guarantee full recovery. Therefore, it is a key problem to reduce the temperature rise of the brake on the premise of ensuring the maximum recovery energy of the battery. An optimal problem therefore is established as follows. tf L(Pbatt (t), PVr (t))dt
min F =
(9)
t0
where L(Pbat (t), PVr (t)) = T (Pb (t)) = T (PVr (t) − Pbat (t))
(10)
where PVr (t) is the demand power of the vehicle. Taking battery SOC as the state variable and combining Eqs. (2) and (3), the state equation can be expressed as
=−
˙ S OC(t) = f (SOC(t), Pbat (t)) 2 (SOC(t)) − 4000P (t)R (SOC(t)) Vbat (SOC(t)) − Vbat bat bat 7200Qnc Rbat (SOC(t))
(11)
An Adaptive Equivalent Heat Minimization Strategy
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In order to make the vehicle running in a reasonable state, the state constraints on the battery are defined as ⎧ ⎪ ⎨ SOC(t) ∈ X(t) = [SOCmin , SOCmax ] SOC(t0 ) = SOCini (12) ⎪ ⎩ SOC(tf ) = SOCter_ max where SOC ini and SOC ter are the initial charge at the top of slope and the maximum charge that can be recovered at the lower of the slope, respectively. SOC min and SOC max are the minimum charge and maximum charge of the batter at time t, respectively. The feasible range of control variables is not only limited by the battery, but also by the electric motor and drum brake. ⎧ Pm_ min (t) Pm_ max (t) ⎨ P (t) ∈ U(t) = [max(P ), min(Pbat_ max (t), )] bat bat_ min (t), ηbat (t)ηm (t) ηbat (t)ηm (t) ⎩ Pb ∈ U(t) = [Pb _ min(t), 0] (13) where Pm_min and Pm_max are the minimum power and maximum power of the electric motor at time t, respectively. Pbat_min and Pbat_max are the minimum and maximum power of the battery at time t, respectively. Pb_min is the maximum brake power of the brake. 3.2 The Optimal Solution Method The equivalent consumption minimization strategy (ECMS) is instantaneous optimization strategy applied in the problem of energy management for HEV. The theory of ECMS based on Pontryagin’s minimum principle has strong implementation ability and practical value. In this paper, an adaptive equivalent heat minimization strategy (AEHMS) based on PMP and considering the braking characteristics is presented. Based on the Eqs. (9)–(11), the Hamilton function H is defined as. H (SOC(t), Pbat (t), λ(t), PVr (t)) = L(Pbat (t), PVr (t)) + λ(t)f (SOC(t), Pbat (t)) (14) where λ(t) is the covariate. The necessary conditions for obtaining the optimal control from the PMP principle are ∗ Pbat (t) = arg
min
Pbat (t)∈U(t)
H (SOC ∗ (t), Pbat (t), λ∗ (t), PVr (t))
˙ ∗ (t) = f (SOC ∗ (t), P ∗ (t)) S OC bat λ˙ ∗ (t) = −
∂H (SOC ∗ (t), Pbat (t), λ∗ (t), PVr (t)) ∂SOC ∗ (t)
(15) (16) (17)
SOC ∗ (t0 ) = SOCini
(18)
SOC ∗ (tf ) = SOCter_ max
(19)
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The problem consist of Eqs. (17)–(21) is a two-point boundary value problem. Taking Eqs. (10), (11), and (14) into (17), it can be solved that λ˙ ∗ (t) is zero because the (10) and (11) are independent of the state SOC(t). Therefore, a conclusion that λ∗ (t) is constant can be drawn. The optimal λ∗ (t) is commonly solved in numerical. But the process of solving depends on complete condition information. Hence, it is a difficult application in real time by this method. To solve this problem, an adaptive law considering the real condition is designed to adjust covariate so that minimize the function Hamilton function H. In long downhills, the potential energy of the vehicle from the top to the bottom of the slope can be expressed as Eg = MgSH
(20)
where S H is the vertical height from top to bottom of slope. S H is obtained from the intelligent transportation system. The electric energy converted by potential energy is not be less than the remaining energy storage space of the battery. Hence, a reference SOC is designed, as follows. SOCref (t) = f (sH (t)) =
(SH − sH (t))SOCter_ max − sH (t)SOCini SH
(21)
where sH is the vertical height from the bottom of the slope at time t. As shown in (21), the reference SOC is a function of vertical height of vehicle, which is directs the battery to remain space before the vehicle arriving to bottom of slope. Considering the environment temperature affects the efficiency of convective heat transfer, which is thus choose as the temperature reference in this study. Combining SOC reference and temperature reference, an adaptive law is designed. λc (t) = (Tdrum (t) − Tref )2 − k(SOC(t) − SOCref )
(22)
4 Simulation Results and Discussion In this Section, the simulation experiment is performed and the results are analyzed. A parallel HET described in Sect. 2 is used as the proved vehicle. The main parameter of vehicle can refer to Yang et al. [6]. Different from the energy management research in the driving condition, there is currently no standard test condition for the braking condition. Therefore, by analyzing the characteristics of typical slope in China, a test condition is designed. The main parameters of the typical slope and the designed conditions are shown in Table 1. The design of the working condition at the same time as the figure driving is shown in Fig. 3. 4.1 Results An expected speed of 40 km/h is set in the simulation experiment. The results of velocity tracking in the four fitting road is shown in Fig. 4. The demand of velocity is satisfied using CACS and AEHMS. The temperature of the drum brake and the SOC of the battery are shown in Fig. 5. In this study, the initial SOC is set 0.6. It can be seen that the SOC
An Adaptive Equivalent Heat Minimization Strategy
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Table 1. The main parameters of the typical slope and the designed conditions. Road
Average slope (%)
Vertical drop (m)
Fitting Road
Length (km)
Average slope (%)
Vertical drop (m)
6.6
3.56
235
Road 1
11
2.73
300
Zhanglong Highway
14.5
3.35
486
Road 2
11
3.26
364
Yuan-Mo Highway
26.7
3.95
1055
Road 3
16
3.0
484.5
3.92
379
Road 4
16
3.26
576
2.97
350
Badaling Highway
Songdai Secondary road Jingzhubei Highway
Length (km)
9.68
11.8
Fig. 3. The fitted long downhill. a Fitting road 1. b Fitting road 2. c Fitting road 3. d Fitting road 4.
using CACS reaches the limited value (0.8) in advance compared with using AEHMS. When the SOC reaches the limited value, the temperature of the drum brake rises rapidly, such as the time 870 s of using CACS in Fig. 5 (a), the time 500 s of using CACS in Fig. 5 (b), the time 600 s of using CACS in Fig. 5 (c), and the time 400 s of using CACS in Fig. 5 (d). In the four group results, the temperature of drum brake using AEHMS is higher than using CACS in the early of condition. But the maximum temperature of drum brake using AEHMS is lower than using CACS in the whole condition. In addition, the SOC using proposed AEHMS reaches the limit value at the bottom of slope. This indicates that the electric motor works in the whole downhill process. 4.2 Discussion The simulation results that the temperature of drum brake is rises rapidly when the SOC reaches the limit. This phenomenon said that the electric motor of HET is helpful to reduce the temperature of brake. And through the reasonable distribution of the braking force between the electric motor and the drum brake, this advantage can be expanded. But the braking capacity of electric motor and battery is limited. As shown in Fig. 5 (d),
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Fig. 4. The results about temperature of drum brake and SOC. a The results in fitting road 1. b The results in fitting road 2. c The results in fitting road 3. d The results in fitting road 4.
although the maximum temperature of drum brake using AEHMS is lower than using CACS, the maximum temperature of drum brake is almost reaches 300 °C. A new simulation experiment in fitting road 4 is performed. The initial SOC is set 0.5, and the result is shown in Fig. 5. The maximum temperature of drum brake drops to about 250 °C. This illustrates the remain storage capacity of battery affects the performance of proposed strategy. It’s also a reminder that battery energy can be drained early to recover more braking energy before reaching a long downhill. In addition, by comparing the four fitted roads, one guess is that the more continuous the slope, the worse the brake performance. These guess will be studied in further.
Fig. 5. The results about temperature of drum brake and SOC in fitting road 4.
5 Conclusion This paper presents an adaptive brake control strategy for a HETs considering brake temperature rise in long downhill. An adaptive equivalent temperature minimization strategy is formulated where the optimal method based on PMP is designed. To improve the adaptability of the proposed strategy to the road, a self-correcting law is designed adjust the costates in the optimization method based on road information and vehicle state. With the proposed AEHMS, the maximum temperature of brake is significantly reduced with the rule strategy in four fitting roads. Moreover, it is also found that the continuous long downhill is more disadvantageous than the staged downhill. Acknowledgements. This work is supported by the National Natural Science Foundation of China (Grant No.51975048, U1764257), and also by Natural Science Foundation of Chongqing, China (Grant No. Cstc2021jcyj-msxmX0879).
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References 1. Ahasan, R., Guneralp, B.: Transportation in urban land change models: a systematic review and future directions. J. Land Use Sci. 17(1), 351–367 (2022) 2. Yevtushenko, A., Topczewska, K., Kuciej, M.: Analytical determination of the brake temperature mode during repetitive short-term braking. Materials 14(8), 1912 (2021) 3. Sathishkumar, S., Ramesh Kuamr, S., Jeevarathinam, A., Sathishkumar, K.S., Ganesh Kumar, K.V.: Temperature dissipation and thermal expansion of automotive brake disc by using different materials. Mater. Today Proc. 49, 3705–3710 (2022) 4. Habtamu, D., Velmurugan, P., Eneyw, G., Ewnetu, T.C., Senthil, K.: Numerical investigation of thermo-mechanical properties for disc brake using light commercial vehicle. Mater. Today Proc. 46, 7548–7555 (2021) 5. Gao, Z.W., Li, D.S., Tian, J.S., Ning, K.Y., Ye, L.Z.: Design and performance analysis of a novel radially distributed electromagnetic-hydraulic retarder for heavy vehicles. IEEE Trans. Energy Convers. 37(2), 892–900 (2022) 6. Yang, C., Zha, M., Wang, W., Yang, L., You, S., Xiang, C.: Motor-temperature-aware predictive energy management strategy for plug-in hybrid electric vehicles using rolling game optimization. IEEE Trans. Transp. Electrif. 7, 2209–2223 (2021) 7. Ko, J., Ko, S., Son, H., Yoo, B., Cheon, J., Kim, H.: Development of brake system and regenerative braking cooperative control algorithm for automatic-transmission-based hybrid electric vehicles. IEEE Trans. Veh. Technol. 64(2), 431–442 (2015) 8. Yang, C., You, S.X., Wang, W.D., Li, L., Xiang, C.L.: A stochastic predictive energy management strategy for plug-in hybrid electric vehicles based on fast rolling optimization. IEEE Trans. Industr. Electron. 67(11), 9659–9670 (2020) 9. Guo, Y.S., Yuan, W., Fu, R.: The temperature rise calculation and research of drum brake. Autom. Technol. 6, 8–10 (2006). (in Chinese) 10. Yang, C., Zha, M.J., Wang, W.D., Liu, K.J., Xiang, C.L.: Efficient energy management strategy for hybrid electric vehicles/plug-in hybrid electric vehicles: review and recent advances under intelligent transportation system. IET Intell. Transport Syst. 14(7), 702–711 (2020)
Field-Oriented Control Strategy Verification Based on Power Hardware in Loop Simulation Technology Menglong Xu, Abdul Hadi Hanan(B) , Zhichuan Wei, Shaokun Wang, Jun Li, and Bin Chen Research and Development Center, PONOVO Power Co., Ltd., Beijing, China [email protected]
Abstract. The Paper presents verification of induction motor control and its characteristics using indirect field-oriented control (IFOC) through a Typhoon Hardware-in-loop (HIL) simulation package with HIL604 configuration for both testbench control and real-time simulation. With field-oriented control, the angle and the magnitude of each phase’s voltage and current are controlled. Typically, torque control is accomplished by modulating the armature with a constant field current. The Field Weakening is used to boost the speed beyond its base value. To decouple the motor torque and flux, a d-q reference frame locked to the rotor flux vector is employed. Therefore, they can be independently controlled by the stator’s quadrature-axis current and direct-axis current, respectively. Using the PI controller and SVPWM approach, satisfactory performance is realized. The rotor flux and magnetizing current are obtained using the proposed control strategy. To control the physical testbench, real-time control signals are amplified using PONOVO voltage and current amplifiers, which also make the output signal from the physical motor return at analog input ports of Typhoon. A dynamometer is used to measure the speed and torque of the induction motor. Software and hardware results are compared, and finally, efficiency is calculated. Keywords: IFOC · Typhoon HIL · SVPWM · Real-time simulation
1 Introduction Many industries have relied on the induction motor (IM) for a long time because of its ability to accurately manage electromagnetic torque and speed yet it has numerous control issues. Vector-based control approaches are recommended for controlling purposes. Direct torque control (DTC) and field-oriented control (FOC) are two well-known vector-based induction motor control methods (FOC). Since its debut in 1986 [1], the direct torque control method has been widely adopted. Using a fast-acting hysteresis controller and a switching table to select inverter states, this control approach responds quickly to changes in load torque. DTC is less affected by the uncertainty of parameters. At low speeds, the DTC’s performance decreases, making it difficult to control flux and torque. DTC’s downsides include a substantial voltage drop in stator resistance [2, 3], © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 32–43, 2023. https://doi.org/10.1007/978-981-99-1027-4_4
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which worsens when the amount of stator resistance is unknown, and a large number of ripples in torque and current. The field-oriented control was adopted for the first time in 1972, and its major objective was to compete with the independently excited-DC machine, which featured independent flux and torque control. The FOC control is executed in a rotating reference frame that is linked with the stator, rotor, or magnetic flux space vector. In addition, the stator current is separated into the parts that produce torque and flux. Depending on the circumstances, FOC may be implemented either directly or indirectly [4]. This work presents a decoupled torque control and rotor flux based on magnetizing current components. This control approach, however, is only effective in steady-state circumstances. A decoupled control system can work in both steady-state and transient environments by combining space vector modulation with a PI control system. To run IFOC on IM drives using SVPWM, the stator voltages, primary angular frequency, stator currents, rotor fluxes, magnetizing currents, and rotor speed must be measured. Magnetizing currents and rotor fluxes, on the other hand, are extremely difficult to detect. The control system relies on the simultaneous solution of Lyapunov equations [5, 6]. The viability of IFOC using SVPWM is verified by simulation in real-time through Typhoon HIL software. The signal is step-up using the PONOVO amplifier’s voltage and current module. PONOVO is committed to producing one of the world’s best power amplifiers. Out of many, the three we are working on are PIV 120, PIC 20, and PIT33 voltage, current amplifier. PIV 120 can step up the voltage signal to a maximum of 120 V, whereas PIC 20 amplifies the current up to 20 A. The PIT33 module is to step down the voltage to a low signal up to 5 V to make a close loop by giving the signal back to the software AI port.
2 Induction Motor Mathematical Model There are certain issues that induction motor is facing during startup and other severe transient operations, causing oscillatory voltage drop and torques, and can also create harmonics in power systems. The DQ equivalent model has proved dependable and precise when investigating such issues. Using a parallel resistance Rc, an induction motor’s internal induced voltage branch is accounted for in the equivalent circuit of an induction motor [7]. The synchronously rotating DQ equivalent circuit of an IM can be seen in Fig. 1. The voltage equations in the stationary frame used for modeling are as follows: uαs = Rs iαs + Ls piαs + Lm piαr
(1)
uβs = Rs iβs + Ls piβs + Lm piβr
(2)
0 = Rr iαr + ir piαr + Lm piαs + ωr Lm iβs + ωr Lr iβr
(3)
0 = Rr iβr + ir piβr + Lm piβs − ωr Lm iαs − ωr Lr iαr
(4)
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Fig. 1. Synchronously Rotating D-Q Axis Equivalent Circuit of Induction Motor
While voltage equations in a rotating frame are: uds = ids (Rs + Ls p) − Ls ωe iqs − Lm ωe idr + Lm piqr
(5)
uqs = iqs (Rs + Ls p) − Ls ωe ids − Lm ωe idr + Lm piqr
(6)
0 = Lm pids − (ωe − ωr )Lm iqs + (Rr +Lr p)idr − Lr (ωe − ωr )iqr
(7)
0 = Lm piqs − (ωe − ωr )Lm ids + (Rr +Lr p)iqr − Lr (ωe − ωr )idr
(8)
The relationship between voltages and currents can be given in matrix form from the four voltage equations: ⎡
⎤⎡ ⎤ ⎤ ⎡ uαs iαs 0 Lm p 0 (Rs + Ls p) ⎢ uβs ⎥ ⎢ ⎥⎢ iβs ⎥ + L p) 0 L p 0 (R s s m ⎢ ⎥⎢ ⎥ ⎥ ⎢ ⎣ 0 ⎦ = ⎣ Lm p ωr Lm (Rs + Ls p) ωr Lr ⎦⎣ ias ⎦ −ωr Lm Lm p −ωr Lr (Rs + Ls p) iβr 0
(9)
3 Indirect Field-Oriented Control In IFOC, instead of employing flux sensors, the rotor flux angle is determined from intermediate variables such as slip speed ωs1 and rotor speed ωr . It uses motor feedforward slip instruction and velocity feedback to allow instant commutation. Since the velocity signal from a PWM converter is often a better control signal than the voltage from a PWM converter, the indirect method is naturally more durable [8]. The primary distinction between this method and others is that the produced outputs and motor model are centered on the motor’s core operating condition as opposed to unrelated data. In other words, it is based on the motor’s essential component terminal currents and voltages. The control model for induction motor is based on the following equations; (10) θe = ωe dt = (ωs1 + ωr )dt
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1 + Tr p iqs Tr ids
(11)
ψs = Ls Is + Lm Ir
(12)
ψr = Lr Ir + Lm Is
(13)
J dw np dt
(14)
ωs1=
Te = TL +
where ωe is synchronous motor speed, Tr and TL rotor and load torque respectively, np is the number of poles, J is rotor’s moment of inertia, ψ represents the lux of rotor or stator, iq and id are quadrature and direct currents. Figure 2 depicts the fundamental speed control strategy using FOC. First, it measures the motor’s two input currents. These input currents are converted to a stationary coordinate frame using Clarke’s transformation module. Using Park’s transformation module, the stationary frame’s currents are transformed into the revolving frame’s currents. When these currents are compared to the reference currents, the current controllers transmit the error. Using the inverse rotating Park’s transformation module, the output of the present controllers in the DQ coordinate frame is transformed into the coordinate frame. This information is provided to the Space Vector PWM module. The output of the Space Vector PWM module controls the three-phase inverter’s gate signal. The Clarke and Park Transformation modules require the rotor flux position, which is a crucial part of machine control [9].
Fig. 2. The Block Diagram of IFOC
4 SVPWM Method in PWM Inverter SVPWM is the preferred technique for PWM voltage source inverters due to its vast low harmonic distortion, linear control range, and quick transient response. The SVPWM generates control signals for inverters. For the primary purpose of approximating the
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reference voltage (Vref) vector, SVPWM uses the inverter’s eight switching patterns to provide an output voltage for the inverter that is small enough to be the same as Vref within the same sampling period. At the same time, it receives the two reference voltages Vd and Vq in a rotating frame. These voltages (V α, V β), are used as a reference point for the stator. During one switching phase, the SVPWM principle relies on the switching between 2 identical operative vectors and a zero vector. As illustrated in Fig. 3, the six active states create a hexagon with six equal sectors named I, II, III, IV, V, and VI [10, 11]. There are just six switching operations per cycle of the fundamental frequency, hence the inverter regulation is simple, and switching loss is modest. Unfortunately, the sixstep voltage wave’s lower order harmonics cause severe distortions in the current wave. Thus, the SVPWM method is applied. The SVPWM technique manages the inverter’s output voltage and optimizes the harmonics.
Fig. 3. Inverter State Representation In a Reference Frame.
5 Typhoon Hil Real-Time Modeling Typhoon HIL is a software that is a platform for the modeling, monitoring, simulation, and testing of electrical machines and drives. Real-time testing and modeling can be done using HIL devices. To control data acquisition implementation and create a drive mode, Schematic Editor provides the essential capabilities of Typhoon HIL’s SCADA then compiles the system model and makes it ready to run, allowing the user to control the operating scenario through a simple and intuitive interface. An FPGA Typhoon processor (HIL 604) simulates and verifies the completed schematic in real-time. Upon connection of SCADA with the HIL device, the PC and CPU can communicate with one other using either a connected USB or an Ethernet connection [12]. There are three different complexity levels to model induction motor in Typhoon: • For the initial level of complexity, constant machine parameter values will be considered; • Machine inductance variations described by lookup tables computed using a frozen permeability technique and taking solely the phenomenon of saturation into account;
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• FEA-derived lookup tables describe the DQ current fluctuations vs the flux linkage variations, taking saturation and cross-saturation phenomena into account. The first level of complexity is used in this paper. Figure 4 depicts the machine model implemented in the software Typhoon using the specified equations and machine data mentioned in Table 1.
Fig. 4. INDM Modeling in Typhoon HIL
Table 1. Induction Motor Parameters Parameter
Value
Unit
Stator Resistance
1.621
Rotor Resistance
1.198
Stator Inductance
0.004
H
Rotor Inductance
0.006
H
Mag. Inductance
0.156
H
Frequency
50
Hz
Rated Voltage
400
V
Rated Torque
27.1
Nm
Rated Speed
1400
rpm
Pole Pairs
2
HIL 604 is a Typhoon HIL device that is used for real-time simulation to monitor results, adjust torque and current PI’s proportionate and integral gains, and input reference values such as torque reference and speed load reference. A diagram depicting the controls is shown in Fig. 5.
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Fig. 5. INDM Control System Model
6 Test Bench Layout Firstly, real-time simulation signals of converter power stage to run induction motor has been obtained through typhoon HIL 604 module. Then that module further connects with PONOVO PIV 120 and PIC 20 (voltage & current) modules through analog and digital inputs and outputs. The signal from the amplifier is then used to run the induction motor which is controlled by the simulation model design in Typhoon. To run the system in hardware in-loop, PONOVO PIT 33 voltage, the current transducer is used, which can step down the voltage or current signal and then give it back to HIL 604 through an analog input port. The detail of PONOVO voltage current amplifiers is mentioned in Table 2. Table 2. PONOVO Voltage/Current Amplifiers Details PIV 120
PIC 20
PIT 33
6 AC/DC output channels
6 AC/DC output channels
6 AC/DC output channels
Input: 6 × 0–7Vrms
Input: 6 × 0–7Vrms
Input: 3 × 0–1000 V 3 × 0–100 A
Output: 6 × 0–120 V
Output: 6 × 0–20 V
Output: ±10 V
Gain error: 0.2%
Gain error: 0.2%
Gain error: 0.2%
Frequency: 0–3 kHz
Frequency: 0–5 kHz
Frequency: 10 kHz
Pout: 60 VA/Phase
Pout: 300 VA/Phase
Pout: 125 VA/Phase
Pout DC: 150 W
Pout DC: 150 W
Pout DC: 125 W
Figure 6-a depicts a complete connection layout including the HIL604 module and a large number of IO ports that are available to the user. Beneath the HIL604 module,
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PONOVO power amplifiers are present to make the system run in-loop. Figure 6-b shows the induction motor that is connected with a load through coupling, which is further connected to the speed and torque sensor.
Fig. 6. Physical Test Bench Model For Induction Motor
7 Results The section describes the simulation results of vector control induction motor done in control hardware in-loop environment. It starts when the control speed signal through FOC is given to the induction motor. As through FOC, we can control the speed accordingly; starting from 0 rpm, it reaches a maximum speed of 1550 with the help of field
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weakening control, and then we run it at its rated speed of 1440 rpm at no-load. The results for both simulated rotor speed and actual rotor speed are compared in Fig. 7. A minimal variation can be seen with an efficiency of around 99.3%. 1800
Rotor Simulaon Speed (rpm)
1600
HIL Rotor Actual Speed (rpm)
Speed (rpm)
1400 1200 1000 800 600 400 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time (s)
Fig. 7. Rotor Simulated vs Actual Speed (rpm) at no-load
Now a sudden load of 120Nm has been added in the system at around 0.7 s (after the machine reached the steady-state). Figure 8 shows some overshoot in speed upon addition of load, but overall the steady state of the motor remains. 1800
HIL Rotor Actual Speed (rpm)
1600 1400 Speed (rpm)
1200 1000 800 600 400 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Time (s)
2
Fig. 8. Rotor Speed (rpm) at 120 Nm Load
At constant speed and torque, the DQ-axis reference and measured current along with inverter output current are shown in Fig. 9. Real-time simulation results including inverter current, mean frequency, torque and speed are given in Fig. 10. The motor is running with the speed of 304 rpm having a torque of 0.15 Nm and mean frequency of 10 kHz.
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Fig. 9. DQ Axis Current Control Reference and Measured Current
Fig. 10. Real-time simulation results
8 Conclusion Complex real-time systems can be developed and tested with the help of hardware in the loop (HIL) simulation. It’s a method for establishing a closed-loop connection between physical components (the controller) and theoretical models (the controlled system). This technique requires a genuine control system and a mathematical simulation model. The configuration of the control system is based on the mathematical model. Actuator variables are produced by the control system and are influenced by the control deviation
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or the gap between the ideal and real values. After the real value (the output variable) leaves the mathematical model, it loops back around to rejoin the control system. Indirect Field-oriented control for induction motor has been implemented on software, and the results are compared with the physical model through hardware control method using PONOVO power amplifiers. Field weakening control helps the motor to run above rated speed, verified by measuring the speed of a physical motor. The compared results proved the system is highly efficient. Acknowledgements. This work was supported in part by National Key R&D Program of China (Grant No. 2018YFE0208100).
References 1. Hadj Dida, A., Bourahla, M.: Field oriented vector control of an induction motor fed by multijunction solar cells. In: 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), 2018, pp. 760–764. https://doi.org/10.1109/ICRERA.2018.856 6868 2. Qinglong, W., Changzhou, Y., Shuying, Y.: Indirect field oriented control technology for asynchronous motor of electric vehicle. In: 2020 IEEE International Conference on Power, Intelligent Computing and Systems (ICPICS), 2020, pp. 673–677. https://doi.org/10.1109/ ICPICS50287.2020.9201983 3. Gashtil, H., Pickert, V., Atkinson, D., Giaouris, D., Dahidah, M.: Comparative evaluation of field oriented control and direct torque control methodologies in field weakening regions for interior permanent magnet machines. In: 2019 IEEE 13th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG), 2019, pp. 1–6. https://doi.org/10.1109/CPE.2019.8862320 4. Liu, Y., Tao, G., Wang, H., Blaabjerg, F.: Analysis of indirect rotor field oriented control-based induction machine performance under inaccurate field-oriented condition. In: IECON 2017— 43rd Annual Conference of the IEEE Industrial Electronics Society, 2017, pp. 1810–1815. https://doi.org/10.1109/IECON.2017.8216306 5. Kim, S.-H.: Electric Motor Control, pp. 243, 197–201. Elsevier (2017). ISBN: 978-0-12812138-2 6. Davari, S.A., Wang, F., Kennel, R.M.: Robust deadbeat control of an induction motor by stable MRAS speed and stator estimation. IEEE Trans. Ind. Informatics 14(1), 200–209 (2018) 7. Gao, L., Liang, Y., Wang, D., Bian, X., Wang, C.: Derivation of mathematic model of megawatt double canned induction motors and analysis of its dynamic performance. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), 2019, pp. 1–4. https:// doi.org/10.1109/ICEMS.2019.8921600 8. Khamis, A.A.H., Abbas, A.M.A., ALgoul, M.A.M.: Comparative study between a novel direct torque control and indirect field oriented control of three-phase induction motors. In: 2022 IEEE 2nd International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering (MI-STA), 2022, pp. 75–80. https://doi.org/ 10.1109/MI-STA54861.2022.9837649 9. Shaija, P.J., Daniel, A.E.: Robust sliding mode control strategy applied to IFOC induction motor drive. In: 2021 Fourth International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2021, pp. 1–6. https://doi.org/10.1109/ICECCT52121. 2021.9616948
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10. Xu, L., Zhu, Z.Q.: A novel SVPWM for open winding permanent magnet synchronous machine with extended operation range. IEEE J. Emerg. Sel. Topics Power Electron. (2022). https://doi.org/10.1109/JESTPE.2022.3200346 11. Peter, A.K., Mathew, J., Gopakumar, K.: A simplified DTC-SVPWM scheme for induction motor drives using a single PI controller. IEEE Trans. Power Electron. (2022). https://doi.org/ 10.1109/TPEL.2022.3197362 12. Moldovan, T., In¸te, R., Neme¸s, R.-O., Ruba, M., Mar¸ti¸s, C.: Typhoon HIL real-time validation of permanent magnet synchronous motor’s control. In: 2021 9th International Conference on Modern Power Systems (MPS), 2021, pp. 1–6. https://doi.org/10.1109/MPS52805.2021.949 2619
Hybrid Estimation of Residual Capacity for Retired LFP Batteries Yulong Ni , Jianing Xu(B)
, He Zhang, Chunbo Zhu, and Kai Song
School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, People’s Republic of China {niyulong,xjn,22S136210,zhuchubo,kaisong}@hit.edu.cn
Abstract. Estimating the residual capacity of retired batteries (RCRB) is a critical component of second-use applications (SUAs). This paper provides a hybrid model that combines a mechanism and a data-driven approach (MDA) to increase the accuracy of battery residual capacity estimation. First, the Levenberg Marquardt algorithm (LMA) is utilized to extract three health indicators (HI) that directly characterize the mechanism of capacity loss (MCL) from the constant current (CC) charging voltage curve. Second, the support vector regression optimized by the improved whale optimization algorithm (IWOA-SVR) is established, where the IWOA algorithm is constructed by an adaptive weight embedded in the WOA algorithm, which can prevent the local optimal value of WOA algorithm. Finally, 500 retired LiFePO4 (LFP) batteries were used to validate the effectiveness of the proposed method, the results reveal that when only the first 10% of the data is utilized, the root mean square error (RMSE) is 2.65% and the mean absolute error (MAE) is 1.82%. An accurate hybrid estimation model for RCRB can reduce the cost and time required for SUAs. Keywords: Residual capacity estimation · Retired batteries · Second-use applications · Hybrid model
1 Introduction Lithium-ion batteries (LIBs) are gaining importance as a result of their high energy density, low self-discharge, and long lifespan [1, 2]. With the service of LIBs, the safety problems caused by the degradation of LIBs have attracted much attention. Due to the hidden danger of safety accidents, it cannot be used in electric vehicles (EVs) when declined to 80% of the nominal capacity [3]. To avoid the waste of sources, the SUAs are the optimal solution, which means these retired batteries can continue to be applied in the market of low performance requirements of battery, such as communication base stations, commercial residential energy storage, low-speed EVs [4]. However, the accurate estimation for battery residual capacity is extremely important to shorten the process of SUAs.
© Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 44–51, 2023. https://doi.org/10.1007/978-981-99-1027-4_5
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At present, there are mainly two methods in battery capacity, including model and data-driven approaches [5]. The model methods mainly include empirical model, equivalent circuit model (ECM), and mechanism model (MM). Most empirical models combine capacity exponential model and filtering algorithm to estimate state-of-health (SOH). However, the accuracy of the empirical model is constrained because it is difficult to capture the dynamic characteristics of load. Through filtering methods such as the Kalman filter (KF) particle filter (PF), the ECM accomplishes the joint estimation of state-ofcharge (SOC) and capacity. However, the model ignores some physical and chemical reaction processes in the equivalent simplification process, and cannot provide accurate estimation. The MM that directly characterize the internal mechanism to derive the analytical solution of battery capacity loss, such as solid electrolyte interphase (SEI) growth and decomposition, lithium inventory loss (LLI), active material loss (LAM), and lithium plating [4]. However, such model parameters are mainly obtained from electrode characteristics. Another data-driven approaches, which mainly extracts the HIs from historical data and does not take into account electrochemical mechanisms, then establishes a regression model between the HI and capacity using techniques, such as Gauss progress regression (GPR), relevance vector machine (RVM), artificial neural networks (ANN). Many authors have established HI for the capacity estimate by using the voltage, current, and temperature data collected during the charging-discharging process [6, 7]. Khaleghi et al. [8] established the voltage change in partial voltage interval as the HI of battery health trajectory, and the nonlinear autoregressive neural network to estimate SOH. Choi et al. [9] employed observable data such as voltage, current, and temperature to build the capacity-charging curve relationship and accurately estimate the SOH. However, these HIs are difficult to directly correspond to the MCL. The data-driven methods can well realize the battery capacity estimation, whereas the estimation accuracy of these methods is not high enough and cannot describe the MCL. The main reason why the accuracy of residual capacity estimation is difficult to greatly improve is how to select the HIs that characterizes the degradation of battery capacity. Besides, the estimation accuracy of the data-driven methods still depends on the quantity of the training set. The following are the significant contributions in this study. (1) For estimating retired battery capacity, a hybrid model of the MDA is provided. (2) The established HIs can directly characterize the MCL and improve the residual capacity estimation accuracy. (3) The proposed hybrid model can achieve accurate estimation based on small samples. To overcome the drawback that the whale optimization algorithm (WOA) readily settles on the local optimal solution, an adaptive weight is added to the algorithm. The crucial task of highly accurate estimation of RCRB may be accomplished using the improved whale optimization algorithm-SVR (IWOA-SVR) method. The remainder of this work is organized as follows: Sect. 2 introduces the related methods, exacts three HIs, and establish the capacity estimation method. Section 3 verify the proposed estimation method. Section 4 presents the conclusions.
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2 Estimation Model Establishment 2.1 Capacity Loss Mechanism Model The retired LiFePO4 (LFP) battery is used in this study. Since LFP battery capacity loss is made up of the lithium inventory loss and active material loss, the prognostic and mechanistic model (PMM) was used in this study [10]. The full voltage can be defined as IL dt IL dt ) − Un (SOCn,0 + ) + Rohm · IL (1) Ut = Up (SOCp,0 − Qp Qn where Qp is the capacity of positive electrode (PE), Qn represents the capacity of negative electrode (NE), SOC p,0 denotes the initial lithium insertion (ILI) of the PE, and the ILI of the NE is represented by SOC n,0 . Due to battery aging, an increase in Rohm represents the change of LLI; significantly changed SOC n,1 also indicates the change of LLI, whereas the change in Qn describes LAM. Thus, the Rohm , SOC n,1 , and Qn were selected as three HIs, which were identification from the CC charging voltage profiles by the LMA. 2.2 Support Vector Regression Method The support vector regression (SVR) [11] is utilized for residual capacity estimation, according to given simple set D = {(xi , yi )|i = 1, 2, ..., n}, (xi ∈ Rn , yi ∈ R), where xi is the ith input value, yi ∈ R denotes the ith output value, and n represents the total samples. The SVR is to map data into high-dimensional space by nonlinear mapping ϕ, and establish the input-output relationship of data, which can be denoted as: f (x) = ωT · ϕ(x) + b
(2)
where ω and b represent the weight and intercept, respectively. The dual problem of SVR can be obtained by introducing the Lagrangian multipliers ai , and aˆ i : min(−
αi ,αˆ i
1 (ˆai − ai )(ˆaj − aj )K(xi , xj ) − ai (yi + ε) + aˆ i (yi − ε)) 2 n
n
n
i,j
i
i
⎧ ⎨ s.t. ⎩
n i
(ai − aˆ i ) = 0,
(3)
(4)
0 ≤ ai , aˆ i ≤ ξ, i = 1, 2, ...n
where K(xi , xj ) is the kernel function, ε denotes the maximum error, and ξ represents the penalty factor. Therefore, the regression function of the SVR can be presented: ⎧ n ⎨ f (x) = (a − aˆ )K i i RBF (xi , xj ) + b (5) i ⎩ KRBF (xi , xj ) = exp(−||xi − xj ||2 /(2σ 2 )) where the KRBF (xi , xj ) is the radial basis function, σ is the parameter of kernel function.
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2.3 SVR Parameters Optimized Using Improved Whale Optimization Algorithm The key to the accuracy of SVR method is the parameters σ and ξ. The improved whale optimization algorithm (IWOA) is established, which through an adaptive weight embeds in the WOA algorithm. 2.3.1 Whale Optimization Algorithm The WOA [12] is a meta-heuristic optimization algorithm that mainly simulates the humpback whale hunting behavior, i.e., the bubble-net hunting method. (1) Encircling the prey: The humpback whales can quickly encircle the prey after noticing the prey, and constantly update its position, which can be denoted as · X ∗ (t) − X (t)| = |C D
(6)
·D X (t + 1) = X ∗ (t) − A
(7)
where t is the current iteration, X ∗ denotes the position of the current optimal and C are the coefficient solution, and X indicates the position of the whale. A vector, which can be calculated as: = 2a · r − a A
(8)
= 2 · r C
(9)
where a is a convergence factor that linearly decreases from 2 to 0 as the number of iterations increases, and the r represents the random number between 0 and 1. (2) Bubble net attacking: Two approaches are presented to model the whale hunting behavior, which can be designed as follows: a. Shrinking encircling mechanism: This behavior can be achieved by decreasing the convergence factor a via Eq. (8). b. The location is updated by spiral: Calculate the distance between the whale individual and the current optimal position, and then simulate the whale to prey the food in a spiral manner, which can be defined as: = |X ∗ (t) − X (t)| D
(10)
· ebl · cos(2π l) + X ∗ (t) X (t + 1) = D
(11)
represents the distance between the i-th whale and the current optimal where D position, b is a constant coefficient utilized to define the logarithmic spiral form, and l denotes the random number between [−1,1].
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This mathematical model can be expressed as: ·D X ∗ (t)−A if p < 0.5 X (t + 1) = bl D · e · cos(2π l) + X ∗ (t) if p ≥ 0.5
(12)
where p denotes the random number between [0, 1]. (3) Search for prey: When |A|≥1, the humpback whales are randomly selected to force them away from a reference whale to find a better prey to enhance the global search ability of the algorithm, which can be represented as: · Xrand − X | = |C D
(13)
·D X (t + 1) = Xrand − A
(14)
where Xrand represents the position vector of the whale randomly selected. 2.3.2 Whale Optimization Algorithm with Adaptive Weight The introduction of adaptive weight in the WOA algorithm (IWOA) makes the algorithm adaptively update the position of the WOA algorithm to improve the optimization accuracy, which can be denoted as: ·D w1 · X ∗ (t)−w2 · A if p < 0.5 (15) X (t + 1) = · ebl · cos(2π l) + w1 · X ∗ (t) if p ≥ 0.5 D w1 = −rand ∗ [cos(0.5π ∗ (t/T )) − 0.5] (16) w2 = rand ∗ [cos(0.5π ∗ (t/T )) + 0.5] where w1 is the adaptive coefficient of the current optimal position, w2 represents the adaptive coefficient of the encircling step, and rand is random function, the value is between [0, 1]. 2.4 The Framework of Residual Capacity Estimation Method The parameters of SVR method optimized by the IWOA algorithm, and Fig. 1 shows the framework for estimating the residual capacity of retired LFP batteries. The detail steps of the estimation framework are listed as follows. (1) HIs establishment and extraction: In the process of constant current charging mode, the LMA method is utilized to obtain the three HIs directly characterize the capacity loss mechanism. (2) Data processing: The dataset composed of residual capacity and three health indicators is divided into a training set and a test set. (3) Parameters normalization: In the IWOA algorithm, the search number is 40; the maximum number of iterations (Max_iter) is 1000; the number of variables is 2; and the search boundary is between [0.01, 1000].
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(4) IWOA–SVR method establishment: The IWOA-SVR method uses the three HIs (Rohm , SOC n,1 , and Qn ) of the training set as input and the residual capacity as output. And the test set is used for verifying the effective of the IWOA–SVR method.
Input Voltage Current
Model: Capacity loss mechanism model
Health Indicator Rohm Health Indicator SOCn,1
Health Indicator Qn
Data-driven: IWOA-SVR Method
Real residual capacity
Dataset
Output
Fig. 1. The estimation framework of RCRB
3 Results Verification and Discussion To verify the feasibility of the proposed hybrid model, 500 retired LFP batteries were used. In addition, the LSTM and GPR methods are used to compare. The first 10%, 30%, and 50% of the full data as the training set, respectively, the estimation results are shown in Fig. 2. As shown in Fig. 2 and Table 1, the smaller error of the proposed method can be represented than the LSTM and GPR methods. For the first 10% of the data, compared with other methods, the IWOA-SVR method can provide smaller error, as shown in Table 1. The errors of the IWOA-SVR method decrease when the first 30% and 50% of the data, whereas the errors of the other two methods increase. As a result, it can be concluded that the IWOA-SVR method show higher estimation accuracy than the other methods.
4 Conclusion This study provides a hybrid model based on the MDA to improve the estimation accuracy of RCRB. The LMA method is used to exact three HIs, which are then fed into the IWOASVR method. Where an adaptive weight is embedded in the WOA algorithm to solve the problem that the WOA algorithm easily falls into the local optimal value. 500 retired LFP batteries were used to verify the feasibility of the proposed method, in addition, the GPR and LSTM methods are employed to compare. The results show that when only the first 10% of the data is used, the small error of the proposed method can be provided, where the MAE is 1.82% and RMSE is 2.65%. Therefore, the development of SUAs is promoted by the estimation method of RCRB suggested in this study, which has a high estimation accuracy.
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(a) 10%
(b) 30%
(c) 50%
(d) Error of 10%
(e) Error of 30%
(f) Error of 50%
Fig. 2. The estimation results of three methods
Table 1. The MAE and RMSE of three methods Training set (%) LSTM
GPR
IWOA-SVR
MAE (%) RMSE (%) MAE (%) RMSE (%) MAE (%) RMSE (%) 10
3.00
4.57
1.92
2.86
1.82
2.65
30
1.68
2.34
1.40
2.04
1.31
1.72
50
2.24
6.21
1.43
2.14
1.29
1.69
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Acknowledgements. This work is supported in part by the National Natural Science Foundation of China (51907082).
References 1. Hu, X.S., Xu, L., Lin, X., et al.: Battery Lifetime Prognostics. Joule 4, 310–346 (2020) 2. Severson, K.A., Attia, P.M., Jin, N., et al.: Data-driven prediction of battery cycle life before capacity degradation. Nat. Energy 4, 383–391 (2019) 3. Xu, J.N., Ni, Y.L., Cao, T.A., et al.: A fast diagnosis method for accelerated degradation fault induced by overcharging of LiFePO4 batteries. J. Energy Storage 46, 103798 (2022) 4. Ni, Y.L., Xu, J.N., Zhu, C.B., et al.: Accurate residual capacity estimation of retired LiFePO4 batteries based on mechanism and data-driven model. Appl. Energy 305, 117922 (2022) 5. Yang, Y.: A machine-learning prediction method of lithium-ion battery life based on charge process for different applications. Appl. Energy 292, 116897 (2021) 6. Ahmeid, M., Muhammad, M., Lambert, S., et al.: A rapid capacity evaluation of retired electric vehicle battery modules using partial discharge test. J. Energy Storage 50, 104562 (2022) 7. Tagade, P., Hariharan, K.S., Ramachandran, S., et al.: Deep Gaussian process regression for lithium-ion battery health prognosis and degradation mode diagnosis. J. Power Sources 445, 227281 (2020) 8. Khaleghi, S., Hosen, M.S., Karimi, D., et al.: Developing an online data-driven approach for prognostics and health management of lithium-ion batteries. Appl. Energy 308, 118348 (2022) 9. Choi, Y., Ryu, S., Park, K., et al.: Machine learning-based lithium-ion battery capacity estimation exploiting multi-channel charging profiles. IEEE Access 7, 75143–75152 (2019) 10. Ouyang, M., Feng, X., Han, X., et al.: A dynamic capacity degradation model and its applications considering varying load for a large format Li-ion battery. Appl. Energy 165, 48–59 (2016) 11. Patil, M.A., Tagade, P., Hariharan, K.S., et al.: A novel multistage support vector machine based approach for Li ion battery remaining useful life estimation. Appl. Energy 159, 285–297 (2015) 12. Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)
Design of a Full-Time Security Protection System for Energy Storage Stations Based on Digital Twin Technology Yuhang Song, Xin Jiang(B) , Jiabao Min, and Yang Jin Research Center of Grid Energy Storage and Battery Application, School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected]
Abstract. Safety is a prerequisite for promoting and applying battery energy storage stations (BESS). This paper develops a Li-ion battery BESS full-time safety protection system based on digital twin technology. Firstly, from the source of safety risk of BESS, the multi-physical characteristics of “electrical-gas-soundimage” in the thermal runaway (TR) process are integrated, and a multi-level early warning protection method for BESS is proposed. It can realize real-time sensing and early warning of multi-time scale safety status from regular operation, micro-overcharge, and TR to fire. Based on the digital twin technology, the core features of the BESS digital twin are described in six aspects: the accurate mapping of virtual reality, real-time sensing, and edge processing, and the overall design framework of the digital twin BESS safety protection system is proposed. The digital twin safety protection system can fully use BESS’s massive operation data, improve BESS’s safety coefficient and uncover potential failure risks, providing a new idea for the digitalization and intelligence of BESS operation supervision and safety production. Keywords: Digital twin · Battery energy storage station · Multi-level warning · Safety protection · Lithium-ion battery
1 Introduction Electrochemical energy storage technology is widely used in power systems because of its advantages, such as flexible installation, fast response and high control accuracy [1]. However, with the increasing scale of electrochemical energy storage, the safety of battery energy storage stations (BESS) has been highlighted [2]. In July 2021, the National Development and Reform Commission pointed out in “Guidance of the National Energy Administration on Accelerating the Development of New Energy Storage (No. [2021] 1051)” that the safety of BESS should strengthen, and should enhance the online monitoring of system operation status. The level of safe operation should be improved. Safety is a prerequisite for promoting and applying BESS. Digital twin technology was first used by NASA in the Apollo project and is now widely used in many fields such as intelligent manufacturing [3], agriculture [4], and © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 52–60, 2023. https://doi.org/10.1007/978-981-99-1027-4_6
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aerospace [5]. The digital twin technology makes it possible to digitize and intellectualize BESS’s operation supervision and safety production. Many cutting-edge scholars and experts have already taken the lead in applying digital twin technology to power equipment, grid dispatching, grid fault detection and other power fields. Weihan Li et al. of RWTH Aachen University realized online monitoring of battery status and health state assessment based on digital twin technology [6]. Shen Shen et al. of Tsinghua University, based on the CloudEPS platform, carried out integrated energy system scheme planning and design for a building-shaped park in the south, realizing intelligent planning and decision making for energy Internet [7]. However, digital twin technology is less studied in the intelligent operation and maintenance of BESS. On the one hand, the application of this technology in BESS is still in its initial stage. On the other hand, the various sensor data of BESS and the complex working conditions of multiple risk sources are difficult to represent by traditional techniques accurately as well as to simulate and deduce the abnormal conditions [8]. This paper takes BESS security protection as the application background and designs a BESS full-time domain security protection system based on digital twin technology. Firstly, we analyze the safety risk sources of BESS and propose a multi-level safety protection method for BESS with the integration of “electrical-gas-sound-image” multiphysical characteristics. Secondly, by describing the core features of the digital twin BESS at the definition level, the overall framework design of the digital twin BESS is proposed, and a BESS digital twin security protection system is built. Compared with the traditional early warning system, the digital twin safety protection system: • Can make full use of BESS’s multi-dimensional monitoring data. • Improve BESS’s safety coefficient and uncover potential failure risks. • It provides a new idea for digital and intelligent BESS operation supervision and safety production.
2 Digital Twin Technology 2.1 Digital Twin Battery Energy Storage Stations The digital twin BESS is a multi-physical, multi-dimensional virtual model that interacts with the real BESS in real-time through digitalization, networking and intelligence. Key data of BESS such as voltage, current, gas concentration, temperature, humidity, sound and images are connected to the network for monitoring. By centralizing data, algorithms and decisions in one, it can model and simulate and visualize all aspects of BESS production scheduling in a virtual computer environment, supporting design planning, simulation verification and analysis and evaluation of each aspect. At the same time, the digital twin BESS monitors and maps changes occurring in the physical BESS in real-time. Providing real-time data collection, optimizing production efficiency, and predicting potential risks helps O&M staff better understand failure risks and provide effective solutions.
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2.2 Features of the Digital Twin BESS Combined with the application requirements of digital twin system in other operation supervision and security protection, six core features of digital twin BESS are sorted out. (1) Accurate mapping of virtual reality. In building the BESS digital twin, the equipment size, performance parameters, assembly relationship and real environment in the entity, BESS should be accurately expressed in the virtual model. (2) Real-time sensing feedback. Realize real-time sensing and monitoring of BESS operation status through sensing collection at various levels such as electrical, sound, image, and temperature signals. (3) Edge data processing. Considering the huge amount of data generated during the operation of BESS, it will be a serious challenge to the server if the data is directly transferred to the central monitoring system, so the data needs to be initially processed, filtered and stored at a specific location before uploading to the cloud. (4) Fault diagnosis and prediction. Based on the abnormal data monitored by multiple sensors, the digital twin system searches for the root cause of the equipment abnormality and predicts it based on the failure model. BESS takes the best measures before the abnormality turns into an accident and avoids it to the maximum extent. (5) Autonomous model learning and optimization. The algorithms, models and decision-making mechanisms in the digital twin system should constantly be selflearning. The system will continuously optimize and update the existing models based on the analysis of massive operational data, enabling the system to adapt to different working conditions and improve the prediction accuracy. (6) Visual interactive presentation. The digital twin system uses the 3D modeling software Blender to build an accurate 3D model and Unity, a virtual engine, to render the real-time data stream. It makes the operation and maintenance personnel intuitively feel the current state of the whole BESS.
3 Digital Twin Technology 3.1 BESS Full-Time Security Protection Method With the massive amount of data from the operation of the BESS, systematic analysis of the risk sources of lithium-ion battery BESS is the core step to build a safety protection system. The risk sources are analyzed as shown in Fig. 1, mainly from five aspects, namely: battery failure, system failure, equipment failure, environmental factors and human factors. According to the current available BESS safety accident investigation report, BESS safety issues are the root of the lithium-ion battery safety issues. The safety of the battery in the charging and discharging process is often the main factor causing the battery thermal runaway (TR) fire or even explosion. Overcharge will lead to the decomposition of the battery solid electrolyte interface, bulging deformation, increased heat production, lithium dendrite growth and the occurrence of TR. Especially when overcharging, the heat accumulation will eventually lead to TR [9], posing a great threat to BESS safety protection if not properly handled in time.
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Fig. 1. BESS risk sources.
3.2 TR Early Warning Method Based on Multi-feature Parameter BESS Batteries present many state parameters at the beginning of an accident, including external and internal signals, and are in a constant state of evolution. It is crucial to select and identify their effective signals as safety warning feature parameters. Based on the team’s years of research, this paper proposes a TR early warning method based on multiple feature parameters from four dimensions: internal temperature monitoring (electrical signal), gas detection (gas signal), sound recognition (sound signal) and image recognition (image signal). 3.3 Full-Time Multi-level Security Protection System Design Using the characteristics of the early TR of Li-ion battery BESS, a full time-domain multi-level safety protection system for Li-ion battery BESS is established from four perspectives of “electrical-gas-sound-image” signals. The system will collect multidimensional parameters to evaluate the safety status of BESS in real-time. Different types of warning signals will be issued for different abnormal conditions, and different protective measures will be linked.
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A collaborative cloud-side approach is adopted to diagnose and predict faults more quickly. The “sound signal-characteristic sound” and “image signal-characteristic image” are processed at the side in compartment units, and only the processed data are sent back to the central monitoring system of the BESS. The “electrical signalcharacteristic impedance” and “gas signal-characteristic gas” are uploaded directly to the central monitoring system of the BESS and compared with the fault model in realtime. A warning signal is immediately issued when a fault signal is detected, and a linkage strategy is adopted. It is sensitive to identifying minor faults (e.g., the high internal temperature of individual cells) and eliminates potential hazards by changing the operation strategy. When “gas signal and characteristic gas” and “sound signal and characteristic sound” are detected, a warning signal is issued, and the faulty battery is withdrawn from operation to avoid the spread of the accident so that it can avoid the occurrence of TR and other accidents more than 10 min in advance. In addition to issuing a warning signal, the “image signal-characteristic image” links with relevant fire-fighting measures to avoid fire and explosion accidents. Through the strategy of multi-level safety protection in the whole time domain, the identification and treatment of multi-level faults of a single unit, module and system are realized.
4 Design of BESS Security Protection System Based on Digital Twin 4.1 Framework Design The digital twin BESS is based on digital models, big data analysis and artificial intelligence. Driven by massive key data and intelligent algorithms, it realizes two-way interaction and real-time information interoperability between digital virtual BESS and real BESS using digital twin technology. Its digital twin BESS framework design is shown in Fig. 2. Combining the current development status and functional requirements of BESS technology in China, the digital twin system is divided into a physical layer, perception layer, communication layer and twin application layer. (1) Physical layer. The physical layer is the cornerstone for building the digital twin system, which creates virtual digital models for physical entities through digital twin technology and provides accurate mapping, behavior simulation and state prediction for the real BESS. (2) Perception layer. The perception layer is the “sensory system” of the digital twin, which obtains key data from the BESS in real-time through various sensors and measurement devices. It is used to drive the operation of the digital twin system. (3) Communication layer. The communication layer is transmitted to the twin application layer via a wired network, LAN, Bluetooth, Beidou communication, WIFI, 5G or 4G, etc., to provide data support for the operation of the twin application layer. (4) Twin application layer. The twin application layer encapsulates models, algorithms, simulations, predictions and specific functions in the digital twin system. It presents them in a visual form to the user side.
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Fig. 2. Digital Twin BESS Security Protection System Framework.
4.2 Digital Twin Security Protection System Implementation Solution The BESS digital twin security protection system is divided into five parts: interactive system, data processing, simulation analysis, edge processing and communication security implementation. The development languages involved are VUE, JavaScript, C#, Egg.js and Python, and the system uses various encryption methods to encrypt the data stream to ensure the system communication security. The main technologies used in each module of the twin system are shown in Table 1. Table 1. Main technologies used in each module of the twin system. Function Modules
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(1) In terms of an interactive system. Use Blender to model the devices in the physical world accurately. The model is rendered using Unity, a virtual engine, and the Unity project package is packaged into Webgl.js and imported to the website for display rendering. The website is mainly written in HTML, CSS, VUE and JavaScript, and Egg.js is chosen as the programming language for the server side. (2) In terms of data processing. Firstly, the sensor acquisition data is processed by the method of the downscaling transformation matrix. After obtaining the characteristic pattern of a certain type of event (disturbance, accident, etc.), it is constantly calibrated with the real collected data to improve the sensing signal’s accuracy. (3) In terms of simulation prediction. COMSOL Multiphysics software is used for battery TR simulation and mechanical simulation. This simulation software is well adapted to the battery TR involving multi-factor coupling, which can solve the problem of TR research requiring a large number of partial differential equations and has strong applicability [10]. The gas simulation uses ANSYS software to optimize the gas detector location by performing a diffusion simulation of the characteristic gas and then studying the propagation velocity and path. Explosion simulation uses FLACS explosion simulation software to give blocking explosion spread protection strategy and fire linkage measures by studying the impact of gas explosion in energy storage compartment triggered by battery TR. (4) In edge processing. For the problem of packet loss or non-deterministic time delay transmission of key information in grid-level energy storage communication systems, a “cloud-edge-end” cooperative processing scheme is adopted. The “end”, i.e., the BESS individual battery, module and cluster side, adopts the sensing information priority classification technology and improves the robustness of the communication system in case of wired network failure based on the wired-wireless redundant master-slave network architecture. The “edge”, i.e., at the TSN gateway, forms an edge computing node to effectively share the load pressure of the BMS in the cloud. The “cloud” is the energy storage battery management system, the unified management of intelligent battery analysis and decision-making. (5) In terms of communication security. Crypto, jwt, sha256 and HTTPS are chosen to encrypt data streams. The Crypto module provides encryption functions, including hashing, HMAC, encryption, decryption, signature and verification functions of OpenSSL, which guarantees the security of information transmission while transmitting information efficiently. Based on the above implementation scheme, our team has built a visual digital twin BESS security protection system, as shown in Fig. 3. Figure 3 shows the main interface of the system. Among them, Fig. 3a shows the main interface of the digital twin safety and security system, Fig. 3b shows the 3D visualization demonstration interface of the digital twin safety and security system, Fig. 3c shows the interface for viewing the operating status of the energy storage compartment, and Fig. 3d shows the interface for monitoring the battery pack inside the energy storage compartment. Among the main pages, from left to right and from top to bottom, are the general overview of on-grid devices, currently selected BESS, historical alarm time statistics, internal and external battery temperature, on-grid power plant selection
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Fig. 3. Digital Twin Security Protection System.
window, space indicator window, energy storage compartment real-time monitoring window 1, energy storage compartment real-time monitoring window 2 and sound warning monitoring window.
Fig. 4. Digital twin security protection system operation mechanism.
The operation mechanism of the digital twin security protection platform is shown in Fig. 4. The system monitors the temperature, humidity, video, sound, hydrogen concentration and carbon monoxide parameters of the storage compartment through various sensors to estimate the state of the storage compartment comprehensively. It visually presents the results of the system. When the system detects abnormal data, it will send an abnormal signal alarm in different forms. It will link with the fire fighting system for necessary failures, thus reducing the chance of accidents. While the alarm occurs in the system, according to the abnormal parameters, the multi-dimensional simulation will also run simultaneously in different sub-systems. The final simulation results will be displayed in the system in virtual rendering.
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5 Conclusion In this paper, we propose to integrate digital twin technology with BESS and give the connotation and core features of digital twin BESS and the framework. Based on this, a lithium-ion battery BESS digital twin safety protection system is constructed, which realizes real-time sensing and mapping of BESS full-time domain multi-level safety protection and status. It also provides comprehensive evaluation for different types of abnormal signals and fire linkage for necessary faults, effectively improving BESS’s safety operation reliability. However, the construction of the overall digital twin system of BESS is a huge project involving extensive technology and difficult integration, and its theoretical system support cannot be achieved overnight. This paper is expected to provide inspiration and reference for the research on the application of digital twin technology in BESS.
References 1. Li, X., Wang, S.: Energy management and operational control methods for grid battery energy storage systems. Csee J. Power Energy Syst. 7, 1026–1040 (2021). https://doi.org/10.17775/ CSEEJPES.2019.00160 2. Wang, Q., Mao, B., Stoliarov, S.I., Sun, J.: A review of lithium ion battery failure mechanisms and fire prevention strategies. Prog. Energy Combust. Sci. 73, 95–131 (2019). https://doi.org/ 10.1016/j.pecs.2019.03.002 3. Liu, Q., et al.: Digital twin-based designing of the configuration, motion, control, and optimization model of a flow-type smart manufacturing system. J. Manuf. Syst. 58, 52–64 (2021). https://doi.org/10.1016/j.jmsy.2020.04.012 4. Verdouw, C., Tekinerdogan, B., Beulens, A., Wolfert, S.: Digital twins in smart farming. Agric. Syst. 189, 103046 (2021). https://doi.org/10.1016/j.agsy.2020.103046 5. Li, S., Liang, Y., Bai, S., Zhuang, C., Cao, Y.: Research on intelligent assembly modes of aerospace products based on digital twin. J. Phys. Conf. Ser. 1756 (2021) 6. Li, W., Rentemeister, M., Badeda, J., Jöst, D., Schulte, D., Sauer, D.U.: Digital twin for battery systems: Cloud battery management system with online state-of-charge and state-of-health estimation. J. Energy Storage 30 (2020) 7. Chen, S., Mengshuo, J., Ying, C., Shaowei, H., Yue, X.: Energy Internet Digital Twins and Their Applications (2020) (in Chinese) 8. Wenjiong, C., Bo, L., Youjie, S., Ti, D., Peng, P., Yaodong, Z., Fangming, J.: Analysis and Reflection on Safety Accidents of Lithium-ion Battery Energy Storage Power Stations in South Korea (2020) (in Chinese) 9. Ren, D., et al.: Investigating the relationship between internal short circuit and thermal runaway of lithium-ion batteries under thermal abuse condition. Energy Storage Mater. 34, 563–573 (2021). https://doi.org/10.1016/j.ensm.2020.10.020 10. Cai, L., White, R.E.: Mathematical modeling of a lithium ion battery with thermal effects in COMSOL Inc. Multiphysics (MP) software. J. Power Sources 196, 5985–5989 (2011). https://doi.org/10.1016/j.jpowsour.2011.03.017
Online Electrical Fault Diagnosis and Low-Cost State Estimation for Lithium-Ion Battery Pack Based Electric Drive System Qiao Wang1
, Min Ye1,1(B)
, Meng Wei2
, Gaoqi Lian1 , and Yan Li1
1 National Engineering Research Center for Highway Maintenance Equipment, Chang’an
University, Xi’an 710064, Shaanxi, China [email protected] 2 Department of Mechanical Engineering, National University of Singapore, Singapore 117576, Singapore
Abstract. The electrical fault diagnosis and state estimation are curial tasks for lithium-ion battery pack based electric drive system. The electrical fault of batteries will lead to abnormal state estimation. Considering the computational cost and limited memory sources of the on-board battery management system, a framework of online electrical fault diagnosis and low-cost state estimation for the lithiumion battery pack is proposed. Firstly, an available capacity based macro-selection method is carried out to select a “representative cell” of the battery pack periodically. Secondly, the correlation coefficient between “representative cell” and non-representative cells is calculated based on an optimal moving window in dual time-scale, then the electrical fault can be compensated based on the correlation coefficient in time. Finally, the Kalman filter framework is adopted for robust closed-loop state estimation for the lithium-ion battery pack, in which the Gaussian process regression is developed for measurement equation and Ampere hour counting is established for state equation, then the low-cost state estimation can be achieved. Experimental tests on battery packs were carried out under several dynamic load conditions considering user habits. The validation results demonstrate the robustness and accuracy of the proposed approach even there exists multiple disturbances. Keywords: Electrical Fault Diagnosis · Dual time-scale · Correlation Coefficient · State of Charge · Kalman filter
1 Introduction Lithium-ion batteries (LIBs) are widely used in electric drive systems [1], such as electric vehicles (EVs), electric construction machineries (ECMs), and electric boats. Battery management system (BMS) is designed for state monitoring, control, and fault diagnosis for the LIBs [2]. Hundreds and thousands of LIBs need to be connected into a battery pack to meet the power requirements before applying to the electric drive systems [3]. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 61–67, 2023. https://doi.org/10.1007/978-981-99-1027-4_7
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Online electric fault diagnosis and state of charge (SOC) estimation are curial tasks, which can ensure the safety and reliability of the electric drive systems. At present, the SOC estimation for LIBs are mainly including the open-loop estimation method and the closed-loop estimation method [4]. It is well known the robustness of the open-loop estimation is limited, which further limited its industrial application value [5]. For the closed-loop estimation method, multiple filters are applied in the existing researches, including Kalman filters, partial filters, and H∞ filters. The state equation and measurement equation need to be set in the closed-loop estimation method [6]. The most widely used state equation of closed-loop estimation is the Ampere hour counting (AHC) equation. However, the initial SOC errors and measurement noise of the current sensor significantly limited the accuracy of the AHC equation [7], which means a measurement equation with high robustness on initial SOC errors, and measurement noise is needed for accurate SOC estimation. Due to the time-consuming experimental test for model-based measurement equations, the data-based measurement equations attracted much attention [8]. To accurately estimate the SOC of LIB pack, three kinds of the method are introduced: the “big-cell” method, “mean-difference” method, and “representative” method [9]. The “representative” method defines the battery pack as two kinds of cells in the battery, which are “representative” cell and “non-representative” cells, and the “representative” cell is further used for state monitoring for a battery pack. However, the measurement noises and electric fault which may occur during the operation of electric drive systems are ignored. Meanwhile, most of the researches on BMS separately studied the mentioned two tasks. The electric fault of LIBs may cause abnormal data collection, which will further cause abnormal SOC estimation for a battery pack. Furthermore, the existing researches rarely considered the actual engineering application scenarios, which makes the results based on existing works questionable. Therefore, we propose a framework of online electric fault diagnosis and state estimation for LIBs packs based electric drive systems in this paper to address the aforementioned limitations. The proposed framework is verified by the experimental dataset considering the actual engineering application scenarios.
2 Workflow of Proposed Method The workflow of proposed approach is shown in Fig. 1. The first stage is the dataset preparation. The power data of a real loader under V-shape working condition was collected in the real world, and the wavelet preprocessed power data were applied for the battery pack test. The second step is the electric fault diagnosis of the battery pack. The “representative” cell selection was carried out based on the available capacity of the cells in-pack, and a backup cell was further selected as an alternative to the “representative” cell. The third step is the state modeling of the LIB pack. A neural network combined with the moving window is adopted for the open-loop estimation, and the closed-loop estimation was further achieved based on the Kalman filter. Then, the evaluation of the proposed method was carried out considering the real working conditions. Finally, the discussion of the deployment was introduced.
Online Electrical Fault Diagnosis and Low-Cost State Estimation Data Preparation
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Fig. 1. Overall framework of the proposed method.
3 Data Preparation The datasets of the charging-to-discharging of the LIB pack are shown in Fig. 2. A four cells series battery pack is employed for the experimental test. All cells in-pack are the same kind of battery, which is produced by the Panasonic with a normal capacity of 3 Ah.
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The electric system of the loader is more complicated than a normal electric vehicle. As shown in Fig. 2 (c, d), the current pulses of the electric loader are at millisecond scale, which means that the AHC method cannot be directly applied in the electric loader due to the limitation of sample frequency. The two stage discharging test is employed to simulate the user habits. Moreover, the thermal chamber is set to change the temperature between 10 and 40 °C every twenty minutes to simulate the real temperature variation. Note that the collected datasets are available upon reasonable request.
4 Theory of Proposed Method The Pearson correlation coefficient is employed for online electric fault diagnosis for the designed battery due to its low-cost calculation and effective results. To realize the online calculation, the moving window is adopted to store the sequence data into numerous segments. The calculation of the original Pearson correlation coefficient is based on the formula below: n i=1 (Xi − X )(Yi − Y ) (1) ρ= n n 2 2 (X − X ) • (Y − Y ) i i i=1 i=1 In which, the X = 1n ni=1 Xi , and the Y = 1n ni=1 Yi . The (Xi , Yi ) is the sample from sequences (X , Y ). Based on the formula mentioned above, we can calculate the correlation coefficient between the LIB by combining the moving window: wl
ρt =
− V1 )(V2i − V1 ) wl 2 2 (V − V ) · 1i 1 i=1 i=1 (V2i − V1 )
wl
i=1 (V1i
(2)
where the wl represents the window length, the wl i=1 V1i represents the data of cell 1 in wl one moving window, and the i=1 V2i represents the data of cell 2 in the corresponding moving window of cell 1. Then the correlation coefficient of ρt at t time can be calculated. The Gaussian process regression (GPR) is employed for the open-loop estimation model in this paper. Based on the GP process, the GPR model shows superior performance when measurement noise exists in the input data [10]. Due to the limitation of the conference paper, the theory of GPR will be presented in the complete article later. To further improve the robustness of the state monitoring for the battery pack, a Kalman filter based closed-loop estimation is introduced, in which the GPR is employed as the measurement equation, and the AHC method is adopted as the state equation. The whole framework of the closed-loop estimation is shown in Fig. 3. The gain of the Kalman filter can effectively compensate the measurement noise caused state estimation error. The detailed procedure of the employed Kalman filter can be found in our previous researches.
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Fig. 3. Whole framework of Kalman filter based closed-loop state estimation for LIB.
Fig. 4. Electric fault diagnosis results and the error compensation: a Voltage data with measurement noise in all cells and stagnation in cell 2&3; b Correlation coefficient results of cell 2&4 in macro-time scale and cell 3 in micro-time scale; c Error compensatory for cell 3; and d Current data with measurement noise.
5 Experimental Validations and Discussion The experimental validation results in this paper are all based on a PC equipped with an Intel core-i7 9700 CPU and MATLAB 2021a. There are four kinds of electric fault may occur in LIB pack, which are internal short fault, external short fault, connection fault, and sensors fault. Among them, neither the external short fault nor connection fault can make a complete electric circuit, and the
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internal short fault may occur in a long-time scale which shows little difference per unit time. Therefore, the V1i and V will be the same value when stagnation occurs, which makes the Pearson function cannot output results. Then, we can make an accurate fault diagnosis without any unreliable threshold. The correlation coefficient results of cells 2&4 in the macro-time scale and cell 3 in the micro-time scale are shown in Fig. 4 (b). As shown in Fig. 4 (b), the results of cell 3 in the micro-time scale show great fluctuation due to the complex working conditions of the electric loader, which makes the choice of a reliable threshold difficult. In contrast, the results of cells 2&4 in the macro-time scale are smoother than that of cell 3. Then, the sensor’s fault can be compensated based on the data of the cell which shows the best consistency with the fault cell in the battery pack.
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As the measurement noise is difficult to avoid in practical engineering application, it must be compensated based on a robust state estimation model. The state estimation results of the proposed method after sensor fault compensation is shown in Fig. 5. It can be seen that the robustness of closed-loop based state estimation is much better than that of open-loop based state estimation. As shown in Fig. 5(c, d), the error of GPR based state estimation shows great fluctuation, while the error of closed-loop based state estimation is smoother. The maximum error of the open-loop state estimation is greater than 6%, while the maximum error of the closed-loop state estimation is less than 1.5% after the fluctuation shown at the beginning of discharging.
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6 Conclusion This paper proposes the online electric fault diagnosis method for LIB pack based on the moving window and Pearson correlation coefficient, and further low-cost state estimation is presented based on the “representative” cell method and closed-loop state estimation. The evaluation results show that the suggested electric fault diagnosis method can accurately locate the sensor stagnation without any unreliable threshold, and the closed-loop estimation shows greatly robustness when measurement noises occur in the collected data. The maximum error of less than 1.5% can be obtained after sensor fault compensation. Due to the limitation of the conference paper, further experimental validation on the fault of the “representative” cell will be presented in the final article, and the speed of the proposed fault diagnosis method will be further improved by using an optimized moving window length.
References 1. Robles, E., Fernandez, M., Andreu, J., Ibarra, E., Ugalde, U.: Advanced power inverter topologies and modulation techniques for common-mode voltage elimination in electric motor drive systems. Renew. Sust. Energ. Rev. 140, 110746 (2021) 2. Lipu, M.H., et al.: Intelligent algorithms and control strategies for battery management system in electric vehicles: progress, challenges and future outlook. J. Clean. Prod. 292, 126044 (2021) 3. Tan, X., Lyu, P., Fan, Y., Rao, J., Ouyang, K.: Numerical investigation of the direct liquid cooling of a fast-charging lithium-ion battery pack in hydrofluoroether. Appl. Therm. Eng. 196, 117279 (2021) 4. How, D.N., Hannan, M.A., Lipu, M.H., Ker, P.J.: State of charge estimation for lithium-ion batteries using model-based and data-driven methods: a review. IEEE Access 7, 136116– 136136 (2019) 5. Hu, C., Ma, L., Guo, S., Guo, G., Han, Z.: Deep learning enabled state-of-charge estimation of LiFePO4 batteries: a systematic validation on state-of-the-art charging protocols. Energy 246, 123404 (2022) 6. Tian, J., Xiong, R., Shen, W., Lu, J.: State-of-charge estimation of LiFePO4 batteries in electric vehicles: a deep-learning enabled approach. Appl. Energy 291, 116812 (2021) 7. Mohammadi, F.: Lithium-ion battery state-of-charge estimation based on an improved coulomb-counting algorithm and uncertainty evaluation. J. Energy Storage 48, 104061 (2022) 8. Ren, X., Liu, S., Yu, X., Dong, X.: A method for state-of-charge estimation of lithium-ion batteries based on PSO-LSTM. Energy 234, 121236 (2021) 9. Zhou, Z., Duan, B., Kang, Y., Cui, N., Shang, Y., Zhang, C.: A low-complexity state of charge estimation method for series-connected lithium-ion battery pack used in electric vehicles. J. Power Sources 441, 226972 (2019) 10. Deng, Z., Hu, X., Lin, X., Che, Y., Xu, L., Guo, W.: Data-driven state of charge estimation for lithium-ion battery packs based on Gaussian process regression. Energy 205, 118000 (2020)
Capacity Prediction of Lithium-Ion Battery Based on HGWO-SVR Qiang Liao(B) , Kui Chen, Kai Liu, Yan Yang, Guoqiang Gao, and Guangning Wu School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611731, China [email protected]
Abstract. The capacity prediction of lithium-ion battery (LIB) plays a very important role in health management and the prediction of the performance degradation degree for battery. Accurate prediction of capacity can guide battery replacement and maintenance, and ensure the security and stability of battery. In this paper, based on the hybrid grey wolf optimizer-support vector regression (HGWO-SVR) algorithm, the capacity of LIB is predicted, and the remaining useful life is represented by the capacity of LIB. Differential evolution algorithm optimizes gray wolf algorithm to avoid it falling into local optimal solution. The hybrid gray wolf algorithm optimizes parameters of the support vector regression algorithm to improve prediction accuracy. The proposed method is simulated and verified by using NASA’s LIB capacity database. By comparing different optimization algorithms and different neural networks, it is verified that the proposed algorithm can forecast the LIB’s capacity more accurately. Keywords: LIB · Capacity prediction · Hybrid grey wolf optimizer · Support vector regression
1 Introduction LIB is broadly used in electronic product, energy storage [1–4] because of their small size, high energy density, no environmental pollution, long charging and discharging cycle, etc. With the increase of charging experiment times of LIB, its capacity will gradually decrease. While the capacity is reduced to less than 80% of the rated capacity, LIB is regarded as the end of its life [5]. The aging of LIB is easy to lead to overcharge and overdischarge of the battery, thus accelerating the aging of the battery [6]. Therefore, accurate prediction of LIB capacity can guide battery health management, prevent premature or late battery replacement, and reduce the occurrence of safety accidents [7]. The capacity prediction of LIB can be divided into two methods: model-driven and data-driven. Model-based LIB prediction needs to comprehensively consider the material properties of the battery and various performance failure mechanisms, so as to build a model of battery to forecast the health state. Kong SoonNg et al. proposed a method for estimating the state of charge (SOC) of LIB by coulomb counting, and established a model by charge discharge efficiency [8]. WeiHe et al. developed a model based on the physical © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 68–78, 2023. https://doi.org/10.1007/978-981-99-1027-4_8
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degradation behavior, and proposed Dempster Shafer (DS) theory and Bayesian Monte Carlo (BMC) to estimate the remaining useful life of LIB [9]. ArijitGuha et al. proposed a LIB model based on fractional order equivalent circuit model, using recursive least square method and variable filter based on voltage and current measurement to determine model parameters, and then using the obtained parameters to generate state estimation of LIB under different aging conditions [10]. Xin Zhang et al. presented a modified trackless particle filter and Markov chain monte Carlo (MCMC) to forecast the remaining useful life of LIB, which solved the problem of sample dilution or insufficient particle diversity caused by the resampling process [11]. Ma et al. presented a prediction model for the capacity of LIB based on the Gaussian Hermite particle filter (PF). They improve the accuracy of health state estimation and reduce the computational complexity [12]. Data-driven LIB capacity prediction methods usually use neural networks to learn and predict historical data. Wang Ping et al. analyzed the battery capacity increment, found two characteristic quantities with high correlation with the health status of battery and forecasted the capacity of LIB with Gaussian process regression [13]. Xu Jianing et al. extracted a factors that can feature the LIB degradation and presented a model for the LIB capacity with improved support vector regression [14]. Wang Yingzhou et al. presented a model for ant lion optimization (ALO) and support vector regression. The ant lion optimization algorithm improves the prediction accuracy of capacity [15]. Li Chaoran et al. proposed a joint estimation method for the state of charge and health of battery with deep learning by analyzing the correlation between the state of charge and the health state [16]. Based on the above research, this paper uses differential evolution (DE) algorithm, grey wolf optimizer (GWO) and support vector regression (SVR) to predict LIB capacity and characterize the health status of lithium battery by capacity. The prediction effect of the parameters of manual assignment support vector regression algorithm on LIB is not satisfactory. It requires multiple manual assignments to select the appropriate parameters, which wastes a lot of time. The grey wolf algorithm can greatly improve the prediction effect and save a lot of time by optimizing its parameters. However, the attack behavior of grey wolf algorithm may fall into local optimization, and the effect of optimizing parameters is poor. DE can effectively solve local optimization by updating the position of gray wolf through mutation, cross-over and other behaviors. The capacity data of LIB use NASA’s B0005, B0006, and B0007 data sets, and the prediction results are compared to verify HGWO-SVR has higher accuracy for the capacity prediction of LIB.
2 HGWO-SVR 2.1 DE Differential evolutionary is a random search technology by group guidance, which belongs to evolutionary algorithm. For the optimization problem in this paper, the equation is as follows: min f (x1 , x2 , ..., xD ) L
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where, xjL , xjU are the boundary value of the jth component xj value range, and D is the dimension. The elementary steps of DE are as follows. (1) Population initialization: Set population number NP to 30, maximum number of iterations to 500, population L U , i = 1, 2, 3..., NP; j = 1, 2, 3..., D generated genes: ≤ xj,i (0) ≤ xj,i xi (0)xj,i L U L xj,i (0) = xj,i + rand (0, 1) · xj,i − xj,i
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where, xj,i (0) represents the j-th gene of the i-th chromosome of the 0th generation. (2) Mutation: The common difference strategy is to randomly select the vector difference between two individuals in the population, and then combine it with the individual to be mutated after scaling. DE mutates through this strategy, namely: vi (g + 1) = xr1 (g) + F · (xr2 (g) − xr3 (g)) i = r1 = r2 = r3
(3)
F is the scaling factor, the value range set in this paper is 0.2–0.8, and xi (g) represents the ith individual in the g generation population. In the process of variation, it is necessary to judge whether the gene meets the boundary conditions, and if not, regenerate the gene through Eq. (2). (3) Crossing. Interindividual crossover between the g-generation population L U , i = 1, 2, 3..., NP; j = 1, 2, ..., D and the mutant inter≤ xj,i (g) ≤ xj,i xi (g)xj,i L U was performed: mediate vi (g + 1)vj,i ≤ vj,i (g + 1) ≤ vj,i uj,i (g + 1) =
vj,i (g + 1), if rand (0, 1) ≤ CR or j = jrand xj,i (g), otherwise
(4)
The CR crossover probability is 0.2, which is a medium random integer. (4) Selection: DE chooses individuals based on greedy algorithm from the next generation of the population: ui (g + 1), if f (ui (g + 1)) ≤ f (xi (g)) (5) xi (g + 1) = xi (g), otherwise 2.2 GWO The GWO is a group-based intelligent algorithm with few parameters and easy implementation. The algorithm divides wolves into groups α, β, δ, ω Four wolves, α, β, δ Wolf (optimal solution) and ω Wolves (candidate solutions) track their prey.
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(1) Enclosing the prey: It updates its position according to the location of the prey. The formula for enclosing the prey is as follows: → − → − → − − → (6) D = C · X P (t) − X (t) − → − − → − → → X (t + 1) = X P (t) − A · D
(7)
− → − → → → A = 2− a · R1 − − a
(8)
− → − → C = 2 · R2
(9)
− → D is the distance between the wolf and its prey, and the wolf updates its posi− → − → tion according to Form (7). T is the total number of iterations, A and C are the − → − → coefficient vectors, X P and X are the location vectors of the prey and the wolf, − → − → → respectively, and − a is the convergence factor. The modulus of R1 and R2 is any number between 0 and 1. (2) Hunting: Wolves surround their prey, α, β, δ The wolves began to track their prey separately by formula: ⎧− → − → − → − → ⎪ D = C 1 · Xα (t) − X (t) ⎪ ⎨ α → − → − → − → − (10) Dβ = C 2 · Xβ (t) − X (t) ⎪ ⎪ ⎩− → − → − → → − Dδ = C 3 · Xδ (t) − X (t) ⎧− → − → ⎪ X (t) = Xα (t) − A1 · Dα ⎪ ⎨ 1 − → − → (11) X2 (t) = Xβ (t) − A2 · Dβ ⎪ ⎪ ⎩− − → → X3 (t) = Xδ (t) − A3 · Dδ − → − → − → X1 (t) + X2 (t) + X3 (t) − → (12) X (t + 1) = 3 − → − → − → − → − → − → Dα , Dβ , Dδ are α, β, δ distance from individual wolf. Xα (t), Xβ (t), Xδ (t) are − → − → − → the of the three wolves, C is the random vector, X (t) and X (t + 1) are the gray wolves current locations and the next time locations which prey is tracked. (3) Attacking prey: While the prey stays still, gray wolf attacks it. The value of A varies between [−a, a]. When |A| < 1, the gray wolf attacks prey and may fall into local optimum. When |A| > 1, the gray wolf is forced not to track its prey. The DE algorithm updates the location information of gray wolves in GWO by mutation crossover to jump out of the local optimal solution. The steps are shown in Fig. 1.
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GWO
Randomly generate the location of prey and gray wolf
Calculate the location of gray wolves and the distance from their prey
Update gray wolf position
DE
Mutation Crosses to Produce New Gray Wolf Positions
Compare the position fitness of new and old gray wolves, and select the best
Attack prey
no Yes Training SVR
Fig. 1. Flow chart of HGWO
2.3 SVR Support vector machine (SVM) can generalize the classification problem to the regression problem to get SVR. SVR has significant advantages in dealing with small samples and non-linear data. Set the dataset S = {xi , yi }ni=1 (xi ∈ X = Rn , yi ∈ Y = R), xi is the ith input, yi is the output of xi , and n is the number of samples. Map the sample from low-dimensional to high-dimensional using a non-linear formula. The formula is: f (x) = ω · ψ(x) + b
(13)
n where b is the weight and intercept respectively. {ξi }ni=1 , ξi∗ i=1 are relaxation variables and can be introduced: 1 ω2 + C (ξi + ξi∗ ) 2 i=1 ⎧ y − f ≤ ε + ξi (x) ⎪ ⎨ i s.t. f (x) − yi ≤ ε + ξi∗ ⎪ ⎩ ξi , ξi∗ , ε ≥ 0 n
min =
(14)
(15)
C is the penalty factor and ε is the maximum allowable error. By introducing Lagrange factors αi , αi∗ , the following results can be obtained: max = −
n 1 ∗ αi − αi αj∗ − αj ψ(xi )ψ xj 2 i,j
−
n i
αi (yi + ε) +
n i
(16) αi∗ (yi
− ε)
Capacity Prediction of Lithium-Ion Battery Based on HGWO-SVR
s.t.
⎧ n ⎪ ⎨ αi − α ∗ = 0 i
⎪ ⎩
i
(17)
αi , αi∗
≤C K = ψ(xi )ψ xj 0≤
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(18)
where K is a kernel function. Radial Basis Function is chosen as the kernel function of this SVR. The function is as follows:
K =e
−
1 x 2 i −x 2σ 2
(19)
where σ is a parameter of the kernel function.
3 Simulation Result In order to accurately predict the capacity of LIB, this paper conducts simulation tests in MATLAB 2019 based on HGWO-SVR algorithm. With regard to GWO, in order to reduce the simulation time with accurate predictions, the number of gray wolf populations was selected at 30 and the maximum number of iterations was chosen at 500. By comparing the absolute percentage error (APE) of the predicted results, the HGWO-SVR algorithm has higher accuracy. Charging experiment scheme of LIB: charge the battery with a constant current, then charge the battery with a constant voltage, and stop charging. Discharge experiment scheme: discharge the battery with constant current, and stop discharging when the voltage at both ends of three groups of B0005, B0006 and B0007 drops to the cut-off voltage of 2.7 V, 2.5 V and 2.2 V respectively. To compare the accuracy of different prediction methods, the smaller the APE, the better the prediction results. The APE calculation formula is as follows: y − yˆ (20) APE = 100 · yˆ where yˆ is the actual value and y is the predicted value. In order to compare the influence of different volume data training proportion on prediction accuracy, this paper selects the mean absolute error (MAE). The MAE formula is as follows: n i=1 y − yˆ (21) MAE = n where yˆ is the actual value and y is the predicted value.
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Fig. 2. The capacity predictions of HGWO-SVR and SVR
3.1 Influence of HGWO Optimization Algorithm on Prediction Results In order to compare the prediction effect of HGWO optimization algorithm on SVR. LIB capacity, the first 50% capacity data of B0005 is used for training to predict the remaining 50% capacity data. The prediction results of B0006 by SVR with or without optimization algorithm are shown in Fig. 2, and the APE predicted by SVR model with or without optimization algorithm is shown in Fig. 3. As shown in Fig. 2, HGWO-SVR and SVR can both predict B0005 capacity, and the optimized SVR prediction effect is closer to the actual value. As shown in Fig. 3, the maximum predicted APE does not exceed 10%, and the APE of the SVR algorithm optimized by HGWO is small.
10
HGWO-SVR SVR
APE(%)
8
6
4
2
0 0
20
40
60
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Fig. 3. The APE of HGWO-SVR and SVR
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3.2 Influence of Different Neural Networks on Prediction Results To compare the prediction effect of HGWO-SVR and Elman neural networks on LIB capacity, the first 50% capacity of B0005 trains the model. The capacity prediction based on different neural networks is shown in Fig. 4, and the APE predicted by different neural networks for LIB is shown in Fig. 5.
1.9
Measured Value HGWO-SVR Elman
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Ah
1.7 1.6 1.5 1.4 1.3 1.2 0
20
40
60
80
100
120
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Fig. 4. The capacity predictions of HGWO-SVR and Elman
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APE(%)
10 8 6 4 2 0 0
20
40
60
80
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Fig. 5. The APE of HGWO-SVR and Elman
As shown in Fig. 4, different neural networks have different prediction accuracy for LIB, and HGWO-SVR has higher prediction accuracy. In Fig. 5, the APE of Elman is larger, exceeding 12% at most, but the maximum average error of HGWO-SVR is less than 6%, so the prediction effect is good. The maximum APE of Elman network is
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twice that of HGWO-SVR network. Compared with the prediction accuracy of the LIB capacity, the prediction effect of the model proposed in this paper is better. 3.3 HGWO-SVR Algorithm Predicting Impact of Different Proportional Capacity Training Data In order to explore the impact of different proportional capacity data on algorithm prediction, five groups of comparison data were made for the first 30%, 40%, 50%, 60% and 70% of the B0007 capacity data. Based on HGWO-SVR, five capacity data groups were trained and each group of residual capacity data was predicted. Compare different prediction effects through MSE. The prediction of five capacity data groups proportion by neural network is shown in Fig. 6, and the MSE is shown in Table 1. Measured value 30%HGWO-SVR 40%HGWO-SVR 50%HGWO-SVR 60%HGWO-SVR 70%HGWO-SVR
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1.6
1.5
1.4 0
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80
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120
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160
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Fig. 6. HGWO-SVR predicts different proportions of capacity data
Table 1. HGWO-SVR predicts different proportions of MAE Training capacity data proportion (%)
30
40
50
60
70
MAE
0.1982
0.0704
0.031
0.0221
0.0208
As shown in Fig. 6, HGWO-SVR has a better prediction effect on capacity with the increase of capacity training data. As shown in Table 1, with the increase of the capacity training data proportion, the MAE of network prediction becomes smaller, and the prediction effect becomes better. The minimum MAE can reach 0.0208. However, with the increase of training capacity data, the network training time increases.
4 Conclusions In this paper, a method based on HGWO-SVR is proposed to forecast the capacity of lithium ion battery. This paper draws three conclusions:
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(1) HGWO can automatically adjust and optimize SVR parameters. The prediction accuracy of HGWO-SVR is significantly higher than that of SVR. (2) Compared with different neural networks, the APE of the proposed method is the minimum, which shows HGWO-SVR algorithm has a high accuracy of capacity prediction. (3) Based on B0007, the higher capacity data proportion, the better the residual capacity prediction effect. When the volume training data only accounts for 30% of the total data, the MAE is less than 0.2, and the prediction effect is still good.
Acknowledgments. This work was funded by Headquarters Management Science and Technology Project of State Grid Corporation of China (SGTYHT/19-JS-215).
References 1. Couto, L.D., Schorsch, J., Job, N., Léonard, A., Kinnaert, M.: State of health estimation for lithium-ion batteries based on an equivalent-hydraulic model: an iron phosphate application. J. Energy Storage 21, 259–271 (2019) 2. Zubi, G., Dufo-López, R., Carvalho, M., Pasaoglu, G.: The LIB: state of the art and future perspectives. Renew. Sustain. Energy Rev. 89, 292–308 (2018) 3. Schneider, F., Zausch, J., Lammel, J., Andrä, H.: An efficient semi-implicit solver for solid electrolyte interphase growth in Li-ion batteries. Appl. Math. Model. 109, 741–759 (2022) 4. Jingwen, W., Guangzhong, D., Songhai, C.: Remaining useful life prediction and state of health diagnosis for LIB using particle filter and support vector regression. IEEE Trans. Industr. Electron. 65(7), 5634–5643 (2018). (in Chinese) 5. Tang Shengjin, Y., Chuanqiang, W.X., et al.: Remaining useful life prediction of LIB based on the Wiener process with measurement error. Energies 7(2), 520–547 (2014). (in Chinese) 6. Chaoran, L., Fei, X., Yaxiang, F., et al.: Joint estimation of SOC and SOH of LIB based on deep learning. Trans. China Electrotech. Soc. 41(2), 681–692 (2021). (in Chinese) 7. Qing, Y., Chen, Y., et al.: A review of LIB safety concerns: The issues,strategies,and testing standards. J. Energy Chem. 59(8), 83–99 (2021). (in Chinese) 8. Ng, K.S.M., et al.: Enhanced coulomb counting method for estimating state-of-charge and state-of-health of LIB. Appl. Energy 86(9), 1506–1511 (2009) 9. He, W.W., et al.: Prognostics of LIB based on Dempster-Shafer theory and the Bayesian Monte Carlo method. J. Power Sources 196(23), 10314–10321 (2011). (in Chinese) 10. Guha, A., et al.: Online estimation of the electrochemical impedance spectrum and remaining useful life of LIB. IEEE Trans. Instr. Measur. 67(8), 1836–1849 (2018) 11. Zhang, X., et al.: Remaining useful life prediction of LIB using an improved UPF method based on MCMC. Microelectron. Reliab. 75, 288–295 (2017). (in Chinese) 12. Ma, Y.C., et al.: Remaining useful life prediction of LIB based on Gauss-Hermite particle filter. IEEE Trans. Control Syst. Technol. 27(4), 1788–1795 (2019). (in Chinese) 13. Ping, W., Qingrui, G., Jiang, Z., et al.: An online health state prediction method of lithium battery based on the combination of data-driven and empirical models. Trans. China Electrotech. Soc. 36(24), 5201–5212 (2021). (in Chinese) 14. Jianing, X., Yulong, N., Chunbo, Z.: Prediction of the remaining life of lithium battery based on improved support vector regression. Trans. China Electrotech. Soc. 36(17), 3693–3704 (2021). (in Chinese)
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15. Yingzhou, W., Yulong, N., Yuqing, Z., et al.: Prediction of remaining useful life of LIB based on ALO-SVR. Trans. China Electrotech. Soc. 41(4), 1445–1457 (2021). (in Chinese) 16. Xinzhong, W., Zhichao, Z., Kai, W.: etc Air volume regulation method of mine air network based on DE-GWO algorithm. J. Central South Univ. Nat. Sci. Edn. 52(11), 3981–3989 (2021). (in Chinese) 17. Smola, A.J., et al.: A tutorial on support vector regression. Stat. Comput. 14(3), 199–222 (2004)
Life Cycle Carbon Footprint Assessment of Power Transmission Equipment Kaibin Sun1 , Changzheng Shao1(B) , Yue Sun2 , Chengrong Lin1 , Xin Cheng3 , Weizhan Li1 , Bo Hu1 , and Kaigui Xie1 1 State Key Laboratory of Power Transmission Equipment and System Security and New
Technology, Chongqing University, Chongqing 400044, China [email protected], [email protected], [email protected], [email protected] 2 China Yangtze Electric Power Co., Ltd., Yichang 443000, China 3 State Grid Shanxi Electric Power Company Economic and Technological Research Institute, Taiyuan 030000, China [email protected]
Abstract. The recognition of life cycle carbon footprint (LCCF) of power transmission equipment is of great significance to the de-carbonization of power systems. Based on the technical features of power transmission equipment, the concept of LCCF is proposed in this paper, which includes fixed carbon emissions and variable carbon emissions. Firstly, to evaluate the LCCF of power transmission equipment, the life cycle of transmission equipment is divided into five stages: raw materials, manufacturing and assembly, transportation, operation, and maintenance, decommissioning and scrapping according to the time series, and the carbon emissions in all stages of the life cycle are calculated in combination with various carbon emission factors and quality criteria. Then, based on the concept of equal annual value, a conversion model for carbon footprint is proposed to realize the comprehensive evaluation of LCCF. Finally, the correctness and effectiveness of the proposed method are verified by simulation analysis. The results show that fixed carbon emissions account for a certain proportion of LCCF. To achieve the double carbon goal on schedule, it is necessary to study the LCCF of power transmission equipment and make independent contributions to accelerating the process of de-carbonization. Keywords: Power transmission equipment · Life cycle · Carbon emissions · Double carbon target
1 Introduction Since entering the 21st century, climate change has attracted more and more attention. The main cause of climate change is greenhouse gases, in 2014, China’s non-carbon greenhouse gas emissions were 2 billion tons of CO2 e, only accounting for 16% of the total greenhouse gas emissions, therefore, low-carbon development is the internal demand of China’s sustainable development [1]. Energy activities are the main source of © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 79–91, 2023. https://doi.org/10.1007/978-981-99-1027-4_9
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CO2 emissions in China, accounting for more than 80% of the total social CO2 emissions, among which the CO2 emissions from the power industry account for more than 40% [2]. Therefore, to cope with climate change, the de-carbonization of the power industry becomes necessary. Facing the urgent need for low-carbon transformation in the power industry, domestic and foreign researchers have carried out a series of research on energy structure optimization and low-carbon optimization technology [3–9]. In terms of energy structure optimization, Ref. [3] analyzes the transformation trend of the electric power discipline research system under the dual carbon goal, and the construction of a new power system with new energy as the main body will be the key to achieve China’s carbon peak and carbon neutrality strategic goals. Reference [4] proposed an energy-carbon integrated price method and low-carbon scheduling strategy for multi-energy systems to optimize the energy structure and reduce system carbon emissions. Reference [5] proposed a low-carbon power grid transformation model, which takes into account the aging and decommissioning of coal-fired power stations, the installation of renewable energy power plants, and the expansion of power grids, and optimizes the power structure to provide more economic and low-carbon decisions. In terms of low-carbon technology optimization, Ref. [6] comprehensively considers energy time-shifting and rapid regulation characteristics of the flexible operation mode of carbon capture power plant, multi-time scale characteristics, and zero carbon emission characteristics of DR resources, to achieve low-carbon economic scheduling of power system. Reference [7] proposed a multi-stage coordinated optimization model that considers carbon capture technology, spinning reserve, and power generation technology to achieve a low-carbon economy. Reference [8] defines the technical and policy targets of low-carbon transformation as a backcasting problem, establishes a bi-level optimization problem, and provides a new perspective for the decarbonization of the power industry. Based on the carbon trading mechanism. Reference [9] proposed a lowcarbon economic scheduling method for power systems considering thermal power unit heat storage transformation, which realizes economy and low-carbon. The above research has studied the energy structure and low-carbon technology in reducing the carbon emissions of power, which can lay a certain theoretical foundation for the de-carbonization of China’s power industry. It is worth noting that the above studies mainly consider the direct carbon emissions from the “source side” of the power system while ignoring the carbon emissions existing in the power industry chain [10]. Therefore, some scholars began to study the LCCF of the power industry. References [11, 12] adopt the life cycle assessment method, established the Chinese typical wind farm in the stage of construction, operation, and removal of carbon footprint calculation model, through calculation, found that although wind farms use clean energy, in the process of its whole life, make wind turbine consumes a lot of steel and copper, and a large amount of CO2 emissions and the responsibility for that CO2 belongs to wind farms. Reference [13] establishes an assessment model for LCCF of EV charging infrastructure, which can realize the mixed de-carbonization of the power grid and further promote the process of net zero emissions. Reference [14] establishes the carbon footprint of the whole process of the integrated community energy system. The above studies have discussed the low-carbon transition based on the concept of LCCF, which has good
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reference significance. However, there is a lack of research on the LCCF of power transmission equipment. In view of the above problems, this paper proposes an LCCF assessment and analysis model for typical power transmission equipment. Firstly, according to the time series, the life cycle of power transmission equipment is modeled into five stages: raw materials, manufacturing and assembly, transportation, operation and maintenance, and decommissioning and scrapping. Combined with various carbon emission factors and quality criteria, the carbon emission accounting of each stage of the life cycle is realized. Then, based on the existing characteristics of fixed and variable carbon emissions, combined with the concept of equal annual value, the present value calculation model of carbon emission intensity is proposed to quantify the carbon intensity index of fixed carbon emissions and guide the direction of power system emission reduction. Finally, the correctness and effectiveness of the proposed method are verified by simulation analysis.
2 Life Cycle Carbon Footprint of Power Transmission Equipment Definition and Calculation Process 2.1 Life Cycle Carbon Footprint Definition of Power Transmission Equipment The power transmission system is an indispensable part of the modern power system, and the function is to transfer the electric energy generated by the generation side to the load side through some power equipment, that is, the bridge between the generation side and the load side, mainly composed of power transformers and transmission lines and other power equipment [10]. Life cycle assessment is an evaluation method used by European and American countries in the 1970s to study the life cycle of industrial products from production to recycling or waste by using the law of conservation of energy and the law of conservation of matter [15]. Carbon footprint refers to the enterprise organization, activities, products, or individuals through transport, food production and consumption, and greenhouse gas emissions caused by all kinds of production processes such as collection, also known as “carbon consumption”, usually refers to a kind of new development, for measuring the institutions or individuals for the daily energy consumption and CO2 emissions to the environment impact indicators [16]. To sum up, the life cycle of power transmission equipment includes five stages: raw materials, manufacturing and assembly, transportation, operation and maintenance, and decommissioning and scrapping. This paper defines its carbon footprint as fixed carbon footprint and variable carbon footprint, as shown in Fig. 1. Fixed carbon footprint refers to the carbon emissions generated by equipment during the raw material, manufacturing and assembly, transportation, and decommissioning and scrapping. The variable carbon footprint represents the carbon emissions generated by the consumption of equipment during the normal operation and maintenance of equipment. Therefore, the LCCF of power transmission equipment is equal to the sum of fixed carbon footprint and variable carbon footprint, which can be expressed as: C fixed,i + C variable,j (1) C total = i∈fixed
j∈variable
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where C total is the carbon footprint of the whole life cycle; i ∈ fixed represents the set of the fixed carbon footprint of transmission equipment at different stages; C fixed,i is the carbon footprint of stage i of transmission equipment; j ∈ variable represents the set of the variable carbon footprint of transmission equipment at different stages; C variable,j is the carbon footprint of transmission equipment stage j.
Fig. 1. The diagram of the life cycle carbon footprint of power transmission equipment
2.2 Life Cycle Carbon Footprint Calculation Process of Power Transmission Equipment The LCCF calculation of transmission equipment includes four steps: selecting functional units, determining system boundaries, collecting data and calculating carbon footprint [13]. The detailed calculation process is shown in Fig. 2.
3 Carbon Footprint Assessment Model of Power Transmission Equipment Based on Life Cycle According to the LCCF of transmission equipment defined in this paper, this section aims to establish the carbon footprint assessment model of transmission equipment raw material acquisition, manufacturing and assembly, transportation, operation and maintenance, and decommissioning and scrapping to quantify the carbon footprint of each stage. The carbon footprint assessment model of each stage is as follows. 3.1 Raw Material Acquisition Stage In the stage of raw material acquisition, the carbon footprint mainly includes the energy consumed by equipment in the manufacturing process and the corresponding carbon emission of materials. Assuming that the equipment needs n kinds of materials and consumes m kinds of energy at the stage of raw material acquisition, its carbon footprint can be expressed as: CM =
n i=1
Mi × MEFi +
m j=1
Ej × EFj
(2)
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where CM represents the carbon footprint of raw material acquisition stage, Mi represents the consumption of class i materials, MEFi represents the production emission factor of class i materials, Ej represents the consumption of class j energy, EFj represents the carbon emission factor of class j energy. It is worth noting that in the raw material acquisition stage, part of the materials can be recycled, so the carbon footprint of the recycled materials should not belong to the equipment raw material acquisition stage. In this paper, the utilization rate of materials is defined as ηM , and the carbon footprint of the raw material acquisition stage can be expressed as: CM = (
n i=1
Mi × MEFi +
m
Ej × EFj )/ηM
(3)
j=1
Fig. 2. The calculation procedure for life cycle carbon footprint of power transmission equipment
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3.2 Manufacturing and Assembly Stage In the manufacturing and assembly stage, the carbon footprint mainly refers to the carbon emission corresponding to the energy consumption in the processing link. Assuming that the equipment consumes n kinds of energy in the manufacturing and assembly stage, its carbon footprint can be expressed as: CP =
n
Ei × EFi
(4)
i=1
where CP represents the carbon footprint of the manufacturing and assembly stage, Ei represents the consumption of type i energy, and EFi represents the carbon emission factor of type i energy. In addition, it is similar to the raw material acquisition stage, the recycling of materials will offset part of the carbon footprint of the manufacturing and assembly stage, and the utilization rate of materials in this stage is defined as ηP , the carbon footprint of manufacturing and assembly stage can be expressed as: CP = (
n
Ei × EFi )/ηP
(5)
i=1
3.3 Transportation Stage In the transportation stage, the carbon footprint mainly refers to the carbon emission corresponding to the energy consumed by the transportation means, which is related to the carbon emission coefficient of different transportation modes, the choice of transportation means, and the distance from the manufacturer to the installation point. The carbon footprint can be expressed as follows: CT =
n
Mi × Di × EFi
(6)
i=1
where CT represents the carbon footprint at the transportation stage, Mi represents the quality of equipment in transportation stage i, Di represents the transportation distance of transportation stage i, and EFi represents the carbon emission factor of transportation equipment in transportation stage i by means of transport. 3.4 Operation and Maintenance Stage In the stage of operation and maintenance, the carbon footprint mainly refers to the energy loss of the equipment during operation and the carbon emission generated by the maintenance of the equipment. Assuming that the service life of the equipment is LT years, its carbon footprint can be expressed as: CU = (E1 × T × 365 × LT + E2 )EF
(7)
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where CU represents the carbon footprint of the operation and maintenance stage, E1 represents the actual daily power consumption of the equipment in the use stage, T represents the operation time, E2 represents the power consumption of equipment maintenance, and EF represents the power carbon emission factor. It should be noted that at this stage, the power carbon emission factor changes dynamically with different operating conditions, namely, the real-time power carbon emission factor. In addition, the electric energy loss and maintenance power consumption of the equipment during operation will also change with the service time of the equipment. Based on this feature, the carbon footprint at this stage is variable. 3.5 Decommissioning and Scrapping Stage In the decommissioning and scrapping stage, the carbon footprint mainly refers to the carbon emission generated by energy consumption during the dismantling and recycling of equipment or the scrapping process. The stage of carbon footprint and raw materials for the carbon footprint of similar, the difference is that in the retirement and scrap stage, the need to plan for raw materials and equipment after removing material recycle access and manufacturing and assembling stage of the influence of the carbon footprint, so need this stage make up for the part of the carbon footprint, the carbon footprint is retired scrap stage can be expressed as follows: CR =
m i=1
Ei × EFi −
n
Mj × MEFj
(8)
j=1
where CR is the carbon footprint at the decommissioning and scrapping stage. Overall, the LCCF of transmission equipment can be expressed as: C total = CM + CP + CT + CU +CR
(9)
4 Proposed Conversion Method for Life Cycle Carbon Footprint Currently, the “average electricity consumption carbon emission factor” widely used at home and abroad cannot perceive the difference in carbon emissions generated by different electricity consumption behaviors in different periods, leading to errors in carbon footprint calculation. With the proposal of dynamic carbon emission factors based on the carbon emission flow theory [17], the temporal and spatial differences of electric carbon emission factors can be effectively perceived, thus providing accurate carbon emission factors for carbon footprint calculation. It should be emphasized that, according to Section I, the LCCF of transmission equipment includes fixed carbon footprint and variable carbon footprint. The equipment service life span is long, the life cycle of fixed carbon footprint and carbon footprint variable dimension will not in the same time, in order to achieve the LCCF of equipment effectively and accurate assessment needs to be fixed carbon footprint within the life cycle of equipment with variable carbon footprint discount to a reference time. Based
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on the concept of the time value of finance, the life-cycle carbon footprint conversion method proposed in this paper is as follows. Assuming that the service life of the equipment is LT years, ir is the discount rate of the annual Carbon footprint, and the carbon footprint conversion factor (CRF) is: CRF =
ir(1 + ir)LT (1 + ir)LT − 1
(10)
According to the concept of equal annual value, the formula for converting fixed carbon footprint into the same time scale as the variable carbon footprint is as follows.
C fixed =
CRF × C fixed 8760
(11)
where CRF is the carbon footprint conversion coefficient, C fixed is the fixed carbon footprint in the whole life cycle of transmission equipment, and C fixed is the equivalent variable carbon footprint in the whole life cycle. To sum up, the converted value of fixed carbon footprint in the k year is:
C fixed =C fixed
(1 + ir)k − 1 ∀k ∈ LT ir(1 + ir)k
(12)
5 Case Study To comprehensively analyze the LCCF of the transmission equipment, transformers and transmission lines in a certain region are selected as research objects in this paper. Besides, to quantify the carbon emissions in each stage of the life cycle, carbon dioxide equivalent (CO2 e) is taken as the evaluation measurement unit. 5.1 Parameter Setting The transformer is mainly composed of the body, voltage regulating device, protection device, cooling device, and outlet device. The following takes the SZ11-5000/110 transformer as an example to evaluate LCCF [18]. And the service life is 25 years. Transmission lines are mainly composed of wires, towers, insulators, and fittings. The following takes a typical 11 kV transmission line as an example to evaluate LCCF per unit length, which service life is 30 years, and the discount rate is set as 8% [19]. In the decommissioning and scrapping stages, some metal materials can be effectively recycled to compensate for the carbon footprint generated in the raw material acquisition stage. In this paper, it is assumed that 90% aluminum, 70% copper, and 50% steel can be recovered.
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Table 1. Carbon emission factors for materials and energy Material or Energy
Carbon Emission Factor
Copper
6.64 kgCO2 e/kg
Aluminum
1.80 kgCO2 e/kg
Iron or Steel
1.72 kgCO2 e/kg
Magnesium
2.83 kgCO2 e/kg
Zinc
3.66 kgCO2 e/kg
Ferroalloy
3.60 kgCO2 e/kg
Diesel fuel
2.73 kgCO2 e/L
Polyethylene
1.6 kgCO2 e/kg
Coal
2.46 kgCO2 e/kg
Sulfur Hexafluoride
23.9 kgCO2 e/kg
Electricity
1.02 kgCO2 e/kWh
Table 2. Carbon footprint of each stage of transformer and transmission lines life cycle Stage
Carbon footprint of transformer (kgCO2 e)
Carbon footprint of transmission lines (kgCO2 e)
Raw material acquisition
5.61 * 10^5
4.06 * 10^5
Manufacturing and assembly
7.56 * 10^4
1.31 * 10^5
Transportation
5.92 * 10^4
2.91 * 10^4
Operation and maintenance Decommissioning and scrapping Total
5.81 * 10^7
8.04 * 10^6
−3.82 * 10^5
−3.21 * 10^5
5.84 * 10^7
8.28 * 10^6
5.2 Numerical Results To reflect the accuracy of carbon footprint calculation of the life cycle of power transmission equipment, it is necessary to use authoritative carbon emission factors. The carbon emission factors [20] of the main materials and energy in this paper are shown in Table 1. Table 2 shows the calculation results of the LCCF of the transformer and transmission lines by using the method proposed in this paper, and the carbon footprint distribution diagram of each stage is shown in Fig. 3. According to the analysis of Table 2 and Fig. 3, in the life cycle of the transformer, the carbon footprint value in the operation and maintenance stage is the largest, which is mainly due to two reasons: one is that sulfur hexafluoride (SF6) will leak from the insulating oil of the transformer, resulting in a large amount of carbon emissions; The
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Fig. 3. Carbon footprint distribution diagram of each stage of transformer life cycle
other is that the transformer will cause about 3% power loss during operation, and this part of the carbon footprint is also considerable in the life cycle. In addition, the carbon footprint of raw material acquisition, manufacturing and assembly, transportation, decommissioning and scrapping is 302000 kgCO2 e. At the same time, in order to quantify the carbon intensity index of carbon emissions in the life cycle, the conversion method proposed in this paper is used to convert the carbon footprint to a reference time with the variable carbon footprint. The results are shown in Fig. 4.
Fig. 4. Schematic diagram of transformer life cycle equivalent carbon footprint
Similarly, the carbon footprint distribution diagram of transmission line at each stage is shown in Fig. 5. It can be seen from Table 2 and Fig. 5, that in the life cycle of transmission lines, the carbon footprint of the operation and maintenance stage is 8040000 kgCO2 e, accounting for 97.1% of the total carbon footprint. Although the fixed carbon footprint of transmission lines accounts for about 3% of the whole life cycle, which is relatively small, it is very necessary to consider the LCCF to decarbonize the power industry. Similarly, the carbon footprint is converted to the same reference time as the variable carbon footprint by using the conversion method proposed in this paper, and the results are shown in Fig. 6. By analyzing Figs. 4 and 6, the carbon footprint conversion model proposed in this paper can convert the LCCF of power transmission equipment into the same resolution
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Fig. 5. Carbon footprint distribution diagram of transmission line at each stage of life cycle
Fig. 6. Schematic diagram of transmission line life cycle equivalent carbon footprint
as the variable carbon footprint, quantify the carbon intensity index of fixed carbon emissions, and realize the comprehensive evaluation of LCCF.
6 Conclusion This paper presents a model for carbon emission measurement and analysis of power transmission equipment based on the life cycle. The following conclusions are drawn from the analysis of examples: (1) The carbon footprint of power transmission equipment is generated in five stages of its life cycle, including raw material acquisition, manufacturing and assembly, transportation, operation and maintenance, and decommissioning and scrapping. The method proposed in this paper can calculate the carbon emissions of each stage in the service life cycle and provide a theoretical basis for the LCCF of power transmission equipment. (2) Based on the carbon footprint conversion model proposed in this paper, the LCCF can be converted into equal annual value and present value carbon emissions, it can realize the comprehensive evaluation of LCCF and provide a more accurate carbon emission model for power transmission equipment.
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(3) The carbon footprint calculated in this paper not only reflects the activities related to the equipment and power operation but also quantifies the carbon footprint generated during the production, transportation, and decommissioning of raw materials, which can guide the direction of carbon emission reduction in the power industry and accelerate the de-carburization process.
Acknowledgments. This work was supported by the National Natural Science Foundation of China (52107072), China Postdoctoral Science Foundation (2021M693711), Fundamental Research Funds for the Central Universities (NO.2021CDJQY-037).
References 1. Project comprehensive report preparation team: Comprehensive report on China’s long-term low-carbon development strategy and transformation path. China Popul. Resour. Environ. 30, 1–25 (2020). (in Chinese) 2. Global energy Internet development cooperation organization: China’s carbon neutral road. China Power Press, Beijing (2021). (in Chinese) 3. Chongqing, K., Ershun, D., Yaowang, L., Ning, Z., Qixin, C., Hongye, G., Peng, W.: “Carbon perspective” of new power system: scientific issues and research framework. Power Syst. Technol. 46, 821–833 (2022). (in Chinese) 4. Cheng, Y., Zhang, N., Zhang, B., Kang, C., Xi, W., Feng, M.: Low-carbon operation of multiple energy systems based on energy-carbon integrated prices. IEEE Trans. Smart Grid 11(2), 1307–1318 (2020) 5. Shen, W., Qiu, J., Meng, K., Chen, X., Dong, Z.Y.: Low-carbon electricity network transition considering retirement of aging coal generators. IEEE Trans. Power Syst. 35(6), 4193–4205 (2020) 6. Yang, C., Guibo, D., Peng, Z., Wuzhi, Z., Yuting, Z., Xinyuan, L.: Multi time scale source load scheduling method of wind power system considering the low-carbon characteristics of carbon capture power plants. Chin. J. Electr. Eng. 1–18 (2022). (in Chinese) 7. Lou, S., Lu, S., Wu, Y., Kirschen, D.S.: Optimizing spinning reserve requirement of power system with carbon capture plants. IEEE Trans. Power Syst. 30(2), 1056–1063 (2015) 8. Zhuo, Z., Zhang, N., Hou, Q., Du, E., Kang, C.: Backcasting technical and policy targets for constructing low-carbon power systems. IEEE Trans. Power Syst. 1–1 (2022) 9. Yuan, P., Suhua, L., Yue, F., Yaowu, W., Shuhao, L.: Low carbon economic dispatching of power system considering thermal storage transformation of thermal power units. Power Syst. Technol. 44, 3339–3345 (2022). (in Chinese) 10. Zeng, B., Zhang, J., Yang, X., Wang, J., Dong, J., Zhang, Y.: Integrated planning for transition to low-carbon distribution system with renewable energy generation and demand response. IEEE Trans. Power Syst. 29(3), 1153–1165 (2014) 11. Ji, S., Chen, B.: LCA-based carbon footprint of a typical wind farm in China. Energy Proc. 88, 250–256 (2016) 12. Liu, P., Liu, L., Xu, X., Zhao, Y., Niu, J., Zhang, Q.: Carbon footprint and carbon emission intensity of grassland wind farms in Inner Mongolia. J. Clean. Prod. 313, 127878 (2021) 13. Zhao, E., May, E., Walker, P.D., Surawski, N.C.: Emissions life cycle assessment of charging infrastructures for electric buses. Sustain. Energy Technol. Assess. 48, 101605 (2021) 14. Bo, H., Kaibin, S., Changzheng, S., Wei, H., Yusheng, Z., Kaigui, X: Carbon perception and optimization method of the integrated community energy system oriented to the whole process carbon footprint. High Volt. Eng. 48(7), 2495–2504 (2022). (in Chinese)
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15. Chau, C.K., Leung, T.M., Ng, W.Y.: A review on life cycle assessment, life cycle energy assessment and life cycle carbon emissions assessment on buildings. Appl. Energy 143, 395– 413 (2015) ˇ cek, L., Klemeš, J.J., Kravanja, Z.: A review of footprint analysis tools for monitoring 16. Cuˇ impacts on sustainability. J. Clean. Prod. 34, 9–20 (2012) 17. Cheng, Y., Zhang, N., Wang, Y., Yang, J., Kang, C., Xia, Q.: Modeling carbon emission flow in multiple energy systems. IEEE Trans. Smart Grid 10(4), 3562–3574 (2019) 18. Xingshuang, D., Hongchun, L., Xiaolong, S.: Analysis of the significance of promoting new energy efficiency power transformers to achieve carbon peak and carbon neutrality. Transformer 59(2), 1–5 (2022) 19. Jones, C.I., McManus, M.C.: Life-cycle assessment of 11kV electrical overhead lines and underground cables. J. Clean. Prod. 18(14), 1464–1477 (2010) 20. IPCC: 2019 Refinement to the 2006 IPCC guidelines for national greenhouse gas inventory (2019)
Performance Optimization of Tesla Valve Microchannel Cold Plates for Li-Ion Battery Fen Liu1 , Jianfeng Wang2(B) , and Yanbing Lu2 1 School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001,
China 2 School of Automotive Engineering, Harbin Institute of Technology, Weihai 264209,
Shandong, China [email protected]
Abstract. The development of energy-efficient battery thermal management technology is of great significance for lithium-ion batteries. In this paper, a Tesla valve type channel cold plate was designed for square batteries, also liquid cooling experimental studies were carried out to verify the optimized cold plate parameters. The maximum error between liquid cooling simulation and experiment under the optimal configuration did not exceed 1.25 °C. The experimental analysis found that when the inlet flow rate exceeded 398mL/min, the improvement of battery cooling effect and temperature uniformity gradually tended to saturate. The coolant inlet temperature was too high or too low would cause the unbalanced performance of the cold plate. Keywords: Battery thermal management · Tesla valve · Optimization experiment
1 Introduction Under the severe situation of global environmental pollution and shortage of fossil energy, electric vehicles with the advantages of environmental protection and energy saving, low noise and simple structure have developed rapidly and become an indispensable part of the automobile market [1, 2]. The performance of automotive lithiumion batteries is more sensitive to temperature, and it is of great significance to develop energy-efficient battery thermal management technologies to ensure that lithium-ion batteries operate within the optimal range of 15–35 °C [3–6]. Liquid cooling is currently the most widely used method of heat dissipation in electric vehicles. Compared with traditional liquid cooling technology, microchannel heat sink is a highly efficient heat exchanger with advantages such as small size, large heat transfer coefficient and high efficiency of heat transfer. Naqiuddin et al. introduced a new segmented microchannel to improve the thermal performance of a straight channel heat sink, which could improve the heat transfer performance with minimum pressure drop [7]. Rao et al. used the Jaya algorithm to optimize the microchannel heat sinks of rectangular and trapezoidal cross-sections, and © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 92–99, 2023. https://doi.org/10.1007/978-981-99-1027-4_10
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obtained better results than other methods [8]. Osanloo et al. investigated a two-layer microchannel heat sink with upper and lower tapered staggered channels and obtained the optimal combination of coolant flow and tapered inclination [9]. Lu et al. proposed a special structure of the Tesla valve to achieve enhanced heat transfer and further improve the heat transfer efficiency of the microchannel heat sink [10]. In this paper, the optimal cold plate parameters obtained by the central composite design response method for different flow rates and different cooling temperature experimental conditions are verified experimentally [10].
2 Battery Microchannel Cooling Simulation As shown in Fig. 1, we proposed a Tesla valve channel cold plate cooling system in our previous study [10].
Fig. 1. Tesla microchannel cooling system
In [10] we obtained the optimal parameters of the cold plate by multi-objective optimization as were: Tesla valve angle α of 120°, Tesla valve spacing L of 23.1 mm, channel spacing B of 28 mm and coolant inlet velocity v of 0.83 m/s (Figs. 2 and 3).
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Fig. 2. The temperature and pressure diagram of the optimal cold plate
Fig. 3. Different simulation results
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3 Battery Microchannel Cooling Experiments As shown in Fig. 4 the designed Tesla valve channel cold plate was machined by milling. The material of the cold plate was aluminium and the internal channel structure parameters of the cold plate were consistent with the optimal channel parameters obtained by multi-objective optimization (Fig. 5).
Fig. 4. Tesla valve channel cold plate 3D modelling.
Fig. 5. Battery liquid cooling system experiments.
The experimental results in Fig. 6 showed that the heat transfer performance of coolant flowing in the reverse direction was significantly better than in the forward direction. At the end of battery 3C discharge, the central temperature of the battery surface was basically maintained at around 30 °C when the coolant flowed in the reverse direction. There were still some deviations between the liquid cooling simulation and the experimental results, with a maximum error of 1.25 °C for forward flow and 1.04 °C for reverse flow. This was due to some factors, such as ignoring the influence of the thermal interface material, the inlet temperature of the coolant fluctuating to a certain extent, the existence of the diverter at the inlet, as well as the accuracy limitations of the instrumentation and the processing errors of the cold plate itself.
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Fig. 6. Comparison of simulation and experimental results for liquid cooling under optimised conditions.
As can be seen from Fig. 7, the designed cold plate could significantly reduce the temperature of the battery and slow down the temperature rise of the battery. As the coolant flow rate increased, the surface central temperature of the battery gradually decreased and the cooling performance of the cold plate was gradually enhanced. But this did not mean that the larger the coolant flow rate the better, because when the coolant flow rate increased from 360 mL/min to 398 mL/min, the surface central temperature of the battery decreased by approximately 0.55 °C. It would consume more pump work when increasing the coolant flow, so the coolant flow rate was selected at 398 mL/min, i.e., the coolant inlet speed was about 0.83 m/s, which was basically consistent with the recommended results of multi-objective optimization. Figure 8 showed that as the flow rate increased, the temperature difference decreased, but the degree of reduction gradually decreased. This indicated that increasing the flow rate also had limited improvement on the temperature uniformity of the whole battery liquid cooling unit. When the coolant flow rate was 398 mL/min, the maximum temperature difference was about 5.42 °C, which was basically consistent with the simulation results of the battery liquid cooling finite element model. Figure 9 showed that a decrease in the coolant inlet temperature would cause a gradual decrease in the central cell surface temperature. In addition, as the coolant inlet temperature decreased, the earlier the central temperature changed into a steady state. Figure 10 showed that as the coolant inlet temperature decreased, the temperature difference of the battery liquid cooling unit became larger. When the inlet temperature was 20 °C, the maximum temperature difference reached 6.09 °C. When the inlet temperature was 28 °C, the temperature difference basically remained within 5 °C. This indicated that the coolant inlet temperature was not the lower the better. Too low coolant inlet temperature would make the temperature uniformity of the whole battery liquid cooling unit worse. Therefore the coolant inlet temperature should be selected in conjunction with the ambient temperature to avoid the uneven performance of the cold plate.
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Fig. 7. Cell surface central temperature variation curve at different coolant flow rates.
Fig. 8. Cell surface temperature variation at different coolant flow rates.
4 Conclusions The experiment for the optimal cooling plate obtained by multi-objective optimization showed the relative error between the liquid cooling experiment and simulation were small. As the coolant inlet flow rate increased, the surface central temperature and temperature difference of the battery would decrease. When the flow rate exceeded 398mL/min, further increasing the flow rate would have limited improvement on the cooling effect and temperature uniformity of the battery. The decrease of the coolant inlet temperature would reduce the surface central temperature, but increase the temperature
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Fig. 9. Cell surface central temperature variation curve at different coolant temperature.
Fig. 10. Temperature difference variation at different coolant temperature.
difference of the liquid cooling unit. Therefore the coolant inlet temperature should be considered comprehensively to avoid uneven performance of the cold plate caused by too high or too low inlet temperature. Acknowledgments. This study was supported in part by the Natural Science Foundation of Shandong Province (Grant No. ZR2020ME129), the National Natural Science Foundation of China (Grant No. 51905121).
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References 1. Liu, J., Yue, M., Wang, S., Zhao, Y., Zhang, J.: A review of performance attenuation and mitigation strategies of lithium-ion batteries. Adv. Func. Mater. 32(8), 2107769 (2022) 2. Ling, J., et al.: Phosphate polyanion materials as high-voltage lithium-ion battery cathode: a review. Energy Fuels 35(13), 10428–10450 (2021) 3. Zhou, H., Zhou, F., Shi, S., Yang, W., Song, Z.: Influence of working temperature on the electrochemical characteristics of Al2 O3 -coated LiNi0.8 Co0.1 Mn0.1 O2 cathode materials for Li-ion batteries. J. Alloys Comp. 847, 156412 (2020) 4. Liu, B., et al.: Safety issues and mechanisms of lithium-ion battery cell upon mechanical abusive loading: a review. Energy Storage Mater. 24, 85–112 (2020) 5. Feng, X., Ouyang, M., Liu, X., Lu, L., Xia, Y., He, X.: Thermal runaway mechanism of lithium ion battery for electric vehicles: a review. Energy Storage Mater. 10, 246–267 (2018) 6. Liu, H., Wei, Z., He, W., Zhao, J.: Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: a review. Energy Convers. Manage. 150, 304–330 (2017) 7. Naqiuddin, N.H., et al.: Numerical investigation for optimizing segmented micro-channel heat sink by Taguchi-Grey method. Appl. Energy 222, 437–450 (2018) 8. Rao, R.V., More, K.C., Taler, J., Ocło´n, P.: Dimensional optimization of a micro-channel heat sink using Jaya algorithm. Appl. Therm. Eng. 103, 572–582 (2016) 9. Osanloo, B., Mohammadi-Ahmar, A., Solati, A., Baghani, M.: Performance enhancement of the double-layered micro-channel heat sink by use of tapered channels. Appl. Therm. Eng. 102, 1345–1354 (2016) 10. Lu, Y., et al.: Performance optimisation of Tesla valve-type channel for cooling lithium-ion batteries. Appl. Therm. Eng. 212, 118583 (2022)
Data-Driven Method Based Wind Power Characteristic Analysis and Climbing Identification Yanli Liu(B) and Junyi Wang Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China [email protected]
Abstract. With the increasing penetration of wind power, how to accurately analyze characteristics of wind power becomes significant to the safe and stable operation of power system. This paper proposes a data-driven based wind power characteristic analysis and climbing identification method. Wind power climbing threshold is extracted firstly to construct climbing event dataset based on k-means clustering. 2D convolutional neural network-based climbing identification method is then proposed, with network parameters trained by transforming 1-dimensional wind power output records into a 2-dimensional matrix to identify future climbing events. Test results on practical wind farm show that the proposed method can effectively analyze characteristics of wind power, which has better climbing identification accuracy compared with traditional methods. Keywords: Wind Power · Characteristic Analysis · Climbing Identification
1 Introduction Wind power output is highly correlated with environmental factors. With the influence of complex weather scenarios, characteristics of wind power output change, and the occurrence of corresponding climbing events poses great challenges in developing scheduling plans for power system [1–5]. Consequently, accurate and reliable wind power characteristic analysis and climbing identification under complex weather scenarios is an important basis for the modern smart grid operation and scheduling, and is an important condition for achieving wind power penetration in the future [6, 7]. According to whether judged by the wind power forecasting results, climbing identification methods can be divided into direct methods and indirect methods [8–10]. Indirect identification methods are based on wind power forecasting results, and the models used contain three main types: physical models based on numerical weather forecasts, statistical models using historical data, and integrated models combining the two. However, the calculation errors of the models usually affect the accuracy of climbing identification results. By contrast, the direct identification method obtains the identification mechanism by training from historical climbing data, and then directly predicts the climbing event © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 100–106, 2023. https://doi.org/10.1007/978-981-99-1027-4_11
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characterization quantity (such as slope magnitude, duration or slope rate, etc.), becoming popular in recent years. However, due to the complexity of the climbing problem, the existing methods still suffer from the problem of low accuracy [4, 5]. This paper proposes a data-driven based wind power characteristic analysis and climbing identification method. Wind power climbing threshold is extracted firstly to construct climbing event dataset based on k-means clustering. 2D convolutional neural network-based climbing identification method is then proposed, with network parameters trained by transforming 1-dimensional wind power output records into a 2-dimensional matrix to identify future climbing events. Test results on practical wind farm show that the proposed method can effectively analyze characteristics of wind power, which has better climbing identification accuracy compared with traditional methods.
2 Data-Driven based Wind Power Characteristic Analysis and Climbing Identification Method 2.1 Wind Power Output Characteristics Supposing Pti means the magnitude of wind power output at time t i , then the characteristics of wind power output under given period t 0 − t 0 + t can be shown in Eqs. (1)–(4). A1 = abs Pti+1 − Pti ti ∈ [t0 , t0 + t] (1) A2 = max Pt0 : Pt+t0 − min Pt0 : Pt+t0 Pt+t0 − Pt0 t : Pt+t0 +1 − sum Pt0 : Pt+t0 t
A3 = A4 =
sum Pt0 +1
(2) (3) (4)
2.2 Extraction for Climbing Threshold K-means algorithm is a division-based clustering algorithm. It uses distance to measure the similarity between samples, which can divide the sample set into K clusters. The mean vector of a cluster is the center of mass of the cluster, as shown in Eq. (5). 1 µi = x (5) |Ci | x∈Ci
The purpose of k-means algorithm is to find K centroids to obtain the minimum distance between the centroid and the sample, that is, to minimize the squared error E. The smaller squared error E is, the higher the similarity of the samples in the cluster is. The squared error E can be expressed as Eq. (6). E=
k
x − µi 2
i=1 x∈Ci
Specifically, the calculation process of k-means is as follows.
(6)
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(1) Supposing there exists a sampling set X = {x 1 ,x 2 , … ,x n }, K samples are chosen at random as the initial center of mass (2) The distance between the rest of the samples in the sample set and the center of mass is calculated, and the samples are grouped with the nearest center of mass. (3) After all samples are grouped into sets, the centroid of each set is recalculated. (4) Finally, this process is repeated continuously until the minimum distance between the calculated new centroid and the old centroid is less than the set threshold, that is, the minimization squared error E is less than the expected value, then the algorithm is considered to converge. In this paper, characteristics of wind power output records (1)–(4) under historical periods are constructed into matrix P, which is further divided into different clusters by using K-means algorithm. Then wind power climbing threshold is extracted, as shown in Fig. 1. Characteristic 2
cluster center operation boundary abnormal operating point
Characteristic 1
Characteristic 3
Fig. 1. Extraction for wind power climbing threshold
2.3 2D Convolutional Neural Network-Based Climbing Identification Convolutional neural network (CNN) is a kind of feedforward neural network that includes convolutional computation and deep structures, which is known as one of the representative algorithms of deep learning. The network is modeled after the biological perceptual mechanisms, and the convolutional kernel parameters shared within the implicit layers and the sparsity of inter-layer connections allow convolutional neural network to feature lattice pointing with small computational effort. In general, CNN algorithms include 1D CNN, 2D CNN and 3D CNN, among which, in 1D CNN, the kernel slides along one dimension and is often used for the processing of temporal data, 2D CNN is often applied to the recognition of image-based text, and 3D CNN is mainly used for medical images and video-based data recognition. The basic structure of CNN is shown in Fig. 2.
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Fig. 2. Basic structure of CNN
Specifically, a convolutional neural network usually consists of the following structures. 1. convolutional layer: the convolutional layer, also called feature extraction layer, is mainly used to extract the features of the input data, each different convolutional kernel extracts different features of the input data, the more convolutional kernels in the convolutional layer, the more features of the input data can be extracted. 2. pooling layer (Pooling), also called down-sampling layer, the main purpose of which is to reduce the amount of data processing and speed up the training network while retaining useful information. 3. flat layer: the data dimension is made to change due to the passage of filters, and the role of this step is to convert the data to be processed into a one-dimensional vector corresponding to the neural units of the input layer before being fed to the neural network. 4. hidden layer, normalization layer, fully connected layer, output layer, etc. Considering the inherent correlation between different characteristics, in this paper, 2D convolutional neural network-based climbing identification method is then proposed, with network parameters trained by transforming 1-dimensional wind power output records into a 2-dimensional matrix to identify future climbing events.
3 Case Study Case study is conducted on practical wind farms in China, firstly, the analysis results for wind power output characteristics is discussed, which is utilized to determine the climbing threshold. Then the comparison results for the climbing identification between different methods are analyzed. 3.1 Analysis Results for Climbing Threshold Extraction The calculation results of different indexes are shown in Fig. 3. It can be found that the clustering of wind power output characteristics can be accurately realized based on the proposed method, and the threshold can be extracted on this basis.
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Fig. 3. Analysis results for climbing threshold extraction
3.2 Analysis Results for Climbing Identification The results of climbing identification are shown in Fig. 4. And the comparison results of different methods under different wind power output periods are shown in Tables 1 and 2. It can be found that the proposed method can realize climbing identification more accurately than other methods.
4 Conclusion This paper proposes a data-driven based wind power characteristic analysis and climbing identification method. Wind power climbing threshold is extracted firstly to construct climbing event dataset based on k-means clustering. 2D convolutional neural networkbased climbing identification method is then proposed, with network parameters trained by transforming 1-dimensional wind power output records into a 2-dimensional matrix to identify future climbing events. Test results on practical wind farm show that the proposed method can effectively analyze characteristics of wind power, which has better climbing identification accuracy compared with traditional methods.
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wind power output/p.u.
0.4 0.3 0.2 0.1 0
0
100
200
300
400
500
time/×15min
Fig. 4. Analysis results for climbing identification
Table 1. Comparison results of different methods under period 1
Accuracy (%)
SVM
BPNN
LSTM
CNN
PM
94.74
90.18
92.58
95.09
98.15
Table 2. Comparison results of different methods under period 2
Accuracy (%)
SVM
BPNN
LSTM
CNN
PM
93.1
87.9
91.3
94.04
97.39
References 1. Wang, H., Zhang, N., Du, E., et al.: A comprehensive review for wind, solar, and electrical load forecasting methods. Global Energy Interconnect. 5(1), 9–30 (2022) 2. Van der Meer, D.W., Widén, J., Munkhammar, J.: Review on probabilistic forecasting of photovoltaic power production and electricity consumption. Renew. Sustain. Energy Rev. 81, 1484–1512 (2018) 3. Tawn, R., Browell, J.: A review of very short-term wind and solar power forecasting. Renew. Sustain. Energy Rev. 153, 111758 (2022) 4. Wang, Y., Zou, R., Liu, F., et al.: A review of wind speed and wind power forecasting with deep neural networks. Appl. Energy 304, 117766 (2021) 5. Wang, H., Lei, Z., Zhang, X., et al.: A review of deep learning for renewable energy forecasting. Energy Convers. Manage. 198, 111799 (2019) 6. Holttinen, H.,Meibom, P.,Orths, A.,et al.: Impacts of large amounts of wind power on design and operation of power systems, results of IEA collaboration. Wind Energy 14(2), 179–192 (201) 7. Chengming, H., Jingang, Y., Hongtao, W., et al.: Response analysis of wind power ramping standby requirements and prevention control. Power Syst. Protect. Control 45(7), 51–57 (2017) 8. Mingjian, C., Jie, Z., Florita A.R.,et al.: An optimized swinging door algorithm for identifying wind ramping events. IEEE Trans. Sustain. Energy 7(1), 150–162 (2015)
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9. Yuzhong, G., Quanyuan, J., Baldick, R.: Ramp event forecast based wind power ramp control with energy storage system. IEEE Trans. Power Syst. 31 (3), 1831–1844 (2016) 10. Xue, X., Yongzhi, Q., Yutian, L.: Limited control strategy of wind power ramp events. Autom. Electr. Power Syst. 38(20), 26–32 (2014)
Nonlinear-Drift-Driven Wiener Process–Markov Chain Switching Model for Predicting Lithium-Ion Battery Remaining Useful Life Yixing Zhang1,2 , Fei Feng1,2(B) , Shunli Wang3 , Jinhao Meng4 , Jiale Xie5 , Hongpeng Yin1,2 , and Yi Chai2 1 School of Automation, Chongqing University, Chongqing 400044, China
{yixingzhang,feifeng,yinhongpeng}@cqu.edu.cn
2 Key Laboratory of Complex System Safety and Control, Chongqing University,
Chongqing 400044, China [email protected] 3 School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China [email protected] 4 College of Electrical Engineering, Sichuan University, Chengdu 610065, China [email protected] 5 School of Automation, North China Electric Power University, Baoding 071003, China [email protected]
Abstract. The accurate prediction of remaining useful life (RUL) is vital to improve the safety and reliability of lithium-ion battery power systems. However, owing to the effects of state (work and storage) switching and retention time randomness, it is difficult to accurately predict the RUL of lithium-ion batteries in real time. This study uses a nonlinear-drift-driven Wiener process to describe the dynamic degradation paths of lithium-ion batteries, and utilizes the Markov chain to establish a switching model and to predict the future state-switching probability. The analytical distribution of the first arrival time of the lithium-ion battery failure threshold is derived, and the model posterior parameters are updated using the Bayesian strategy. Finally, the model is verified using a lithium-ion battery dataset from the National Aeronautics and Space Administration. The RUL prediction model that considers state switching is superior to models that do not consider state switching. Moreover, the model shows a relative error of only 5.9388%. Overall, this study provides a theoretical basis for the research and development of lithium-ion battery RUL prediction and health management systems. Keywords: Lithium-ion battery · RUL · Switching state · Wiener Process · Bayesian strategy
© Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 107–118, 2023. https://doi.org/10.1007/978-981-99-1027-4_12
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1 Introduction 1.1 Motivation As the energy source and core component of new energy vehicles, lithium-ion batteries are characterized by high energy density, a lack of memory effect, and long life. Moreover, the life of lithium-ion batteries is directly related to the service life and safety of electric vehicles [1, 2]. Therefore, the accurate prediction of remaining useful life (RUL) can improve battery management level, reduce battery operation risk, and prolong battery service life. Thus, the accurate prediction is essential for battery management systems (BMSs) and can improve the availability and reliability of electric vehicles [3–5]. 1.2 Literature Review The common methods for predicting the RUL of lithium-ion batteries include physical models, data-driven models, and combined models [6, 7]. Ramadass et al. developed a model for battery capacity degradation by coupling a pseudo-2D model with a semiempirical model capable of expressing capacity degradation due to side reactions. This model used the Bulter–Volmer kinetic equation to calculate the rate of side reaction and the rate of increase in membrane impedance. The model could predict battery cycle life but can only be used at low charge/discharge multipliers, as the transport of lithium ions through the electrolyte was neglected [8]. Richardson et al. proposed two methods that use prior information to improve the regression performance of the Gaussian process. First, according to the known battery degradation model, the explicit average function was used to obtain prior knowledge of capacity degradation. Second, a multioutput Gaussian process was used to analyze the correlation between different units. Therefore, the data were effectively utilized [9]. Qin et al. used a particle filtering algorithm, applied a double exponential model as the state equation, and used an equation based on an artificial neural network. After a resampling process, the degradation curve of the battery was obtained and the RUL was then estimated. The results showed that the fusion model could fit the degradation curve of the battery, and the prediction accuracy gradually improved with increasing cycles [10]. 1.3 Research Gaps and Contributions Gaps: The above-mentioned studies focused on batteries in continuous work mode or assumed that the batteries followed the same degradation mechanism in different states. However, the actual operating state of batteries constantly varies between storage and work modes, with uncertainties in the duration and switching pattern of each state. Numerous studies have ignored the interaction between the storage and work states. The different switching states result in different degradation paths for lithium-ion batteries, which makes it difficult for the BMS to accurately predict the RUL over a calendar time. Although Peng et al. and Zhang et al. designed spatially degenerate models with switching states to predict RUL, the final forms of semi-analytic and numerical solutions will limit the applications of the models for research on BMSs [11, 12].
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Contributions: To address the above problems, this study proposes a switching model that combines the nonlinear-drift-driven Wiener process and Markov chain for predicting the RUL of lithium-ion batteries. The Wiener process is used as a degradation model, which can capture the dynamic characteristics of the batteries. The Markov chain is used to establish a switching model to predict the switching probability. Then, the analytical distribution of the first time at which the lithium-ion battery reaches the failure threshold is derived, and expert knowledge is introduced into the analytical distribution using a fuzzy system. The model adopts a Bayesian strategy for updating posterior parameters. 1.4 Organization The rest of this study is organized as follows: Sect. 2 presents a dual-state switching model based on a nonlinear-drift-driven Wiener process–Markov chain, and describes model parameter estimation and parameter update; Sect. 3 presents algorithm validation; and Sect. 4 presents the conclusions of the study.
2 Nonlinear-Drift-Driven Wiener Process–Markov Chain Switching Model First, this section presents a flowchart of the nonlinear-drift-driven Wiener process– Markov chain switching model, followed by a degenerate expression for the nonlinear drifting Wiener process. Second, the switching probability is predicted through the Markov chain. Furthermore, the analytical distribution of the first hitting time (FHT), that is, the time at which the lithium-ion battery first reaches the threshold, is obtained. Finally, the model is fused using a fuzzy system, and then the model posterior parameters are updated through the Bayesian strategy. 2.1 Collective Structure Figure 1 shows the flowchart of the entire algorithm, which is composed of three parts: (1) The nonlinear-drift-driven Wiener process is used to simulate the degradation paths of the lithium-ion batteries, and parameter estimation is performed using historical data. (2) The switching probability is modeled using a Markov chain. The offline parameters are estimated using historical data. (3) A fuzzy system is used to fuse the two models, and a Bayesian updating strategy with posterior parameters is used to accurately predict the RUL of lithium-ion batteries.
2.2 Degradation Model Based on Nonlinear-Drift-Driven Wiener Process As a stochastic process, the Wiener process can capture dynamic characteristics and randomness and is widely used in degradation modeling and life prediction. As a nonlinear function of time, the nonlinear Wiener process is suitable for modeling high-nonlinearity
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Fig. 1. Collective structure of the proposed method.
devices such as lithium-ion batteries [13–15]. The nonlinear-drift-driven Werner process is defined as t ξ(τ ; η)d τ + σ B(t), (1) X (t) = X (0) + ϕ 0
where X (t) denotes the degradation rate of the lithium-ion battery at time t, and X (0) denotes the degradation rate at time t0 , which is generally considered to be 0. ϕ is a random parameter that describes the individual variation in lithium-ion batteries, and t it is usually considered to follow a normal distribution. ϕ 0 ξ(τ ; η)d τ is the nonlineardrift-driven degradation; σ is the diffusion parameter, σ > 0; B(t) is the standard Brownian motion (BM), which relates to the random dynamic properties of the lithiumion batteries. The safety of systems with complex internal chemistry, such as lithium batteries, is a major concern for the new energy industry. The batteries should be immediately retired after reaching the retirement threshold for the FHT to ensure reliability and safety. According to the FHT concept, the retirement time can be expressed as T = inf{t : X (t) ≥ ω|X (0) < ω}.
(2)
Here, the useful life of a lithium-ion battery is taken as the time at which the battery first reaches the retirement threshold ω. Therefore, tk denotes the present time, and the lk denotes the RUL. According to the definition of equipment life , lk = t − tk . The definition of the RUL L k of the equipment at time tk is written as Lk = inf{lk > 0 : X (tk + lk ) ≥ ω}.
(3)
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Suppose that a standard BM has not been crossed boundary before a certain time t [16]; the probability density function (PDF) of the FHT is at a fixed threshold ω for X (t), t ≥ 0: fX (t) (ω, t) ≈
S 2 (t) 1 SB (t) ξ(t; η) ( + ) exp{− B }, 2π t t σ 2t
(4)
where fX (t) = (ω, t) denotes the PDF of the FHT at a fixed threshold ω. SB (t) is the time-dependent boundary function corresponding to the standard BM, SB (t) = (w − t 0 ξ(τ ; η)d τ )/σ . 2.3 Switching Model Based on Markov Chain Since Markov chains are widely used for describing the state transition of stochastic time-varying processes, a switching model based on Markov chains is derived[12, 17]. During operation, lithium-ion batteries switch between work and storage states; therefore, according to the definition of the Markov chain lithium-ion battery state space, S = {0, 1}, where 0 state represents the lithium-ion battery in the work state, and 1 state represents the battery in the storage state. Without loss of generality, the first work time of the lithium-ion battery is recorded as T1 , and T1 follows an exponential distribution related to the parameter λ. Its expectation is taken as 1/λ. Each subsequent work time is independently and identically distributed with T1 . Similarly, the first storage time of the lithium-ion battery is recorded as T2 . T2 is set as the compliance parameter μ, and its expectation is taken as 1/μ. The exponential distribution of each subsequent storage time and T2 is independent and identically distributed. The state of the lithium-ion battery at time t is denoted as X (t). The transfer probability function is proved by the Kolmogorov forward equation: 1 λ −(μ+λ)τ ] −(μ+λ)τ ] λ+μ [μ + λe λ+μ [1 − e E= (5) μ 1 −(μ+λ)τ ] −(μ+λ)τ ] . λ+μ [1 − e λ+μ [λ + μe The probability distributions of the lithium-ion battery work and storage states in a future time can be determined at any time according to the values of parameters λ and μ. To simplify the notation, κ(λ, μ) is defined as the set of parameters λ and μ. 2.4 Combined Model Based on Fuzzy System After the degradation and the switching models are built, both models are fused. The PDF for the FHT failure threshold of a lithium-ion battery is obtained using the full
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probability equation: fLk (lk ) ∼ =
2 ( 2π lk2 [σϕ,k
lk +tk
(ω − xk ) × (w0 p0 + w1 p1 ) − [
tk
1 ξ(τ ; η)d τ )2 + σ 2 lk ]
lk +tk
ξ(τ ; η)d τ − ξ(lk + tk ; η)lk ]
tk
⎫ 2 (ω − x ) × (w p + w p ) lk +tk ξ(τ ; η)d τ + μ 2 ⎬ σϕ,k 0 0 1 1 tk k ϕ,k σ lk , 2 ( lk +tk ξ(τ ; η)d τ )2 + σ 2 l ⎭ σϕ,k k tk ⎧ ⎫ ⎨ [(ω − xk ) × (w0 p0 + w1 p1 ) − μϕ,k lk +tk ξ(τ ; η)d τ ]2 ⎬ tk exp − 2 ( lk +tk ξ(τ ; η)d τ )2 + σ 2 l ] ⎩ ⎭ 2[σϕ,k k tk
(6)
where w0 and w1 denotes the influence probabilities of work and storage on the capacity degradation of lithium-ion batteries; p0 and p1 are the distribution probabilities of work and storage in the future. It is assumed that the initial probability distribution of battery work and storage is π0 (1, 0), which means that the probability of the system running at the beginning of the work state is 100%, and the probability of the lithium-ion battery working and storing at a future time can be obtained using the E state transition probability matrix (p0 , p1 ). Han et al. found that lithium-ion battery degradation occurred in three stages: early accelerated degradation, steady degradation, and late accelerated degradation [18]. Therefore, this study designs a single-input and dual-output fuzzy controller [19]. Battery remaining capacity is the only input to the fuzzy system, which is divided into the early stage, middle stage, and later stage. The above-calculated future work and storage probability will affect the lithium-ion degradation as output. The work state contains natural degradation domains and those affected by capacity recovery degradation, while the storage state exhibits domains of small, medium, and large degradation effects of capacity recovery over different periods. The fuzzy control rules are set as follows, considering the actual situation of lithiumion batteries: (1) If the remaining capacity (x1 ; i.e., w − xk , Eq. 6) is in the early stage, the influence x2 will be slightly reduced (to prevent rapid degradation, low analytically derived remaining capacity, and low predicted RUL), and the influence x3 of the early recovery probability will be relatively large. (2) If x1 is in the middle stage, x2 will have a natural weight (because the middle stage is relatively stable, there is no rapid capacity degradation), and x3 will be moderate. (3) If x1 is in the later stage, x2 will be larger (if the influence will be reduced as in the early stage, the RUL predicted using the analytical equation will be larger, which will reduce the final-use safety performance; therefore, the probability should be larger to ensure the reliability of the final use) and x3 will be slightly larger.
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Thus, the fuzzy membership degree of the lithium-ion batteries (Table 1) is obtained. The coordinate value in Table 1 is determined according to the specific capacity value of the lithium-ion batteries. Table 1. Fuzzy function of lithium-ion batteries. Input-output
Capacity input membership
Work influence degradation membership
Storage influence degradation membership
Membership function
2.5 Parameter Identification In this section, the model parameters are estimated using the maximum likelihood method, and the Bayesian theory is applied to update the posterior parameters. We assume that M lithium-ion batteries are available and contain relevant degradation history data. Let the number of degradation data for the ith lithium-ion battery be Ni (0 ≤ i ≤ M ) and the measurement time for the ith battery be ti,j (1 ≤ j ≤ Ni ), where j represents the jth measurement. Thus, X (ti,j ) represents the amount of degradation for the ith battery at the jth measurement. Therefore, the following equation is written as ti,j ξ(τ ; η)d τ + σ B(ti,j ) (7) Xi,j = X (0) + ϕ0 0
where Xi,j denotes X (ti,j ), and X (0) is the degradation amount at time t0 . It is generally considered that the degradation amount of the lithium-ion battery at time t0 is 0, X (0) = 0; ϕ0 is a priori of the random parameter ϕ, π0 (ϕ) ∼ N (μϕ,0 , σ 2 ϕ,0 ). According to Eq. (1) and the independent incremental property of the standard BM process, the M degradation data obey the multivariate Gaussian distribution. The degradation data of the i th lithium-ion battery is Xi = (Xi,1 , Xi,2 , Xi,3 , . . . , Xi,Ni ), from which the mean and covariance can be obtained as μi = μϕ,0 Ii , (8) i = σϕ,0 Ii Ii + σ Ki ⎞ ti,1 · · · ti,1 t t t ⎟ ⎜ where Ii = ( 0i,1 ξ (τ ; η)d τ, 0i,2 ξ (τ ; η)d τ, . . . , 0i,j ξ (τ ; η)d τ ),Ki = ⎝ ... . . . ... ⎠. ti,1 · · · ti,j The log-likelihood function generated by the degraded data from all M degraded devices ⎛
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is as follows: 1 1 1 ( |X1:M ) = − ln(2π ) Ni − ln| i | − (Xi − μi ) i−1 (Xi − μi ). 2 2 2 M
M
M
i=1
i=1
i=1
(9) We choose the general and applicable drift function, i.e., ξ(τ ; η) = ηt η−1 . Equation (9) is maximized by finding the first-order partial derivative at 0, to obtain the model parameters = (μϕ,0 , σϕ,0 , η, σ ). Consequently, to obtain the offline parameters of the switching model, the shape parameters and scale parameters of the gamma distribution can be obtained by directly fitting the historical data with the MATLAB GAMFIT function. In the Bayesian framework, the posterior distribution of the random parameter ϕ follows the Bayesian theory. From the definition of the distribution of ϕ and the BM property, the likelihood function of the degraded data can be obtained as n k [xn − xn−1 − ϕ ttn−1 ξ(τ ; η)d τ ]2 1 . exp − p(x1:k |ϕ ) = k 2 2σ 2 (tn − tn−1 ) n 2π σ (tn − tn−1 ) n=1
(10) At this point, the mean and variance of the updated ϕ parameters are obtained as μϕ,k =
μϕ,k−1 2 σϕ,k−1
2 σϕ,k =
η
η
η
(tk −tk−1 )2 σ 2 (tk −tk−1 )
+
η
(tk −tk−1 )2 σ 2 (tk −tk−1 )
+
(11)
1 2 σϕ,k−1
1 η
η
[(xk −xk−1 )(tk −tk−1 )] σ 2 (tk −tk−1 )
+
1
.
(12)
2 σϕ,k−1
To perform parameter updates of the switching model under Bayesian systematics, the prior distribution of p(κ) is assumed to be the gamma distribution. The relevant parameters are λ ∼ gama(α0 , β0 ) and μ ∼ gama(α1 , β1 ), where α0 and α1 are shape parameters, and β0 and β1 are scale parameters. The posterior distribution PDF is expressed as λn0→1 (tk )+a0 −1 exp −λ(d0 (tk ) + β0−1 ) fκ (κ|Ck ) = (n0→1 (tk ) + a0 )(d0 (tk ) + β0−1 )−(n0→1 (tk )+a0 ) μn1→0 (tk )+α1 −1 exp −μ(d1 (tk ) + β1−1 ) (13) × (n1→0 (tk ) + α1 )(d1 (tk ) + β1−1 )−(n1→0 (tk )+a1 ) λa0,k −1 exp −λ/β0,k μa1,k −1 exp −μ/β1,k = × . α0 ,k α1 ,k (α0,k )β0,k (α1,k )β1,k According to Eq. (13), the parameters of the switching model can be updated in real time. n0→1 (tk ) is the number of times the lithium-ion battery transitions from the
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work state to the storage state in [0, tk ] time, and n1→0 (tk ) is the number of times the lithium-ion battery transitions from the storage state to the work state in [0, tk ] time; that is, n(tk ) satisfies n(tk ) = n0→1 (tk ) + n1→0 (tk ). Let d0→1 (tk ) and d1→0 (tk ) be the cumulative retention times of lithium-ion batteries at intervals [0, tk ] in the work and storage states, respectively. Then, tk = d0→1 (tk ) + d1→0 (tk ).
3 Algorithm Verification Experimental verification is performed using the above-mentioned model. First, the battery degradation dataset used in the experiment is presented. Second, the RULs of the batteries in the dataset are predicted. Finally, the proposed model is compared with other models. 3.1 Battery Degradation Data The lithium-ion battery degradation dataset published by the National Aeronautics and Space Administration is used for verification. The dataset contains detailed degradation information of multiple batteries. In this study, B0005, B0006, B0007, and B0018 batteries are used to verify the dual switching model. The lithium-ion batteries have an initial capacity of 2 Ah. Figure 2 shows the different degradation paths of the four batteries over calendar time. B0018 is used as the validation set, while the other three batteries are used as the training set; thus, the work–storage retention times for the B0018 battery at different switching times are extracted (Fig. 3).
Fig. 2. Four battery degradation paths
Fig. 3. B0018 switching times versus retention time
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3.2 RUL Prediction Results To demonstrate the superiority of the nonlinear-drift-driven Wiener process–Markov chain switching model, several similar models are selected for comparison. Peng et al. established a general linear model, and Si et al. developed a degenerate model for nonlinear Wiener processes [20, 21]. To illustrate the importance of a switching mechanism, this study introduces expert knowledge into a fixed-weight model, so that the switching model parameters are canceled by a fixed value, and the term w − xk is modified. The final results are shown in Fig. 4. The linear Wiener process shows the most significant deviation from the true RUL curve. This confirms that the degradation of lithium-ion batteries is nonlinear and that the RUL cannot be accurately predicted using the linear model. The nonlinear Wiener process model and the fixed weight model slightly outperform the linear model, but both models feature large deviations and fluctuations regarding lithium-ion battery capacity recovery, because the models do not consider the influence of actual switching states on the degradation of lithium-ion batteries. The proposed nonlinear-drift-driven Wiener process–Markov chain switching model considers the influence of the switching state on the lithium-ion battery. It features less volatility in the prediction process, and the predicted RUL is closer to the true RUL.
Fig. 4. Comparison of RULs predicted by different models.
Finally, the absolute errors (AE), relative errors (RE), mean time to failures (MTTF), and mean square errors (MSE) of different models are compared (Table 2). The nonlineardrift-driven Wiener process–Markov chain switching model predicts the RUL of lithiumion batteries with excellent accuracy, and its absolute error is only 5.9388%, which is less than those of other models. The real lifetime of B0018 is 964 h, and the average failure time of the B0018 battery predicted using the proposed method is 937.3236 h; thus, the proposed model features high prediction accuracy and can ensure battery usage safety. Therefore, the model is better than other models in terms of reliability and safety.
4 Conclusion Lithium-ion batteries feature different degradation paths in different work and storage states. The effect of state switching on lithium-ion batteries makes it difficult to accurately
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Table 2. Comparison of different models. AE (h)
RE (%)
MTTF (h)
MSE (h)
Linear
173.6708
320.5241
994.8976
123.0040
Nonlinear
134.1870
247.6535
989.8691
104.0669
16.4295
30.3220
935.2542
114.3484
3.2178
5.9388
937.3236
77.5059
Fixed Proposed
predict battery RUL; thus, in this study, a nonlinear-drift-driven Wiener process–Markov chain switching model is proposed to predict the RUL of lithium-ion batteries. First, the degradation model of lithium-ion batteries is built through the nonlinear-drift-driven Wiener process, and the dual-state switching model is established using the Markov chain. Second, the analytical equation of RUL is obtained by deriving the first threshold time reached. Finally, the analytical equation is adjusted for the influence of weights using a fuzzy system. The experimental results show that the proposed model more accurately predicts lithium-ion battery RUL compared with other models that do not consider state switching. Overall, this study provides ideas for the development of RUL prediction and health management systems of lithium-ion batteries using embedded and cloud platforms. Acknowledgments. This work was supported by China Postdoctoral Science Foundation (grant No. 2021M690177) and the Joint Funds of the National Natural Science Foundation of China (grant No. U2034209).
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Estimation of Battery State Based on Discharge Voltage Drop and AC Impedance at Full Charge Shengli Kong1 , Xiaochuan Huang2 , Guangjin Zhao1 , Yu Chen1 , and Wei Han1(B) 1 State Grid Henan Electric Power Research Institute, Changsha, China
[email protected] 2 State Grid Kaifeng Electric Power Supply Company, Kaifeng, China
Abstract. Valve-regulated lead-acid batteries are the preferred power supply equipment in substation DC power supplies due to their advantages of small selfdischarge, airtightness and easy maintenance. SOH is an important parameter that reflects the current capacity of a battery. In recent years, there have been a variety of algorithms to study SOH state estimation. However, considering its accuracy, engineering application and other factors, it is difficult to meet accurate online measurement. In this paper, the differences in electrical parameters of 2 V 500 Ah VRLA batteries under different health states are analyzed, and the voltage drop value of 0–150 s in the fully charged state and the AC impedance value at 50 Hz frequency are used to estimate the battery. Under the premise of not applying any algorithm optimization and data screening, two electrical parameters are used to estimate the state of the battery. The results show that using the voltage drop and the AC impedance value in the fully charged state has a high accuracy in estimating the state of the battery. This shows a good value for engineering application. Keywords: Discharging voltage drop · AC impedance · Lead-acid batteries · SOH status estimation
1 Introduction The automation, intelligence and unattended operation of power grid substations are the main trends of power grid development [1]. The national grid companies are gradually implementing unmanned substations at different voltage levels such as 500 kV, 330 kV, 220 kV, 110 kV, 66 kV, 35 kV and 10 kV, of which 110 kV and below are basically unmanned. Due to the increasing degree of automation and intelligence in substations and the promotion of unmanned operation, the role of DC power supplies in substations is becoming more and more important [2]. In the substation, the battery bank of the DC system is connected in parallel with the charger to jointly undertake the important DC load power supply tasks such as relay protection, automatic device, automatic equipment, circuit breaker tripping and closing mechanism [3]. When the AC power is lost, the charger cannot output DC power, and the battery bank is used as the only DC power source to supply DC loads. Therefore, the safe and stable operation of the DC system is an important part of the safe and reliable operation of the power grid. Valve Regulated © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 119–126, 2023. https://doi.org/10.1007/978-981-99-1027-4_13
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Lead Acid Battery (VRLA) is gradually becoming an indispensable backup power source in various industries such as communication, electric power, transportation and finance because of its maintenance-free, low self-discharge and sealed characteristics [4–6]. Battery SOH (State of Health) is the ratio of the current full capacity of the battery to the nominal capacity of the battery, mainly reflecting the current capacity of the battery for a freshly shipped battery [7]. Its SOH value is often greater than or equal to 100% [8]. IEEE Standard 1188–1996 states that a battery should be replaced when its SOH is ucarr (3) uS2 = uS3 = 0 uPWM ≤ ucarr
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For the gate signals S1 and S4 , S5 and S6 , S1 and S6 are always in the on state when the reference wave uref is in the positive half cycle, while S4 and S5 are in the off state; their states are reversed from the positive half cycle when uref is in the negative half cycle. uref ustair
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0 G2 G3 G1 G4 G6 G5
Fig. 2. Modulation scheme of the high-frequency part.
The low-frequency modulation part are realized by the Si based three-level H-bridge sub-modules. Each sub-module is composed of two DNPC legs. Different from the requirement to control six active switches in the ANPC leg, the DNPC leg only needs to form a staircase wave by controlling its four Si IGBTs. In order to maintain the voltage balance of the Si based three-level H-bridge submodule, a voltage sorting algorithm is employed to control the charge and discharge of each battery. Since the SiC/Si hybrid sub-module is always engaged for high-frequency modulation, two battery voltages of the hybrid sub-module are combined into one average value. Then this average value is sent to the voltage sorting algorithm. In the voltage sorting algorithm, all the battery voltages are arranged from low to high and the sorting result nbi of each battery is obtained. Since the input voltage reference uref is a sinusoidal wave, which is composed of a staircase wave ustair and a PWM wave uPWM . uPWM is generated by the high-frequency switching modulation part, while ustair is obtained by the low-frequency switching modulation part. Therefore, all the Si based three-level H-bridge sub-module should generate a staircase wave ustair . This means that the number of batteries engaged in the power loop needs to be equaled to the absolute value of ustair , that is |ustair |. When |ustair | increases, the battery with the order of nbi = |ustair | is switched in; when the ustair decreases, the battery with the order of nbi = |ustair |+1 will be bypassed. The structure of the Si based three-level H-bridge sub-module is illustrated in Fig. 1 and its switching states are given in Table 1. Because Sl1 and Sl4 , Sl2 and Sl3 , Sl5 and Sl8 , Sl6 and Sl7 are complementary pairs, only the switch states of Sl1 , Sl2 , Sl5 , Sl6 are listed in this table. According to the different sorting results of the batteries and inductor current directions, there are eight switch cases, and the Si based three-level H-bridge sub-module can generate 5 levels voltage.
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Conditions
Switching signals
Switching states
Inductor current
Battery voltage sorting results
Sl1
Sl2
Sl5
Sl6
iL ≥ 0
nb1 , nb2 ≤ |ustair |
1
1
0
0
2
nb1 > |ustair |≥ nb2
1
1
0
1
1
nb2 > |ustair |≥ nb1
0
1
1
0
1
nb1 , nb2 > |ustair |
0
1
0
1
0
nb1 , nb2 > |ustair |
0
1
0
1
0
nb1 > |ustair |≥ nb2
0
0
1
1
−1
nb2 > |ustair |≥ nb1
0
0
0
1
−1
nb1 , nb2 ≤ |ustair |
0
0
1
1
−2
iL < 0
2.3 System-Level Control Schemes The system-level control of the proposed electric vehicle charging station are made up of multiple control loops. For the high-voltage rectifier, a current inner loop (using d-q axis current control) and a voltage outer loop are employed in the system controller. This control scheme can realize the separate control of the active power and reactive power. Then the voltage reference uref is generated and sent the PWM module. Finally, the gate signals are generated according to the modulation scheme presented in Sect. 2.2. Besides, the isolation stage LLC converters are operated at the resonant frequency in order to improve the system efficiency. For the low voltage DC/DC converter, a voltage outer loop and a current inner loop are employed to control the charging voltage and current of the electric vehicle battery.
3 Simulation Results In order to verify the validations of the proposed electric vehicle charging station and control schemes, a simulation model is built in MATLAB/Simulink. The simulation parameters are tabulated in the Table 2. The simulation results of the high-voltage stage and the isolation stage are shown in Figs. 3 and 4, respectively. The input voltage waveform of each module is shown in Fig. 3a. The input voltage of module #1 is a 5-level PWM waveform, while the input voltage of module #2 and module #3 are only 5-level staircase waveforms. The input voltage ranges of all sub-modules are ± 1600 V. It can be seen all the high-frequency switching actions are concentrated on hybrid sub-module. Figure 3b shows the total input voltage of the high voltage rectifier, it is a 13-level voltage waveform. The input voltage range of the high voltage rectifier is ± 4800 V. The output voltages of module #1, module #2 and module #3 are shown in Fig. 3c. The output voltages of all sub-modules are stable and equal to 1600V. Figure 3d shows the input current waveform, the root-mean-square (RMS) value of input current is 24.2A.
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Table 2. System parameters Parameters
Quantity
Unit
High voltage stage input voltage
3
kV
High voltage stage input voltage frequency
50
Hz
Number of the high-voltage stage sub-modules
3
–
High voltage stage inductor
3
mH
Battery Nominal Voltage of the high voltage stage
760
V
Battery response time of the high voltage stage
0.3
s
Battery Initial state-of-charge of the high voltage stage
50%
–
Carrier wave frequency of the high voltage stage
20
kHz
Resonant inductance of the isolation stage
23.115
µH
Magnetizing inductance of the isolation stage
115.58
µH
Resonant capacitor of the isolation stage
438.33
nF
Transformer ratio of the isolation stage
1200:1600
–
2000 1000 0 -1000 -2000 2000 1000 0 -1000 -2000 2000 1000 0 -1000 -2000 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
(b) 5000 4000 3000 2000
Voltage(V)
Voltage(V)
(a)
0 - 1000 - 2000 - 3000 - 4000 - 5000 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
Time(s)
Time(s)
(d)
(c)
1601.0
50
1600.5
40
1600.0
30
1599.5 1601.0
20
Current(A)
Voltage(V)
1000
1600.5 1600.0 1599.5 1601.0
10 0 -10 -20
1600.5
-30
1600.0
-40
1599.5 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
Time(s)
-50 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
Time(s)
Fig. 3. Simulation results of the high voltage rectifier. a Input voltage of each sub-modules. b Total input voltage. c Output voltage of each sub-modules. d Input currents.
The zero-voltage switching (ZVS) and zero-current switching (ZCS) are realized as shown in Fig. 4a. The LLC converter primary side MOSFET Si1 is turned on after
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its drain-source voltage uds reaches to zero, so ZVS is achieved. The LLC converter secondary side currents iD1 and iD3 can reach to zero, so ZCS is also achieved.
800
Vgs1
(b)
Vds1
1600 1400
600
1200
Voltage(V)
400 200 0
iD3
iD1
80
Current(A)
Voltage(V)
(a)1000
60
800 600 400
40
200
20 0 0.50000
1000
0.50001
(c ) 150
0.50002
0.50003
Time(s)
0.50004
0 0.50000
0.50005
0.50002
0.50004
0.50006
Time(s)
0.50008
0.50010
( d )1064.0
iLr
1063.5
100
iLm
Voltage(V)
Current(A)
1063.0 50 0 - 50
1062.5 1062.0 1061.5 1061.0
- 100 - 150 0.50000
1060.5 0.50001
0.50002
0.50003
Time(s)
0.50004
0.50005
1060.0 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
Time(s)
Fig. 4. Simulation results of the isolation stage. a Realization of ZVS and ZCS. b Resonant capacitor current. c Resonant inductor current and magnetizing current. d Low voltage output voltage.
The voltage waveform of the resonant capacitor is shown in Fig. 4b, the dc bias voltage is 800 V. Figure 4c shows the waveforms of the resonant inductor current and the magnetizing current. The RMS values of the resonant inductor current and the magnetizing inductor current are 72.9 A and 20.0 A, respectively. There is only one intersection point between these two current waveforms, so the LLC converter works at the resonant frequency. The low voltage output voltage waveform is shown in Fig. 4d. The value of the voltage is 1062 V, and the output voltage ripple is 0.4 V.
4 Conclusion An electric vehicle charging station based on SiC MOSFETs and Si IGBTs hybrid cascaded three-level H-bridge converter is proposed in this paper. Only two SiC MOSFETs are employed in the high voltage rectifier, so the cost of the system can be significantly reduced. Meanwhile, all the high frequency switching events are concentrated on SiC MOSFETs by using a specialized modulation scheme, other sub-modules are only switched with line frequency. The simulation results show the validations of the proposed electric vehicle charging station and control schemes. Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grant 52067010 and Yunnan Fundamental Research Project under Grant 202201AT070155.
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References 1. Jiang, W., Ren, K., Xue, S., Yang, C., Xu, Z.: Research on the asymmetrical multilevel hybrid energy storage system based on hybrid carrier modulation. IEEE Trans. Ind. Electron. (99), 1–1. (2020) 2. Mao, W., Zhang, X., Zhao, T., Hu, Y., Cao, R.: Research on power equalization of threephase cascaded H-bridge photovoltaic inverter based on the combination of hybrid modulation strategy and zero-sequence injection methods. IEEE Trans. Ind. Electron. (99), 1–1 (2019) 3. Anthon, A., Zhe, Z., Andersen, M., Holmes, D.G., Mcgrath, B., Teixeira, C.A.: The benefits of sic mosfets in a t-type inverter for grid-tie applications. IEEE Trans. Power Electron. 32(4), 2808–2821 (2017) 4. Quan, C., Wang, Q., Li, G., Ding, S.: The control of unequal power losses distribution in three-level neutral-point-clamped VSC. In: Electrical Machines and Systems (ICEMS), 2012 15th International Conference on. IEEE (2012) 5. Yi, D., Li, J., Shin, K.H., Viitanen, T., Saeedifard, M., Harley, R.G.: Improved modulation scheme for loss balancing of three-level active NPC converters. IEEE Trans. Power Electron. 32(4), 2521–2532 (2017) 6. Millan, J., Godignon, P., Perpina, X., Perez-Tomas, A.: A survey of wide bandgap power semiconductor devices. IEEE Trans. Power Electron. 29(5), 2155–2163 (2014) 7. Yang, X., Liu, J., Wang, B., Zhang, G.: Pulsed overcurrent capability of power semiconductor devices in solid-state circuit. In: IEEE Conference and Exposition—APEC, pp. 966–973 (2022) 8. Zhang, L., Yang, D., Ren, L., Cheng, Y., Yuan, Y.: The method of the sic mosfet replacing the si igbt in the traditional power electronics converter without redesigning the main circuit and the driver circuit. Energy Eng. 118(4), 1155–1170 (2021) 9. Mo, Y., et al.: Auxiliary power supply with SiC MOSFET for wide-range high voltage input applications. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference (IPEMC2020-ECCE Asia) (2020) 10. Guan, Q.X., Li, C., Zhang, Y., Wang, S., Xu, D.D., Li, W., et al.: An extremely high efficient three-level active neutral-point-clamped converter comprising sic and si hybrid power stages. IEEE Trans. Power Electron. 33(10), 8341–8352 (2019) 11. Yin, T., Xu, C., Lin, L., Jing, K.: A sic mosfet and si igbt hybrid modular multilevel converter with specialized modulation scheme. IEEE Trans. Power Electron. (99), 1–1 (2020)
A Simulation Study on Magnetic Field Distribution of Two-Cells Proton Exchange Membrane Fuel Cell Stack Yuning Sun1
, Lei Mao1,2(B) , Kai He1 , Zhongyong Liu1 , Shouxiang Lu2,3 , and Lisa Jackson4
1 Department of Precision Machinery and Precision Instrumentation, University of Science and
Technology of China, Hefei 230026, China [email protected] 2 Institute of Advanced Technology, University of Science and Technology of China, Hefei 230026, China 3 State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China 4 School of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, UK
Abstract. As the promising device in automotive, stationary, and portable applications, proton exchange membrane fuel cell (PEMFC)’s performance has attracted growing attention, which can be strongly affected by its current distribution. With the characteristic of online and nondestruction, magnetic field can be used to evaluate the current distribution and PEMFC state, while further study is still lacked for understanding the effect of PEMFC stack structure and operation conditions on its magnetic field distribution. In this study, a numerical model of two-cells PEMFC stack is established to investigate its magnetic field distributions at different current densities and states, from which the coupling effect of magnetic field of each cell is clarified. In this PEMFC stack model, the distributions of magnetic field at different states and current densities are constant while the magnitude of magnetic field will vary. Moreover, coupling effect will be weakened with the cell distance between two cells. From the results, these findings can be utilized to monitor the operation state of PEMFC stack in the further researches. Keywords: Proton exchange membrane fuel cell (PEMFC) · PEMFC stack · Model simulation · Magnetic fields
1 Introduction With carbon peaking and carbon neutrality goals in China, various new power generation sources, such as photovoltaic and wind powers, have been equipped widely in the applications. Due to the characteristics including fluctuations in power generation capability, energy storage techniques and devices are usually required. Among various energy storage techniques, hydrogen and fuel cells (especially proton exchange membrane fuel © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 186–193, 2023. https://doi.org/10.1007/978-981-99-1027-4_20
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cell, PEMFC) are considered as one of the potential devices for medium to long term energy storage [1, 2]. Nevertheless, the PEMFC reliability and durability issues have attracted growing attention because the performance and lifetime of PEMFC stack will be critically influenced due to the occurrence of PEMFC faults, which greatly hinder its widespread commercialization in energy storage applications. It is well known that the reliability and durability of PEMFC system depends strongly on its current distribution. Therefore, to improve system efficiency and guarantee its safety, monitoring PEMFC current distribution during the operation is necessary. It can be learned from Biot-Savart law that PEMFC current will excite magnetic field around PEMFC, thus with analyzing the change of magnetic field, the variation of PEMFC current can be induced. From the literatures, some scholars evaluated PEMFC current distribution with its excited magnetic field. A array of magnetic sensors are designed to detect the magnetic field of PEMFC stack and thus current density was reconstructed [2, 3]. Moreover, In the researches of Akimoto et al. [4, 5], by inserting a magnetic sensor probe into PEMFC stack, the magnetic field on the cathode side of PEMFC cell was measured to monitor the current variation of steady and faulty state, such as drying conditions. Nevertheless, in these researches only some specific PEMFC experiments are conducted to investigate magnetic field variation in different states, while model analysis is still lacked for understanding the magnetic field coupling effect of PEMFC stack on magnetic field variation. Therefore, it is still needed to clarify the magnetic field coupling effect of PEMFC stack for performance monitoring of practical PEMFC systems further researches. On such basis, in this paper a numerical model of two cells PEMFC stack is established to investigate its magnetic field distributions at different states and current densities, where coupling effect of magnetic field of each cell is clarified. Additionally, the influence of the cell distance between two cells on magnetic field distribution is further discussed, indicating that the coupling effect will be weakened with the cell distance. These findings can be utilized to monitor the operation state of PEMFC stack in the further researches.
2 Modeling and Simulation of PEMFC In this section, the background theory and modeling process of the simulation model in COMSOL are presented. 2.1 Background Theory of Numerical Analysis Inside PEMFC, at the anode hydrogen is oxidized to produce protons, which pass through the proton exchange membrane (PEM) from anode to cathode to complete reduction reaction at the cathode, and produced electrons reach the cathode by the external circuit. Therefore, electrochemical reactions, mass transports, current distribution and magnetic field distribution will be calculated in a multi-physics coupling model, which will be clarified in the next section.
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2.2 Modeling of PEMFC A three-dimensional, single-phase (Water is considered in vapor phase) [6, 7], multicomponent model of PEMFC stack is established in the version 6.0 of the ‘COMSOL Multiphysics’ software and the ‘Batteries & Fuel Cell Module’, as shown in Fig. 1. In this model, PEMFC stack is simulated by two single channel cells, where each cell includes a PEM, flow channel, gas diffusion layers (GDLs), and electrodes (CLs). The parameters of PEMFC model can be found in Table 1 [8, 9]. Moreover, to investigate the magnetic field distribution, the air and the infinite element domain should be noted to set outside PEMFC stack, as depicted in Fig. 1b.
Fig. 1. The diagram of PEMFC stack model.
Table 1. Parameters of the PEMFC components. Parameter (unit)
Value
PEMFC length (mm)
20
Rib width (mm)
0.8
Flow channel width (mm)
0.8
Flow channel height (mm)
1
GDL width (µm)
380
CL thickness (µm)
50
PEM thickness (µm)
100 (continued)
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Table 1. (continued) Parameter (unit)
Value
Electric conductivity of PEM (S/m)
9.825
Electric conductivity of GDL (S/m)
222
CL permeability (A/m2 )
2.35 × 10–12
GDL permeability (A/m2 )
1.18 × 10–11
CL porosity
0.3
GDL porosity
0.4
Anode exchange current density (A/m2 )
100
Cathode exchange current density (A/m2 )
0.001
Cathode transfer coefficient
1
Anode viscosity (Pa · s)
1.19 × 10–5
Cathode viscosity (Pa · s)
2.46 × 10–5
Anode stoichiometry
1.5
Cathode stoichiometry
3.5
PEMFC temperature (K)
353.15
3 Result and Discussion 3.1 The Polarization Curve and Power Curve of PEMFC Model The polarization curve is the most crucial characteristic for PEMFC, which can be applied to diagnose, design and control PEMFC systems. As depicted in Fig. 2, the polarization curve shows the relationship between its voltage and current density, indicating its output performance. Moreover, with the polarization curve, Fig. 2 predicts the power curve, which is also a key parameter for practical PEMFC systems, especially in the power generation applications. 3.2 Magnetic Field Distribution of PEMFC Stack According to Biot-Savart law, PEMFC current will produce external magnetic field around PEMFC stack. Therefore, as shown in Fig. 3a, magnetic field around membrane electrode assembly (MEA) is greatest and gradually decreases in the air. While it can be seen that in Fig. 3b–c that distribution and magnitude of magnetic field in PEMFC stack will vary because of the coupling effect of magnetic field due to each cell in the stack, where the magnetic field is greatest between two cells and the magnitude enhances. Moreover, as shown in Fig. 2, two points of polarization curve are selected, that is 1.01 A/cm2 at 0.4 V and 0.006 A/cm2 at 0.9 V, which denote the operation conditions with low and high current densities of PEMFC stack, whose magnetic field distribution are depicted in Fig. 3b–c. It can be observed that magnetic field distributions are constant while the magnitudes of magnetic field rise remarkably with higher current density.
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1.0 0.45
Voltage(V)
0.8 0.30 0.6 0.15
0.4
0.2
0
0.2
0.4
0.6
0.8
1.0
1.2
Power density(W/cm2)
Polarization curve Power curve
0
Current density(A/cm2) Fig. 2. The polarization and power curve of PEMFC stack model.
Fig. 3. Magnetic field distributions of PEMFC stack at different current densities. Arrows denote the direction of magnetic flux density, and color-bars denote the magnitude of magnetic flux density (similarly hereinafter). For better illustration, the scale factor of arrows in Fig. 3b increases, and the infinite element domain is hidden for ease of illustration and the air domain is divided into several pieces to facilitate mesh sweeping.
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Furthermore, to investigate magnetic field distributions of PEMFC stack at different states, Fig. 4 depicts the magnetic field distribution of PEMFC stack with different polarization curves, and magnetic field distributions are unchanging with PEMFC state variation.
Fig. 4. Magnetic field distributions of PEMFC stack at different states.
3.3 Influence of Cell Distance on Magnetic Field As the magnetic field distribution of PEMFC stack can be influenced by the coupling effect of magnetic field due to each cell, the influence of cell distance between two cells needs to be discussed in this section. In the analysis, the cell distance between two cells varies from 0 mm to 4.5 mm. Figure 5 depicts magnetic field distributions of PEMFC stack with various cell distances and to better illustrate the coupling effect of magnetic field, Fig. 6 shows these magnetic field distributions in xy section. In Figs. 5a and 6a, with the cell distance of 0 mm, the greatest magnetic field is collected at the intersection of two cells, where the magnetic field of two cells is maximum coupling and the magnetic field is highly concentrated around two cells. Figures 5b and 6b depicts that greatest magnetic field is observed at the cathode channel of upper cell and anode channel of lower cell with the cell distance of 1.5 mm, indicating the coupling effect is slightly reduced. In Figs. 5c and 6c, the coupling effect continues to weaken, that is the maximum magnetic field is around MEA, while the magnetic field between two cells is still larger than other areas below the lower
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cell and above the upper cell. From Figs. 5d and 6d, the magnetic field is still largest around MEA, while the magnetic field be-tween two cells decreases, and the magnitude of magnetic field drops, which indicates that the coupling effect basically does not exist with larger cell distance. Therefore, it can be concluded that the coupling effect will be weakened with large distance of two cells in the stack.
Fig. 5. The magnetic field distribution of PEMFC stack with various cell distances.
Fig. 6. Magnetic field distributions of PEMFC stack with various cell distances in xy section.
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4 Conclusion This paper proposes a three-dimensional, multi-component and multi-physics model, which clarifies the magnetic field distribution of the PEMFC stack, which is simulated by two single channel cells. Firstly, compared with magnetic field distribution due to a PEMFC, the coupling effect of magnetic field distribution in PEMFC stack is clarified, that is the greatest magnetic field is observed between two cells of PEMFC stack. Secondly, with developed PEMFC stack model, the magnetic field distributions at different current densities and states are investigated, where the distributions are constant while the magnitude will vary. Last but not least, the influence of the cell distance between two cells on magnetic field distribution is investigated, indicating that coupling effect will be weakened with the cell distance. The results can be utilized to monitor the operation state of PEMFC stack in the further researches. Acknowledgments. This work is supported by National Natural Science Foundation of China (NSFC) (Grant No. 51975549), Key R&D Plan of Anhui Province (Grant No. 202104h04020006), Anhui Provincial Natural Science Foundation (Grant No. 1908085ME161), Hefei Municipal Natural Science Foundation (Grant No. 2021022), and CAS Pioneer Hundred Talents Program.
References 1. Song, Q.C., Chen, J.W., Cai, K.C., et al.: A highly reliable power allocation technology for the fuel cell-battery-supercapacitor hybrid power supply system of a more electric aircraft. Trans. China Electrotech. Soc. 37(2), 445–458 (2022) (in Chinese) 2. ˙Inci, M., Büyük, M., Demir, M.H., et al.: A review and research on fuel cell electric vehicles: topologies, power electronic converters, energy management methods, technical challenges, marketing and future aspects. Renew. Sustain. Energy Rev. 137, 110648–110675 (2021) 3. Ifrek, L., Rosini, S., Cauffet, G., et al.: Fault detection for polymer electrolyte membrane fuel cell stack by external magnetic field. Electrochim. Acta 313, 141–150 (2019) 4. Le Ny, M., Chadebec, O., Cauffet, G., Rosini, S., Bultel, Y.: PEMFC stack diagnosis based on external magnetic field measurements. J. Appl. Electrochem. 45(7), 667–677 (2015). https:// doi.org/10.1007/s10800-015-0844-x 5. Akimoto, Y., Okajima, K.: Experimental study of non-destructive approach on PEMFC stack using tri-axis magnetic sensor probe. J. Power Energy Eng. 3(3), 1–8 (2015) 6. Nasu, T., Matsushita, Y., Okano, J., et al.: Study of current distribution in PEMFC stack using magnetic sensor probe. J. Int. Counc. Electr. Eng. 2(4), 391–396 (2014) 7. Haghayegh, M., Eikani, M.H., Rowshanzamir, S.: Modeling and simulation of a proton exchange membrane fuel cell using computational fluid dynamics. Int. J. Hydrog. Energy 42(34), 21944–21954 (2017) 8. Ubong, E.U., Shi, Z., Wang, X.: Three-dimensional modeling and experimental study of a high temperature PBI-based PEM fuel cell. J. Electrochem. Soc. 156(10), B1276–B1282 (2009) 9. Kwon, O.J., Shin, H.S., Cheon, S.H., et al.: A study of numerical analysis for PEMFC using a multiphysics program and statistical method. Int. J. Hydrog. Energy 40(35), 11577–11586 (2015) 10. Mohanty, S., Desai, A.N., Singh, S., et al.: Effects of the membrane thickness and ionomer volume fraction on the performance of PEMFC with U-shaped serpentine channel. Int. J. Hydrog. Energy 46(39), 20650–20663 (2021)
3D Modeling and Performance Analysis of a PEM Water Electrolyzer Based on Multiphysics Couplings Jihua Wang, Xiaming Ye(B) , Ruyi Qin, Haojin Qi, Fangyi Ying, Qi Li, Jiajie Yu, and Yueping Yang State Grid Zhejiang Electric Power Co., Ltd. Ningbo Electric Power Supply Company, Ningbo 315000, China [email protected]
Abstract. Hydrogen production by proton exchange membrane water electrolyzer (PEMWE) has a good match with wind power and photovoltaics, so in recent years, it has gradually become an important technology for large-scale comprehensive development and utilization of renewable energy. An analysis of the PEMWE modeling method is presented in this paper, and establishes a threedimensional model of the PEMWE single cell based on the coupling of multiphysics fields, including heat transfer, mass transfer, and electrochemical kinetics. We studied the effects of temperature, pressure, and membrane thickness on PEMWE performance, and determined the optimal configuration of PEMWE single cell based on polarization curves and material distributions in the electrolyzer. Based on the calculation and comparison, under the conditions of 80 °C and 40 bar, the PEMWE with 127 µm thick membrane provides better performance, can control costs and meets hydrogen safety standards. Keywords: PEM Water Electrolyzer · Multiphysics · 3D Modeling · Computational Fluid Dynamics
1 Introduction The application of energy storage technology to enhance the grid access rate of renewable energy generation has become a research hotspot in recent years as renewable energy capacity has grown. Among the preferred solutions for large-scale comprehensive power generation and storage, hydrogen as a clean energy source, has high capacity, large energy density, easy storage and transportation, and long life [1–3]. Water electrolysis is a mature method for producing hydrogen, and there are three types of water electrolysis hydrogen production technology: alkaline electrolysis (AE), proton exchange membrane water electrolysis (PEMWE), and solid oxide electrolysis (SOE) [4]. In contrast to the other two types of water electrolyzer, PEMWE conducts protons through a polymer film, which has a quick response to power fluctuations, good matching, which facilitates load changes, and high current density, which improves electrolysis efficiency significantly [5]. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 194–205, 2023. https://doi.org/10.1007/978-981-99-1027-4_21
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PEMWE’s internal structure and operation mechanism are complex, and its performance is affected by several factors, and many scholars have studied its numerical modeling. Omez et al. [6] summarized the PEMWE electrical domain numerical modeling studies in the last decade and concluded that most of the current models are built based on semi-empirical and empirical equations, and there are fewer models that consider the dynamic operation of electrolytic cells. The electrochemical processes in PEMWE cannot be accurately predicted by empirical modeling because it relies on simplifying assumptions and approximations. PEMWE modeling has been applied to computational fluid dynamics (CFD) models based on multi-physics fields coupling in recent years. Toghyani et al. [7, 8] compared the differences in temperature, pressure drop, gas concentration and current density of PEMWE under different flow fields by building a CFD model of PWMWE. Kaya et al. [9] studied the different anode catalysts using a CFD model and found that Pt-Ir catalyst as anode catalyst can obtain more hydrogen. Olesen et al. [10] used ANSYS to numerically analyze the two-phase flow in the flow field of a circular-planar high-voltage PEMWE anode, and the results showed that reducing the channel bending could improve the electrolyzer performance. The above CFD models are all two-dimensional, in terms of three-dimensional PEMWE modeling, according to Zhang et al. [11], a single-channel three-dimensional PEMWE model can be developed, which was used to investigate the impact of water flow direction and flow channel width on temperature distribution, water distribution, and gas distribution in electrolytic cells, and concluded that water heat transfer can be improved by reducing channel depth and increasing channel width. Ojong et al. [12] created a semi-empirical fully coupled model with a three-dimensional porous transport layer to simulate electrolytic cell operation with no flow field. In current PEMWE 3D modeling research, the majority of components, such as flow channels, are modeled locally, and electrolyzer performance analysis is carried out using semi-empirical models, which are not well integrated with CFD. This paper establishes a 3D model of the PEMWE single cell based on the coupling of multi-physics fields, including heat transfer, mass transfer, and electrochemical kinetics. Our study examined the effects of membrane thickness, pressure, and temperature on the performance of PEMWE, and determined the optimal configuration of PEMWE single cell based on polarization curves and material distributions in the electrolyzer. Based on the calculation and comparison, under the conditions of 80 °C and 40 bar, the PEMWE with 127 µm thick membrane provides better performance, can control costs and meets hydrogen safety standards.
2 Model Description 2.1 Basics of PEMWE and Geometric Model PEMWE single cells consist of polymer exchange bipolar plates (BP), gas diffusion layers (GDL), catalyst layers (CL), and a polymer exchange membrane (PEM). Figure 1 shows a schematic diagram of a PEMWE single cell. At the anode, DC voltage causes water to dissociate into oxygen, protons, and electrons. Protons migrate through the PEM
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and combine with electrons that are conducted from an external circuit on the cathode side to form hydrogen gas. The anodic reaction equation in Fig. 1 as follows: 2H2 O(l) → O2 (g) + 4H+ (aq) + 4e−
(1)
The cathodic reaction equation is: 4H+ (aq) + 4e− → 2H2 (g)
(2)
Fig. 1. Schematic diagram of a PEMWE single cell
Taking the single-channel serpentine flow field as an example, this study establishes the PEMWE single cell geometric model is developed as shown in Fig. 2, and Table 1 lists the detailed geometric parameters of the model.
Fig. 2. PEMWE single cell geometric model
2.2 Numerical Model In the analysis of the mathematical model for PEMWE, it is divided into three main physical fields: electrochemical kinetics, mass transfer, and heat transfer.
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Table 1. Geometry parameters of PEMWE single cell Geometry
Length (mm)
Width (mm)
Thickness (mm)
Anode/Cathode BP channels
19
1
0.5
Anode/Cathode GDL
20
20
0.2
Anode/Cathode CL
20
20
0.01
PEM
20
20
It will be changed
Electrochemical Kinetics. The operating voltage of a PEMWE single-cell consists of open circuit voltage V oc , activation voltage V act , concentration voltage V con , and ohmic voltage V ohm , expressed by the following equation [13]: Vcell = Voc + Vact +Vcon + Vohm The open circuit voltage can be calculated from the Nernst equation: √ aH2 aO2 RT Voc = E0 + ln 2F aH2 O
(3)
(4)
where R represents the general gas constant, F represents Faraday’s constant, and T represents the operating temperature. ax represents the activity of H2 , O2 and H2 O. E 0 represents the standard electric potential of the electrolyzer, and many scholars use 1.23 V as the value of E 0 . The actual standard electric potential is affected by the temperature of the external environment, which is expressed in this paper by the following equation: E0 = 1.229 − 0.9 × 10−3 (T − 298)
(5)
The activation voltage is caused by the slowness of the electrode reaction kinetics, using the Butler-Volmer equation for the electrode surface reaction, the current density in terms of activation voltage as follows: αan FVact αcat FVact − exp − (6) i = i0 exp RT RT where i0 denotes the exchange current density, α an and α cat denote the anode and cathode charge transfer coefficient. So the activation voltage can be expressed as follows: RT i i RT + (7) arcsinh arcsinh Vact = αan F 2ian,0 αcat F 2icat,0 Since the reactants on the surface of the porous electrode are consumed, the electrode surface will produce a concentration difference with the solution itself, so the reactants will slowly diffuse to the active site, causing a loss of electrolyzer voltage. Therefore, the concentration difference overpotential is essentially the external manifestation of particle diffusion, combining the Nernst equation with Fick’s law, the expression of concentration difference voltage is as follows: Vcon =
CO2 CH2 RT RT ln( ln( )+ ) 4F CO2 ,0 2F CH2 ,0
(8)
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where CO2 and CH2 denote the concentration of oxygen and hydrogen on the intersection of membrane and electrode, respectively, and CO2 ,0 and CH2 ,0 denote the reference values. Ohmic polarization arises from the resistance to ion flow and the equivalent resistance present in the electrodes and the bipolar plate itself. According to Ohm’s law, the ohmic voltage V ohm appears to be linearly proportional to the electrolytic current during electrolysis, as shown in the following equation: Vohm = (2RBP + 2RGDL + 2RCL +RPEM + Rin )iA
(9)
where A is the membrane area. The ohmic resistance of BP and GDL is calculated from the material resistivity, while CL and PEM are very thin, and the ohmic resistance is generally ignored. Rin represents the resistance of the ion in passing through the membrane, we use the study in the [14] to calculate in this paper: ⎧ δmem ⎪ ⎪ ⎨ Rin = σ mem (10) 1 1 ⎪ ⎪ ⎩ σmem =(0.005139λ−0.00326) exp 1268 − 303 T where δ mem , σ mem and λ denote the thickness, conductivity and water content of PEM respectively. Mass Transfer. When we describe the mass transfer of mixtures within a single cell of PEMWE., the mass conservation and momentum conservation equations are the focus of study [7]:
∇ · ερf V = 0 (11) ∇ · ερf VV = −ε∇p + ∇ · (εμV ) + Sv where ε denotes the porous medium porosity. μ and ρ f denote the mixture viscosity and average density. S v denotes the source term. V denotes the mixture volume average velocity [15]. A complex gas-liquid flow exists in the porous medium of the PEMWE single cell, with different convection and diffusion mechanisms for different components. This part can be described by Maxwell-Stefan equations:
(12) ∇ · (εVk Ck ) = ∇ · ε1.5 Dk ∇Ck + Sk where S k denotes the specie k mass source term. Dk and C k denote the k-th phase the effective diffusion coefficient and molar concentration material. And Dk is the function of temperature and pressure: Dk = Dk0
T T0
1.5
p0 p
where Dk0 denotes the binary component diffusion coefficient.
(13)
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Heat transfer. Electrochemical reactions and heat generation and consumption occur simultaneously during the operation of the PEMWE. While electrolysis of water is typically an endothermic process, in electrolysis cells there is a tendency for heat to be generated. Thus, the PEMWE is more complicated in terms of heat transmission. An electrolysis cell’s thermal equilibrium can be described by its energy equation: (14) ∇ · ρeff Cp,eff vk T = ∇ · (keff ∇T ) + ST where ρ eff denotes the effective density, C p,eff denotes the effective heat capacity, and k eff denotes the effective thermal conductivity, which can be calculated as: ⎧ ⎪ ⎨ ρeff = (1 − ε)ρs + ερf Cp,eff = (1 − ε)Cp,s + εCp,f (15) ⎪ ⎩ keff = (1 − ε)ks + εkf where ρ s and ρ f , represent the density heat of the solid areas and fluid mixture, C p,s and C p,f represent the density heat capacity of the solid areas and fluid mixture, and k s and k f represent thermal conductivity of the solid areas and fluid mixture. S T is the source term which can be calculated by [8]. In Table 2, the fixed parameters used in the model are summarized. Table 2. Fixed parameters used in the model Names
Parameters
Value
Unit
Faraday constant
F
96,486
C/mol
Gas constant
R
8.314
J/(mol·K)
Anode transfer coefficient
α an
0.5
–
Cathode transfer coefficient
α cat
0.5
–
Exchange current density at anode
ian,0
1 × 10–8
A/cm2
Exchange current density at cathode
icat,0
1 × 10–3
A/cm2
Membrane ion conductivity
σ PEM
10
S/m
GDL conductivity
σ GDL
530
S/m
Membrane porosity
εPEM
0.5
–
GDL porosity
εGDL
0.77
–
Membrane permeability
–
5 × 10–9
m2
GDL permeability
–
1 × 10–11
m2
Thermal conductivity of Membrane
k PEM
0.67
W/(m·K)
Thermal conductivity of GDL
k GDL
15.2
W/(m·K)
Thermal conductivity of H2
k H2
0.204
W/(m·K)
Thermal conductivity of O2
k O2
0.0296
W/(m·K)
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3 Results and Discussion From the numerical model analysis, it is clear that the pressure and temperature of PEMWE, the membrane thickness, and the flow of gas-liquid substances will directly affect the electrolyzer operating voltage and thus the efficiency. In this section, the degree of influence of the above aspects on the PEMWE operation is verified, and the parameter settings are shown in Table 3. Table 3. Parameters of numerical model Names
Value 1
Value 2
Value 3
Value 4
Operating temperature (°C)
25
10
50
80
Operating pressure (bar)
1
10
40
70
Membrane thickness (µm)
100
50
127
183
We validated the model using the “value 1” setting to derive the PEMWE single-cell polarization curve and compared it with the data from the experimental study by Weiß et al. [16] as shown in Fig. 3.
Fig. 3. PEMWE single cell model polarization curve (Value 1)
The experimental data basically fit the simulated curve, which proves the validity of the model. In the study of the effect of different factors, the “value 1” configuration was used as the control group, and only the currently studied factor was changed by the control variable method. 3.1 Operating Temperature PEMWE polarization curve are illustrated in Fig. 4 as a function of temperature. The electrolyzer’s performance improves when operating temperatures increase, as the voltage and electrical input decrease, and the input power also be reduced. As the
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Fig. 4. Effect of temperature on the polarization curve
temperature increases, the Gibbs free energy decreases, but enthalpy changes remain constant; therefore, at higher temperatures, less electricity is required to split the water. Additionally, the ohmic voltage reduces by increasing temperature as the catalyst layer’s reaction kinetics and the membrane’s conductivity improve. A high thermally stable Nafion membrane should be used in order to prevent membrane dehydration from excessive temperatures. Although temperature increases have a positive effect on the performance of the electrolzer, excessive temperature increases will result in membrane dehydration.
(a) 10 ℃
(b) 80 ℃
Fig. 5. Molar fraction of oxygen at PEMWE anode at different operating temperatures
With the same inlet water flow rate, we used the material molar fraction of oxygen on the anode side to compare the PEMWE operation at the same voltage (1.7 V was taken for this study) and different temperatures (as well as pressure and membrane thickness in the following), as shown in Fig. 5.The figure illustrates that the molar fraction of oxygen is 0.39 at 10 °C and 0.44 at 80 °C under 1.7 V operating voltage, so the higher the temperature the more water is cracked in the electrolyzer and the more
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hydrogen and oxygen are generated, further confirming that the performance of PEMWE is proportional to the operating temperature. 3.2 Operating Pressure The impact of operating pressure on the performance of PEMWE is illustrated in Fig. 6. As the pressure increases in the electrolzer, the size of gas bubbles decreases, resulting in lower surface shielding and a lower cell voltage. In other words, operating at higher pressures is beneficial for achieving PEMWE performance gains. Excessive cathode pressure, on the other hand, may cause hydrogen crossover phenomena, putting the electrolyzer’s safety at risk.
Fig. 6. Effect of operating pressure on the polarization curve
As shown in Fig. 7, the molar fraction of oxygen is 0.39 at 1 bar and 0.46 at 70 bar under 1.7 V operating voltage, the analysis for the PEMWE polarization curve is also verified.
(a) 1 bar
(b) 70 bar
Fig. 7. Molar fraction of oxygen at PEMWE anode at different operating pressures
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3.3 Membrane Thickness PEMWE’s polarizations curve is illustrated in Fig. 8 by decreasing membrane thickness, which improves electrolyzer performance. We used commercial Nafion 112 (50 µm), Nafion 115 (127 µm), and Nafion 117 (183 µm) as the materials for this study. As thicker membranes have greater ionic resistances, they transport hydrogen ions less efficiently and perform electrochemical reactions at a slower pace. Despite thinner membranes performing better, their stability decreases at low thicknesses. Moreover, the use of thicker PEM in the electrolyzer can reduce the effect of hydrogen crossover phenomenon and improve PEMWE safety.
Fig. 8. Effect of membrane thickness on the polarization curve
As can be seen in Fig. 9 film thickness has a huge impact on PEMWE performance, with PEMWE using Nation 112 having almost twice the molar fraction of oxygen on the cathode side as that using Nation 117.
(a) 1 bar
(b) 70 bar
Fig. 9. Molar fraction of oxygen at PEMWE anode at different operating pressures
According to the above analysis, higher operating temperature and pressure and thinner proton exchange membrane can lead to better performance and energy utilization of
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PEMWE without considering the cost and safety of hydrogen production. However, high temperature and pressure imply higher auxiliary equipment costs and are accompanied by problems such as membrane dehydration and hydrogen crossover. Meanwhile, proton exchange membranes with thickness less than 100 µm have lower strength and shorter lifetime, and are prone to penetration damage under extreme operating conditions.
4 Conclusion This paper establishes a three-dimensional model of the PEMWE single cell based on the coupling of multi-physics fields, including heat transfer, mass transfer, and electrochemical kinetics, investigates the effects of temperature, pressure, and film thickness on the hydrogen production performance of PEMWE, and the molar fraction of oxygen at the anode of PEMWE under different conditions was analyzed and compared. The following conclusions were drawn: • higher operating temperature and pressure and thinner proton exchange mem-brane can lead to better performance and energy utilization of PEMWE without considering the cost and safety of hydrogen production. • Combined with the actual engineering application, under the conditions of 80 °C and 40 bar, the PEMWE with 127 µm thick membrane provides better performance, can control costs and meets hydrogen safety standards. The three-dimensional PEMWE model based on the coupling of multiphysics fields established in this study has some general applicability and reference significance in electrolyzer modeling studies, and the effects of electrolyzer structure and operating conditions on cost and hydrogen safety will be further quantified subsequently. Acknowledgments. This work was supported by Science and Technology Projects of State Grid Zhejiang Electric Power CO., LTD(5211NB21N001).
References 1. Li, Z., Zhang, R., Sun, H., et al.: Review on key technologies of hydrogen generation, storage and transportation based on multi-energy complementary renewable energy. Trans. China Electrotech. Soc. 36(3), 446–462 (2021) (in Chinese) 2. Li, Q., Zhao, S., Pu, Y., et al.: Capacity optimization of hybrid energy storage microgrid considering electricity-hydrogen coupling. Trans. China Electrotech. Soc. 36(3), 486–495 (2021) (in Chinese) 3. Caparrós Mancera. J.J., Segura, F., Marquez. J. M. A.: Francisco José Vivas Fernández, & Antonio J. Calderón.: An optimized balance of plant for a medium-size pem electrolyzer: design, control and physical implementation. Electronics 9(871), 1–27 (2020) 4. Buttler, A., Spliethoff, H.: Current status of water electrolysis for energy storage, grid balancing and sector coupling via power-to-gas and power-to-liquids: a review. Renew. Sustain. Energy Rev. 82(3), 2440–2454 (2018)
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5. Falco, D.S., Pinto, A.: A review on PEM electrolyzer modelling: guidelines for beginners. J. Clean. Prod. 261, 121184 (2020) 6. Omez, A.G., Ramirez, V., Guilbert, D.: Investigation of PEM electrolyzer modeling: electrical domain, efficiency, and specific energy consumption ScienceDirect. Int. J. Hydrog. Energy 45(29), 14625–14639 (2020) 7. Toghyani, S., Afshari, E., Baniasadi, E.: Metal foams as flow distributors in comparison with serpentine and parallel flow fields in proton exchange membrane electrolyzer cells. Electrochim. Acta 290, 506–519 (2018) 8. Toghyani, S., Afshari, E., Baniasadi, E., et al.: Thermal and electrochemical analysis of different flow field patterns in a PEM electrolyzer. Electrochim. Acta 267, 234–245 (2018) 9. Kaya, M.F., Demir, N.: Numerical investigation of PEM Water electrolysis performance for different oxygen evolution electrocatalysts. Fuel Cells 17(1), 37–47 (2017) 10. Olesen, A.C., Romer, C., Kaer, S.K.: A numerical study of the gas-liquid, two-phase flow maldistribution in the anode of a high pressure PEM water electrolysis cell. Int. J. Hydrog. Energy 41(1), 52–68 (2016) 11. Zhang, Z., Xing, X.: Simulation and experiment of heat and mass transfer in a proton exchange membrane electrolysis cell. Int. J. Hydrog. Energy 45(39), 20184–20193 (2020) 12. Ojong, E.T., Kwan, J., Nouri-Khorasani, A., et al.: Development of an experimentally validated semi-empirical fully-coupled performance model of a PEM electrolysis cell with a 3-D structured porous transport layer. Int. J. Hydrog. Energy 42(41), 25831–25847 (2017) 13. Han, B., Steen, M.I., Mo, J., et al.: Electrochemical performance modeling of a proton exchange membrane electrolyzer cell for hydrogen energy. Int. J. Hydrog. Energy 40(22), 7006–7016 (2015) 14. Aubras, F., Deseure, J., Kadjo, J.J.A., et al.: Two-dimensional model of low-pressure PEM electrolyser: two-phase flow regime, electrochemical modelling and experimental validation. Int. J. Hydrog. Energy 42(42), 26203–26216 (2017) 15. Chen, Y., Mojica, F., Li, G., et al.: Experimental study and analytical modeling of an alkaline water electrolysis cell. Int. J. Energy Res. 41(14), 2365–2373 (2017) 16. Weiß, A., Siebel, A., Bernt, M., et al.: Impact of intermittent operation on lifetime and performance of a PEM water electrolyzer. J. Electrochem. Soc. 166(8), 487–497 (2019)
State of Health Estimation of Lithium-Ion Battery Considering Random Charging Wensai Ma1 , Jiangwei Shen1(B) , Chengzhi Gao1 , Zheng Chen1 , and Yonggang Liu2 1 Faculty of Transportation Engineering, Kunming University of Science and Technology,
Kunming 650500, China [email protected], [email protected] 2 State Key Laboratory of Mechanical Transmissions &, School of Mechanicaland VehicleEngineering, Chongqing University, Chongqing 400044, China [email protected]
Abstract. To address the problems of the random and incomplete charging process of the vehicle-mounted lithium-ion batteries, this paper proposes a machine learning method that can realize state of health (SOH) estimation under random charging conditions. Firstly, the complete voltage curve prediction in the constantcurrent (CC) charging phase under the short-term charging scenario is realized by constructing fitting polynomials, which effectively solves the problem of feature vector acquisition in short-term random charging scenarios. Then, the effects of charging durations of different constant-current charging voltage intervals on SOH estimation are compared to determine the feature vectors. The gaussian process regression (GPR) algorithm is employed to establish the SOH of the battery. Finally, the feasibility of the proposed voltage estimation method is verified at different aging cycles and in random charging scenarios, respectively. The effectiveness of battery SOH estimation based on short-term random charging data is verified. The results show that the proposed method has good feasibility with the SOH estimation error of less than 1.64%. Keywords: State of Health · Voltage Estimation · Gaussian Process Regression · Lithium-ion Battery
1 Introduction With the rapid development of electric vehicles, the lithium-ion battery has become the mainstream energy storage material due to its excellent performance [1]. However, with the continuous use of lithium-ion batteries, the performance of the battery can be affected by battery aging and capacity decline. When the SOH of the battery is below 80%, problems may occur, such as over-charge, over-discharge, thermal runaway, etc. Therefore, accurately estimating the SOH of the battery is beneficial to the evaluation of the operating state of the battery, and is of great significance to the safe use and full performance of the battery. At present, the common SOH estimation methods of lithium-ion batteries are mainly divided into three categories [2]: impedance analysis method, model-based method, machine learning method. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 206–215, 2023. https://doi.org/10.1007/978-981-99-1027-4_22
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The impedance analysis method uses changes in battery impedance characteristics to infer battery SOH [3], however, the specific correspondence still needs massive data to verify. The acquisition of battery impedance spectrum also relies on special equipment, it needs to take a long time. Therefore, the method of obtaining the battery SOH by only relying on the analysis of the battery impedance spectrum cannot be applied to the field of electric vehicles at present. The battery model-based method simplifies the battery into a basic battery model, and the battery SOH is predicted by observing the model parameters. The current battery models mainly include equivalent circuit models, electrochemical models and empirical models. The equivalent circuit model treats the battery as a basic circuit model, and predicts the battery SOH by observing the changes of key parameters [4]. The basic equivalent circuit models include Rint model, RC model and Thevenin model. Reference [5] simulates the battery characteristics through the equivalent circuit model, the SOH is obtained via the model parameters, and the accurate estimation of the SOH is realized by combining the Kalman filter algorithm. However, the equivalent circuit model is difficult to cover the full working conditions, and the SOH obtained often does not meet the requirements of EV battery management system well, and the model accuracy is relatively influenced by the parameter identification results and temperature. The electrochemical model is based on partial differential equations to realize the simulation of the internal mechanism of the battery [6], and the SOH is estimated by the model parameters. Common electrochemical models include the two-dimensional electrochemical model and the single-particle model. Reference [7] simplifies the partial differential equation by making reasonable assumptions, the optimization of the electrochemical model is completed, and the computational load of the model is reduced. However, the large number of partial differential equations causes the electrochemical model to be computationally intensive and it is difficult to identify the model parameters in real time, so the application to the actual vehicle battery management system is still limited. The machine learning method is based on a large amount of data to establish the mapping relationship between the battery SOH and measurable features. The establishment of mapping relation is one of the key points of machine learning method, and the mapping relation is usually achieved by choosing a suitable machine learning algorithm. Common algorithms include gaussian process regression (GPR), extreme learning machines (ELM), long and short-term memory (LSTM) neural networks, and their optimization algorithms [8]. Meanwhile, obtaining suitable feature variables reflected the changes of the SOH is also one of the key points of the machine learning approach [9]. The advantage of the method is that it does not rely on fixed physical or chemical models. Reference [10] extracts the features that characterize the change of SOH in the capacity increment curve, and uses the long short-term memory recurrent neural network as the basic model to achieve accurate SOH estimation. Reference [11] analyzes the relationship between the characteristics of the charging process and the aging of the battery, and uses four characteristics as the input of the GPR to achieve an accurate estimation of the battery SOH. However, machine learning methods often need to extract features from the complete charge/discharge process or a fixed charge/discharge interval, it does not meet the characteristics of random charging by users.
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To address the above problems, this paper proposes a SOH estimation method based on the stochastic charging process. The CC charging voltage distribution was estimated by polynomials and optimized using the whale optimization algorithm. The estimated voltage is used as an aid to obtain SOH estimation feature vectors in random charging scenarios, and SOH estimation considering random charging is achieved.
2 Voltage Estimation of the CC Charging Phase This section details the voltage estimation method, and the method is validated at different aging cycles and in different charging intervals. Battery data tested at MIT [12] are used for method validation and the cell is named cell 1. 2.1 Voltage Estimation Method The purpose of voltage estimation is to estimate the voltage distribution during the CC charging phase with short-term random charging data. First, the historical constantcurrent charging curve of battery 1 is fitted, the curves are fitted every 200 cycles from 1th cycle to 1000th cycle, as: Vn = fv (SOCk ) =
9
αi SOCk9−i
(1)
i=1
where Vn is the fitted curve, SOC is the state of charge, and αi is the polynomial coefficient. After obtaining Vn , the desired estimated voltage can be obtained by combining the coefficients αi , as: V = a1 V1 + a2 V2 + · · · + a6 V6
(2)
therefore, the optimal coefficients ai need to be obtained by a reasonable method. After obtaining the short-term CC charging voltage V0 , such as SOC range of [40%, 55%], V1 − V10 in Vn at the same point in time as V0 are obtained. The charging time of Vn can be estimated by the charging time of V0 . After getting V1 −V10 , the estimated value of V0 can be obtained: Ve = a1 V1 + a2 V2 + · · · + a6 V6
(3)
To provide a more accurate estimate of Ve , division of (3) based on estimation of the known SOH, as: ⎧ ⎨ Ve = a1 V1 + a2 V2 + · · · + a4 V4 SOH ≥ 95% (4) 94% ≤ SOH < 95% V = b1 V3 + b2 V4 + b3 V5 ⎩ e SOH < 94% Ve = c1 V4 + c2 V5 + c3 V6 where ai , bi , ci are the coefficients, and they are obtained by the whale optimization algorithm (WOA) due to its excellent optimized performance. The fitness function of the WOA is as follows: fit = RMSE + |K1 − K2 |
(5)
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where RMSE is the root mean square error, K1 , K2 denote the slope of the line connecting the first and the last points of the Ve and V0 . The whale counts and the iterations of the WOA are both set to 15, and the optimization boundary is set to [0,1]. When the fit is less than 0.001, optimization results are pulled. Then, the voltage of the CC phase can be estimated as: ⎧ ⎨ V = a1 V1 + a2 V2 + · · · + a4 V4 SOH ≥ 95% (6) 94% ≤ SOH < 95% V = b1 V3 + b2 V4 + b3 V5 ⎩ SOH < 94% V = c1 V4 + c2 V5 + c3 V6
2.2 Verification for Different Cycles To verify the effects of the proposed voltage estimation method, the voltages of the CC phase are estimated at different cycles and in different charging intervals. From 55th cycle to 955th cycle, the estimates are performed every 100 cycles, the results are plotted in Fig. 1, the RMSE errors of the estimations are shown in Table 1. It can be seen from Fig. 1, the nine estimated voltages are closely distributed around the measured value. According to the statistical results of RMSE in Table 1, the maximum root mean square error is 1.44%. The above results demonstrate that the proposed method performs well, the voltage distributions can be well estimated over the lifespan of the battery.
Fig. 1. Estimated voltages of CC charging phase of different cycles
2.3 Verification for Different Cycles To verify the effectiveness of the voltage estimation in random charging scenarios. Four SOC charging ranges [20%, 35%], [35%, 50%], [50%, 65%] and [65%, 80%] are selected
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Cycle
55
155
255
355
455
555
655
755
855
955
RMSE (%)
1.08
1.08
1.21
1.44
1.37
1.07
1.10
1.23
1.07
0.98
to estimate the voltage distribution during the CC charging phase of 300th cycle. The estimated voltages are shown in Fig. 2, and the RMSE errors are shown in Table 2. As can be seen from Fig. 2, the voltage estimations based on different charging SOC ranges have satisfactory effects. The estimated RMSE errors for the four voltage intervals are 1.28%, 1.01%,1.06% and 1.16%, respectively. The estimation results prove that the proposed voltage estimation method can achieve accurate estimations of the CC charging voltage when the user charges randomly.
Fig. 2. Estimated voltages of CC charging phase of different SOC range
Table 2. RMSE of estimated voltages of CC charging phase of SOC range Range (%)
[20, 35]
[35, 50]
[50, 65]
[65, 80]
RMSE (%)
1.28
1.01
1.06
1.16
3 SOH Estimation In this section, the detail and the implementation method of SOH estimation are introduced. The GPR algorithm is leveraged to build the base model. The charging durations for fixed voltage intervals are chosen as the feature vectors for SOH estimation. Finally, the effect of different feature vectors on SOH estimation is verified, and the feasibility of the proposed SOH estimation method in random charging scenarios is proved.
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3.1 Gaussian Process Regression Algorithm The GPR model is a nonparametric regression model based on gaussian process and Bayesian theory. In the training set: D = {xi , yi }m i=1
(7)
xi and yi are the feature vector and the corresponding estimated value, respectively. The y can be obtained from the implicit function of x and the observation noise ε, as: y = f (x) + ε,
ε ∼ N (0, σm2 )
(8)
where ε is gaussian noise with the mean value 0 and the variance σm2 . The f (x) was supposed to follow a priori gaussian distribution: ⎧ ⎪ ⎨ f (x) ∼ N (m(x), k(x, x )) (9) m(x) = E(f (x)) ⎪
⎩ k(xi , xj ) = E (f (xi ) − m(xi )) × f (xj ) − m(xj )
where m(x) is the mean value of the f (x), k(x, x ) is the covariance kernel function of f (x). In this paper, an isotropic rational quadratic covariance function and a linear kernel function are selected to form a composite kernel function. Then, the prior distribution can be transformed into a posterior distribution, the joint distribution of training output y and test output y* can be expressed as:
y K(x, x) + σm2 Im K(x,x∗ ) (10) ∼ N 0, K(x∗ ,x∗ ) K(x∗ , x) y∗ where Im is the identity matrix, K is the covariance matrix, x* is the test input. The posterior distribution can be expressed as: y∗ x, y, x∗ ∼ N y∗ |y∗ , cov(y∗ ) (11) y∗ = K(x, x∗ )T [K(x, x) + σm2 Im ]−1 y
(12)
cov(y∗ ) = K(x∗ , x∗ ) − K(x, x∗ )T [K(x, x) + σm2 Im ]−1 K(x, x∗ )
(13)
where y∗ is the estimated value of y* . cov(y∗ ) is the variance matrix of y* . To avoid the GPR algorithm from falling into local optimum and reduce the amount of computation in the training phase. The whale optimization algorithm (WOA) is exploited to optimize the hyperparameters of the GPR model for its satisfactory optimization effect.
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3.2 SOH Estimation Based on Different Voltage Ranges To verify the effects of different feature vectors on SOH estimation, three different sets of feature vectors are compared, and the parameters are shown in Table 3. Note that the first 50% of the data of cell 1 are used to train the model, and the remaining 50% data are used to test the model. The results of the SOH estimation are plotted in Fig. 3, and the estimation error are shown in Fig. 4. Moreover, the indicators of the errors are counted in Table 4. As can be seen from Fig. 3, when the three ranges are used as feature vectors, the proposed method completes the SOH estimation with the errors of less than 2%. Although the estimation accuracy of Range1 is slightly lower than that of Range2 and Range3, maximum error (ME), mean absolute error (MAE) and root mean square error (RMSE) are 1.64%, 0.37% and 0.47%. It demonstrates that the proposed method has good SOH estimation effect. Meanwhile, the best estimation results are obtained when Range2 are used as the feature vectors, and ME, MAE, RMSE are only 1.08%, 0.25%, 0.32%, respectively. Therefore, in the following validation, the Range3 is chosen as the feature vectors. Table 3. SOH estimation errors of different voltage ranges Range
Segment 1
Segment 2
Segment 3
Range 1 Range 2
[3V, 3.45V]
[3.1V, 3.45V]
[3.2V, 3.45V]
[3.2V, 3.5V]
[3.3V, 3.5V]
[3.4V, 3.5V]
Range 3
[3V, 3.5V]
[3.1V, 3.5V]
[3.2V, 3.5V]
Fig. 3. SOH estimation results of different voltage ranges
3.3 SOH Estimation in Random Charging Scenarios To verify the effectiveness of the proposed SOH estimation method in random charging scenarios. We assume that the battery is charged at three random SOC ranges [25%, 40%], [40%, 50%] and [50%, 70%], and named Range1, Range2, Range3 respectively
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Fig. 4. SOH estimation errors of different voltage ranges Table 4. SOH estimation errors of different voltage ranges Parameters
MAE (%)
ME (%)
RMSE (%)
Range 1
0.37
1.64
0.47
Range 2
0.26
1.06
0.33
Range 3
0.25
1.08
0.32
The CC charging voltages of 10 cycles are estimated based on the three charging SOC ranges, and the SOH are estimated based on the feature vectors extracted from the estimated voltage. The results of the SOH estimations are shown in Fig. 5, and the MAE errors are shown in Fig. 6 and Table 5. It can be seen in Fig. 5 that the estimated values distribute around the measured value, and the error is less than 1.5% in Fig. 6. According to the errors in Table 6, it is known that the maximum error of Range3 for cycle 555 is 1.26%. This shows the good feasibility of the proposed SOH estimation method considering random charging. The estimation results show that the proposed method can complete SOH estimation considering random charging, and the error remains within 1.64%.
Fig. 5. SOH estimation results of different voltage ranges
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Fig. 6. SOH estimation results of different voltage ranges
Table 5. MAE errors of SOH estimation Cycle
Range 1 (%)
Range 2
Range 3
55
0.12
0.19
0.22
155
0.18
0.43
0.36
255
0.14
0.05
0.04
355
0.16
0.28
0.17
455
0.33
0.47
0.51
555
0.27
0.26
1.26
655
0.25
0.33
0.15
755
0.36
0.18
0.46
855
0.86
0.20
0.80
955
0.44
0.50
0.20
4 Conclusion In this paper, a framework for SOH estimation considering random charging is proposed. First, the estimations of the voltages in the CC charging phase are completed based on the charging segment data. Then, the effects of different voltage ranges as feature vectors on SOH estimation are verified, and the optimal feature vectors are determined. Finally, the SOH estimation effects of the proposed method are verified based on the estimated voltage extraction features. Acknowledgments. This work is supported by the National Natural Science Foundation of China (No. 52162051).
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References 1. Lipu, M.S.H., Hannan, M.A., Hussain, A., Hoque, M.M., Ker, P.J., Saad, M.H.M.: A review of state of health and remaining useful life estimation methods for lithium-ion battery in electric vehicles: Challenges and recommendations. J. Clean. Prod. 205, 115–133 (2018) 2. Harper, G., Sommerville, R., Kendrick, E., Driscoll, L., Slater, P., Stolkin, R.: Recycling lithium-ion batteries from electric vehicles. Nature 575(7781), 75–86 (2019) 3. Li, X., Zhang, L., Wang, Z., Dong, P.: Remaining useful life prediction for lithium-ion batteries based on a hybrid model combining the long short-term memory and Elman neural networks. J. Energy Storage 21, 510–518 (2019) 4. Yang, S., Zhang, C., Jiang, J., Zhang, W., Zhang, L., Wang, Y.: Review on state-of-health of lithium-ion batteries: characterizations, estimations and applications. J. Clean. Prod. 314, 128015 (2021) 5. Vichard, L., Ravey, A., Venet, P., Harel, F., Pelissier, S., Hissel, D.: A method to estimate battery SOH indicators based on vehicle operating data only. Energy 225, 120235 (2021) 6. Wang, D., Zhang, Q., Huang, H., Yang, B., Dong, H., Zhang, J.: An electrochemical–thermal model of lithium-ion battery and state of health estimation. J. Energy Stor. 47, 103528 (2021) 7. Nejati Amiri, M., Torabi, F.: A computationally efficient model for performance prediction of lithium-ion batteries. Sustain. Energy Technol. Asses. 43, 100938 (2021) 8. Chen, L., Wang, H., Liu, B., Wang, Y., Ding, Y., Pan, H.: Battery state-of-health estimation based on a metabolic extreme learning machine combining degradation state model and error compensation. Energy 215, 119078 (2021) 9. Guo, Y., Huang, K., Hu, X.: A state-of-health estimation method of lithium-ion batteries based on multi-feature extracted from constant current charging curve. J. Energy Storage 36, 102372 (2021) 10. Chen, Z., Xue, Q., Wu, Y., Shen, S., Zhang, Y., Shen, J.: Capacity prediction and validation of lithium-ion batteries based on long short-term memory recurrent neural network. IEEE Access 8, 172783–172798 (2020) 11. Yang, D., Zhang, X., Pan, R., Wang, Y., Chen, Z.: A novel Gaussian process regression model for state-of-health estimation of lithium-ion battery using charging curve. J. Power Sour. 384, 387–395 (2018) 12. Severson, K.A., Attia, P.M., Jin, N., Perkins, N., Jiang, B., Yang, Z.: Data-driven prediction of battery cycle life before capacity degradation. Nat. Energy 4(5), 383–391 (2019)
Unified Control of Bidirectional H4 Bridge Converter in Single-Phase Energy Storage Inverter Yuyan Ju1 , Yu Fang1(B) , Xiaofei Wang1 , and Li Zhang2 1 College of Information Engineering, Yangzhou University, Yangzhou 225000, China
[email protected] 2 College of Energy and Electrical Engineering, Hohai University, Nanjing 210000, China
Abstract. The classic proportional integral (PI) controller will produce steadystate inaccuracy and poor anti-interference performance while following sinusoidal current commands. On this basis, this paper introduces a quasi proportional resonance (QPR) controller, in which the current inner loop is controlled by a QPR controller and the voltage outer loop is controlled by a PI controller. Firstly, the working principle of bidirectional H4 bridge converter under rectifier condition is analyzed, and the design method of double closed-loop control and its controller is given. The power flow direction of the converter is controlled by voltage regulator, and a set of bidirectional feasible control parameters is derived, that is, the unified control method of bidirectional H4 bridge converter is proposed, The stable control of bidirectional AC/DC in single-phase photovoltaic energy storage system is realized and good dynamic performance is obtained. Simulation and experiments show that the unified control method can realize the seamless switching between rectifier and active inverter. Keywords: H4 bridge converter · Unified control · QPR · Seamless switching
1 Introduction Photovoltaic energy storage system is widely used in microgrid and smart grid, which can promote the development of “carbon peak” and “carbon neutralization” [1–3]. In the single-phase photovoltaic energy storage inverter, H4 bridge topology is widely used in the bidirectional AC/DC circuit at the grid side because of its simple structure and low cost, so as to realize the bidirectional energy flow between the grid and the energy storage battery [4, 5]. Most references [6–10] designed the controller parameters of bidirectional AC/DC circuit in single-phase inverter mode to ensure the stable operation of the converter. Li et al. [6] proposes a bi-directional operation control method of modular AC/DC parallel system, which adopts split positive and negative voltage regulators to ensure the consistent power flow direction of parallel modules, and the rectifier and inverter operate at different DC bus voltages, resulting in seamless and smooth switching between them. Zhiyuan [7] proposes a variable parameter QPR digital control method, which increases © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 216–224, 2023. https://doi.org/10.1007/978-981-99-1027-4_23
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the bandwidth through the QPR controller to reduce the problem of grid side current and voltage phase synchronization caused by grid frequency offset [8]. However, since there is no sudden change in the energy storage in the circuit at the moment of circuit change, the reference of two sets of control parameters will have an oscillation with a delay of nearly 10ms, so the seamless switching between rectifier and inverter of bidirectional AC/DC circuit cannot be truly realized. Therefore, [9] proposed a uniform unipolar modulation method for bidirectional H6 bridge converter. Based on the stable control of DC bus voltage loop, the bidirectional energy flow of bidirectional H6 bridge converter is realized. However, it is not analyzed whether the control parameters of the voltage regulator are suitable for the rectifier state, and the bandwidth is very narrow, which cannot meet the dynamic response performance of rectifier and inverter state switching of bidirectional AC/DC circuit. Therefore, this paper studies the unified control method of rectification and inverter for the bidirectional H4 bridge converter of single-phase photovoltaic energy storage inverter. The QPR controller introduced in the current inner loop should be suitable for Rectifier and Inverter modes. For the voltage outer loop, the single-phase H4 bridge converter has different control models in the rectification operation and the inverter operation mode, so the rectification operation mode is analyzed and its mathematical model is established. Based on the power balance Methods, the open-loop transfer function of the rectifier is deduced, and the method for setting the parameters of the voltage outer-loop PI controller is obtained. The voltage outer loop control parameters of the single-phase H4 bridge converter in the rectifier mode are substituted into the model in the inverter mode for verification and optimization, and the grid-connected inverter and rectifier operation modes of the single-phase H4 bridge converter are realized. The switch is used to verify the feasibility and correctness of the unified control method. The remainder of this paper is organized as follows. After Sect. 2, The rectifier principle of single-phase H4 bridge converter is introduced, which lays a foundation for the design of controller. Then, in Sect. 3, the controller design and analysis are illustrated. Section 4 shows the results of the simulation and experiment. Finally, in Sect. 5, the paper’s conclusion is drawn.
2 Rectification Operating Principle of Single-Phase H4 Bridge Converter The main circuit structure of H4 bridge converter is shown in Fig. 1. According to the functional requirements of energy storage inverter, H4 bridge bidirectional converter can work in inverter state and rectifier state.
3 Control Method of Bidirectional H4 Bridge Converter In this paper, the bidirectional H4 bridge converter in single-phase photovoltaic energy storage inverter adopts the double closed-loop control of voltage outer loop and current inner loop.
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idc
+
+ V1
is L uac
VD1
V3
V1
VD3
is
a
Cdc
C
L
R L Vdc
uac
VD1
V3
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E
Cdc
R L Vdc
a
C b
b V2
VD3
V4
V2
VD4
VD2
V4
VD4
−
−
(b)
(a)
Fig. 1. Bidirectional H4 bridge topology. a Rectifier state. b Inverter state
3.1 Modeling and Control of Current Inner Loop The control block diagram of the current inner loop of single-phase H4 bridge converter is shown in Fig. 2. kif iref +
− is
1+Tss kpwm 1+0.5Tss
1
+ −
uac
is
rL+Ls
Fig. 2. Approximate block diagram of current loop structure
The current closed-loop transfer function can be derived, which can be described as: kpwm 1 )( ) 1 + 0.5Ts · s L · s + rL kif 2Kr ωc s ( )(KP + 2 ) 1 + Ts · s s + 2ωc s + ω02
Gi_open_reg (s) = (
(1)
When considering that the current inner loop requires fast current following performance, the current regulator can be designed in accordance with the representative type I system, and the zero point of QPR regulator can offset the pole of the transfer function of the current control object [10]. Considering the above factors, the parameters of QPR controller are determined as K p = 1.6, K r = 100, ωc = 5 rad/s. As shown in Fig. 3. The corrected current loop phase angle margin is 63.7°, and the amplitude margin is 32.8 dB, which meets the design requirements. The current inner loop modeling method during inverter operation is the same as that under rectifier operation, so the QPR controller can adopt the same control parameters. 3.2 Parameter Tuning of Voltage Outer Loop Controller Based on Power Balance G(s) is the transfer function from the control of single-phase H4 bridge rectifier to the output, and Gc (s) is the voltage controller.To design Gc(s), the expected open-loop model Q(s) is chosen based on the characteristics of G(s). m 1 + Tp S Q(s) = (2) Gc (s) = G(s) KTz S(1 + Tz S)
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Fig. 3. Regulated current closed loop Bode diagram
In order to ensure that the bandwidth of the voltage control loop is much lower than that of the current tracking control loop, and realize the complete tracking of current, the open-loop bandwidth of the voltage control loop should be less than 1/5 of the switching frequency. Here, the bandwidth of the voltage control loop is 156 rad/s, and it is known from Eq. (2) that the bandwidth is equal to m/T z , T z = 0.00008, so that m = 0.012. In this topic, the output filter capacitor is larger and the power capacity of the converter is smaller, so T z 0, E (n) = E (n − 1) + P (n)tη ESS D i ESS ESS
(8)
In the equation, EESS (n − 1) is the energy of the n−1th sequence of energy storage; PESS (n) is the charging and discharging power of the nth sequence of energy storage; t is the duration of each time the energy storage is charged and discharged; ηc is the discharging efficiency of the energy storage; ηD is the charging efficiency of the energy storage. (6) Energy balance constraints for energy storage plants, i.e.
T
Pstore (i) · t = 0
(9)
i=1
The equation t is the duration of each charge/discharge of the energy storage; P store (i) it represents the charge/discharge power of the energy storage system at the first moment i. 2.3 Economic Analysis (1) Investment cost of energy storage
CESS (i) = Cicc (i) + CRc (i) + COm (i)
(10)
(2) Peak and valley reduction benefits of energy storage
CHpc (i) =
24 365
(M (k)EESS (i, j, k))
(11)
j=1 k=1
where CESS (i) is the investment cost of energy storage; M (k) is the initial construction cost of energy storage, which appears only in the first building year of energy storage k; EESS (i, j, k) is the renewal cost of energy storage; and is the operation and maintenance cost of energy storage.
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(3) Grid loss gains from energy storage
CLOSS (i) =
24 365
(M (k)ELOSS (i, j, k))
(12)
j=1 k=1
where, CLOSS (i) denotes the net loss gain from energy storage; M (k) represents the price of electricity at the first hour k of the day; ELOSS (i, j, k) denotes the value of the net loss as the energy storage charge and discharge power changes at the first hour of the first day of the year. (4) Total cost of energy storage
CA = CESS (i) + CHpc (i) + CLOSS (i)
(13)
where CA represents the total cost of energy storage.
3 Adaptive Multi-target Particle Swarm 3.1 Adaptive Inertia Weights In multi-objective particle swarm algorithms, the selection of the value of inertia weights has a significant impact on the convergence of the operation results. When using inertia weights, the values are often subjective and lack some scientific guidance due to the neglect of the particles’ own characteristics. Therefore, the position vector of the particle is difference from the selected global optimum solution of the population and is reflected by the resulting difference. 3.2 Crossover Variation The specific steps are shown below. (1) Determine Xmin , crossover rate pc and variation rate pm . (2) Determine the size i of the first particle Xi and compare it with Xmin that of the first particle, if Xi < Xmin , then do the crossover variation for the first particle, otherwise end the crossover variation directly. (3) The crossover operation is done for the particle that has completed the mutation, and the position component is introduced rid . If rid < pc , then the first dimension of the position vector d is crossed, and the crossover object is the global optimal solution.
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3.3 Non-disadvantageous Solution Set Update After solving for the dense distance of the Pareto solution, the solution set needs to be sorted by dense distance, and the solution set is updated and appropriately filtered using a retention and removal method that compares the size of the solution with that of the desired solution one by one. 3.4 Multi-attribute Decision Making Based on TOPSIS Method The multi-objective particle swarm algorithm results in a Pareto solution set, which needs to be compared to select the optimal solution, using preference information as the basis for analysis. Therefore, the TOPSIS method, based on information entropy, is introduced to select the optimal solution set. 3.5 Problem Solving The flow chart of the improved particle swarm algorithm in this paper is shown in Fig. 1.
Start
Inialize the populaon posion and velocity variables Calculate the objecve funcon value of each parcle according to equaons (1), (2) and (3) and put it into the non-inferior soluon set Determine the historical opmal soluon and the global opmal soluon for each parcle Update the velocity and posion components of each parcle according to (15)(16)
Variant crossover operaon on parcles
Selecng the global opmal soluon N Meet the terminaon condions? Y Output the opmal Pareto soluon set
Determine the opmal access scheme and capacity configuraon using TOPSIS method
Economic analysis according to secon 2.3
End
Fig. 1. Distribution grid shared energy storage plant site selection flow chart
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4 Analysis and Study of Algorithms In this paper, a distribution system with IEEE-33 nodes [10] is used as an example for theoretical verification. The planning period of energy storage is set as 10 years, and the initial construction cost, renewal cost and annual maintenance cost are 2.5, 2.5, 0.05 Yuan/(MWH) respectively. In the simulation, 200 kW PV is connected at nodes 8 and 21, and 200 kW wind power is connected at nodes 25 and 32 (Fig. 2).
19 20 21 22 1
2 3
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23 24 25
6
7
8
9 10 11 12 13 14 15 16 17 18
26 27 28 29
30 31 32 33
(a) IEEE-33-node
(b) Load
(c) WP and PV
Fig. 2. IEEE-33-node distribution network system and Typical daily characteristic curves of WP, PV and load output
4.1 Simulation Analysis 4.1.1 Energy Storage Location, Capacity and Economic Analysis See Table 1. Table 1. Comparative analysis of energy storage location, capacity and economic benefits Number Optimal Energy Energy Peak shaving Net loss of energy Location Storage Power storage revenue/million gain/million storage Capacity/MW investment yuan yuan access cost/million yuan
Total cost/ million yuan
1
15
1.0
2800
−465.3
100.1
2434.8
2
17 33
0.5 0.5
2800
−959.3
100.1
1940.8
3
17 26 33
0.5 0.5 0.9
5861
−1193.5
100.2
4767.8
4
2 12 20 33
0.5 0.5 0.5 1.1
7287
−1926.3
100.3
5461.4
As can be seen from the table, it is fully demonstrated that the economics of access to 2 energy storage is better. The following is a specific analysis of access to 2 battery energy storage systems.
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4.2 Access to 2 Battery Energy Storage Systems Analysis • Node voltage fluctuation analysis Through the curves, it is obvious that the overall voltage level after optimization does improve to some extent, with an average voltage increase of about 0.82% at each moment of node 17 and an average voltage increase of about 1.1% at each moment of node 32. Table 2 shows the voltage fluctuation, load fluctuation and network loss before and after the energy storage configuration. The data show that the voltage fluctuation and load fluctuation are significantly reduced after the configuration of the energy storage system, with a decrease of 56.32% and 74.33%, respectively, and the network loss is also reduced, by about 16.51%. The above data show that the energy storage system can, to a certain extent, have a good suppression effect on node voltage, load fluctuation and network loss (Fig. 3). Table 2. Optimization results before and after energy storage configuration Optimization Goals
Voltage fluctuations/pu
Load fluctuation/pu
Network loss/MW
Before energy storage configuration
2.45
3.35
2.12
After energy storage configuration
1.07
0.86
1.77
(a) node 17
(b) node 32
Fig. 3. Voltage variation at each moment of node 17 and 32
5 Conclusion (1) When the energy storage system is connected in the distribution network, the node voltage level is improved and the voltage deviation is further reduced, which proves that the energy storage system can effectively suppress the system voltage deviation to a certain extent. (2) When two battery energy storage systems are connected to the distribution network, the economic benefits can be maximized. The investment cost of energy storage increases with the increase of the number of accesses, the benefit of energy storage
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peak shaving and valley filling also increases with the increase of the number of accesses of energy storage, and the difference of energy storage network loss benefit is not large. (3) The optimal access location and capacity configuration of the battery storage system is 0.5MW for node 17 and 0.5MW for node 32.
Acknowledgements. This research is supported by Beijing Natural Science Foundation Project (NO.21JC0026); The project was supported by the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network, Nanjing Institute of Technology (No. XTCX202208) and Innovation and entrepreneurship topics for college students (108051360022XN296).
References 1. Li, J.L., Wang, Z., Zeng, W., et al.: A review of energy management research on 100 MWscale electrochemical energy storage power plants [J/OL]. High Voltage Technology, 1–15 (2022). https://doi.org/10.13336/j.1003-6520.hve.20211835. Author, F., Author, S.: Title of a proceedings paper. In: Editor, F., Editor, S. (eds.) Conference 2016, LNCS, vol. 9999, pp. 1–13. Springer, Heidelberg (2016). (in Chinese) 2. Shujun, Z., Xiao, Q., Cong, B.: A multi-application scenario-oriented approach for optimal configuration of energy storage systems. Zhejiang Electr. Power 41(5), 22–31 (2022). https:// doi.org/10.19585/j.zjdl.202205004 (in Chinese) 3. Zheng, C., Wu, Y„ Chen, Y., Ye, J., Zheng, T., Wei, L., Wu, S.: Energy storage system siting and capacity determination based on non-dominated sorting improved bat algorithm. Power Supply 38(10), 107–115 2021https://doi.org/10.19421/j.cnki.1006-6357.2021.10.014 (in Chinese) 4. Jianlin, L., Zhonghao, L., Yaxin, L., Haitao, L.: The development status of lithium battery energy storage system modeling and its preliminary discussion on data-driven modeling. Oil Gas New Energy 33(4), 75–81 (2021) (in Chinese) 5. Zhang, Y., Dai, F.: A new scheme for feeder protection in distribution networks with distributed power sources. Power Syst. Autom. 33(12), 71–74 (2009) (in Chinese) 6. Huang, D.Q., Mithulananthan, N.: Community energy storage and capacitor allocation in distribution system. In: 21st Australasian Universities Power Engineering Conference, September 25–28, 2011, Brisbane, Australia:6p. (in Chinese) 7. Celli, G., Mocci, S., Pilo, F., et al.: Optimal integration of energy storage in distributed energy storage devices in smart grids. In: IEEE Power Tech Conference, June 28–July 2, 2009, Bucharest, Romania:7p 8. Carpinelli, G., Celli, G., Mocci, S., et al.: Optimal integration of distributed energy storage devices in smart grids. IEEE Trans. Smart Grids 4(2), 985–995 (2013) 9. Ghofrani, M., Arabali, A., Etezadi-Amoli, M., et al.: A framework for optimal placement of energy storage units within a power system with high wind penetration. IEEE Trans. Sustain. Energy 4(2), 434–442 (2013) 10. Ramirez-Rosado, Dominguez-Navarro.: New multi-objective tabu search algorithm for fuzzy optimal planning of power distribution systems. IEEE Trans. Power Syst. 21(1), 224–233 (2006)
Coupling Forecasting of Short-Term Power Load and Renewable Energy Sources Generation Based on State-Space Equations Jinzhong Li1 , Yuguang Xie1 , Hu Wang2(B) , and Lei Mao2,3 1 State Grid Anhui Electric Power Research Institute, Hefei, China 2 Precision Machinery and Precision Instrumentation, University of Science and Technology of
China, Hefei, China [email protected], [email protected] 3 Institute of Advanced Technology, University of Science and Technology of China, Hefei, China
Abstract. As the global energy transition accelerates, renewable energy sources are now widely used in power system. Consequently, accurate forecasting of shortterm power load demand and renewable energy sources generation (photovoltaic and wind power) play a key role in energy management system (EMS), power market and grid-building integration. Currently, a large number of separated models about short-term power load demand and renewable energy sources generation forecasting have emerged, while the coupling effect between photovoltaic and wind power hasn’t been considered, which will affect the forecast accuracy. To fill this gap, this paper proposes a physically interpretable coupling forecasting model to explore the coupling relationship, which contains state-space equations and error correction model. The state-space equations investigates the coupling relationship and the error correction model learns the transfer relationship of the forecast error. The numerical results on public datasets show that the proposed method holds great promise, and the proposed forecast model can effectively explore the coupling relationship between short-term power load and renewable energy sources generation, thus can provide accurate and efficient predictions. Keywords: Coupling forecasting model · State-space equations · Error correction model · Power system · Short-term power load and renewable energy sources generation forecasting
1 Introduction The penetration rate of renewable energy sources is increasing with the promulgation of low-carbon policies and the severe depletion of fossil fuel in the power system, this has promoted the rapid development of integrated energy systems (IESs), which is considered to be an efficient way to accommodate large-scale renewable energy sources and achieve environmental sustainability. Renewable energy sources, e.g., solar and wind, not only have been recognized as novel solutions to the aforementioned issues, © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 234–241, 2023. https://doi.org/10.1007/978-981-99-1027-4_25
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but also are an important part of IESs. However, renewable energy sources are well known to be intermittent and uncertain, which makes them non-dispatchable energy sources. In order to balance energy supply and demand in an energy management system (EMS) of IESs, short-term power load demand and renewable energy sources generation (photovoltaic and wind power) must be forecasted with good quality for cooperating with other energy sources, such as energy storage systems (ESS). Furthermore, accurate forecasting of short-term power load demand and renewable energy sources generation can also beneficial for improving power quality and maintaining safe and stable operation of the power system. With the improvement of computer processing ability and the advancement of artificial intelligence (AI), a set of univariate prediction models have been proposed, including single model, ensemble model, and hybrid model. In terms of short-term power load prediction, Yang et al. [1] proposed an interval decomposition-ensemble technology to reduce the complexity of the hybrid model. Zheng et al. [2] applied Kalman filter-based bottom-up approach for predicting short-term load. Wang et al. [3] proposed decomposition and denoising strategy to improve prediction accuracy, but in the strategy, future prediction is only affected by its historical behavior. Sharma et al. [4] proposed blind Kalman filter algorithm within the framework of expectation maximization and allowed on-the-fly forecasting. Wang et al. [5] developed a multi-energy load prediction model based on deep multi-task learning and ensemble approach, where the impact of renewable energy sources generation is not considered. On the other hand, regarding short-term renewable energy sources generation, Shi et al. [6] dynamically extracted the spatiotemporal features of photovoltaic power station based on the GeoMAN model, which was then used for better forecast accuracy. Eseye et al. [7] proposed a hybrid forecasting model combining wavelet transform, particle swarm optimization and support vector machine to improve forecast accuracy. Wang et al. [8] applied data cleaning and feature reconfiguration methods based on multidimensional data to improve the accuracy of short-term wind power prediction. Plessis et al. [9] combined state-of-the-art deep learning and unique inverter-clustering technique to capture low-level utility-scale photovoltaic system behavior. Ye et al. [10] proposed an ensemble learning method based on rolling error correction strategy, which aimed to improve the accuracy and generalization ability of the short-term wind power prediction model. However, among the above studies, either the short-term power load demand or renewable energy sources generation is considered in the prediction, the coupling effect between them is ignored, which may affect the prediction performance. Since in IESs, different energy types are not only related to their own historical data, but also have coupling relationship among them, for example, that photovoltaic and wind power can also affect power load demand, and vice versa. To address the above issue, this paper proposes a physically interpretable coupling forecasting model to explore the coupling relationship between the short-term power load demand and renewable energy sources generation, which contains state-space equations and error correction model. The state-space equations investigates the coupling relationship, and the error correction model learns the transfer relationship of the forecast error.
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The rest of this paper is organized as follows: Section 2 expounds the proposed coupling forecasting model. Section 3 explains the experimental settings and data, and demonstrates effectiveness of the proposed method for coupling forecasting and provides discussion. Section 4 is the conclusion.
2 Methodology This section proposes a physically interpretable coupling forecasting model to explore the coupling relationship in the multi-variable forecasting. The methodology consists of two components. Firstly, state-space equations is developed for investigating the coupling relationship, and a parameter estimation algorithm based on historical data is proposed to estimate unknown coefficients in the state-space equations. Moreover, an error correction model is designed for learning the transfer relationship of the forecast error. 2.1 State-Space Equations In order to quantitatively describe the coupling relationship between multi-variate variables, the following state-space equations is applied, for time k = 1,…, K: X˙ (k) = AX (k) + BU (k)
(1)
Y (k) = CX (k) + DU (k)
(2)
Moreover, Eqs. (3) and (4) are proposed to simplify Eqs. (1) and (2), from which Eq. (5) is derived. X (k + 1) = X˙ (k)
(3)
Y (k) = X (k)
(4)
X (k + 1) = AX (k) + BU (k)
(5)
X (k) = [x1(k), x2(k), x3(k)]
(6)
where X(k) is the multi-variate matrix, composed of short-term power load demand (x1(k)) and renewable energy sources generation (x2(k) stands for wind power, x3(k) stands for photovoltaic power). A is the time-varying state transition matrix, which is used to describe the coupling relationship between multi-variate variables. U(k) is the input signal of the system (forecast error) and B is the control matrix of the system input signal, which are used to learn the transfer relationship of the forecast error (generally, forecast error is zero mean, which means that U(k) is equal to zero), this will be further explained in Sect. 2.2. Therefore, with known A, the forecast can be successfully provided with Eq. (5). However, in practical situations, A is unavailable, thus estimation technique is usually required.
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In this study, a parameter estimation algorithm based on historical data to estimate unknown coefficient A is proposed, the solution, which relies on historical data in a time window (L), can be inferred as below. [X (k), · · · , X (K − L)] = A[X (k − 1), · · · , X (K − L − 1)]
(7)
M = [X (k), · · · , X (K − L)]
(8)
N = [X (k − 1), · · · , X (K − L − 1)]
(9)
Equation (7) is further modified using Eqs. (8) and (9), and the parameter estimation algorithm can be calculated as: −1 A = MN NN
(10)
At the time step k, the parameter is estimated with Eq. (10) only rely on the past L observations, in a sliding-window manner. It is worth noting that if A is calculated as a diagonal matrix from Eq. (10), which means that there is no coupling relationship between the multi-variate variables. In other words, in such scenario, photovoltaic and wind power cannot affect power load demand, and vice versa. 2.2 Error Correction Model In the sliding-window manner, it is assumed that the forecast error at time step k can affect the forecast accuracy at time step k + 1. With this in mind, we propose the error correction model to learn the transfer relationship of the forecast error. Although the mean forecast error equals to zero over a long operating period, the forecast error, U(k), will fluctuate at each moment. The error correction model consists of two parts: (i) calculate the forecast error U(k) at time step k with Eq. (11), where U(0) is set to zero at the initial time; (ii) bring the U(k) into Eq. (5) to forecast the values at time step k + 1, where B is defined to 1. U (k) = Error(k) = X (k) − X (k)
(11)
−1 X (k + 1) = MN NN X (k) + X (k) − X (k)
(12)
where X represents the forecasted value, and X represents the actual value. Equation (12) is the derived coupling forecasting algorithm, which combines the coupling relationship (the first component) and error correction (the second component). It should be mentioned that since the proposed model does not require large amount of historical data, compared to artificial neural networks (ANN) and machine learning (ML), the proposed model is computational efficient. Therefore, the proposed method can be used for providing online and accurate prediction. The illustration of the coupling forecasting model proposed in this paper based on state-space equations and error correction mode is shown in Fig. 1.
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Multivariate data (X) Time k-2 k-1 k k+1
Coupling relationship
Error correction
State transition matrix A N A(3x3) M
Input X and A Initialize k and U(k) Calculate the U(k) by Eq. (11)
N M
Output forecast Forecast value X (k +1) Power load demand Wind power Photovoltaic power
Correct forecasting error by Eq. (12)
Fig. 1. Illustration of coupling forecasting model proposed in this paper.
3 Result and Discussion In this study, to verify the effectiveness of the proposed method, an open-access dataset used in previous studies [11] is selected, which is Belgium’s 2021 actual power load demand and renewable energy sources generation data (photovoltaic and wind power) from Elia, with the interval of 15 min, as shown in Fig. 2. As can be seen, power load demand and photovoltaic power have periodicity, but wind power shows random trend. In addition, their peaks and valleys appear almost at the same time, which confirms the coupling effect exists between power load demand and renewable energy sources generation.
Fig. 2. Belgium’s power load demand and renewable energy sources generation data for December 2021.
In the analysis, the length of the sliding-window is determined with time-varying properties of the state transition matrix A, and the smaller the L, the stronger the timevarying, thus the L is simply chosen to be 1 herein. In order to reflect the prediction performance of the proposed model, the mean absolute percentage error (MAPE) and the normalized root mean square error (NRMSE) are selected as indicators [12], which
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are written as follows: 1 |xi − xi | × 100% n xi i=1 n 1 (xi − xi )2 n n
MAPE =
NRMSE =
i=1
max(xi ) − max(xi )
(13)
× 100%
(14)
3.1 Coupling Relationship The coupling relationship is described by the state transition matrix A, described in Sect. 2. If A is a diagonal matrix calculated from Eq. (10), it means that there is no coupling relationship between multi-variate variables, and each variable only affects its own forecast, no contribution to the forecast of remaining variables. To visually describe the coupling relationship, a heat map generated with the value in A is utilized to depict coupling effect between multi-variate variables. The result is shown in Fig. 3. In the figure, the darker the blue color is, the greater the value becomes. Figure 3a shows a non-diagonal relationship, which indicates that x(1) has significant effect on the forecast of x(2) and x(3). Nevertheless, x(2) and x(3) have small effect on the forecast of x(1). This can be explained by that only the power load demand has a great effect on the forecast of photovoltaic and wind power. To further demonstrate the coupling effect, Fig. 3b shows that a heat map generated with the A of a model with independent variables. As shown in the figure, only diagonal entries have significant values, which indicates that each variable has no effect on the forecast of the other variables. The reason for this phenomenon is that the coupling relationship is not considered in separated forecast models. In conclusion, it can be validated that the proposed model can reflect the coupling relationship, which cannot be captured in separated forecast models.
(a)
(b)
Fig. 3. The composition of the coefficients of the state transition matrix A: a A is calculated by the proposed model, b A is calculated by separated forecast models.
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3.2 Analysis of Forecast Results The proposed model is validated with an open-access dataset, and Fig. 4 depicts forecast results on the typical day. It can be seen from Fig. 4 that accurate forecast performance can be obtained using the proposed method. Furthermore, Table 1 lists MAPE and NRMSE of forecast results, and the errors are within acceptable range (less than 4%), which achieves lower error compared to the separated forecast models in [13]. Compared to renewable energy sources generation, power load demand achieves the best accuracy on MAPE explained by strong periodicity so that the proposed model has better application prospects in power system. However, it should be noticed that the forecasted value fluctuates around the actual value in Fig. 4, thus it can be inferred that the filtering and smoothing algorithm can be applied to further improve the forecast accuracy, which is worthy of further study. Besides, the forecast horizon and temporal granularity are limited to a single step, which restricts the long-term application of the proposed model. Therefore, in the future, the coupling forecasting model should be further developed for higher accuracy, finer temporal granularity, and longer forecast horizon.
(a)
(b)
(c)
Fig. 4. Results of the single step forecasting on typical day: a Power load demand, b Wind power, c Photovoltaic power.
Table 1. Forecast error based on the proposed model. Forecast variable
MAPE (%)
NRMSE (%)
Power load demand
0.8508
3.5106
Wind power
3.3923
2.1967
Photovoltaic power
1.3418
1.3078
4 Conclusion In this study, a coupling forecasting model is proposed to demonstrate coupling relationship between power load demand and renewable energy sources generation, which can reduce forecast error from previous studies using separated forecast models. The
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proposed model consists of two components, state-space equations is proposed for investigating the coupling relationship, and an error correction model is designed for learning the transfer relationship of the forecast error. Due to the simplicity of proposed model, it has great potential to be used for online forecasting scenarios. Acknowledgments. This work is supported by State Grid Corporation of China Science and Technology Project (Grant No. SGAHDK00DJJS2200281), National Natural Science Foundation of China (NSFC) (Grant No. 51975549), Key R&D Plan of Anhui Province (Grant No. 202104h04020006), Anhui Provincial Natural Science Foundation (Grant No. 1908085ME161), Hefei Municipal Natural Science Foundation (Grant No. 2021022), and CAS Pioneer Hundred Talents Program.
References 1. Yang, D., Guo, J.-E., Sun, S., Han, J., Wang, S.: An interval decomposition-ensemble approach with data-characteristic-driven reconstruction for short-term load forecasting. Appl. Energy 306, 117992–118007 (2022) 2. Zheng, Z., Chen, H., Luo, X.: A Kalman filter-based bottom-up approach for household short-term load forecast. Appl. Energy 250, 882–894 (2019) 3. Wang, J., Gao, J., Wei, D.: Electric load prediction based on a novel combined interval forecasting system. Appl. Energy 322, 119420–119438 (2022) 4. Sharma, S., Majumdar, A., Elvira, V., Chouzenoux, E.: Blind Kalman filtering for short-term load forecasting. IEEE Trans. Power Syst. 35(6), 4916–4919 (2020) 5. Xuan, W., Shouxiang, W., Qianyu, Z., Shaomin, W., Liwei, F.: A multi-energy load prediction model based on deep multi-task learning and ensemble approach for regional integrated energy systems. Int. J. Electr. Power Energy Syst. 126, 106583–106598 (2021) 6. Shi, M., Wang, J., Yin, R., Zhang, P.: Short-term photovoltaic power forecast based on grey relational analysis and GeoMANModel. Trans. China Electrotech. Soc. 36(11), 2298–2305 (2021). (in Chinese) 7. Eseye, A.T., Zhang, J., Zheng, D.: Short-term photovoltaic solar power forecasting using a hybrid Wavelet-PSO-SVM model based on SCADA and Meteorological information. Renew. Energy 118, 357–367 (2018) 8. Wang, S., Li, B., Li, G., Yao, B., Wu, J.: Short-term wind power prediction based on multidimensional data cleaning and feature reconfiguration. Appl. Energy 292, 116851–116862 (2021) 9. du Plessis, A.A., Strauss, J.M., Rix, A.J.: Short-term solar power forecasting: Investigating the ability of deep learning models to capture low-level utility-scale photovoltaic system behaviour. Appl. Energy 285, 116395–116410 (2021) 10. Ye, L., Dai, B., Li, Z., Pei, M., Zhao, Y., Lu, P.: An ensemble method for short-term wind power prediction considering error correction strategy. Appl. Energy 322, 119475–119490 (2022) 11. Public dataset website. https://www.elia.be/en/grid-data. Last Accessed 18 Aug 2022 12. Sobri, S., Koohi-Kamali, S., Rahim, N.A.: Solar photovoltaic generation forecasting methods: a review. Energy Convers. Manag. 156, 459–497 (2018) 13. Lin, J., Ma, J., Zhu, J., Cui, Y.: Short-term load forecasting based on LSTM networks considering attention mechanism. Int. J. Electr. Power Energy Syst. 137, 107818–107827 (2022)
Active Equalization of Lithium Battery Based on WOA and FLC Algorithm Zhongan Yu, Junling Zhang(B) , and Zezhou Hu School of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Jiangxi Ganzhou 341000, China [email protected], [email protected], [email protected]
Abstract. A novel active equalization circuit based on ring structure is proposed to solve the problems of over equalization, slow equalization time and inconsistent equalization energy of lithium-ion battery packs. The structure adopts distributed equalization of multiple inductors to quickly realize energy transfer between batteries. The battery state of charge is selected as the equilibrium variable, and the optimization path model is established through the Whale Optimization Algorithm (WOA) to integrate the state of charge. On this basis, the fuzzy control system adjusts the active equalization current according to the input current and input voltage. In order to verify the effectiveness of the proposed topology, the simulation is carried out in the software, and six lithium-ion batteries are built for the equalization experiment. The results show that compared with the traditional structure, it can effectively reduce the inconsistency of the battery pack. Keywords: Battery management · Battery equalization · Whale optimization algorithm · Fuzzy logic control algorithm · Buck-Boost circuit
1 Introduction Lithium battery as the core component of electric vehicle They have the advantages of high safety, long life, and low cost [1]. Overcharge or overdischarge of battery cells will reduce the life of the entire battery pack, increase the aging speed, and may even cause safety problems [2]. In order to improve the endurance and service life of electric vehicles during operation, the most effective way is to add the equalization function to the BMS [3]. The equalizer can be divided into energy consumption type and non energy consumption type according to the way of energy transfer [4]. The energy type uses a switch to intervene the resistance in the circuit, which has low cost but potential safety hazards. The non energy consumption type circuit mainly uses a resistor in parallel at both ends of the battery module, and the excess energy is dissipated through the resistor. Energy transfer circuits mainly rely on inductors, capacitors or transformers to store and transfer excess energy to batteries with low energy. This paper proposes an improved Buck-Boost circuit and makes it select a shorter transmission path in the equalization process, thereby improving energy utilization. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 242–249, 2023. https://doi.org/10.1007/978-981-99-1027-4_26
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2 Equalizing Circuit Topology Buck-Boost circuits require low-cost components, strong scalability, and high equalization efficiency [5, 6]. Energy is transferred between two adjacent batteries through the inductance or capacitance of the energy storage element, as shown in Fig. 1.
Q10 Is
B1
Q1 L1
B2 L5
Q2
B3
Q3 L2
B4
Q4
B5
Q5 L3
B6
Q6
Q9
Q8 L4 Q7
Fig. 1. Conventional Buck-Boost equalization topology circuit
For this reason, this paper designs an active equalization circuit based on a ring structure, as shown in Fig. 2.
Q13
Q14
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Q1 L1
Q10 B2 L5
Q2
Q9
B3
Q3 L2
Q8
B4 L4
Q4
L6 Q11
Q12
Q7 B5 B6
L3
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Fig. 2. Improved Buck-Boost equalization topology circuit
In the structure, B1 and B6 are adjacent through L6, assuming that B1SOC > B6SOC to analyze the equilibrium process: (1) Q13 is turned on, and the battery B1, Q13, L6, and Q14 form a discharge loop. (2) Q12 is turned on, and the battery B6, Q11, L6, and Q12 form a charging loop.
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3 Circuit Equilibrium Strategy and Algorithm This paper proposes a balanced energy path optimization based on the whale optimization algorithm [7, 8], the path optimization model is established based on the battery state of charge to maximize energy utilization and minimize the distance. Fuzzy logic control algorithm (FLC) [9–12] is an intelligent control strategy based on language variables and anti fuzzy controller. 3.1 Energy Balance Path Optimization Based on Whale Algorithm The algorithm is divided into two steps [13]: (1) Search and surround prey Each whale represents a separate individual. The position of whales falls randomly in the set search space. The optimization strategy is used to update the self position and estimate the prey position to achieve convergence to the optimal position. The expression is: − → · X ∗ (t) − X (t) = C (1) D − → ·D X (t + 1) = X ∗ (t) − A
(2)
= 2a · r − a A
(3)
= 2r C
(4)
and C are coefficient vectors, t is the number of iterations, and X ∗ (t) is the current A optimal position. a is a linearly varying convergence factor, and r is a random vector between 0 and 1. (2) Bubble network attack The humpback whales do spiral ascending motion, and at the same time they spit out bubbles of different sizes to surround the prey. The expression is: − → − → X (t + 1) = X ∗ (t) + D · ebl · cos(2π l)
(5)
− → − → D = X ∗ (t) − X (t)
(6)
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Assuming that the probability of each behavior pattern is 50%, the next iteration model is expressed as: − − → → X ∗ (t) + D · ebl · cos(2π l), p ≥ 0.5 (7) X (t + 1) = − → · D, p < 0.5 X ∗ (t) − A Since humpback whales depend on the positions of other whales in the random search process, when A ≥ 1, it means that the whales’ moving position is not near the prey, and new positions are searched by random direction To find more suitable prey. Its position updating formula is: · Xrand (t) − X (t) = C D (8) ·D X (t + 1) = Xrand (t) − A
(9)
In this paper, WOA is used to optimize the battery energy balance path, as shown in Fig. 3. S2 = E2 + S1
S1 E1
E2
Si = Ei + Si −1 E6
E3
S 3 = E3 + S 2 E5
S5 = E5 + S4
E4
S 4 = E4 + S3
Fig. 3. Closed-loop path diagram
The average charge state of n batteries is: SOC =
(SOC1 + SOC2 + · · · + SOCn ) n
(10)
The difference between the battery state of charge of section i and the average battery state of charge is: Ei = SOCi − SOC , i = 1, 2, ..., n (11) When Ei < 0, the inductor charges the battery in section i; At Ei > 0, the inductor is charged by the battery in section i. The SOC transfer amount of battery in section i is: S1 , i = 1 (12) Si = Ei + Si−1 , i = 2, 3, ..., n The sum of energy transferred by battery SOC is: Ssum = |S1 | + |S2 | + · · · + |Sn |
(13)
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Use WOA algorithm to find S1 , and then the optimal value of Ssum is obtained by iteration, so as to obtain the optimal solution of the equilibrium energy path. Set WOA algorithm iteration parameter to 20 and stop when the maximum number of iterations is reached. In the loop based active equalization circuit, set SOC1 = 97% , SOC2 = 84% , SOC3 = 82% , SOC4 = 81% , SOC5 = 80% , SOC6 = 79% . The optimization result is shown in Fig. 4. The global optimal solution is 24.5%. The optimal energy transmission path strategy is B1 charging 8.66% to B2, B2 charging 8.83% to B3, B3 charging 7% to B4, B4 charging 4.17% to B5, B5 charging 0.34% to B6, B1 charging 4.49% to B6.
Fig. 4. Iterative process of WOA algorithm
3.2 Fuzzy Logic Control Strategy In this paper, there are two inputs in FLC, namely, the average battery charge SOC and the difference SOCdif , which are expressed as: SOC =
(SOCi + SOCi+1 ) 2
SOCdif = |SOCi − SOCi+1 |
(14) (15)
The membership function of fuzzy linguistic variables is a triangular membership function. The field values of SOC, SOCdif and Ieq are set to [0,1], [0,1] and [0,5] respectively. The fuzzy subsets of the last time duty cycle and output duty cycle are defined as NB, NS, Z0, PS, and PB. Fuzzy logic rule is shown in Table 1.
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Table 1. Fuzzy logic rule table Ieq
SOCdif
SOC
NB
NS
Z0
PS
PB
NB
NB
NS
Z0
PS
PS
NS
NS
Z0
PS
PS
PB
Z0
Z0
PS
PS
PB
PB
PS
NS
Z0
PS
PS
PB
PB
NB
NS
Z0
PS
PS
(1) When both inputs are small, the output decreases to improve the equalization speed and prevent battery overcharge and overdischarge. (2) When both inputs are large, the output increases to reduce the equalization time. (3) When both inputs are larger than one hour, the output is medium. The result obtained by the defuzzer is generally a fuzzy set, which needs to be converted into an executable precise value. Its expression is: z ∗ λzdz (16) Ieq = λzdz
4 Simulation Results and Analysis Build a battery simulation system model in MATLAB/simulink. Figures 5 and 6 are respectively experimental diagrams of the battery pack static equilibrium of the improved topology circuit and the traditional topology circuit. In the static state, the improved circuit needs 455 s to complete the equalization, and the traditional circuit needs 645 s to complete the equalization. The battery energy conversion efficiency is calculated in the static state, conversion efficiency of the improved circuit is 2.42% higher than that of the traditional circuit. The energy efficiency calculation formula is as follows: 6 SOCB (i) (17) δ = i=1 6 i=1 SOCA (i) SOCA (i) is the SOC value of the i-th cell before balancing, and SOCB (i) is the SOC value of the i-th cell after balancing.
5 Conclusion The whale algorithm is used to optimize the path in the ring based active equalization topology circuit, which improves the energy utilization by 2.42%. In equalization, fuzzy control algorithm is used to control the current required for equalization. Experiments show that the topology can achieve rapid equalization between batteries, and shorten the balanced energy transfer path, which proves the effectiveness of the scheme.
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Fig. 5. Improved Buck-Boost circuit topology
Fig. 6. Topology of conventional buck-Boost circuit
Acknowledgments. This research was partially funded by the Project of Jiangxi Provincial Department of Education under grant GJJ150678, and by Jiangxi Postgraduate Innovation and Entrepreneurship Special Fund Project (XY2021-S102).
References 1. Wang, J., Xiong, R., Mu, H.: Co-estimation of Li-ion battery capacity and capacity for electric vehicles driven by the integration of temperature and aging awareness. J. Electr. Technol. 35(23), 4980–4987 (2020) (in Chinese) 2. Zhang, X., Xu, Y., Xiao, X.: High power density resonant cascaded H-bridge solid state transformer suitable for medium and high voltage distribution network. J. Electrotech. Technol. 33(2), 310–321 (2018) (in Chinese)
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3. Liu, Z., Xia, D., Yao, L., Yang, K.: Research on active equalization scheme of lithium battery pack based on coupling winding. J. Electr. Mach. Contr. 25(2), 54–64 (2021) (in Chinese) 4. Omariba, Z.B., Zhang, L., Sun, D.: Review of battery cell balancing methodologies for optimizing battery pack performance in electric vehicles. IEEE Access (99), 1–1 (2019) 5. Liu, B„ Li, L.,Q., Ye, C., Li, J.: A new and efficient multifunctional buck/boost/buckboost power factor correction circuit. Power Grid Technol. 45(3), 1142–1149 (2021) (in Chinese) 6. Cai, M., Zhang e, Lin, J., Wang, K., Jiang, K.: Zhou min Overview of equalization topology of series lithium ion battery pack. Chin. J. Electr. Eng. 41(15), 5294–5311 (2021) (in Chinese) 7. Shi, Y., Li, J., Ren, J., Zhang, K.: Prediction of remaining service life of lithium ion battery based on WOA xgboost. Energy Stor. Sci. Technol. 1–12 (2022). (in Chinese) 8. Li, J., Zhang, W., Zhao, X., Liu, B., Zheng, Y.: Sss improved whale algorithm to optimize support vector regression for photovoltaic maximum power point tracking. J. Electrotechn. Technol. 36(9), 1771–1781 (2021) (in Chinese) 9. Ma, Y., Duan, P., Sun, Y., et al.: Equalization of lithium-ion battery pack based on fuzzy logic control in electric vehicle. IEEE Trans. Ind. Electron. 1–1 (2018) 10. Zhang, Z., Du, W., Liang, J., Zhang, Y., Wu, Y.: Research on layered control of loader based on fuel cell composite power supply. J. Beijing Univ. Aeronaut. Astronaut. 1–15 (2022) (in Chinese) 11. Ridong, Z., Jili, T., Huiyu, Z.: Fuzzy optimal energy management for fuel cell and supercapacitor systems using neural network based driving pattern recognition. IEEE Trans. Fuzzy Syst. 27(1), 45–57 (2019) 12. Wang, B., Qin, F., Zhao, X., et al.: Equalization of series connected lithium-ion batteries based on back propagation neural network and fuzzy logic control. Int. J. Energy Res. 44(6) (2020) 13. Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)
Bi-level Optimal Sizing and Scheduling of Hybrid Thermal Power-Energy Storage System for Peak Shaving Deng Yang1 , Guo Xu1 , Bao Yusheng1 , Chen Feixiang1 , Chen Xiaoxia1 , Zhou Sheng1 , Yan Shiye2 , and Ye Jilei2(B) 1 Huaneng International Power Jiangsu Energy Development Co., Ltd. Nantong Power Plant,
Nantong 226003, China 2 Nanjing Tech University, Nanjing 211800, China
[email protected]
Abstract. The targets of peaking carbon dioxide emissions and carbon neutrality can be achieved by the large-scale penetration of renewable power production, but the intermittent nature of renewable sources imposes a burden on the operating stability of power system. To improve the peak-shaving capability of power system, a bi-level optimal sizing and dispatch model for hybrid coal-fired power-energy storage system considering different electrochemical energy storage technologies is proposed. The lower-layer scheduling model minimizes the operational cost of thermal power units and penalty cost for unmet load and wind curtailment, while the upper-layer sizing model minimizes the investment cost of energy storage and the overall scheduling cost, which is solved by an iterative method nested with quadratic programming. Finally, the results show that (1) the inclusion of energy storage can eliminate the unmet load and improve power supply reliability; (2) Nickel-Cadmium battery is the most cost-effective option for peak-shaving operation because of its high depth of discharge and long design lifetime; (3) The economic sensitivity analysis of rated power and capacity verifies the optimality of sizing results. Keywords: Coal-fired power plant · Energy storage · Peak shaving · Hierarchical optimization · Quadratic programming · Sensitivity analysis
1 Introduction The large-scale penetration of renewable power production is beneficial to alleviate the depletion of non-renewable fuels and mitigate the environmental problems such as global warming, sea level rising and climate change [1]. Meanwhile, the development of renewable energy is also crucial to achieve the dual-carbon goals [2]. However, the penetration of intermittent and volatile wind power will present a challenge to the operating reliability and stability of the power system, as well as lead to severe energy curtailment [3]. The pattern of wind power is reverse to that of load demand, so higher peak-valley gap of the net load will be originated from its integration [4]. To promote the proportion of renewable energy in the power system, higher regulated capacity is required for © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 250–261, 2023. https://doi.org/10.1007/978-981-99-1027-4_27
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traditional thermal power plants, while frequent and deep peak-shaving regulation will significantly increase its operational cost and even cause damage to the healthy condition of coal-fired power units [5]. Fortunately, energy storage (ES) can decrease the peak-valley gap of the net load via charging and discharging process, so it can operate coordinately with coal-fired power units and alleviate the peak-shaving stress [6]. Thus, how to determine the coordinated energy management strategy of hybrid thermal power-ES system is essential to achieve the regulation of the net load in a cost-effective way. Many researchers investigated the peak-shaving operation of coal-fired power plants. Gu et al. [7] reviewed the peak regulation of coal-fired power units in China, and policy recommendations were proposed to mitigate the peak-shaving challenges and ensure the sustainability of modern power system. Wang et al. [8] analyzed the peak-shaving operational flexibility of coal-fired combined heat and power plants and established a scheduling model from the plant-level perspective. Xue et al. [9] conducted the multicriteria thermodynamic analysis of a coal-fired power plant with pump-thermal electrical ES for peak-shaving application. Wang et al. [10] utilized steam turbine ES to formulate a novel flexibility improvement method for thermal power plants to achieve the large-scale integration of renewable energy. Besides, some researchers investigated the optimal sizing of ES in power systems. Li et al. [11] proposed an ES optimal sizing model in the application of auxiliary peakshaving regulation. He et al. [12] conducted a multi-objective capacity optimization of off-grid hybrid renewable energy systems with four typical ES technologies. Javed et al. [13] assessed the technical and economic performance of an autonomous power system, and optimized the component sizes with genetic algorithm. However, none of the aforementioned literatures investigated the bi-level optimal sizing and peak-shaving scheduling of coal-fired thermal power-ES hybrid system considering different types of batteries, and the quantitative techno-economic comparison of different ESs was rarely conducted in the scenario of auxiliary peak-shaving operation. On the basis of the above research gaps, a bi-level optimal sizing and peak-shaving scheduling model of coal-fired power plant with different batteries is proposed, including Lead-acid battery, Lithium-ion battery and Nickel-Cadmium battery. Then, the techno-economic performance of different batteries is quantitatively compared, and the economic sensitivity analysis of sizing is conducted to verify the optimality.
2 System Configuration The configuration of the coal-fired thermal power-ES hybrid system is shown in Fig. 1. ES can charge the excess electricity from wind power in valley load, and then discharge the stored electricity to supply the peak load, thus alleviating the peak-shaving stress of thermal power plant as well as improving the power supply reliability via the power time-shifting characteristics.
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Thermal power plant Loads
Wind power
Energy storage
Fig. 1. The configuration of hybrid thermal power-ES system.
3 Optimization Model The schematic diagram of the bi-level sizing and operation optimization model is shown in Fig. 2. The detailed objective functions and constraints of the proposed bi-level model are introduced as below. Sizing of energy storage
Upper-layer: optimal sizing model Economic parameters
Lower-layer: optimal operation model Wind power Load profiles
Technical parameters
Sizing parameters
Decision variables Rated power of energy storage Rated capacity of energy storage
Decision variables Output of thermal power units and wind power Charging / discharging power of energy storage
Objectives Minimization of the investment cost and operational cost in lower-layer model
Objective Minimization of the operational cost of thermal power units and penalty cost
Solver: Iterative method
Solver: Quadratic programming Optimal operational cost
Fig. 2. The schematic diagram of the bi-level optimization model.
3.1 Objective Function of Lower-Layer Model The optimal scheduling considers the minimization of the power generation cost of thermal power units, penalty cost for wind curtailment and penalty cost for unmet load. The lower-layer objective function and detailed components are separately illustrated as below. objlower = Cth + PCwc + PCum
(1)
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Cth =
T N t
2 ai Pth.i.t + bi Pth.i.t + ci
253
(2)
i
PCwc = λwc
T
Pwc.t
(3)
Pum.t
(4)
t
PCum = λum
T t
where, objlower is the lower-layer objective. Cth is the operating cost of thermal units. PCwc is the penalty cost for wind curtailment. PCum is the penalty cost for unmet load. Pth.i.t is the units power output at time t. ai , bi and ci are the cost factors of units. N is the number of units. T is the simulation duration. λwc is the unit penalty cost for wind curtailment. Pwc.t is the wind curtailment. λum is the unit unmet load penalty cost. Pum.t is the unmet load. 3.2 Constraints of Lower-Layer Model The lower-layer constraints include operational constraints of thermal power units and ES, as well as the energy balance constraints, which are described as below. (1) Operational constraints of thermal power units uth.i.t Pth.i. min ≤ Pth.i.t ≤ uth.i.t Pth.i. max
(5)
max |Pth.i.t − Pth.i.t−1 | ≤ Pth.i
(6)
where, Eq. (5) ensures that thermal power units operate within the operational range. The maximum ramp rate of coal-fired thermal power units is constrained by Eq. (6). uth.i.t is a binary variable showing on or off. Pth.i. min and Pth.i. max are the units minimum max is the units maximum ramp rate. and maximum power output. Pth.i (2) Operational constraints of ES 0 ≤ Pes.c.t ≤ ues.c.t Pes
(7)
0 ≤ Pes.d.t ≤ ues.d.t Pes
(8)
ues.c.t + ues.d.t ≤ 1
(9)
Ees.t = Ees.t−1 + ηes.c Pes.c.t t −
Pes.d.t t ηes.d
(10)
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(1 − DOD)Ces ≤ Ees.t ≤ Ces
(11)
where, Eqs. (7) and (8) are the ES operating constraints. Equation (9) ensures that ES cannot charge and discharge simultaneously. Equation (10) describes the renovation of ES. Equation (11) is the ES capacity constraints. ues.c.t and ues.d.t are the ES operating binary variables. Ees.t is the available energy of ES. Pes.c.t and Pes.d.t are the ES charging and discharging power of ES at time t. ηes.c and ηes.d are the ES charging and discharging efficiency. t is the simulation timescale. DOD is the depth of discharge. Pes and Ces are the ES rated power and rated capacity. (3) Energy balance constraint N
uth.i.t Pth.i.t + Pw.t + ues.d.t Pes.d.t − ues.c.t Pes.c.t − Pum.t − Pwc.t ≥ Pload .t
(12)
i
where, Eq. (12) ensures the supply-demand balance. The left side of the energy balance constraint is the decision variables of lower-layer scheduling model. 3.3 Objective Function of Upper-Layer Model The optimal sizing minimizes the investment cost of ES as well as the overall cost in lower-layer model. The upper-layer objective function is described as below. objupper = Cinv + objlower Cinv =
(λes.p Pes + λes.c Ces ) 365
life x
(13) (14)
(1 + disc)x−1
where, Cinv is the ES amortized investment cost. λes.p and λes.c are unit ES power and capacity investment cost respectively. life is the ES design lifetime. disc is the discount rate. 3.4 Constraints of Upper-Layer Model The upper-layer constraints include the power and capacity constraints for ES, which are illustrated as below. Pes. min ≤ Pes ≤ Pes. max
(15)
Ces. min ≤ Ces ≤ Ces. max
(16)
where, Pes. min and Pes. max are the ES minimum and maximum allowed rated power. Ces. min and Ces. max are the ES minimum and maximum allowed rated capacity. Pes and Ces are the decision variables of upper-layer sizing model.
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4 Results and Discussion 4.1 Data Descriptions To validate the proposed bi-level optimal sizing and dispatch model and investigate the ES impact on the peak-shaving operation of coal-fired thermal power units, several cases are comprehensively conducted and compared in this work. The wind power and load profile [6] are shown in Fig. 3. The case settings and system descriptions are stated in Table 1. The technical and economic parameters of different batteries are shown in Table 2. The boundary condition parameters are shown in Table 3.
Fig. 3. The wind power and load profile.
Table 1. The case setting and system descriptions. Case settings
System descriptions
Case 1
10 thermal power units without ES
Case 2
10 thermal power units with Lead-acid battery
Case 3
10 thermal power units with Lithium-ion battery
Case 4
10 thermal power units with Nickel-Cadmium battery
Table 2. The technical and economic parameters of different batteries [14]. Battery type
ηes.c /ηes.d
DOD
λes.p ($/MW)
λes.c ($/MWh)
Lead-acid
0.85
50%
0.233
0.213
4
Lithium-ion
0.95
50%
0.233
1.27
15
Nickel-Cadmium
0.90
85%
0.233
0.8
20
life (a)
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Parameters
Value
Unit
λwc
10000
$/MWh
λum
10000
$/MWh
Pes. min ∼ Pes. max
[50, 500]
MW
Ces. min ∼ Ces. max
[500, 5000]
MWh
disc
8%
–
4.2 Optimization Results Setting the iterative steps of the rated power and capacity of ES as 50 MW and 500 MWh respectively, Table 4 shows the optimal sizing and operation results of different cases. Figure 4 presents the cost breakdown of different cases. The total cost of Case 1 (without ES) is the largest at 10.278 · 106 ·$, because of the considerable penalty cost for unmet load. The total cost of other three cases (with ES) is lower than the figure for Case 1 even though the investment cost of ES is added, indicating that the inclusion of ES can efficiently reduce the penalty cost for unmet load. The total cost of Case 4 (with Nickel-Cadmium battery) is the lowest at 3.282 · 106 $, followed by the figure for Case 2 (with Lead-acid battery). The investment cost of Case 3 (with Lithium-ion battery) is significantly higher than that of Case 2 and Case 4 because of the highest unit cost. The economically optimal sizing for Nickel-Cadmium battery is (150 MW, 1500 MWh), lower than the figure for Lead-acid and Lithium-ion battery (200 MW, 200 MWh). The investment cost of Nickel-Cadmium battery is thus the lowest due to the highest depth of discharge and the longest design lifetime. Overall, Nickel-Cadmium battery is the most cost-effective option for peak-shaving operation of coal-fired thermal power-ES hybrid system. Table 4. The optimal simulation results of different cases. Case
Total cost (106 $)
Cth (106 $)
PCum (106 $)
PCwc (106 $)
Cinv (106 $)
Pes (MW)
Ces (MWh)
Case 1
10.278
0.640
9.638
0
0
–
–
Case 2
3.499
0.662
0.485
0
2.353
200
2000
Case 3
5.641
0.658
0
0
4.983
200
2000
Case 4
3.282
0.660
0.548
0
2.074
150
1500
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Fig. 4. The cost breakdown of different cases.
4.3 Operation Analysis Figure 5 presents the optimal operation of different cases. There is unmet load in Case 1 during the peak period 10:00 ~ 21:00, because the load demand is greater than the maximum output of thermal power units and wind power. Concerning Case 2 ~ Case 4, ES can be charged by the excess wind power during the valley period 23:00 ~ 8:00 and 16:00 ~ 17:00, and it can discharge the stored electricity to reduce or avoid the occurrence of unmet load during the peak period. Lithium-ion battery can completely eliminate the unmet load because of its higher round-trip efficiency and depth of discharge. Overall, ES can effectively assist thermal power units in peak-shaving regulation and improve the power supply reliability.
Fig. 5. The optimal operation profile of different cases.
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Figure 6 shows the available energy variation of different ES technologies. It coincides with the charging and discharging pattern shown in the operation profiles. The available energy increases to the maximum capacity during the valley period, and then experiences two drops during the peak periods. The available energy will return to the initial state at the ending time to satisfy the restoration constraint, which is beneficial to subsequent operation.
Fig. 6. The available energy variation of ES in different cases.
4.4 Economic Sensitivity Analysis of Different Sizing The economic sensitivity analysis of different rated power and capacity for various ES technologies are shown in Figs. 7, 8 and 9. The variation trends for different batteries are basically the same although the optimal sizing point may be different. The investment cost of ES rises linearly with the increase of rated power and capacity, while the penalty cost for unmet load may change in a nonlinear trend. As the rated power or capacity increases, the total cost first decreases due to the significant decline of penalty cost, and then increases because the penalty cost cannot be further reduced and the investment cost are steadily increasing. Besides, the variation of rated capacity is more economically sensitive than that of rated power, as the iterative step and unit investment cost for ES capacity is larger. When the sizing variables are (200 MW, 2000 MWh) or (150 MW, 1500 MWh), the total cost reaches the lowest point respectively. Overall, the economic sensitivity analysis verifies the optimality of different sizing results.
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Fig. 7. The total cost of different ES sizing for Lead-acid battery.
Fig. 8. The total cost of different ES sizing for Lithium-ion battery.
Fig. 9. The total cost of different ES sizing for Nickel-Cadmium battery.
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5 Conclusions This paper proposes a bi-level optimal sizing and peak-shaving dispatching model for coal-fired thermal power-energy storage hybrid system considering different battery technologies, which is solved by quadratic programming and iterative nested method. The drawing conclusions are summarized as: (1) The optimization results shows that the total cost of cases with battery is markedly lower than the case without battery, indicating that the inclusion of battery can eliminate the unmet load and improve the power supply reliability. (2) The techno-economic comparison shows that the total cost of Case 4 with NickelCadmium battery is the lowest, indicating that Nickel-Cadmium battery is the most cost-effective option for peak-shaving operation because of its high depth of discharge and long design lifetime. (3) The economic sensitivity analysis shows the variation trend of total cost versus different rated power and capacity of various ESs, which verifies the optimality of sizing results.
Acknowledgement. This work was supported by Huaneng International Power Jiangsu Energy Development Co., Ltd. Nantong Power Plant science and technology project (No. K-491021007).
References 1. Li, Q., Zhao, S., Pu, Y., et al.: Capacity optimization of hybrid energy storage microgrid considering electricity-hydrogen coupling. Trans. China Electrotech. Soc. 36(3), 486–495 (2021) (in Chinese) 2. Jia, Z., Lin, B.: How to achieve the first step of the carbon-neutrality 2060 target in China: the coal substitution perspective. Energy 233, 121179 (2021) 3. Javed, M.S., Zhong, D., Ma, T., et al.: Hybrid pumped hydro and battery storage for renewable energy based power supply system. Appl. Energy 257, 114026 (2020) 4. Ye, Z., Li, X., Jiang, F., et al.: Hierarchical optimization economic dispatching of combined wind-PV-thermal energy storage system considering the optimal energy abandonment rate. Power Syst. Technol. 45(6), 2270–2279 (2021) (in Chinese) 5. Cui, Y., Zhou, H., Zhong, W., et al.: Optimal dispatch of power system with energy storage considering deep peak regulation initiative of thermal power and demand response. High Volt. Eng. 47(5), 1674–1683 (2021) (in Chinese) 6. Li, J., Wang, S.: Optimal combined peak-shaving scheme using energy storage for auxiliary considering both technology and economy. Autom. Electr. Power Syst. 41(9), 44–50 (2017). (in Chinese) 7. Gu, Y., Xu, J., Chen, D., et al.: Overall review of peak shaving for coal-fired power units in China. Renew. Sustain. Energy Rev. 54, 723–731 (2016) 8. Wang, C., Song, J., Zhu, L., et al.: Peak shaving and heat supply flexibility of thermal power plants. Appl. Therm. Eng. 193, 117030 (2021) 9. Xue, X.J., Zhao, Y., Zhao, C.Y.: Multi-criteria thermodynamic analysis of pumped-thermal electricity storage with thermal integration and application in electric peak shaving of coalfired power plant. Energy Convers. Manag. 258, 115502 (2022)
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10. Wang, D., Liu, D., Wang, C., et al.: Flexibility improvement method of coal-fired thermal power plant based on the multi-scale utilization of steam turbine energy storage. Energy 239, 122301 (2022) 11. Li, J., Zhang, J., Li, C., et al.: Configuration scheme and economic analysis of energy storage system participating in grid peak shaving. Trans. China Electrotech. Soc. 36(19), 4148–4160 (2021) (in Chinese) 12. He, Y., Guo, S., Zhou, J., et al.: The quantitative techno-economic comparisons and multiobjective capacity optimization of wind-photovoltaic hybrid power system considering different energy storage technologies. Energy Convers. Manag. 229, 113779 (2021) 13. Javed, M.S., Song, A., Ma, T.: Techno-economic assessment of a stand-alone hybrid solarwind-battery system for a remote island using genetic algorithm. Energy 176, 704–717 (2019) 14. Kaabeche, A., Bakelli, Y.: Renewable hybrid system size optimization considering various electrochemical energy storage technologies. Energy Convers. Manag. 193, 162–175 (2019)
Economic Optimal Dispatch of Integrated Energy System Considering Market Plan Li Jia, Wei Wang(B) , Na Li, Xinyu Duan, and Zhenya Ji NARI School of Electrical and Automation Engineering Nanjing Normal University, Nanjing 210046, China [email protected], [email protected], [email protected], [email protected], [email protected]
Abstract. With the adjustment of the energy structure, wind power plants, photovoltaic power plants and other renewable energy power stations are connected to the integrated energy system on a large scale. Based on the typical daily scenario of wind and solar output, a system economic optimization operation method considering market planning is proposed, taking into account factors such as energy storage, grid interaction, energy abandonment penalty, consumption incentive and market planning penalty, etc., to establish a comprehensive energy system economy. According to the optimization results, the output plan of various equipment and the purchase of electricity and gas are reasonably arranged. Finally, through an example analysis based on the actual data in a certain area, it is verified that the optimal dispatching model of the integrated energy system considering the planning penalty can promote the consumption of wind and solar energy and improve the economy of the optimal dispatching of the integrated energy system. Keywords: Integrated energy system · Wind and solar energy consumption · Market planning · Economic optimization
1 Introduction The severe environmental pollution problems brought by traditional power generation have brought opportunities for the access of new energy sources such as wind and solar [1, 2]. In recent years, the scale of new energy access has been increasing day by day. Combined with multi-energy coupling energy supply methods, it can meet the diversified needs of users. In order to make the optimization and adjustment of the integrated energy system more flexible and economical, how to promote the wind and solar energy consumption and realize the economical optimization of the integrated energy system has become the research focus at this stage [3, 4]. At present, domestic and foreign scholars have conducted in-depth research on the economic optimization operation of the integrated energy system. Among them, [5] considers the three energy forms of cooling, heating and power, and proposes an optimal operation strategy for a multi-energy complementary distributed cooling, heating and power cogeneration system applied in a special scenario. Teng et al. pay attention to the © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 262–271, 2023. https://doi.org/10.1007/978-981-99-1027-4_28
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innovation of solution methods and the establishment of intelligent optimization algorithms [6]. Sun Yongxin et al. take the minimum sum of processing costs as the goal, a day-ahead scheduling scheme is proposed [7]. Zhou et al. took the large-scale wind power connection to the power system as the background, expressed the uncertainty of wind power output with intervals, smoothed various nonlinear factors, combined with the nonlinear dual theory and the original dual theory solve the optimistic and pessimistic models, and finally obtain the optimal output interval. Multi-time-scale optimal operation scheduling methods are often used to overcome uncertainties [8]. Tan et al. overcame the uncertainty of output, quantified the system operation flexibility index, and proposed an intraday rolling wheel optimization scheduling strategy for the cogeneration system microgrid including the scheduling decision-making stage and the real-time adjustment stage [9]. Gu et al. [10] proposed an online cogeneration microgrid optimization operation method including rolling optimization and feedback correction. The rolling optimization part uses a hybrid algorithm to predict the load size, and performs feedback correction according to the ultra-short-term prediction error. To sum up, many scholars have carried out research in different directions, which is of great significance to the optimal operation of the system economy. However, there are still problems such as incomplete consideration of economic-related factors, insufficient flexibility in optimization and adjustment methods, and limited applicable scenarios. In order to cope with the actual situation, this paper constructs the uncertainty scenario of wind and solar output, and considers the market plan penalty and other factors, and establishes the comprehensive energy system optimization operation model. Strong applicability can greatly improve the system economy.
2 Integrated Energy System Model 2.1 System Physical Model This paper takes electricity, gas, and heat as load demand objects, which are composed of energy generation part, energy conversion and storage part, and energy demand part. Its specific system physical framework is shown in Fig. 1.
Power grid
Electrical load ES EB HS
WT PV GT Electric energy P2G Gas energy Heat energy Natural gas network
HRS Heat load GB GS Gas load
Fig. 1. Physical framework of the integrated energy system
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From Fig. 1, the connection and coupling between devices can be visually displayed, where the energy generation part consists of the main grid, natural gas grid, wind turbine (WT) and photovoltaic (PV) power station. The storage part consists of P2G equipment, gas turbine (GT), heat recovery system (HRS), gas boiler (GB), electric boiler (EB), electrical storage (ES), gas storage (GS) and heat storage (HS). 2.2 Landscape Uncertainty The two-parameter Weibull distribution is used to describe the probability distribution of wind speed v, the probability density function of wind speed can be expressed as: f (v, c, k) =
k v k−1 −( v )k e c c c
(1)
where k and c are the shape parameters and scale parameters of the distribution curve. The Beta distribution is used to describe the distribution of the light intensity I, and the probability density function of the light intensity can be expressed as: f (I ) =
(τ + υ) (I /Imax )τ −1 (1 − I /Imax )υ−1 (τ ) + (υ)
(2)
where represents the gamma function, τ , υ represents the shape parameter, and I max represents the maximum light intensity. The sample sequence of wind and wind output is generated by the Monte Carlo simulation method, and a typical daily scene curve of wind and wind output considering the uncertainty of wind and scenery is formed.
3 Economic Optimization Model of Integrated Energy System 3.1 Optimize the Target The planned electricity and gas purchases are reported in advance. Only when the actual energy demand and the planned error are small, the electricity market and the natural gas market will be in a stable equilibrium state. Therefore, this paper formulates a market plan penalty to encourage the planned electricity and gas purchases to reduce errors. In this paper, the optimization objective is to minimize the sum of the operating cost, gas purchase cost, grid interaction cost, energy abandonment penalty, consumption incentive cost, and market plan penalty. The objective function is as follows: min C = Cop + Cex + Cpenalty +Cencourage + Cpenalty
(3)
(1) Operating costs
Cop =
24
t t t t Re Pet + Rg Pgt + Rh Pht +UHRS CHRS + UGT CGT + UGB CGB + UEB CEB
t=1
(4)
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The equipment operation cost includes the operation cost of energy storage equipment and the start-stop cost of other equipment, Ri is the operation cost of energy storage equipment per unit power, Pi is the energy storage power, C HRS , U HRS , C GT , U GT , C GB , U GB , C EB , U EB are the operating cost and start-stop status of the waste heat recovery device, gas turbine, gas-fired boiler, and electric boiler, respectively. If it is different from the switch status at the previous time, it is 1; otherwise, 0. (2) Gas purchase cost and grid interaction cost
Cex =
24 g,t e,t e,t t t t cin,g · Pin + cin,e · Pin − cout,e · Pout
(5)
t=1 t where cin,g is the unit price of natural gas purchased at time t when the gas is planned to g,t
t is the unit price be purchased, Pin is the amount of natural gas purchased at time t; cin,e e,t of electricity purchased at time t, Pin is the amount of electricity purchased at time t, e,t is the power on the grid at time t. Pout
(3) Energy abandonment penalty cost
Cpenalty =
24
t e g h cpenalty PW + PPt +cpenalty · Pet + cpenalty · Pgt + cpenalty · Pht
t=1
(6) where cpenalty is the penalty cost factor for curtailing wind and solar, which is regarded t , P t as the minimum electricity purchase price of the external power grid, and PW P g e are the amount of abandoned wind energy and solar energy at time t. cpenalty , cpenalty h and cpenalty are the penalty cost coefficient of abandoning electric energy, abandoning gas energy, and abandoning heat energy, respectively, Pet , Pgt and Pht are power abandonment, gas abandonment, and heat abandonment at time t, respectively. (4) Consume incentive costs
Cencourage = −
24 t
cencourage PW + PPt
(7)
t=1 t and P t are where cencourage is the wind and solar absorption excitation coefficient, PW P the actual dispatched output of the wind and photovoltaic stations at time t, respectively.
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(5) Market planning penalty e,t e,t =ce,penalty (Pin − Pout − Ee )+cg,penalty (Pin − Vg ) Cpenalty g,t
(8)
where E e and V g are the electric energy and gas energy actually required by the system is the penalty factor for unreasonable planned electricity purchase, on that day, ce,penalty and cg,penalty is the penalty factor for unreasonable planned gas purchase. 3.2 Restrictions (1) Energy balance Electricity, gas, heat supply and demand balance constraints: e,t e,t e,t e,t e,t e,t t +Pbuy +PGT − PP2G − PEB + PES,release − PES,store Lte = PPt + PW g,t
g,t
g,t
g,t
g,t
(9)
e,t Ltg = Pbuy + PP2G − PGB − PGT + PGS,release − PGS,store
(10)
h,t h,t h,t h,t h Lth = PEB + PGB + PHRS + PHS,release − PHS,store
(11)
where Lti represent the electrical, gas, and heat load demands of the system at time t. t , P e,t are photovoltaic power generation, wind power generation, and electricity PPt , PW buy e,t e,t e,t is the output of gas turbine at time t, PP2G , PEB are the electricity purchase at time t. PGT e,t e,t , PES,store consumption of electric-to-gas equipment and electric boiler at time t, PES,release g,t g,t are storage and discharge at time t. Pbuy and PP2G are the gas purchase volume and the g,t
g,t
output of the power-to-gas equipment at time t. PCHP and PGB are the gas consumption g,t g,t of the cogeneration unit and the gas boiler at time t. PGS,release and PGS,store are the gas h,t h,t h storage and gas release volume at time t. PEB , PGB and PHRS are the output of the electric h,t h,t boiler, gas boiler, and waste heat recovery device at time t. PHS,release , PHS,store are heat storage and heat release at time t.
(2) Device constraints Considering the capacity limitations of various energy conversion equipment and energy storage equipment, the operating constraints of each equipment are as follows: 0 ≤ Pit ≤ Pi,max (12) 0 ≤ Pit ≤ Pi,max where Pi,max is the upper limit of equipment output, and Pi,min is the lower limit of equipment output.
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(3) Planning constraints e,t ⎧ P − P e,t ⎪ out in ⎪ ⎪ 1− < σe ⎪ ⎨ E e g,t ⎪ Pin ⎪ ⎪ ⎪ < σg ⎩1 − Vg
(13)
where σe is the maximum relative error between the planned electricity consumption and the actual electricity consumption that the electricity market can bear, and σg is the maximum relative error between the planned gas consumption and the actual gas consumption that the natural gas market can bear.
4 Case Analysis 4.1 Example Introduction The model in this paper is optimized by the improved fast particle swarm optimization algorithm (APSO). The validity and reliability of the proposed method are verified by simulation analysis. In this paper, the actual data of a certain area is used as the basic data to carry out numerical simulation. The installed capacity of WT is 150 kW, and the installed capacity of PV is 150 kW. The typical daily wind forecast and electricity, gas and heat loads are shown in the Fig. 2. (b) 350
Wind power Photovoltaic power
300
Electrical load Gas load
Heat load
250 200 150 100
50 0
8 7 6 5 4 3 2 1 0
Gas load/m3
Power/kW
140 120 100 80 60 40 20 0
Electrical and heat load/kW
(a) 160
Fig. 2. Wind and photovoltaic power and typical daily load curve generation curves
The fixed natural gas price is 2.28 yuan/m3 (0.23 yuan/kW·h), and the time-of-use electricity price [11] is shown in Table 1. 4.2 Optimization Results and Analysis In order to study and analyze the influence of market planning factors on the economic dispatch of the integrated energy system, two different operation schemes were constructed, and the output and economy of each equipment in the integrated energy system under the two schemes were compared and analyzed. The plan is as follows:
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Period
Unit price of electricity purchased/(yuan/kW·h)
Unit price of electricity sold/(yuan/kW h)
Peak electricity consumption period (10:00–12:00, 19:00–21:00)
1.350
1.040
Normal electricity consumption 0.900 period (8:00–9:00, 13:00–18:00)
0.693
Low electricity consumption period (0:00–7:00, 22:00–23:00)
0.385
0.500
Scheme 1: An integrated energy system optimization operation plan that does not consider market planning penalties; Scheme 2: A comprehensive energy system optimization operation plan considering market planning penalties. (1) Analysis of optimization results. Through the calculation of the optimized operation scheme in this paper, the interaction of various energy conversion equipment, power grids, and gas grids on a typical day is shown in the Fig. 3. From Fig. 3a–c, since this paper assumes that the gas price remains unchanged, the output of electricity, gas, and heat is closely related to changes in electricity prices. During low electricity consumption period, the electricity price is lower, and the electricity purchased is relatively large. The electricity load is supplied by wind and solar output and electricity purchase, and the output base of the gas turbine is close to zero. The electric boiler is in operation, and the gas boiler and heat storage device are adjusted according to the gas output. During normal electricity consumption period, the output of the gas turbine supplements the electricity load demand of the wind and solar power supply; the gas purchased from the gas grid is large, and the gas turbine and the electricto-gas device are both in operation; both the gas turbine and the electric boiler are in operation to supply power and heat load. During peak electricity consumption period, the electricity price is the highest, and the electricity storage device continues to discharge, which is used to sell or supply electricity loads to maximize economic benefits; the gas turbine consumes gas energy, and the electricity-to-gas device operates to supplement electricity; the gas turbine and gas boiler supply heat load. Two schemes are used to optimize the calculation of the example system. Under the two schemes of considering the market plan penalty and not considering the market plan penalty, the integrated energy system optimally dispatches the purchase of electricity and natural gas as shown in Fig. 3d. It can be seen that, due to the restraining effect of the market plan penalty, the electricity purchased by the second scheme is generally lower than that of the first scheme. While satisfying the normal supply of the load demand
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Fig. 3. Three energy dispatch strategies and gas purchase volume and electricity purchase curve
by the integrated energy system, the electricity and natural gas markets maintain stable operation. The gas purchase volume of the two schemes is not much different. The gas purchase volume of the second scheme is generally slightly higher than that of the scheme one. In order to meet the multi-load demand, sufficient complementary energy supply is required. After adding the market plan penalty, the purchase of electricity and gas will be more scientific, and the system economy will also be indirectly improved. (2) Economic comparative analysis of the two schemes. The economic comparison of the two schemes is shown in the Table 2. Table 2. Economic comparison of the two schemes Program
Running cost/yuan
Gas purchase cost/yuan
Grid interaction cost/yuan
Renunciation penalty/yuan
Market plan penalty/yuan
Total cost/yuan
Scheme 1
909.39
1912.14
1923.18
524.31
417.31
5686.33
Scheme 2
1014.49
2065.46
1608.56
254.12
292.55
5235.18
It can be seen that compared with the optimized scheme 1, the total cost of scheme 2 is reduced by 7.93%, and the system economy is significantly improved. Scheme 2 increases the system operating cost by 11.55% and gas purchase cost by 8.02% compared to scheme 1. Under the effect of market planning penalties, the operating cost and gas
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purchase volume are increased to meet the demand for multiple loads; compared with scheme 1, scheme 2 grid Interaction costs are reduced by 16.36%, energy abandonment penalties and consumption incentive costs are reduced by 51.53%, and market planning penalties are reduced by 29.90%, which greatly promotes wind and solar energy consumption, and improves the economy of optimal operation of the integrated energy system.
5 Summarize This paper proposes a comprehensive energy system economic optimal dispatch model considering planning penalties. Based on typical scenarios of wind and solar output, considering wind and solar energy consumption factors, the operating cost, gas purchase cost and grid interaction cost, energy abandonment penalty, consumption incentive cost and the minimum sum of market planning penalties is taken as the optimization goal, and the output plans of various equipment are reasonably arranged. The result shows: (1) The objective of the integrated energy system optimization model proposed in this paper takes into account the penalty cost of energy abandonment and the incentive cost of consumption, which can reduce and promote wind and solar energy consumption, effectively improve the utilization rate of new energy, and reduce environmental pollution. (2) Compared with the traditional economic optimization, the economic optimization of the integrated energy system considering the market plan penalty is more reasonable, which makes the purchase of electricity and gas more scientific and realizes the economic operation of the integrated energy system.
Acknowledgments. This research was funded by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province and the Jiangsu Provincial Postgraduate Research and Practice Innovation Program Project 1812000024991.
References 1. Shuai, W., Zhu, Z., Li, X., Luo, Z., Zhu, H., Zhang, Y.: “Source-network-load-storage” coordinated optimization operation for an integrated energy system considering wind power consumption. Power Syst. Protect. Contr. 49(19), 18–26 (2021) (in Chinese) 2. Geng, J., Yang, D., Gao, Z., Chen, Y., Liu, G., Chen, H.: Optimal operation of distributed integrated energy microgrid with CCHP considering energy storage. Electr. Power Eng. Technol. 40(1), 25–32 (2021) (in Chinese) 3. Chen, M., Sun, Y., Xie, Z.: The multi-time-scale management optimization for park integrated energy system based on the bi-layer deep reinforcement learning. Trans. China Electrotech. Soc. 1(16), 1000–6753 (2022) (in Chinese) 4. Liu, N., Tan, L., Sun, H., Zhou, Z., Guo, B.: Bilevel heat-electricity energy sharing for integrated energy systems with energy hubs and prosumers. IEEE Trans. Ind. Inf. 18(6), 3754–3765 (2022)
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5. Wang, Q., Liu, J., Hu, Y., Zhang, X.: Optimal operation strategy of multi-energy complementary distributed CCHP system and its application on commercial building. IEEE Access 7, 127839–127849 (2019) 6. Teng, Y., Gong, W., Leng, O., Wang, Z., Zhou, D., Chen, Z.: Coordination operation model of microgrid cluster for improving electricity-gas networks regulation capability. Proc. CSEE 41(2), 642–655 (2021) (in Chinese) 7. Su, Y., Nie, W., Tan, M.: Day-ahead interval optimization of integrated energy system considering wind power integration and gas-electricity transformation. Autom. Electr. Power Syst. 43(17), 63–71 (2019) (in Chinese) 8. Zhou, W., et al.: Interval nonlinear economic dispatch in large scale wind power integrated system. Proc. CSEE 37(2), 557–564 (2017) (in Chinese) 9. Tang, J., Ding, M., Lu, S., Li, S., Huang, J., Gu, W.: Operational flexibility constrained intraday rolling dispatch strategy for CHP microgrid. IEEE Access 7, 96639–96649 (2019) 10. Gu, W., Wang, Z., Wu, Z., Luo, Z., Tang, Y., Wang, J.: An online optimal dispatch schedule for CCHP microgrids based on model predictive control. IEEE Trans. Smart Grid 8(5), 2332–2342 (2017) 11. Li, K., Song, T., Han, X., Zhang, D.: Bidding strategy of energy storage considering electricity price uncertainty and loss cost. Autom. Electr. Power Syst. 44(17), 52–59 (2020) (in Chinese)
Analysis of Energy Loss and Heat Generation Characteristics of Supercapacitors Wentao Zhang1 , Jilin Liu2 , and Bing-Ang Mei1(B) 1 School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
{3220200389,meiba}@bit.edu.cn
2 Representative Office of Chinese Army, Datong 037000, China
[email protected]
Abstract. As a new type of energy storage device, supercapacitors (SCs) have the advantages of high power density, long cycle life and wide operating temperature range. However, there is energy loss in the working process of SCs, and the main way is heat loss. Therefore, this paper analyzed the heat generation characteristics of commercial SCs through heat flux measurement experiments, and studied the relationship between the heat generation characteristics of devices and the energy loss of charge and discharge. The results showed that the energy loss increases with the increase of charging current, and the heat loss accounts for more than 85% of the total energy loss. In addition, the total heat generation during the charging and discharging process of the SCs are greater than the Joule heat generation. The difference is partly caused by the irreversible Faraday reaction heat generation and charge redistribution. Keywords: Supercapacitors · Energy loss · Heat flux measurement · Joule heat generation
1 Introduction In recent years, with the rapid growth of population, rapid economic development and increasingly serious environmental problems, the consumption of non-renewable energy such as coal and oil is increasing, global warming and fossil fuel depletion are making mankind face a great challenge that has not been seen in a century [1]. As the most widely used form of energy in today’s society, improving the storage and utilization efficiency of electric energy is undoubtedly a sword for energy conservation and emission reduction. Nowadays, as a new type of green power storage device, SCs have begun to enter people’s field of vision [2]. SCs combine the characteristics of traditional capacitors and batteries. They have high power density and can store large amounts of charge. In addition to high power density, compared with traditional capacitors and batteries, SCs have the characteristics of long cycle life, wide operating temperature range, maintenance free and environmental protection [3]. At present, most of the studies on the energy storage characteristics of SCs only analyze their energy density and power density, and greatly improve their energy storage characteristics by improving their electrode © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 272–280, 2023. https://doi.org/10.1007/978-981-99-1027-4_29
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structure, electrolyte types, etc. [4–8]. The relevant research lacks the analysis of the charging and discharging efficiency and energy loss of the super capacitor, which is of great significance for increasing the energy storage efficiency of energy storage devices such as vehicle power supply and reducing potential safety hazards. Therefore, this paper analyzes the energy loss of SCs monomer by constant current charge and discharge tests with different currents. In addition, the curved surface measurement of the heat flux sensor is corrected to obtain more accurate surface heat loss. Combined with the energy loss analysis based on constant current charging and discharging, the relationship between heat loss and energy loss is established and analyzed, which provides a research basis for reducing the energy loss of SCs.
2 Experimental Device and Method Figure 1a shows the calibration experimental device. The signal generator outputs an equivalent sine heat flow signal heating flow analog signal to simulate the actual heat generation under constant current charge and discharge. Simulate the heat generation of different sizes by changing the different magnification of the power amplifier, connect two identical electric heating pieces in series, stick the electric heating pieces on the heat flux sensors that are normal and bent to a radius of 18 mm, measure their values respectively, and calibrate the bent heat flux sensors.
(a) Heat flux sensor calibration.
(b) Electrical and thermal tests test.
Fig. 1. Schematic diagram of device connection
Figure 1b shows the experimental device used to measure the surface heat dissipation of SCs monomer. BCAP0050P270S01 cylindrical SCs from Maxwell are used, and their parameters are shown in Table 1. The heat flux sensor is used to measure the heat dissipation of SCs monomer during charging and discharging. The FHF04 heat flux sensor is used, and the size of the test area is 30 mm × 30 mm, measuring range (± 10) × 103 W/m2 , thermal resistance 30 × 10–4 W/m2 ; The data acquisition (DAQ901A) is used to collect the heat flux signal measured by the heat flux sensor. The electrochemical workstation (SolarLab XM) is used for cyclic constant current charging and discharging of SCs.
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˙ i0 (t) [9]: For the calculation of heat flux Q ˙ i0 (t) = Vi (t) · A Q S
(1)
where, Vi (t) is the potential difference signal from the sensor (V), S is the sensitivity of heat flux device (μV/(W/m2 ), A is the measured area (m2 ). For the correction of the heat flux sensor in Fig. 1a, the heat flux sensor provides a potential signal u(t) by making the signal generator, as shown in Fig. 2a. The applied potential signal u(t) is modulated by the high-frequency carrier potential and the lowfrequency modulation potential to obtain the final sinusoidal heat flow qs (t) [10]. As shown in Fig. 2b, the heat flux is measured by changing different magnification through the power amplifier, and compared with the control group (non curved heat flux sensor), fitting and correcting the true readings of the curved heat flux sensor under different heat generation. Table 1. SCs parameters. Parameters
Value
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2.7
Standard capacity C/F
50
Size D*L/mm
18*40
Maximum continuous current I c /A
6.1
Peak current I/A
37
From Fig. 1b, the heat flux sensor is wrapped in the center of the side of the SCs monomer after being bent. By designing a cyclic charge and discharge procedure, the electrochemical test bench can conduct cyclic constant current charge and discharge for the SCs with different currents (2A, 3A, 4A and 5A), as shown in Fig. 3. The surface temperature and heat flux of the capacitor can be stabilized and maintained for a period of ˙ i (t) of the capacitor surface is calculated time after several cycles. The heat dissipation Q according to the corrected heat flux Qi : itcd
Qi =
˙ i (t)dt Q
(2)
(i−1)tcd
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potential signal u(t)
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Time, t
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(b) Equivalent heat flow signal.
Fig. 2. Principle of simulated heat flow input.
The equivalent internal resistance Rs [11], irreversible Joule heat generation Qirr and energy loss E i of the supercapacitor are calculated from the current I and voltage V(t) signals in the charging and discharging equipment: Rs =
U 2I
(3)
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(4)
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Ec =
V (t)Idt
(5)
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Ed = −
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(6)
(n−1)tc +td
Ei = Ein − Eout
(7)
where, U is the voltage drop (V) when the current reverses during cyclic charging and discharging, tc and td is charge time and discharge time (s) respectively, Ec and Ed is the input energy of capacitor charging and the output energy of discharge (J). Finally, the relationship between energy loss and heat flux loss, irreversible Joule heat generation is analyzed according to the obtained energy loss under different charge discharge ratios.
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Fig. 3. Voltage time curve under cyclic constant current charge discharge with current of 5A
3 Calibration of Measuring Devices Applying 9 ~ 2 times of magnification to the amplifier in turn, heating two electric heating plates attached to the heat flux sensors of different measuring forms, and obtain the heat flux values measured by the two heat flux sensors at different magnification, as shown in Fig. 4a. It can be seen that the amplitude and frequency of the two groups of heat flux sensor are consistent under the sinusoidal heat flow, but the reference values are different. Therefore, the bending group can be corrected according to the relationship between the measured heat fluxes of the two groups. In order to avoid the uncertainty of thermal measurement, four measurements are carried out. The fitting correction results are obtained by taking the measured heat flux value of the curved surface group as the independent variable and the ratio between the measured values of the plane group and the curved surface group as the dependent variable, as shown in Fig. 4b. Obtained by linear fitting λ (Ratio of measured values of plane group and bending group): λ = 5.302 ∗ 10−5 q + 1.544
(8)
In this paper, the actual measured heat flux signal is less than 200 (W/m2 ), and the heat flux coefficient of equal sign curved surface can be ignored. When calculating the actual surface heat dissipation Q˙ i (t) after correction λ = 1.544 is substituted into (1) as the correction coefficient, namely: ˙ i0 (t) = λ Vi (t) · A Q˙ i (t) = λQ S
(9)
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Fig. 4. a Changes of measured values of plane group and bending under different heating rates, b λ versus Curved surface heat flux measurement value q
4 Results and Discussion 4.1 Electrical Analysis of SCs Figure 5a shows the voltage time curve under 2A ~ 5A charging and discharging current in a single cycle. The irreversible Joule heat generation Qirr is calculated according to Eq. (4), and the input energy Ec , output energy Ed and energy loss Ei in the charging and discharging process are calculated according to Eqs. (5), (6) and (7). Take 10 cycles to calculate the average values E and Qirr as shown in Fig. 5b. Part of the energy loss is dissipated in the form of Joule heat generation, and with the increase of current, both the energy loss and Joule heat generation increase. Therefore, a part of the energy loss is consumed in the form of non Joule heat generation energy. 4.2 Thermal Analysis of SCs In order to further study the energy loss of SCs, this paper analyze the surface heat loss under the constant current charge and discharge of capacitor cycle. Figure 6 shows that under 2A ~ 5A charging and discharging current, the surface heat flux of the SCs starts to rise at different rates with the number of cycles and eventually fluctuates to a constant value. This is the result of the combined effect of reversible and irreversible heat generation generated by the SCs in the process of constant current charging and discharging. The reversible heat generation is mainly due to the internal entropy change of the capacitor charging and discharging, charging and discharging heat absorption, Is the cause of curve fluctuation. At first, due to the low temperature of the capacitor, part of the heat generated is used for the temperature rise of the capacitor itself, and the surface heat flux is gradually rising. With the temperature rise of the capacitor, the surface heat flux increases and approaches the dynamic equilibrium stage. In addition, because the input and output energy of reversible heat generation are equal in a complete charging and discharging cycle, that is, the heat generation rate is zero integral to time. Therefore, the total external surface area of the capacitor removed is A by integrating the dynamic
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stable region within the cycle, and the surface heat dissipation of the irreversible part ˙ only can be obtained Q(t).
Fig. 5. a Voltage versus time, b energy loss and irreversible Joule heat generation versus current
Fig. 6. a Surface heat flux versus time, b Energy loss and surface heat loss versus current
Figure 6b shows the comparison of energy loss and surface heat dissipation under different currents. It can be seen that the surface heat loss accounts for 86.8% ~ 91.1% of the total energy loss in the process of constant current charging and discharging, and the current size has little influence on its proportion. In addition, about 10% of the energy is dissipated in the form of non heat generation. Next, this paper will continue to analyze the remaining energy. 4.3 Energy Loss Analysis of SCs According to 4.1, the energy loss can be divided into the sum of Joule heat generation part and other parts of energy. Figure 7 shows the comparison between surface heat loss, Joule heat generation and residual energy loss. It can be seen that part of the remaining
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energy (Qi -Qirr ) is lost through the surface in the form of heat. It is analyzed that during the charging and discharging process of commercial capacitor electrolyte, there are often some irreversible Faraday reactions inside which generate heat or lead to the asymmetry of electrode ion concentration, so that the input of reversible heat generation of capacitor in the actual charging and discharging cycle is greater than the output energy [11], so that the surface heat dissipation is increased, but some energy (E-Qi ) is lost in the form of non heat generation, which has nothing to do with chemical reaction, It is analyzed that due to the influence of electrode structure, part of the charges in the electric double-layer capacitor move in the opposite direction during charge redistribution, and can’t continue to participate in the reaction in the deeper pores, resulting in energy loss.
Energy, Q / J
Residual energy loss Joule heat generation Surface heat loss
Current, I / A
Fig. 7. Analysis of energy loss under different charging and discharging currents
5 Conclusions In this paper, the electrical, thermal and energy loss characteristics of Maxwell SCs under cyclic constant current charge and discharge are studied. First, the calibration device of the heat flux sensor is designed to obtain the correction coefficient λ = 1.544, so that the bent heat flux sensor can accurately measure the surface heat dissipation of the cylindrical SCs. Secondly, the electrical and thermal characteristics of SCs under cyclic constant current charge and discharge are studied by using different charge and discharge currents (2A–5A). It is found that the greater the current is, the more energy loss will be. In addition, the surface heat dissipation during the charge and discharge process is more than the Joule heat generation, accounting for 86.8% ~ 91.1% of the total energy loss, of which the surface heat loss under 3A charge and discharge current accounts for 91.1% of the maximum. Finally, by analyzing its energy loss, it is believed that part of its residual energy loss is caused by irreversible Faraday reaction and charge redistribution without chemical reaction. However, this part of energy loss often affects the life and performance of the capacitor. Therefore, in actual use, it’s necessary to comprehensively consider the factors such as energy loss, surface heat dissipation and service life to reasonably select its charge discharge ratio.
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Acknowledgments. This material is based upon work supported by National Natural Science Foundation of China (52107221), Beijing Natural Science Foundations (3214055) and Beijing Institute of Technology Research Fund Program for Young Scholars.
References 1. Wang, Y., et al.: Recent progress in carbon-based materials for supercapacitor electrodes: a review. J. Mater. Sci. 56(1), 173–200 (2020). https://doi.org/10.1007/s10853-020-05157-6 2. Lukatskaya, M.R., Dunn, B., Gogotsi, Y.: Multidimensional materials and device architectures for future hybrid energy storage. Nat. Commun. 1(7), 12647 (2015) 3. Song, Z., Hou, J., Hofmann, H.: Sliding-mode and Lyapunov function-based control for battery/SCs hybrid energy storage system used in electric vehicles. Energy 122(1), 601–612 (2017) 4. Shao, H., Wu, Y.C., Lin, Z., et al.: Nanoporous carbon for electrochemical capacitive energy storage. Chem. Soc. Rev. 49(10), 3035–3039 (2020) 5. Di, Y., et al.: Sophisticated structural tuning of NiMoO4@MnCo2O4 nanomaterials for high performance hybrid capacitors. Nanomaterials 12(10), 1674 (2022) 6. Zhen, S., Xa, A., Hao, Z., et al.: Houttuynia-derived nitrogen-doped hierarchically porous carbon for high-performance supercapacitor—ScienceDirect. Carbon 1(161), 62–70 (2020) 7. Wang, D.: A high-performance carbon-carbon(C/C) quasi-solid-state scs with conducting gel electrolyte. Int. J. Electrochem. Sci. 13(3), 2530–2543 (2018) 8. Luo, Y.X.: A high-performance electrochemical SCs based on a polyaniline/reduced graphene oxide electrode and a copper(II) ion active electrolyte. Phys. Chem. Chem. Phys. 1(20), 131–136 (2018) 9. Munteshari, O., Lau, J., Ashby, D.S., et al.: Effects of constituent materials on heat generation in individual EDLC electrodes. J. Electrochem. Soc. 165(7), 1547–1557 (2018) 10. Li, Z., Mei, B.A.: Complex thermal analysis of SCs by thermal impedance spectroscopy. Thermochim. Acta 710(1), 179175 (2022) 11. Mei, B.A., Munteshari, O.: Physical interpretations of Nyquist plots for EDLC electrodes and devices. J. Phys. Chem., C. Nanomater. Interf. 122(1), 194–206 (2018)
Grid-Supported Modular Multi-level Energy Storage Power Conversion System Ziqing Cao, Yichao Sun(B) , and Kai Yang School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China [email protected], [email protected], [email protected]
Abstract. In order to deal with the stability and security problems of power system operation brought by large-scale new energy grid connection, this paper proposes a modular multilevel energy storage power conversion system (MMCESS) with grid support capability. It utilizes the modular structure of the modular multi-level converter, and connects the battery energy storage in its sub-modules in a distributed manner to form a modular multi-level energy storage power conversion system. By using the access of the energy storage unit, the grid-connected stability of the system can be improved. At the same time, the Virtual Synchronous Generator (VSG) is introduced into the MMC-ESS, so that it has inertia and damping characteristics similar to the synchronous generator during operation, which enhances the power system’s ability to deal with frequency disturbances. Simulation results show that the proposed grid-supported MMC-ESS can suppress power fluctuations, provide frequency support, and effectively improve grid stability. Keywords: Modular multi-level energy storage power conversion system · Virtual synchronous generator control · Grid-supported control · Frequency support
1 Introduction The large-scale application of new energy can effectively reduce the demand for traditional energy, and it has the advantages of strong renewable capacity and low emission pollution, which is of great significance for alleviating the energy crisis and environmental degradation. However, due to the strong volatility, intermittency and uncertainty of the output of new energy, the inertial support capacity of the power system is greatly weakened. This makes the frequency regulation and voltage regulation capability of the system continue to decrease, and it is very easy to cause power accidents [1, 2]. Therefore, it is usually combined with energy storage devices in its large-scale grid connection process [3]. Battery energy storage technology plays a pivotal role in the promotion of new energy and the construction of smart grids [4]. Among them, the energy storage system is mainly composed of two parts, the power conversion system (PCS) and the energy storage unit. The energy storage and release of the whole system is realized through © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 281–288, 2023. https://doi.org/10.1007/978-981-99-1027-4_30
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the effective control of PCS, and PCS directly affects the control of grid-side voltage and power. If the energy storage PCS and the modular multilevel converter (MMC) are combined to form a modular multilevel energy storage power conversion system (MMCESS), the modular structure of the MMC can be fully utilized. This can realize the direct grid connection of the energy storage system and save the investment of the transformer cost [5]. In addition, the number of series-parallel cells in the sub-module is less, which facilitates the precise regulation of the energy storage unit by the system, and improves the operating efficiency and reliability of the system. The Virtual Synchronous Generator (VSG) can control the grid-connected inverter to imitate the output characteristics of the synchronous machine, provide virtual inertia, effectively solve the problem of insufficient power generation support capacity of new energy [6–8]. However, there are still few literatures on the application of VSG in the topology of MMC. Reference [9] utilizes MMC as a virtual synchronous generator to maintain frequency stability in power systems with high renewable energy penetration. Reference [10] proposes an improved frequency-regulated virtual synchronous generator based on a modular multilevel converter, proving that the VSG can function without disturbing the internal operation of the MMC converter. However, the above-mentioned virtual synchronous control applied to MMC has not been combined with energy storage research, and the virtual synchronous control for MMC-ESS still belongs to the blank stage. In order to solve the above problems, this paper studies the modular multi-level energy storage power conversion system with grid support capability. First, the topology and mathematical model of MMC-ESS are introduced. Then, the working principle and control strategy of grid-supported control are analyzed. Finally, the correctness and effectiveness of the proposed scheme are verified by simulation results. U dc 2
idc ipa
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ipb
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ipc
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C
upk
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ia L s ib L s ic
unk _ U dc 2
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inb
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inc
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Fig. 1. Topology of MMC-ESS.
uga
~u gb ~ ugc ~
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2 Topology of MMC-ESS The MMC-ESS topology is shown in Fig. 1. The structure used in this paper is that the energy storage unit is connected in parallel to the DC side of each sub-module through a DC/DC converter. Each phase of this topology includes upper and lower two groups of bridge arms, and each group of bridge arms is composed of N identical heating battery sub-modules and one reactor in series. Each battery sub-module is connected in parallel to the capacitor end of the sub-module through a bidirectional DC converter. Among them, uga , ugb , ugc are the three-phase grid voltage, ia , ib , ic are the three-phase grid current, L arm is the bridge arm filter inductance, and L s is the output filter inductance.
3 Grid-Supported Control Strategy of MMC-ESS 3.1 The Principle of Grid-Supported Control The core idea of the VSG control strategy is to make the grid-connected inverter simulate the mechanical characteristics of the traditional synchronous generator through the control strategy, so as to obtain the operating characteristics similar to the synchronous generator and have the excellent performance of the power electronic equipment. In this paper, the working principle of the synchronous generator is introduced into the MMCESS, so that the energy storage unit exhibits external characteristics similar to those of the synchronous generator. The MMC-ESS can respond to changes in grid frequency and provide the necessary inertia support capability for the grid. Its control principle is shown in Fig. 2. Energy Storage Unit
gPWM PWM mPWM abc/dq
Prime Mover
ea
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ud uq
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eb ica
icb
ec icc
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u
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ia ib ic
~ uga ~ ugb ~ gc
iabc uabc PQ Calculation Qe Pe
Virtual ThreeSpeed phase Sine Controller Wave Virtual Eu Generator Excitation Controller
Synchronous Generator
O
Pref wn Qref Un
~
Grid
Fig. 2. Grid-supported control strategy.
From the point of view that the MMC-ESS main circuit is equivalent to the electrical part of the synchronous generator, the fundamental waves ea , eb and ec of the midpoint voltage of the bridge arm simulate the internal potential of the synchronous generator. The output filter inductor Ls simulates the synchronous reactance of the synchronous generator. The voltage at the PCC point simulates the terminal voltage of the synchronous generator.
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3.2 Grid-Supported Control Strategy The virtual speed controller can realize the simulation of inertia characteristics and damping characteristics. It can adjust the reference active power by adjusting the system frequency. This simulates the voltage and frequency regulation of a synchronous generator.
Fig. 3. Virtual speed controller
As shown in Fig. 3, the virtual speed control controller is mainly composed of two parts: the power frequency adjustment part and the mechanical part. The main function of the power frequency adjustment part is to adjust the virtual mechanical power, and its mathematical model can be expressed as: Pm = Pref − Kω (ω − ωn )
(1)
In Eq. (1), K w is the droop coefficient of the virtual governor. The mechanical part is the key part of simulating the rotor motion equation of the synchronous generator, and its mathematical model is: ⎧ dω dω ⎪ ⎪ ≈ J ωn ⎨ Pm − Pe − Dω = J ω dt dt (2) ⎪ ⎪ ⎩ δ = ω−ωn dt Among them, J and D represent the virtual inertia and virtual damping coefficient, respectively, and wn represents the reference angular velocity. w represents the virtual angular velocity of the virtual rotor. Pm stands for virtual mechanical power. Pe represents the output power of the virtual synchronous machine. δ is the virtual rotor angular position. The virtual excitation controller can simulate the voltage regulation of the machine terminal of the synchronous generator, and adjust the output reactive power of the virtual synchronous machine by adjusting the voltage. Its control block diagram is shown in Fig. 4. The reactive power-voltage regulation function of the virtual excitation controller mainly refers to the reactive power-voltage droop curve of the synchronous generator for voltage regulation: Qm − Qref = Kq (U − Un )
(3)
In the formula, Qref and Qe are the reactive power reference value and output reactive power, respectively, and K q is the voltage-reactive droop coefficient.
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Fig. 4. Virtual excitation controller
In order to ensure that the output terminal voltage is consistent with the reference voltage, voltage modulation is performed by controlling the voltage deviation between the reference voltage and the actual output voltage: Eu =Un +
1 U Ks s
(4)
In the formula, K s is the integral coefficient of the integral link, and E u is the voltage amplitude of the output terminal voltage. The output phase angle of the virtual governor is taken as the phase angle of the reference electromotive force, and the amplitude of the output voltage of the virtual excitation controller is taken as the amplitude of the reference electromotive force. Then through the three-phase sine wave modulation, the reference electromotive force voltage vector output by the virtual synchronous machine can be obtained: ⎤ ⎡ Eu sin δ · ⎥ ⎢ (5) Uabc = ⎣ Eu sin(δ − 2π/3)⎦ Eu sin(δ + 2π/3)
4 Simulation and Experiment of the System In order to verify the correctness and effectiveness of the proposed grid-supported control method based on MMC-ESS, Matlab/Simulink software is used to build the simulation model shown in Fig. 1, and the circuit parameters are shown in Table 1. Table 1. Simulation parameters of MMC-ESS. Parameter
Numerical value
Parameter
Numerical value
Rated voltage on AC grid ug (V)
380
Number of bridge arm modules N
2
Rated voltage on DC side Udc (V)
800
Bridge arm filter inductor L arm (H)
1.5e−3
Rated power (W)
10,000
Sub-module capacitance C L (uF)
600
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4.1 Load Sudden Change The simulation conditions are: at the moment of 1 s, the load power is reduced from 10,000 W to 5000 W. At 1.5 s, the load power suddenly changes to 15,000 W. As shown in Fig. 5a, in the rated state, the grid frequency is stable at 50Hz. After the load power suddenly decreases at 1 s, the grid frequency oscillates within the range of ±0.2Hz, and stabilizes at about 50.035Hz after 0.15 s of adjustment. When the load power suddenly increases to 15,000 W at 1.5 s, the frequency of the grid is stabilized at about 49.96Hz after 0.15 s adjustment. At this time, the waveform change corresponding to the active power on the AC side is shown in Fig. 5b. It meets the given simulation conditions. 2
50.5
104
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f / Hz
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1 0.5
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1 1.5 t/s a Waveform of system frequency when the load suddenly changes ua ub uc
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600 500 400
1 1.5 t/s c Waveform diagram of AC grid voltage when the load suddenly changes
2
380 0.8
-40 0.5
50
460 0.85
SOC / %
-500 0.5
1 1.5 t/s d Waveform diagram of AC grid current when the load suddenly changes
2
49.925
49.95 49.9
49.91 0.8
0.85
SOCpa1 SOCna1 SOCpb1 1
SOCnb1 49.85 SOCpc1 upc1 upa1 upb1 SOCnc1 una1 unb1 unc1 300 49.8 0.5 1 1.5 2 0.5 1.5 2 t/s t/s f The waveform diagram of the sub-module battery e Waveform diagram of sub-module capacitor SOC when the load suddenly changes voltage when the load suddenly changes
Fig. 5. System waveform diagram when the load suddenly changes
Figure 5c and d show the waveforms of the voltage and current on the AC side respectively. When the load power changes, the AC side voltage is hardly affected. When the load power is 10,000 W, the AC side current is the sine value of the upper and lower limits ±22 A. When the load power is reduced to 5000 W, the AC side current becomes a sine value of the upper and lower limits ±11 A. When the load power suddenly increases to 15,000 W, the AC side current becomes a sine value of the upper and lower limits ±33 A. The change factor is the same as the load power. As shown in Fig. 5e, when the load power is 10,000 W, the sub-module capacitor voltage fluctuates between 380 and 448 V. When the load power is reduced to 5000 W, the fluctuation range of the sub-module capacitor voltage becomes smaller and fluctuates
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between 398 and 440 V. When the load power becomes 15,000 W, the voltage fluctuation range of the sub-module capacitor becomes larger to 360–450 V. It can be seen from Fig. 5f that when the load changes, the SOC state of the battery unit changes accordingly. When the load power suddenly decreases, the decrease in the SOC of the battery unit becomes smaller, and the discharge speed of the battery unit becomes slower. When the load power suddenly increases, the SOC of the battery unit decreases greatly, and the discharge speed of the battery unit becomes faster. It can be confirmed that when the system power changes, the energy storage unit can respond quickly and provide corresponding inertia support for the system. 4.2 Frequency Sudden Change The simulation conditions are: at 1 s time, the system frequency is reduced from 50 Hz to 49.8 Hz. At 1.5 s, the system frequency returns to 50 Hz. The frequency waveform at this time is shown in Fig. 6a.
P/W
1.05
50
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600
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0.85
400 300
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1.5 2 t/s c Waveform diagram of sub-module capacitor voltage when the frequency suddenly changes
10 4
1
0.95 0.5
1 1.5 2 t/s b The waveform diagram of the active power on the AC side when the frequency suddenly changes 50 49.74
49.8 49.68 0.8
49.6 49.4 49.2 0.5
SOCpa1 SOCna1 SOCpb1
0.85
SOCnb1 SOCpc1 SOCnc1
1 1.5 2 t/s d The waveform diagram of the sub-module battery SOC when the frequency suddenly changes
Fig. 6. System waveform diagram when the frequency suddenly changes
As shown in Fig. 6b, when the frequency fluctuates, the active power on the AC side changes accordingly. At the moment of 1 s, when the system frequency is reduced to 49.8 Hz, the active power of the AC side is stabilized at around 10,100 W after 0.1 s adjustment. At the moment of 1.5 s, when the system frequency is restored to 50 Hz, the active power of the AC side is restored to 10,000 W after 0.1 s adjustment. In Fig. 6c, the capacitor voltage of each sub-module can achieve a better balance. At the same time, it can be seen from Fig. 6d that when the frequency fluctuates, the load power does not change, so the SOC of the energy storage battery can smoothly decrease, and the SOC drops from 49.82% to 49.31% after 1.5 s, and a good SOC balance can be achieved.
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5 Conclusion This paper studies the MMC-ESS topology with decentralized management and control of energy storage units, and proposes a modular multi-level energy storage power conversion system with grid support capability. Using the MMC modular topology, the energy storage unit can be managed and controlled in a decentralized manner, which can ensure that the energy storage unit can output safely and stably when the system is disturbed, which improves its safety and reliability. At the same time, the energy storage technology based on power electronic technology can flexibly match the grid, but the traditional control method cannot use the energy storage to provide inertia for the grid. In this paper, virtual synchronous control is adopted to make MMC-ESS imitate the output characteristics of the synchronous machine and provide virtual inertia for the power system. The reliability of the proposed grid-supported MMC-ESS is verified by simulation. Acknowledgements. This research was partially funded by the Jiangsu Postgraduate Research and Practice Innovation Program Project 1812000024994.
References 1. Asmine, M., Langlois, C.-É.: Field measurements for the assessment of inertial response for wind power plants based on Hydro-Quebec TransEnergie requirements. IET Renew. Power Gener. 10(1), 25–32 (2016) 2. Zhao, E.S., Han, Y., Zhou, S.Y., et al.: Review and prospect of inertia and damping simulation technologies of microgrids. Proc. CSEE 42(04), 1413–1428 (2022) 3. Wang, K.F., Xie, L.R., Qiao, Y., et al.: Analysis of frequency regulation performance of power system improved by battery energy storage. Autom. Electr. Power Syst. 46(01), 174–181 (2022). (in Chinese) 4. Zhang, C., Wei, Y.L., Cao, P.F., et al.: Energy storage system: current studies on batteries and power condition system – ScienceDirect. Renew. Sustain. Energy Rev. 82, 3091–3106 (2018) 5. Cheng, C.Z., Xu, C., Dai, K., et al.: Three-level balancing control for battery state-of-charge based on MMC-BESS. Power Syst. Prot. Control. 49(15), 100–108 (2021). (in Chinese) 6. Vasudevan, K.R., Ramachandaramurthy, V.K., Venugopal, G., et al.: Variable-speed PICO hydel energy storage with synchronverter control to emulate virtual inertia in autonomous microgrids. IEEE Syst. J. 16(1), 452–463 (2021) 7. Zhang, B., Zhang, X.L., et al.: Configuration method for energy storage unit of virtual synchronous generator based on requirement of inertia support and primary frequency regulation. Autom. Electr. Power Syst. 43(23), 202–209 (2019). (in Chinese) 8. Xing, D.F., Tian, M.X.: Relationship between frequency characteristics of virtual synchronous generator and parameters of energy storage equipments. Power System Technology 45(9), 1000–3673 (2021). (in Chinese) 9. Panda, D., Raipurohit, B., Monti, A.: Synthetic inertia for frequency regulation of electric grid using modular-multilevel converter. In: IEEE Industry Applications Society Annual Meeting (2019) 10. Ali, H., Li, B., Xu, Z., et al.: Virtual synchronous generator design based modular multilevel converter for microgrid frequency regulation. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS) (2019)
On-line Monitoring and State of Health Estimation Technology of Lead-Acid Battery Danyang Li1 , Gang Zhang1,2(B) , Zhaofeng Gong1,3 , and Xingyuan Ma1 1 Beijing Jiaotong University, Beijing, China
{18291230,gzhang}@bjtu.edu.cn
2 Rail Transit Electrical Engineering Technology Research Center, Beijing, China 3 Power Supply Branch of Beijing Metro Operation Co., Ltd., Beijing 100082, China
Abstract. Valve regulated lead-acid (VRLA) battery is in the floating charge state for a long time, and the online accurate assessment of its state of health (SOH) is of great significance. In this paper, the online monitoring platform is built, and the discharge characteristics of battery are tested. Based on the phenomenon of terminal voltage “steep drop and rise again” during discharge, nine characteristics were extracted, including trough voltage, plateau voltage, voltage difference, trough current, plateau current, current difference, trough time, plateau time and time difference. The health factors were obtained by dimension reduction through principal component analysis (PCA) and Pearson correlation coefficient. The BP neural network is built to estimate SOH of the battery and is optimized using genetic algorithm (GA). The accuracy of the battery SOH assessment model is verified by comparing with the capacity check discharge experiment data, and the feasibility of the proposed battery SOH assessment method is also proved. Keywords: Valve regulated lead-acid (VRLA) battery · State of Health (SOH) · Neural Network · Principal Component Analysis
1 Introduction VRLA batteries, as backup power sources, is in the floating charge state for most of the time, and their actual life is statistically much lower than the expected life [1]. This is due to the lack of monitoring and maintenance in practical applications, which leads to problems such as active substance shedding, water loss, electrolyte leakage and sulfation of the battery after long working time [2]. These problems, if not solved in time, will reduce the capacity of the battery and greatly shorten its service life. Therefore, the battery SOH needs to be estimated in order to detect problematic batteries in time and improve the life of the battery pack. As backup power sources, the maximum available capacity that a battery can release is its most important characteristic. As defined by the battery SOH, under certain discharge conditions, the value is the ratio of the capacity released by the battery from the full state at a certain rate to its cut-off voltage to its nominal capacity [3]: SOH =
Cnow × 100% C
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(1)
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Where C now and C are the current available capacity and nominal capacity of the VRLA battery. The traditional method measures the exact value of SOH by fully discharge the battery through a discharge test, and this method is also known as the capacity check discharge experiment method. However, the capacity check discharge experiment method has the disadvantages of off-line operation, thus requiring much time and effort, so it is generally performed annually [4], which is only suitable for the planned maintenance and operation mode. With the development trend from planned maintenance to condition maintenance, the battery management system has higher requirements for its automation and intelligence. Scholars have conducted research on online estimation methods for VRLA battery SOH, and the methods can be mainly divided into two categories: empirical model method and data-driven method. The empirical model method simulates the battery by establishing the equivalent circuit model of the battery, and the internal parameters such as internal resistance and open circuit voltage are identified from the battery terminal voltage and current data by parameter identification and the changes of internal parameters are tracked by algorithms such as Kalman filtering (KF) to estimate the battery SOH. The literature [5] uses the UKF algorithm to estimate the ohmic internal resistance of the battery in real time, and then the ratio of the ohmic internal resistance to the initial internal resistance is used as the SOH of the battery, but it requires parameter identification under complex operating conditions to ensure the accuracy of the identification, which is not in line with the long-term floating charge operating state of the backup battery. In the literature [6], the DEKF algorithm was used to evaluate both SOC and SOH, and the absolute error of SOH estimation was within 3%, but it took about 250 h for the algorithm to converge. The data-driven method mainly includes the use of machine learning algorithms such as support vector machine (SVM), relevance vector machine (RVM) and artificial neural network (ANN). It is relatively simple, which does not need to focus on the complex degradation mechanism inside the battery, but only from the perspective of the historical degradation data of the battery, with the help of machine learning algorithms to learn from the historical data. And battery SOH is estimated by the trained black box model. The data-driven method not only gets rid of the study of the complex mechanism inside the battery, but also has strong applicability to batteries with different operating conditions. In the literature [7], the author used the whole life cycle data of VRLA batteries, and a SOH estimation model was constructed using deep neural network algorithm (DNN) with voltage, current, SOC and differential voltage of the battery as feature parameters. In the literature [8], the capacity prediction model of lead-acid battery was constructed based on LSTM neural network with the parameters of float voltage, average charge voltage, average charge duration, discharge cut-off voltage and discharge duration of the battery as the input and the capacity of the battery as the output. To address the overfitting problem caused by small data samples, the paper optimizes the LSTM network structure using the Dropout algorithm, and the research result shows that the model not only has high prediction accuracy but also has good generalization ability. In the literature [9], an SVM-based model was developed by choosing the ‘steep drop and rise again’ characteristics of VRLA batteries as the input. To improve the accuracy of the
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model, the paper used the WCPSO algorithm to optimize the model, and the validation result shows that the optimized model could be used for the prediction of battery SOH with the accuracy of more than 93%. In summary, the empirical model method requires complex operating conditions for parameter identification, and the model takes a long time to reach convergence in practical applications, which is not suitable for the operating conditions of long-term float charging of backup batteries. The data-driven method ignores the internal mechanism of the battery and builds SOH estimation models based on historical data, which are usually optimized in combination with other algorithms in order to overcome the shortcomings of traditional machine learning algorithms. In this paper, the data-driven method is used to establish a BP neural network model to realize battery SOH estimation, and it is optimized by genetic algorithm to improve the estimation accuracy. Finally, an online monitoring platform is built to verify the effectiveness of the chosen method. It turns out that the chosen method can accurately estimate the SOH of the tested VRLA battery.
2 VRLA Battery Working Principle 2.1 VRLA Battery Electromotive Force (EMF) The negative terminal of a VRLA battery loses electrons when discharging and gains electrons when charging [10], and its complete electrochemical reaction is shown in Eq. (2): − Pb + SO2− 4 PbSO4 + 2e
(2)
The equilibrium potential of the electrode can be calculated by substituting it into the Nernst equation as: 0 EPb/ PbSO4 = EPb / PbSO4 +
αPbSO4 RT ln nF αPb · αSO2−
(3)
4
are the concentrations of lead sulfate, lead and Where α(PbSO4 ), α(Pb) and α(SO4 sulfate ions, T is the standard thermodynamic temperature value, R is the ideal gas constant value, n is the number of molar electrons in the electrochemical reaction, and F is the Coulomb constant.Then, bring these parameters into the reaction Eq. (3) for a simplified calculation process, the equilibrium potential of the negative electrode can be obtained as: 2− )
EPb/ PbSO4 = −0.358 − 0.029 lg αSO2− V 4
(4)
From Eq. (4), it can be seen that when the concentration of SO4 2− in the electrolyte is increased, the equilibrium potential of the negative electrode will continue to move in the negative direction, that is, the negative potential is linearly related to the SO4 2− concentration. Under the condition of constant SO4 2− concentration, the equilibrium potential of the negative electrode is only influenced by the temperature and is not related to the acidity value of the electrolyte.
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The positive electrode gains electrons when discharging and loses electrons when charging, and the complete electrochemical reaction is shown in Eq. (5): PbSO4 + 2H2 O PbO2 + SO42− + 4H + + 2e−
(5)
The equilibrium potential of the electrode can be calculated by substituting it into the Nernst equation as: 0 EPbO2 / PbSO4 = EPbO + 2 / PbSO4
4 RT αPbO2 · αSO42− · αH + ln 2 nF αPbSO4 · αH 2O
(6)
Where α(PbO2 ), α(H 2 O) and α(H + ) are the lead oxide, water and hydrogen ion concentrations. Similarly, the positive potential can be obtained as: EPb/ PbSO4 = 1.683 − 0.118pH − 0.059 lg αH2 O + 0.029 lg αSO2− V 4
(7)
From Eq. (7), it can be seen that the equilibrium potential of the positive electrode has a linear relationship with the pH of the electrolytic solution, that is, the equilibrium potential of the electrode increases by 0.118 V for each unit increase in the pH as the hydrogen ions of the electrolyte solution are continuously consumed. However, the value of the positive electrode potential E is independent of the concentration of SO4 2− ions. The EMF is determined by the difference in equilibrium potential between the positive and negative electrodes expressed as shown in Eq. (8). E = EPbO2 / PbSO4 − EPb/ PbSO4
(8)
The reactions in the battery can be expressed in a general reaction equation, as shown in Eq. (9). Pb + PbO2 + 2H2 SO4 2PbSO4 + 2H2 O
(9)
Therefore, the EMF of the VRLA battery can be expressed as: E = 2.041 + 0.059 lg
αH2 SO4 αH2 O
(10)
Where α(H 2 SO4 ) is the sulfuric acid concentration and α(H 2 O) is the water concentration. From the above, the EMF of the VRLA battery is related to the concentration of hydrogen ions in the electrolyte. When the concentration of sulfuric acid and the concentration component content of water in the electrolyte are known, they can be substituted into Eq. (10) to solve for the EMF of the VRLA battery. 2.2 VRLA Battery Voltage “steep drop and rise again” (Coup de fouet) Studies have shown [11, 12] that when a battery is discharged from the fully charged state, its terminal voltage will undergo a “Coup de fouet” (CDF) phenomenon, that is,
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Fig. 1. Coup de fouet curve
the terminal voltage first drops rapidly to the trough voltage, and then automatically rises to the plateau voltage. The CDF phenomenon is shown in Fig. 1. From Eq. (10), the electric potential E of the battery is determined by the ratio of sulfuric acid concentration and water concentration. When the battery is discharged, the active material in both poles first consumes H + ions in the electrolyte near the poles, so the sulfuric acid concentration near the poles drops rapidly. At this time, the terminal voltage of the battery drops rapidly due to the decrease of sulfuric acid concentration near the poles. According to the diffusion phenomenon, the material with high concentration spreads to the direction of low concentration, the H + ions in the surrounding electrolyte which are not involved in the reaction will move to the vicinity of the two poles, and when the rate of movement of the surrounding H + ions is enough to offset the rate of consumption of the two poles, the voltage will no longer fall and will rise again. However, the continuous discharge will continue to consume H + ions in the electrolyte, so the terminal voltage will fall after rising for a period of time.
3 Battery SOH Estimation Method At present, the method to accurately measure the actual capacity of the battery is the traditional capacity check discharge experiment, but it requires off-line and complete discharge, so it is time-consuming. And complete discharge will jeopardize the operational life of the battery. Research shows [1] that the trough and plateau voltages of the CDF phenomenon are correlated with the capacity. Combining with the actual use of the battery in the subway power supply system, the CDF phenomenon is perfectly fitted to evaluate the battery SOH, because it only requires shallow discharge. In this paper, based on the CDF phenomenon, 9 characteristics are extracted, including trough voltage, plateau voltage, voltage difference, trough current, plateau current, current difference, trough time, plateau time and time difference. Then, the 9 features are subjected to PCA to reduce the feature dimension. Secondly, the correlation between the
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reduced features and SOH is then judged by Pearson correlation coefficient to determine the health factors of the battery SOH estimation model. Finally, the SOH estimation model is established by ANN. 3.1 Principal Component Analysis (PCA) Since the SOH estimation model is based on the battery data collected by the monitoring platform in real-time monitoring, if too many features are selected it will increase the space required for data storage and the calculation time used for calculation, so the usability of the algorithm needs to be improved by dimensionality reduction. PCA is the most commonly used linear dimensionality reduction method, and it focus on the variance of the transformed data. When the variance is the largest, the dimensionality of the transformed axes is lowest, but the original data information is relatively well preserved. The output of PCA is reduced from the original dimension of X to k dimensions. PCA can calculate both principal component weights and indicator weights. Specific steps are as follows: (1) Standardization of initial data with uniform magnitudes (2) Calculate the correlation coefficient matrix and find the eigenvalues and eigenvectors (3) Principal component analysis (4) Calculate principal components The relationship between the features obtained after PCA and SOH is unknown, so the correlation coefficient should be determined, and the features whose correlation satisfies the linear relationship should be extracted as the health factor input of the model. Pearson correlation coefficient is used to measure the correlation between groups of data, based on the deviation of two groups of data from their respective means, and reflects the correlation between two variables by multiplying the two deviations. Pearson’s correlation coefficient is defined as the quotient of the covariance and standard deviation between two variables, which can be calculated as: r=
Xi −X Yi −Y 2 n 2 i=1 Xi −X i=1 Yi −Y
n
n
i=1
(11)
3.2 SOH Estimation Model Battery SOH is affected by the charge and discharge voltage, current, and time and there is no obvious functional relationship, so it is impossible to establish an accurate physical circuit equivalent model. The neural network has the ability of nonlinear mapping and generalization, which can achieve accurate estimation as long as the training data is sufficient, so this paper use ANN to build the SOH estimation model. BP neural network mainly including input layer, implicit layer and output layer, and the model training process is mainly forward transmission and error back propagation.
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BP neural network relies on the completeness of the training data, and the trained models tend to fall into the local extrema of the error function. To address this problem, this paper introduces the genetic algorithm, which is a global search optimization algorithm based on biological mechanisms. The genetic algorithm is used to optimize the initial weights and thresholds of the BP neural network, so that the optimized BP neural network can work better. The basic elements of a genetic algorithm include population initialization, fitness function, genetic operations (selection, crossover, and mutation), and operational parameters. The working principle of the genetic algorithm is shown in Fig. 2.
Fig. 2. Working Principle Diagram of Genetic Algorithm
In this paper, the health factor after dimensionality reduction is used as input. Firstly, the network structure is determined and the initial parameters of neural network weights and thresholds is the initial population. The obtained thresholds and weights are assigned to the BP neural network and the network is trained with training data and tested with test samples. After the error calculation, the error is genetically optimized, and the optimization is stopped when the set number of iterations meets the requirements, and the best threshold and weights are output. The GA-BP neural network model developed in this paper is based on the relationship between the selected features, which establishes the following functional relationship: SOH = f (U1 , U2 , U3 , I1 , I2 , I3 , T1 , T2 , T3 )
(12)
Where U 1 , U 2 and U 3 are trough voltage, plateau voltage and voltage difference; I 1 , I 2 and I 3 are trough current, plateau current and current difference; T 1 , T 2 and T 3 are trough time, plateau time and time difference.
4 Experimental Validation 4.1 Online Monitoring Platform The block diagram of the battery online monitoring system is shown in Fig. 3, including four parts: backup series battery pack, signal acquisition module, data transmission module and monitoring platform. In this paper, single batteries are connected in series as a group for charging and discharging. The signal acquisition module collects battery voltage and charging/discharging current, and transmits the collected data to the data processing center through Ethernet. The upper computer is embedded with the SOH estimation model,
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Fig. 3. Online monitoring platform
which brings the pre-processed data into the model and displays the battery SOH in the monitoring platform. According to the actual battery operation, this paper discharges the battery pack in three current cases: 6.9 A, 4.5 A and 2.7 A. After PCA, 5 principal components were extracted from the 9 feature quantities by principal component analysis, and 3 principal components with high linear correlation with SOH were selected as the health factors. 4.2 SOH Estimation Results and Analysis SOH estimation model accuracy validation. The data with discharge currents of 6.9 A, 4.5 A and 2.7 A were mixed together for data processing, and after the dimensionality reduction, the processed data were randomly divided into two parts one as the training set and the other as the test set to verify the accuracy of the model. From Fig. 4, it can be seen that the BP neural network and the GA-BP neural network have similar trends in the estimation and some data points have a high degree of overlap between the two models. However, the average relative error of the BP model is 4.01% and the average relative error of the GA-BP model is 2.22%, which shows that the optimized model has more accurate estimation results and the accuracy of SOH estimation is verified by this set of data. Effect of different discharge currents on the model. To verify the effect of discharge current on the accuracy of the model, two sets of experimental data were used for validation. The first group is to put the data collected at 4.5A through PCA and then used to train the model, and the data collected at 2.7A is used for testing. In the second group, the data collected at 6.9A were used for testing. The results are shown in Fig. 5. The error of the SOH estimated by the GA-BP neural network does not fluctuate much with the change of current, and the relative error maxima of the SOH are all around 5% without getting significantly larger, so it can be seen that the change of current does not have an impact on the model accuracy. This feature can increase the applicability of the SOH estimation model and make its generalization ability stronger. Effect of different voltage sampling frequency on the model. To verify the effect of voltage sampling frequency on the recovery of the CDF curve and the accuracy of the SOH estimation model, two sets of different frequency experimental data were used to verify. Comparing Fig. 6 (a) and (b), it can be seen that the maximum value of the relative
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Fig. 4. Comparison of relative error between BP and GA-BP models
(a)
(b)
Fig. 5. Estimation results of different discharge currents (a) the first group (b) the second group
error of SOH estimated by the GA-BP neural network is less than 5%, so it can be seen that the variation of the sampling frequency within a certain range will have no effect on the model accuracy.
5 Conclusion This paper investigates the online estimation method of battery SOH based on the CDF phenomenon of lead-acid batteries. The following work has been accomplished. (1) Based on the battery discharge CDF curve, this paper used PCA and Pearson correlation coefficient to finish the feature extraction and dimensionality reduction of the features. (2) Established a GA-BP SOH estimation model.
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(a)
(b)
Fig. 6. Estimation results at different voltage sampling frequency (a) 0.025 Hz (b) 0.01 Hz
(3) Based on the real-time data obtained from the battery online monitoring platform, the accuracy of the SOH estimation model was verified. The effects of different discharge currents and different voltage sampling rates on the model were studied. The experimental results show that the proposed SOH estimation method can achieve accurate SOH estimation, and is not affected by the discharge current and sampling frequency, which ensures the applicability of the model. Acknowledgments. This paper is supported by Beijing Metro Research Project (2021HTJS-008).
References 1. Yang, J., Chen, H.U., Wang, H., et al.: Research progress of failure model and mechanism analysis of lead-acid battery. Chin. J. Power Sour. 42(03), 459–462 (2018). (in Chinese) 2. Ge, L.H., Song Zheng, X., Zhang, G.G.: Study on float life of valve regulated lead acid batteries for substation. Power Capacit. React. Power Compens. 41(06):191–195+201(2020). (in Chinese) 3. Li, C.R., Xiao, F., Fan, Y.X., Yang, G.R., Tang, X.: An Approach to lithium-ion battery SOH estimation based on convolutional neural network. Trans. China Electrotech. Soc. 35(19), 4106–4119 (2020). (in Chinese) 4. Li, R.J., Liu, B., Zhang, X.M., Shu, Z.Y.: Life prediction of lead-acid battery in substation based on improved LSTM. Batter. Bimon. 50(06), 560–564 (2020). (in Chinese) 5. Zhou, X.B.: Research on estimation of battery health based on improved Kalman filter. Chinese Master’s Theses Full-text Database (2017). (in Chinese) 6. Tran, N.-T., Abdul, K., Woojin, C.: State of charge and state of health estimation of AGM VRLA batteries by employing a dual extended Kalman filter and an ARX model for online parameter estimation. Energies 10(1), 137 (2017) 7. Hu, C., Jin, Y., Cui, B.H., Du, C.Y.: State of health estimation of lead-acid battery based on deep learning. Batter. Bimon. 51(01), 63–67 (2021). (in Chinese) 8. Shu, Z.Y., Zhai, E.J., Li, Z.H., Huang, Z.P.: Prediction of lead-acid battery capacity based on dropout optimization algorithm and LSTM. J. Power Supply, 1–12 (2021). (in Chinese)
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9. Zhuang, H.M., Xiao, J.: VRLA battery SOH estimation based on WCPSO-LVSVM. In: Applied Mechanics and Materials. Changsha, pp. 396–400. Trans Tech Publications Ltd., China (2014) 10. Luo, Z.J., Lin, H.C., Zhang, D.X., Lu, S.F., Zhang, C.L.: Influence of internal resistance in balance on temperature field of VRLA batteries, 45(09):1189–1192 (2021). (in Chinese) 11. Shi, D.J., Song, Z.X.: A review on the state of health estimation methods of lead-acid batteries. J. Power Sour., 517230710 (2022) 12. Mahendra, N., Kumar, S.: Charge coup de fouet phenomenon in soluble lead redox flow battery. Chem. Eng. Sci., 154 (2016)
Distributed Optimal Allocation of Renewable Energy and Energy Storage Based on Alternating Direction Method of Multipliers Mingyu Ma, Jinpeng Shen, LiGao Junjie(B) , Jun Yang, Song Ke, and Hongli Wang School of Electrical and Automation, Wuhan University, Wuhan 430072, Hubei, China [email protected], [email protected], {junjie_lg,Saturn,kesong1997, 2017302540221}@whu.edu.cn
Abstract. In the context of high proportion of renewable energy access, in order to promote the consumption of renewable energy, the cooperation between renewable energy stations and energy storage (ES) has become increasingly close. In previous studies, renewable energy stations and ES are often regarded as a whole, but in actual scenarios, the two often belong to different stakeholders. Aiming at the characteristics of distributed autonomous decision-making between renewable energy stations and ES, taking ES allocation capacity and power as shared variables, and decomposing the coordination mechanism based on the alternating direction method of multipliers(ADMM), a distributed collaborative allocation model of two operators is established. Through a small number of iterations of information, the optimal ES allocation strategy under the distributed framework is obtained. Finally, the effectiveness and applicability of the proposed algorithm is verified by comparing the calculation results of the proposed algorithm with the centralized algorithm using the data of a small integrated energy system in North China. Keywords: ADMM · Distributed decision · Energy Storage · Renewable Energy
1 Introduction In recent years, the development of renewable energy represented by distributed energy sources (DESs) has been very rapid, and the total installed capacity of DESs in the system is expected to reach 130 GW by 2030 [1]. However, due to the impact of wind speed and solar, the randomness and the spatial-temporal matching will have an increasingly negative impact on the system operation. The energy storage (ES) can effectively reduce the impact of wind power and photovoltaic access to the distribution network. How to consider the scenery uncertainty and integrate various objectives to optimize the ES allocation has become an urgent issue to be solved [2]. The scholars have conducted many studies on the optimal ES allocation in terms of enhancing the distribution system ability to consume DESs. Reference [3] established an expected value-assisted decision model for ES allocation based on the simulation of grid-connected renewable energy based on stochastic programming theory. References © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 300–309, 2023. https://doi.org/10.1007/978-981-99-1027-4_32
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[4] and [5] developed an optimal dispatching model with ES, considering both the gridconnected value of wind power and the total system operation cost. References [6] and [7] proposed an optimal allocation method for ES systems in the active distribution network considering economics, and an improved multi-objective particle swarm algorithm is used. References [8] and [9] developed a multi-energy coordinated ES configuration model to enhance system economics. The robust optimization allocation model was established in [10]. Meanwhile, the spatial constraint parameters were introduced to adjust the uncertain boundaries ensemble to compensate for the shortcomings of the traditional robust optimization which is conservative. Reference [11] proposed an ES optimal allocation strategy considering demand response and source load uncertainty, and constructed a two-stage collaborative model for ES system planning and operation. References [12] and [13] established an optimal allocation model for hybrid energy storage considering electro-hydrogen coupling, which fully exploits the potential of ES. For the distributed problem of ES allocation to promote renewable energy consumption, in this paper, a decomposition synergy mechanism that considers the autonomous decision-making characteristics of renewable energy and ES is proposed. An ADMMbased distributed collaborative algorithm is used. The distributed collaborative algorithm takes the ES allocation capacity as a shared variable, and obtains the optimal ES allocation strategy considering the renewable energy uncertainty through a small number of information iterations. Finally, the calculation results of the centralized algorithm and the distributed collaborative algorithm are compared using real data. The effectiveness and applicability of the proposed algorithm in solving the ES optimal configuration problem in a distributed framework are verified.
2 Centralized Optimization Model 2.1 Objective Function In order to allocate ES to promote renewable energy consumption, the total system cost is minimized as the goal, i.e., the sum of abandoned wind cost, abandoned solar cost, ES investment cost, operation cost and unit output cost is minimized. min f1 = fes + fw + fv + fg
(1)
where: f1 is the total cost, fes is the investment and operation cost of ES, fw is the abandoned wind cost, fv is the abandoned light cost, fg is the cost of unit output. (1) ES day investment costs and operating costs fes = Ces
T t=1
(Pes,dis (t) + Pes,cha (t) +
P P + C E E ) r(1 + r)Ts (Ces es es es 365 (1 + r)Ts − 1
(2)
where: Ces is the ES unit operating cost coefficient; Pes,dis (t) is the ES discharge power in the t period; Pes,cha (t) is the ES charging power in the t period; T is the P is the investment cost per unit power total number of periods in a dispatch cycle. Ces E of ES; Ces is the investment cost per unit capacity of ES; Pes is the rated power of the ES; Ees is the rated capacity of the ES; r is the discount rate; T S is the life cycle of the ES device.
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(2) Wind and light abandonment costs fw = Cw
T
Pwd (t), fv = Cv
t=1
T
Pvd (t)
(3)
t=1
where: Cw is the penalty cost per unit of wind abandonment; Pwd (t) is the power of wind abandonment in the t period; Cv is the penalty cost per unit of light abandonment; Pvd (t) is the power of light abandonment power in the t period. (3) Unit operating cost fg = Cg
T
aPg2 (t) + bPg (t)
(4)
t=1
where: Cg is the output cost of the unit; Pg (t) is the unit power during the t period; a and b are the fitting coefficients of the unit output cost. 2.2 Constraints The above optimization objectives are subject to the following constraints: power balance constraint, unit output constraint and ES constraint. (1) Power balance constraint Pl (t) = Pg (t) + Pv (t) + Pw (t) + Pes,dis (t) − Pes,cha (t) − Pwd (t) − Pvd (t)
(5)
where: Pl (t) is the load power in the t period; Pw (t) is the wind power in the t period; Pv (t) is the photovoltaic power in the t period. (2) ES charging and discharging constraints 0 ≤ Pes,cha (t) ≤ Ucha Pes , 0 ≤ Pes,dis (t) ≤ Udis Pes where: Ucha and Udis are Boolean variables. (3) ES charge constraints Ees (t) = (1 − σes )Ees (t − 1) + ηes,cha Pes,cha (t − 1) − Ees,min ≤ Ees (t) ≤ Ees,max
Pes,dis (t−1) ηes,dis
(6)
(7)
where: Ees (t) is the ES energy state in the t period; σes is the self-loss rate of the ES device; ηes,cha and ηes,dis are the charging efficiency and the discharging efficiency, respectively; Ees,max and Ees,min are the upper/lower limits of the ES energy state. In order to ensure that ES can be used in a sustainable cycle, the energy stored by the ES at the end/beginning of the dispatch period should be the same. Ees (0) = Ees (24)
(8)
Pgmin ≤ Pg (t) ≤ Pgmax
(9)
(4) Unit output constraint
where: Pgmax and Pgmin are the upper and lower limits of unit output, respectively.
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3 ADMM-Based Distributed Cooperative Optimization Model The centralized optimization method relies on the complete interaction of information between ES and renewable energy station to carry out the unified allocation of ES. In the actual power system, ES and renewable energy station do not always belong to the same interest subject, and some information between each subject needs to be kept confidential and cannot be fully interacted with. To avoid this problem, this section establishes a distributed autonomous decision making and collaborative optimization model for ES and renewable energy station using ADMM algorithm for the multi-subject decision making characteristics of renewable energy stations and ES. 3.1 Decomposition of Synergistic Mechanisms The core idea of distributed cooperative optimization allocation of renewable energy field station and ES is shown in Fig. 1. Renewable Energy System Autonomous Configuration Center Update multiplier coefficients
Issuing configuration commands
Renewable Energy System
Energy Storage System Autonomous Configuration Center Update multiplier coefficients
Passing shared variables
Upload basic parameters
Issuing configuration commands Energy storage configuration capacity and power
Upload basic parameters
Energy Storage System
Information flow
Fig. 1. Distributed Collaborative Optimization Framework
The goal of the renewable energy station is to allocate ES to promote renewable energy consumption, while the goal of the ES side is to minimize the investment and operating costs of ES. Therefore, the ES allocation capacity and power can be selected as the collaborative shared variables of the two parties. The allocation capacity and power of ES are introduced into the renewable energy station sub-problem, and the following relationship is satisfied: ne c ne c = Ees , Pes = Pes Ees
(10)
ne and P ne are the ES capacity and power allocation demand of the renewable where: Ees es c and P c are the ES capacity and power allocation supply of the energy respectively; Ees es ES side. Equation (10) is the key to realize the distributed cooperative optimization. And according to the ADMM proposed below, the renewable energy side and the ES side can be solved separately to develop the ES allocation demand plan and the ES allocation supply plan. Through optimal decomposition and autonomous coordination to realize the supply and demand matching.
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3.2 Distributed Collaborative Optimal Allocation Algorithm Based on ADMM, the centralized optimal allocation problem of renewable energy station and ES is decomposed into renewable energy station sub-problem and ES sub-problem. With the goal of minimizing the respective costs, the optimal allocation of ES is achieved through a small amount of information exchange between the two sub-problems. 3.2.1 Renewable Energy Station Optimization Subproblem The optimization objective of the renewable energy side sub-problem is to minimize the sum of wind abandonment cost, light abandonment cost and unit output cost, and the decision variables are generator unit output and ES capacity and power allocation demand. min f2 = fw + fv + fg + ϕn ϕn = λ1(k)
(11)
T T ne c(k) ne c(k) Pes + λ2(k) Ees + − Pes − Ees t=1
t=1
2 ρ 2 ρ1 2 ne ne c(k) c(k) − Ees Pes − Pes + Ees 2 2 2 2
(12)
ne and E ne are the ES capacity where: f2 is the total cost of the renewable energy station; Pes es c(k) and power allocation demand of the renewable energy station, respectively; Pes and c(k) Ees are the ES capacity and power allocation supply obtained after the kth iteration of the ES subproblem, respectively; ρ1 and ρ2 are penalty factors; λ1 and λ2 are lagrange multiplier coefficients; ϕn is the penalty term. The constraints are the same as in the centralized optimization model. At this time, the sub-problem of the renewable energy field station can be expressed as:
min f2 = fw + fv + fg + ϕn s.t.(5)−(9)
(13)
3.2.2 ES Side Optimization Subproblem The optimization objective of the ES side sub-problem is to minimize the daily investment and operating costs of ES, and the decision variables are ES capacity and power allocation supply. min f3 = fes + ϕg (k)
ϕg = λ1
T t=1
(14)
T (k) ne(k+1) c ne(k+1) c Pes + λ2 Ees + − Pes − Pes t=1
2 ρ 2 ρ1 2 ne(k+1) ne(k+1) c c − Pes − Ees + Ees Pes 2 2 2 2
(15)
c and E c are the ES capacity and power where: f3 is the total cost of the ES side, Pes es ne(k+1) ne(k+1) allocation supply, respectively; Pes and Ees are the ES capacity and power
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allocation demand obtained after the k + 1th iteration of the renewable energy side, respectively; ϕg is the penalty term. The constraints are the same as in the centralized optimization model. At this point, the ES side sub-problem can be expressed as: min f3 = fes + ϕg s.t.(6)−(8)
(16)
3.2.3 Convergence Criterion of ADMM 2 2 ne(k) ne(k) c(k) c(k) − Ees (t) ≤ ε Pes − Pes, ≤ ε, Ees 2
2
(17)
where: ε is the original residual tolerance limit. 3.2.4 Algorithm Flow Step 1: Initialization. Assign the number of iterations k to 1, given the original residuals ε, penalty factors ρ1 and ρ2 , set the initial values of ES capacity and power of the ES c(0) c(0) side subproblem Ees and Pes , and the initial values of lagrange multiplier coefficients (0) (0) λ1 and λ2 . Step 2: Calculate the renewable energy subproblem Eq. (13) and the ES side subproblem Eq. (16) sequentially. In this process, the results of solving the ES capacity and power allocation demand for the renewable energy subproblem and the results of solving the ES capacity and power allocation supply for the ES side subproblem are iterated sequentially, and the lagrange multiplier coefficients λ1 and λ2 are updated according to Eqs. (18). (k+1)
λ1
(k)
(k+1)
ne(k) c(k) = λ1 + ρ1 (Pes − Pes ), λ2
(k)
ne(k) c(k) = λ2 + ρ2 (Ees − Ees )
(18)
Step 3: judge the convergence according to (17), if the convergence criterion holds, stop the calculation and output the calculation result; otherwise, make k = k + 1 and go to step 2 for the next round of iterative optimization calculation until convergence.
4 Example Analysis In order to verify the effectiveness of the proposed algorithm, the ADMM and the centralized optimal allocation code are written on a Windows 10 system (2.50 GHz, 16 GB) using MATLAB, and the YALMIP toolbox and the GUROBI commercial solver are called for the solution. Taking a small power grid in North China as the research object, a typical winter day scene is selected for simulation analysis. The operation is based on 24 h of the whole day as one cycle and 1 h as a period. The wind, PV and load data are shown in Fig. 2. The key parameters of ES are listed in Table 1.
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Fig. 2. Wind and light output and load curves.
Table 1. ES parameters Parameters
Unit
Value
Parameters
Unit
Value
Ces
¥/kWh
0.05
Ts
Year
10
E Ces P Ces
¥/kWh
1000
r
%
8
¥/kW
1000
Ees,min /Ees,max
–
0.2/0.9
4.1 Distributed Collaborative Optimal Allocation Analysis Based on the wind power and load characteristics in the above typical day scenario, in order to promote the maximum consumption of wind and PV, the ES demand is configured according to the distributed cooperative optimization allocation model proposed in this paper, and the storage capacity/power allocation demand in this scenario is 303 kWh/106 kW. The consumption of wind power and PV power before and after the ES allocation is shown in Figs. 3 and 4. It can be seen from the figure that through the optimal allocation of ES, the complete consumption of wind power and photovoltaic has been achieved.
Fig. 3. Comparison of wind abandonment before and after allocation
Table 2 shows the comparison of the calculation results obtained by the centralized allocation method and the ADMM-based distributed allocation method.
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Fig. 4. Comparison of light abandonment before and after allocation
Table 2. Cost and calculation time Optimization methods
Total cost/yuan
ES costs/yuan
Wind and light abandonment costs/yuan
Calculation time/s
Centralized
951.84
185.73
766.11
0.11
Distributed
952.06
185.83
766.23
47.81
From the comparison results, it can be seen that the ADMM-based distributed cooperative optimal allocation method of renewable energy and ES can obtain the same solution as the centralized optimal allocation, and the cost of both ES and renewable energy is basically the same, which verifies the effectiveness and correctness of the model and the proposed method in this paper. Because the centralized method does not require iterative computation, the calculation time is shorter compared to the distributed method.
Fig. 5. Residual convergence curve
The residual convergence curves during the calculation of the ADMM-based allocation method are shown in Fig. 5, which shows that the model has extremely fast convergence. Under this example, the shared variables are updated quickly, and the same solution as the centralized optimization method can be obtained in a short time.
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5 Conclusion Aiming at the characteristics of multi-agent distributed autonomous decision-making between renewable energy station and ES, a distributed collaborative allocation method for renewable energy stations and ES based on ADMM is proposed. Through the comparative analysis with the centralized allocation method, it is found to have the following characteristics: (1) Facing the multi-subject decision-making characteristics of renewable energy field stations and ES, it avoids the disadvantages of centralized optimal allocation method with a large amount of data and difficult to solve, and makes the allocation process more consistent with the characteristics that renewable energy station and ES are decided by different interest subjects separately. (2) It has good convergence and can get the same allocation strategy as the centralized allocation method in a short time.
Acknowledgements. This work is supported by the Science and Technology Project of Lishui Power Supply Company of State Grid Zhejiang Electric Power Co., Ltd. (2021ZK22).
References 1. Li, C., Dong, Z., Li, J.: Optimal control strategy of distributed energy storage cluster for prompting renewable energy accommodation in distribution network. Autom. Electr. Power Syst. 45(23), 76–83 (2021). (in Chinese) 2. Yang, X., Ding, L., Li, Y.: Study on optimal allocation of hybrid energy storage system considering wind power uncertainty. Power Demand Side Manag. 23(06), 69–74 (2021). (in Chinese) 3. Si, X., Li, C., Yang, H.: Auxiliary decision-making method of energy storage configuration under uncertainty. Sci. Technol. Eng. 21(07), 2699–2704 (2021). (in Chinese) 4. Dong, W., Gu, X., Luo, Z.: Research on optimal dispatching of energy storage device to increase the value of wind power grid. Thermal Power Gener. 50(08), 47–53 (2021). (in Chinese) 5. Li, D., Lv, X., Li, J.: Optimal capacity allocation method of energy storage system for increasing wind power integration. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference (IPEMC2020-ECCE Asia), pp. 3240–3244 (2020) 6. Yan, Q., Dong, X., Mu, J.: Optimal configuration of energy storage in an active distribution network based on improved multi-objective particle swarm optimization. Power Syst. Prot. Control 50(10), 11–19 (2022). (in Chinese) 7. Wang, K., Zhou, C., Jia, R.: Optimal configuration and economic analysis of energy storage system in regional power grid. In: 2021 3rd Asia Energy and Electrical Engineering Symposium (AEEES), pp. 540–545 (2021) 8. Jin, H., Teng, Y., Leng, O.: Multi-energy coordinated energy storage model in zero-waste cities based on situation awareness of source and load uncertainty. Trans. China Electrotech. Soc. 35(13), 2830–2842 (2020). (in Chinese) 9. Pontes, L.R., Espinoza, H.R., Molina, Y.P.: Optimal allocation of energy storage system in distribution systems with intermittent renewable energy. IEEE Latin Am. Trans. 19(02), 288–296 (2021)
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10. Wang, S., Han, X., Wang, H.: Robust optimization configuration strategy for energy storage system of new energy station. Mod. Electr. Power 38(06), 636–644 (2021). (in Chinese) 11. Nan, B., Dong, S., Tang, K.: Optimal configuration of energy storage in PV-storage microgrid considering demand response and uncertainties in source and load. Power Syst. Technol. (J/OL), 1–12 (2022). (in Chinese) 12. Li, Q., Zhao, S., Pu, Y.: Capacity optimization of hybrid energy storage microgrid considering electricity-hydrogen coupling. Trans. China Electrotech. Soc. 36(3), 486–495 (2021). (in Chinese) 13. Li, S., Gao, S., Guo, C.: Multi-objective capacity optimal allocation of hybrid energy storage system. In: 2017 6th International Conference on Energy, Environment and Sustainable Development (ICEESD), vol. 129, pp. 978–987 (2017)
Optimization of Moisture Absorption of High Temperature Composite Phase Change Thermal Storage Materials Qiao Geng1(B) , Chaomurilige1 , Jin Lu1 , Ma Hongkun2 , Deng Weiyu2 , Jiang Zhu3 , Huang Zibo1 , and Ding Yulong2 1 Global Energy Interconnection Research Institute Europe GmbH, Kantstr.162, 10623 Berlin,
Germany [email protected] 2 University of Birmingham, Birmingham B15 2TT, UK [email protected] 3 Southeast University, Sipailou No. 2, Nanjing 2100096, Jiangsu Province, China
Abstract. High temperature composite form-stable phase change material is a promising technology to promote and utilize renewable energy and improve the system efficiency. The hygroscopic property of Na2 CO3 -K2 CO3 -based composite form-stable phase change material was studied. This study focuses on the effects of material modification and surface treatment on the moisture absorption properties of phase change materials. Experimental results show that the methods of doping zeolite, silica gel and modified magnesium oxide have limited influence on the hygroscopicity of phase change materials. Some methods are not practical because of the limitation of operating temperature. The surface treatment methods can effectively suppress the hygroscopicity of the phase change material. Especially, when the metal film is wrapped, the moisture absorption of the material can be effectively controlled. The combination of coating and wrapping can further protect the material from the moisture as in long-term experiments, the weight gain by moisture absorption is no more than 5%. Keywords: Form-Stable Phase Change Material · Hygroscopicity · Thermal Energy Storage Material
1 Introduction Composite form-stable phase change thermal storage materials are commonly used as a general term for a class of materials that combine a structural support material with a phase change material matrix to form a specific structure, where the structural support material is a material (often inorganic) with a melting point higher than the melting point of the phase change material. By encapsulation, form-stable thermal storage materials could alleviate corrosion, phase separation, and low thermal conductivity problems that often arise in phase change materials in applications. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 310–319, 2023. https://doi.org/10.1007/978-981-99-1027-4_33
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Carbonates are one of the potential candidates for high-temperature thermal storage. However, its hygroscopicity is the main challenge in application. Hygroscopicity is the property of a substance to absorb moisture from the air resulting in changes in microscopic morphology and physicochemical properties, usually due to the substance’s affinity for water. On the one hand, it can be a hygroscopic agent, such as calcium chloride particles, molecular sieves with high specific surface area, etc. On the other hand, in the heat storage and exothermic applications of molten salt phase change materials, moisture absorption will exacerbate crushing, deformation, and material failure, which is an issue in reducing the service life of the equipment. At present, there are few studies on the hygroscopicity of phase change materials. Lu et al. [1] used Na2 CO3 K2 CO3 salt as phase change material, added glass powder as a binder, and sintered with MgO to prepare phase change composite materials. The moisture absorption experiment at 25 °C and 80%RH (relative humidity) for 72 h found that the hygroscopicity of the composite material decreased from 15% to 4%. Zhang et al. [2] prepared a phase change composite of Na2 CO3 -K2 CO3 molten salt first wrapped by SiO2 , then mixed with MgO and sintered; the hygroscopicity of the composite decreased from 31% to 19% after moisture absorption experiments (96 h at 28 °C and 80% RH). Chen et al. [3] designed a phase-change thermal storage material, which can be used for building temperature and humidity control by utilizing the hygroscopic properties of the material. They prepared the phase change microcapsules with alkane mixture as the phase change material and methyl triethoxysilane (MTES) as the shell material by the sol-gel method. This material was combined with diatomaceous earth and a composite phase change material for building materials was prepared. Compared with general building materials such as gypsum, the material’s hygroscopicity is significantly improved. Royo et al. [4] concluded that most salt-based phase change materials generally either have moistureabsorbing properties or water-loss properties, so it is recommended that the materials be sealed during use to maintain the thermal storage properties of the phase change materials. In this paper, high temperature composite form-stable phase change material for the practical application of moisture absorption problems, research to explore feasible improvement options; formulations, encapsulation, etc. were targeted to enhance and optimize.
2 High Temperature Composite Form-Stable Phase Change Material System Screening 2.1 Screening of Phase Change Materials and Their Hygroscopicity In accordance with the results of previous experimental studies, carbonate K2 CO3 Na2 CO3 has the characteristics of suitable melting point, good heat storage performance and safety performance, so it is a suitable phase change material for this project. The phase diagram is an effective tool to find out the eutectic points of binary mixtures. According to the K2 CO3 -Na2 CO3 phase diagram, when the molar ratio of Na2 CO3 and K2 CO3 -Na2 CO3 is 0.585, the two reach the eutectic point and melt into the eutectic salt. In this point, the phase change temperature of the eutectic salt is 709 °C, the mass ratio of Na2 CO3 to K2 CO3 is 51.9: 48.1, and the latent heat is about 173 kJ/kg.
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2.2 Screening of Skeleton Materials Since the pure carbonate system has the problems of low thermal conductivity, low heat transfer efficiency, and phase separation, it is necessary to consider making composite materials to make up for its shortcomings. The skeleton carrier acts as structural support, making the phase change material less likely to leak and flow in the molten state. The screening of structural support materials should generally follow the following points: 1. Acceptable stability and compatibility at high temperature; 2. High porosity and good wettability; 3. Good mechanical properties; 4. Affordability. The first consideration in the screening is the chemical compatibility of the framework material with Na2 CO3 -K2 CO3 , and then the porosity and cost of the framework material itself are screened. Ceramic-based materials in framework materials are widely studied, including MgO, Al2 O3 , SiO2 , and some honeycomb ceramics, foamed ceramics, etc. Although these framework materials do not contain porous structures themselves, they can be processed to generate porous frameworks or use interparticle. The pores provide load space for inorganic salts and can effectively prevent the surrounding inorganic salts from leaking by capillary force and surface tension. In addition, such materials usually have good high-temperature resistance and chemical stability. The table lists the common physical parameters suitable for medium and high temperature ceramic framework materials. According to the material characteristics [6, 7], MgO was used as the framework material in this study. 2.3
Screening of Thermally Conductive Materials
To enhance the heat charging and discharging rate of the thermal storage system and improve the thermal storage performance, usually thermal conductivity enhancing materials are added. Metals, graphite and highly thermally conductive ceramic particles have been shown in studies to be excellent alternative materials that can improve the thermal conductivity of the system. Metals have very high thermal conductivity, so adding metal particles is the most effective way to enhance the thermal conductivity of thermal storage materials. However, the high density of metals tends to increase the mass of the entire thermal storage system, thus reducing the overall mass thermal storage density. Most of the metals are corroded by chemical reaction with molten salt [9]. Therefore, metal particles are rarely used as thermal conductivity materials in high-temperature thermal storage systems. Graphite is a good thermal conductive material and is widely used to enhance heat transfer. The thermal conductivity of graphite may be enhanced by structural modifying. Pop et al. [10] found that the thermal conductivity of graphite can reach 2 000–4 000 Wm−1 ·K−1 within the laminar structure. Balandin et al. [11] investigated the thermophysical properties of graphite at different temperatures and showed that the onedimensional structure of carbon nanotube bodies makes them exhibit extremely high thermal conductivity (6 000 Wm−1 ·K−1 ). However, since the elemental composition of graphite is carbon monolithic, it is susceptible to oxidation at high temperatures, which partially weakens the thermal conductivity enhancement effect. Silicon carbide has the advantages of high thermal conductivity, high-temperature resistance, high oxidation resistance, high-temperature strength, good wear resistance,
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good thermal stability (2 600 °C), low coefficient of thermal expansion, high hardness, thermal shock resistance, chemical corrosion resistance, etc. [12]. It is widely used in aerospace, nuclear energy, military industry and other fields. The vast majority of applications are closely related to the high thermal conductivity of silicon carbide. The thermal conductivity of silicon carbide ceramics is 270 Wm−1 ·K−1 [13, 14, 15] at room temperature. In summary, K2 CO3 -Na2 CO3 is used as the phase change material and MgO as the skeleton material in this paper. Meanwhile, considering the high-temperature application environment, SiC with better high-temperature stability is chosen as the thermal conductivity enhancer.
3 3.1
Experimental Materials and Methods Sample Preparation Process
Raw material treatment: high-temperature thermal storage materials are prepared by first drying each raw material at a drying temperature of 120 °C for 4 h. Ball milling: The phase change material of the high temperature composite heat storage material adopts Na2 CO3 -K2 CO3 eutectic salt, and the mass ratio of Na2 CO3 and K2 CO3 is 51.9: 48.1. The two kinds of salts were put into a planetary high-speed ball mill for full mixing for 10 min, the material-to-ball ratio was 1:1, and the ball mill rotational speed was 150 rpm. Then, the mixed salt, MgO and SiC are weighed and prepared according to a certain proportion. Mixing: The above mixture of powders was mixed in a planetary high-speed ball mill. According to the experience of the previous project, a mixing time of 10 min (5 min clockwise and 5 min counter clockwise) will give a homogeneous sample and the powder particles will not stick to the walls. According to the operation protocol, the material-to-ball ratio is 1:1 and the speed of the ball mill is 100 rpm, which is not too high to mix the components well. Forming: The mixed powder was pressed into 13 mm diameter, 4–5 mm thick discs with a molding pressure of 40 MPa and a holding time of 10 s. The pressed blanks were then dried at a drying temperature of 120 °C for 4 h. Sintering: The sintering was performed in a muffle furnace, as well as under air atmosphere. The sintering was performed according to the process shown in Error! Reference source not found.. The materials used in the experiments are all from Sigma-aldrich, in which the purity of molten salt (Na2 CO3 , K2 CO3 ) and MgO is >99%, and the purity of SiC is >97%. 3.2 Measurement Method Because the relative moisture content of the carbonaceous material in the composite form-stable phase change material is around 40%; its skeleton material MgO is not hydrophobic and is easy to absorb moisture in the air; its porous skeleton material cannot inhibit the external moisture from entering the material, so the composite form-stable phase change material is not suitable for use or storage in a high humidity environment.
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For the problem of moisture absorption in composite materials (700PCM), the two main means are material modification and surface treatment of the material module to mitigate the moisture absorption of the material. Currently, the main methods used to treat the surface of the material module include: 1. High-temperature sealing coating encapsulation; 2. Metallic thermal conductive film coating. The moisture absorption test was performed by dynamic vapor adsorption instrument DVS to detect the water absorption of the prepared composite fixed phase change materials with the test conditions of 20 °C, 80%RH and 150 mL/min nitrogen atmosphere. The samples modified by different methods were tested separately to evaluate their moisture resistance.
4 Results and Discussion 4.1
Material Modification
Doped Zeolite. Zeolite, as a high temperature resistant and structurally stable porous material with poor water absorption, can be used as a carrier for phase change materials and by becoming a competitor for absorbing water in phase change materials, it is hoped that the capillary action can fix water in the pore channels without allowing carbonate to absorb water and deliquesce. The structure of the sintered zeolite-based composite phase change material was not deformed, and no leakage of phase change material occurred, so the composite could be used for the next step of water absorption testing. Figure 1 shows the comparison of the results between the composite zeolite-based phase change material and the composite set phase change material. It can be seen from Fig. 1 that the zeolite-based composite phase change material has a smaller mass change after water absorption compared to the original MgO-based composite phase change material, with a 19.43% reduction in mass change. The possible reasons are that the particle size of zeolite particles is larger than that of MgO, and the specific surface area of salt particles wrapped with zeolite particles as skeleton material is smaller, which makes the area of salt in contact with water smaller; zeolite particles contain microporous structure, and part of the molten salt enters the pore without contacting the wet air. Therefore, the use of zeolite-based composite phase change materials can slightly alleviate the absorption of moisture but cannot completely block the penetration and diffusion of water molecules. Doped Silica Gel. The silica powder was used as a carrier to wet the surface of the salt, and then the silica powder was used to agglomerate, and surface wrap the salt particles to compete for the absorption of water molecules, thus inhibiting the moisture absorption of the inorganic salt. However, during the sintering process of the prepared composites, comparing with the other two zeolite-based composites and MgO-based composites, the silica-based composites have expansion leakage (e.g., Fig. 2), and the silica in the silica reacts with the molten carbonate to generate silicates (potassium silicate and sodium silicate) during the high-temperature sintering process, and the resulting silicate impurities will affect the thermal storage performance of the phase change materials, so this method is not desirable.
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180 170 MgO-700PCM Zeolite-700PCM
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Fig. 1. Water absorption rates of zeolite/-MgO-700PCM versus MgO-700PCM.
Fig. 2. Sample diagram of high temperature sintering after doping.
Hydrophobic modification of the carrier magnesium oxide MgO. Common MgO modifiers are mainly titanate coupling agents, which can be divided into monoalkoxy type, monoalkoxy pyrophosphate type, coordination type, stinging type, etc. according to the difference of functional area groups. Among them, chelating type titanate coupling agent is suitable for high moisture filler and aqueous polymer system, such as wet silica, clay, talc, aluminum silicate, water treatment glass fiber, etc. In high moisture systems, the general monoalkoxy type titanate.
4.2 Material Surface Treatment For the problem of moisture absorption of MgO-700PCM material, the moisture absorption of the material can also be mitigated by treating the surface of the material module. As mentioned in Sect. 3.2, the methods used in this study to treat the surface of the material module are: 1. High temperature resistant coating application, 2. Metal thermal conductive film encapsulation. The three methods are studied separately, and their moisture-absorbing effects are compared. High temperature resistant coating application. Using high temperature resistant coatings to coat and seal the surface of materials is also a common method. High temperature resistant coatings are widely used in automotive parts, semiconductor processes, petrochemical industries, medical industries, electronic appliances and other fields. There are
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various kinds of high temperature coatings, and different kinds of coatings can be selected according to the application requirements and application conditions. SGC4000-HT (Aremco Products, Inc.) is a high temperature resistant coating made of spinel, ceramics and glass, which can withstand high temperature of 760 °C for a long time and matches the temperature of the phase change material selected for this research. The coating is used in the sealing of electronic devices. The coating can form a dense ceramic coating on the carrier surface after curing, which can effectively block the intrusion of water molecules and has good high temperature stability at the same time. Apply this high-temperature coating to the phase change material module (two coats with a brush at 20-min intervals according to the instructions) and heat at high temperature for curing: Heat from room temperature to 538 °C and maintain that temperature for 30 min followed by cooling process.
Fig. 3. High temperature paint encapsulation and post-curing results
The effect after curing is shown in Fig. 3. From Fig. 4 the water absorption rate of the material after coating has been significantly reduced, especially compared with the coated encapsulated material, after 420 min at 20 °C 80% RH, the total water absorption weight gain has decreased from 40% to only 15%. It can be inferred that the coating SGC4000-HT still tightly wraps the coating after curing, forming a dense protective film, and therefore a good sealing effect is obtained. Metallic Thermal Conductive Film Wrapping. After the above study, it was found that coating the surface of the modules made of MgO-700PCM by high-temperature coatings had a relatively good effect and significantly reduced the water absorption rate of the substrate material. However, the use of high-temperature coatings alone does not completely prevent water absorption. Therefore, a further method of metallic thermal conductive film coating was considered. The use of metal thermally conductive film for cladding has the following advantages: 1. simple operation, low cost, and suitable for batch application; 2. metal film has good thermal conductivity, which can promote the heat transfer of the material module; 3. metal film has good high temperature stability. Considering the good thermal conductivity as well as the ductility of copper, a viscous Cu film was used to wrap the substrate material, as shown in Fig. 5. We tested the water absorption rate of the wrapped material, and the results are shown in Fig. 6. The water absorption rate after wrapping by Cu film has an obvious reduction, and after more than 800 minutes of water absorption test, its quality is almost unchanged, indicating that this
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Fig. 4. Water absorption mass of materials with high temperature coating on the surface
method can achieve the effect of complete water barrier. This method is also the best and practically feasible solution for water barrier effect so far in the study.
Fig. 5. Cu film-wrapped sample
Fig. 6. Water absorption mass of the material after the surface has been wrapped with a Cu film
To test the high temperature stability of different metal films, the phase change composites wrapped with Cu film and stainless steel SS304 metal film were heated in a high temperature cycling furnace from 680 °C to 730 °C after five cycles as shown in Fig. 7. The Cu film wrapped material showed a serious discoloration problem after cycling, while the stainless-steel metal material showed only a slight color change, and the change in the shape and strength of the metal was not obvious. Therefore, it can be
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seen that the choice of metal film needs to take into account both good high temperature resistance characteristics and corrosion resistance.
Fig. 7. Phase change material wrapped in metal film after five cycles
5 Conclusion In this paper, methods to mitigate the moisture absorption characteristics of hightemperature composite phase change materials are studied from the perspective of practical applications and the actual effects are compared. The first is the raw material modification method, changing the composite material carrier to doped zeolite, doped silica, etc., all of which have very limited effect on improving moisture resistance; the second is the material module improvement, including high temperature resistant coating, and metal thermal conductive film coating. The moisture-absorbing weight gain mass of the moisture-absorbing weight gain mass of the material module coated with hightemperature resistant coating is reduced by about 25%. Nevertheless, both methods still fall short of the requirements for long-term moisture resistance. The use of stainlesssteel film coating in combination with high-temperature resistant coatings showed a moisture-absorbing weight gain mass of only 5% in long-term experiments. It can be concluded that the coating can physically isolate the water vapor to a certain extent, thus alleviating the material in the high humidity environment storage and dampness, but with the increase in the number of charging and discharging heat, the volume of the material scaled several times, the coating will inevitably chapped phenomenon, thus can no longer effectively block the intrusion of external water vapor; and through the stainless steel film wrapped macro-encapsulation method, physically isolated from the outside world and the material, so the surface coating and metal film wrapping methods can be used simultaneously to get the best experimental results. However, the cladding process will affect the internal material and the cladding material interface contact, there may be a certain impact on the thermal conductivity, worth further investigation. Acknowledgements. This study is funded by the research and development project of State Grid Corporation of China (Project No.: 5500-201958507A-0-0-00).
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References 1. Lu, Y., et al.: Fabrication and characterization of the novel shape-stabilized composite PCMs of Na2 CO3 -K2 CO3 /MgO/glass. Sol. Energy 189, 228–234 (2019) 2. Zhang, G., et al.: Study on the influence of glass encapsulating on the hygroscopicity of high temperature phase change heat storage materials. In: IOP Conference Series: Earth and Environmental Science, vol. 474(5), p. 052094 (2020) 3. Chen, Z., et al.: Synthesis and characteristics of hygroscopic phase change material: composite microencapsulated phase change material (MPCM) and diatomite. Energy Build. 106, 175– 182 (2015) 4. Royo, P., et al.: Multiple-Criteria Decision Analysis and characterisation of phase change materials for waste heat recovery at high temperature for sustainable energy-intensive industry. Mater. Des. 186, 108215 (2020) 5. Schröder, J.: Thermal energy storage and control. J. Eng. Ind. 97(3), 893–896 (1975) 6. Li, A.: Study on the high temperature stability of salt/ceramic composite heat storage material. Mater. Rev. 25, 78–81 (2011) 7. Jiang, F., et al.: Skeleton materials for shape-stabilization of high temperature Salts based phase change materials: a critical review. Renew. Sustain. Energy Rev. 119, 109539 (2020) 8. Leng, G., et al.: Recent progress in diatomite based composite phase change materials for thermal energy storage. Energy Storage Sci. Technol. 2(3), 199–207 (2013) 9. Kadowaki, M., et al.: Pitting corrosion resistance of martensite of AISI 1045 steel and the beneficial role of interstitial carbon. J. Electrochem. Soc. 164(14), C962–C972 (2017) 10. Pop, E., Varshney, V., Roy, A.K.: Thermal properties of graphene: fundamentals and applications. MRS Bull. 37(12), 1273–1281 (2012). https://doi.org/10.1557/mrs.2012.203 11. She, J., et al.: Development and application of silicon carbide ceramics. Ceram. Eng. 32(35), 3–11 (1998) 12. Nakano, H., et al.: Microstructural characterization of high-thermal-conductivity SiC ceramics. J. Eur. Ceram. Soc. 24(14), 3685–3690 (2004) 13. Watari, K., et al.: Effect of grain boundaries on thermal conductivity of silicon carbide ceramic at 5 to 1300 K. J. Am. Ceram. Soc. 86(10), 1812–1814 (2003) 14. Slack, G.: Nonmetallic crystals with high thermal conductivity. J. Phys. Chem. Solids 34(2), 321–335 (1973)
Research Progress of Coordination Control Strategy for Flywheel Array Energy Storage System Yongming Zhao1,2 , Qingquan Qiu1,2,3(B) , and Zipan Nie1,2,3 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
{zhaoyongming,qiuqingquan,znie}@mail.iee.ac.cn
2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology, Qilu
Zhongke, Jinan 250000, China
Abstract. Restricted by cost and technology, increasing the power of a single flywheel energy storage device is difficult. Using flywheel array can not only increase the total energy storage capacity of the flywheel system, but also reduce the development and production cost of the unit. For the flywheel array energy storage system, the research on the control strategy of coordinated control and mutual cooperation of each energy storage unit is the solution to realize the efficient and safe operation of the array. This paper firstly discusses the research progress of coordinated control strategies for flywheel array energy storage systems internationally in recent years, and summarizes and analyzes the advantages and disadvantages of various control strategies in flywheel energy storage power distribution and array parallel control. By summarizing and researching the coordinated control strategies of flywheel array energy storage systems in the fields of grid regulation, UPS, rail transit energy recovery, pulse power supply, and integrated energy storage technology, the paper provides reference for the design and innovation of array control strategy of the integrated physical energy storage system. Keywords: Flywheel array energy storage system (FAESS) · flywheel energy storage unit · coordination control · parallel operation
1 Introduction For dealing with environmental problems, China put forward “dual carbon goals” of 2030 carbon peak and 2060 carbon neutrality at the United Nations General Assembly in 2020. In view of the “dual carbon goals”, we should gradually reduce the use of fossil energy in future development and increase the proportion of renewable energy consumption. However, new energy power has the characteristics of randomness and intermittentness due to its own energy distribution, and its large-scale grid connection will have a significant effect on power quality control and stability of the power grid [1]. The access of large-capacity energy storage equipment can well solve the problems © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 320–329, 2023. https://doi.org/10.1007/978-981-99-1027-4_34
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of randomness and discontinuity in new energy power generation, effectively adjust power generation output and grid fluctuations caused by power grid, and elevate the consumption capacity of new energy power [2]. Therefore, large-scale flexible energy storage devices have become a research hotspot in the world. Based on the characteristics of high efficiency, small size, long performance life, high instantaneous power and response rapidly, flywheel energy storage system (FESS) is widely used in new energy power stations, aerospace, UPS and grid regulation [3]. Restricted by materials, technologies and production costs, it is difficult to increase the capacity of a single FESS unit. For fully utilizing the FESS’s advantages and meet application requirements for rapid load regulation in the power system, multiple FESS units can be combined to build a large-capacity FAESS, which the discharge duration can reach several minutes, and reduce production and construction costs. Therefore, the coordinated control strategy of the FAESS is an important research direction to increase the efficiency and storage capacity of flywheel array, and realize more efficient and safer application of the FAESS [4]. The paper mainly summarizes and analyzes the coordinated control strategies adopted by FAESS in the fields of grid regulation, UPS, rail transit energy recovery and integrated energy storage technology in recent years. The advantages and disadvantages of flywheel array power distribution and array parallel control provide reference for the future promotion of coordinated control strategies in other mechanical energy storage technologies and integrated physical energy storage technologies.
2 FAESS Topology FAESS topologies are mainly divided into the following two types: DC bus parallel and AC bus parallel structures, as shown in Figs. 1 and 2, respectively [5].
Fig. 1. FAESS with DC-bus parallel structure
For FAESS devices with DC bus parallel topology: the vehicle-mounted FESS of Beacon Power, USA, supports 10 FESS units with 2.5 MW power [6]. Active Power’s product supports 8 FESS units with power up to 2MW; FAESS has been applied to metro lines such as New York Far Rockaway Line, Los Angeles Gold Line and Beijing Fangshan Line in the United States, effectively suppressing DC bus voltage fluctuations and significantly improving energy conservation and energy utilization [7].
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Fig. 2. FAESS with AC-bus parallel structure [5]
Jinliang Lv et al. of Tsinghua University proposed a novel parallel topology for DC bus, in which the positive and negative polarities of adjacent flywheel units are connected together and eventually connected to the DC bus [10]. For FAESS devices using AC bus parallel topology: Active Power’s UPS products can support eight FESS units with about 2400 kW; Beacon Power’s flywheel array demonstration project consists of seven flywheel units connected in parallel with 100 kVA power and a 20 MW FM power station was built in New York. The original Canadian company Temporal Power built a 5 MW FESS power station in Ontario.
3 FAESS Power Coordination Control Strategy 3.1 DC Bus Parallel FAESS Power Coordination Control Taking FAESS of UPS for example, its circuit topology is shown in Fig. 3, which is mainly composed of a rectifier, a FAESS, and an inverter. Institute of Electrical Engineering Chinese Academy of Sciences has summarized and simulated FAESS structure and three control strategies. The summary shows that three discharge control strategies can stabilize and control the DC bus voltage accurately. The control structure of the equal power strategy is relatively simple; the equal torque strategy is more functional; the equal time length strategy can make FAESS discharge longer, and the power control effect is better, but the control structure is more complicated. Chenhui Jin et al. of Tsinghua University studied the coordinated control strategy of FAESS connected in parallel to the same DC bus, analyzed the change rate of state of charge (SOC) under three classical power control strategies, and gave three kinds of power control strategies. The relationship between SOC change rate and SOC size under the control strategy. Afterwards, the simulation through the equivalent torque control strategy proves the correctness of the relationship between the SOC change rate and the SOC size derived before [9]. The power coordination control strategy used consists of the following. (1) The strategy of equal power, equal torque and equal time length
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Fig. 3. FAESS topology for UPS[5]
Equal power discharge is to make the output electromagnetic power of each unit equal, as shown in Fig. 4. The equal torque strategy is to make the output electromagnetic torque of each flywheel unit equal, as shown in Fig. 5. The equal time length strategy is to make the discharge time of each unit equal, as shown in Fig. 6.
Fig. 4. Equal power strategy[10]
Fig. 5. Equal torque strategy[10]
China Electric Power Academy and Tsinghua University have studied the coordinated control of FAESS, and have studied the discharge control strategy based on residual energy for power distribution [11]. For shore power micro-grid control system, Ping Liu of China Power Construction Road and Bridge Company adopted an equal time allocation strategy for FAESS to obtain the longest charging and discharging time connected to the grid and ensure the synergy between the flywheels [12]. (2) Proportional allocation strategy by rotational speed
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Fig. 6. Equal time duration strategy[10]
The proportional allocation strategy by rotational speed is a power allocation strategy based on the remaining energy of FESS units by converting the control of flywheel output power into the control of rotational speed to achieve the same ratio of the stored or released power of FESS units to the charge/discharge margin. The constructed power allocation target adopts the principle of “more work for those who can” [13, 14]. In the light of flywheel array speed control and SOC management, Jin Li et al. of Beijing Jiaotong University proposed two types of FAESS based on slip correction control and three closed-loop control which ensure that the rotational speed of each flywheel unit is balanced, and avoid the waste of energy storage array capacity [15]. Chenwei Wang et al. optimized the equal discharge time length control strategy used in power coordination control of FAESS, and proposed a SOE power distribution strategy based on residual energy [16]. Yulong Chen et al. of North China Electric Power University proposed an improved power coordination control strategy, which considered the upper limit constraint of the power allocated by the unit, and ensured the stability of the power control and realized that the SOC values of each unit gradually tended to be consistent [17]. (3) Power allocation strategy considering efficiency and residual energy balance The each flywheel unit’s power distribution of FAESS needs to be comprehensively considered. When ensuring the balance of the remaining energy of each flywheel unit, the overall power loss is at a low level. Jingpan Ren et al. of Beijing Institute of Technology raised the integrated control strategy that considers both the efficiency and the flywheel unit’s energy balance. The particle swarm optimization algorithm is used to distribute the power of FESS unit, and to coordinate the balance of the remaining energy of the FESS unit. The relationship between the operating efficiencies can avoid large differences in the remaining energy between the individual monomers in the system [18]. Long Zhou et al. of Tsinghua University proposed a strategy of FAESS two-level direct power control consisting of the power distribution criterion and the residual energy control method. The principle of equal increment rate is used to distribute the power to the flywheel unit, which can reduce the energy consumption of FESS, and prevent flywheel module overcharging and flywheel motor overcurrent faults [19, 20]. 3.2 AC Bus Parallel FAESS Power Coordination Control AC bus parallel FAESS power coordination control strategy mainly includes: average distribution, distribution under speed, and distribution under residual energy. Xisheng
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Tang conducted a simulation study on three power coordination control strategies for the AC bus parallel FAESS, which shows that all three discharge control strategies can steady and control the DC bus voltage accurately. The average distribution strategy is simple, but the discharge time is the shortest; under the speed distribution strategy, the discharge time is shorter, and the control structure is more complicated; under the residual energy distribution strategy, the discharge time is the longest, but the control structure is complex [8]. Under traditional droop control strategy, there are problems of inflexible power allocation and static errors in the amplitude and frequency adjustment of bus voltage. Chenhui Jin et al. of Tsinghua University proposed a droop control strategy with improved coefficients, which distributes the corresponding power according to proportion of FESS unit SOC. The improved control strategy has good control result through the simulation research of the microgrid model including wind turbine and FAESS [21]. Foreign scholars Nemsi et al. proposed the use of droop control strategy to achieve power distribution between two FESS, photovoltaics and wind power [22]; Italian scholars Barelli et al. The dynamic performance changes under different operating conditions are simulated and compared, and the results show that the AC busbar structure has better compatibility with the power grid [23].
4 FAESS Array Parallel Control Strategy Depending on the topology, the FAESS parallel charging and discharging control uses centralized control, master-slave control and distributed cooperative control. (1) Centralized control The centralized control adopts two levels of controllers. The central master controller completes the power coordination control algorithm of all flywheel units and is responsible for generating the electromagnetic torque command of each unit in lower level. Each flywheel unit controller in lower level drives FESS unit to achieve the control of power, torque, speed and other parameters. Yulong Chen et al. of North China Electric Power University optimized the centralized control strategy by using a hierarchical grouping control strategy to ensure power control accuracy and response speed [16]. This control strategy is simple and convenient, and its control effect basically depends on the algorithm of the central master controller. There is no problem of chaotic control signals received by each flywheel unit. However, it is less fault-tolerant, and when the master controller fails, the whole FAESS will be in error. (2) Master-slave control Master-slave control strategy is to use the controller of one flywheel unit in the flywheel array as the master controller to complete the total control function of power coordination of all flywheel units. When the master controller fails, the master controller is removed and any other slave controller is used as the master controller to complete the power coordinated total control function. Wuling Zhao used the strategy for UPS to
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realize the control of each unit of FAESS: the master and slave are determined using a parity ordering mode; once the master fails, it is disconnected from the DC bus, and the new master re-distributes the power according to the number of units currently; each flywheel module controller uses blockchain technology to achieve decentralized consistent storage and decides itself in master or slave mode based on the stored data and the current operating state [24]. This control strategy improves the reliability of the system, but the system will be in the master less controller state during the master-slave controller switching, which affects the reliability of the system. (3) Distributed cooperative control In distributed cooperative control strategy, there is no master controller and slave controller, and each flywheel unit can communicate with neighboring flywheel units. Through this distributed communication method, a communication network is built among all flywheel units of the array, and each unit realizes information interaction with others through this network. Qiangang Wang et al. of Chongqing University proposed a distributed cooperative-based control method for FAESS, then controlled FAESS based on the average consistency control algorithm to solve the problem of slow response speed of FAESS due to centralized control strategy [25]. Jiqing Zhao et al. of North China Electric Power University proposed a distributed and coordinated control strategy based on consistency algorithm to achieve the output power’s reasonable distribution of the combined photovoltaic flywheel system according to the scheduling plan [26]. This control strategy does not require a total controller and improves the response speed and reliability. However, this control strategy has high requirements for algorithms, and controller design in the array is more complex.
5 FAESS Coordinated Control Strategy Application Extension The current research on the coordinated control strategy of FAESS is mostly aimed at the synergy with large grid or microgrid to realize the large capacity storage and high power output of electric energy. The coordinated control strategy about the array can also be applied to other fields of pulse power supply, integrated physical energy storage technology and achieving grid frequency regulation. In terms of pulse power supply, Shenyang New Energy Technology Company proposes that a high-power pulse power supply system of MW level or higher can be built according to the demand by integrating flywheel arrays and realizing the power transient control function [27]. In integrated physical energy storage, Institute of Electrical Engineering Chinese Academy of Sciences proposes to use FAESS to realize intermittent power compensation of gravity storage output and frequency regulation of the grid to ensure the output power stability and frequency stability [28]. In addition, the response time of pumped storage variable speed units is generally tens of seconds, so it does not have the ability of fast power regulation at the second level. Tsinghua University proposed the use of FAESS to assist pumped storage to improve the response speed of pumped storage units and achieve frequency regulation of the grid [29]. In terms of coordinating with other generating units, Shandong University proposed using FAESS to assist thermal power units to
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complete primary frequency regulation: the residual energy-based sag control strategy of FAESS was used to meet the demand for frequency regulation, efficiency improvement and power storage continuity [30, 31].
6 Conclusion and Outlook For bettering meet the different application requirements for fast active load regulation in power systems, the parallel connection of FESS units to build FAESS is a key technology to realize the application of FESS technology in the field of high power, high capacity and high efficiency energy storage, and flywheel array coordination control strategy is an important means to ensure the efficient and operation safely. This paper summarizes the FAESS’ topology and control strategy, analyzes the advantages and shortcomings of the control strategy, and provides the basis for the types of flywheel array coordinated control strategy used in different application scenarios. The control strategy of FAESS will be continuously optimized and innovated to develop in the direction of more efficient, more stable and higher integration, so that FAESS can play an significant role in the grid regulation and new energy consumption fields. Acknowledgment. This work has been funded by Research on Key Technologies for Gravitational Potential Energy Storage, funded by Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology, Qilu Zhongke.
References 1. Dai, X.J., Deng, Z.F., Liu, G., et al.: Review on advanced flywheel energy storage system with large scale. Trans. China Electrotech. Soc. 26(07), 133–140 (2011). (in Chinese) 2. Tan, J.Y.: Application of energy storage technology in power system. Electron. Technol. 49(10), 140–141 (2020). (in Chinese) 3. Dai, X.J., Wei, K.P., Zhang, X.Z., et al.: A review on flywheel energy storage technology in fifty years. Energy Storage Sci. Technol. 7(05), 765–782 (2018). (in Chinese) 4. Li, X.J., Palazzolo, A.: A review of flywheel energy storage systems: state of the art and opportunities. J. Energy Storage 46(6), 103576 (2022) 5. Tang, X.S., Liu, W.J., Zhou, L., et al.: Flywheel array energy storage system. Energy Storage Sci. Technol. 2(03), 208–221 (2013). (in Chinese) 6. Lazarewicz, M.L., Rojas, A.: Grid frequency regulation by recycling electrical energy in flywheels. In: Proceedings of the Power Engineering Society General Meeting, pp. 2038–2042 (2004) 7. Kenny, B., Kascak, P., Jansen, R., et al.: Control of a high-speed flywheel system for energy storage in space application. IEEE Trans. Ind. Appl. 2015(4), 1029–1038 (2015) 8. Lv, J., Jiang, X., Gong, G.: A novel flywheel array energy storage system with DC series connection. In: IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society, pp. 1740–1743 (2020) 9. Jin, C.H., Jiang, X.J., Dai, X.J.: Coordinated control strategy of flywheel energy storage array for micro-grid. Energy Storage Sci. Technol. 7(05), 834–840 (2018). (in Chinese) 10. Liu, W., Tang, X., Zhou, L., et al.: Research on discharge control strategies for FESS array based on DC parallel connection. 2012 Asia-Pacific Power and Energy Engineering Conference, pp. 1–5 (2012)
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11. Dai, X.J., Zhang, X.Z., Jiang, X.J., et al.: Flywheel energy storage technology in Tsinghua University. Energy Storage Sci. Technol. 1(1), 64–68 (2012) 12. Liu, P., Li, S.S.: Modeling analysis on flywheel energy storage array-based shore power micro-grid control system. Small Spec. Electr, Mach. 48(06), 33–39+44 (2020). (in Chinese) 13. Guo, W., Zhang, J.C., Li, C., et al.: Control method of flywheel energy storage array for gridconnected wind-storage microgrid. Energy Storage Sci. Technol. 7(05), 810–814 (2018). (in Chinese) 14. Wu, H.N., Zhang, P., Wang, G.C., et al.: Capacity configuration method of flywheel energy array for wind power output smoothing. Ningxia Electr. Power 5(05), 6–11+27 (2021). (in Chinese) 15. Li, J., Zhang, G., Liu, Z.G., et al.: Control strategy of flywheel energy storage array for urban rail transit. Trans. China Electrotech. Soc. 36(23), 4885–4895 (2021). (in Chinese) 16. Wang, C.W., Yao, G., Wei, Z.: Power allocation strategy for energy storage flywheel array based on residual energy. In: 2021 Academic Annual Meeting of China Nuclear Society, pp. 134–139 (2021). (in Chinese) 17. Chen, Y.L., Wu, X., Teng, W., et al.: Power coordinated control strategy of flywheel energy storage array for wind power smoothing. Energy Storage Sci. Technol. 11(02), 600–608 (2022). (in Chinese) 18. Ren, J.P., Ma, H.W., Yao, M.Q.: A coordinated control strategy of flywheel array based on particle swarm optimization algorithm. Trans. China Electrotech. Soc. 36(S1), 381–388 (2021). (in Chinese) 19. Zhou, L., Tang, X.S., Qi, Z.P.: Control method for flywheel array energy storage system in energy harvesting from electric railway. In: 2014 IEEE Conference and Expo Transportation Electrification Asia-Pacific, pp. 1–5 (2014) 20. Zhou, L., Liu, W., Tang, X.: Direct power control method for grid-connected flywheel array energy storage system. In: 2014 International Conference on Power System Technology, pp. 3052–3057 (2014) 21. Jin, C., Jiang, X., Zhong, G., et al.: Research on coordinated control strategy of flywheel energy storage array for island microgrid. In: 2017 IEEE Conference on Energy Internet and Energy System Integration, pp. 1–6 (2017) 22. Nemsi, S., Belfedhal, S., Makhloufi, S., et al.: Parallel operation of flywheel energy storage systems in a microgrid using droop control. In: 2018 International Conference on Wind Energy and Applications in Algeria, pp. 1–6 (2018) 23. Barelli, L., Bidini, G., Pelosi, D.: Comparative analysis of AC and DC bus configurations for flywheel-battery HESS integration in residential microgrids. Energy 204(2020), 117939 (2020) 24. Zhao, W.L., Yao, G., Zhao, N.: The design of DC bus parallel discharge control system for flywheel energy storage array. Electr. Eng. 13(13), 45–47+49 (2019). (in Chinese) 25. Wang, Q.G., Wang, J., Tian, Y.H., et al.: Charge and discharge control method of flywheel energy storage array based on distributed coordination. CN113036789A (2021). (in Chinese) 26. Zhao, J.Q., Zhang, J.C., Song, Z.X., et al.: Distributed coordinated control strategy based on flywheel energy storage array system. J. North China Electr. Power Univ. 45(06), 28–34 (2018). (in Chinese) 27. Wang, W.L., Zhang, Q.Y., Chen, Y., et al.: Pulse power supply system and control method based on flywheel energy storage. CN110504700A (2019). (in Chinese) 28. Qiu, Q.Q., Zhao, Y.M., Xiao, L.Y., et al.: A comprehensive physical energy storage system and energy storage method combining gravity with flywheel. CN202210318924.0 (2022). (in Chinese) 29. Jiang, X.J., Tian, G.L., Gong, G.X., et al.: A control method for a hybrid frequency modulation system of flywheel energy storage and doubly-fed variable speed pumped-storage energy storage. CN112865147A (2021). (in Chinese)
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30. Luo, Y.D., Tian, L.J., Wang, Y., et al.: coordinated control strategy and optimal capacity configuration for flywheel energy storage participating in primary frequency regulation of power grid. Autom. Electr. Power Syst. 46(09), 71–82 (2022). (in Chinese) 31. Li, B.H., Liang, L., Hong, F., et al.: Research on primary frequency modulation of thermal power unit based on flywheel energy storage. Electr. Eng. 9(09), 15–18 (2022). (in Chinese)
Lifetime Test Platform of Mica Paper Capacitors Under Microsecond Pulse Shifei Liu1(B) , Jiande Zhang1 , Zicheng Zhang1 , Jilu Xia1 , and Teli Qi2 1 College of Advanced Interdisciplinary Studies, National University of Defense Technology,
Changsha 410073, China [email protected] 2 PLA 75836 Troops, Guangzhou 510020, China
Abstract. In recent years, the development of mica capacitor technology has greatly improved the withstand voltage and energy storage density of capacitors, which is suitable for Marx generators. Before using mica paper capacitors to assemble Marx generators, it is important to study the electrical performance and life characteristics of the capacitors. In this paper, a repetitive-rate microsecond pulse test platform was established to research the lifetime characteristic of mica paper capacitors. The test platform is mainly divided into two parts. The first part includes an air-core pulse transformer, a primary electrolytic capacitor, a thyristor and a diode. Another part contains a mica paper capacitor, a SF6/N2 gas switch and a water dummy load. This platform can output voltage up to 60 kV and operate in a repetitive rate of 20 Hz for 50 s or 10 Hz for 100 s. Voltage jitter is lower than 1%. When working continuously, it can charge mica capacitor 2000 pulses for a time. With an interval of about 30 s each time, the test platform can work continuously for one hour. Keywords: Air-core pulse transformer · Test platform · Mica paper capacitor
1 Introduction PFN (Pulse Forming Network, PFN)-Marx generator possesses natural compact genes and can realize both pulse voltage accumulation and pulse formation. It gradually becomes a hot spot for domestic and international research [1, 2]. In recent years, ceramic and mica paper capacitors have been rapidly developed. The withstand voltage and energy storage density of these capacitors have been greatly improved, and their initial inductance has been gradually reduced [3–6]. Mica paper capacitors (hereinafter referred to as MPC) have been gradually applied in PFN-Marx generators because of their excellent performance [7–9]. The internal structure of mica paper capacitor is generally wound. As for this type of capacitor, charging and discharging in a long period of time will gradually enlarge the original defects in mica paper medium, while the temperature rise of mica capacitor during test will further aggravate the damage of mica paper medium and thus cause the capacitor breakdown. Based on the application demands and in order to provide a design © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 330–339, 2023. https://doi.org/10.1007/978-981-99-1027-4_35
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reference for those devices using mica capacitors under microsecond pulse, it is of great significance to study the lifetime characteristic of MPC. In this paper, a repetitive-rate microsecond pulse test platform was established to research the lifetime characteristic of mica paper capacitors under microsecond pulse. The platform allows the study of the variation of the electrical parameters of MPC in relation to the lifetime of MPC. The circuit composition of the test platform and its working principle, the design and simulation of key subcomponents, and the operation of the platform are presented in this paper.
2 Operation Principle The design goal of lifetime test platform is to provide stable microsecond output pulses with a repetitive rate of up to 30 Hz. The repetitive-rate microsecond pulse test platform includes a primary energy source, an air-core pulse transformer, a gas spark gap switch, an MPC to be tested, a water load, and a measurement system. The primary power supply provides energy for the system with energy recovery. The air-core pulse transformer reduces the heat generated by the magnetic core during long-time high-frequency operation, and the internal SF6 gas insulation is used to reduce weight. The gas spark gap switch is a triggered switch that adopts brass electrodes and controls the capacitor charging voltage by adjusting the air pressure. The resistive load is made of CuSO4 aqueous solution. The equivalent circuit diagram is shown in Fig. 1. Initially, the primary capacitor C p is charged to U 0 by a 12-kW high voltage DC source. When the main thyristor S1 is triggered, the primary capacitor C p charges the MPCs C mica up to 60 kV through the air-core pulse transformer. When the gas switch is triggered, the MPC discharges to the water load in nanosecond level. Then the primary capacitor C p reverses the remaining negative voltage -U 1 to a positive voltage through the diode D1 and resonant inductance L h . Finally, the high voltage DC source charges the primary capacitor C p to U 0 , which completes the energy recovery process and supplement. The charging voltage waveforms of MPC are captured by a capacitor divider with the attenuation of 1400. The output voltage of the load is captured with a high voltage probe (NorthStar PVM-5) with the attenuation of 2000.
Fig. 1. Equivalent electrical circuit of the test platform
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3 The Design of Subsystems 3.1 Air-Core Pulse Transformer The air-core pulse transformer is the core component of the primary energy part to realize energy transfer and voltage transformation. The air core pulse transformer contains primary and secondary windings. The primary windings are a parallel structure of three sets of coils, and a single set of coils is made of thick copper wire. This structure can reduce the loop impedance of the primary windings and ensure effective coupling with secondary windings, thus, improving the quality factor; the secondary windings are densely wound with enameled wires. The transformer is filled with 0.1 MPa SF6 gas insulation. The schematic diagram of the structure of the air-core pulse transformer is shown in Fig. 2. The design of the air-core pulse transformer needs to consider that the charging voltage of the primary capacitor is not higher than 1.5 kV, which is convenient for fast thyristor control. The energy transfer efficiency of the transformer needs to be greater than 25%, and the maximum charging voltage of MPC is up to 60 kV. The transformation ratio of the transformer is required to be more than 40 times. The calculated primary capacitance is 40 µF. Considering the space size, the radius r p of the primary windings is 85 mm. The insulation distance between the primary and secondary coils is 5 mm. The lengths of the primary and secondary windings are the same to ensure effective coupling. The coupling coefficient target should be above 0.82. The derivation starts around the coupling coefficient below. The primary windings are a parallel structure of three sets of coils. To simplify the calculation, the magnetic induction in the primary winding is considered to be uniformly distributed, and the magnitude is the average value of the magnetic induction on the axis of the primary winding. The approximate value of the inductance of a single set of primary windings and the approximate value of the mutual inductance between the three sets are calculated by Faraday’s law of electromagnetic induction, and then use the parallel inductance method to obtain the approximate value of the primary winding inductance. According to the Biot-Savart theorem, the approximate inductance of a single set of primary windings is calculated as [10]: Lp1 ≈
π μ0 Np12 rp2 2 lp1
2 + r2 − r lp1 p p
(1)
where lp1 is the length of a single set of primary windings, r p is the radius of the primary coil, N p1 is the number of turns of a single set of primary windings, and μ0 is the vacuum permeability. In the same way, the mutual inductance between the three sets of coils can be calculated as: ⎡ ⎤ 2lp1 π μ N 2 r 2 0 p1 p lp1 − x x ⎣ ⎦dx M12 ≈ + (2) 2 2lp1 2 2 2 lp1 (l − x) + r x + r2 p1
M13 ≈
3lp1 2lp1
π μ0 Np12 rp2 2 2lp1
⎡ ⎣
p
⎤
lp1 − x (lp1
− x)2
p
+ rp2
x ⎦dx + 2 x + rp2
(3)
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where M 12 represents the mutual inductance of adjacent coils, and M 13 represents the mutual inductance of the other coils, M 23 = M 12 . The circuit of three sets of equal coils in parallel is shown in Fig. 3.
Fig. 2. Transformer structure
Fig. 3. Equivalent electrical circuit of primary windings
According to Kirchhoff’s law, It can be calculated that the equivalent inductance L p is: Lp ≈
π μ0 Np12 rp2 lp2
lp2 + rp2 − rp
(4)
where lp is the total length of the primary windings. According to the expression (4), it can be considered that the three sets of primary windings are equivalent to a coil with a length of l p , a number of turns of N p1 , and a radius of r p . This inductance of the equivalent coil is coupled with the secondary windings. Using the same principle to obtain the secondary coil inductance L s , the primary and secondary coil mutual inductance M ps , and then obtain the coupling coefficient k ps expression: lp2 + rp2 − rp rs Mps ≈
(5) kps =
Ls Lp rp ls2 + rs2 − rs where ls is the secondary coil length and r s is the secondary coil radius. ls = l p .
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Important assumptions for the above calculations are that the magnetic field inside the coil is uniform and that the primary coil is an equivalent coil. In practical applications, there will inevitably be a situation where the coupling coefficient is reduced due to the insufficient tightness of the coils. It is necessary to use CST simulation software to simulate and verify the transformer and select the appropriate coil length. The 3D simulation model is shown in Fig. 4. In the simulation process, three sets of primary windings are set as equivalent coils. lp is taken as several times of r p respectively, and the theoretical calculation value is compared with the simulation result, as shown in Fig. 5.
Fig. 4. CST model of air-core transformer
Fig. 5. Coupling coefficient comparison of the simulation and theoretical calculation
It can be seen from Fig. 5 that when l p > 2r p , the theoretical calculation value is basically consistent with the simulation result. When lp becomes longer, the coupling effect of the transformer becomes better, but the changing trend gradually becomes stable. According to the results of simulation and theoretical calculation, under the premise of ensuring an acceptable coupling effect between the primary and secondary coils and the structure as compact as possible, it is more appropriate to take the length of the windings as 3r p . Table 1 gives the final parameters of the air-core pulse transformer. The theoretical calculation value of the coupling coefficient is 0.895, and the CST simulation calculation value is 0.909, both of which are greater than 0.82 and are in line with the design expectations.
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Table 1. Comparison of typical device parameters l p1 (mm)
l p (mm)
r p (mm)
r s (mm)
N p1
Ns
L p (µH)
Ls(mH)
k
k cst
80
240
85
80
16
510
21.6
19.7
0.895
0.909
3.2 Low Jitter Triggered Gas Switch The test platform requires gas switches with low jitter and long life. The gas switch used in the platform is shown in Fig. 6. The two-electrode head is a spherical design, the switch adopts a three-electrode trigger mode, and the electrode spacing is 5 mm. The trigger needle passes through the ground electrode, and the middle is insulated with a polymer material. The switch conduction flow is the trigger pin discharge to the high-voltage electrode, followed by the high-voltage electrode discharging to the ground electrode conduction. The key to using this switch is that the added trigger pin cannot affect the electrostatic field distribution of the original two electrodes too much. Otherwise, the high-voltage electrode will easily discharge to the trigger pin, resulting in damage to the trigger. The following is a simulation of the electrostatic field of the switch electrode using CST, and compared with the same size without the trigger pin. The results are shown in Figs. 6 and 7.
Fig. 6. Electrostatic field simulation of switch electrode (with trigger pin)
Fig. 7. Electrostatic field simulation of switch electrode (without trigger pin)
After adding the trigger pin, the distortion of the switch electrostatic field is mainly concentrated on the trigger pin, ensuring that the trigger pulse discharges to the high voltage electrode first. The difference between the spherical electrode and the flat electrode
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is that the electric field distortion of the spherical electrode is slightly larger and relatively concentrated. Within the allowable range of the withstand voltage, the spherical electrode tip has a more stable switch on voltage.
4 Experimental Result The mica capacitor life test platform is shown in Figs. 8 and 9, including the primary source and the test box. The mica capacitor and gas switch are put in a test box. The test box is filled with SF6 gas at atmospheric pressure for insulation. The operating air pressure of the triggered gas switch is a mixture of SF6 /N2 with a relative air pressure of 60 kPa, of which the proportion of SF6 was 14%. It had been proved that this proportion could improve the switching performance and the switch had a higher self-breakdown voltage and lower jitter than pure gases [11]. The voltage on the mica capacitor is measured by a capacitor voltage divider, and the voltage divider ratio is 1320. The resistance on the water resistance is measured with a high-voltage probe (NorthStar PVM-5), and the voltage divider ratio is 2000. Through measurement by a LCR meter (Keysight E4980A), the measured primary coil inductance L p of the air-core pulse transformer is 22.1 µH, the resistance of the primary winding is 15 m, the inductance of the secondary winding is 18.73 mH, the resistance of secondary windings is 33 , and the coupling coefficient can be calculated as 0.84. The primary windings loop quality factor is 49. The secondary coil loop quality factor is 53. The transformation ratio of the transformer is 44. The results meet the theoretical design expectations. The primary capacitor is charged to 1300 V, and after the switch is turned on, the charging waveform on the mica capacitor to be measured and the output waveform on the water resistance can be measured. The test platform can output 50 kV at 20 Hz for 50 s or 10 Hz for 100 s at a time. It can work at this mode for one hours continuously. The lifetime test of MPCs is carried out under the conditions of charging voltage of 40– 60 kV, charging time of 16 µs, and repetition frequency of 20 Hz. A group includes 2000 pulses. Each group interval is 5 min for enough time to dissipate heat. During the interval, the essential parameters of the mica capacitor are recorded by a precision LCR meter (Keysight E4980A) at 10 kHz until the capacitor breaks down. The typical charging and load voltage waveform are shown in Figs. 10 and 11. The mica test platform can obtain better consistent output. The charging voltage dispersion on the mica capacitor does not exceed 1%. The triggered switch works stably. Four sets of MPCs with each set of 4 MPC samples are tested under 40 kV, 45 kV, 50 kV and 60 kV, respectively. The test results of MPCs are shown in Fig. 12. We can calculate the lifetime of capacitors at different voltages through the following empirical model formula (6). By fitting the data of Fig. 12, the parameter a can be calculated as 2.4. L 0 is the average lifetime of an MPC under a voltage of U 0 . U 0 is the rated voltage of 50 kV of an MPC. −a U L0 (6) L= U0
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Fig. 8. Primary energy (including air core transformer)
Fig. 9. Test box (ncluding switch, mica capacitor)
Fig. 10. Charging waveform of MPC (overlap mode, 20 Hz, 400 pulses)
Fig. 11. Output waveform on water load (overlap mode, 20 Hz, 400 pulses)
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Fig. 12. Test results of 4 sets of MPC and fitting curve for acceleration factor of voltage
5 Conclusion In the application needs of research on the performance characteristics of MPC, this paper developed a rep-rate operation test platform to study the life characteristics of MPC under microsecond pulse. The test platform uses an air-core pulse transformer and a primary source system with energy recovery process and supplement. The optimally designed air-core pulse transformer has a high coupling coefficient, which can effectively reduce the heat generation and improve the continuous working ability. The optimal design spherical belt trigger electrode has the characteristics of low jitter. The test platform can output 50 kV at 20 Hz for 50 s or 10 Hz for 100 s at a time. It can work at this mode for one hours continuously. The charging voltage dispersion on the mica capacitor does not exceed 1%, which meets the test requirements. This platform allows to study the lifetime characteristics of MPC. It provides support for the next step of developing highly reliable and long-life PFN-Marx generators using mica capacitors.
References 1. Kekez, M.M.: A 480 joule, 650 kV, 1(BS) >100(PCS)
Continuity of protective earthing/
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Accuracy rate of fault diagnosis/%
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Operation coefficient/%
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Availability coefficient/%
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4.3 Results Analysis and Optimization Suggestions Analysis of charge-discharge performance. As shown in Table 3, the degradation rate of the actual available capacity is 0.12%, and the energy retention rate of BESU is 99.91%, which means there is no obvious performance degradation in the second month after the BESS is put into operation, and it still maintains good charging-discharging performance. Analysis of energy efficiency performance. The comprehensive energy efficiency of the BESS is 82.95%, which is affected by energy losses of various parts, including auxiliary energy consumption, energy loss for power distribution and transmission, energy loss of battery BS and energy loss of PCS. Their respective proportions are shown in Fig. 4. Among them, the energy loss of BS accounts for 5.11%, which is the link with more loss. The energy efficiency of BS is mainly affected by some factors, such as cycle number, depth of discharge, operating temperature and uniformity of battery. Through operating data analysis, uniformity of battery is the key factor for the new BESS affecting the energy efficiency of the BS. The battery uniformity of one random battery cluster
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3.49%
3.37%
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Comprehensive energy efficiency Energy loss rate of BS Rate of auxiliary energy consumption Rate of energy loss for power distribution and transmission Energy loss rate of PCS
Fig. 4. Energy loss Proportion of the BESS
0.2
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voltage range / V
0.18
10 voltage range
time
Fig. 5. Daily voltage range and temperature range curves of one battery string
is analyzed according to the voltage and temperature data of single battery in one day. The daily voltage and temperature range curves of single battery are shown in Fig. 5, and the maximum temperature range is 3 °C, showing good consistency. However, the voltage range is large in the period from 7:00 to 8:00, and the maximum value is 0.173 V with poor consistency. Therefore, the battery cluster with poor consistency should be the focus of attention for the future operation and maintenance.
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Analysis of safety performance. The value of insulation resistance and continuity of protective earthing are obtained through field testing, which coincide with IEC specifications. The accuracy rate of fault diagnosis is 83.33%, calculated according to the operation data. And there are some faults of the BESS during operation that were not diagnosed and alerted in time Therefore, the protection functions of the BS, PCS and monitoring system should be checked regularly to improve the fault diagnosis accuracy and ensure the safe operation of the BESS. Analysis of reliability performance. Through operation data analysis, it can be seen that the availability coefficient of the BESS is 94.35%, the operation coefficient is 81.85%, and the unplanned outage coefficient is 5.65%. Since the BESS was only put into operation for one month, there were some equipment failures in the initial stage, leading to a high unplanned outage coefficient and the reliability performance of the BESS still needs to be improved. Analysis of economic performance. The total initial investment cost of the BESS is about 30 million RMB, and the service life is 7 years. In April, a cumulative income of 360,000 RMB was obtained from peak-load shifting based on TOU electricity price. At the same time, the revenue from participating in the auxiliary service of the power market is 90,000 RMB. By calculation and analysis, the economic benefit per unit capacity of the BESS in April is 5800 RMB/MWh. But if the BESS only benefits from the peakvalley difference, the revenue per unit capacity will be 2900 RMB/MWh, meaning the service life of 7 years will not recover the cost. It can be seen that the participation of the user-side BESS in the auxiliary service of the electricity market can significantly improve the economic benefits and effectively shorten the investment return period.
5 Conclusion According to the characteristics of the user-side BESS, this paper proposes five dimensions of operation evaluation indexes, including charge-discharge performance, energy efficiency, safety, reliability and economic performance. The operation performance of a typical user-side BESS for peak-load shifting is quantitatively analyzed and evaluated, based on the operation data and field test data. And the optimization suggestions are given for future operation and maintenance of the BESS. The results show that the proposed e indexes and methods can realize the quantitative evaluation of the actual operation performance and is of great significance to the efficient, safe and reliable operation of the user-side BESS. Acknowledgments. This research is supported by National Key Research and Development Program of China (Grant No. 2018YFF0215903).
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References 1. Ecology China Homepage. http://www.eco.gov.cn/index.php/news_info/54859.html. Accessed 11 October 2022 2. Saini, P., Gidwani, L.: An investigation for battery energy storage system installation with renewable energy resources in distribution system by considering residential, commercial and industrial load models. J. Energy Storage 45(5), 443–454 (2022) 3. Yibin, T.A.O., Jinhua, X.U.E., Deshun, W.A.N.G., et al.: Comprehensive performance evaluation of BESS for power grid peaking and frequency regulation. Chin. J. Power Sour. 45(6), 764–767 (2021). (in Chinese) 4. Jianlin, L.I., Meng, N.I.U., Shangxing, W.A.N.G., et al.: Operation and control analysis of 100 MW class battery energy storage station on grid in Jiangsu power grid of China. Autom. Electr. Power Syst. 44(2), 28–35 (2020). (in Chinese) 5. Jiaqi, L., Jian, C., Wen, Z., et al.: Integrated control strategy for battery energy storage systems in distribution networks with high photovoltaic penetration. Trans. China Electrotech. Soc. 34(1), 437–446 (2019). (in Chinese) 6. Bahloul, M., Daoud, M., Khadem, S.K.: A bottom-up approach for techno-economic analysis of battery energy storage system for Irish grid DS3 service provision[J]. Energy 245, 1–15 (2022). (in Chinese) 7. Jinhua, X.U.E., Jilei, Y.E., Qiong, T.A.O., et al.: Economic feasibility of user-side battery energy storage based on whole-life-cycle cost model. Power Syst. Technol. 40(8), 2471–2476 (2016). (in Chinese) 8. Yingyuan, H.E., Yongchong, C.H.E.N., Yong, L.I.U., et al.: Analysis of cost per kilowatthour and cost per mileage for energy storage technologies. Adv. Technol. Electr. Eng. Energy 38(9), 1–10 (2019). (in Chinese) 9. Li, Y., Qian, F., Gao, W., et al.: Techno-economic performance of battery energy storage system in an energy sharing community. J. Energy Storage 50, 1–15 (2022) 10. Kejun, Q., Zhenkai, Z., Jie, S., et al.: An economic evaluation model for user-side energy storage considering uncertainties of demand response. In: IEEE International Power Electronics and Motion Control Conference, pp. 3221–3225 (2020) 11. Hartmann, B., Divényi, D.: Evaluation of business possibilities of energy storage at commercial and industrial consumers–a case study. Appl. Energy 222(5), 59–66 (2018)
Discussion on Key Components Design for Off-Grid Photovoltaic Electrolysis Hydrogen Production System Yong Zhao, Mingyu Lei(B) , Yuanyuan Chen, Yanjiao Hou, Zhuo Chen, and Yibo Wang Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190, China {zhaoyong,leimingyu,chenyuanyuan,hyj,chenzhuo, wyb}@mail.iee.ac.cn
Abstract. Hydrogen production using renewable energy is an important way to promote new energy power consumption and achieve zero carbon emissions. Compared with the traditional grid-tied water electrolysis, off-grid photovoltaic water electrolysis has the advantages of low cost and flexible deployment. The applicability of three kinds of hydrogen production electrolyzers in combination with renewable energy was investigated. The structure of off-grid hydrogen production system based on alkaline electrolysis water hydrogen production equipment is emphatically expounded. The design methods of photovoltaic DC power supply unit, hydrogen production auxiliary system AC power supply unit and the power supply for control unit of electrolyzer are discussed. The design schemes of capacity allocation of energy storage and the reliable power supply of dual backup are proposed as a technical reference for off-grid photovoltaic hydrogen production systems. Keywords: Hydrogen production · Water electrolysis · Photovoltaic consumption · Off-grid photovoltaic · DC power supply
1 Introduction As of the end of 2020, sixteen of the 27 countries that account for 52% of global GDP have developed national hydrogen strategies, and the other 11 countries are formulating national hydrogen energy strategies. In 2014, the United States stated that hydrogen energy will play a leading role in the transformation of transportation, and put forward suggestions to promote the development of hydrogen production technologies. Japan formulated the “Plan for 2050 Energy and Environmental Innovation Strategy” to promote the development of hydrogen production, hydrogen storage, hydrogen power generation technologies and ultimately build a clean and pollution-free “hydrogen energy society” [1]. The EU, from 2020 to 2024, will support the installation of at least 6 GW of renewable hydrogen electrolyzers in the EU and produce up to 1 million tons of renewable hydrogen. In 2016, China released the “Roadmap for Key Innovations in the Energy © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 361–372, 2023. https://doi.org/10.1007/978-981-99-1027-4_38
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Technology Revolution”, which pointed out that it is necessary to achieve large-scale, low-cost production, storage, transportation, and application of hydrogen. Hydrogen energy has been written into the “14th Five-Year Plan” by 30 provinces under the goal of energy conservation and emission reduction [2]. At present, more than 96% of commercial hydrogen in the world is produced from fossil fuels. Due to the large amount of carbon dioxide emitted during the hydrogen production process, this type of hydrogen is also called “grey hydrogen”. Hydrogen production from renewable energy sources such as wind power and photovoltaics can not only achieve “zero carbon emissions” and obtain truly clean “green hydrogen”, but also convert intermittent and unstable renewable energy into chemical energy to promote renewable energy consumption [3]. The renewable energy hydrogen production system includes three schemes: photovoltaic grid-connected centralized hydrogen production, full off-grid photovoltaic hydrogen production, and photovoltaic grid-tied or off-grid multi-mode hydrogen production [4]. As the power grid is a stable source and the main equipment is mature, most of the renewable energy hydrogen production systems are connected to the grid in China [5]. With the expansion of the scale of hydrogen production from renewable energy, photovoltaic off-grid hydrogen production has many advantages compared with the gridconnected mode. Grid-tied hydrogen production from renewable energy needs multiple transformations of inverter and rectification, and the final electric energy utilization efficiency is about 89%. In the off-grid mode, the power supply system efficiency can be promoted to 96% [6]. Compared with grid-tied water electrolysis, off-grid system cost can be reduced by about 40% without rectification, and grid-connection investment. Especially in some areas that are not covered by large power grids, such as offshore energy platforms, highway gas stations in remote areas and islands in the far sea, the offgrid hydrogen production system can implement the combining supply of heat, electricity and gas [7]. Researches on off-grid wind/solar and hydrogen combined operation systems are focused on topology design and capacity configuration, including model construction, control strategies, and capacity configuration optimization. An independent energy supply system architecture for photovoltaic hydrogen storage in alpine region is proposed, which realizes the supply of thermal and power [8]. A hybrid energy storage system of batteries and supercapacitors based on photovoltaic hydrogen production is established, and corresponding control strategies are proposed. A wind-hydrogen complementary system is proposed, and the capacity allocation scheme is studied considering the cost of production, storage, and combustion of hydrogen, load power shortage rate and system output power fluctuation rate. A residential combined energy supply renewable energy system based on wind/solar combined hydrogen production, hydrogen storage, and hydrogen fuel cell has been established [9]. An off-grid wind power electrolysis water hydrogen production system is constructed, which realizes 100% efficient and low-cost utilization of wind power. Based on water electrolysis by renewable energy and underground heat storage devices, a comprehensive hydrogen and heat cogeneration system is constructed, which improves the energy utilization efficiency of hydrogen plants. The water electrolysis hydrogen production system in an off-grid microgrid can be operated in different modes including wind or solar power, combined wind and solar, and separate electrolysis by energy storage [10]. It solves the problem of equipment
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life reduction caused by frequent startup and shutdown of electrolyzer, and improves equipment utilization efficiency. A capacity matching method for an off-grid wind power hydrogen production system is proposed, which can minimize the equipment investment cost while ensuring the economic benefits of the system [11]. An off-grid wind powerto-hydrogen conversion system is designed, which uses a bidirectional DC converter to control the energy storage unit. The instantaneous power imbalance between the rectifier unit and the electrolytic DC conversion unit is suppressed, and the power supply stability of the electrolytic cell is improved [12]. The above studies are focused on renewable energy hydrogen system design involving wind, PV, and hydrogen overall structural design and configuration for general scenarios. Electric equipment for off-grid photovoltaic hydrogen production, such as photovoltaic drive units of electrolyzers, power supply units of balance components of hydrogen production systems, and control units, have been less studied. In this paper, the domestic and foreign cases of the off-grid photovoltaic hydrogen generation system are summarized, and the design of photovoltaic DC supply unit for electrolyzer, AC supply unit for hydrogen production auxiliary system and control unit are emphasized.
2 Design of Off-Grid Photovoltaic Electrolysis Hydrogen Production System Off-grid photovoltaic hydrogen production systems can be established in houses, communities, and renewable energy bases according to application scenarios and scales. The main parameters and application scenarios of the three types of systems are shown in Table 1. As shown in the table, the main differences among the three types of hydrogen production systems are the capacity. The main purpose of the home and community hydrogen production systems is to provide electricity and heat for a certain number of users in the form of comprehensive energy, so as to realize energy saving and emission reduction. The hydrogen production systems in large-scale renewable energy bases can provides external power and hydrogen products. Most of them are not equipped with hydrogen fuel cells, and the chemical battery capacity can be determined by the output power fluctuation of renewable energy bases. The flow chart of the community distributed off-grid photovoltaic hydrogen production and hydrogen energy utilization system is shown in Fig. 1. The system can realize photovoltaic direct hydrogen production and electricity/hydrogen energy storage without grid support. The stored electricity and hydrogen provide users with continuous power supply and hot water supply, and can also provide hydrogen refueling services for hydrogen fuel vehicles. The system consists of photovoltaic power generation unit, water electrolyzer, chemical battery, electrolyzer power converter, hydrogen storage tank, heat storage device, water tank and hydrogen fuel cell and so on. Their functions are shown in Table 2. The electrolyzer is one of the most critical equipment in the hydrogen production system. At present, electrolyzer technologies include alkaline electrolysers (ALK), proton exchange membrane electrolysers (PEM), and solid oxide electrolysis cell (SOEC). The parameters of various water electrolyzers are shown in Table 3.
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Classification
Family
Community
Renewable energy base
Renewable energy installed capacity
500 kW
Hydrogen production
200 Nm3 /h
Hydrogen storage capacity
5000 Nm3
Battery capacity
0.5 ⎪ ⎪ ⎩ 0x < 0.3
x > 6.0
0x < 2.0 or
⎧ x−3.0 ⎪ ⎪ ⎨ 3.0 3.0 ≤ x < 6.0 1x > 6.00 ⎪ ⎪ ⎩ 0x < 3.0
⎪ ⎪ ⎪ ⎪ ⎩
⎧ x−0.2 0.2 ≤ x < 0.4 ⎪ ⎪ ⎪ 0.2 ⎪ ⎨ 0.5−x 0.4 ≤ x ≤ 0.5 0.1 ⎪ 0x > 0.5 or ⎪ ⎪ ⎪ ⎩ x < 0.2
0x > 0.2.
0.2−x 0.1 ≤ x ≤ 0.2 0.1
⎧ x−2.0 2.0 ≤ x < 5.0 ⎪ ⎪ 3.0 ⎪ ⎪ ⎨ 6.0 − x5.0 ≤ x ≤ 6.0
⎪ ⎪ ⎩ ⎧ x−0.1 0.1 ≤ x < 0.3 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.4−x 0.3 ≤ x ≤ 0.4 0.1 ⎪ 0x > 0.4 or ⎪ ⎪ ⎪ ⎩ x < 0.1
0x > 2.0.
2.0 − x1.0 ≤ x ≤ 2.0
Average current (A) ⎧ ⎪ 1x < 0.1 ⎪ ⎨
⎧ ⎪ x − 11.0 ≤ x ≤ 2.0 ⎪ ⎪ ⎪ ⎨ 4.0−x 2.0 ≤ x ≤ 4.0 2.0 ⎪ 0x < 1.0 or ⎪ ⎪ ⎪ ⎩ x > 4.0
⎪ ⎪ ⎩
Energy storage time (s) ⎧ ⎪ 1x < 1.0 ⎪ ⎨
Table 1. Membership function of energy storage motor.
0x > 0.8.
0.8−x 0.4 ≤ x ≤ 0.8 0.4
⎧ x−0.3 ⎪ ⎪ ⎨ 0.8 1.2 ≤ x ≤ 2.0 1x > 2.0 ⎪ ⎪ ⎩ 0x < 1.2
⎧ x−0.8 0.8 ≤ x < 1.6 ⎪ ⎪ ⎪ 0.8 ⎪ ⎨ 2.0−x 1.6 ≤ x ≤ 2.0 0.4 ⎪ 0x > 2.0 or ⎪ ⎪ ⎪ ⎩ x < 0.8
⎧ x−0.4 0.4 ≤ x < 1.2 ⎪ ⎪ 0.8 ⎪ ⎪ ⎨ 1.6−x 1.2 ≤ x ≤ 1.6 0.4 ⎪ 0x > 1.6 or ⎪ ⎪ ⎪ ⎩ x < 0.4
⎪ ⎪ ⎩
Peak current (A) ⎧ ⎪ 1x < 0.4 ⎪ ⎨
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Failure
Warning
Normal
Excellent
Evaluation level
⎧ x−0.3 ⎪ ⎪ ⎨ 0.2 0.3 ≤ x ≤ 0.5 1x > 0.5 ⎪ ⎪ ⎩ 0x < 0.3
x > 0.8
0x < 0.4 or
0.1
⎧ 0.7−x ⎪ ⎪ ⎨ 0.2 0.5 ≤ x ≤ 0.7 1x > 0.7 ⎪ ⎪ ⎩ 0x < 0.5
⎪ ⎪ ⎪ ⎪ ⎩
⎧ x−0.2 0.2 ≤ x ≤ 0.4 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.5−x 0.4 < x ≤ 0.5 0.1 ⎪ 0x > 0.5 or ⎪ ⎪ ⎪ ⎩ x < 0.2
0x > 0.2.
0.2−x 0.1 ≤ x ≤ 0.2 0.1
⎧ x−0.4 0.4 ≤ x ≤ 0.7 ⎪ ⎪ 0.3 ⎪ ⎪ ⎨ 0.8−x 0.7 < x ≤ 0.8
⎪ ⎪ ⎩ ⎧ x−0.1 0.1 ≤ x < 0.3 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.4−x 0.3 ≤ x ≤ 0.4 0.1 ⎪ 0x > 0.4 or ⎪ ⎪ ⎪ ⎩ x < 0.1
0x > 0.9
x−0.7 0.7 ≤ x ≤ 0.9 0.2
Average current (A) ⎧ ⎪ 1x < 0.1 ⎪ ⎨
⎧ x−0.6 0.6 ≤ x < 0.8 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.9−x 0.8 ≤ x ≤ 0.9 0.1 ⎪ 0x < 0.6 or ⎪ ⎪ ⎪ ⎩ x ≥ 0.9
⎪ ⎪ ⎩
Average speed (m/s) ⎧ ⎪ 1x < 0.7 ⎪ ⎨
Table 2. Membership function of tripping operation.
0x > 0.2.
0.2−x 0.1 ≤ x ≤ 0.2 0.1
⎧ x−0.3 ⎪ ⎪ ⎨ 0.2 0.3 ≤ x ≤ 0.5 1x > 0.5 ⎪ ⎪ ⎩ 0x < 0.3
⎧ x−0.2 0.2 ≤ x ≤ 0.4 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.5−x 0.4 < x ≤ 0.5 0.1 ⎪ 0x > 0.5 or ⎪ ⎪ ⎪ ⎩ x < 0.2
⎧ x−0.1 0.1 ≤ x < 0.3 ⎪ ⎪ 0.2 ⎪ ⎪ ⎨ 0.4−x 0.3 ≤ x ≤ 0.4 0.1 ⎪ 0x > 0.4 or ⎪ ⎪ ⎪ ⎩ x < 0.1
⎪ ⎪ ⎩
Peak current (A) ⎧ ⎪ 1x < 0.1 ⎪ ⎨
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parameters of the circuit breaker closing operation in this paper are average speed: 4.2 m/s, average current: 0.90 A, peak current: 1.03 A. The membership function of closing operation is the same as that of tripping operation.
4 Case Analysis 4.1 Normal Working Condition In order to verify the feasibility of the fuzzy comprehensive evaluation model in practical application, this paper uses the data measured by the circuit breaker on-line monitoring device to calculate the fuzzy comprehensive evaluation of type ZF6-252 hydraulic high voltage circuit breaker. Figures 1, 2 and 3 are the mechanical characteristic curves under normal working conditions measured by the experiment.
Fig. 1. Current of energy storage motor
Fig. 2. Curves of opening coil current and opening distance
Fig. 3. Curves of closing coil current and closing distance
The mechanical characteristic data given by the circuit breaker on-line monitoring device is shown in Table 3.
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Table 3. Mechanical characteristic data of circuit breaker under normal working conditions. Object
Monitoring items
Value
Energy storage motor
Energy storage time
25.2 s
Average current
1.18 A
Peak current
7.20 A
Average speed
8.60 m/s
Average current
0.57 A
Peak current
1.17 A
Average speed
3.84 m/s
Average current
0.72 A
Peak current
0.86 A
Tripping operation
Closing operation
Through the analytic hierarchy process and expert experience, the secondary weight of each evaluation factor of the energy storage motor is obtained, and the secondary judgment matrix is established as follows: ⎡
⎤ 1 5 7 P2 = ⎣ 1/5 1 2 ⎦ 1/7 1/2 1 The maximum eigenvalue of the matrix is calculated λmax and the maximum eigenvector w are: λmax = 3.014w = (0.9680.2180.123)T According to the analytic hierarchy process, the general consistency index CI and the random consistency ratio CR of the judgment matrix are calculated as follows: CI =
CI 1 1 (λ (3.014 − 3) = 0.007 CR = = 0.012 − n) = n − 1 max 3−1 RI
where, RI is the average random consistency index, and its value is determined to be 0.58 by looking up the table. Since CI < 0.1, it indicates that the judgment matrix meets the consistency. Finally, the secondary weight of each evaluation factor of the energy storage motor is obtained as follows: A2 = (0.7400.1670.094) For tripping operation and closing operation, the judgment matrix is the same as that of the energy storage motor, and the final secondary weight is also the same. According to the analytic hierarchy process and combined with expert experience, carry out a primary weight distribution for the circuit breaker energy storage motor,
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tripping operation and closing operation, and establish a primary judgment matrix as follows: ⎡ ⎤ 1 2 3 P1 = ⎣ 1/2 1 2 ⎦ 1/3 1/2 1 The maximum eigenvalue of the matrix is calculated λmax and the maximum eigenvector w are: λmax = 3.010 w = (0.847 0.466 0.257)T Similarly, according to the analytic hierarchy process, the general consistency index CI and the random consistency ratio CR of the judgment matrix are calculated as follows: CI =
CI 1 1 (λ (3.010 − 3) = 0.005 CR = = 0.009 − n) = n − 1 max 3−1 RI
Since CI < 01. It indicates that the judgment matrix meets the consistency. Finally, the primary weight of the circuit breaker energy storage motor, tripping operation and closing operation is obtained as follows: A1 = (0.5400.2970.163) Bring the evaluation factors into the membership function table, and the calculated secondary evaluation matrices are: ⎡ ⎤ 1 0 00 Rmotor = ⎣ 0.2 0.4 0 0 ⎦ 0.5 0.25 0 0 ⎡
⎤ 0.394 0.894 0.212 0 Ropening = ⎣ 0.5 0.25 0 0 ⎦ 0.4 0.3 0 0 ⎡ ⎤ 0 0.489 0.992 0.012 Rclosing = ⎣ 0.2 0.4 0 0 ⎦ 0.3 0.35
0
0
Combined with the weight distribution, use formula (1) to obtain the secondary evaluation results: Bmotor = A2 · Rmotor = (0.820.0900) Bopening = A2 · Ropening = (0.4120.7310.1570) Bclosing = A2 · Rclosing = (0.0620.4610.6820.009)
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Taking the above evaluation results as the evaluation factors again, the primary fuzzy comprehensive evaluation of the circuit breaker is carried out, and the evaluation matrix is obtained: ⎡ ⎤ 0.82 0.09 0 0 Rbreaker = ⎣ 0.412 0.731 0.157 0 ⎦ 0.062 0.461 0.682 0.009 Bbreaker = A1 · Rbreaker = (0.5480.3410.1580.001) Combined with the comments of the fuzzy comprehensive evaluation model, according to the principle of maximum membership degree, the membership degree of the excellent state of the circuit breaker is the largest, and the value is 0.548, which shows that the circuit breaker is in excellent condition. 4.2 Abnormal Working Condition The manufacturer conducted a high-pressure oil leakage simulation experiment on the circuit breaker, and Figs. 4, 5 and 6 are the mechanical characteristic curves measured in the experiment.
Fig. 4. Current of energy storage motor
Fig. 5. Curves of opening coil current and opening distance
The mechanical characteristic data given by the circuit breaker on-line monitoring device is shown in Table 4. Using the data in Table 4 and according to the membership function, the evaluation factors are brought into the corresponding membership function for calculation.
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Fig. 6. Curves of closing coil current and closing distance
Table 4. Mechanical characteristic data of circuit breaker under abnormal working conditions. Object
Monitoring items
Value
Energy storage motor
Energy storage time
28.0 s
Average current
1.18 A
Peak current
7.92 A
Average speed
8.60 m/s
Average current
0.57 A
Peak current
1.17 A
Average speed
3.81 m/s
Average current
0.72 A
Peak current
0.86 A
Tripping operation
Closing operation
Combined with the weight of the evaluation factors obtained in example 1, the fuzzy comprehensive evaluation information is obtained. ⎡
⎤ 0 0.5 0.33 0 Rmotor = ⎣ 0.2 0.4 0 0 ⎦ 0.5 0.25 0 0 ⎡ ⎤ 0 0.348 0.899 0.152 Ropening = ⎣ 0.5 0.25 0 0 ⎦ 0.4 0.3 0 0 ⎡ ⎤ 0 0.277 0.857 0.223 Rclosing = ⎣ 0.2 0.4 0 0 ⎦ 0.3 0.35
0
0
Bmotor = A2 · Rmotor = (0.080.460.2440) Bopening = A2 · Ropening = (0.1210.3270.6650.112) Bclosing = A2 · Rclosing = (0.0620.3040.690.165)
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⎡
Rbreaker
⎤ 0.080 0.46 0.244 0 = ⎣ 0.121 0.327 0.665 0.112 ⎦ 0.062 0.304 0.69 0.165
Bbreaker = A1 · Rbreaker = (0.0890.3950.4320.06) Combined with the comments of the fuzzy comprehensive evaluation model, according to the principle of maximum membership degree, the membership degree of the warning state of the circuit breaker is the largest, with a value of 0.432. It can be seen that the circuit breaker is in the warning state, there are hidden dangers that may affect the safe operation, and maintenance shall be arranged.
5 Conclusion This paper analyzes the mechanical characteristic of the hydraulic HV circuit breaker in the smart substation, selects the energy storage motor combined with the fuzzy comprehensive evaluation model, opening circuit operation and closed circuit operation as the comprehensive evaluation factors, determines the weight distribution according to the analytic hierarchy process and expert experience, and determines the membership function according to the fuzzy distribution method and expert experience, Using the mechanical characteristic data given by the on-line monitoring device of the circuit breaker, the fuzzy comprehensive evaluation of the working state of the HV circuit breaker is carried out. The experiments show that the evaluation method can reflect the normal and abnormal working conditions of circuit breakers in time and accurately provides a feasible scheme for the real-time online evaluation of hydraulic HV circuit breakers in smart substations.
References 1. Li, C., Zhong, J., Wang, Y., et al.: Research on fuzzy control of motor operating mechanism of high-voltage circuit breaker. Electrotech. Electr. 41(12), 7–10 (2021). (in Chinese) 2. Zang, C.: Research on status real-time monitoring fault diagnosis system of high voltage circuit breaker. Electr. Eng. 23, 126–128 (2021). (in Chinese) 3. Li, C., Ma, G., Qi, B., et al.: Condition monitoring and diagnosis of high-voltage equipment in China-recent progress. IEEE Electr. Insul. Mag. 29(5), 71–78 (2013) 4. Razi-Kazemi, A.A., Vakilian, M., Niayesh, K., et al.: Circuit-breaker automated failure tracking based on coil current signature. IEEE Trans. Power Deliv. 29(1), 283–290 (2014) 5. Wan, S., Ma, X., Chen, L., et al.: State evaluation and fault diagnosis of high-voltage circuit breaker based on short–time energy entropy ratio of vibration signal and DTW. High Volt. Eng. 46(12), 4249–4257 (2020). (in Chinese) 6. Huang, N., Wang, B., Cai, G., et al.: Mechanical fault diagnosis containing unknown fault of high voltage circuit breaker based on Tsallis entropy and hybrid classifier. High Volt. Eng. 45(5), 1518–1525 (2019). (in Chinese) 7. Zhao, L., Zhao, M., Xia, W., Wang, Z.: Status assessment of high voltage circuit breaker operating mechanism based on K–means and SOM hybrid algorithm. High Volt. Appar. 56(1), 0036–0042 (2020). (in Chinese)
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8. Razi-Kazemi, A.A.: Circuit breaker condition assessment through a fuzzy-probabilistic analysis of actuating coil’s current. IET Gener. Transm. Distrib. 10(1), 48–56 (2015) 9. Lin, P., Yang, M., Gu, J.: Intelligent maintenance model for condition assessment of circuit breakers using fuzzy set theory and evidential reasoning. IET Gener. Transm. Distrib. 8(7), 1244–1253 (2014) 10. Guo, L., Li, K., Liang, Y., et al.: HV circuit breaker state assessment based on gray-fuzzy comprehensive evaluation. Electr. Power Autom. Equip. 34(11), 161–167 (2014). (in Chinese)
State of Charge Estimation for Lithium-Ion Battery Based on Particle Swarm Optimization Algorithm and Multi-Kernel Relevance Vector Machine Shuyuan Zhou, Kui Chen(B) , Kai Liu, Guoqiang Gao, and Guangning Wu School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China [email protected]
Abstract. Lithium-ion batteries are key components of energy storage systems and electric vehicles, and their accurate State of Charge (SOC) estimation is important for battery energy management, safe operation and extended service life. In this paper, Multi-Kernel Relevance Vector Machine (MKRVM) and Particle Swarm Optimization (PSO) are used to estimate the SOC of Li-ion batteries under different operating conditions. PSO is used to automatically adjust and optimize the weights and kernel parameters of MKRVM to improve estimation accuracy. The proposed method is validated on three battery operation experiment under different operating conditions. The test results show that the proposed PSO-MKRVM can precisely estimate the battery SOC under different operating conditions with an accuracy higher than 0.99 and its maximum average error does not exceed 2%. Keywords: Lithium-ion battery · Particle swarm optimization · Multi-Kernel relevance vector machine · State of charge
1 Introduction The crisis of energy and environmental are major problems with human development, and the environmentally non-polluting energy sources is important method to resolve this conjuncture. With its high energy density, long cycle life, environmental friendliness, low self-discharge rate, light weight and high and low temperature adaptability, lithium batteries are extensively used in scenarios such as electric vehicles and power systems [1–3]. Accurate estimation of the state of charge (SOC) of Li-ion batteries can prevent overcharging and over-discharging of the battery [4, 5]. Therefore, accurate estimation of SOC is important. In order to accurately estimate the battery SOC, scholars at home and abroad have made a lot of research, and there are three main types of battery SOC estimation methods commonly used: 1. Traditional measurement methods: the open-circuit voltage method works better at the beginning and end of charging, but requires the battery to stand for too long; © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 448–458, 2023. https://doi.org/10.1007/978-981-99-1027-4_46
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the impedance in the internal resistance method is more sensitive to temperature, and when the temperature changes drastically, the estimation accuracy is lower; the ampere hour method is simple to calculate and easy to implement, but the error will accumulate over time and the initial SOC cannot be obtained, and is usually used in combination with other methods [6], and its implementation process is as follows: ηI (t)dt (1) SOC(t) = SOC0 − Qr where SOC(t) is the value of SOC at time; SOC 0 is the initial value; η is the coulombic efficiency; I(t) is the cell current at time t; Qr is the reference capacity. 1. Model-driven methods: The main existing battery models are equivalent circuit models and electrochemical models (P2D model, SP model, ESP model, MC model, etc.) [7]. Usually used in combination with filtering algorithms, the Kalman filter [8] based method for estimating SOC is more common. 2. Data-driven method: This method is based on a large amount of offline data, training the battery temperature, current, voltage and other data to establish a mapping relationship with the battery SOC. Commonly used algorithms include neural network method [9, 10], support vector machine method [11], relevance vector machine method [12–14], etc. Dai Haifeng et al. [14] proposed to build a relevance vector machine model with radial basis functions as kernel functions to estimate the battery capacity. Renjing Gao et al. proposed to use the grey wolf optimization algorithm to determine the kernel function weights and kernel parameters of a multicore relevance vector machine [12]. Chen Kui et al. proposed a new polymer electrolyte membrane fuel cell aging estimation model, using the whale optimization algorithm to adjust and optimize the weights and kernel parameters to improve the estimation accuracy, and the experimental results show that the multicore function is better than the single kernel function estimation [13]. Huang Kai et al. showed the wide use of particle swarm optimization algorithm in model parameter identification, and proposed a particle swarm algorithm based on information feedback [15]. Based on the above research, this paper proposes a model based on PSO and MultiKernel Relevance Vector Machine (MKRVM) to estimate the SOC of Li-ion batteries. The SOC of the Li-ion battery is estimated by automatically adjusting and optimizing the weights and kernel parameters of the MKRVM through a particle swarm algorithm to establish the mapping relationship between the discharge voltage, current, temperature and SOC of the Li-ion battery. Finally, the feasibility of the PSO-MKRVM estimation model is verified by three different operating conditions of battery operation data.
2 SOC Estimation Model Based on PSO-MKRVM 2.1 Multicore Relevance Vector Machine Algorithm A RVM is a machine learning method that uses sparse probabilistic models to build probabilistic learning models based on Bayesian inference theory. The model learns
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historical data using hyperparameter-controlled prior probabilities in a Bayesian framework and removes irrelevant points by Automatic Relevance Determination (ARD) to obtain a kernel-based sparsity model. Given a training sample set (xi ,ti ), i = 1, 2, . . . , N , xi is the input variable, ti is the target value, N is the number of samples, x represents the discharge voltage, current and temperature of the battery, y and represents the battery SOC, the RVM model can be defined as Eq. (2) ti = y(x, w) =
N
wi K(x, xi ) + wi + ε
(2)
i=1
where K(x, xi ) is the kernel function, ε is the sample error following a Gaussian distribution N (0, σ 2 ), and wi is the weighting factor. The likelihood function is as follows: p(t|w, σ 2 ) =
n
N (ti |y(xi , w), σ 2 )
i=1
= (2π σ 2 )
− 2n
(3)
t − (x)w2 exp(− ) 2σ 2
where N(*) is the Gaussian distribution function, t = (t1 , t2 , . . . , tN )T is the target vector, w = (w1 , w2 , . . . , wN )T is the parameter vector, (x) = [ϕ(x1 ), ϕ(x2 ), . . . , ϕ(xN )] is the basis function, and ϕ(xn ) = [1, K(xn , x1 ), K(xn , x2 ), . . . , K(xn , xN )]T . In calculating the unknown target values, in order to avoid the problem of overfitting by directly using the great likelihood method to solve for w and σ 2 , the hyperparameters α = [α1 , α2 , . . . , αn ] are introduced and each weight corresponds to a hyperparameter, using the sparse Bayesian principle to obtain a priori distributions with mean is 0 and variance is αi−1 about w as in Eq. (4): p(w|α) =
N
N (wi |0, αi−1 )
(4)
i=0
Based on the Bayesian formula, the posterior distribution of the unknown parameters is obtained from Eqs. (3) and (4) as Eq. (5) and the posterior distribution of the weights as Eq. (6): p(w, α, σ 2 |t) = p(w|t, α, σ 2 )p(α, σ 2 |t) p(t|w, σ 2 )p(w|α, σ 2 ) p(t|α, σ 2 ) n+1 1 1 = (2π )− 2 − 2 exp(− (w − μ)T ψ −1 (w − μ)) 2 −1 = σ −2 T + A
(5)
p(w|t, α, σ 2 ) =
(6)
(7)
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(8)
RVM is a kind of recognition method that uses kernel functions to realize a nonlinear transformation of feature space, category space and data space through kernel mapping. Kernel functions have a significant impact on the RVM accuracy. Traditional RVM uses a single kernel function to complete the mapping process. When the training data is abounding, the feature information is multifarious and the mapping produces less than smooth data, the single kernel function has greater boundedness for the nonlinear transformation of the high-dimensional space and cannot fit to the complexity and multiformity of the data. In order to enhance the accuracy of RVM, this paper uses a multicore function [13] to obtain MKRVM. The multicore function is represented by Eq. (9): K(x, xi ) = ωK1 (x, xi ) + (1 − ω)K2 (x, xi )
(9)
where ω is the weight and 0 < ω < 1; K1 (x, xi ) and K2 (x, xi ) are the sigmoid kernel function and Gaussian kernel function. 2.2 Particle Swarm Optimization Algorithms The PSO algorithm is a global optimization algorithm based on population optimization techniques, which seeks the optimal particles of an individual and the optimal particles of a population by means of a particle search of the population [16]. The algorithm first initializes a set of random particles in a D-dimensional target search space with a total number of particles M, position of particle i: xi = (xi1 , xi2 , . . . , xiD ), particle velocity: vi = (vi1 , vi2 , . . . , viD ). In each iteration, the position and velocity of each particle changes. The two “best positions” it tracks determine the principle of change. The first position is the optimum solution Pbest currently found by the particle itself, and the other position is the optimum solution gbest currently found by the whole population of particle. Each particle performs (k + 1) iterations according to Eqs. (10) and (11): vi (k + 1) =ωvi (k) + c1 r1 (pibnest (k) − xi (k) + c2 r2 (gibnest (k) − xi (k))
(10)
xi (k + 1) = xi (k) + vi (k + 1)
(11)
where ω is the inertia factors, and c1 , c2 ∈ (0, 1), vi (k) and xi (k) are the velocity and position of the i-th particle in the k iteration, respectively. 2.3 PSO-MKRVM Algorithm Steps The proposed PSO-MKRVM based SOC Li-ion batteries estimation method is shown in Fig. 1, and the steps of the PSO-MKRVM are as follows: 1. The battery SOC estimation model was developed using MKRVM to determine the input quantities as discharge current, voltage and temperature and the output quantity as SOC, normalizing all data.
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2. Initialize the particle population: set the number of iterations, population size, velocity factor and position factor of the PSO to randomly generate the initial position and initial velocity. 3. Calculating fitness: Based on the training data, the estimated SOC of the lithium battery is obtained by MKRVM. The overall fitness is evaluated using the mean squared error and the equation is as in (12): 1 (yi − yi )2 n n
fMSE =
(12)
i=1
where n is the sample size; yi is the estimated SOC of MKRVM; yi is the actual SOC of the cell. 4. Termination condition judgment: when the maximum number of iterations is reached or the adaptation degree is under the desired adaptation degree, execute step 6, otherwise execute step 5. 5. Produce a new particle population: update, get new particle positions and velocities from Eqs. (10) and (11), and set the new particle population. 6. Obtain optimization weights and kernel parameters for MKRVM. 7. Estimate lithium battery SOC using the PSO-MKRVM model.
Data initialisation MKRVM model PSO
Initialize particle swarm Suitability function Judging the end condition
Update particle position, velocity and optimum values Updates gbest No
Updates pbest
Yes
Output optimal weighting parameters, kernel parameters Estimated results Fig. 1. PSO-MKRVM algorithm for flow chart
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3 Experimental Results and Analysis Experiments were conducted to validate the PSO-MKRVM Li-ion battery SOC estimation model using data from batteries CX2-16, CX2-8 and CS2-35. Battery CX2-16 was discharged at a constant current of 0.5C, battery CX2-8 was discharged at a constant current of 3C and battery CS2-35 was discharged at a constant current of 1C and discharging was stopped when the discharge voltage of the three batteries was reduced to 2.7V. The experiment was divided into two main parts: In the first part, the batteries CX2-16, CX2-8 and CX2-35 were trained with one discharge data to estimate the next discharge SOC respectively. In the second part, the first 25 discharges of battery CX2-16 were used for training to estimate the second 25 discharge SOC (Table 1). Table 1. Division of experimental data Battery type The first part
The second part
Number of training samples
Number of samples tested
CX2-16
177
177
CX2-8
39
39
CX2-35
125
125
CX2-16
4388
4388
3.1 Data Pre-processing Prior to the start of the experiment, the CALCE Research Centre Li-ion battery measurement data set was pre-processed to contain real-time changes in voltage, current, temperature and SOC data with discharge. To reduce the complexity of the data, deal with dissimilar data in the data set, speed up the gradient descent to find the optimal solution, and improve the model accuracy and convergence speed. The above data is normalized and the normalization formula is shown below: Yi =
yi − ymin ymax − ymin
(13)
where yi is the sample value before normalization; Yi is the sample value after normalization; ymin is the minimum value of the sample; ymax is the maximum value of the sample. 3.2 Evaluation Indicators The mean absolute error (MAE), root mean squared error (RMSE) and coefficient of determination (COD) were selected as comprehensive evaluation indicators to assess the
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model estimation performance. The calculation formulae and evaluation criteria are as follows: m 1 RMSE =
(yi − yi )2 (14) m
i=1
1 yi − yi m i=1 m (yi − yi )2 SSE 2 R =1− = i=1 m 2 SST i=1 (yi − y) m
MAE =
(15)
(16)
where yi is the true SOC value of the sample; yi is the estimated SOC value of the ith sample; y indicates the mean of the true value of the sample; m is the number of samples; the smaller the RMSE and MAE values, the better the estimation, and the closer the R2 -value to 1, the better the fit and the better the estimation. 3.3 Estimated Results from One Measurement Experiments were conducted using the battery CX2-16, CX2-8, and CS2-35 datasets to validate the feasibility of the PSO-MKRVM estimation model. Training was performed with one discharge data to estimate the next discharge SOC. The actual and estimated values of SOC for one discharge case for the three batteries are shown in Figs. 2, 3, 4, and the estimation errors are shown in Table 2.
Fig. 2. Once discharge SOC estimation of CX2-16
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Fig. 3. Once discharge SOC estimation of CX2-8
Fig. 4. Once discharge SOC estimation of CX2-35
From Table 2, the MAE in estimating the primary discharge SOC of batteries CX216, CX2-8 and CS2-35 using PSO-MKRVM does not exceed 0.8%, the RMSE does not exceed 0.9% and the maximum error does not exceed 2%, which is higher than 0.99. It can be seen that PSO-MKRVM has a high accuracy in estimating the SOC and a good fitting effect, which verifies the feasibility of the method.
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Battery type
MAE (%)
RMSE(%)
R2
Maximum error (%)
CX2-16
0.4865
0.5963
0.9995
1.3716
CX2-8
0.7668
0.8996
0.9991
1.7453
CX2-35
0.6466
0.7968
0.9993
1.9705
3.4 Estimated Results from Multiple Measurements The experiments were trained using the first 25 discharges of the battery CX2-16 to estimate the second 25 discharges of SOC. The actual and estimated values of SOC are shown in Fig. 5 and the multiple estimation errors are shown in Table 3.
Fig. 5. Repeatedly discharge SOC estimations of battery CX2-16
Table 3. MAE、RMSE and R2 of several estimations Battery type
MAE (%)
RMSE (%)
R2
Maximum error (%)
CX2-16
1.9893
2.4344
0.9928
5.9982
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From Table 3 it can be seen that the error in estimating the SOC of the battery CX2-16 for 25 discharges using PSO-MKRVM is significantly higher than the error in estimating the SOC for one discharge, with the MAE not exceeding 2%, the RMSE not exceeding 2.5% and the maximum error not exceeding 6%, which is higher than 0.99. This shows that the PSO-MKRVM can also meet the practical needs when performing multiple discharge SOC estimation.
4 Conclusions This paper proposes a way to estimate the SOC of lithium-ion batteries using the PSO algorithm in combination with MKRVM, applying the proposed PSO-MKRVM to estimate the batteries SOC and concluding that: (1) PSO-MKRVM can accurately construct a mapping relationship between battery discharge current, voltage and temperature and SOC, and SOC can be accurately estimated from the battery discharge current, voltage and temperature. (2) The average error in the single estimation of SOC for the three batteries under different operating conditions does not exceed 0.8%, and the average error in the multiple estimation of SOC for battery CX2-16 does not exceed 2%. Therefore, the proposed PSO-MKRVM can precisely estimate the battery SOC under different operating conditions.
Acknowledgments. This work was funded by State Grid Corporation Headquarters Management Technology Project (SGTYHT/19-JS-215).
References 1. Li, J., Li, H.: Review of state of charge estimation methods for electric vehicle lithium-ion batteries. Sci. Technol. Eng. 22(06), 2147–2158 (2022). (in Chinese) 2. Hannan, M.A., Li pu, M.S.H., Hussain, A., et al.: A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations. Renew. Sustain. Energy Rev. 78, 834–854 (2017) 3. Lu, L., Han, X., Li, J., et al.: A review on the key issues for lithium-ion battery management in electric vehicles. J. Power Sources 226, 272–288 (2013). (in Chinese) 4. Li, C., Xiao, F., Fan, Y., et al.: Joint estimation of the state of charge and the state of health based on deep learning for lithium-ion batteries. Proc. CSEE 02(41), 618–692 (2020). (in Chinese) 5. Chen, Y., Kang, Y., Zhao, Y., et al.: A review of lithium-ion battery safety concerns: The issues, strategies, and testing standards. J. Energy Chem. 59, 83–99 (2021) 6. Li, C., Xiao, F., Fan, Y., et al.: A hybrid approach to lithium-ion battery SOC estimation based on recurrent neural network with gated recurrent unit and Huber-M Robust Kalman Filter. Trans. China Electrotech. Soc. 35(09), 2051–2062 (2020). (in Chinese) 7. Longxing, W., Pang, H., Jin, J., et al.: A review of SOC estimation methods for lithium-ion batteries based on electrochemical model. Trans. China Electrotech. Soc. 07(37), 1703–1725 (2022). (in Chinese)
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8. Chunling, W., Wenbo, H., Meng, J., et al.: State of charge estimation of lithium-ion batteries based on maximum correlation-entropy criterion extended Kalman filtering algorithm. Trans. China Electrotech. Soc. 24(36), 5165–5175 (2021). (in Chinese) 9. Pan, J., Wang, M., Kan, W., et al.: State of charge estimation of lithium-ion battery based on Adam optimization algorithm and long short-term memory neural network. Electr. Eng. 04(23), 25–30 (2022). (in Chinese) 10. Cao, X., Peng, F., Li, L., et al.: SOC estimation of lithium battery based on IBAS-NARX neural network model. Energy Storage Sci. Technol. 10(06), 2342–2351 (2021). (in Chinese) 11. Zhang, T., Ming, Y., Li, B., et al.: Capacity prediction of lithium-ion batteries based on wavelet noise reduction and support vector machine. Trans. China Electrotech. Soc. 14(35), 3126–3136 (2020). (in Chinese) 12. Renjing Gao, Xianguo Huang, Zhiqiang Lu. A Li-Ion battery capacity estimation method based on multi-Kernel relevance vector machine optimized model. Trans. China Electrotech. Soc. 1–10 (2022) (in Chinese) 13. Dai, H., Jiang, B., Wei, X., et al.: Capacity estimation of lithium-ion batteries based on charging curve features. J. Mech. Eng. 55(20), 52–59 (2019). (in Chinese) 14. Chen K, Badji A, Laghrouche S, et al.: Polymer electrolyte membrane fuel cells degradation prediction using multi-kernel relevance vector regression and whale optimization algorithm. Appl. Energy 318 (2022) 15. Huang, K., Guo, Y., Li, Z.: High precision parameter identification of lithium-ion battery model based on feedback particle swarm optimization algorithm. Trans. China Electrotech. Soc. 34(S1), 378–387 (2019) (in Chinese) 16. Zhang, C., Zhao, S., He, Y.: State-of-health estimate for lithium-ion battery using information entropy and PSO-LSTM. J. Mech. Eng. 58(10), 180–190 (2022). (in Chinese)
Research on Variation Rules of Characteristic Parameters and Early Warning Method of Thermal Runaway of Lithium Titanate Battery Zhilin Shan1 , Qixing Zhang1(B) , Yongmin Zhang1 , Shuping Wang2 , and Yifeng Chen2 1 State Key Laboratory of Fire Science, University of Science and Technology of China,
Heifei 230031, China [email protected] 2 State Grid Anhui Electric Power Research Institute, Hefei 230601, China
Abstract. Aiming at prominent problems such as thermal runaway triggered by heating, thermal runaway triggered by overcharge and thermal runaway triggered by nail penetration of lithium titanate battery, the paper studied the variation rules of characteristic parameters such as battery surface temperature, environment temperature, battery voltage, characteristic gas and electrolyte vapor and studied the early warning method of thermal runaway of lithium titanate battery. The results showed that both overcharging and heating could trigger thermal runaway of lithium titanate battery, and there was less chance of thermal runaway triggered by nail penetration; a large amount of electrolyte vapor and smoke would be generated in the early stage of thermal runaway; the characteristic parameters of thermal runaway changed dramatically. In the enclosed space, the reference values of the thermal runaway characteristic parameters of lithium titanate battery change like this: The battery surface temperature or the environment temperature can reach 180 °C, or the average heating rate can reach 5 °C/s and above and last for 3 s; the battery voltage drops to 0 V in a short time, and the peak rate of decline can reach 0.4 V/s and above; the concentration of H2 can reach 100 ppm, the increase rate of H2 concentration can reach 5 ppm/s and above, and can last for 3 s and above; VOC gas concentration can reach 10000 ppm, and its concentration increase rate attains 1000 ppm/s and above, and can last for 3 s and above. Keywords: Lithium titanate battery · Thermal runaway · Analysis of characteristic parameters · The characteristics of gas · The early warning method
1 Introduction Lithium ion battery has been developed rapidly and widely used since it came into being in 1970s. Lithium titanate battery has the advantages of strong sustainable output capacity, excellent power performance, wide service temperature range, long cycle life and high safety, and has been introduced into urban rail vehicles and other fields [1]. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 459–470, 2023. https://doi.org/10.1007/978-981-99-1027-4_47
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Although the safety of lithium titanate battery is relatively high, the safety risk brought by its characteristics as power lithium electronic battery cannot be ignored in large-scale and frequent use, especially in the environment of densely populated rail vehicles. It is of great significance to study the thermal runaway detection and early warning technology of lithium titanate battery and eliminate hidden dangers of battery safety [2]. In order to realize the detection and early warning of lithium ion battery safety and thermal runaway, thermal runaway characteristic parameters can be studied and an early warning model can be constructed [3]. Some scholars explored the rule of heat generation of lithium-ion batteries by real-time monitoring of battery surface temperature, and proposed three-level early warning strategies based on different temperature thresholds [4]. Some scholars conducted battery state of health assessment (SOH) based on the change of internal resistance of lithium electron batteries and its relationship with temperature and time [5]. Some scholars use voltage, smoke, characteristic gas and other characteristics to construct the threshold value, change rate or multi-feature coupling model of single characteristic parameter to realize the early warning and judgment of lithium battery fire safety [6–8]. At the same time, new methods and models based on pattern recognition and deep learning are constantly proposed. According to the author, for the thermal runaway detection and early warning of lithium batteries, the discrimination method cannot be generalized according to different batteries and their application conditions. In order to get a more accurate thermal runaway warning method, it is necessary to carry out targeted research. For lithium titanate battery thermal runaway detection and early warning method is less, a square lithium titanate battery cell monomer as the research object, based on the single side method such as heating, overcharge, nail penetration, trigger thermal runaway on cell surface temperature, environment temperature rise rate, battery voltage, combustion features such as gas, electrolyte steam parameter analysis, analyze the development rule of the above parameters. The reasonable warning parameters in thermal runaway model are given. At the same time, the experimental design focuses on gas detection. For example, electrolyte vapor is the typical feature in the early stage of thermal runaway, and characteristic gas generated inside lithium battery is the typical feature in the occurrence of thermal runaway [9–11], which supports the design of thermal runaway detection and early warning system for lithium titanate battery used in energy storage.
2 Development Process and Judging Method of Thermal Runaway of Lithium Battery 2.1 Thermal Runaway Development Process of Lithium Ion Batteries Thermal runaway may be caused by mechanical abuse, electrical abuse and thermal abuse. Mechanical abuse includes extrusion and nail penetration, etc. Electrical abuse includes overcharge, overrelease, external short circuit and other situations. Heat abuse mainly refers to battery overheating. Thermal runaway inducement leads to part overheating of lithium ion batteries, then lithium batteries appear lithium evolution or internal short circuit. With the occurrence of internal short circuit, several reactions occur inside the battery, including electrode-electrolyte reaction, electrolyte reaction, SEI membrane
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decomposition, membrane melting, adhesive decomposition reaction, etc. [12]. The internal chemical reactions produce a large amount of heat release, leading to pressure relief, gas and smoke release, and even combustion. A large amount of heat accumulation will add to the internal reactions of the battery, and finally trigger thermal runaway [13]. 2.2 Thermal Runaway Judging Criterias of Lithium Ion Batteries GB38031-2020 “Electric vehicle power battery safety requirements”, recommended power lithium battery thermal runaway trigger judgment conditions: ➀ The trigger object generates a voltage drop, and the drop value exceeds 25% of the initial voltage; ➁ The temperature of the monitoring site reaches the maximum operating temperature specified by the manufacturer; ➂ The temperature rise rate of the monitoring site dT/ dt ≥ 1 °C/s and lasts for more than 3 s. When ➀ and ➂ or ➁ and ➂ occur, it is judged that thermal runaway has occurred. At the same time, the cell supplier of lithium titanate battery used in this paper recommends using the above method as the judgment condition for triggering thermal runaway of lithium battery.
3 Design of Experiment 3.1 Samples of the Battery In this study, the same batch of soft coated lithium titanate cells provided by the original supplier were adopted. The main component of the anode material was lithium titanate, the main material of the positive electrode was ternary material NCM, and the main material of the shell was aluminum plastic film. Cell capacity is 40 Ah; SOC capacity of the cell is 80%; Voltage range is 1.5–2.8 V; Nominal voltage is 2.35 V; AC internal resistance ≤ 0.55 m; DC internal resistance ≤ 1.2 m; Operating temperature −25 ~ 55 °C; The size is 161*227*11.3 mm; The weight is 0.92 kg. This experiment was carried out in accordance with the experimental environment described in GB/T 31485-2015 “Safety Requirements and Test Methods for Power Batteries for Electric Vehicles”. 3.2 Experimental Facility and Design Figure 1 shows the multi-characteristic parameter measurement system for thermal runaway of lithium battery. The experiment described in this paper is carried out in the closed reactor system, and the internal volume of the reactor is 80 L. In the experiment, the square soft coated lithium battery was placed in the thermal runaway reaction still of lithium battery to carry out nail penetration, heating and overcharge experiments. The
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reaction still is equipped with nail penetration device, unilateral heating device, gas sensor, thermocouple, battery fixture, power and signal cable; Reaction still is configured with gas inlet and outlet. The top is equipped with LED lighting. Outside of toughened glass window is equipped with HD camera.
Fig.1. Multi-characteristic parameters measurement system for Thermal Runaway of Lithium battery
The experiment can measure the characteristic parameters of thermal runaway process of lithium battery under different operating conditions, including cell surface temperature, ambient temperature at 20cm above the cell, cell voltage, electrolyte gas (VOC gas), characteristic gas (carbon monoxide and hydrogen). The device can export the gas produced by thermal runaway through the gas inlet and outlet, and furtherly analyze it through the gas analyzer. The experimental conditions designed in this experiment are shown in Table 1 below: Table 1. Table of experimental conditions No. of experimental conditions
1
Trigger mode
Heating
2
3
4
Overcharging
5
6
Nail penetration
In this experiment, three kinds of thermal runaway inducements were used, namely heating, overcharging and nail penetration, and each method was repeated 2–3 times to analyze the development process of characteristic parameters of lithium titanate battery in different thermal runaway methods and their warning methods.
4 Analysis of Characteristic Parameters of Thermal Runaway The general process of thermal runaway of lithium battery will be accompanied by the rise of battery temperature, gas and smoke injection, combustion, flame jet, gas secondary injection, combustion explosion and other phenomena. However, due to the influence
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of lithium battery material system, shell strength, experimental working conditions, safety valve design, thermal runaway triggering mode and other factors, the development process of thermal runaway has similarities and differences. 4.1 Thermal Runaway Phenomenon Heating experiment was conducted on lithium titanate soft-coated battery in this experiment. The video image process of thermal runaway in working condition 1 was similar to that in working condition 2, as shown in Fig. 2: When the battery was heated in a closed reaction still, the thermal runaway process was accompanied by battery bulge, releasing smoke and gas, but there is no flame, combustion, or explosion occurred after heavy smoke eruption.
(a)The initial state,
(c)Release smoke and gas
(b)battery bulge
(d)Spewing heavy smoke and gas
Fig. 2. Heating thermal runaway process
Overcharge experiment was conducted on lithium titanate soft-coated battery in this experiment. The thermal runaway video image process in working condition 3 is similar to that in working condition 4, as shown in Fig. 3: When the battery is heated in a closed reaction still, the thermal runaway process is accompanied by battery bulge, smoke injection, combustion and flame jet. The nail penetration experiment was conducted on the lithium titanate soft-coated battery in this experiment. The video image process of thermal runaway in working condition 5 was similar to that in working condition 6, as shown in Fig. 4: The nail penetration experiment was conducted on the soft-coated battery in a closed reaction still, and it was found that the battery did not experience thermal runaway.
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(a)
(b)
(c)
(d)
(e)
Fig. 3. Thermal runaway process of lithium battery by overcharge. a The initial state, b battery bulge, c Release smoke and gas, d burning, e Flame jet
(a) nail penetration before
(b) nail penetration after
Fig. 4. The experiment of nail penetration
4.2 Analysis of Characteristic Parameters of Heating Thermal Runaway According to the sampling frequency of 1Hz, the characteristic parameter data of the heating thermal runaway process are collected. The characteristic parameters of thermal runaway are lithium battery pyrolysis mixed VOC gas (Vocs), carbon monoxide gas (CO), hydrogen gas (H2 ), Cell Voltage, battery Surface temperature and Ambient temperature, respectively. The time-domain variation data of thermal runaway characteristic parameters are obtained, where the abscissa is time (unit: second). The ordinate C-g represents the quantity of CO and H2 in PPM; Ordinate Vocs represents the number of Vocs, and the unit is PPM; The ordinate V represents the voltage data of cells (unit: V). The ordinate T represents the data of Surface temperature and Ambient temperature and the unit is Celsius (°C). The characteristic parameter curve of thermal runaway process is shown in the Fig. 5 and 6. The heating thermal runaway is completed within one hour. According to the analysis of the time domain data curve of the characteristic parameters, the heating thermal runaway can be divided into two stages, namely, the initial exhaust stage and the thermal runaway stage. In the initial exhaust stage, when the surface temperature of lithium titanate battery rises to 180 °C, a gas emission occurs. The pyrolysis of lithium battery generates a large amount of gas decomposed by electrolyte and reaches the full scale of VOC sensor. A certain amount of CO and H2 are generated in the exhaust, and the concentration of CO and H2 gradually increases for a period of time after exhaust. That is, the exhaust lasted for a period of time, so that it can be judged that partial pyrolysis
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and chemical reactions occurred inside the battery, and and the characteristic products of thermal runaway are released. At this time, the cell voltage and ambient temperature did not change suddenly, and the battery surface temperature dropped for a period of time after exhaust, which was caused by the release of heat from a large number of gases, leading to the reduction of battery temperature, and the thermal runaway of battery did not occurred in the initial exhaust stage.
Fig. 5 Parameter curves of thermal runaway triggered by heating in exhaust stage
Five minutes before the occurrence of thermal runaway, CO concentration reaches the full scale of the sensor 1286ppm, H2 concentration reaches the full scale of the sensor 1000ppm and the temperature of the battery keeps rising. The chemical reaction inside the battery is intensified, and the thermal runaway occurs within a few minutes. The performance of the monitored characteristic parameters during thermal runaway is as follows: the concentration of VOC, CO and H2 all exceeds 1000ppm before thermal runaway. When thermal runaway occurs, the battery voltage rapidly decreases to 0V. The battery surface temperature and the ambient temperature rise suddenly. The maximum battery surface temperature rises to nearly 400 °C, and the ambient temperature rises to 350 °C.
Fig. 6 Parameter curves of thermal runaway triggered by heating
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Analysis is conducted according to the time domain rate curve of each characteristic paramete, as is shown in Figures 7 and 8 below. The abscissa is time with unit second (s). The ordinate kc-g represents the change rate of gas CO and H2 with unit ppm/s. The ordinate kvocs represents the change rate of VOC gas with unit ppm/s. The ordinate kv represents the changing rate of Cell Voltage in volts per second (V/s). The ordinate kt represents the changing rate of Surface Temperature and Ambient Temperature in degrees Celsius per second (°C/s). The sliding window filtering algorithm is used to deal with the discontinuities and glitch noise. The time domain curve of the characteristic parameter rate of thermal runaway process is shown in the figure below.
Fig. 7 Rate curves of characteristic parameters of thermal runaway triggered by heating in exhaust stage
Figure 7 shows the exhaust phase of the whole process of thermal runaway. The temperature change rate of the battery surface firstly increases positively and then decreases until it becomes negative, with a maximum of 0.39 °C/s and a minimum of −0.47 °C/s. The ambient temperature rate is lagging behind the cell surface temperature, and the maximum value is 0.31 °C/s. VOC release rate exceeds 2000 ppm/s; The gas generation rate of H2 and CO showed a rapid rise. The maximum growth rate of H2 concentration was 1.45 ppm/s, and the maximum growth rate of CO concentration was 3.67 ppm/s. The peak value of CO rising rate was greater than H2 . There is no significant change in cell voltage. Figure 8 shows the occurrence stage of thermal runaway. Before thermal runaway occurs, the rate of CO concentration rises earlier than that of H2 , and the peak rate is smaller than that of H2 . The maximum increase rate of CO concentration is 2.53 ppm/s, and the maximum increase rate of H2 concentration is 4.99 ppm/s. The rate change trend of characteristic gas is earlier than that of voltage and temperature. At the moment of thermal runaway, the change rate of the surface temperature and the ambient temperature increases rapidly, and the peak rate of the surface temperature is 3.25 °C/s, and the peak rate of the ambient temperature is 8.89 °C/s. The peak value of the cell voltage change rate is −0.425 V/s.
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Fig. 8 Rate curves of characteristic parameters of thermal runaway triggered by heating
4.3 Analysis of Characteristic Parameters of Overcharging Thermal Runaway According to the sampling frequency of 1 Hz, the characteristic parameter data of the thermal runaway process of overcharge was collected (Figs. 9 and 10).
Fig. 9 Parameter curves of thermal runaway triggered by overcharge in exhaust stage
The characteristic parameter time domain curve of lithium titanate battery in thermal runaway process of overcharge was analyzed and divided into initial exhaust stage and thermal runaway stage. In the initial exhaust stage, the surface temperature of the battery is accompanied by a small decrease and increase, and the change range is not large, and the value change is about 1 °C, and the surface temperature was around 74 °C. The ambient temperature has no obvious change. Compared with the heating process, the release rate of thermal runaway is faster and the emission is larger. The electrolyte decomposition gas reached the full scale of VOC sensor 10000 ppm in 20 s. Within 3 s of a large amount of exhaust, H2 concentration reaches 105 ppm, CO concentration reaches 50 ppm within 10 s. In the short period that followed, H2 and CO reached the sensor full scale of more than 1000 ppm. The cell voltage showed a significant drop and then gradually increased.
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Fig. 10 Parameter curves of thermal runaway triggered by overcharge
Before thermal runaway occurred, the gas characteristic parameters VOC, H2 and CO exceeded 10000 ppm, 1000 ppm and 1286 ppm respectively, which all exceeded the upper limit of sensor measurement. When thermal runaway occurs, the battery voltage rapidly decreases to 0 V. The surface temperature of the cell and the ambient temperature rise to more than 450 °C in a short time, and the peak temperature is significantly higher than that of heating thermal runaway, and the heat release is greater than that of heating thermal runaway (Figs. 11 and 12).
Fig. 11 Rate curves of characteristic parameters of thermal runaway triggered by overcharge in exhaust stage
In the exhaust stage, the VOC release rate exceeds 4000ppm/s; The maximum increase rate of H2 concentration was 54.6 ppm/s. The maximum increase rate of CO concentration was 6.34 ppm/s. A large amount of H2 release, so that the late thermal runaway deflagration and flame jet added favorable factors; The peak growth rate of gas is higher than that of heating process. The change of pyrolysis VOC gas is earlier than that of H2 and CO. At the moment of thermal runaway, the peak rate of surface temperature and ambient temperature is 12.42 °C/s and 13.2 °C/s respectively. The peak value of the cell voltage change rate is −0.55 V/s. The change rates of surface temperature and ambient temperature show a negative increase first and then a positive increase. It can be concluded
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Fig. 12 Rate curves of characteristic parameters of thermal runaway triggered by overcharge
from the analysis that a large amount of gas will be generated at the moment when the overcharging heat is out of control, resulting in a decrease in temperature, followed by a violent combustion reaction, explosion and flame jet, and a huge amount of heat.
5 Conclusion The thermal runaway of lithium titanate cell can be triggered by heating and overcharging. Nail penetration is not easy to trigger the thermal runaway of lithium titanate cell. For the single cell lithium titanate battery, the magnitude and change rate of the characteristic parameters of heating thermal runaway are weaker than that of overcharge thermal runaway. In a specific closed environment, the characteristic parameters including temperature, cell voltage, H2 , CO and VOC gas can be monitored to realize the thermal runaway warning of lithium battery. (a) Early exhaust judgment of battery thermal runaway: lithium battery pyrolysis VOC gas is used as early exhaust characteristic signal, and its threshold is 1000-2000 ppm. The temperature change rate of the cell surface is taken as the characteristic signal of early exhaust gas. The temperature change rate firstly increases positively and then decreases to negative value. (b) Exhaust judgment before battery thermal runaway: VOC gas concentration exceeds 10000 ppm and change rate exceeds 2000 ppm/s. The characteristic gas H2 concentration reaches 100 ppm or the maximum increase rate of H2 concentration is 4.99 ppm/s. The characteristic gas CO concentration reaches 50 ppm or the CO concentration increase rate is 2.53 ppm /s at most. Gas is produced when the cell surface temperature reaches 80 °C. (c) Judgement of battery thermal runaway: battery surface temperature or ambient temperature reaches 180 °C–400 °C. The peak rate of surface temperature is 3.25 °C/s. The peak rate of ambient temperature is 8.89 °C/s. The peak value of cell voltage change rate is −0.425 V/s. Above rate parameters are accompanied by a curve of growth and decline.
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In conclusion, combining with the changes of characteristic gases H2 , CO, surface temperature and VOC in the thermal runaway process of lithium battery, early warning of thermal runaway can be carried out in the exhaust stage. Based on the development trend of multiple characteristic parameters in the time domain, the combined feature coupling judgment method can effectively realize the thermal runaway warning of lithium battery. Acknowledgments. Supported by Anhui Provincial Natural Science Foundation(2021 Anhui Energy Internet Joint Fund Project, 2108085UD04).
References 1. Mei, H.W., Liwei, Z., Bo, P., Jiao, C., Rui, Y.: State of charge estimation of lithium titanate battery for electric multiple units[J]. Trans. China Electrotech. Soc. 36(S1), 362–371 (2021) (in Chinese) 2. Hai-bin, D., Guo-rui, Y., Pu-chun, A., Xue-lei, X., Cheng-yi, Y.: Research on thermal runaway propagation suppression technology of lithium titanate battery module[J]. Fire Sci. Technol. 40(06), 779–782 (2021). (in Chinese) 3. Xiang-jun, T., Ya-zhou, G., Ze, L., Zhen-yao, Z.: Thermal runaway characteristics study of lithium ion power battery under various abuse conditions[J]. Chin. J. Power Sources 44(05), 679–681+692 (2020) (in Chinese) 4. Yun, Y., Kai, L., Xiang-yu, C., Zhi-rong, W., Su-pan, W.: The research and of explosion early warning device for type 18650 lithium ion battery fire[J]. Fire Sci. Technol. 37(07), 939–942 (2018). (in Chinese) 5. Srinivasan, R., Demirev, P.A., Carkhuff, B.G.: Rapid monitoring of impedance phase shifts in lithium-ion batteries for hazard prevention. J. Power Sources 405, 30–36 (2018) 6. Ohsaki, T., Kishi, T., Kuboki, T., et al.: Overcharge reaction of lithiumion batteries. J. Power Sources 146(1), 97–100 (2005) 7. Yuan, L.M., Dubaniewicz, T., Zlochower, I., et al.: Experimental study on thermal runaway and vented gases of lithium-ion cells[J]. Process Saf. Environ. Prot. 144, 186–192 (2020) 8. Lee, C.-Y., et al.: Integrated microsensor for real-time microscopic monitoring of local temperature, voltage and current inside lithium ion battery. Sens. Actuators, A 253, 59–68 (2017) 9. Bingxiang, S., Pengbo, R., Yuzhe, C., Zhengtao, C., Jiuchun, J.: Analysis of influencing factors of degradation under different interval stress and prediction of aging trend in any interval for lithium-ion battery. Trans. China Electrotech. Soc. 36(3), 666–674 (2021). (in Chinese) 10. Wenger, M., Waller, R., Lorentz, V.R.H., et al.: Investigation of gas sensing in large lithium-ion battery systems for early fault detection and safety improvement[A]. In: IECON 2014 – 40th Annual Conference of the IEEE Industrial Electronics Society[C], pp. 5654–5659. Dallas, USA (2015) 11. Hill, D., Gully, B., Agarwal, A., et al.: Detection of off gassing from Li-ion batteries[A]. In: 2013 IEEE Energytech[C], pp. 142–149. Cleveland, USA, 2013 12. Zheng, H., Peng, Q., Shi Han, W., Jingyun, Y.L., Qingsong, W.: Study on thermal runaway behavior of 86 Ah lithium iron phosphate battery under overheat condition[J]. High Voltage Eng. 48(03), 1185–1191 (2022). (in Chinese) 13. Larsson, F., Bertilsson, S., Furlani, M., Albinsson, I., Mellander, B.-E.: Gas explosions and thermal runaways during external heating abuse of commercial lithium-ion graphite-LiCoO2 cells at different levels of ageing. J. Power Sources 373, 220–231 (2018)
Study on Parameter Characteristics and Sensitivity of Equivalent Circuit Model of Lithium Iron Phosphate Battery in Decay Dimension Yuan Zhang1 , Bingxiang Sun1(B) , Mao Li2 , Xiaojia Su1 , and Shichang Ma1 1 National Active Distribution Network Technology Research Center Beijing Jiaotong
University, Beijing 100044, China [email protected] 2 Beijing Electric Power Corporation, Beijing, China
Abstract. Accurately simulating the terminal voltage characteristics of lithiumion batteries in the whole life cycle is the key index to evaluate the performance of batteries. In this paper, Thevenin model is established, and the sensitivity analysis of the OCV and impedance parameters of lithium iron phosphate battery to the accuracy of the model is carried out. Euclidean distance is used to characterize the changes of the parameters of different decay states and new battery models. The results show that with the decline of the battery, the Euclidean distance of thermodynamic and kinetic parameters presents d(RP ) > d (OCV) > d (R0 ); The voltage estimation accuracy of the battery under various working conditions at different stages is verified by the model. The accuracy of the updated OCV, R0 , RP , C P model of the battery is 1%, the accuracy of the updated R0 , RP , C P model is less than 2%, and the accuracy of the updated OCV model is less than 3%. Therefore, it is recommended to update the R0 , RP , C P . Keywords: Aging recession · Battery model · Model parameter · Euclidean distance
1 Introduction Under the situation of global warming and energy crisis, the development of electric vehicles has become an important measure of energy conservation and emission reduction in the world. Lithium-ion batteries have become the mainstream secondary battery products due to their high energy density, long cycle life, low self-discharge rate and other advantages, and are widely used in new energy vehicles, energy storage power stations and other fields [1]. The battery model is the basis for battery state of charge (SOC) estimation, performance analysis, efficient management and use. Precise battery model is of great significance to power battery simulation, optimization and management [2]. Literature [3, 4] analyzed the modeling principles, uses and shortcomings of various battery models. Among them, the equivalent circuit model does not describe the internal © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 471–478, 2023. https://doi.org/10.1007/978-981-99-1027-4_48
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micro reaction of lithium-ion battery, with simple structure. It is more suitable for online estimation of battery SOC, fault detection and early warning methods during charging, etc. However, with the increase of battery use times, the available capacity of the battery and the internal parameters of the battery change nonlinearly, leading to the reduction of the accuracy of the battery model and SOC estimation, which also has a certain impact on the battery fault detection and early warning [5]. Scholars have done a lot of research on the modeling and ap-plication of lithium-ion battery equivalent circuit model. At present, the commonly used battery model parameter identification methods can be divided into offline parameter identification and online parameter identification [6, 7]. Hybrid Pulse Power Characteristic (HPPC) experiment is often used for off-line identification of battery model parameters. Reference [8] gives a general and efficient offline parameter identification method based on Simulink and Matlab optimization toolbox, which improves the efficiency of parameter identification by optimizing data processing and parameter setting process. As battery model parameters will change with battery aging, the accuracy of offline parameter identification results will decrease. In order to get a more accurate battery model, it is necessary to identify the parameters online. Reference [9] studied the parameter identification of lithium-ion battery under acoustic noise, and used the recursive least square method with forgetting factor for error compensation to im-prove the parameter identification accuracy of colored noise data. The OCV–SOC curve of the battery is an important basic curve of the lithium-ion battery equivalent circuit model. With the decline of the battery, the OCV– SOC curve of the battery will change. Most previous studies used nonlinear functions (such as polynomial equations) to apply the SOC–OCV relationship. In literature [10], the OCV estimation is generally improved through two-dimensional look-up tables, and then adjusted through Kalman filtering. Literature [11] proposed an OCV curve modeling based on statistical information rather than electrochemistry. This model is based on the capacity update OCV curve at the aging stage, which can significantly reduce the average error of the aging OCV curve. These require a large number of OCV test experiments in advance, which are obtained through historical data processing, and take a long time. Literature [12] extracted battery aging characteristics based on capacity increment analysis (ICA) as the transformation rule of aging OCV curve, and then used multi population genetic algorithm (MPGA) to reconstruct the OCV curve. At present, most of the researches on equivalent circuit models in the decay dimension consider how to update the dynamic parameters and thermodynamic parameters, but there is less sensitivity analysis for both of them. First, analyze the change rate of R0 , RP and OCV by selecting the same SOC point in the aging process, and then verify the analysis results through the first-order RC model.
2 Test Bench and Experimental Procedures In order to acquire experimental data of Lithium-ion batteries, a test bench is built. The test bench is composed of a battery test system Arbin, a host computer, a temperature chamber and tested batteries. The Arbin can provide a maximum current of 10 A for the battery, and its voltage and current measurement accuracy is ±0.02%FSR and ±0.05%FSR, respectively. The experimental data measured by Arbin, such as current,
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voltage, capacity and energy, are recorded by the host computer. The temperature chamber can provide manageable temperatures for the tested battery. The LiFePO4 batteries with a rated capacity of 3.6 Ah were used in this test. The cut-off voltage of charge and discharge are 3.65 V and 2 V respectively. The specific experimental steps are as follows: (1) Carry out the activation experiment on the battery, use 0.5 C to charge to 3.65 V, switch to constant voltage charging, and then keep it for 1 h when the current is less than or equal to 0.05 C, discharge to 2 V at 0.5 C, keep it for 1 h, and cycle for three times; (2) Conduct performance test; (3) Use 1C charging and 2C discharging for 200 cycles; (4) Repeat steps (2)–(3) until 1000 cycles. The performance test includes 25 °C capacity test, 25 °C pulse charge and discharge test, and dynamic working condition test in each aging stage.
3 Battery Model Where R0 is the ohmic internal resistance of the battery, RP is the polarization resistance, and C P is the polarization capacitance. The charging direction of the current is defined as the positive direction. The state space equation of the Thevenin model can be expressed as (Fig. 1): ⎧ ⎨ u (t) = U (0) × e− τt + i × R 1 − e− τt p p p (1) ⎩ u (t) = u (t) + i × R + u (t) o
ocv
0
p
i Rp R0
Cp
+
up
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uo
Fig. 1. Thevenin equivalent circuit model.
τ is the time constant, uocv represents open circuit voltage, up is the polarization voltage on the RC network, uo represents terminal voltage. 3.1 Difference Analysis This paper shows the OCV–SOC of new battery, 400, 600, 800, 1000 cycles and identification results (Fig. 2). The OCV–SOC curves of batteries in different aging stages are shown in Fig. 3a. The curves are measured through performance tests after 0, 400, 600, 800, 1000 cycles. Qualitative judgment shows that the OCV–SOC curve changes slightly in the middle
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range of SOC (20–90%). When the SOC is 50%, the OCV of new batteries is 3.305 V, and the OCV under 1000 cycles is 3.3043 V, which only changes by 0.7 mV. At the same time, there will be a rise of voltage platform at 70% SOC, where the voltage change is relatively large. The OCV of the new battery is 3.33147 V, and the OCV of 1000 cycles is 3.3123 V, which has changed by 19 mV. (b)
(v)
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Fig. 2. a OCV–SOC curves of battery at different aging stages. b OCV difference between different cycle stages and new battery.
Figure 3b shows the quantitative analysis of the OCV difference between different cycle stages and new batteries. In the whole SOC interval, at 5% SOC, the OCV change is the largest, in which the OCV difference between 1000 cycle and new batteries reaches 0.3V, in the middle SOC interval, the difference is small (excluding the voltage platform lifting part), and the OCV difference between 1000 cycle and new batteries reaches 7.79mV, the difference is large, 19 mV maximum. For this LFP, after 0–1000 cycles, the battery capacity declined from 3.62 Ah to 3.08 Ah, a decline of 15%, but the maximum OCV in the middle SOC range only changed by 7 mV.
(b)
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Fig. 3. a R0 at different aging stages. b Difference of R0 in different cycle stages.
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As shown in Fig. 4a, the value of R0 is identified by 0.5C charging pulse in different cycle stages. With the battery aging, R0 increases. In the whole SOC range, the 0% SOC, R0 is larger, and at 1000 cycle, the R0 of 0% SOC reaches 50 m. At the same time, R0 changes more obviously than OCV in 0–1000 cycles. As shown in the Fig. 4b, the difference between R0 at different cycle stages and R0 of new battery is the largest, and the maximum difference is 0.013 at 0% SOC. (a)
(b)
(Ω)
difference of Rp (Ω)
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Fig. 4. a RP at different aging stages. b Difference of RP in different cycle stages.
Figure 4a shows the RP values at different cycle stages. The RP changes slightly in the middle SOC range. The RP of 1000 cycles at 50% SOC is 0.01296 , and the RP of new batteries is 0.01225 , which only changes by 0.19 m. At the high and low end SOC, especially at the high end SOC, the RP of 1000 cycles at 100% SOC is 0.18723 , the RP of new batteries is 0.15832 , and the RP changes by 28.91 m. Fig. 4b shows the difference of RP between and new battery in different recession stages. In the 0–80% SOC range, RP changes little. At 5% SOC, the maximum RP difference between 1000 cycles and new battery is 5 m, 80–100% SOC range, and the RP difference between 1000 cycles and new battery is 30 m. 3.2 Change of Euclidean Distance Analysis Parameters Euclid distance, abbreviated as Euclid distance, refers to the distance between two points in Euclid space. Euclidean distance represents the change of each point between two lines with a numerical value, which more clearly reflects the distance between two curves. This paper calculates the distance between OCV, R0 , RP , C P and new battery parameters at different cycle stages based on OCV, R0 , RP , C P of new battery. This paper takes the sum of the squares of the difference between the parameters of different cycle stages and the parameters of the new battery at the same SOC, and then opens the root sign as the Euclidean distance of the two curves. The distance between
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the cycle and the new battery is as follows: n
di0 = (xik − v0k )2
(2)
k=0
n takes 5%, 10%, 15%, 20%, 25%, 35%, 45%, 55%, 65%, 75%, 85%, 90%, 95%, 100%. Calculate the OCV at different cycle stages and the Euclidean distance between R0 , RP , C P and the new battery. As shown in the figure below (Fig. 5).
(a)
(b) OCV R0 Rp
Euclidean distance
Euclidean distance
OCV R0 Rp
cycle
cycle
Fig. 5. a Euclidean distance between parameters in different cycle stages and new battery parameters. b Remove the Euclidean distance at the low end.
With the aging of the battery, the Euclidean distance between R0 , RP and OCV and the new battery shows an upward trend. The Euclidean distance of OCV is the largest, which is 0.02984, 0.05366, 0.10896, 0.31072 at 400, 600, 800 and 1000 cycles, respectively. Compared with OCV, the Euclidean distance of RP is smaller, which does not exceed 0.05. Considering that the use range of the battery in the actual process is usually 10% SOC-100% SOC, the Euclidean distance between 0% SOC and 5% SOC is removed, and the results are as follows. After removing the low-end SOC, the Euclidean distance of RP in different cycle stages is the largest, which are 0.02621, 0.03406, 0.02866, and 0.05477 respectively. Therefore, after comprehensive consideration, it is speculated that the update of R0 and RP in the decay dimension has high simulation accuracy for the battery model.
4 Simulation Verification Using the test results of various working conditions in different decay stages, the battery voltage is simulated through the equivalent circuit model to verify the above conjecture. The verification objects are 400 cycles. It is verified that R0 , RP and C P have greater influence on the battery model from charging, discharging and dynamic conditions.
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As shown in Fig. 6a, the simulation results of the 400 cycle constant current charging for OCV and circuit parameter updates are shown.The down figure shows the respective errors. When OCV and R0 , RP and C P are not updated, the error is the largest, and the error basically exceeds 3%. When OCV and R0 , RP and C P are both updated, the error is the smallest, and the maximum error does not exceed 1%. Then, when only R0 , RP and C P are updated, the error is the second, and does not exceed 2%. When only OCV is updated, the error is larger, and the error exceeds 3%. It is concluded that under the 400 cycle, 1C constant current charging, the simulation effect of only updating R0 , RP and C P is better than that of only updating OCV parameter voltage. The simulation results of dynamic condition FUDS and 2C discharge condition have the same conclusion.
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Fig. 6. a Simulation and error of 400 cycle 1C constant current charging voltage. b 2C constant current discharging voltage. c FUDS voltage.
In addition, various situations of 600 cycle, 800 cycle and1000 cycle are also analyzed. The conclusion is consistent with that of 400 cycle and 1000 cycle, and will not be repeated in this paper.
5 Conclusion In this paper, a commercial LFP are tested, and the thermodynamic and kinetic parameters under different aging conditions were identified. The specific conclusions are as follows: (1) The kinetic parameters and thermodynamic parameters of different decay stages were analyzed by Euclidean distance. With the deepening of the aging degree of LFP, the Euclidean distance of battery model parameters presented d (RP ) > d
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(OCV) > d(R0 ) within the commonly used SOC interval of the battery, and the difference of battery model parameters presented the relationship of RP > OCV > R0 . (2) By comparing the measured voltage data of different working condition in five aging stages with the simulation voltage data of the model, it is concluded that the voltage simulation accuracy of the battery model with only updated dynamic parameters is 33% higher than that of the battery model with only updated thermodynamic parameters.
Acknowledgment. This work is supported by the“National Key R&D Program of China”(Grant NO. 2021YFB2501900) and the Joint Fund of Ministry of Education of China for Equipment Pre-research (Grant NO. 8091B022130).
References 1. Huanhuan, L.I., Huayang, S.U.N., Biao, C.H.E.N.: SOC estimation based on gas-liquid dynamics model and FFRLS-EKF algorithm[J]. Chin. J. Power Sources 45(11), 1435– 14381481 (2021). (in Chinese) 2. Rui, X., Hongwen, H., Yin, D.: Study on identification approach of dynamic model parameters for lithium-ion batteries used in hybrid electric vehicles[J]. Power Electron. 45(04), 100–102 (2011). (in Chinese) 3. Ying-, J.I., Ming-, W.A.N.G., Wei, S.U.N.: Review in power battery modeling and application[J]. Chin. J. Power Sources 40(3), 740–742 (2016). (in Chinese) 4. Chen, Z., Xiao, J., Shu, X.: Model-based adaptive joint estimation of the state of charge and capacity for lithium-ion batteries in their entire lifespan[J]. Energies 13, 1410 (2020) 5. Garg, A., Shaosen, S., Gao, L.: Aging model development based on multidisciplinary parameters for lithium-ion batteries[J]. Energy 44, 2801–2818 (2020) 6. Runqin, L.: Research on model parameter identification and state of charge estimation of ternary lithium-ion battery for electric vehicle[D]. Chang’an University, 2020 (in Chinese) 7. Xiaohui, W., Xinggan, Z.: Parameters identification of second order RC equivalent circuit model for lithium batteries[J]. J. Nanjing Univ. (Natural Sciences) 56(5), 754–761 (2020) (in Chinese) 8. Changqing, H.U.O.: A general parameter identification method for lithium battery model[J]. Chin. J. Power Sources 45(4), 455–458 (2021). (in Chinese) 9. Klintberg, A., Klintberg, E., Fridholm, B., Kuusisto, H., Wik, T., Statistical modeling of OCV-curves for aged battery cells[J], IFAC-PapersOnLine 50(1), 2164–2168, 2405–8963 (2017) 10. Sun, J., Tang, Y., Ye, J., Jiang, T., Chen, S., Qiu, S., A novel capacity and initial discharge electric quantity estimation method for LiFePO4 battery pack based on OCV curve partial reconstruction[J]. Energy 243, 122882,0360–5442 (,2022) 11. Xiao, R., Hu, Y., Jia, X., Chen, G.: A novel estimation of state of charge for the lithiumion battery in electric vehicle without open circuit voltage experiment[J]. Energy 243, 123072,0360–5442 (2022) 12. Park, J., Kim, K., Park, S., Baek, J., Kim, J.: Complementary cooperative SOC/capacity estimator based on the discrete variational derivative combined with the DEKF for electric power applications[J]. Energy 232, 121023,0360–5442 (2021)
Research on Defect Simulation and Diagnosis Method of On-Load Tap Changer Jiangang Bi1,2(B) , Jinpeng Jiang1,2 , Yuan Xu1,2 , Yanpeng Gong1,2 , Shuai Yuan1,2 , Guangzhen Wang1,2 , and Dehui Fu1,2 1 China Electric Power Research Institute, Beijing 100192, China
{bijg,jiangjinpeng,xuyuan,ypgong,yuans,wangguangz, fudehui}@epri.sgcc.com.cn 2 National Engineering Research Center for UHV Technology, Beijing 100192, China
Abstract. The on-load tap changer (OLTC) is a device which can operate under the excitation or load state of transformer and is used to change the tap connection position of winding. The mechanical fault accounts for nearly 90% of the OLTC fault, so it is necessary to detect the mechanical fault of OLTC. Vibration signals recorded from the operation of OLTCs contain lots of information about mechanical properties. And the mechanical defects can be diagnosed with the help of short-time energy method. In this paper, in order to study the defect simulation and diagnosis method of OLTCs, M-type 220 kV transfer switch and voltage output accelerometer are selected, the tap changer is placed in a 1.98 m high and 1m diameter oil tank. Three typical mechanical defects, such as fracture of energy storage spring, fracture of transition contact guide rod and falling off of fixed contact, are replicated under laboratory conditions. The acoustic fingerprint data of repeated tests of normal condition and 36 tests of defect condition are statistically analyzed. Each vibration signal is processed by the short-time energy method. The vibration characteristics of typical mechanical defects are investigated by analyzing the acoustic fingerprint and short time energy curve. Keywords: On-load tap changer · Typical mechanical defect · Short time energy method · Defect diagnosis
1 Introduction Serving as an indispensable part in voltage adjustment, on-load tap changers (OLTCs) also feature in connection with the power system and load regulation [1, 2]. As the only part of transformer that needs mechanical action, OLTC needs to undertake the task of breaking and closing with large current for many times for a long time. Under such working conditions, its mechanical stability is closely related to the safe operation of on-load voltage regulating transformer. Mechanical faults, taking up more than 93.4% of the faults on OLTCs of 110 kV and above, become the most dangerous conditions disproportionately threatening the safe and steady operation of OLTCs. Therefore, in order to ensure safe and reliable operation of OLTCs, it is imperative to carry out state monitoring and fault diagnosis on OLTCs [3]. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 479–486, 2023. https://doi.org/10.1007/978-981-99-1027-4_49
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When an OLTC is in operation, the contact of moving and fixed contacts will produce impulse impact force, thus producing vibration signals. These vibration signals spread to terminal through fixed contact or transformer oil, and to the transformer tank. Thus monitoring vibrations of terminals, transformer, or the surface of tank can provide us with contacts action condition [4–6]. Vibration signals recorded from the operation of OLTCs contain a lot of information about mechanical properties. The mechanical defects of OLTCs can be identified by analyzing mechanical vibration signals. Many researchers has focused on the vibration signal analysis method and mechanical fault diagnosis method of OLTCs. A. Hussain et al. [7] detected and processed vibration signals generated by OLTC, and compared the envelope of vibration signals generated by the tap switch in good operating condition in the past with that generated now to judge whether a fault occurred. P. Kang et al. [8] proposed a data analysis method based on self-organizing map-ping by monitoring vibration signals of OLTC switching in oil, the characteristic parameters of vibration signals describing the aging and wear of contacts in oil were obtained, and a simple online detection scheme was proposed. Z. T. Yu et al. [9] proposed a separation method for OLTC vibration signals of transformer in operation based on morphological component analysis. The effectiveness and efficiency of the method are verified by calculation and analysis of the measured vibration signals during OLTC switching of a 220 kV transformer in operation. Y. C. Lu et al. [10] analyzed the time domain and frequency domain characteristics of the typical vibration signal of the converter transformer OLTC. Based on the proposed characteristic parameters, the difference of vibration signals of different contact positions of the same OLTC and the difference of vibration signals of the same contact position of different OLTCs are studied. Z. X. Zhang et al. [11] established an anomaly diagnosis method of OLTC with the local outlier factor as the diagnostic parameter, where the abnormal state of OLTC can be detected and diagnosed by comparing the sample to be tested with the normal sample set. In this paper, M-type 220 kV transfer switch and voltage output accelerometer are selected. Three typical mechanical defects, such as fracture of energy storage spring, A-phase transition contact guide rod and falling off of fixed contact, are replicated under laboratory conditions. The acoustic fingerprint data of 108 repeated tests of normal condition and 36 tests of defect condition are statistically analyzed. Each vibration signal is processed by the short-time energy method. The vibration characteristics of typical mechanical defects are investigated by analyzing the acoustic fingerprint and short time energy curve.
2 Experiment Preparation 2.1 Detection Platform Construction Acoustic fingerprint detection platform includes an M-type 220 kV transfer switch, with B type selector. Besides an oil tank with 1.98 m height and 1m radius is built for OLTC to put in. The detection platform and sensor installation mode are shown in Fig. 1. Sensor from Kistler Company is in a weight of 500 g and owns the frequency character over 10 kHz. The sensor sensitivity is chosen as 20 mV/g. The sensor convert the vibration into charge signal. Besides IC amplifier circuit is installed in it, and output signal is
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voltage signal with low impedance. The acceleration sensor and charge amplifier are shown in Fig. 2.
Fig. 1. Detection platform and sensor installation mode
Fig. 2. 5134b sensor and Charge amplifier
2.2 Signal Processing Short Time Energy Method In this paper, short time energy method is adopted to analyze the short time energy distribution characteristics of vibration signals of OLTCs. Function of short time energy S(n) is defined as: S(n) =
+∞
x2 (i)w(n − i)
i=−∞
=
n
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(1)
i=n−M +1 2
= x (n)w(n)
where is the local energy of the signal at time n, and is window function, n = 0, 1, 2, …, (M − 1).
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In other words, short time energy is a kind of signal transportation. The signal is firstly transformed exponentially and then weighted by a moving finite window. Short time energy method can further reduce the influence of noise, which weaken the noise signal and reinforce the useful acoustic fingerprint signal. The reason for this could be summarized as the effects of normal distribution. If the noise obeys normal distribution, it could be a rather small value during the most of time and vice versa. However when it comes to acoustic fingerprint signal, the instantaneous amplitude at the moment when vibration occurs would be relatively large while it is small at other moments. Furthermore, real acoustic fingerprint signal could be locally continuous, which is difficult to guarantee for the noise. In terms of these explains, squaring the signal could intensify acoustic fingerprint signal. And accordingly, most of the noise signal could be attenuated or even negligible.
3 Defect Simulation of OLTCs During the transformation operation of OLTCs, the moving and fixed contact systems of the switching mechanism close and collide with each other after the energy storage of the fast mechanism is released, and mechanical vibration occurs. Loosening and shedding of fixed contact in contact switching mechanism is one of the common defects. Falling off of a specific fixed contact of phase A is simulated, shown as Fig. 3.
Fig. 3. Falling off of fixed contact
The action faults of the fast mechanism include non-switching, too fast or too slow switching and failure of switching. These defects may cause the transition resistance even the contact system to burn out, resulting in transformer accidents. The fatigue deformation or fracture of the spring is the cause of this defect. Fracture of energy storage spring is simulated, shown as Fig. 4. OLTC action sequence error refers to the mismatch between change switch and tap selector action. The main reason is the failure of the contact action of the tap selector, which includes the mechanical transmission of the tap selector sticking, mechanical transmission defect or component falling off, assembly error of the parts, the shift of
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Fig. 4. Fracture of energy storage spring
the moving and fixed contact of the selector and other mechanical failures. Fracture of A-phase transition contact guide rod is simulated, shown as Fig. 5.
Fig. 5. Fracture of A-phase transition contact guide rod
Above all, switching slip, non-switching and too slow switching or switching failure are belong to mechanism failure, which occur frequently and cause severe transformer fault. In the following part, the short-time energy method is used to detect and diagnose the acoustic fingerprint of OLTC with different typical mechanical defects.
4 Diagnosis Method of OLTCs While the OLTC work normally, on the same measurement conditions, acoustic fingerprint and short time energy have similar amplitude and a high similarity. However, according to Fig. 6, while on the fault conditions, no matter acoustic fingerprints or short time energy curves change dramatically in the aspect of amplitude and waveform. Specifically, it’s reflected that:
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(1) When the fixed contact of phase A drop, the amplitude of short time energy dramatically declines. In addition, the waveform of short time energy also deform from normal one. (2) When the energy storage spring is broken, the waveform of short time energy curve has high similarity with normal ones. In the meantime, the amplitude has a certain decrease; (3) When it comes to the broken transition contact guide rode, the amplitude of short time energy curve decreases obviously, and the waveform change a lot than normal one. Including amplitude and waveform, short time energy curve has provided large quantity of information from which we can diagnose OLTCs with different defects. In other words, when measurement conditions remains the same, if the amplitude and waveform of the short time energy curve resembles the normal ones, it can be considered that OLTC basically works normally. Instead, if the peak value of short time energy drops intensively and waveform distorts apparently, we indicate that there might exist mechanical defects in OLTC.
5 Conclusion In this paper, the M-type OLTC acoustic fingerprint detection and test device is built, which could simulate and detect the switching process and defect of OLTC in transformer. The typical mechanical defects are identified and diagnosed based on the short-time energy method. Under the same measurement conditions, if the amplitude level of the short-term energy curve is basically unchanged and the curve similarity is high, the switch is basically normal; if the amplitude level of the short-term energy curve is significantly reduced and the curve shape is significantly changed, the switch may have a defect.
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Fig. 6. Acoustic fingerprint and short time energy curve of on load tap changer. (a) Normal condition, (b) Falling off of fixed contact, (c) Fracture of energy storage spring, (d) Fracture of A-phase transition contact guide rod
Acknowledgements. This work is supported by State Grid Corporation Headquarters Technology Project (5500-202055357A-0-0-00).
References 1. Duan, R.C., Wang, F.H.: Fault diagnosis of on-load tap changer in converter transformer based on timeCfrequency vibration analysis. IEEE Trans. Industr. Electron. 63(6), 3815–3823 (2016) 2. Pan, Z., Zhang, J., Zhou, H., et al: Mechanical condition assessment of vacuum on-load tap changer for converter transformer based on time-frequency domain characteristics of
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J. Bi et al. vibration Signal. In: Proceedings of the 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE) (2020) Li, Q., Tong, Z., Li, Z., et al.: Mechanical fault diagnostics of on-load tap changer within power transformers based on hidden markov model. IEEE Trans. Power Delivery 27(2), 596–601 (2012) Yang, R., Zhang, D., Li, Z., et al.: Mechanical fault diagnostics of power transformer on-load tap changers using dynamic time warping. IEEE Trans. Instrum. Meas. 68(9), 3119–3127 (2019) Rivas, E., Burgos, J.C., Garcia–Prada, J.C.: Condition assessment of power OLTC by vibration analysis using wavelet transform. IEEE Trans. Power Delivery 24(2), 687–94 (2009) Rivas, E., Burgos, J.C., Garcia-Prada, J.C.: Vibration analysis using envelope wavelet for detecting faults in the OLTC tap selector. IEEE Trans. Power Delivery 25(3), 1629–1636 (2010) Hussain, A., Lee, S.J., Choi, M.S., et al.: An expert system for acoustic diagnosis of power circuit breakers and on-load tap changers. Expert Syst. Appl. 42(24), 9426–9433 (2015) Kang, P., Birtwhistle, D.: Condition monitoring of power transformer on-load tap changers. II. IEE Proc. Gen. Trans. Distrib. 148(4), 307–311 (2001) Yu, Z.T., Li, D.J., Chen, L.Y., et al.: Vibration signal separation of on-load tap changers in power transformer based on morphological component analysis. Transformer 58(12), 5 (2021). (in Chinese) Lu, Y.C., Wang, T.L., Wei, C., et al.: Research on vibration signal detection technology of converter transformer’s on-load tap changer. High Voltage Apparatus 56(12), 0184–0190 (2020). (in Chinese) Zhang, Z.X., Chen, W.G., Tang, S.R., et al.: State feature extraction and anomaly diagnosis of on-load tap changer based on complementary ensemble empirical mode decomposition and local outlier factor. Transactions of China electrotechnical society 34(21), 11 (2019). (in Chinese)
Internal Short Circuit Warning Method of Parallel Lithium-Ion Module Based on Loop Current Detection Wenfei Zhang, Nawei Lyu(B) , and Yang Jin Research Center of Grid Energy Storage and Battery Application, School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected]
Abstract. Internal short circuit is one of the main triggers for thermal runaway of Li-ion batteries, however, internal short circuit is incidental and cannot be predicted in advance. Therefore, improving the sensing capability of internal short circuit is especially important to improve the safety of electric vehicles. In this paper, we propose an algorithm for detecting internal short circuit of Li-ion battery based on loop current detection, which enables timely sensing of internal short circuit of any battery in a multi-series 2-parallel battery module by detecting the loop current. The method only needs to detect the voltage at both ends of the diagnostic resistor (3 measurement points), which has the advantages of fewer detection points and less additional wiring to the battery module, and can avoid the safety hazards caused by excessive wiring while protecting the battery module. The experimental results show that the method is able to detect internal short circuits in parallel lithium-ion battery packs in a timely manner. Keywords: Lithium-ion battery · Internal short circuit · Thermal runaway
1 Introduction The environmental problems caused by burning fossil fuels and the reduction of nonrenewable resources continue to promote the adoption of new energy sources represented by solar energy and wind energy, and the energy storage system supporting the new energy sources has developed rapidly [1]. Lithium-ion batteries have the advantages of high potential, high specific energy, and long cycle life [2], and are therefore widely used in electric vehicles, consumer electronics, and energy storage power stations. However, lithium-ion batteries have potential safety issues, and internal short circuits is one of the mean causes of lithium-ion battery accidents [3]. There are many reasons for triggering the internal short circuit of lithium-ion batteries, which can be divided into three categories: Mechanical abuse, electrical abuse, and thermal abuse. Mechanical abuse includes collision, extrusion, and puncture [4]. Mechanical abuse has the potential to destroy the separator, resulting in direct contact between the cathode and anode materials, causing an internal short circuit. Electrical abuse is usually caused by an external short circuit, overcharge, or over-discharge [5], © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 487–493, 2023. https://doi.org/10.1007/978-981-99-1027-4_50
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which can cause the cells to experience excessive internal temperature and lead to an internal short circuit. For example, an external short circuit will cause a large current that flows through the cell, and a large amount of ohmic heat and polarization heat will be generated inside the cell, causing the temperature inside the cell to rise rapidly, causing the separator to melt, resulting in an internal short circuit in the battery [6]. Overcharge will lead to a series of side reactions inside the cell, the most important of which is that it will lead to lithium plating on the surface of the anode, which will develop to a certain extent to form lithium dendrites and eventually puncture the diaphragm and cause internal short circuit. The over-discharge will lead to the dissolution of copper in the anode and deposition on the cathode [7]. With the continuous deposition of copper ions on the cathode, copper dendrites continue to grow on the cathode and gradually pierce the separator, resulting in an internal short circuit in the battery [8]. Thermal abuse is usually caused by the cell operating in a high temperature environment. The materials inside the lithium battery undergo a chain decomposition reaction when they reach their decomposition temperature, releasing a large amount of heat and eventually leading to thermal runaway. In this process, the melting of the diaphragm leads to direct contact of the cathode and anode materials, resulting in an internal short circuit. To prevent the internal short circuit from developing into thermal runaway and causing serious consequences, researchers have proposed many methods to detect the internal short circuit. These internal short circuit detection methods can be classified into internal short circuit detection methods based on self-discharge [9], inconsistency, machine learning, and remaining charging capacity, etc. The existing internal short circuit detection methods require a high consistency of the module, a reasonable threshold or a large amount of data to train the model. A simple and reliable internal short circuit warning method is urgently needed. Therefore, this paper proposes an internal short circuit early warning method for parallel lithium-ion module based on loop current detection. The rest of this paper is arranged in this way: Experiments on parallel lithiumion batteries and 4-series-2-parallel lithium-ion battery packs with pinpricks to simulate internal short circuits are conducted in Sect. 2, and the experimental results are analyzed. Section 3 concludes.
2 Internal Short Circuit Loop Current Characteristic Experiment Commonly used internal short circuit simulation experimental methods are the shape memory alloy trigger method, equivalent resistance method, artificially induced dendrite growth method, phase change material trigger method, and acupuncture experiment method. Although the shape memory alloy trigger method has good repeatability, the manufacturing process of the test cell is complicated [8]. Although the equivalent resistance method can simulate the electrical characteristics of the internal short circuit well, it cannot simulate the thermal characteristics of the internal short circuit [10]. Although the artificially induced dendrite growth method is highly similar to the actual internal short circuit, the reproducibility is poor [10]. The phase change material triggering method has good repeatability and can control the type of internal short circuit, but the modification of the cell is very complicated [8]. The acupuncture experiment is not
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only simple, easy and repeatable but also causes the most likely cathode–anode material short circuit among the types of internal short circuits and will not cause safety problems such as fire and explosion. Therefore, this paper adopts acupuncture experiments to simulate the internal short circuit. 2.1 Acupuncture Simulation of Internal Short Circuit Experiments of Parallel Lithium-Ion Batteries The loop current detection device is designed in this paper to verify whether the internal short circuit of the parallel battery can be pre-warned by monitoring the diagnostic voltage, as shown in Fig. 1a. The loop current detection device includes two 0.1 highpower high-precision diagnostic resistors and a pair of voltage measurement units to collect the real-time voltage on the diagnostic resistors. It also contains a self-powered system that can draw power from the module it monitors to maintain the regular operation of its microcontroller and voltage measurement unit. When the current detection device is in use, the charging current first passes through the cells of the two branches and then passes through the diagnostic resistor inside the device. Through this topology, the device can detect and record the loop current of the two branches and the real-time current of each branch by collecting the voltage across the two resistors. The parallel battery acupuncture experiment is then carried out using the loop current detection device, the battery test device and the acupuncture machine. The steps are as follows. 1. Select 2 square hard case batteries with a capacity of 13 Ah and set the SOC to 50%, then let stand for 4 h; 2. Connect the inlet of the loop current detection device to the battery test device, and the outlet to the module, and set the steel needle of the acupuncture machine to align with the front center of the cell 2, as shown in Fig. 1b; 3. Start charging with a constant current of 0.5 C at 0 s. Then acupuncture cell 2 to the depth of 5 mm, 10 mm and 18 mm respectively at 300 s, 330 s and 360 s.
Fig. 1. Experimental setup for acupuncture simulated internal short circuit of parallel lithium-ion batteries
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The experimental data are shown in Fig. 2. At 300 s, acupuncture 5 mm, the diagnostic voltage suddenly increased from 0 V to 0.01 V; at 330 s, acupuncture 10 mm, the diagnostic voltage rose from 0.01 V to 0.105 V; at 360 s, acupuncture 18 mm, the diagnostic voltage increased from 0.105 V to 0.363 V.
Fig. 2. Experimental data diagram of acupuncture simulated internal short circuit of parallel lithium-ion batteries
Before the acupuncture, the voltages of the two cells were the same. After the acupuncture of Cell2, the voltage of Cell2 dropped. At this time, there is a circulating current in the circuit formed by Cell1, Cell2 and two diagnostic resistors. Therefore, the diagnostic voltage increased significantly during the three acupuncture times. 2.2 4-Series 2-Parallel Lithium-Ion Battery Pack Acupuncture to Simulate Internal Short Circuit Experiment The practical steps for acupuncture on a 4-series 2-parallel lithium-ion battery pack to simulate an internal short circuit are as follows. 1. Select 8 square hard case cells with a capacity of 13 Ah and set the SOC to 50%, then let stand for 4 h; 2. Connect these 8 cells into 4 series and 2 parallel and put them into the a module, as shown in Fig. 3b; 3. Connect the inlet of the loop current detection device to the battery test device, and the outlet to the module, and set the steel needle of the acupuncture machine to align with the front center of the cell at the top of branch 2, as shown in Fig. 3a;
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4. Start charging with a constant current of 0.5 C at 250 s; and stop charging at 290 s. Then start charging again with 0.5 C at 390 s, and acupuncture the cell to the depth of 5 mm, 10 mm and 18 mm respectively at 440 s, 490 s and 540 s. Finally, stop charging at 590 s.
Fig. 3. 4-series 2-parallel battery pack with acupuncture to simulate internal short circuit experiment setup
Figure 4 shows the experimental data of the 4-series 2-parallel battery pack for acupuncture-caused internal short circuit. The detailed data of some key moments are shown in Table 1 (where I 1 is the current flowing through the branch 1, I 2 is the current flowing through the branch 2, and I L is the loop current). At 250 s, it began to charge with a constant current of 0.5 C, and the diagnostic voltage suddenly increased from 0 V to 0.073 V. At 290 s, the charging is stopped, and the diagnostic voltage suddenly dropped to 0 V. At 390 s, the charging start again at 0.5 C, and the diagnostic voltage suddenly increased to 0.076 V. The diagnostic voltage roses to 0.084 V, 0.133 V and 0.273 V when the cell is acupunctured 5 mm, 10 mm and 18 mm respectively at 440 s, 490 s and 540 s. It can be seen that both charging and acupuncture produce relatively stable loop currents.
3 Conclusion The timely detection of internal short circuit of any single cell in a n-series 2-parallel lithium-ion module based on loop current detection through simulation exploration, experimental exploration, algorithm design and experimental verification is realized in this paper Compared with directly detecting the voltage change at both ends of the cell, this method requires only to detect the voltage at the two ends of the diagnostic resistor, which is only 3 measurement points. This method has the advantages of fewer detection points and less additional wiring for each module. This method has certain promotion significance as it protects the battery module while avoiding the safety hazards caused by excessive wiring.
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Fig. 4. 4-series 2-parallel battery pack acupuncture simulated internal short circuit experimental data Table 1. Key moment data of 4-string 2-parallel battery pack acupuncture simulated internal short circuit experiment t/s
I 1 /A
I 2 /A
I L /A
Description
250
6.9
7.63
0.73
Start charging
290
0
0
0
Stop charging
390
6.97
7.73
0.76
Start charging
440
7.03
7.87
0.84
Needle punch 5 mm
490
6.77
8.1
1.33
Needle punch 10 mm
540
6.17
8.9
2.73
Needle punch 18 mm
References 1. Rabaia, M.K.H., et al.: Environmental impacts of solar energy systems: a review. Sci. Total Environ. 754, 141989 (2021). https://doi.org/10.1016/j.scitotenv.2020.141989 2. Deng, J., Yang, X., Zhang, G.: Simulation study on internal short circuit of lithium ion battery caused by lithium dendrite. Mater. Today Commun. 31, 103570 (2022). https://doi. org/10.1016/j.mtcomm.2022.103570 3. Yiding, L., Wenwei, W., Cheng, L., Fenghao, Z.: High-efficiency multiphysics coupling framework for cylindrical lithium-ion battery under mechanical abuse. J. Clean. Prod. 286, 125451 (2021). https://doi.org/10.1016/j.jclepro.2020.125451 4. Wenwei, W., Fenghao, Z., Yiding, L.: Research on influencing factors about temperature of short circuit area in lithium-ion power battery. J. Electrochem. Energy Convers. Storage. 18, 020910 (2021). https://doi.org/10.1115/1.4049470
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5. Song, L., Zheng, Y., Xiao, Z., Wang, C., Long, T.: Review on thermal runaway of lithiumion batteries for electric vehicles. J. Electron. Mater. 51(1), 30–46 (2021). https://doi.org/10. 1007/s11664-021-09281-0 6. Ren, D., et al.: Investigating the relationship between internal short circuit and thermal runaway of lithium-ion batteries under thermal abuse condition. Energy Storage Mater. 34, 563–573 (2021). https://doi.org/10.1016/j.ensm.2020.10.020 7. Zhang, G., Wei, X., Chen, S., Zhu, J., Han, G., Dai, H.: Revealing the impact of slight electrical abuse on the thermal safety characteristics for lithium-ion batteries. Acs Appl. Energy Mater. 4, 12858–12870 (2021). https://doi.org/10.1021/acsaem.1c02537 8. Huang, L., et al.: A review of the internal short circuit mechanism in lithium-ion batteries: Inducement, detection and prevention. Int. J. Energy Res. 45, 15797–15831 (2021). https:// doi.org/10.1002/er.6920 9. Haussmann, P., Melbert, J.: Self-discharge observation for onboard safety monitoring of automotive li-ion cells: accelerated procedures and application concept. Sae Int. J. Altern. Powertrains. 7, 249–262 (2018). https://doi.org/10.4271/2018-01-0449 10. Zhang, G., Wei, X., Tang, X., Zhu, J., Chen, S., Dai, H.: Internal short circuit mechanisms, experimental approaches and detection methods of lithium-ion batteries for electric vehicles: a review. Renew. Sustain. Energy Rev. 141, 110790 (2021). https://doi.org/10.1016/j.rser. 2021.110790
Prediction Method of Ohmic Resistance and Charge Transfer Resistance for Lithium-Ion Batteries Based on CSA-SVR Jiamin Zhu, Kui Chen(B) , Kai Liu, Guoqiang Gao, and Guangning Wu School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China [email protected]
Abstract. With the rapid development of new energy sources, lithium-ion batteries have been widely used in electric vehicles due to their advantages such as large capacity, long cycle life and good temperature performance. Battery health status assessment has become more and more important. The impedance is an important parameter to measure the battery life, its size will change with the use of time, and closely related to the health of the battery. In this paper, the charging curve and Incremental Capacity (IC) curve of lithium batteries are analyzed, and five relevant feature quantities are extracted. By establishing Cuckoo Search Algorithm (CSA) optimized Support Vector Regression (SVR) model to predict ohmic resistance and charge transfer resistance. The CSA-SVR model is verified by experimental data. The mean square error and mean absolute error are less than 6 × 10−6 and 0.2, respectively, indicating high prediction accuracy. Keywords: Lithium-ion battery · CSA-SVR · Ohmic resistance · Charge transfer resistance
1 Introduction In order to promote sustainable development of society and economy, the new energy industry has received widespread attention in recent years, and new energy vehicles with batteries as energy storage systems are considered as the most potential alternative to traditional fuel vehicles. However, in the practical application of lithium batteries, it has been found that with the change of the environment and the increase of the service time, the battery will be aging, leading to the performance decline, which is mainly reflected in the decrease of capacity and the increase of resistance [1]. In order to improve the safety and reliability of electric vehicle operation, the evaluation of battery status has raised higher requirements [2, 3]. Currently, the analysis of the battery capacity is a common method to evaluate battery health status. There are two main methods of analysis: Model-based and data-driven. The model method is to evaluate the capacity by establishing the battery model to obtain the relevant parameters [4]: establishes an empirical model based on the physical degradation behavior of lithium-ion batteries. Through the battery capacity monitoring, the Bayesian Monte Carlo (BMC) algorithm was used to update the model parameters, and © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 494–505, 2023. https://doi.org/10.1007/978-981-99-1027-4_51
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the capacity was predicted according to the available data [5]. Proposes an alternative framework based on degradation model, which is conducive to the prediction of battery life when battery parameters are dynamic. However, in practical applications, it is difficult to accurately describe the true performance degradation state of lithium-ion batteries. Data-driven methods have gained widespread attention because they use the historical data of lithium-ion batteries for predictive analysis and do not require in-depth understanding of the internal aging mechanism of the batteries. Most of these methods are used in combination with algorithms such as Autoregressive Integrated Moving Average (ARMA) model [6, 7], Support Vector Regression (SVR) [8, 9] and Artificial Neural Network (ANN) algorithm (Artificial Neural Network, ANN) [10, 11], etc. Electrochemical impedance spectroscopy (EIS) is one of the most promising methods to characterize the aging effect of lithium-ion batteries, because impedance is closely related to the internal electrochemical changes of the battery and is widely used to assess the battery performance and health status. Fig. 1 shows a typical impedance spectrum of a lithium-ion battery, which consists of five different parts related to different processes: (1) at very high frequencies, the impedance spectrum contains only inductance, which is used to represent the stray inductance due to the collector fluid and the wire; (2) the resistance of the impedance spectrum at the intersection with the real axis is the ohmic resistance Re , which is related to the internal conduction process of the battery; (3) the small semicircle is related to the presence of the solid electrolyte interface (SEI) layer and characterizes the SEI impedance of the battery; (4) The larger semicircle is related to the charge transfer process and the double layer capacitance, which is the charge transfer resistance Rct of the interface reaction; (5) The low frequency corresponds to the diffusion process, which is the diffusion impedance.
Fig. 1. Typical impedance spectra of lithium ion batteries
Domestic and international scholars have proposed the use of different EIS parameter variations to study the aging mechanism of the battery in order to grasp the state of health of the battery [12–15]. [16] Studies t the relationship between the ohmic resistance Re of the battery and the available capacity to assess the State of Health (SOH) of the battery through the Dempster-Shafer (DS) [17] analysis the variation trends of ohmic resistance Re and charge transfer resistance Rct at different battery SOH levels, and the results showed that EIS is an effective method for diagnosing SOH in lithium-ion batteries; [18] found that the combination of ohmic resistance and constant phase Angle element can obtain the health status of the battery, and it can be measured only by using the current and voltage of the battery [19]. Proposes and verifies a method that can convert
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Rct of different temperature and charge states to a standard state, and based on this method the battery SOH was effectively evaluated. Using the parameters of EIS to characterize the aging state of the battery has practical physical significance, and the ohmic resistance Re and charge transfer resistance Rct of the parameters are more related to the performance of the battery. However, the current measurement method of EIS usually by applying a sinusoidal current (voltage) signal with a small amplitude to the battery, and measuring the phase and amplitude of the output voltage (current) signal respectively, so as to calculate the impedance. The process is usually repeated at multiple frequencies and the operation is tedious to keep the test temperature and environment consistent. Therefore, this paper proposes a Support Vector Regression (SVR) method optimized by Cuckoo Search Algorithm (CSA). The method can predict Re and Rct of the battery directly by extracting the characteristic quantity related to the battery impedance, and the simulation results of lithium-ion battery prove the superiority of the method.
2 Feature Extraction and Analysis 2.1 Experimental Data of Cycle Life Attenuation of Lithium Ion Battery The experimental data in this paper are obtained from the lithium-ion battery dataset from NASA prediction center of excellence (PCOE) [20] with battery models B0005 (B05), B0006 (B06), and B0007 (B07) [20]. The battery charging process includes a constant-current charging phase and a constant-voltage charging phase. At the test temperature of 24 °C, the battery is first charged at constant current with a charging current of 1.5 A until the battery voltage reaches 4.2 V. The battery is then charged in constant voltage mode until the current drops below 20 mA. The battery discharge process is performed in constant current discharge mode at a current of 2 A until the battery voltage drops to the cutoff voltage and the discharge stops. The cut-off voltages of B5, B6 and B7 are 2.7 V, 2.5 V and 2.2 V, respectively. 2.2 Feature Extraction Based on Charging Curve The charging voltage curves of B05 battery under different cycles are shown in Fig. 2. It can be seen that as the number of cycles increases, the time of the constant-current charging phase of the battery becomes shorter, and the slope of the curve also changes. The decrease of the time of the constant-current charging process represents the aggravation of the polarization of the battery, which affects the capacity and impedance of the battery. Therefore, this paper considers the charging time difference of different voltage stages under constant current charging as a characteristic factor. Since the battery voltage changes rapidly before reaching 4.2 V, this time period is considered to be divided into three parts: (1) F1 represents the time difference from 3.85 V to 4.0 V; (2) F2 represents the time difference from 4.0 V to 4.1 V; (3) F3 represents the time difference between 4.1 V and 4.2 V.
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Fig. 2. Typical impedance spectrum of lithium-ion battery charging voltage curve of B05 battery under different cycles
2.3 Feature Extraction Based on Incremental Capacity Curve IC curve refers to the capacity increment curve of battery. It is an important analytical method, which can effectively detect and quantify the deterioration state of battery. This method has high sensitivity to the phase transition process of battery, and can reflect the aging process of battery from the electrochemical mechanism. The principle is that when the battery is charged or discharged at constant current, the capacity–voltage (Q − V ) curve is differentiated to obtain dQ/dV data, so as to draw dQ/dV − V curve. The IC curve can be expressed by Eq. (1): ⎧ ⎪ ⎪ ⎨ Q = Idt (1) ⎪ Idt dt dQ ⎪ ⎩ = =I dV dV dV Figure 3 shows the IC curve of B05 battery at the 50th cycle. After filtering with Savitzky-Golay filter, there is an obvious peak between the charging voltage of 3.95 V and 4 V. Ref. [21] found that the peak value of IC curve would decrease with the increase of the number of cycles, and its position would gradually move to the right.Moreover, the movement of the peak is positively correlated with the change of battery capacity, so the values of the horizontal coordinate and vertical coordinate of the peak of the IC curve are considered to be set as the characteristic factors F4 and F5. 2.4 Grey Relation Analysis of Features Grey Relation Analysis (GRA) is a method that can quantitatively describe the development trend of a system. Its principle is mainly to compare the similarity degree of sequences through mathematical geometric shapes. Generally, the higher the similarity degree, the greater the correlation degree. The advantage of GRA is that it does not require a high number of samples and requires a small amount of calculation. Therefore, this paper adopts GRA method to judge the correlation between feature and impedance values.
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Fig. 3. IC curve of B05 battery (Cycle50)
The specific steps are as follows: (1) Determine the sequences involved in the correlation degree analysis, including the parent sequence and sub sequence. The parent sequence refers to the reference sequence and the sub sequence refers to the comparison sequence. The parent sequence of this paper refers to the Re and Rct , and the sub-sequence refers to the five characteristic factors F1–F5 extracted above; (2) Pre-processing the sequence, mainly normalization of different types of data to facilitate subsequent comparison; (3) Find the grey correlation coefficient of parent sequence and sub sequence ζ (xi ): ζi (k) =
min min|x0 (k) − xi (k)| + ρ · max max|x0 (k) − xi (k)| i
i
k
k
|x0 (k) − xi (k)| + ρ · max max|x0 (k) − xi (k)| i
(2)
k
where max max|x0 (k) − xi (k)| and min min|x0 (k) − xi (k)| are the maximum difi
i
k
k
ference and minimum difference of two levels respectively, ρ is the resolution coefficient, and its magnitude is negatively correlated with resolution. The value range of ρ is generally between 0 and 1, usually 0.5, so ρ = 0.5 in this paper. (4) Find the grey correlation coefficients of the parent and sub sequences: ri =
N 1 ξi (k) N
(3)
k=1
The correlations of features F1–F5 with as well as are shown in Tables 1 and 2, and it can be found that the calculated results are all greater than 0.5, showing a strong correlation. From the theoretical analysis, features F1–F3 are closely related to the capacity of the battery at the corresponding voltage; meanwhile, F4 and F5 are consistent with the capacity change trend of the battery, so these five features have a high degree of correlation with the impedance. Therefore, these features are extracted for subsequent processing in this paper.
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Table 1. Grey correlation degree between features and Re of B05 battery F1
F2
F3
F4
F5
B05 battery
0.521
0.753
0.665
0.599
0.571
B06 battery
0.575
0.829
0.758
0.611
0.518
B07 battery
0.592
0.682
0.634
0.591
0.586
Table 2. Grey correlation degree between features and Rct of B05 battery F1
F2
F3
F4
F5
B05 battery
0.607
0.809
0.706
0.628
0.589
B06 battery
0.569
0.794
0.731
0.601
0.516
B07 battery
0.595
0.723
0.650
0.594
0.594
3 CSA Optimized SVR Prediction Model 3.1 Cuckoo Search Algorithm CSA is an optimization algorithm mainly based on the behavior of cuckoos laying eggs in the nests of other birds, combined with the Levy Flight pattern of birds [22]. Its advantages are conceptual simplicity, easy implementation, high robustness, and fewer parameters compared with other algorithms. The main ideas of CSA are: (1) Each cuckoo lays one egg at a time, randomly placed in a nest, and each egg represents a solution; (2) The nest where the high-quality eggs are located will be retained for the next generation, that is, the good solution will be left; (3) The number of host nests is fixed, and the probability of the host finding foreign eggs is pa , pa ∈ (0, 1), if the host bird finds foreign eggs, it will choose to discard the eggs or nests, so as not to affect the search for other better solutions. The main steps of the algorithm are as follows: (1) Initial random generation of n nests: t t t , xi,2 , ..., xi,d xt = xi,1
(4)
where i = 1, 2, ..., n, t = 1, 2, ..., NIter , d is the length of the solution vector, n is the overall size, NIter is the number of iterations. In this paper, d = 2, that corresponds to Re and Rct . (2) Each cuckoo can produce a new solution using Levy flight, as follows: xit+1 = xit + α ⊕ Levy(θ )
(5)
where α is the step size, ⊕ is i element-wise multiplications, xit represents the i-th nest location of generation t, and Levy(θ ) represents the random search path.
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(3) After the position update, a random number r is generated, r ∈ (0, 1), if r < pa , then the position xit+1 remains unchanged, otherwise the position changes randomly, and finally the nest yit+1 with better test value is left, still recorded as xit+1 , until the maximum number of iterations is reached and the cycle stops. 3.2 Support Vector Regression SVR is a regression algorithm whose idea is to model the nonlinearity of highdimensional data, make all sample points approximate the regression hyperplane, and minimize the total deviation between the sample points and the hyperplane. The specific idea is as follows: Firstly, the input samples are mapped into the high-dimensional space by nonlinear mapping, and then a linear model is established in the feature space: f (x) = w · ϕ(x) + b
(6)
where w is the weight vector and b is the offset. For a given input data, a new loss function is introduced and the constrained optimization problem can be expressed as: 1 (ξi + ξi∗ ) min w2 + C 2 i=1 ⎧ y − w · ϕ(x) − b ≤ ε + ξi ⎪ ⎨ i s.t w · ϕ(x) + b − yi ≤ ε + ξi∗ ⎪ ⎩ ξi , ξi∗ ≥ 0 n
(7)
(8)
where C is the penalty parameter, ξi and ξ ∗ is the slack variable, which is used to judge the relative position. By introducing Lagrange function, the optimization problem is transformed into a dual problem: n n n 1 ∗ ∗ (ai − aj )K(xi , x) − ε (ai + ai ) + yi (ai − ai∗ ) max − 2 i=1 i i,j=1 ⎧ m ⎪ ⎨ (ai − ai∗ ) = 0 i = 1, 2, ..., n s, t ⎪ ⎩ i=1 ∗ 0 ≤ ai , ai ≤ C
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(10)
Among them, ai and ai∗ are Lagrange multipliers, and K(xi , x) is the kernel function. The kernel function can transform the low-latitude non-separable problem into the highdimensional space separable problem by mapping the low-dimensional space to the high-dimensional space. By solving the dual problem, the solution of Eq. (6) can be obtained as follows: f (x) =
nsv i=1
(ai − ai∗ )K(xi , x) + b
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3.3 CSA-SVR Method When using the SVR method to deal with regression problems, the effect is basically determined by the kernel parameters, which are generally chosen artificially or determined by experience, which can result in reduced prediction accuracy and unsatisfactory results [23]. In order to improve the accuracy of SVR in dealing with nonlinear problems, this paper uses CSA to optimize the SVR parameters and proposes a CSA-SVR algorithm for predicting the lithium-ion battery and. The algorithm flow is shown in Fig. 4, and the main steps are as follows: (1) Data processing: Normalize the feature data extracted from batteries to facilitate the use and comparison of data: y=
x − min(x) max(x) − min x(x)
(12)
Then the processed data is divided into two groups: Training set and test set. (2) Set the parameters of the algorithm: In this paper, the number of n = 40, the solution vector d = 2, the probability of the host discovering foreign eggs pa = 0.25, the number of iterations NIter = 40, the lower bound lb = 0.01, and the upper bound ub = 100; (3) Determine the SVR model through the initial parameters, input the training set data, and obtain the fitness value; (4) Set up the fitness function: Use the mean-square error (MSE) to establish the fitness function, which can well reflect the deviation between the actual value and the predicted value: 1 ∧ ( y −yi )2 n i n
MSE =
(13)
i
∧
where y is the predicted value of the i-th cycle and yi is the actual value of the i-th i
cycle. (5) The CSA algorithm is iterated and the step 3) is repeated to obtain the nest with better fitness; (6) After reaching the maximum number of iterations is reached, the best parameters are retained and the SVR model is used to predict Re and Rct .
4 Simulation Results and Analysis In this experiment, the test data of all three batteries are taken from the 20th cycle, and one set of data is taken every 10 cycles, 15 sets each. In this experiment, the test data of the three batteries started from the 20th cycle, and a group of data was taken every 10 cycles, each of which was 15 groups. Among them, the first 9 groups of data are used as the training set, and the last 6 groups of data are used as the prediction set. The data include five features, F1 to F5, ohmic resistance and charge transfer resistance.
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Fig. 4. Flow chart of CSA-SVR algorithm
In order to analyze the prediction effect of CSA-SVR algorithm, In this paper, Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute percentage Error (MAPE) is used as the evaluation criterion. The error formula is shown in (14): ⎧ n ⎪ 1 ∧ ⎪ ⎪ MSE = ( y −yi )2 ⎪ ⎪ n ⎪ i ⎪ i=1 ⎪ ⎪
⎪ ⎪ n ⎪ ⎪ 1 ∧ ⎪ ⎪ ⎪ RMSE = ( y −yi )2 ⎪ ⎪ n i ⎪ ⎪ i=1 ⎨
n (14)
1
∧ ⎪
⎪ y MAE = −y i ⎪
i
⎪ n ⎪ ⎪ i=1 ⎪ ⎪
⎪ ⎪
∧
⎪ ⎪
y n ⎪ ⎪
i −yi 1 ⎪ ⎪
⎪ MAPE = 100 · ⎪
y ⎪ n i ⎪
⎩ i=1
∧
where y is the predicted value of the i-th cycle and yi is the actual value of the i-th cycle. i
Figure 5a–c shows the prediction results of the ohmic resistance of the three batteries. It can be seen that the predicted output is very close to the actual value, and the predicted error results are shown in Table 3. MSE, RMSE, MAE and MAPE of the three batteries were less than 2×10−6 ,0.2%, 0.2 and 2.5%, respectively. Fig. 6d–f and Table 4 show the prediction results of the charge transfer resistances of the three batteries, whose MSE, RMSE, MAE and MAPE are less than 6 × 10−6 , 0.3%, 0.2 and 2%, respectively. The smaller the error result value is, the higher the accuracy of the prediction is. Combined with the error results of 1 and 2, it can be concluded that the four kinds of errors MSE, RMSE, MAE and MAPE of the proposed CSA-SVR for predicting lithiumion battery and are lower than 6 × 10−6 , 0.3%, 0.2 and 2.5%, respectively. It can be proved that the prediction accuracy of this model is high, which is helpful for better battery health management.
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(a) Re prediction diagram of B05
(d) Rct prediction diagram of B05
(b) Re prediction diagram of B06
(e) Rct prediction diagram of B06
(c) Re prediction diagram of B07
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(f) Rct prediction diagram of B07
Fig. 5. Re and Rct prediction diagram of three battery
5 Conclusions In this paper, we proposed a method based on CSA-SVR algorithm to predict battery ohmic resistance Re and charge transfer resistance Rct . The main conclusions of this paper are as follows:
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RMSE/%
MAE
MAPE/%
B05 battery
1.70
0.13
0.10
1.86
B06 battery
0.60
0.08
0.06
0.84
B07 battery
1.97
0.14
0.11
2.29
Table 4. Error results for Rct of three batteries MSE/10–6
RMSE/%
MAE
MAPE/%
B05 battery
2.54
0.16
0.12
1.46
B06 battery
5.38
0.23
0.16
1.56
B07 battery
3.95
0.20
0.14
1.86
(1) Five features are extracted from battery charging curve and increment capacity (IC) curve, which have high grey correlation with Re and Rct ; (2) The CSA-SVR algorithm is used to train and predict the battery Re and Rct . The results show that the mean square error (MSE) and mean absolute error (MAE) of impedance prediction by this method are less than 6 × 10−6 and 0.2, respectively.
Acknowledgments. This work was funded by State Grid Corporation Headquarters Management Technology Project (SGTYHT/19-JS-215).
References 1. Guo, Z., Qiu, X., Hou, G., et al.: State of health estimation for lithium ion batteries based on charging curves [J]. J. Power Sources 249(mar.1), 457–462 (2014) 2. Languang, L., Han, X., Li, J.: A review on the key issues for lithium-ion battery management in electric vehicles[J]. J. Power Sources 226(MARa15), 272–288 (2013) 3. Waag, W., Fleischer, C., Uwe Sauer, D..: “Critical review of the methods for monitoring of lithium-ion batteries in electric and hybrid vehicles.” J. Power Sources 258, 321–339 (2014) 4. Wei, H., Williard, N., Osterman, M., et al.: Prognostics of lithium-ion batteries based on Dempster-Shafer theory and the Bayesian Monte Carlo method[J]. J. Power Sources 196(23), 10314–10321 (2011) 5. Thomas, E.V., Bloom, I., Christophersen, J.P., et al.: Rate-based degradation modeling of lithium-ion cells[J]. J. Power Sources 206(May 15), 378–382 (2012) 6. Zhou, D., Al-Durra, A., Zhang, K., et al.: Online remaining useful lifetime prediction of proton exchange membrane fuel cells using a novel robust methodology[J]. J. Power Sources 399(Sep.30), 314–328 (2018) 7. Yuan, C., Liu, S., Fang, Z.: Comparison of China’s primary energy consumption forecasting by using ARIMA (the autoregressive integrated moving average) model and GM(1,1) model[J]. Energy 100(Apr.1), 384–390 (2016)
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8. Qin, T., Zeng, S., Guo, J.: Robust prognostics for state of health estimation of lithium-ion batteries based on an improved PSO-SVR model. Microelectron. Reliab. 55, 1280–1284 (2015) 9. Dong, H., Jin, X., Lou, Y., et al.: Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter[J]. J. Power Sources 271(Dec.20), 114–123 (2014) 10. You, G., Park, S., Oh, D.: Diagnosis of electric vehicle batteries using recurrent neural networks[J]. IEEE Trans. Ind. Electron. 64(6), 4885–4893 (2017) 11. Marra, D., Sorrentino, M., Pianese, C., et al.: A neural network estimator of solid oxide fuel cell performance for on-field diagnostics and prognostics applications[J]. J. Power Sources 241(Nov.1), 320–329 (2013) 12. Seki, S., Kobayashi, Y., Miyashiro, H.: Degradation mechanism analysis of all-solid-state lithium polymer secondary batteries by using the impedance measurement[J]. J. Power Sources 146(1/2), 741–744 (2005) 13. Trltzsch, U., Kanoun, O., Trnkler, H.R.: Characterizing aging effects of lithium ion batteries by impedance spectroscopy[J]. Tm Technisches Messen 51(8), 1664–1672 (2006) 14. Eddahech, A., Briat, O., Bertrand, N., et al.: Behavior and state-of-health monitoring of Li-ion batteries using impedance spectroscopy and recurrent neural networks[J]. Int. J. Elect. Power Energy Systems 42(1), 487–494 (2012) 15. Eddahech, A., Briat, O., Henry, H., Delétage, J.-Y., Woirgard, E., Vinassa, J.-M.: Ageing monitoring of lithium-ion cell during power cycling tests[J]. Microelect. Reliab. (2011) 16. Matteo Galeotti, A., et al.: “Performance analysis and SOH (state of health) evaluation of lithium polymer batteries through electrochemical impedance spectroscopy.” Energy 89, 678– 686 (2015) 17. Stroe, D.I., Swierczynski, M., Stan, A.I., Knap, V., Teodorescu, R., Andreasen, S.J.: Diagnosis of lithium-ion batteries state-of-health based on electrochemical impedance spectroscopy technique. IEEE Energy Conversion Congress and Exposition (ECCE) 2014, 4576–4582 (2014). https://doi.org/10.1109/ECCE.2014.6954027 18. Mingant, R., Bernard, J., Sauvant-Moynot, V.: Novel state-of-health diagnostic method for Li-ion battery in service[J]. Applied Energy 183(dec.1), 390–398 (2016) 19. Qi, G., Ma, D., Zhou, L. B., et al.: Analysis of dual three-phase fractional-slot PM brushless ac motor with alternate winding connections[C]. IEEE Int. Conf. Elect. Electron. Berlin, Heidelberg 793–800 (2011) 20. Goebel, K., Saha, B., Saxena, A., Celaya, J.R., Christophersen, J.P.: Prognostics in Battery Health Management. IEEE Instrum. Meas. Mag. 11(4), 33–40 (2008). https://doi.org/10.1109/ MIM.2008.4579269 21. Sijia, L., Jiang, J., Shi, W., Ma, Z., Guo, H.: “State of charge and peak power estimation of NCM/Li4Ti5O12 battery using IC curve for rail tractor application.” 2014 IEEE Conf. Expo Transport. Elect. Asia-Pacific (ITEC Asia-Pacific), 1–3 (2014) 22. Yang and Suash Deb: Cuckoo Search via Lévy flights. World Congress on Nature & Biologically Inspired Computing (NaBIC) 2009, 210–214 (2009) 23. Ghazvinian, H., Mousavi, S.F., Karami, H., et al.: Integrated support vector regression and an improved particle swarm optimization-based model for solar radiation prediction[J]. PLoS ONE 14(5), e0217634 (2019)
Research on Experimental System of Magnetically Mediated Thermoacoustic Detecting Method Yanju Yang1,2(B) , Shengming Zhang1 , Chunlei Cheng1,2 , Wenyao Yang1 , Chong Zeng1,2 , Yongchen Huo1 , and Yu Zhang1 1 School of Electronic Information and Electrical Engineering, Chongqing University of Arts
and Sciences, Chongqing 402160, China [email protected] 2 Chongqing Engineering Research Center of New Energy Storage Devices and Applications, Chongqing 402160, China
Abstract. For the sake of measuring the conductivity without damaging the energy storage materials of the energy storage devices, Magnetically mediated thermoacoustic detecting method (MMTDM) is used in this experiment. MMTDM is a new detection technology based on electrical impedance imaging technology and ultrasonic imaging technology, which has the merits of high contrast of electrical impedance imaging technology and high resolution of ultrasonic imaging technology. Its principle is to generate an induced magnetic field by inputting a certain pulsed current to the exciting coil. The energy storage material continuously traps joule heating in the induced magnetic field and expands instantaneously, sending out sound waves reflecting the conductivity information. The sound waves are collected to reconstruct the conductivity information. The paper mainly builds the platform of the MMTDM, compares and analyzes the experimental results of the one-layer excitation system to four-layer excitation system, and observes the strength of the sound waves which are emitted by the energy storage materials under the one-layer excitation system to the four-layer excitation system. This experiment has better verified the feasibility of applying the MMTDM system to test the conductivity of energy storage materials, and provided a relatively perfect theoretical and experimental basis for the development of non-contact testing the conductivity of energy storage materials in the future. Keywords: MMTDM · Non-contact detection · Excitation system · Energy storage materials
1 Introduction As the continual development of society and new energy technology, in order to adapt to the social development and people’s material life needs, higher requirements are put forward for the performance of energy storage devices. Therefore, developing energy
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storage devices with smaller capacity and more energy storage density is the key breakthrough direction in the current research of super-capacitors [1, 2]. For the sake of developing energy storage devices with high storage energy per unit capacity, and effectively improving the conductivity of super-capacitors, it is extremely important to develop devices that can more accurately measure the conductivity of super-capacitors. The current commonly used methods for measuring the conductivity of supercapacitors are directly in contact with the super-capacitors, such as conductivity meter technology and four point probe method [3, 4]. Neither of these two methods can accurately measure the conductivity without damaging the energy storage materials. In order to make up for this defect, a device for detecting the conductivity of energy storage materials through a non-contact detection system is designed in this experiment. In the process of measuring the conductivity, there is no need to contact with the energy storage materials, so that the energy storage materials will not be polluted and damaged, and this method could test the conductivity of super-capacitors in any shape. So the conductivity information of the super-capacitors could be obtained without touching. The detection method we use is the MMTDM [5], which is a new electrical impedance imaging method stemmed from the association with magnetic, thermal and acoustic physical fields. The MMTDM is from Magnetically Mediated Thermoacoustic Imaging in medical imaging [6–9]. It is based on thermoacoustic effect [10, 11], combining the advantages of various physical field detections. Comparing to the classical electrical impedance imaging, it is provided with the strong point of high resolution, high sensitivity, high contrast and so on. MMTDM uses the method of mutual coupling of magnetic, thermal and acoustic fields to test thermoacoustic signals by applying alternating magnetic field around the target to reflect the internal conductivity information of the target. In this paper, the energy storage material used in this experiment is self-made graphene energy storage material, through the MMTDM, the non-contact conductivity detection of the target is studied. Different layers of excitation systems are used to excite the target, and the ultrasonic signal intensity of the target is compared.
2 Principle of MMTDM It is assumed that the conductivity of the experimental target was σ (r ), which was set at the magnetic induction intensity of B(r ,t) in uniform induction alternating magnetic field, the induced electric field intensity and the eddy current of the experimental target are E(r ,t) and J(r ,t), respectively. Where, r is the vector location of the target, and t is the time when the target is put into the pulsed magnetic field. Materials begin to trap joule heating under a uniform alternating magnetic field, then the thermoacoustic source is calculated through the heating function. The heating function H(r ,t) is the power density, whose definition is the energy absorbed per unit volume per unit time, and the expression is as follows: 2 (1) H r ,t = σ r E r , t After the target traps joule heating, its internal thermodynamic equilibrium is destroyed, so transient thermal expansion occurs, and then thermoacoustic signals are
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radiated. The sound pressure sound wave equation is: 1 ∂2 β ∂H r , t 2 ∇ p(r, t) = − + 2 2 p(r, t) Cp ∂t cs ∂t
(2)
In the above equation, p(r,t) is the sound pressure of the position vector r at time t, cs is the propagation sound velocity of the ultrasonic wave, and C p and β is the specific heat capacity of the target and the volume expansion coefficient of the target, respectively. The expression of p(r,t) can be obtained by solving the sound pressure with the Green function method: R ˚ β ∂ r , t δ t − CS 1 d (3) p(r, t) = 4π ∂t R Cp where Ω is the area which contains the thermal sound source, and R is the distance from the position of the experimental target to the ultrasonic inspection point. When the material emits thermoacoustic wave, the ultrasonic transducer is used to collect the signal. Then all the collected signals are analyzed combined with the time reversal technology getting the representation of the heating function. Using the heating function can obtain the conductivity distribution of the target. The principle diagrammatic sketch of MMTDM is shown in Fig. 1.
Fig. 1. Principle diagrammatic sketch of MMTDM
3 Construction of Experimental System So as to verify the feasibility of MMTDM, an MMTDM experimental platform has been built, which is roughly divided into two parts: pulse excitation source system and detection system. The pulse excitation source system is chiefly formed by voltage regulator part, boost part, rectifier part and exciting coil part. It is an excitation system sending high-frequency narrow pulse time-varying magnetic field, which is a self-made system to offer induction time varying magnetic field for the detection system. The detection system majorly contains low noise amplifier, acoustic transducer and oscilloscope. When the pulse excitation source system generates a time varying magnetic field, put the target into the insulated oil tank covered by the time varying pulse magnetic field, place the oil inundate ultrasonic transducer in the tank and aim at the target detection material.
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By applying a magnetic field with a pulse width of 1 µs to the target detection material, an induced vortex electric field is generated into the conductive target, and the joule heating is generated to excite the sound wave containing the information of the target conductivity. The ultrasonic signal is collected, and the conductivity graduation image is reconstructed by using the inverse part of ultrasonic field and electromagnetic field. The data flow diagram of the imaging detection system as shown in Fig. 2.
Fig. 2. MMTDM data flow diagram
Pulse excitation system is an important part of MMTDM experimental device. Its power, pulse width, rising edge and other parameters determine the frequency and intensity of thermoacoustic signals. The drive circuit unit of the pulse excitation system adopts the structure of solid-state transfer switch to control the fast charging and discharging of capacitors. The whole system needs multiple drive circuit units in series and parallel. First, eight drive circuit units are connected in series to form an excitation part of one layer, and then the excitation parts between layers are connected in parallel. Firstly, a double-layer excitation system is built according to a single-layer excitation system, which aims to make the pulse excitation system, which aims to make the pulse excitation part emit a stronger magnetic field and make the collected ultrasonic signal more accurate. Then, a three-layer excitation system is built according to a doublelayer excitation system and finally a complete four-layer excitation system is built. The specific experimental results can be obtained by measuring the induced magnetic field of the built single-layer excitation system to four-layer excitation system, as shown in Fig. 3.
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Fig. 3. Induced magnetic field wave form under different layers of excitation system
It can be seen from the comparison of (a) to (d) in Fig. 3 that by increasing the number of layers of the excitation system, the induced magnetic field waveform sent out from the pulse excitation part could be effectively enhanced, which lays a good foundation for subsequent experiments.
4 Experimental Results and Analysis For verifying the correctness of MMTDM theory, this paper uses self-made graphene model as the experimental target. The physical figure is shown in Fig. 4. The experimental model is a square, whose side length is 2 cm. The model is fixed with gel. The sound speed of ultrasonic signal in machine oil is tested to be 1440 m/s. The experimental models are placed in different layers of excitation systems, and the positions of the sound probe and the first boundary of the square model is about 7 cm. The acquired ultrasonic wave is shown in Fig. 5. On the oscilloscope, the horizontal axis is the time, each grid is 20 ms, and the longitudinal axis is the amplitude of the acquired ultrasonic wave. The beginning of each waveform is the ultrasonic transducer couples with the induced signal produced from the space pulse magnetic field, and this time is looked on as the start reference time point of MMTDM wave.
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Fig. 4. Physical drawing of graphene square model
Fig. 5. Ultrasonic signals under different layers of excitation system
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It may be found out from Fig. 5 that the received ultrasonic signal has two wave clusters, which correspond to the time when the ultrasonic wave excited by the boundaries of the square model, propagating to the sound probe, and the time between signal clusters is about 14 µs. Theoretical value is 0.02/1440 = 13.9 µs. Considering the measurement error in the experiment, that is, the measurement error of the experimental model and the measurement error of the distance between the model and the ultrasonic probe, arguably that the experimental value is basically consistent with the theoretical value. It can be obtained from the experimental results that the wave cluster collected on the oscilloscope is the MMTDM signal generated by the graphene model after being excited by the pulsed magnetic field, that is, under this experimental system, the energy storage material can generate MMTDM signal through the excitation of the pulsed magnetic field.
5 Conclusion According to the comparison of ultrasonic signal waveforms measured by the singlelayer to four-layer excitation system under single pulse and the comparison of induced magnetic field waveforms of each layer, increasing the number of layers can effectively make the graphene model send out stronger ultrasonic signals. This experiment has better verified the feasibility of applying the MMTDM system to the conductivity measurement of energy storage materials, and provided a relatively perfect fundamental of theory and experiment for the development of the non-contact detecting conductivity of supercapacitors in the future. Acknowledgments. The work was supported by the National Natural Science Foundation of China (NSFC) (Nos. 51907013 and 61971112); the Natural Science Foundation of Chongqing (Nos. Cstc2019jcyj-msxmX0474 and cstc2021 jcyj-msxmX0271); Scientific and Technology Research Program of Chongqing Municipal Education Commission (Nos. KJZD-K202201306, KJQN202201342, KJQN202101317 and KJQN201901304).
References 1. Xiao, X., Zou, L.L., Pang, H., et al.: Synthesis of micro/nanoscaled metal-organic frameworks and their direct electrochemical ap-plications[J]. Chem Soe Rev. 49(1), 301–331 (2020) 2. Zhu, J.J., Gao, J.: Research on preparation and electrochemical performance of low temperature tolerant organic electrolyte for supercapacitor[J]. Chemical Engineer 316(1), 8–10, 21 (2022) 3. Dhas, S., Maldar, P.S., Patil, M., et al.: Probing the electrochemical properties of NiMn2O4 nanoparticles as prominent electrode materials for supercapacitor applications[J]. Materials Sci. Engineer. B 115298 (2021) 4. Li, D.Q., Lu, Q.J., Zhang, J., et al.: Research progress of metal oxide electrode materials in supercapacitors[J]. Journal of Functional Materials and Devices. 1, 16–25 (2021) 5. Yang, Y.Y., Liu, C.B., Sun, T., et al.: Development of non-contact detection system for energy storage materials. In: 2021 IEEE 4th International Electrical and Energy Conference, Institute of Electrical and Electronics Engineers Inc. (2021) 6. Feng, X., Gao, F., Zheng, Y.: Magnetically mediated thermoacoustic imaging toward deeper penetration[J]. Appl. Phys. Lett. 103(8), 083704–083707 (2013)
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7. Feng, X., Gao, F., Zheng, Y.: Modulatable magnetically mediated thermoacoustic imaging with magnetic nanoparticles [J]. Appl. Phys. Lett. 106(15), 153702 (2015) 8. Yang, Y., Liu, G., Li, Y., et al.: Conductivity reconstruction for magnetically mediated thermoacoustic imaging[J]. Journal of Medical Imaging and Health Informatics 8(1), 66–71 (2018) 9. Yang, Y., Cheng, C., Yang, W., et al.: Study of acoustic source excited by pulsed magnetic field[J]. Journal of Mechanics in Medicine and Biology 21, 2140008 (2021) 10. Tang, Y.H., Zheng, Z., Xie, S.M.: Thermoacoustic imaging based on noise suppression of multichannel amplifier and additive circuit[J]. Acta Physica Sinica 69(24), 20201036 (2020) (in Chinese) 11. Xie, S.M., Huang, L., Wang, X.: Reflection mode photoacoustic/thermoacoustic dual modality imaging based on hollow concave array[J]. Acta Physica Sinica 70(10), 100701 (2021) (in Chinese)
Research on Mobile Energy Storage Vehicles Planning with Multi-scenario and Multi-objective Requirements Yuanyuan Chen1,2(B) , Shaobing Yang1 , Zhuo Chen2 , Yong Zhao2 , and Yibo Wang2 1 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100091, China
[email protected] 2 Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190, China
Abstract. Aiming at the optimization planning problem of mobile energy storage vehicles, a mobile energy storage vehicle planning scheme considering multiscenario and multi-objective requirements is proposed. The optimization model under the multi-objective requirements of different application scenarios of source, network and load side is established, and the constraints that should be satisfied are given. The optimization solution method based on the second-order cone is adopted, and the large-scale mixed-integer nonlinear model is converted into a mixed-integer second-order cone optimization model, which improves the solution speed of the optimization problem. The calculation example analysis shows that the proposed mobile energy storage vehicle planning scheme utilizes the stored electricity to the greatest extent, and can meet various needs in different application scenarios with limited investment cost. Keywords: Multi-scenario · Multi-objective · Mobile Energy Storage Vehicle
1 Introduction With the high-speed development of renewable energy technology, the penetration rate of renewable energy such as photovoltaics has been increasing in last few years, and the grid connection of a high proportion of renewable energy has brought huge security risks to the power grids stable operation. In recent years, energy storage system (ESS) is often used in conjunction with renewable energy sources to improve power quality, support power grids, and provide emergency power supplies. However, the investment cost of ESS is relatively high, and stationary ESS also has disadvantages such as long construction period and inflexible geographical location. The mobile energy storage system (MESS) emerging in the last few years combines the characteristics of the vehicle and the ESS to realize the movement of the ESS. Compared with fixed energy storage, MESS can be dynamically transferred, dispatched in a wide area and at multiple points, can adapt to extreme environments, has more application scenarios, and is more flexible than fixed energy storage [1]. In view of the characteristics of compact size, small footprint and fast response, MESS equipment is widely used in various scenarios of source, network and load. For © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 514–524, 2023. https://doi.org/10.1007/978-981-99-1027-4_53
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the source side, due to the intermittent characteristics and randomness of wind power, photovoltaic and other renewable energy output, reference [2] analyzes the distribution characteristics of wind power prediction error, and proposes an ESS power and capacity that can track the planned output of wind power. Configure optimization methods. Reference [3] proposes wind power and photovoltaic models for the uncertainty of wind and solar output power, and then builds an optimal configuration model for solar and wind storage. For the grid side, in view of the problem of the voltage exceeding the limit, the references [4] considers the adjustment effect of the energy storage, and coordinates and optimizes the voltage from two aspects of the active and reactive power. For the load side, uninterrupted power supply for key loads can be guaranteed. In [5], considering the effects of natural disasters on the distribution network, an annual comprehensive lossof-load cost model during the emergency response period of the power grid is proposed, and a distribution network ESS planning model to ensure uninterrupting power supply for important loads is constructed. Reference [6] proposed a representative line identification method for faults, and based on this, a joint planning scheme of distribution network and ESS considering N − 1 faults was established. For the energy storage side, some literatures consider the benefits and costs. Reference [7] considers the interaction between the ESS and the demand-side interruptible load response, and proposes a planning model aiming at maximizing the comprehensive economic benefits of the whole society. Reference [8] builds a multi-stage joint planning model for ESS and electric vehicle charging station, aiming to minimize the total investment cost, operating cost and load loss cost. References [9, 10] proposes a two-stage optimization model for the investment problem of ESS, which optimizes the investment of MESS in the first stage, and optimizes the dispatch of MESS in the second stage. To sum up, most of the above documents focus on the research on disaster prevention and emergency planning of a single scenario, such as MESS. However, the actual mobile energy storage vehicle (MESV) needs a lot of scenarios, and the probability of a single scenario such as failure and natural disaster is very small, resulting in unreasonable configuration capacity of the MESS. At present, there is a lack of MESS configuration that can consider the demand of multiple scenarios on the source side, the network side and the load side.
2 Design of MESV The MESV includes a MESS, a vehicle platform, and an intelligent controller for the MESV. The MESS consists of energy storage units and power convert system (PCS). The vehicle platform uses a new energy light bus. Compared with traditional emergency power sources such as box-type heavy truck MESVs, the new energy light bus adopts a pure electric vehicle chassis, which can not only break through the road travel restrictions in big cities, but also have no noise pollution. The intelligent controller of the MESV can construct the vehicle energy management system (EMS) and the battery management system, and realize the strategy design of the multi-level control system of the MESV under multiple application scenarios and multiple control objectives. The schematic diagram of the structure of the MESV studied in this paper is shown in Fig. 1. In terms of battery selection, the lithium iron phosphate battery with high energy
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Fig. 1. Schematic diagram of the structure of the MESV.
density is selected for safety. In terms of PCS, a multi-port energy storage converter and a multi-port DC converter. The multi-port energy storage converter can match the complex AC power events in the power distribution area, and is mainly composed of DC/AC links. The converter needs to meet the needs of mobile energy storage power sources for flexible and highperformance access to AC power emergency services for a variety of energy storage devices under different working conditions. The multi-port DC converter can match the needs of various DC power scenarios, and can meet the flexible access of multiple energy storage devices and DC loads. The power flow direction of each port of the DC converter is bidirectional and independent, so that the MESV can not only receive the support of the energy storage device, but also charge it (Fig. 2). 350V~700V
380V
DC/DC
DC/AC
750VDC Energy storage system of mobile energy storage vehicle
Fig. 2. Schematic diagram of MESS.
According to the multi-scenario and multi-mode switching and intelligent control requirements of mobile charging vehicles, the intelligent controller for MESVs is developed to realize the functions of whole vehicle status collection, performance analysis and remote interaction, including MESVs under multi-application scenarios and multicontrol targets and multi-level control strategy design. The intelligent controller of the MESV includes the energy storage vehicle EMS platform and the inverter control platform. The schematic diagram of the intelligent controller is shown in Fig. 3. The energy storage vehicle EMS platform mainly realizes the uploading of vehicle information to the cloud platform and the measurement and measurement of local electric power. The converter control platform mainly realizes local control, including switching control of various working modes of the MESV.
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Cloud platform MQTT
Energy Storage Vehicle EMS Platform CAN
Vehicle controller CAN
Modbus
Measurement calculation
Modbus
AC control platform Modbus
AC charging gun DC charging gun
DC/DC converter
CAN
AC/DC converter
Energy storage battery
Fig. 3. Schematic diagram of intelligent controller of MESV.
3 Models and Algorithms 3.1 MESV Target Model The application scenarios of MESVs are distributed renewable energy generation side, load side, and distribution network side. It can participate in the adjustment of fluctuations on the power generation side of distributed renewable energy, power demand on the load side, and power quality on the distribution grid side. This paper comprehensively considers the above three aspects, and proposes an objective function to make MESVs meet the needs of different scenarios. During the orderly charging optimization period, the MESV can meet the needs of use in different scenarios. For the power generation side of distributed renewable energy, the power fluctuation of renewable energy power generation can be effectively suppressed by moving the energy storage battery unit, so as to achieve smooth power fluctuation and stable grid connection. Therefore, the minimum fluctuation model of distributed renewable energy power generation power is established, which is as follows: flu
Pmin =
T N MESS DG MESS DG + Pt,i )−(Pt−1,i + Pt−1,i ) (Pt,i
(1)
i=1 t=1 flu
Pmin is the power fluctuation of distributed renewable energy generation. DG Pt,i is the active power of distributed renewable energy at t moment and MESS is the power of the MESV t moment and node i. The node i. Pt,i sum of the total power fluctuation differences between consecutive moments T MESS DG MESS DG + Pt,i ) − (Pt−1,i + Pt−1,i ). The sum of the total at node i are t=1 (Pt,i power fluctuation differences between consecutive moments at all nodes are N T MESS DG MESS DG + Pt,i ) − (Pt−1,i + Pt−1,i ), Where i is a node in a certain area i=1 t=1 (Pt,i and i is 1 to N and N is an integer greater than 1. t is defined as time in hours and t is 1 to T and T is an integer greater than 1. For the distribution network side, MESVs mainly solve power quality problems such as voltage deviation and power emergency. By calculating the absolute value of the deviation between the distribution network voltage and the nominal voltage value at t
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moment and node i, the minimum voltage deviation model on the distribution network side is established as bla Umin =
T N Ut,i − Ut,i∗ U i=1 t=1
(2)
t,i
bla is the absolute value of voltage deviation, U is the distribution network voltage Umin t,i at t moment and node i, Ut,i = Ut,i max − Ut,i min is the maximum voltage deviation value at t moment and node i, Ut,i∗ is the nominal voltage value of grid voltage at t moment and node i. This formula mainly calculates the absolute value of the deviation between the distribution network voltage and the nominal voltage value at t moment and node i. For the load side, the MESV needs to combine the local power grid peak-valley electricity price policy, through the mobile energy storage battery unit to discharge when the grid electricity price is high, and to obtain benefits by charging when the grid electricity price is low. Build a load-side user maximum benefit model:
u = Pmax
T N
MESS Et Pt,i t
(3)
i=1 t=1 u is the income obtained by the load side, Et is the time-of-use electricity price, Pmax MESS is the charging and discharging power of the mobile energy storage unit required Pt,i MESS > 0 is discharge, P MESS < 0 is charging, t is at t moment and node i, where Pt,i t,i charging/Discharge time. This formula mainly calculates the income obtained by users on the load side. For MESVs, a minimum cost model on the energy storage side is established.
cos Pmin =
T N
MESS (Cp Pt,i + CL LMESS ) t,i
(4)
i=1 t=1 cos is the lowest cost of energy storage vehicles. C is the unit power investment Pmin p MESS is the charging/discharging power of the MESV at t moment cost of the MESV. Pt,i and node i. CL is the unit cost of the route distance between different locations of the is the distance from the current location of the MESV to the node i. MESV. LMESS t,i According to the model established above, the overall target model under different scenario requirements can be established. flu
bla u cos +λ3 Pmax +λ4 Pmin P = λ1 Pmin +λ2 Umin
(5)
λ1 is the weight coefficient of the power fluctuation of the distributed renewable energy generation on the source side. λ2 is the weight coefficient of the absolute value of the grid-side voltage deviation. λ3 is the weight coefficient of the income value obtained by the load side. λ4 is the weight coefficient of the energy storage side cost value. The needs of multi-scene and multi-objective can be realized by adjusting the weight coefficient.
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3.2 MESV Constrained Boundary Model Operating constraints of MESVs. Consider the carrying range of each MESV to ensure the normal use of the battery of the MESV. The charging/discharging power constraints of the MESV is: ESS MESS ESS −Pt,i ≤ Pt,i ≤ Pt,i
(6)
ESS is the maximum charging/discharging power of the MESV at t moment and Pt,i node i. Consider the status of health of the energy storage battery of the MESV to prevent the impact on the life caused by frequent charging and discharging. The state of charge control range of the MESV is as follows: min MESS max SOCt,i ≤ SOCt,i ≤ SOCt,i
(7)
min and SOC max are the upper and lower upper and lower limits of the state of SOCt,i t,i charge of the MESV at t moment and node i respectively. MESV planning constraints. Considering the limited activity range of the MESV, set the activity range:
≤ Lmax LMESS t,i t,i
(8)
Lmax t,i is the maximum movable range of the MESV t moment and node i. Consider the number and distribution range of MESVs, set the total number of MESVs, and restrict the number of MESVs. N
δi ≤ nMESS
(9)
i=1
δi indicates whether a mobile car can be configured on the node i. δi =1 indicates the configuration of MESVs. δi = 0 means no MESV is configured. nMESS is the maximum number of MESVs allowed to be configured in the area. Power flow constraints in distribution network. ⎧ N 2 ⎪ ik∈ Pt,ik = ji∈ (Pt,ji − rji It,ji ) + Pt,i ⎪ ⎪ N ⎪ 2 ⎪ ⎪ ik∈ Qt,ik = ji∈ (Qt,ji − xji It,ji ) + Qt,i ⎪ ⎪ DG MESS LOAD ⎪ ⎪ Pt,i = Pt,i + Pt,i − Pt,i ⎪ ⎨ DG MESS LOAD Qt,i = Qt,i + Qt,i − Qt,i (10) 2 +Q 2 ⎪ P ⎪ t,ij 2 = t,ij ⎪ I ⎪ 2 t,ij ⎪ Ut,i ⎪ ⎪ ⎪ 2 2 2 =0 ⎪ U − Ut,j − 2(rij Pt,ij + xij Qt,ij ) + (rij2 + xij2 )It,ij ⎪ ⎪ ⎩ t,i s s 2 2 (Pt ) + (Qt ) ≤ r(Sg + ZSg ) In the formula: is the branch set. rij is the resistance of branch ij. xij is the reactance of branch ij. Pt,ij , Qt,ij , Pt,ji , Qt,ji , Pt,ik , Qt,ik are the active power and reactive power flowing on the branches ij, ji and ik at the moment t respectively. Pt,i and Qt,i are the
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sum of active power and reactive power injected by node i at moment t respectively. DG and Q DG are the active power and reactive power injected by the distributed power Pt,i t,i MESS and Q MESS are the active power generation on node i at moment t respectively. Pt,i t,i LOAD and reactive power output by the converter on node i at moment t respectively. Pt,i LOAD are the active power and reactive power consumed by the load on node i and Qt,i at moment t respectively. Pts is the active power actually flowing from the high-voltage side of the main transformer to the distribution network at moment t. Qts is the reactive power flowing from the high-voltage side of the main transformer to the distribution network at moment t. r is the load rate of the substation. 3.3 Solving Algorithm The multi-scenario and multi-objective optimal configuration problem of MESVs is a large-scale mixed-integer nonlinear programming problem in its mathematical essence. The speed or precision of traditional mathematical optimization methods and heuristic algorithms to solve such problems cannot meet the requirements at the same time. The second-order cone programming algorithm is essentially a convex programming, and the optimality and computational efficiency of the solution are guaranteed, and it can effectively solve large-scale mixed integer nonlinear programming problems. When solving the optimal configuration problem of MESVs, the second-order cone programming algorithm can meet the requirements of fast convergence and optimal solution at the same time. When solving, it is necessary to perform corresponding cone transformation processing on the objective function and constraint model in advance, so as to meet the requirements of the linear objective function and convex cone search space, so as to convert the difficult-to-solve large-scale mixed integer nonlinear model into one that can be Efficiently solved mixed-integer second-order cone optimization model. Based on the above analysis, the planning process of MESVs under multi-scenario and multi-objective requirements proposed in this paper is shown in Fig. 4. Specific steps are as follows: Step 1: According to the selected power distribution system, input line parameters, load level, network topology connection relationship, distributed power access location and capacity, ESS parameters, system node voltage and branch current limit, system reference voltage and the initial value of the reference power; Step 2: Establish a mixed integer nonlinear model of the MESV, determine the optimization objective function, and comprehensively consider the power flow constraints of the power distribution system, the operation constraints of the ESS, and the planning constraints of the ESS; Step 3: Convert the model obtained in Step 2 into a mixed-integer second-order cone programming model that can be efficiently solved, including objective function linearization, equality constraint linearization, and inequality constraint linearization, and introducing a rotating cone according to the network structure and scale Constraints to obtain a mixed-integer second-order cone programming model; Step 4: Use the mature mathematical optimization tool CPLEX to solve the mixed integer second-order cone programming model obtained in step 3;
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Step 5: Output the configuration and planning results of the MESVs, that is, the power, capacity, number, and action range of the MESVs. Start Input initial values such as network parameters, distributed renewable energy parameters, etc. Objective function
Run constraints
Objective function linearization
Planning constraints
Current constraints
Equality Constrained Linearization
Inequality Constraint Linearization
Introduce swivel cone constraints based on distribution network and mobile scale Form cone optimization model
Solved with cone optimization tool Output mobile energy storage vehicle planning results Finish
Fig. 4. MESV planning process under multi-scenario and multi-objective requirements.
4 Case Analysis The proposed planning strategy is verified based on IEEE33 nodes, and the node wiring diagram is shown in Fig. 5. The source of the time-of-use electricity price is the sales price of the Tianjin power grid, as shown in the Table 1. Nodes 2, 6, and 15 are installed with photovoltaic power plants, and the relevant parameter settings of energy storage and photovoltaic power plants are shown in Table 2. Assuming that the location of the MESV is fixed, renewable energy can be consumed locally. When the voltage deviation occurs in the distribution network, the MESV has enough time to move to the adjacent nodes of the distribution network to participate in the adjustment. Using the CPLEX solver on the MATLAB platform to solve the built model, the optimal planning results of the MESV are shown in Table 3. It can be seen from Table 3 that the planned and constructed addresses of MESVs are nodes 2, 6, and 15. This is because nodes 2, 6, and 15 are important load nodes and are equipped with photovoltaic power stations. In daily operation, MESVs are used to shave peaks and fill valleys and
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Fig. 5. Node Wiring Diagram.
Table 1. Time-of-use electricity price Period
Electricity selling price (yuan/kWh)
Electricity purchase price (yuan/kWh)
00:00–08:00
0.4
0.365
08:00–12:00,17:00–21:00
2
0.869
12:00–17:00,21:00–24:00
1.2
0.687
Table 2. The relevant parameter settings of energy storage and photovoltaic power plants. Parameter
Value
Energy storage vehicle investment/vehicle
800,000 yuan
Operating cost of MESV
1 yuan/kWh
Total PV installed capacity
1 MW
Distribution network substation capacity
315 kVA
Comprehensive cost of photovoltaic operation
0.1 yuan/kW
MESVs sell electricity
2 yuan/kWh
consume renewable energy. The optimal planned construction capacity of the energy storage device is 250 kWh, because the weight of the MESV in urban areas is limited (the maximum weight is 4500 kg), and the rated capacity of the transformer is 315 kVA, considering that 20% of the reserve capacity is reserved, the upper limit of the power that the transformer can provide should be 252 kVA, so the 250 kWh MESV is the most ideal technical solution. Considering the state of charge of the battery and the configured capacity and quantity, the algorithm solves the maximum action radius of 500 km. The following is an analysis of the economic indicators of the optimal planning and construction scheme obtained by the planning model of the mobile energy storage device in this region. The values of each economic indicator are shown in Table 4. It can be seen from Table 4 that under the obtained optimal planning scheme, the annual comprehensive income reaches 990,000 yuan, of which the annual income from electricity sales is 540,000 yuan. The annual investment cost of mobile energy storage devices is 240,000 yuan, accounting for 24.2% of the annual comprehensive income. The comprehensive
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Table 3. Planning parameters of MESVs. Parameter
Value
MESV (green card) capacity
250 kWh
Configuration quantity
3
Configuration node
2,6,15
Action radius
500 km
annual operating cost of the mobile energy storage device is 1,095 yuan, accounting for 0.11% of the annual comprehensive annual income. It can be seen that the investment cost accounts for a relatively low proportion of the income when the optimal planning scheme of the MESV is obtained without overloading the transformer. This solution not only achieves the goal of economy, but also achieves smooth distributed renewable energy power generation and improves the reliability of power supply of the distribution network, and meets the multi-objective operation requirements of the city’s internal source-grid-load-storage multi-application scenarios. Table 4. Economic index parameter value. Parameter
Value
Annual comprehensive income/yuan
990000
Annual revenue of electricity sales/yuan
540000
Comprehensive cost of MESV operation/yuan
1095
Annual electricity sales/kWh
750
5 Conclusion Combined with the mobile characteristics of the MESV and the multi scene application of the load storage side of the urban source network, a multi-objective planning model of the MESV is proposed. Aiming at the large-scale mixed integer nonlinear optimization problem of the optimal configuration of MESVs, the optimization solution method based on the second-order cone is adopted, and the complex optimization problem is replaced by the mixed integer second-order cone optimization model. A configuration solution flow based on the second-order cone optimization is proposed. The results of the example analysis show that the proposed MESV planning scheme can improve the grid connection of renewable energy friendly power generation under the limited investment cost, ensure the power supply reliability of the distribution network, create profits by using peak valley arbitrage, and maximize the use of the electricity stored by the MESV.
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Acknowledgments. This research was funded by “Regional key projects of the Science and Technology Service Network Program (STS Program) of the Chinese Academy of Sciences (ID, KFJ-STS-QYZD-2021–02-005)” and Qinghai Science and Technology Project “Key technologies for renewable energy and energy storage integration applications (ID, 2019-GX-A9)” and National Key R&D Program Intergovernmental International Science and Technology Innovation Cooperation Project “Sino-US Green Community DC Microgrid Technology Cooperation Research and Demonstration (ID, 2019YFE0120200)” and National key research and development program “Research on test methods and evaluation techniques of multi-site photovoltaic application (ID, 2019YFE0192400)”.
References 1. Chen, Y., Zheng, Y., Luo, F., et al.: Reliability evaluation of distribution systems with mobile energy storage systems[J]. IET Renew. Power Gener. 10(10), 1562–1569 (2017) 2. Xiangwu, Y., Zijun, S., Sen, C., Ying, S., Tiecheng, L.: Primary frequency regulation strategy of doubly-fed wind turbine based on variable power point tracking and supercapacitor energy storage. Trans. China Electrotech. Soc. 35(3), 530–541 (2020). (in Chinese) 3. Jun, H.E., Changhong, D.E.N.G., Qiushi, X.U., et al.: Optimal configuration of distributed generation system containing wind PV battery power sources based on equivalent credible capacity theory [J]. Power Syst. Technol. 37(12), 3317–3324 (2013). (in Chinese) 4. Yang, T., Li, X., Qi, L.: A schedule method of battery energy storage system to track dayahead photovoltaic output power schedule based on short term photovoltaic power prediction. In: International Conference on Renewable Power Generation, pp. 1–4 (2015) 5. Haibo, Z, Shentong, M.A., Xin, C, Xianfu, G., Kai1, W.: Distribution network energy storage planning ensuring uninterrupted power supply for critical loads. Power Syst. Technol. 45(1), 259–268 (2021) (in Chinese) 6. Joint planning of distribution network expansion and distributed energy storage systems under N-1 criterion. Proc. CSEE 41(13), 4390–4402 (2021) (in Chinese) 7. Xiulei, L.I., Guangfei, G.E.N.G., Yuqi, J.I., Lingzhi, L.U.: Integrated optimal planning of energy storage and demand side response in active power distribution network. Power Syst. Technol. 40(12), 3803–3810 (2016). (in Chinese) 8. Long, J.I.A., Zechun, H.U., Yonghua, S.O.N.G., Huajie, D.I.N.G.: Joint planning of distribution networks with distributed energy storage systems and electric vehicle charging stations [J]. Proc. CSEE 37(01), 73–84 (2017). (in Chinese) 9. Kim, J., Dvorkin, Y.: Enhancing distribution system resilience with mobile energy storage and microgrids [J]. IEEE Trans. Smart Grid 10(5), 4996–5006 (2018) 10. Jianlin, L., Meng, N., Xichao, Z., Xiaoqing, X., Jinghua, Z.: Energy Storage Capacity Planning and Investment Benefit Analysis of Micro-Energy System in Energy Interconnection. Trans. China Electrotech. Soc. 35(4), 874–884 (2020). (in Chinese)
A Novel Control Strategy of Air-Core Pulsed Alternators for Driving Electromagnetic Railgun Jiasong Wang , Xianfei Xie(B)
, and Kexun Yu
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China [email protected]
Abstract. The pulse power system based on the air-core pulse alternator (ACPA) takes into account the high energy storage density and high power density, has the advantages of miniaturization, lightness and high repetitive output frequency, and is an important technical way of pulse power for electromagnetic railgun. It is necessary to make the speed of electromagnetic rail gun controllable and reduce the muzzle current in the process of actual combat, but the proposed working principle has not yet studied the speed control of rail gun and the strategy of reducing the muzzle current. In this paper, the two-phase discharge process of the ACPA is analyzed through the superconducting loop magnetic chain conservation and the characteristics of its commutation overlap process are analyzed. Then the feedback predictive control of rail gun speed based on pulse wave number control is derived on the basis of two-phase discharge, and the relationship between the initial excitation current of the discharge and the discharge speed of the rail gun is analyzed, and a possible continuous control of the speed of the rail gun based on the pulse power system of the ACPA is proposed. Keywords: Air-core pulse alternator · Electromagnetic railgun · Load current · Speed control
1 Introduction The rotor of ACPA uses high-strength alloy material to increase the maximum operating speed to obtain higher energy storage and power density, while the stator uses composite material to reduce the overall weight of the system. Because there is no magnetically conductive material in the stator and rotor materials, the magnetic circuit in the motor has high reluctance and low inductance, so the ACPA can output higher peak current at the same induced voltage, and the current rises quickly [1–3]. The use of ACPA system as a power supply system for electromagnetic railguns greatly reduces the size of the power supply system. When the excitation current reaches tens of kA, the ACPA can output MA level current to the rail gun load. The system structure of the ACPA is shown in the Fig. 1. In this paper, we take a seven-phase ACPA as an example, which has been well studied in paper [4–6]. The excitation of ACPA © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 525–535, 2023. https://doi.org/10.1007/978-981-99-1027-4_54
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requires a current of several tens of kA, which requires a large excitation power supply. This will increase the size of the system and is not conducive to improving the energy storage density of the system, so the self-excitation structure is used [4, 7]. In paper [8], the amplitude of the output current is proportional to the initial excitation current of discharge. In paper [9], the phase current equation about the sudden short circuit using synchronous motor is introduced, considering the steady-state component and transient component, but only its amplitude is used as a reference, however, in the actual discharge process, because there is no external excitation power supply, there is no steady-state component of the phase current, and its waveform differs greatly from the sinusoidal waveform, so it is necessary to find a suitable method to analyze its discharge process and to control its discharge process. In paper [10], the relationship between the projectile exit velocity and the flat-top discharge current when using a supercapacitor as a power source for a rail gun was studied, while the relationship between the projectile velocity and the discharge current control has not been studied in a system using ACPA as a power source.
Self-excitation Module
field
Field-Initiation Module
Air-core Pulsed Alternator
Discharge Module
Railgun
Fig. 1. Structure diagram of rail gun system based on ACPA
The waveforms of load current and armature winding phase current during its discharge stage without control are shown in Fig. 2. The Fig. 2 shows that when the projectile is already very close to the muzzle, the next phase will still be conducted, at this time, the current of the next phase will only have small increase on the projectile discharge speed, but will greatly increase the muzzle current. The arc suppression device of the striking arc rail gun was studied in paper [11]. Figure 3a and b show the velocity of projectile and the muzzle current for conducting different phases. Therefore, it is necessary to control the conduction phase before discharging the projectile, and this also leads to the velocity control method of the railgun controlled by pulse wave number.
2 Single-Phase Short-Circuit Discharge In order to obtain the transient characteristics of the ACPA better, the law of superconducting circuit excitation conservation is directly used to analyze, ignoring the influence
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Fig. 2. Discharge current of ACPA without control
(a) Railgun armature current.
(b) Railgun discharge speed.
Fig. 3. ACPA discharge with control.
of eddy current effect. The interaction of only one armature winding with the excitation winding during a sudden single-phase short circuit can be obtained as follows: isa = iF0 MaF cos(θ0 )/La − iF MaF cos(ωt + θ0 )/La
(1)
iF = iF0 − isa MaF cos(ωt + θ0 )/LF
(2)
The phase and excitation current and adding a time constant correction are solved as: isa = −
iF =
iF0 MaF (cos(ωt + θ0 ) − cos θ0 ) La (1 −
2 cos2 (ωt+θ ) MaF 0 ) La LF
2 cos(ωt+θ ) cos θ MaF 0 0 ) −t La LF e tF 2 cos2 (ωt+θ ) MaF 0 1− La LF
iF0 (1 +
t
e − ta
(3)
(4)
where, iF0 is the initial value of the excitation current during a sudden short circuit, θ 0 is the electric angle between the excitation winding axis and the phase winding axis, L a is the phase winding self-inductance, L F is the excitation winding self-inductance, and maF is the amplitude of the armature winding and excitation winding mutual inductance. T a is the armature winding time constant, and t F is the excitation winding time constant.
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(a) phase current.
(b) excitation current.
Fig. 4. Single-phase short-circuit discharge phase current
The comparison between the analyzed and simulated waveforms of the excitation current and phase current when θ 0 is taken as 90° is shown in Fig. 4(a) and (b). The analytic equation shows that after 0.639 ms, the excitation current reaches the peak value of 49.73 kA, which is 2.44% error in time and 0.5% error in amplitude from the 0.655 ms in the simulation analysis, which reaches the peak value of 49.98 kA. The theoretical waveform of the excitation current and the simulated waveform are not only very small errors in amplitude and time to reach amplitude, but also are very accurate throughout the half-wave process. The analytical formula of short-circuit phase current shows that the current reaches the peak value of 523.61 kA after 0.641 ms, and the simulation analysis shows that the current reaches the peak value of 528.03 kA after 0.655 ms, with a time error of 2.14% and a magnitude error of 0.844%. Compared with the traditional analytic transient process of sudden short circuit of synchronous motor, the single-phase short circuit of ACPA is no longer sinusoidal variation, its single-phase short circuit phase current and its tangent slope are shown in Fig. 5. It can be seen that after the current reaches the peak, the slope of its current drop changes very little and can be approximated as a straight line drop.
Fig. 5. Single-phase short-circuit discharge current and its tangent slop
3 Discharge with Inductive Load During the discharge stage, in order to get the discharge current closer to the ideal trapezoidal wave, the thyristor is selected to trigger sequentially in a phase-controlled
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rectification manner. As can be seen from the formula (3), when the trigger angle is less than 90°, there will be a DC component, and the larger the amplitude of phase current, the fewer number of pulses that can be output to the railgun at the same discharge speed. In order to get the discharge current closer to the ideal trapezoidal wave, and to get the largest possible speed on the same length of railgun, the trigger angle of the thyristor is chosen to be 90°. As the value of the initial line inductance of the railgun is close to the phase inductance of ACPA, so the initial discharge cannot be treated as a short circuit discharge, can be simplified as a discharge with a constant inductive load, so it’s single-phase discharge current is modified as follows: isa = −
iF0 MaF cos(ωt + θ0 ) (La + L0 )(1 −
iF =
2 MaF
cos(ωt+θ0 ) ) La +LF
iF0 1−
(a) phase current .
2 MaF
t
cos2 (ωt+θ0 )
e
e − ta
− tt
F
(5)
(6)
(La +L0 )LF
(b) excitation current.
Fig. 6. Single-phase discharge phase current with inductive load
As can be seen in Fig. 6(a) and (b), the current amplitude of single-phase discharge decreases from 528.03 kA to 413.86 kA due to the initial inductance, and the discharge time remains unchanged, and the analyzed waveform still matches well with the simulated waveform at this condition. Where the maximum value of the phase current can be approximated as being at the midpoint of the discharge interval and the expression is as follows: isa max =
if 0 Maf M2 La 1 − (La +Laf0 )Lf
(7)
During the discharge process, there is a serious phenomenon of overlapping commutation, which is mainly affected by the mutual inductance between the stator and rotor and the mutual inductance between the stator phases. Due to the large mutual inductance between two adjacent phases in the seven-phase ACPA and the mutual inductance of other phases is very small, only the mutual inductance between two adjacent phases is considered. When the second phase starts conduction, according to the law of superconducting
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circuit excitation conservation, the following equation can be obtained: isa (La + L0 ) + isb (Mab + L0 ) − ifMaF sin(ωt) = isa1 (La + L0 ) − if1 MaF sin( 2π = isa1 (Mab + L0 ) isa (Mab + L0 ) + isb (La + L0 ) − ifMaF sin ωt − 7 2π isa1 sin 7 MaF isb sin ωt − 2π isa sin(ωt)MaF 7 MaF + + iF = iF1 − LF LF LF The two-phase currents are solved and corrected for the time constants as: iF2 MaF k3 sin(ωt) − k2 sin ωt − 2π − k2 c1 + k3 c2 − (t−t0 ) 7 isa = e ta 2 k1 k3 − k2 (t−t ) iF2 Maf k1 sin ωt − 2π 7 − k2 sin(ωt) + k1 c1 − k2 c2 − ta 0 e isb = 2 k1 k3 − k2
2π ) 7 (8) (9) (10)
(11) (12)
Among them: 2 k1 = La + L0 − MaF sin2 (ωt)/LF 2 2 k2 = Mab + L0 − MaF sin(ωt) sin ωt − π /LF 7 2 2 sin2 ωt − π /LF k3 = La + L0 − MaF 7
(14)
c1 = isa1 (Mab + L0 )
(16)
c2 = isa1 (La + L0 ) − iF1 MaF sin
2 π 7
(13)
(15)
(17)
The analyzed and simulated waveforms of the two phase currents are shown in Fig. 7, where the analyzed peak value of the first phase discharge current is reduced from 405.19 kA to 327.05 kA, and the peak value of the second phase discharge increases to 548.24 kA. The first phase conducting time of the analyzed waveform is 1.049 ms and the second phase conducting time is 1.499 ms, while the first phase conducting time of the simulated waveform is 1.043 ms and the second phase conducting time is 1.402 ms, within 7% error. This leads to the following characteristics of the 7-phase ACPA commutation overlap process. (1) When the second phase is conducting, due to the first phase to the second phase of the auxiliary magnetic effect, the second phase current exists non-periodic component, the current amplitude increases, and the conducting time becomes longer. (2) Due to the additional magnetic field added to the first phase winding by the second phase current, the first phase of the current amplitude decreases, and early over zero, the conducting time decreases. (3) After the first phase current crosses zero, the interaction between the second phase current and the excitation winding is the same as the single-phase discharge process.
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Fig. 7. Two-phase discharge phase currents with inductive load
4 Speed Control The ideal discharge current of the rail gun is a trapezoidal wave, and its ideal situation during the descent should be a straight line. From the previous analysis, it can be concluded that the process of discharging the last phase alone under the neglect of the muzzle current can be considered as a straight line down for the current, and further approximated that the current has been a straight line down after conducting the last phase current. The relationship between the force on the armature and the current is as follows: F=
1 2 Li 2
(18)
Discharge current detection can be obtained through the discharge stage at any moment, to obtain the armature force, assuming that the armature force from the last phase of conduction is also a straight line down. Due to F ∝ i2 , in the premise that the current is approximately a straight line down, the predicted speed should be corrected as follows: v = v0 +
1 L i02 t0 6 m
(19)
During the discharge process, when the number of conducted phases is greater than or equal to 10, the current in the last phase before the projectile is discharged will first decrease and then increase, as shown in Fig. 8. This is because when the current is not yet reduced to 0, the voltage of the phase is again greater than the load voltage, resulting in the thyristor not shutting down. A solution is proposed here to ensure that the thyristor of the last phase is shut down, and its circuit is shown in Fig. 9. The improved discharge current waveform is shown in Fig. 10, the last phase current can be guaranteed to be over zero, so that the phase thyristor shutdown, because the improved circuit cannot guarantee that the last phase current is over zero and make the load current over zero, so in the premise of making the phase current over zero, the load
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Fig. 8. Conducting 10 pulse-wave railgun armature currents
field
Diversion Branch
Fig. 9. Improved discharge circuit
current due to the reduction of the equivalent impedance of the renewal circuit, its current slightly increased, resulting in the muzzle current may still exist when discharging, compared with the muzzle current before the improvement it is greatly improved. The comparison of the muzzle current before the improvement and the improved muzzle current is shown in Table 1. After the velocity prediction pulse control, the predicted velocity corresponding to the number of pulse waves and the simulated velocity are shown in Table 2. The muzzle current below the output of 15 pulse waves is less than 200 kA, and the velocity of the projectile at the output of 9 pulse waves has reached the design requirement. Using the velocity prediction pulse control can effectively predict the discharge velocity of the projectile under the corresponding number of pulse waves. From the 13th pulse wave to 15th wave, the discharge velocity of the projectile does not have an obvious increase, but the muzzle current increases rapidly. From Eqs. (11) and (12), it can be seen that the phase currents in the two-phase commutation overlap process and the single-phase discharge process are proportional
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Table 1. Previous muzzle current and Improved muzzle current Pulse numbers
Previous muzzle current/kA
Improved muzzle current/kA
8
0
0
9
0
0
10
182.4
0.62
11
89.77
3.35
12
38.28
13.32
13
81.54
42.41
14
175.5
88.69
Fig. 10. Improvement of phase current and output current of air core pulse generator
to the initial value of the excitation current at the initial moment of discharge, so the total discharge current is proportional to the excitation current. In the case of the same number of phases of conduction and there is no muzzle current, the discharge current is proportional to the initial value of the excitation current, and it can be obtained that the final discharge velocity of the projectile is proportional to the square of the initial value of the excitation current. Given an excitation current of 40 kA and a discharge velocity of 2180 m/s as the reference value, the projectile discharge velocity is shown in the Table 3, and the error of the theoretical discharge velocity is within 5% of the simulated discharge velocity.
5 Conclusion In this paper, we analyze the discharge process of a seven-phase ACPA, derive the analytical expression of single-phase short-circuit discharge from the conservation of magnetic chain of superconducting loop, and extend it to the analytical expression of single-phase and two-phase discharge with inductive load and analyze the overlapping
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Pulse numbers
Predicted speed/(m/s)
Simulation speed/(m/s)
Error/%
2
322.2
341.7
5.707
3
649.6
652.8
0.490
4
989.9
982.1
0.794
5
1300.1
1287.3
0.994
6
1568.5
1557.6
0.700
7
1793.6
1789.4
0.235
8
1984.3
1987.5
0.161
9
2118.0
2179.4
2.87
10
2289.6
2320.4
1.327
11
2414.3
2438.2
0.980
12
2523.7
2550.1
1.035
13
2621.4
2649.4
1.057
14
2708.1
2731.5
0.857
15
2786.4
2781.6
0.173
Table 3. Relationship between excitation current and railgun discharge velocity Excitation current/kA
Theoretical Discharge Speed/(m/s)
Simulation of discharging speed/(m/s)
Error/%
36
1766
1855
4.798
38
1967
2038
3.484
42
2403
2382
0.882
process of two-phase discharge commutation, which is verified by simulation. The theoretical waveform is in high agreement with the simulated waveform. Through the derived single-phase discharge analytical find that the current drop process can be approximated as a straight line drop, which leads to a new method of predictive control of railgun speed. The predictive control is found to have high accuracy through comparison simulation and analysis, and the muzzle current at the discharge of the projectile can be reduced by controlling the number of pulse waves of the conduction. The relationship between the excitation current and the projectile discharge velocity is also analyzed, which provides a theoretical basis for the continuous velocity control of the rail gun system powered by a ACPA. Acknowledgments. This research is supported by the National Natural Science Foundation of China 52007072, and the Interdisciplinary program of Wuhan National High Magnetic Field Center (WHMFC 202110).
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References 1. Miller, T.J.E., Hughes, A.: Comparative design and performance analysis of air-cored and ironcored synchronous machines. Proceedings of the Institution of Electrical Engineers 124(2), 127–132 (1977) 2. Yu, K., Bao, Z., Xie, X.: "Structural design and process technology of a seven-phase air-core pulsed alternator, In: " 2021 IEEE 2nd China International Youth Conference on Electrical Engineering (CIYCEE), pp. 1–7 (2021). doi: https://doi.org/10.1109/CIYCEE53554.2021. 9676807 3. Wu, S., Huang, X., He, L., Cui, S., Zhao, W.: Mechanical strength analysis of pulsed alternator air-core rotor. IEEE Trans. Plasma Sci. 47(5), 2387–2392 (2019). https://doi.org/10.1109/ TPS.2019.2891300 4. Xie, X., Yu, K., Ye, C., Tang, L., Zhang, H.: Transient analysis of air-core pulsed alternators in self-excitation mode. IEEE Trans. Plasma Sci. 43(5), 1415–1420 (2015). https://doi.org/ 10.1109/TPS.2015.2416371 5. Yu, K., Ding, J., Xie, X., Guo, S., Bao, Z.: Analysis and preliminary experimental research of a multiphase air-core pulsed alternator. IEEE Transactions on Transportation Electrification 7(4), 2551–2561 (2021). https://doi.org/10.1109/TTE.2021.3071383 6. Yu, K., et al.: Loss analysis of air-core pulsed alternator driving an ideal electromagnetic railgun. IEEE Transactions on Transportation Electrification 7(3), 1589–1599 (2021). https:// doi.org/10.1109/TTE.2021.3051630 7. Ye, C., Yu, K., Zhang, H., Yuan, P., Xin, Q., Sun, J.: Comparison between self-excitation and pulse-excitation in air-core pulsed alternator systems. IEEE Trans. Plasma Sci. 41(5), 1243–1246 (2013) 8. Pratap, S.B., Driga, M.D.: Compensation in pulsed alternators. IEEE Trans. Magn. 35(1), 372–377 (1999). https://doi.org/10.1109/20.738434 9. Wang, S., Wu, S., Cui, S.: Analytical expression for discharge process of multiphase air-core pulsed alternators. IEEE Trans. Plasma Sci. 44(12), 3330–3336 (2016). https://doi.org/10. 1109/TPS.2016.2628087 10. Zhang, H., Cheng, G., Guo, W., Su, Z., Zhang, T., Yang, Y.: Calculating timing sequence of capacitor-based railgun with given muzzle velocity. IEEE Trans. Plasma Sci. 43(9), 3298– 3303 (2015). https://doi.org/10.1109/TPS.2015.2464319 11. Ge, X., et al.: Analysis and research on muzzle arc suppression device of arc striking railgun. IEEE Trans. Plasma Sci. 50(5), 1337–1344 (2022). https://doi.org/10.1109/TPS.2022.316 3265
Optimal Dispatch Strategy of a Flexible Energy Aggregator Considering Virtual Energy Storage Zeyu Liang1 , Zhengzheng Ge5 , Sheng Chen1 , Haohui Ding2 , Yiheng Liang3,4 , and Qinran Hu2(B) 1 College of Energy and Electrical Engineering, Ho Hai University, Nanjing 210098, China 2 School of Electrical Engineering, Southeast University, Nanjing 210098, China
[email protected]
3 NARI Group Corporation(State Grid Electric Power Research Institute), Nanjing 211106,
China 4 NARI Technology Co., Ltd., Nanjing 211106, China 5 School of Electrical and Automation Engineering, Nanjing Normal University,
Nanjing 210033, China
Abstract. As distributed energy resources continue to be connected to the grid, the supply side and demand side of the power system are becoming increasingly uncertain in both directions. At the same time, many flexible loads have emerged. We can take advantage of their adjustable characteristics, which can be considered virtual storage to cut peaks and fill valleys for the grid. Data centers and buildings are gradually becoming a hot topic in recent years due to their substantial annual energy consumption. In this paper, we considered a flexible energy aggregator considering virtual energy storage. The cold energy from the data center and the heat energy from the ground source heat pump system(GSHP), i.e., the building, are incorporated as broad energy storage to participate in the aggregator’s dispatch. In this case, the data center(DC) and GSHP hybrid systems have outstanding performance. Then, a two-stage optimal scheduling strategy was used to minimize total cost, which includes day-ahead cost and real-time cost and determine appropriate real-time temperatures for data centers and buildings. We performed a detailed numerical comparison to prove the economy and validity of the proposed model. Keywords: Data center · Elastic energy aggregator · Virtual energy storage
1 Introduction As the power output of various distributed resources in the grid continues to increase, the uncertainty between the demand and supply side of the grid leads to increasing difficulty in achieving the stable operation of the grid [1]. In particular, high proportion of renewable energy penetration has brought great uncertainty for dispatch strategy. Therefore, solving the uncertainty caused by renewable energy access to the power grid has become a hot issue in current research [2]. Due to the thermal characteristics of the building and data center, providing it with heat and cooling is considered an elastic load, which significantly benefits the grid’s © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 536–546, 2023. https://doi.org/10.1007/978-981-99-1027-4_55
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stable operation. Some data show that in 2016, the total residential energy use in Canada was 1458 PJ [3], of which 60% was used for space heating and cooling applications. This energy used for cooling and heating is mainly provided by energy-inefficient equipment such as electric boilers and air conditioning, which not only increases the cost of electricity for users and the burden on grid companies but harms the low-carbon operation of the social environment [4]. In this case, using ground source heat pumps will become the future market trend. As a kind of flexible load, data centers consume a large amount of electric power, which has reached 100 billion kW·h [5]. The high energy consumption of data centers not only directly restricts the expansion of their scale [6] but also endangers the safe operation of the grid due to the uncertainty it brings to the load side. Therefore, better utilization of power is a critical point for data centers. Some research results in recent years have shown that data centers can collaborate with the grid for load shifting to cut peaks and fill valleys [7]. It is well known that energy storage is an effective way to improve grid operation stability [8]. Generalized energy storage, as an expansion of conventional energy storage, refers to the characteristics of flexible load changing with the kinetic and thermal energy of a specific carrier and exhibits the same energy absorption and release characteristics. During peak and valley periods, they can be matched with conventional energy storage to mitigate the risk brought by the uncertainty of renewable energy effectively [9]. Grid operation models considering generalized energy storage are becoming a hot research direction. The grid operation model proposed in [10] considering electric vehicles as virtual electric energy storage and residential houses as thermal energy storage is proved more economical than an operation method using traditional energy storage. Moreover, the model in [11] proved the economic effectiveness of the battery-supercapacitor hybrid energy storage system. Reference [12] builds a power grid model in which residential electricity consumption is used as a micro-battery and proves its robustness. To better promote aggregators’ benign and stable operation, this paper proposes a flexible energy aggregator considering virtual energy storage. The proposed model considers the energy use characteristics of data centers and building residents to reduce the cost of purchasing electric energy. We incorporate the temperature and energy consumption of buildings and data centers into a plannable category, taking the minimum cost of purchasing electricity as the objective function. Furthermore, we demonstrate the economic efficiency of the proposed hybrid operation model through arithmetic examples.
2 Model 2.1 Data Center Model 2.2 Flexible Scheduling Model of Data Load in Data Center The real-time data load requirements can be divided into interactive and batch [13]. An interactive data load that typical application scenarios include data query needs to be processed in time after it arrives at the server; Batch data load, which typical application scenarios include batch computing, has low real-time requirements.
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Average queuing delay and average processing delay of data load are two significant factors affecting the quality of service. The relationship between data center storage loads and the factors are shown as follows: St = St−1 + 0 ≤ St ≤ S
Nk
dk,γ ,t − Stde
k=1 max
(1)
St max = 0 1
q
Tt = N k q Tt
+ Tth
k=1 Rk,t − dc,t < Ttmax
(2)
where: k represents the type of server, γ represents the type of data load; Nk represents the number of data center server categories. dk,γ ,t represents type γ data load to be processed by type k server of the data center. St is the batch data load stored by the data center, and the last time point, Stde is the batch data load calculated, and S max is q the maximum data load that can be stored by the data center; Tt and Tth are the average queuing delay and the average processing delay of data load, Tth has little change under normal circumstances, Rk,t represents the computing capacity that type k server can provide of data center, and Ttmax is the maximum delay time of data load. 2.3 Data Center Power Consumption Model Based on DVFS Technology Power consumption of data centers can be divided into three categories: power consumption of IT equipment, power consumption of refrigeration equipment, and power consumption of internal equipment (such as lighting), as is shown below: PtDC = PtIT + PtCO + PtL
(3)
where: PtDC is the power consumption of the data center, PtIT is the power consumption of IT equipment, PtCO is the power consumption of cooling equipment, and PtL is the power consumption of internal equipment in the data center. According to DVFS technology, the operating voltage of the CPU is related to its working frequency and data load to be processed. The power consumption of IT equipment in the data center can be expressed as: PtIT =
Nk
server Mi × Pk,t
k=1
(4)
fix
server CPU Pk,t = Pk,t + Pk,t CPU CPU 2 = C1 × (Fk,t ) × dk,t Pk,t
CPU = Fk,t
Ns s=1
fk,s × ak,s,t
(5)
(6)
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ak,s,t = 1, ak,s,t ∈ {0, 1}
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(7)
s=1
dt =
Nk
dk,t × Mi
(8)
k=1 server is the active where: Mi represents the number of each type of servers in data center. Pk,t fix
CPU are the fixed power consumption power consumed by each Type k server. Pk,t and Pk,t and CPU power consumption of type k servers respectively. C1 represents the power represents data load to be processed by type consumption coefficient of the server; dk,t CPU k servers in data center; Fk,t is the working frequency of class k servers of the data center; ak,s,t represents the s-block working frequency flag bit of k-type server CPU of data center; fk,s indicates the s-block working frequency of the k-type server CPU in the data center. dk,γ ,t indicates the data load of class γ that needs to be processed by class k servers in the data center. The computing resources provided by dc servers are related to the service efficiency of servers and the number of servers, as follows:
Rk,t = uk,t Mi CPU uk,t = C2 Fk,t
0.9Rk,t ≥
Nγ
dk,γ ,t
(9)
(10)
γ =1
where: C2 is the computing efficiency coefficient of the server, and uk,t represents the computing capacity provided by a single server of class K in time period t of the data center. 2.4 Data Center Model Based on the First Law of Thermodynamics The PUE value of data center is the ratio of all equipment power consumption and computing power consumption in the center, which can be expressed as follows: IT CO L IT PUEDC = (Pc,t + Pc,t + Pc,t )/Pc,t
(11)
The model of data center that embodies the thermal inertia is modeled as reference [7] represents. 2.5 Residential Building Model The relationship between GSHP input power and output heat/heat is: Qth = COP HP Pth Qtc = EERHP Ptc
(12)
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where: Qth and Qtc are the heat and cooling output of GSHP to the building, Pth and Ptc are the electricity input to the ground source heat pump for heating and cooling, and COP HP and EERHP are the heating and cooling efficiency coefficients of the ground source heat pump. The relationship between building room temperature and time can be modeled as reference [8] represents. 2.6 Demand-Side and Supply-Side Equilibrium Equations In order to match the power input and output balance of an aggregator, the following relationships must be satisfied. PtGSHP + PtDC = Ptsub + (PtPV − Ptcut ) − Ptch + Ptdis PtGSHP = Ptc + Ptres + Pth
(13)
where: PtGSHP represents the sum of electric power the building consumes; PtDC represents the total power consumption of the data center; Ptsub is electricity purchase from superior power grid; PtPV represents real-time photovoltaic output; Ptcut represents the PV power shaving. 2.7 Generalized Energy Storage Model 2.8 Battery Storage The relationship between battery power and time can be expressed as follows: 0 ≤ Ptch ≤ utch Ptch max 0 ≤ Ptdis ≤ utdis Ptdis max
(14)
utdis + utch ≤ 1
(15)
Et+1 = κEt + Ptch ηch − Ptdis /ηdis
(16)
Emin ≤ Et ≤ Emax
(17)
where: t stands for time interval; Ptch and Ptdis respectively represent the charge and discharge power of energy storage; P ch max and P dis max are respectively the maximum charging and discharging power of energy storage; utch and utdis are respectively the state of charge and discharge of energy storage; Et is energy storage; κ is the selfdischarge coefficient of energy storage; ηch and ηdis respectively represent the charge and discharge efficiency of energy storage; Emin and Emax respectively represent the minimum and maximum energy storage.
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2.9 Virtual Energy Storage In this paper, we only consider a typical winter day with a minimum temperature of − 10 °C and a maximum temperature of 5 °C [13]. The virtual energy storage in data centers and residential buildings, although both are temperature dependent, behave differently. The data center stores cold energy while the building stores heat energy, and its virtual energy storage model is shown below. EtDC = H DC ∗ (T DC max − TtDC ) EtGSHP = H B ∗ (TtB − T B min )
(18)
where: EtGSHP represents the virtual energy storage of the building, EtDC represents the virtual energy storage of the data center, T DC max represents the maximum temperature allowed in the data center, and T B min represents the minimum temperature allowed in the building. 2.10 Aggregator Objective Function Aggregator operation takes the minimum cost as the objective function and consists of day-ahead cost and real-time cost [14], as shown in the following equation. ⎧ t max t max ⎪ ⎪ ess ch dis pv ⎪ C × (P + P ) + C × PtPvcut ⎪ t t ⎪ t max ⎨ t=1 t=1 Ctotal = Ct × Psubt + t max t max ⎪ ⎪ temp−dw temp−up t=1 ⎪ temp−dw temp−up ⎪ C × (T ) + C × (Tt ) ⎪ t ⎩ day - ahead cost t=1 t=1 real - time cost
(19) where: Ctotal represents the total cost of the aggregator, which is also the objective function of the optimal operation, Ctt represents the real-time price of electricity, C ess represents the cost of battery charging and discharging, C pvcut represents the penalty for PV power removal, C tempup represents the penalty for the upward adjustment of the building room temperature, and C tempdw represents the penalty for the downward adjusttemp−up temp−down ment of the building room temperature, Tt and Tt denote the upward and downward adjustment of temperature, respectively.
3 Case Study The rated capacity of PV in this model is 0.4MW, 10 PV output scenarios are considered, and stochastic optimization is performed. The reduction cost of PV is 0.95(Yuan/kW·h), the rated capacity of chemical energy storage is 0.1MW, the upper and lower limits of its charge state are 90% and 10% respectively [15], and the charging and discharging cost of energy storage is 0.05(Yuan/kW·h).The specific parameters of the data center model are shown in Table 1 [1].
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The specific heat capacity of building is 4 (°C/kW·h) and the specific heat capacity of the building walls is 0.64 (°C/kW·h). The heat exchange coefficient between the building and the outside world is 24, and the heat exchange coefficient between the walls and the outside world is 0.46[2]. Table 1. Data center parameters Parameter
Numerical value Server type 1
Server type 2
Data center CPU rated frequency
0.6/2.0/3.0
1.0/2.2/3.4
Server fixed power consumption
0.053(units/KW)
0.068(units/KW)
Number of data center servers
512
512
CPU power factor
0.0013
0.0011
CPU computing efficiency factor
5
5
The PUE value of data center
1.2
Maximum data load storage capacity
10^9
The specific heat capacity of data center
2
The aggregator operation example shown in Fig. 1 is used to verify the economy and safety of the proposed model, which is solved based on the CPLEX solver under GAMS. Virtual energy storages PV output
Heat exchange
Buildings
Power purchase
Discharge Data center
Charge
Fig. 1. Topology diagram of Aggregator
3.1 Comparison of Power Purchase, PV Output Curve and Load Curve The intermittent power consumption of PV is crucial to the safe operation of the grid. The comparison of aggregator power purchase, the load of the grid, and PV power output are shown in Fig. 2, from which it can be seen that the power issued by PV at peak hours has exceeded 60% of the load. In the proposed model, the PV power removal is 0 kW·h, and the Photovoltaic consumption rate is 100%, which essentially reduces the amount of power purchased by the aggregator from the up grid during time 9–17.
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100
100
50 0
4
8
12
16
20
24
Load and PV output(KWH)
Electricity purchase (KWH)
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543
0
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Fig. 2. Comparison of aggregator power purchase, load of grid and PV output
3.2 Thermal Characteristics and Power Consumption of Data Centers and Buildings Under Different Operation Models It is generally believed that there are two strategies to control the temperature of data centers and buildings. Plan A: The temperature of the data center and the building is within a comfortable temperature range. For residential buildings, considering the difference between working hours and non-working hours, the difference between the upper and lower temperature limits of the temperature interval is more minor than the standard at work during nonworking hours, which is also residential home time. Plan B: Data center and building temperatures are constant and do not change over time, reducing the difficulty of optimal scheduling for optimal power system operation. The variation of data center and building temperatures with time for the two specific scenarios is shown in Fig. 3. In Plan A, data centers and buildings tend to purchase large amounts of electricity when the electricity price is relatively low, and they store thermal energy. In Plan B, the aggregator purchases large amounts of electricity at each moment to meet the temperature requirements of this period. In Plan B, the aggregator purchases large amounts of power at each hour to meet the temperature requirements of the hour, such as 12–14 noon and 6–8 p.m. This not only increases the operating costs of the data center and the building but also increases the operational burden and risk of the grid. Similarly, it can be seen in Fig. 4 that if data centers and buildings choose Plan B, it is also not conducive to consuming the power emitted from distributed power sources such as PV, which may result in the phenomenon of removing a large amount of power emitted from PV, causing more significant losses to the operation of the grid. 3.3 Hourly SOC of Virtual Energy Storage The aggregator energy storage in this example can be divided into two categories: traditional chemical energy storage and virtual energy storage of data centers and buildings. Compared with chemical energy storage, virtual energy storage is not only more flexible, not limited by specific equipment, and more environmentally friendly. When PV increases in the morning and noon, to entirely consume PV output power, all kinds of energy storage will enter the state of absorbing energy at this time. After entering the
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Temperature(°C)
Building temperature limit 25 24 23 22 21 20 19 18 17 2 4 6 a)
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Data center temperature
Temperature(°C)
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b)
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40 20 0 -20
4
8
12 time (h)
16
20
24
0.5
0.4
-40
Electricity price(yuan)
Data Center Power Consumption (KWH)
Fig. 3. Temperature variation over time in data centers and buildings
-60 0.3
-80
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Electricity price
0.8
20
0.7
15 10
0.6
5 0.5
0 -5
4
8
12 16 time (h)
-10 -15
(b)
20
24
Electricity price(yuan)
Building Power (KWH)
25
0.4 0.3
Fig. 4. Difference in power consumption between data centers and buildings under different operating modes
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Energy Storage (KWH)
100 80 60 40 20 0
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evening hours, energy storage will gradually release the absorbed heat to reduce the power purchase from the higher power grid and better achieve the effect of peak shaving and valley filling. The change of various energy storage with time is shown in Fig. 5.
4 Conclusion This paper presents a flexible energy aggregator considering virtual energy storage for aggregators’ economic and stable operation with data centers and residential buildings. Detailed modeling is carried out for various distributed resources inside the aggregator, including batteries, data centers, and buildings. In this paper, we establish a data center model considering multiple data loads, i.e., in some cases, the data load can be considered a flexible load, and the thermal characteristics of the data center are also considered based on the first law of thermodynamics. For the model of the building, this paper considers the influence of various factors on its temperature, including external solar radiation, heat exchange with the building walls and facade, and so all. It simulates the relationship between the temperature of the actual building and the temperature of the external environment, and the output heat and cooling capacity of the ground source heat pump. Meanwhile, the cost of power purchase is the day-ahead cost, the excision penalty of PV power, and the charging and discharging cost of the battery are the real-time cost, and the objective function is the minimum total cost, i.e., the sum of the day-ahead cost and the real-time cost. Therefore, the model proposed in this paper is expected to provide a good idea for the economical and efficient operation of the grid. However, some aspects are not well thought out in this paper. We ignore the impact of many complex processes on the model, such as the spatially tunable characteristics of data loads in multiple data centers and the cooling and heating coefficients of ground source heat pumps in buildings concerning room temperature variations, which would improve energy use efficiency. Acknowledgments. This work is supported by Key Research and Development Program of Jiangsu Province, China (BE2020081–2).
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References 1. Cui, H.T., Li, F.X., Hu, Q.R., et al.: Day-ahead coordinated operation of utility-scale electricity and natural gas networks considering demand response based virtual power plants. Appl. Energy 176, 183–195 (2016) 2. Xu, Y., Hu, Q.R., Li, F.X.: Probabilistic model of payment cost minimization considering wind power and its uncertainty. IEEE Trans. Sustain. Energy 4(3), 716–724 (2013) 3. Peralta, D., Canizares, C.A., Bhattacharya, K.: Ground source heat pump modeling, operation, and participation in electricity markets. IEEE Trans. Smart Grid. 13(2), 1126–1138 (2022) 4. Radovanovic, A., Koningstein, R., Schneider, I., et al.: Carbon-aware computing for datacenters. IEEE Trans. Power Syst. 1–1 (2022) 5. Rao, L., Liu, X., Xie, L., et al.: Hedging against uncertainty: a tale of internet data center operations under smart grid environment. IEEE Trans. Smart Grid 2(3), 555–563 (2011) 6. Zhang, Y.W., Wang, Y.F., Wang, X.R., et al.: Capping the electricity cost of cloud-scale data centers with impacts on power markets. In: 20th international symposium on high performance distributed computing 271–272 (2011) 7. Wang, H., Huang, J.W., Lin, X.J., et al.: Proactive demand response for data centers: a win-win solution. IEEE Trans. Smart Grid 7(3), 1584–1596 (2016) 8. Huang, W.J., Zhang, X., Li, K.P., et al.: Resilience oriented planning of urban multi-energy systems with generalized energy storage sources. IEEE Trans. Power Syst. 37(4), 2906–2918 (2022) 9. Huang, W.J., Zhang, N., Yang, J.W., et al.: Optimal Configuration Planning of Multi-Energy Systems Considering Distributed Renewable Energy. IEEE Transactions on Smart Grid. 10(2), 1452–1464 (2019) 10. Zhu, X., Yang, J., Liu, Y., et al.: Optimal Scheduling Method for a Regional Integrated Energy System Considering Joint Virtual Energy Storage. IEEE Access. 7, 138260–138272 (2019) 11. Jing, W.L., Lai, C.H., Wong, S.H.W., et al.: Battery-supercapacitor hybrid energy storage system in standalone DC microgrids: a review. IET Renew. Power Gener. 11(4), 461–469 (2017) 12. Werth, A., Kitamura, N., Tanaka, K.: Conceptual study for open energy systems: distributed energy network using interconnected DC nanogrids. IEEE Trans. Smart Grid 6(4), 1621–1630 (2015) 13. Ding, H.H., Hu, Q.R., Hou, K., et al.: The coordinated operation of dual batteries energy storage system for cold areas. Energy Rep. 7, 84–91 (2021) 14. Ge, P.D., Hu, Q.R., Wu, Q.W., et al.: Increasing operational flexibility of integrated energy systems by introducing power to hydrogen. IET Renew. Power Gener. 14(3), 372–380 (2020) 15. Chen, T., Cui, Q.S., Gao, C.W., et al.: Optimal demand response strategy of commercial building-based virtual power plant using reinforcement learning. IET Gener. Transm. Distrib. 15(16), 2309–2318 (2021)
State of Charge Estimation of Lithium-Ion Battery Based on EKF with Adaptive Fading Factor Na Li1 , Xusheng Yang1 , Shuangle Liao1 , Guangjun Liu2(B) , Shuai Cheng3 , Kai Kang3 , Yufeng Xia3 , Nian Shi3 , and Chaochong Pan4 1 Comprehensive Energy of State Grid Integrated Energy Service Group Co., LTD, Wuhan,
China 2 Xiangyang Industrial Institute of Hubei University of Technology, Wuhan, China
[email protected]
3 Hubei Electric Power Survey and Design Institute Co., LTD, Wuhan, China 4 Intelligent Energy Research Center, University of Science and Technology, Beijing, China
Abstract. The power generation system with renewable energy supply is susceptible to the influence of external environment. Lithium battery and other energy storage devices need to be added in the new energy field to smooth the output of renewable energy generation system and improve the stability of the integrated system. Accurately estimating the state of charge (SOC) of energy storage batteries can effectively improve the use and reasonable scheduling of batteries. This paper takes ternary lithium battery pack as the research object and builds a second-order RC equivalent circuit model to estimate the SOC. According to the time-varying characteristics of battery model parameters, recursive least square method with forgetting factor was used to identify the parameters, the model parameters are modified using the current data. To solve the problem of accumulated error of extended Kalman filter (EKF) algorithm, an adaptive fading factor was introduced to correct prediction error covariance matrix and suppress the influence of historical data on the current state. Matlab simulation and dynamic stress testing experiments show that, compared with EKF algorithm, the adaptive fading EKF (AFEKF) algorithm has higher accuracy. Keywords: State of Charge · Recursive Least Square Method · Error Covariance Matrix · Adaptive Fading Factor
1 Introduction With the continuous progress of strategic goal of ‘carbon peak and carbon neutrality’, increasing the proportion of photovoltaic and wind power generation and the other renewable energy systems in the power grid is an important measure, and the installed capacity of renewable energy continues to increase. Due to the inherent uncertainty and low inertia of distributed photovoltaic and other renewable energy sources, coupled with the off-peak output of load, it brings great challenges to the frequency stability of power © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 547–557, 2023. https://doi.org/10.1007/978-981-99-1027-4_56
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system and the consumption of renewable energy sources [1, 2]. The energy storage system can be used to suppress power fluctuation and play the role of peak cutting and valley filling, which is an indispensable part of the new energy field to main source-load balance. Lithium-ion batteries are widely used in electric vehicles and energy storage systems due to their advantages of high energy density, high efficiency and long service life [3, 4]. Accurately estimating the SOC of energy storage batteries can effectively improve the battery life and the rationality of system scheduling. At present, the SOC estimation methods of Lithium-ion battery mainly include ampere-hour integration, open circuit voltage method, internal resistance method, neural network method and Kalman filter method. As early methods, ampere-hour integration method, open-circuit voltage method and internal method have low estimation accuracy [5]. Ampere-hour integral method has a high requirement on the initial value of the charged state, and the initial error will gradually accumulate with time, and the error will gradually increase. The open-circuit voltage method requires a long period of time to achieve equilibrium within the battery and is not suitable for on-line estimation of SOC. The use of internal resistance methods has been gradually reduced because of the need for specialized equipment and the susceptibility of impedance to temperature. Neural network method requires large data and high cost [6, 7]. This method not only requires a large number of data sets and a long time of training, but also depends on the accuracy of training data to a large extent. If the data amount or conditions are insufficient, the accuracy will be reduced and it is difficult to achieve. Kalman filter algorithm is widely used in linear systems and extended Kalman algorithm extends it to nonlinear systems. It is a mainstream direction of current research to estimate SOC using Kalman algorithm based on the state equation and observation equation of battery equivalent model [8, 9]. The principle of equivalent model is clear, the calculation is simple, and it is suitable for real-time system. At present, the estimation method based on equivalent model combined with Kalman filter has attracted a lot of scholars’ research. According with the above analysis, this paper constructed the second-order Thevenin equivalent model of lithium-ion battery. The parameters of the model were identified online by recursive least square method, and the SOC of lithium ion battery was estimated by AFEKF algorithm. The adaptive fading factor was introduced into Kalman filter algorithm to reduce the influence of historical data on filtering results. Finally, combined with the experimental results, the AFEKF algorithm is analyzed and compared to verify the superiority of the proposed algorithm.
2 Equivalent Model and Parameter Identification of Lithium-Ion Battery 2.1 Equivalent Circuit Model of Lithium-Ion Battery The battery model and parameter identification determine the accuracy of SOC estimation. Thevenin model is shown in Fig. 1. RC parallel network is used to characterize the polarization reaction in the battery, which reflects the nonlinear characteristics of the dynamic charge and discharge response of the battery to a certain extent. In order to simulate the battery polarization transition process and more accurately describe the
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polarization process and dynamic response behavior of lithium-ion battery, the secondorder Thevenin equivalent circuit model was adopted in the experiment, which can improve the accuracy of the model to a certain extent [10–12].
R0
+
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C1
C2
U1
_
+
Ib + _
U2
Ub
+ Uoc _
_
Fig. 1. Second-order Thevenin equivalent circuit model
Subsequent paragraphs, however, are indented. The equivalent model is shown in Fig. 1, where U oc is the open-circuit voltage and U b is the battery terminal voltage. U 1 and U 2 are polarization voltages; I b is battery load current, R0 is ohmic resistance; R1 and R2 are polarization resistors; C 1 and C 2 are polarization capacitors. According to Kirchhoff’s law, the second-order Thevenin model can be expressed as: U˙ 1 = − R11C1 U1 + C11 It U˙ 2 = − R21C2 U2 + C12 It Ub = Uoc − R0 It − U1 − U2
(1)
SOC is defined as the ratio of the remaining battery power to the actual capacity, which can be expressed by ampere-hour integral as follows: ηt St = S0 − Qc
t It dt
(2)
t0
where, η is the Coulomb efficiency coefficient, Qc is the standard capacity of the battery, and S 0 is the initial SOC of the battery pack. Combining Eq. (1), the battery state space equation in discrete form can be obtained as follows: ⎛
⎞
⎛
1
0
SOCk+1 ⎜ ⎟ ⎜ − τT1 ⎝ U1,k+1 ⎠ = ⎜ ⎝0 e U2,k+1 0 0
⎛
⎞ − ηT ⎛ ⎞ Qc
⎜ ⎟ w1,k ⎟ ⎜ SOCk ⎟ ⎜ R 1 − e− τT1 ⎟ ⎟ ⎜ 1 ⎟ × It,k + ⎜ 0 ⎟ ⎝ w2,k ⎠ ⎟ ⎠ × ⎝ U1,k ⎠ + ⎜
T ⎝ − U2,k w3,k −T ⎠ e τ2 R2 1 − e τ2 0
⎞
⎛
⎞
(3) The observation equation is as follows: Ut,k = Uoc (SOCk ) − U1,k − U2,k − R0 It,k + vk
(4)
where, T is the sampling time; w is process noise; v is measurement noise; τ1 and τ2 are T the time constants of the polarization loop; The state variable is SOCk , U1,k , U2,k , the control variable is It,k , and the observation variable is Ut,k .
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2.2 SOC-OCV Relationship Curve of Battery There is a nonlinear functional relationship between the open-circuit voltage (OCV) and SOC of the power battery [9, 10]. In order to obtain the OCV-SOC relation curve of battery, the constant current intermittent charge-discharge method was used for ternary lithium battery. The specific parameters of ternary lithium battery were as follows: standard capacity is 2.5Ah, charging cut-off voltage is 4.2V, and discharge cut-off voltage is 2.75V. On the Arbin(BT2000) battery test system, firstly, after the battery in full charge state stands for 1h, the constant current of 0.5C is used to discharge the ternary lithium battery. After 12 min of the discharge time, the battery will stand for 1h again, so that the battery will return to its equilibrium state before running the next cycle. Repeat the above steps until the battery terminal voltage is lower than 2.75V, stop discharging, record the data and perform fitting. The fitting accuracy increases with the increase of the fitting order. Therefore, the ninth order curve fitting is carried out for OCV-SOC to reduce the reduction of SOC estimation accuracy caused by the fitting curve error. The curve fitting relation is as follows: UOC = −14.12x9 + 130.2x8 − 521.3x7 + 1095.2x6 − 1341.7x5 +1007.6x4 − 437.4x3 + 95.84x2 − 8.22x + 3.92
(5)
The obtained OCV-SOC relation curve is shown in Fig. 2.
Fig. 2. OCV-SOC Relation Curve
2.3 Parameter Identification of Battery Model Recursive least squares operation is a method developed from adaptive filtering theory for model identification and data mining [11, 12]. The recursive least square method has a small amount of computation and can identify the characteristics of the dynamic system in real time. Therefore, this method is adopted in this paper to identify the parameters of the equivalent model. The principle is as follows: yk = ϕkT θk + ek
(6)
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where, yk is the system output; ϕk is data vector; θk is the parameter vector to be measured, and ek is the equation error. The recursion formula is as follows: ⎧ ⎪ ˆ = θˆk−1 + Kk yk − ϕ T θˆk−1 θ ⎪ k ⎨ P ϕk (7) Kk = 1+ϕk−1 T ⎪ ⎪ k Pk−1 ϕTk ⎩ Pk = I − Kk ϕk Pk−1 The recursive least square method revises the results obtained at the last moment according to the recursive formula through the newly introduced data, and obtains the new estimated value. The product of the estimated error and the system gain is taken as the estimated update value at the current time. The estimated value at the current time can be obtained by adding the estimated updated value and the estimated value at the last time. Finally, the covariance matrix at this time can be calculated according to the covariance matrix at the last time and the system gain to prepare for the next round of parameter estimation. The transfer function of the system is as follows R0 s2 + Ub (S) =− G(s) = Uoc (S)
R0 R1 C1 +R0 R2 C2 +R2 R1 C1 +R1 R2 C2 1 +R2 s + RR01+R R1 C1 R2 C2 C1 R2 C2 1 2 C2 s2 + RR11CC11+R R2 C2 s + R1 C1 R2 C2
Z function corresponding to the S-transformed function can be written as Ut z −1 − Uoc z −1 θ3 + θ4 z −1 + θ5 z −2 G z −1 = = 1 − θ1 z −1 − θ2 z −2 −It z −1
(8)
(9)
where θ1 , θ2 , θ3 , θ4 and θ5 are the coefficients related to the model parameters, and their values are ⎧ 8b−2T 2 ⎪ θ1 = 4b+2cT ⎪ ⎪ +T 2 ⎪ ⎪ 4cT ⎪ θ = −1 2 ⎪ 4b+2cT +T 2 ⎨ +dT θ3 = − 4ab+2eT 4b+2cT +T 2
2
⎪ ⎪ 8ab−2dT 2 ⎪ ⎪ ⎪ θ4 = 4b+2cT +T 2 ⎪ ⎪ ⎩ θ = − 4ab−2eT +dT 2 5 4b+2cT +T 2
(10)
where a = R0 , b = τ 1 τ 2 , c = τ 1 + τ 2 , d = R0 + R1 + R2 , e = R0 (τ 1 + τ 2 ) + R1 τ 2 + R2 τ 1 . The data vector and parameter vector are respectively as ⎧ T ⎨ θ (k) = θ θ θ θ θ 1 2 3 4 5 (11) ⎩ ϕ(k) = E(k − 1) E(k − 2) I (k) I (k − 1) I (k − 2) By substituting Eqs. (6) and (11) into the recursive least square method, the corresponding parameters of the battery model can be obtained.
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3 Extended Kalman Filter with Adaptive Fading Factor 3.1 Traditional Extended Kalman Filter Kalman filter algorithm is a method widely used in linear systems, and extended Kalman filter algorithm extends Kalman algorithm to nonlinear systems [5–7]. EKF linearizes the nonlinear model locally to obtain an approximate linearized model, and then completes the estimation of the target state. The EKF state space expression is shown as follows: xk+1 = f (xk , uk ) + wk (12) yk = h(xk , uk ) + vk In Eq. (12), xk represents the state vector of the system at time k, uk represents the input vector of the system at time k; f (xk , uk ) represents the state transition function of the system, h(xk , uk ) represents the observation function in the system; wk represents the state noise in the system, vk represents the measurement noise in the system, w ∼ (0, Q) and v ∼ (0, R) satisfies the normal distribution, and represents the value of the state of the system and the covariance of the measurement equation respectively. Using the local linear characteristics of the nonlinear system, the nonlinear model is locally linearized, and the first-order Taylor expansion is carried out on the state transition function and measurement function in Eq. (12), and the higher-order terms higher than the second-order are omitted, and Eq. (13) is obtained: xk+1 ≈ f xˆ k , uk + ∂∂fxˆ xk − xˆ k + wk k (13) xk − xˆ k + vk yk ≈ h xˆ k , uk + ∂∂h xˆ k
The parameters of nonlinear system can be transformed into matrix form by mathematical calculation. Ak = ∂f (x∂ xkˆ ,uk ) k (14) Ck = ∂h(x∂ xkˆ ,uk ) k
Substituting Eq. (14) into Eq. (13), it yields: xk+1 ≈ f xˆ k , uk + A k xk − xˆ k + wk yk ≈ h xˆ k , uk + Ck xk − xˆ k + vk Initialize the state variable. x0 = E(x 0) P0 = E x0 − xˆ 0 x0 − xˆ 0
(15)
(16)
The flow chart of EKF is shown in Fig. 3. Steps (3) and (4) are collectively called − prior estimation, Steps (5) and (6) compose the posterior estimation. In Fig. 3, xˆ k+1 − represents the prior estimated value of the system at time k + 1; Pk+1 represents the + prior estimated covariance of the system at time k + 1; Pk represents the posterior estimated covariance of the system at time k; Kk+1 is the Kalman gain at time k + 1, + represents the it is improved based on state estimation and covariance estimation. Pk+1 posterior estimate of the error covariance output of the system at time k + 1.
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Fig. 3. Flow Chart of EKF Algorithm
3.2 Analysis of EKF with Adaptive Fading Factor The traditional extended Kalman filter algorithm is difficult to be used in the estimation process with complex environment, and the extended Kalman filter algorithm will diverge due to the error of mathematical model of nonlinear system, which will affect the accuracy of estimation [2–4]. To solve this problem, on the basis of EKF algorithm, a fading factor is introduced to weaken the proportion of old observations in the prediction process, increase the weight of new observations in the prediction correction process, and then suppress the filtering divergence. The expression is as follows: − (17) = λk+1 Ak+1 Pk ATk+1 + Qk+1 Pk+1 λk+1 is the fading factor, and the calculation method is as follows: The innovation dk+1 at time k is defined as the difference between the actual and predicted observations of the filter − dk+1 = yk+1 − yˆ k+1
(18)
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When the Kalman gain is the optimal gain matrix, the innovation sequences are uncorrelated, that is, the innovation sequences are all orthogonal. Thus, it yields: T = Ck+j Ak+j E − Kk+j Ck+j−1 · · · Ak+2 (E − Kk+2 Ck+1 ) E dk+j dk+1 − T · Ak+1 Pk+1 Ck+1 − Kk+1 Vk+1 = 0 (19) For the optimum λk, the following equation should hold: − T Pk+1 Ck+1 − Kk+1 Vk+1 = 0
(20)
Substituting Kalman gain into the above equation, yields: −1 − − T T E − Ck+1 Pk+1 Ck+1 Ck+1 + Rk+1 Vk+1 = 0 Pk+1 Since
Pk−
is a positive definite matrix,
CkT
is a nonsingular matrix, then yields
⎧ −1 ⎪ − T ⎨ E − Ck+1 Pk+1 Ck+1 + Rk+1 Vk+1 = 0 ⎪ ⎩ λk+1 Ck+1 Ak+1 Pk AT + Qk+1 C T = Vk+1 − Rk+1 k+1 k+1
Set the minimum value of
λk
(22)
is 1, yields:
λk+1
(21)
tr(Vk+1 − Rk+1 ) T = max 1, tr Ck+1 Ak+1 Pk ATk+1 + Qk+1 Ck+1
(23)
According to innovation covariance theory, the matrix fading factor is set to modify the prediction error covariance matrix, and then the filtering divergence caused by the continuous monotonic change of the gain matrix is contained, so as to achieve the purpose of improving the estimation accuracy and suppressing filtering divergence. The SOC estimation process of AFEKF algorithm is shown in the Fig. 4.
4 Experiment and Simulation Analysis In order to verify the robustness and accuracy of the above algorithm, the dynamic stress testing (DST) condition was used for experimental verification. The current curve under DST condition is shown in Fig. 5. The initial SOC value of the battery is set to 100%. When the initial value is known and accurate, the SOC value of each time point is calculated by ampere integration method as the reference value, and then compared and analyzed with the estimated value of various algorithms. Figure 6 shows the comparison between the estimation results of EKF algorithm and AFEKF algorithm and the reference values. Fig. 7 shows the error curves between the estimation results of the two algorithms and the reference values.
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Fig. 4. Flow Chart of EKF with Adaptive Fading Factor
Fig. 5. Curve of Charging and Discharging in DST Condition
As can be seen from the figure, the SOC curve estimated by AFEKF algorithm is more consistent with the real SOC curve, which indicates that the effect of AFEKF algorithm is better than that of EKF algorithm. EKF is affected by the cumulative error of historical data, resulting in a relatively large SOC estimation error. AFEKF modifies the covariance matrix of prediction error by adding an adaptive fading factor, thereby curbing the filtering divergence caused by the continuous monotonicity change of the gain matrix, and achieving the improvement of SOC estimation accuracy. The estimation errors of different algorithms is listed in Table 1. As can be seen from the table, the accuracy of AFEKF in estimating SOC under DST conditions can be stable within 1.5%, which is about 3.5% higher than that of EKF.
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Fig. 6. SOC Estimation Results under DST Conditions
Fig. 7. Estimation Error Curve under DST Conditions
Table 1. Estimation error of different algorithms Algorithm
Average error (%)
Root mean square error (%)
EKF
4.23
4.67
AFEKF
1.05
1.16
5 Conclusion Aiming at the problem of error accumulation when using EKF algorithm to estimate SOC of lithium-ion batteries, this paper proposes a SOC estimation method based on adaptive fading extended Kalman (AFEKF). Selects the Thevenin equivalent model, using the least squares method for model parameter identification, adaptive fading factor, introduced the EKF, correct prediction error covariance matrix, which contain continuous gain matrix caused by filtering divergence of monotonous, decrease the results, the influence of old data to the filter achieve the goal of ascension estimation precision and restrain filtering divergence. The experimental results show that compared with EKF algorithm, AFEKF algorithm has smaller estimation error and smaller fluctuation range of SOC estimation error. The SOC estimation error is 1.38%, and the accuracy is increased by 3.51%, which achieves better SOC estimation accuracy.
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Acknowledgements. This research is supported by Science and Technology Project of State Grid Integrated Energy Service Group Co. LTD of China (Grant No. 52789921N00A) and Open Research Project of Xiangyang Institute of Industrial Technology, Hubei University of Technology of China (Grant No. XYYJ2022C01).
References 1. Yong, L., Tianyu, Y., Xuebo, Q., et al.: Optimal configuration of distributed photovoltaic and energy storage system based on joint sequential scenario and source-network-load coordination. Trans. China Electrotech. Soc. 37(13), 3289–3303 (2022) (in Chinese) 2. Qian, Z., Xiaosong, D., Huazhan, Y., Tao, S., et al.: Coordinated optimization strategy of electric cluster participating in energy and frequency regulation markets considering battery lifetime degradation. Trans. China Electrotech. Soc. 37(1), 72–81 (2022) (in Chinese) 3. Wei, Z., Jie, M., Zhangyi, L., et al.: Energy utilization efficiency estimation method for seconduse lithium-ion battery packs based on a battery consistency model. Trans. China Electrotech. Soc. 36(10), 2190–2198 (2021) (in Chinese) 4. Zifa, L., Yunyang, L., Xinyue, W., et al.: Operation schedule optimization of energy storage and electric vehicles in a distribution network with renewable energy sources. Proc. CSEE 42(5), 1813–1826 (2022) 5. Wadi, A., Mamoun, A., Ala, A.H.: Computationally efficient state-of-charge estimation in Li-ion batteries using enhanced dual-Kalman filter. Energies 3717(15), 1–5 (2022) 6. He, L., Guo, D., Zhang, J., et al.: A threshold extend Kalman filter algorithm for state of charge estimation of lithium-ion batteries in electric vehicles. IEEE J. Emerg. Sel. Top. Ind. Electron. 3(2), 190–198 (2022) 7. Mohammadi, F.: Lithium-ion battery state-of-charge estimation based on an improved coulomb-counting algorithm and uncertainty evaluation. J. Energy Storage 48(104061), 1–10 (2022) 8. Chung, D. -W., Ko, J. –H., Yoon, K. Y.: State-of-charge estimation of lithium-ion batteries using LSTM deep learning method. J. Electr. Eng. Technol. 17, 1931–1945 (2022) 9. Maheshwari, A., Nageswari, S.: Real-time state of charge estimation for electric vehicle power batteries using optimized filter. Energy 254(124328), 1–15 (2022) 10. Ziyi, W., Chengzhi, Z., Yanglin, Z., et al.: OCV-SOC estimation based on dynamic reconfigurable battery network. Proc. CSEE 42(8), 2919–2928 (2022) 11. Chunling, W., Wenbo, H., Jinhao, M., et al.: State of charge estimation of lithium-ion batteries based on maximum correlation-entropy criterion extended Kalman filtering algorithm. Trans. China Electrotech. Soc. 36(24), 5165–5175 (2021) (in Chinese) 12. Wei, L., Geng, Y., Deyue, M., et al.: Modeling method of lithium-ion battery considering commonly used constant current conditions. Trans. China Electrotech. Soc. 36(24), 5186– 5200 (2021) (in Chinese)
On-Line Evaluation Method of Battery Bank Inconsistency for DC Power System Haihong Huang, Chuangming Ma(B) , and Haixin Wang School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China [email protected]
Abstract. Valve-controlled battery is the main component of DC power supply system in mainstream substation. The method of determining the inconsistency of battery banks by measuring the capacity of independent charge and discharge experiments has some limitations, and the single battery needs to be separated independently, which is not suitable for the DC battery system running in series online. Aiming at this problem, an inconsistency evaluation model of battery banks for DC power system based on the combination of comprehensive weighting method and grey clustering is constructed. Firstly, entropy weight method and analytic hierarchy process (AHP) were used to obtain the subjective and objective weights of the battery performance parameters, and then the comprehensive weights of the judgment indicators were obtained. Grey clustering was used to comprehensively evaluate the inconsistency of each performance index, and the evaluation model was verified by online detection of battery performance parameters in substation. The evaluation model can evaluate the inconsistency of battery banks under multiple indexes, which provides a practical method and theoretical basis for online screening of backward batteries and ensuring the stable operation of DC battery system. Keywords: Online assessment · Entropy weight method · Analytic hierarchy process · Grey clustering
1 Introduction Valve-controlled lead-acid battery is the core component of DC power supply system in current mainstream substation. It can supply power for DC load when AC power failure occurs [1]. The battery management system of the battery bank in the substation can monitor the terminal voltage of the single battery, the terminal voltage change when the nuclear capacity is discharged, the electrode surface temperature and the floating charging current in the floating charging state. At the same time, timed internal resistance test can be realized. However, how to make use of the relevant battery performance parameter information obtained to evaluate the inconsistency of the battery bank [2] with multiple indicators online only adopts simple parameter comparison and lacks quantitative evaluation method. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 558–565, 2023. https://doi.org/10.1007/978-981-99-1027-4_57
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2 Comprehensive Weighting Method and Grey Clustering Entropy weight method is an objective method to find the weight, that is, to determine the weight according to the amount of information transmitted by the objective evaluation index. If there are M performance indicators and N objects, the evaluation matrix R = [r ij ] can be obtained after the performance indicators are standardized, which is the normalized value of the Jth performance indicator of the Ith object [3, 4]. For the Jth performance index in the system, the index parameter entropy can be defined as: ⎧ n 1 ⎪ ⎪ ⎪ (yi j ln yi j ) ⎨ sj = − ln n i=1 (1) ⎪ ri j ⎪ ⎪ ⎩ yi j = n i=1 ri j The entropy weight of the Jth index δ ij is: δj =
1 − sj m− m j=1 sj
(2)
Analytic hierarchy Process (AHP) combines qualitative judgment with quantitative calculation to judge the relative importance of each performance index, and then constructs the fuzzy discrimination matrix to obtain the relative weight of each index. The specific steps are as follows: (1) Let ξ 1 ,ξ 2 ,…,ξ m index in the system be respectively, and the weight assigned is δ 1 , δ 2 ,…, δ m, respectively. The relative importance of each index is reflected through quantitative data. Get the judgment matrix P ⎞ a11 . . . a1m ⎟ ⎜ P = ⎝ ... . . . ... ⎠ am1 · · · amm ⎛
(3)
(2) Consistency check of judgment matrix: If the judgment matrix is not reasonable, the weight obtained is not reliable, so consistency (CI) check should be carried out, and its calculation formula is: CI =
λmax − m m−1
(4)
Query the average random consistency index RI. The random consistency values of each order matrix are shown in Table 1.
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Order
1
2
3
4
5
6
7
8
9
RI
0
0
0.52
0.89
1.12
1.26
1.36
1.41
1.46
The consistency ratio CR was calculated CR =
CI RI
(5)
When CI is less than 0.1, the judgment matrix P is considered acceptable [5, 6]. (3) The subjective weight of each parameter indicator is: ωj =
ωj∗ m ωj∗
(6)
j=1
ωj∗ =
m m M ; M = ai j ; i = 1, 2, …, m; j = 1, 2, …, m. j j i=1
The objective entropy weight method and subjective hierarchical analysis method are combined to obtain the comprehensive weight W: W = kW1 + (1 − k)W2
(7)
W 1 is the weight of each index obtained by entropy weight method, denoted as objective weight; W 2 is the weight of each index obtained by analytic hierarchy process, denoted as subjective weight; k is the proportion of entropy weight in the comprehensive weight, which is generally taken as 0.4. Grey clustering refers to the qualitative and quantitative judgment of the state based on the principle of grey system by comprehensively considering the performance parameters of the system [7, 8]. Its basic principle is as follows: If there are N decision objects, M decision indicators and S different grey classes, then there is: μLi =
m
fjL (xi j ) ∗ Wj
(8)
j=1
μLi = μ1i , μ2i , · · · , μsi i = (1, 2, · · · n)
(9)
∗
If max {μLi } = μLi , it is said that the evaluation object I belongs to L* category [9, 1≤L≤s
10]. To judge the reliability of cluster evaluation, Theil disequilibrium index was used. T i = ln(s) +
s L=1
μLi ln μLi
(10)
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The higher the Theil imbalance index, the higher the reliability of the evaluation results. Set the total score of 10 points and the score of gray L as cL , c1 > c2 > · · · > cs . To further quantitatively evaluate the gray clustering results, set the total score of 10 points and the score of gray L as cL ,c1 > c2 > … > cs , ensure that the interval of each score section is equal,set c1 = 10, cs = 0, the score of evaluation object I is: Qi =
s
μLi ci
(11)
L=1
The score value can quantitatively evaluate the status of the object. The result is intuitive and easy to compare, and can provide a reference for further detection and maintenance strategies of batteries.
3 Establishment of Evaluation Model for Battery Bank This paper is based on the main performance parameters of the online testing of battery sets, referring to the “GB_T 19638.1-2014 fixed type valve-controlled lead acid battery Part 1 Technical conditions” and “GB_T 19638.1-2014 fixed type valve-controlled lead acid battery Part 2: Product varieties and specifications” to establish an online comprehensive evaluation system for battery group inconsistency (Fig. 1). Comprehensive online evaluaƟon of baƩery group inconsistency
30min
30min
30min
30min
1h
1h The resistance value
Fig. 1. Battery inconsistency comprehensive evaluation system
At present, there is no clear qualitative division of the inconsistency of lead-acid battery sets. Based on the fault maintenance diagnosis of battery sets, experimental data and expert analysis, this paper divides the inconsistency of battery sets into five grades: very good, good, average, poor and very poor. In this paper, the inconsistency of battery banks is divided into five gray classes. The gray clustering function is shown in Fig. 2.
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1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fig. 2. Battery bank inconsistency gray clustering function
According to the inconsistent online evaluation system of battery sets established above, three categories of seven battery performance parameters are selected to evaluate indicators. When the battery group is under constant current charging condition, the terminal voltage of the single battery appreciates in 30 min, denoted as U1 ; the surface temperature of the electrode of the single battery appreciates in 30 min, denoted as T1 ; When the battery group is under constant current discharge condition, the terminal voltage of the single battery decreases in 30 min, denoted as U2 ; the electrode surface temperature of the single battery increases in 30 min, denoted as T2 ; When the battery group is in the floating charge state, the average terminal voltage of 1H single battery is denoted as U , the average floating charging flow of 1H single battery is denoted as I , and the internal resistance value obtained by the internal resistance test is denoted as R. Eight random 2V500Ah valve-controlled lead-acid batteries in the station were selected as the experimental group, and relevant performance parameters required for online testing were obtained as evaluation indexes. Detailed data are shown in Table 2, and standardized data are shown in Table 3. Table 2. Storage battery group inconsistency levels 序号
A
B
C
U1 (V)
U2(V)
T1(°C)
T2(°C)
R(m)
U (V)
I (A)
1
0.1469
0.2257
6.4
5.4
2.0137
2.2330
12.4
2
0.1123
0.1826
5.8
4.5
1.7047
2.2450
15.8
3
0.1091
0.2148
6.5
4.6
1.9170
2.2370
14.2
4
0.1237
0.1898
5.7
4.2
1.7568
2.2420
15.3
5
0.1346
0.2135
6.3
4.5
1.8265
2.2380
13.7
6
0.1253
0.1967
5.4
4.1
1.7742
2.2420
15.4
7
0.1284
0.1986
5.8
4.6
1.7904
2.2390
14.3
8
0.1437
0.2268
6.8
5.5
1.9864
2.2350
13.2
Calculate the entropy of the data in the above table H = [0.8620 0.8288 0.8790 0.8789 0.8682 0.8785 0.8920]
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Table 3. Standardized data of battery evaluation index 序号
A
B
C
U1
U2
T1
T2
R
U
I
1
0.0000
0.0249
0.2857
0.0714
0.0000
0.0000
0.0000
2
0.9153
1.0000
0.7143
0.7143
1.0000
1.0000
1.0000
3
1.0000
0.2715
0.2143
0.6429
0.3129
0.3333
0.5294
4
0.6138
0.8371
0.7857
0.9286
0.8314
0.7500
0.8529
5
0.3254
0.3009
0.3571
0.7143
0.6058
0.4167
0.3824
6
0.5714
0.6810
1.0000
1.0000
0.7751
0.7500
0.8824
7
0.4894
0.6380
0.7143
0.6429
0.7227
0.5000
0.5588
8
0.0847
0.0000
0.0000
0.0000
0.0883
0.1667
0.2353
Find the entropy weight method W1 = [0.1513 0.1876 0.1326 0.1327 0.1444 0.1331 0.1184] The fuzzy judgment matrix is obtained ⎡
⎤ 1 24 PC = ⎣ 21 1 2 ⎦ 1 1 4 2 1
The subjective weights of the subindexes of online floating state were obtained WC = [0.7273 0.1818 0.0909] Similarly, the subjective weights of other index layers and sub-index layers are obtained WA = [0.2500 0.7500] WB = [0.3333 0.6667] WABC = [0.1429 0.28570.5714] Determine the final subjective weight of the analytic hierarchy process. W2 = [0.0357 0.1072 0.0952 0.1905 0.4156 0.1039 0.0519] The subjective and objective weights obtained by the comprehensive entropy weight method and the analytic hierarchy process are obtained, and the comprehensive weights are obtained W = [0.0819 0.1393 0.1101 0.1674 0.3071 0.1156 0.0785]
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H. Huang et al. Table 4. Grey clustering of battery banks
NUM
Very poor
Poor
General
Good
Very good
Resuit
1
0.3886
0.0944
0.0000
0.0000
0.0000
Very poor
2
0.0000
0.0000
0.0000
0.0396
0.1645
Very good
3
0.0000
0.1154
0.0956
0.0000
0.0819
Poor
4
0.0000
0.0000
0.0707
0.1821
0.0956
Good
5
0.0000
0.2464
0.0000
0.0239
0.0000
Poor
6
0.0000
0.0000
0.1084
0.0000
0.2775
Very good
7
0.0000
0.0000
0.2553
0.0157
0.0000
General
8
0.4988
0.0000
0.0000
0.0000
0.0000
Very poor
The gray clustering results of the battery group are shown in Table 4. The maximum value of the clustering coefficient indicates the inconsistency evaluation result of a single battery for the whole battery group. According to different evaluation results, corresponding maintenance measures should be taken for the battery group. If the evaluation result is “very poor”, the battery is in the discarded state. To ensure that the online running of the battery group is not affected, replace the battery in a timely manner.If the evaluation result is “poor”, it indicates that the battery has safety risks, which further shortens the detection period. Once the evaluation result becomes poor, replace the battery in a timely manner.If the evaluation result is “general”, it is necessary to strengthen the index detection, shorten the detection period, and pay attention to the change of the evaluation result in time.For the battery whose evaluation result is in the same grade, the battery is scored to further quantify the inconsistency of the battery group in the same grade, as shown in Fig. 3.
Fig. 3. Score of the battery group
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4 Conclusions (1) The gray clustering was used to evaluate the inconsistency of the battery group, and the grade and score values of the single battery relative to the battery group were obtained. A multivariate evaluation system was established to realize the quantitative evaluation of the inconsistency of the battery group. (2) The entropy weight method only obtains the weight according to the difference degree of index data, which is objective, but it cannot reflect the difference of importance of each index. The weight obtained by combining analytic hierarchy process will be more reasonable. (3) The determination of the relative importance of each index of the analytic hierarchy process (AHP) has a great impact on the evaluation results, so it is necessary to study the related performance parameters of the battery to optimize the selection. When the evaluation index is too many, the calculation is avoided to increase and the precision value is reduced, and the judgment can be divided into multiple levels.
Acknowledgments. This work was funded by The National Natural Science Foundation of China, China (No. 51177037).
References 1. Shengrong, X., Xinxin, F., Hongmei, Y.: Design and simulation of a low noise amplifier for detecting low frequency noise. Chin. J. Electron Devices 42(02), 383–386 (2019) 2. Yuewen, L.: Research on operation and maintenance management of substation DC power system. Shandong university (2020) 3. Ming, D., Yi, G., Jingjing, Z., et al.: Node vulnerability assessment for complex power grids based on effect risk entropy-weighted fuzzy comprehensive evaluation. Trans. China Electrotech. Soc. 30(03), 214–223 (2015) 4. Yang, Z., Qianling, H., Jinding, C.: Comprehensive evaluation of transformer oil-paper state based on combined weight-double base point method. Trans. China Electrotech. Soc. 34(20), 4400–4408 (2019) 5. Zhenpo, W., Fengchun, S., Chengning, Z.: Study on inconsistency of electric vehicle battery pack. Chin. J. Power Sources (05), 438–441 (2003) 6. Haihong, H., Rui, G., Niantao, J., et al.: Reference current amplification effect of secondary pulsation and its in-fluence for APF. J. Electron. Meas. Instrum. 31(06), 968–973 (2017) 7. Haihong, H., Xiaopeng, Z., Haixin, W.: Optimal design of voltage-balance loop for threephase four-wire APF. Electr. Power Autom. Equip. 40(07), 103–108 (2020) 8. Haihong, H., Wei, W., Yeping, S, et al.: Optimization design of voltage loop for shunt active power filter. J. Electron. Meas. Instrum. 29(10), 1529–1535 (2015) 9. Jian, L., Caixin, S., Weigen, C., et al.: Study on fault diagnosis of insulation of oil immersed transformer based on grey cluster theory. Trans. China Electrotech. Soc. 04, 80–83 (2002) 10. Jiang, D., Mingyang, S.: Hierarchical assessment method of transformer condition based on weight-varying grey cloud model. Trans. China Electrotech. Soc. 35(20), 4306–4316 (2020)
A Coordinated Control Strategy for PV-BESS Combined System and Optimal Configuration of Energy Storage System Chu Jin1(B) , Yan Yang1 , Zhengmin Zuo1 , Shuxin Luo1 , and Jinyu Wen2 1 Grid Planning & Research Center of Guangdong Power Grid Corporation,
Guangzhou 510080, China [email protected] 2 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract. With the increase of photovoltaic (PV) power penetration level in the system, the requirements for PV integration is becoming stricter to guarantee the secure and stable operation of the grid. PV stations will be possibly required to perform like a synchronous generator which could participate in frequency regulation, reactive power support as well as provide inertia apart from ramp rate control and the energy storage system is a promising solution. A coordinated control strategy for Photovoltaic-Battery Energy Storage System (PV-BESS) based on virtual synchronous generator (VSG) and reactive current injection is proposed in this paper. The PV station is able to provide virtual inertia, deal with energy exchange between PV-BESS system and conventional power grid as well as response to the system frequency change, thus improving the stability of the power system effectively. Moreover, the influences of control parameters on system performance are studied and the optimal configuration method of BESS is illustrated by using sensitivity analysis, providing reference for BESS configuration in the system. Keywords: PV-BESS combined system · Coordinated control strategy · Virtual synchronous generator · Frequency support · Influences of control parameters · Energy storage configuration
1 Introduction The construction of new power system is essential to achieve emission peak and carbon neutrality. Under this background, the new energy field has received widespread attention and the photovoltaic (PV) power generation is developing rapidly. However, the inherent characteristics of intermittence and fluctuation pose a threat to the transient stability and secure operation of the power ststem with high penetration of PV [1, 2]. Similar to wind power generation, Maximum Power Point Tracking (MPPT) of PV power system is realized through the power electronic devices. During the loss of generation and the consequent fall in system frequency, the rotor speed of a wind turbine can be reduced © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 566–578, 2023. https://doi.org/10.1007/978-981-99-1027-4_58
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to release stored energy from the rotor and provide “hidden” inertia to improve system stability. However, the lack of rotating parts in PV arrays makes PV integration a more challenging problem to power system [3]. In recent years, energy storage devices such as Battery Energy Storage System (BESS) have been widely utilized to improve the friendliness of renewable energy integration mainly to smooth the output fluctuation [4, 5], enhance the ability of Low Voltage Ride Through (LVRT) [6, 7] and help providing limited frequency support [8, 9]. However, coordination of PV power and energy storage to save energy storage costs and improve system frequency stability has rarely been addressed in the literature. It is of great significance to study how to make full use of energy storage to realize the optimal operation of PV power stations. Although no requirement is given in current Chinese Grid Code, it is of great value that PV stations could operate like synchronous generators (SG) during disturbance and provide support to the system frequency, damping as well as virtual moment of inertia to improve the power system stability [10]. The existing control strategies include droop control, Virtual Inertia (VI) control and Virtual Synchronous Generator (VSG) control [11, 12]. The droop control only makes a rough approximation for the external characteristics of SG, while VI control depends purely on the proportion-derivative calculation of the measured outer system frequency which is invalid without precise measurement. The VSG control can operate without direct measurement of the frequency because it maintains a virtual rotational speed itself just like SG, but it provides the reference value only for a single inverter, which is difficult to be used for the control of whole PV-BESS power station. Besides, in these existing control methods, no adjustment of PV power is considered. As a result, very large capacity of BESS must be equipped to fulfill the active power response requirements. Moreover, these methods do not reserve the inverter capacity required for Reactive Current Injection (RCI) described in the Grid Codes when assigning the active current/power references. To solve the above-mentioned problems, a cooperative and harmonic control strategy for PV-BESS combined system based on the technology of VSG is proposed in this paper, taking into consideration of active and reactive power orders among multiple inverters of BESS, PV and STATCOM equipped in the power station. Simulations are carried out to verify the effectiveness of the control method and the influences of different control parameters are studied. Moreover, a practical configuration method suitable for the centralized energy storage is proposed with the analysis of sensitive factors impacting the configuration results, providing reference for BESS configuration in the system.
2 Coordinated Control Strategy of PV-BESS System 2.1 Definition of the Inertial Constant of PV-BESS System According to the definition in Physics, moment of inertia J is defined as the sum of product of every particle’s mass and square of their distance to a given axis in component. The moment of inertia of a conventional generator is the measurement of its tendency to maintain the rotating speed when rotating around the shaft. Inertia time constant T J is defined as the time a generator needs to accelerate from stationary state to rated speed
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under rated torque. J and T J are both essential parameters of generators and T J can be calculated with J according to Eq. (1)(4.27), reflecting the influence of unit capacity. TJ =
ω2 J ω02 M2 = r × 0 SN 4 SN
(1)
where S N is generator apparent power, ω0 is the rotor rotating speed, and Mr is the torque of generator rotor. From Eq. (1)(4.27) it can be seen that the rotor tends to accelerate or decelerate more easily with a smaller T J . In this paper inertia constant H is adopted to describe the inertia of units, and it is defined as follows: H=
J ω02 1 = TJ 2SN 2
(2)
When disturbance occurs, the imbalance of active power will result in the fluctuation of system frequency. Studies have shown that the frequency deviation decreases with the increase of H, but it tends to take longer time to reach the steady state. A relatively large inertia constant is beneficial to the frequency stability of the power system. The inertia constant of PV-BESS system is defined as follows: HPV _BESS =
EPV + EBESS SPV
=
1 2 2 JPV _ES ωg
SPV
(3)
where E BESS is the equivalent kinetic energy of storage devices, S PV is the rated capacity of PV power station, J PV_ES is the equivalent moment of inertia, ωg is the angular velocity of power system. If PV power station does not take part in the system frequency regulation, which means E PV = 0, the required energy from the energy storage system is E BESS = H PV_BESS ·S PV ; while if the coordinated control strategy is used in PV-BESS system and the PV power station could play a role in the frequency regulation process, the required capacity of energy storage system could be reduced. The output power of PV-BESS system during the system frequency change can be calculated using Eq. (4).(3.17) dω (4) dt Take it into Eq. (3) and the per-unit value of Eq. (3.18) could be expressed as: P = PPV + PES = JPV _ES ω
dfpu Ppu HPV _ES = dt 2 The integral formula of Eq. (5)(3.19)should be: fpu
2 2 Ppu t = HPV _ES · [fpu (t + t) − fpu (t)]
fpu (t + t) =
2 (t) Ppu t/HPV _ES + fpu
(5)
(6) (7)
According to Eq. (7)(3.21), as the equivalent inertia constant H PV_ES increases, the system frequency deviation after disturbance will decrease, which is beneficial to the system stability.
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2.2 Dynamic Control Strategy Based on VSG The control scheme is designed for the power station level control, aiming to achieve the following functions: (1) Simulate system inertia and provide frequency support to improve system stability; (2) Fulfill the standard/grid code requirements for reactive current injection during faults. Meanwhile, maximization of the PV output except for necessary curtailment in case of limited BESS capacity is considered whenever possible. The overall diagram of the proposed dynamic control scheme is shown as follows: (The steady-state active power references are from the upper control, and the reactive power compensation device in the station is considered as STATCOM) (Fig. 1).
Fig. 1. Diagram of the dynamic control scheme
Virtual Synchronous Generator (VSG) Control. The control scheme consists of the mechanical equation, electromagnetic equation and primary frequency regulation (PFR) function as conventional synchronous generators. Similar to SG, the virtual rotational speed Ñ and power angle ϕ can be calculated by the following virtual mechanical equation: ⎧ SS (t) VSG (t) Pref Pref ⎪ dω ⎪ ⎨J = − − D(ω0 − ω) dt ω ω (8) ⎪ ⎪ ⎩ dϕ = ω dt where parameter J is the virtual moment of inertia, D is the damping coefficient, and Ñ0 SS (t) is the steady-state output reference of is the reference rotation speed. Moreover, Pref SVG (t) is the calculated instantaneous power reference of the whole PV power station, Pref the whole station.
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The virtual electromagnetic equation is described as follows: ⎧ diaref ⎪ ⎪ LVSG = E0 sin(ϕ + ϕa0 ) − RVSG iaref − ua ⎪ ⎪ ⎪ dt ⎪ ⎨ dibref LVSG = E0 sin ϕ + ϕa0 − 120◦ − RVSG ibref − ub ⎪ dt ⎪ ⎪ ⎪ ⎪ dicref ⎪ ⎩ LVSG = E0 sin ϕ + ϕa0 + 120◦ − RVSG icref − uc dt
(9)
where parameter L VSG and RVSG are the equivalent inductor and resistor, respectively, E 0 is the virtual internal voltage, ua , ub , uc are the measured instantaneous voltages at PCC and iaref , ibref , icref are the calculated instantaneous currents, ϕ a0 is the measurement of PCC voltage angle in phase A when the control process starts. Moreover, the PFR module is added to the control scheme. The needed power can be determined by Eq. (10).
PV PV f0 − f (t) (10) PPFR (t) = kPFR where the parameter k PFR is the coefficient of PFR, f 0 is the rated frequency and f is the real-time system frequency. Finally, in order to conveniently allocate the PV arrays’ active power references and meet the reactive current injection (RCI) requirements in Grid Code GB/T 19964–2012, calculated by Eq. (11), the output references of VSG control are translated from threeVSG and phase instantaneous current references iaref , ibref , icref to VSG references of Pref VSG iQref by Eq. (12)(1). (I T is injected reactive current, U T is the PCC voltage magnitude in per unit value, I N is the rated output current of the PV station, ϕ PCC is the phase A voltage angle at PCC given by PLL) ⎧ ⎨ IT ≥ 1.5(0.9 − UT )IN (0.2 ≤ UT ≤ 0.9) (11) IT ≥ 1.05IN (UT ≤ 0.2) ⎩ IT = 0 (UT > 0.9) VSG Pref = ua iaref + ub ibref + uc icref (12) VSG iQref = iaref sin(ϕPCC ) + ibref sin ϕPCC − 120◦ + icref sin ϕPCC + 120◦ As a result, the dynamic characteristics of SG can be completely simulated by the control scheme including the dynamics of inertia and frequency response. VSG (t) is allocated Active Power Distribution. The active power reference of vsg Pref between all the PV arrays and BESS inverter. The distribution strategy is shown in Fig. 2. In the control process, the total active power output reference of pv inverters always tries to approach its steady-state reference Ppvref (t) when energy storage capacity is sufficient (Fig. 2a). BESS is used to smooth the difference between the reference and the PV inverters output (Fig. 2(B)). If the PV arrays are forced to adjust its active power output, it is distributed according to the weather-decided maximum output of each arrays and limited by the inverters’ capacities (Fig. 2(C)). The output of energy storage system
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limitation (P BES , P BES ), is determined by SOC and the PCC voltage UgPU as shown in Eq. (13)(2.25) and Eq. (2.26)(14). ⎧ P DIS ⎪ ⎪ Bmax ⎪ ⎨ 2
BESS 2 − i BESS (t) ¯PBES (t) = min P DIS , 3 ug imax Bmax 2 Qref ⎪ ⎪ ⎪ ⎩ 0 SOC(t) > SOCmin, UgPU (t) ≥ 0.9p.u. SOC(t) > SOCmin, UgPU (t) < 0.9p.u. SOC(t) ≤ SOCmin ⎧ CH −PBmax ⎪ ⎪ ⎪ ⎨
2 2 CH , 3 u BESS (t) BESS P BES (t) = − min PBmax imax − iQref 2 g ⎪ ⎪ ⎪ ⎩ 0 SOC(t) < SOCmax, UgPU (t) ≥ 0.9p.u. SOC(t) < SOCmax, UgPU (t) < 0.9p.u. SOC(t) ≥ SOCmax
(13)
(14)
CH and P DIS are the battery charging and discharging power limits, i BESS and where PBmax max Bmax BESS iQref are the max current and reference of energy storage system.
Fig. 2. Active power distribution strategy
Reactive Current Distribution. The reactive current distribution strategy is shown in Fig. 3. The allocation is made between PV, BESS and STATCOM inverters. in the control process, the total reactive current reference is calculated by comparing the VSG VSG (t) and RCI requirement i reference iQref DRC (t) in grid code to avoid abrupt transitions between them. Then a PI controller is introduced to compensate the reactive power loss
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induced by transformers. The order of the utilization of reactive capacity is STATCOM, then energy storage and finally PV power. BESS (t) and the total reactive The upper limit of energy storage reactive current iQ max AVA (t) can be obtained by Eqs. (15) and (16). current iQ BESS iQmax (t)
BESS 2 − i BESS (t) 2 U PU (t) ≥ 0.9p.u. imax g P = BESS UgPU (t) < 0.9p.u. imax
(15)
BESS are the real-time and upper limit current BESS inverter. where iPBESS (t) and imax
⎧ 2 BESS 2 PV 2 PV 2 ⎨ STAT BESS imax,k − iP,k (t) + imax − iP (t) + k i AVA iQ (t) = Qmax ⎩ STAT + i BESS + PV iQmax max k imax,k UgPU (t) ≥ 0.9p.u. UgPU (t) < 0.9p.u.
(16)
STAT represents STATCOM current upper limit, i PV (t) and i PV where iQmax P,k max,k are the real-time and maximum output and of each inverter.
Fig. 3. Reactive reference value for PV, BESS and STATCOM inverters
It should be noticed that when the inverters’ capacities are not sufficient, the reactive current references are firstly satisfied when system failure happens (to meet the Grid Code requirement) otherwise active power references are firstly considered. These priorities
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are ensured by changing the bounds of the hard limiters/PI controller in both Figs. 2 and 3. To sum up, with the proposed dynamic control strategy, the whole PV-BESS station can mimic the dynamics of conventional SG and fulfill the RCI requirements in Grid Codes. And the requirements of BESS and STATCOM are reduced with the allocation strategy and coordination between the inverters. Furthermore, since the allocated references can be directly accepted by the traditional d-q decoupled control in each inverter, the proposed strategy can be implemented easily in the existing PV power stations.
3 Control Verification and Impacts Analysis of Different Control Parameters 3.1 Verification of Dynamic Control Scheme Simulations on PSCAD/EMTDC are carried out to verify the effectiveness of the proposed coordinated control strategy. In the two-generator test system shown in Fig. 4, each SG capacity is 300MW and the system power load is 516MW. The installed PV power station 90MW. The PV power station, energy storage system and the reactive power compensation device STATCOM are connected to the system bus.
G
1
2
PG1
G
PG2
PV+BESS
PD1
∆PD PD2 STATCOM
Fig. 4. Two-generator test system diagram
Various control methods and their control effects are compared in the paper. The frequency response and voltage of PCC curve with load change of 50MW are presented in Fig. 5a and b, respectively. (1) Conventional inverter control strategy with no other optimization measures; (2) Simply Consider PFR function; (3)Cooperative and harmonic control method based on virtual synchronous generator. From the simulations results it can be concluded that the lowest frequency after disturbance with conventional inverter control, PFR control only and improved VSG control is 49.6863Hz, 49.7592Hz and 49.7983Hz, respectively. The proposed control strategy has the best performance in the frequency change value, recovery time and the voltage fluctuation after system disturbance. It can be seen that with the cooperative and harmonic control method base on VSG helps system with PV power and energy storage operate as a SG, providing damping and moment of inertia when system state changes.
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3.2 Impact Analysis of Control Parameters Since the values of control parameters in the proposed method can be decided according to different control requirements, covering a larger range than the SG, the control strategy based on VSG is more flexible. System frequency and power response of PV-BESS system with different damping coefficient D, inertia constant H, primary frequency regulation coefficient k f , virtual reactance L and virtual resistance R under the condition of three-phase ground fault are shown in Fig. 6a–j. It can be summarized from the simulation results that with higher D, H and k f , the system is more likeyl to maintain a stable operation state. However, control parameter L mainly influences the amplitude and frequency of the oscillation of PV-BESS system output power and R mainly decides the operation point of VSG. 3.2.1 Optimal Configuration of PV-BESS System A practical configuration method suitable for the centralized energy storage is proposed in this research to mitigate PV power output fluctuation as well as improve the system stability, and the sensitive factors impacting the configuration results such as different control parameters and PV penetration level are discussed. In the system shown in Fig. 4 we change the energy storage power capacity Pbmax and calculate the maximum and average system frequency deviation (calculated by Eqs. (17) and (18)) when three-phase ground fault or 10% sudden load increase in the system. Figure 7 shows the relationship between the system frequency deviation and power capacity of BESS. (17) fmax = max(fmax − fsteady , fmin − fsteady ) favg =
N −1 k=0
(f (t + k · t) − fsteady )2 N
(18)
where f max , f min and f steady are the peak frequency value, valley frequency value and steady state value respectively. And t represents the time instant when the disturbance occurs, N represents the length of data and t is the time step. Simulations show that with the increase of energy storage power capacity, both the maximum and average system frequency deviation have a tendency to decrease and when the power capacity is larger than 15 MW, the improvement in control effect is no
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longer obvious. Thus, the process to define the capacity of BESS can be described as Fig. 8. When considering the sensitive factors of the capacity design process, different control parameters and PV penetration level are discussed here. Changing the control
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According to Fig. 9, as the damping coefficient D, H, k f or PV penetration level increases with other control parameters unchanged, the need for BESS capacity tends to increase. For a given system with certain PV capacity, the control parameters can be determined by the frequency regulation requirements. Therefore, the power capacity of BESS needed during the dynamic process are convenient to obtain by referring to
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the curves which indicate the relationships between the index and capacity of BESS. Taking the inflection point as the requirements for configuration is considered effective and practical.
4 Conclusions The existing VSG control as well as primary frequency control is adapted for station level PV power control by defining a novel distribution method of the active power and reactive current references. The proposed cooperative and harmonic control method based on VSG for system integrated with PV, energy storage and other reactive compensation device is proved to be effective in dealing with system disturbance by imitating the outer characteristics of a synchronous generator. Research on the influences of different control parameters and simulation results show that relatively large damping coefficient D, PFR coefficient k f and inertia constant H are beneficial to the transient stability of the power system. Besides, the optimal configuration of energy storage in the PV station is discussed and the capacity of BESS could be conveniently and scientifically determined with the proposed practical method. Acknowledgments. This work is supported by Planning and Research Project of China Southern Power Grid Corporation (031000QQ00210029).
References 1. Zhuo, Z., Zhang, N., Xie, X., et al.: Key technologies and developing challenges of power system with high proportion of renewable energy. Automation of Electric Power Systems 45(9), 171–191 (2021). (in Chinese) 2. Lin, Y.: Research on active frequency control of large-scale grid connection of new energy photovoltaic power stations. China Energy Environ. Prot. 44(5), 210–215 (2022). (in Chinese) 3. Zhao, Z., Lei, Y., He, F., et al.: Key Overview of large-scale grid-connected photovoltaic power plants. Autom. Electr. Power Syst. 35(12), 101–107 (2011). (in Chinese) 4. Shi, X., Shi, X., Dong, W., et al.: Research on energy storage configuration method based on wind and solar volatility. In: 2020 10th International Conference on Power and Energy Systems (ICPES), 464–468 (2020) 5. Zheng, H., Xie, L., Ye, L., et al.: Hybrid energy storage smoothing output fluctuation strategy considering photovoltaic dual evaluation indicators. Trans. China Electrotech. Soc. 36(9), 1805–1817 (2021). (in Chinese) 6. Guo, W., Xiao, L., Dai, S.: Enhancing low-voltage ride-through capability and smoothing output power of DFIG with a superconducting fault-current limiter–magnetic energy storage system. IEEE Trans. Energy Convers. 27(2), 277–295 (2012) 7. Miao, L., Wen, J., Xie, H., et al.: Coordinated control strategy of wind turbine generator and energy storage equipment for frequency support. IEEE Trans. Ind. Appl. 51(4), 2732–2742 (2015) 8. Xiangwu, Y., Zijun, S., Sen, C., Ying, S., Tiecheng, L.: Primary frequency regulation strategy of doubly-fed wind turbine based on variable power point tracking and super capacitor energy storage. Trans. China Electrotech. Soc. 35(3), 530–541 (2020). (in Chinese)
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9. Johnston, L., Díaz-González, F., Gomis-Bellmunt, O., et al.: Methodology for the economic optimization of energy storage systems for frequency support in wind power plants. Appl. Energy 137(1), 660–669 (2015) 10. Lv, Z., Sheng, W., Zhong, Q., et al.: Virtual Synchronous Generator and Its Applications in Micro-grid. Proc. CSEE 34(16), 2591–2603 (2014). (in Chinese) 11. Tian, Y., Wang, T., Xing, Q., et al.: Transient stability analysis of a photovoltaic generation system considering virtual inertia control and low voltage ride-through. Power Syst. Prot. Control. 50(2), 52–59 (2022). (in Chinese) 12. Thomas, V., Kumaravel, S., Ashok, S.: Virtual synchronous generator and its comparison to droop control in microgrids. In: 2018 International Conference on Power, Instrumentation, Control and Computing (PICC), 1–4 (2018)
Multi-objective Optimal Scheduling Strategy of EVs Considering Customer Satisfaction and Demand Response Zhihua Wang1 , Hui Hou1(B) , Tingting Hou2 , Rengcun Fang2 , Jinrui Tang1 , and Changjun Xie1 1 School of Automation, Wuhan University of Technology, Wuhan 430070, China
{289805,houhui,tangjinrui,jackxie}@whut.edu.cn
2 Economics and Technology Research Institute, State Grid Hubei Electric Power Company,
Wuhan 430062, China [email protected], [email protected]
Abstract. Disorderly charging of large-scale electric vehicles (EVs) will seriously threaten the safe and stable operation of the power grid. This paper proposes a multi-objective optimal scheduling strategy for EVs based on the price-based demand response (PDR) to solve the above problem. Firstly, it combines the period shift model and the user psychological model according to the user trip characteristics of EVs. And the charging load of EVs is obtained by Monte Carlo simulation. Then, the minimum load variance and the maximum customer satisfaction index (CSI) is taken as the objective functions. The non-dominated sorting genetic algorithm (NSGA-II) is used to solve the problem. The optimal compromise solution is chosen as the final solution after the algorithm obtains the Pareto solution set. The results show that the proposed optimization method can balance the relationship between load fluctuation and customer satisfaction. Keywords: Electric vehicle · Peak-valley power price · Demand response · Customer satisfaction index · Multi-objective optimization
1 Introduction The electric vehicle (EV) industry has ushered in a blowout stage of development with the proposal of the carbon neutrality [1]. However, allowing disorderly charging of largescale EVs will have a noticeable impact on the power grid [2]. Making full use of the demand response (DR) characteristics of EVs can not only reduce the impact of EV charging power on the power grid, but also play an important role in peak shaving and valley filling for the original load of the power grid [3]. Some researches have considered Vehicle-to-grid (V2G) technology [4], but most of EVs still use slow charging now. The price-based demand response (PDR) based on time of use (TOU) power price is a relatively mature scheduling method for slow
© Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 579–587, 2023. https://doi.org/10.1007/978-981-99-1027-4_59
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charging at present [5]. Sun et al. [6] proposes a joint optimal scheduling model of the wind-storage hybrid system and the DR resources of EVs, with the maximum system revenue as the objective function. Chen et al. [7] establishes an EV mobility model considering randomness based on the parking generation rate theory, with the minimum load fluctuation and the minimum charging cost as the objective functions. However, the above researches only consider the economy in the scheduling process, ignoring the psychological expectations of EV users in the response process. The DR strategies that comprehensively consider the economy, timeliness and convenience of EV groups will become the breakthrough direction of the follow-up researches. Based on the above background, this paper proposes an EV optimal scheduling strategy based on PDR. The main contributions are as follows: (1) The period shift model and the user psychological model are combined to measure the response effect of EV users to TOU power price. The combined model accurately depicts the behavior of users who change their original charging habits after receiving the price signal. (2) The optimal scheduling strategy not only suppresses the load fluctuation, but also takes into account the satisfaction of users’ participation in DR, and reasonably improves users’ adhesion and sensory experience. The rest of this paper is organized as follows: Sect. 2 establishes the DR model of EVs. Section 3 explains the optimal scheduling method in this study. Section 4 analyzes the optimization results according to specific cases. Section 5 draws a conclusion for this paper.
2 Demand Response Model of Electric Vehicle 2.1 Overall Framework of the System Based on the user trip characteristics, the DR model of EVs is constructed by combining the period shift model and the user psychological model. The system specifies power price for EV users according to this DR model. The users will change their original power consumption habits according to their own conditions after receiving the price signal, so as to achieve the effect of peak shaving and valley filling. The non-dominated sorting genetic algorithm (NSGA-II) is used to solve the problem, and the minimum load variance and the maximum customer satisfaction index (CSI) are the objective functions. CSI includes the comfort satisfaction (CSIcom ) and the economy satisfaction (CSIeco ). The system obtains the Pareto solution set, substitutes each solution into the fuzzy membership function, and selects the optimal compromise solution. The overall framework is shown in Fig. 1.
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Fig. 1. Overall framework diagram of the system
2.2 User Trip Characteristics There are many factors that may affect the charging load of EVs under disorderly charging, including EV users’ return time, driving mileage and battery parameters, etc. [8]. This paper considers the slow constant power charging of EVs, assuming that the charging process is not disturbed by external factors. The daily return time, driving mileage and charging time of EV users are shown in (1)-(3). ⎧ 2 ⎨ √1 exp − (t0 −μ2t ) , μt − 12 < t0 ≤ 24 2σt σt 2π (1) ft (t0 ) = 2 ⎩ √1 exp − (t0 −μt +24) , 0 < t0 ≤ μt − 12 2 2σ σt 2π t 1 1 (ln S − μs )2 fs (S) = (2) √ exp − S σs 2π 2σs2 Tc =
S ×E Pc × ηc
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where, t0 is the return time, and the mean μt and variance σt of its normal distribution are 17.6 and 3.4 respectively. S is the daily mileage, the mean μs and variance σs of its lognormal distribution are 3.2 and 0.88 respectively. Tc is the corresponding charging duration, E is the power consumption per kilometer of EV, Pc is the charging power of EV, and ηc is the charging efficiency of EV. 2.3 Period Shift Model and User Psychological Model This paper combines the period shift model [9] and the user psychological model [10] based on peak-valley power price. The combined model can more accurately describe the behavior of users who change their original charging habits after receiving the price signal. TOU power price divides a day into three periods: peak period, off peak period and valley period, as shown in Table 1. When the difference of the power prices is too large in different periods, some users will consider transferring the power consumption period to pocket the difference.
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Peak period
Off peak period
Valley period
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0:00–8:00
In the EV user psychological model, there are three zones: saturation zone, linear zone and dead zone. Peak-valley load transfer rate λp - v is shown in (4). The models of peak-off peak λp−o and off peak-valley λo - v are similar and will not be repeated here. lp−v and hp−v are threshold and saturation values respectively. πp−v refers to the difference between peak and valley power price. λmax is the maximum load transfer rate. ⎧ 0 0 < πp−v < lp−v ⎪ ⎨ πp−v −lp−v λmax lp−v < πp−v < hp−v λp−v = (4) h −l ⎪ ⎩ p−v p−v λmax πp−v > hp−v There will be λp−v × Npeak EV users who voluntarily transfer charging from peak period to valley period. Npeak is the number of users returning during peak period. The charging start time tsc of these users follows a certain rule, as shown in (5):
t + α1 (tv − Tc ), 0 ≤ Tc < tv (5) tsc = v1 tv1 , tc > tv where, tv is the duration of valley period. tv2 and tv1 are the end and start time of valley period respectively. tv = tv2 − tv1 . α1 is a random number between 0 and 1. Based on the above models, the calculation process of EV load can be obtained, as shown in Fig. 2. In this study, the new charging start time tsc is used to replace the return time t0 . The output charging load PEV can be obtained through Monte Carlo simulation, and the specific principle can be referred to [11]. 2.4 Customer Satisfaction Model of Electric Vehicle This paper introduces the customer satisfaction index (CSI) [12] to quantify the satisfaction of EV users in all aspects. CSI includes two sub indexes: the customer comfort satisfaction (CSIcom ) and the customer economy satisfaction (CSIeco ), as shown in (7)– (8). CSIcom represents the change of users’ sense of experience in DR, while CSIeco represents the benefits obtained by users in DR. Most of the current researches focus on improving the economic benefits of EV users, ignoring the discomfort caused by users’ changing their original power consumption habits, and CSI can make up for this deficiency. CSI = CSIcom + CSIeco
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t V2 > V1 . Therefore, when loading irregular areas, standard modules with lower heights are preferred [6]. Figure 3 shows an example of parameter calculation for standard modules in different areas of the entire air container. Intelligent Loading Algorithm. The complete flowchart of the intelligent loading algorithm is shown in Fig. 4.
3 Experiment Using the standard module loading algorithm based on greedy search, the loading experiment of four standard modules of AKE air container with the height of 10 cm, 20 cm,
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Si-Stmax 1.5 ⎨ 0, RFij = 0.5, 1.2 < RIij ≤ 1.5 (6) ⎪ ⎩ RIij ≤ 1.2 1, Generally speaking, when RI is greater than 1.5, the transfer should not be adopted; When RI is less than or equal to 1.2, the detour can be omitted, that is, RF is 1; RF is considered as 0.5 when RI is between 1.2 and 1.5. Since both TF and RF are both belong to [0, 1], the smaller the TF and RF are, i.e., the smaller the connection quality index (QCI) is, the worse the connection service is. Finally, the hub connectivity indicator (HCI) of the two airports can be expressed by the sum of the connecting quality QCIs of all effective connecting flights, as shown in Eq. (7): xij × QCIij (7) HCI = i∈I a j∈I d
3 Case Study—Evaluation of Flight Connection of Beijing Dual Airports 3.1 Operation Status of Beijing Double Airport With the official opening of Beijing Daxing International Airport (IATA: PKX, ICAO: ZBAD) in September 2019, Beijing has officially entered the development stage of dual international airports. According to the 2020 Civil Aviation Airport Production Statistics Bulletin [12], Daxing Airport has completed a passenger throughput of 16.09 million person-times, cargo throughput of 70000 tons, and take-off and landing sorties of 133000 aircraft in 20 years. According to reports [13], the passenger throughput of Daxing Airport has exceeded 25 million person-times in 2021 with the trend of rapid growth. 3.2 Evaluation of the Connecting Quality of Beijing Double Airports At present, the following ground transport modes are available for passengers from Daxing Airport to Capital Airport: 1. Public transport. Passengers mainly take public transport from Daxing Airport Line to Caoqiao metro station, then transfer through Line 10 and Line 19, and finally transfer to the Capital Airport Line and arrive at the Capital Airport. It takes about 2 h, and the ticket price is 65 yuan (0.14 US dollars/yuan). 2. Taxi. It takes about one hour by taxi, and the fare is 210 yuan. See Table 1 for the associated times and costs.
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65
On the whole, it is not convenient to transfer by the public transport between Beijing’s dual airports at present. The number of transfers by using public transport is about three and taxis are expensive. Passengers need a long time or a high cost to complete the transfer between the two airports. First of all, according to the transfer time between Beijing’s two airports and the recommended value in the literature [17], the MCT and MACT within the same airport and between the dual airports, in this case, are shown in Table 2. Table 2. Minimum and maximum transfer time of Beijing double airport. Transfer airport
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150
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This case study selects all domestic and foreign flight information of Beijing Capital Airport and Daxing Airport on October 1, 2021, including takeoff and landing airport, airport code, airport longitude and latitude, and the airlines. However, due to the difficulty in obtaining data, this study has the following limitations: 1. The terminal building of the flight that affects the transfer time is not available, so it is impossible to distinguish between the same terminal building and the double terminal buildings in the single airport transfer; 2. The flight information of airports other than Daxing Airport and Capital Airport has not been obtained, so it is impossible to judge whether there is a direct flight corresponding with the transfer flights, and it is unable to distinguish the attractiveness of connecting flights since whether there is a direct service is unknown. In the flight information obtained, 2518 flights are taking off and landed at the two airports on the day. Specifically, 770 flights took off from the Capital Airport, 756 flights landed, 498 flights took off from Daxing Airport, and 494 flights landed. The number of dual airport takeoff and landing flights in each period are shown in Fig. 1. The calculation of flight connection quality HCI of dual airports is applied to the case
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study. Considering the different transfer time requirements of the same airport and dual airports, the great circle distance between airports is calculated by the longitude and latitude coordinates of each airport in the data. The great circle distance is calculated by the python’s geopy package. The flight time is estimated by the distance and the average speed of the aircraft, and the average speed is set as 500km/h. As for the determination of the transfer time penalty factor σ in the time index, it is considered here that the same airport transfer time is 1, and the double airport transfer time is 1.5. In addition, due to the greater inconvenience caused by the suspension of public transport operations at night, the transfer penalty factor for the double airports from 0:00 to 6:00 am is set as 2. The calculated total number of connecting flights (QVC), effective connecting flights (QCI > 0), and airport connecting quality index (HCI) of airlines at individual Capital Airport, individual Daxing Airport, and dual airports as a whole are shown in Table 3 (airlines with two few connecting flights are not shown).
(a) The num of flights in Capital Airport (PEK)
(b) The num of flights in Daxing Airport (PKX)
Fig. 1. The number of flights taking off and landing Beijing dual airports
Table 3. Connection quality of each airline in Beijing dual airports. Capital airport
Daxing airport
Double airports
Airlines
QVC
(QCI > 0)
HCI
QVC
(QCI > 0)
HCI
QVC
(QCI > 0)
HCI
Summary
35860
11504
6416.90
15540
4175
2093.87
156420
49032
18600.57
Air China
5160
1891
1135.46
125
42
18.20
8442
2979
1501.44
China Southern
11
0
0
1955
502
277.09
2516
561
298.40
Hainan
314
74
41.82
−
−
−
314
74
41.82
China United
−
−
−
239
99
48.87
239
99
48.87
China Eastern
46
0
0
1383
293
131.61
2459
459
164.91
Shenzhen
1620
505
259.52
5
0
0
1791
574
272.18
First of all, it can be seen that HCI of the dual airports as a whole is significantly greater than their own respective HCIs independently, which indicates that the two airports have the advantage of significantly expanding flight connection services. In
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addition, the HCI index can be converted into the number of effective connecting flights provided, that is, the number of indirect connections. It can be seen that the transfer between Beijing’s two airports can significantly increase the number of indirect services and provide a wider range of airport services. In addition, it can be observed that Hainan Airlines, Shenzhen Airlines, China Southern Airlines, and China United Airlines cannot provide good connection services at one of the airports, but more effective connections can be obtained after the joint transfer between the two airports. To sum up, the effective connection quality under the Beijing dual airport model has been greatly improved, which brings huge benefits. Optimizing flight schedules to provide more effective connections should be the focus of all airlines.
(a)
(b)
Fig. 2. Evaluation of Beijing double airport connection quality.
In addition, the ratio between the number of flights to be continued by each airline and the total number of flights, as well as the average connection index is analyzed, as shown in Fig. 2. It can be seen that in the average number of effective connections generated per flight, Air China has a huge advantage of 4.47, with Shenzhen Airlines ranking second with 1.67 and China Southern Airlines ranking third with 1.59. Among the effective connections, Hainan Airlines has the highest average connection quality, China Southern Airlines and Air China International are the second and third, and China Eastern Airlines has the worst average HCI performance. Considering that the Beijing double airport intercity railway connection line will be opened in recent years, with a technical speed of 200km/h, the transfer time between the two airports will be reduced to 40 min to achieve a seamless air-rail connection. Here, it is qualitatively considered that the transfer time penalties for the two airports will be reduced to 1.2 and 1.6 (at night), and the minimum transfer time will be reduced to 130 (domestic) and 160 (foreign). The changes in the number and time of flights will not be considered temporarily, According to the above parameter settings, after the opening of the intercity railway in the future, the effective number of connections between Beijing’s two airports will reach 55223 (currently 49032), and the connection quality index (HCI) will reach 22541.2 (currently 18600.57), that is, the opening of the intercity railway connecting Beijing’s two airports will bring higher benefits for the connection between the two airports, and further promote the joint development of the two airports.
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4 Conclusions This paper analyzes the flight connection quality of Beijing dual airports. First, it analyzes the characteristics, advantages, and disadvantages of current dual airports and regional multi-airports, and summarizes the current development and research status of dual airports. Then, it elaborates on the calculation method of the connection and transfer quality of dual airports in detail, and applies the calculation method to Beijing dual airports, using actual flight data, this paper analyzes the effective connecting quantity and connecting service quality of each airline in Beijing dual airport, and analyzes the influence of the construction of the future dual airport intercity railway on the transfer quality. The future research direction should take into account the impact of different terminal buildings on the transfer when the data are complete and consider the reduced attractiveness of transfer flights when there is a direct service. Further research should also consider the transfer service discrepancy among different airports, evaluation method can be referred to Shi [14], where they evaluate the service in a railway station. Acknowledgments. This work is supported by the Major Program of Fundamental Research Funds for the Central Universities (No.2021JBZ106) and the Joint Funds of the National Natural Science Foundation of China (No.U2034208).
References 1. Statistical Bulletin of Civil Aviation Industry Development in 2020 Civil Aviation Administration of China (2021) 2. Yang, Z., Yu, S., Notteboom, T: Airport location in multiple airport regions (MARs). The role of land and airside accessibility. J. Transp. Geogr. 52, 98–110 (2016) 3. Doganis, R., Dennis, N: Lessons in hubbing. Airl. Bus., 42–47(1989) 4. Usami, M., Manabe, M., Kimura, S: Airport choice and flight connectivity among domestic and international passengers-Empirical analysis using passenger movement survey data in Japan. J. Air Transp. Manag., 58(jan.), 15–20 (2017) 5. Veldhuis, J.: The competitive position of airline networks. J. Air Transp. Manag. 3, 181–188 (1997) 6. Burghouwt, G., de Wit, J.: Temporal configurations of European airline networks. J. Air Transp. Manag. 11, 185–198 (2005) 7. Huang, J., Wang, J: A comparison of indirect connectivity in Chinese airport hubs: 2010 versus. J. Air Transp. Manag, 65, 29–39 (2017) 8. Li, W.K., Miyoshi, C., Pagliari, R.: Dual-hub network connectivity: An analysis of all Nippon Airways’ use of Tokyo’s Haneda and Narita airports. J. Air Transp. Manag. 23, 12–16 (2012) 9. Yang, H., Liu, W.: Dual-hub connectivity: a case study on China Eastern Airlines in Shanghai. Eur. Transp. Res. Rev. 11, 1 (2019) 10. Gong, Z.G: Research on airport site selection in multi-airport area and optimization of land use and industrial cluster in airport area. Dalian Maritime University(2019). (in Chinese) 11. Qiu, B., Fan, W.: Travel time forecasting on a freeway corridor: a dynamic information fusion model based on the random forests approach. Smart Resilient Transp. 3(2), 131–148 (2021) 12. Civil Aviation Administration of China.: Production statistics bulletin of civil aviation airport in 2020. (in Chinese)
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13. The passenger throughput of Daxing International Airport will exceed 25 million person times in 2021.: https://baijiahao.baidu.com/s?id=1720763981967464323&wfr=spider&for=pc. (in Chinese) 14. Shi, R., Feng, X., Li, K., Tao, Z.: Evaluation of passenger service within the area of Beijing west railway station. Smart Resilient Transp. 4(1), 2–11 (2022)
Recognition of Remote and Small Intrusion Targets Around High-Speed Railway Based on Deep Learning Method Mengting Lu1 and Zhengyu Xie1,2,3,4(B) 1 School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
[email protected]
2 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University,
Beijing 100044, China 3 Key Lab of Proactive Safety and Risk Control in Railway Operation, Beijing 100044, China 4 Beijing Research Center of Urban Traffic Information Sensing and Service Technologies,
Beijing 100044, China
Abstract. With the rapid development of high-speed railway, its operation management and traffic safety are becoming more and more important. Foreign matter intrusion around high-speed railway needs to be timely prevented and identified. The current intrusion target recognition system still has the problems of high miss rate and false detection rate for the recognition of small intrusion targets beyond 100m. In this paper, aiming at this practical problem, combined with the deep learning target detection algorithm and the requirements of high-speed railway perimeter prevention and control, a system with better intrusion target recognition effect is designed to make up for the shortcomings of current high-speed railway perimeter video monitoring. Based on the actual video monitoring picture of highspeed railway, this experiment establishes a data set of far and small intrusion target recognition of high-speed railway perimeter, and establishes a complete evaluation standard system. Through the selection of algorithm model, it improves the ability of far and small intrusion target recognition of high-speed railway perimeter, and combines the algorithm to establish a far and small intrusion target recognition system of high-speed railway perimeter. Keywords: High-speed railway · Small target · Target detection · Deep learning
1 Foreword 1.1 Research Background and Significance With the rapid development of modern science and technology and the significant improvement of national economic level, and the safety of high-speed railway perimeter has been promoted to a new height. It has become an important content of modern traffic security work to be able to timely and accurately identify the intrusion targets of high-speed railway perimeter. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 935–945, 2023. https://doi.org/10.1007/978-981-99-1027-4_98
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However, due to the large track space of high-speed railway and the imperfect infrastructure protection facilities around the track, it is impossible to use intrusion target detection devices on a large scale, resulting in serious traffic accidents caused by the intrusion of vehicles, non motor vehicles, pedestrians and other foreign matters around the railway. It can be seen from Fig. 1 that there are objects or human intrusion around the track, which has a certain impact on the safety of high-speed train operation.
Fig. 1. People intrude into the railway track
It can be seen that the current high-speed railway perimeter intrusion target recognition technology has defects, and the research on the track perimeter intrusion recognition technology is becoming more and more difficult. It is urgent to improve and improve it to reduce casualties, economic losses, and ensure the safety and order of railway operation. 1.2 Research Status at Home and Abroad 1.2.1 Abroad Research Status Houssam Salmane and others are committed to realizing intelligent video monitoring of level crossings. By detecting, separating and tracking moving objects at intersections, they establish the trajectory of moving objects, stop the dangerous state of the detected objects, estimate the risk level of the target, and achieve the prediction and evaluation of various traffic accidents [1]. Alin Achim proposed a new combined detection method based on pixel statistics, which combines the Gaussian mixture model with the block based detection technology, and can effectively detect moving objects in the measured area [2]. TB Nguyen proposed a real-time monitoring gait detection method based on embedded technology, using histogram and selective search technology, and using background difference method and mixed Gaussian model to limit candidate areas [3]. Ciresm D proposed a target detection algorithm based on DNN, which was completed by using a parameterized CPU. Without additional feature extractor, the traffic signal can be quickly recognized [4].
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1.2.2 Domestic Research Status Liu Yang of the Third Railway Exploration Institute and others proposed a non-contact target detection method, which uses the dual grid power system to determine whether there is foreign matter intrusion around the railway through the signals sent by sensors, but is vulnerable to misinformation due to the impact of external environmental factors [5]. Li Feng from the University of Science and Technology of China proposed a target detection method for pedestrian movement in surveillance video. Using mixed Gaussian model and directional gradient, moving objects in the video image area are segmented, and the detected moving objects are divided into non human and human. Qu Jianming of Xi’an University of Science and Technology proposed an algorithm for target detection of pedestrians and moving vehicles on the road. He combined AdaBoost classifier and directional weighting to classify moving targets in the pixel area of the image, which can recognize the posture of pedestrians on the road and track and detect moving vehicles [6]. 1.2.3 Analysis of Research Status At present, most of the railway tracks in our country use contact target detection technology, but because of its high equipment costs, the equipment cannot withstand the interference of external environmental factors, and cannot achieve large-scale coverage around the railway tracks. And the current paper only analyzes the performance of perimeter intrusion target detection in the depth learning method, which is aimed at target detection for pictures. It does not take into account the actual application functional requirements of high-speed railway perimeter intrusion target recognition, and lacks a high-speed railway perimeter intrusion target recognition system with fusion algorithm, which can be put into practical application and has clear functions. 1.3 Main Contents of This Article The research work of this paper is to use the target recognition method based on deep learning to detect high-speed railway perimeter intruders, that is, select the deep learning algorithm model and train it to achieve accurate positioning and classification of intrusion targets, and establish a set of high-speed railway perimeter intrusion recognition system based on deep learning method, which can be put into practical application, improve the safety of high-speed railway driving, and provide guarantee for the normal operation of the railway. The experimental environment designed in this paper is the surrounding area of the railway with a good vision, and the appropriate deep learning network is selected for training to achieve the purpose of accurate identification of the perimeter intrusion target.
2 Target Detection Algorithm Based on Deep Learning 2.1 Single State Target Detection Network The typical algorithms based on deep neural network are YOLO (You Only Look Once) series algorithms, which are mainly used for target recognition and location. They run
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fast and can be applied to target detection in real-time systems. YOLO network mainly includes three parts: Part I: Backbone convolution neural network, which can accurately aggregate various images to form image features; The second part: Neck, a group of hybrid networks containing multiple image features, transfers these features to the prediction layer; Part III: Head, image feature prediction, edge box generation and target classification prediction [7]. This algorithm is a typical single-stage target detection algorithm. Its detection speed is faster than that of two-stage detection algorithm, and it greatly makes up for the fatal disadvantage of the lack of accuracy of single-stage algorithm and greatly improves the detection accuracy. The experimental data shows that YOLO V4 algorithm has significantly improved both in speed and accuracy. On the COCO dataset, using YOLO V4 for target detection, its average detection accuracy (AP) has increased by 10%, and the frame rate (FPS) of target detection has increased by 12%. Combining the significant advantages of the deep learning target detection method in recent years, YOLO V4 is combined with the YOLOV3 algorithm network [8]. YOLO V4 performs well in the field of target detection, with a detection speed of 65FPS per second. The enhanced feature extraction network in YOLO V4 is upgraded through the Feature Pyramid Network (FPN) adopted by YOLO V3 and combined with the Spatial Pyramid Pool (SPP); The prediction network still adopts YOLO Head in YOLO V3, while DIOU_ NMS is used to filter the prediction box to finally generate a model framework of “CSPParknet53 + SPP_PANet + YOLO Head”. Figure 2 is the algorithm schematic diagram of YOLO V4 [9].
Fig. 2. Network architecture diagram of YOLO V4
2.2 Two-Stage Target Detection Network Compared with the traditional target detection algorithm, the two-stage target detection algorithm has the same target detection process. First, obtain the target candidate box, then extract features from the candidate box, and finally generate the detection results. The commonly used two-stage target detection networks are R-CNN and Fast R-CNN and Fast R-CNN based on it. Faster R-CNN adds a neural network edge extraction algorithm to find candidate boxes. This algorithm includes PRN candidate block extraction and Fast R-CNN detection. PRN is a full convolution neural network. Faster R-CNN extracts candidate blocks
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from PRN and performs target recognition in the candidate block area [10]. On this basis, the four basic steps of target recognition (generating candidate regions, extracting features, classifying, and positioning refinement) are integrated into a deep network architecture. To sum up, we can see that a typical two-stage target detection algorithm, Faster R-CNN, divides the target detection process into two stages [11]. The first step is to generate a candidate region containing the approximate location information of the target, and the second step is to fine adjust the classification and specific location of the target in the region. The recognition error rate of this method is low, but the speed is very slow. It is difficult to achieve the real-time detection effect that high-speed railway perimeter intrusion target recognition wants. The prediction speed is stable at 0.7 fps. If the parameters are adjusted and the number of candidate boxes is reduced, the accuracy rate will drop by about 4%, and the speed can reach about 2 fps. But this speed is still very slow for real-time detection [12]. YOLO V4 algorithm is much faster than the RCNN system, and it is kept within the range of 2.4 fps. In addition, the feature extraction layer of YOLO V4 adopts the structure of feature pyramid and down sampling. Mosaic is used for data enhancement during training, so it can also achieve good results in small target detection. This paper mainly detects the intrusion targets around the high-speed railway [13]. The existing intelligent video analysis system is suitable for the intrusion target recognition within 0–100m. However, for the detection of the 100−200m intrusion targets, namely “far small” targets, there is still a problem of insufficient detection accuracy, false positives, missing reports, etc.
3 Experiment Data Set 3.1 Definition of Small Target In the surrounding environment of high-speed railway, the identification of small targets is a very important link, which plays a vital role in ensuring the safety and order of train operation. In the standard COCO dataset, the pixel area is used as the division unit. The definition of small targets is shown in Table 1. Table 1. Definition of small target in standard COCO dataset Minimum rectangular area
Maximum rectangular area
Small target
0*0
32*32
Medium target
32*32
96*96
Big target
96*96
∞*∞
This paper focuses on solving the “far and small” intrusion targets at the perimeter of high-speed railway, as shown in the framed targets in Fig. 3. Compared with ordinary pictures, such targets occupy less pixel areas in the image, and the target is fuzzy and easy
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to be overlooked. It is relatively difficult to identify the target objects in such images, and it is easy to miss detection and false detection. The performance requirements for target detection algorithms are more stringent [14].
Fig. 3. Schematic of far and small invasion targets
3.2 Data Set Construction 3.2.1 Dataset Content The high-speed railway perimeter intrusion data in this paper is collected from the monitoring video of a high-speed railway perimeter. The filtered video is divided into image format, data amplification and processing, data classification, and image annotation. Finally, the intrusion data around the high-speed railway is obtained. 3.2.2 Dataset Tags After the video framing, filtering and amplification operations are completed, the data in the data set has reached 420 * 7 = 2940 pictures in total. The test set, verification set and training set are selected according to the proportion of 8:1:1. The selection method of each set and the number of selected pictures are as follows: (1) According to the same interval sequence, 294 images are selected from the data set as the verification set, and 2646 images remain; (2) 336 images of each type after data set amplification are selected as training sets. There are 2352 test sets in total, and 294 images remain; (3) All the remaining pictures are used as the test set, 294 pictures in total; The images of test set and training set are marked with LabelImg software.
4 Analysis of Experimental Results Under the same data set and experimental conditions, the calculation results of YOLO V4 algorithm and Faster R-CNN are compared in terms of evaluation indicators. The loss value of the YOLO V4 target detection algorithm selected in this paper continues to
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Fig. 4. YOLO V4 loss function curve image
decrease during the training process. After the loss value data is extracted and visualized, the loss image can be seen as shown in Fig. 4. As shown in Figs. 5 and 6 below, YOLO V4 can accurately identify two intruders within the high-speed railway perimeter in the picture under the same data set and hardware facilities training conditions, and mark the category attributes of the target classification, such as “person” and “car” in the picture. After Faster R-CNN network training, the intruders will be identified, and the intruders in the picture are relatively close, Faster R-CNN can also carry out accurate marking and classification.
Fig. 5. YOLO V4 close range recognition
Fig. 6. Faster R-CNN short range recognition
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As shown in the figure below, YOLO V4 can accurately identify small targets that are far away, but Faster R-CNN has a poor recognition effect on small targets and generates two candidate boxes for the same target in case of false positives.
Fig. 7. Faster R-CNN remote recognition
The performance of the detection results of the two algorithms is analyzed, and the established target recognition evaluation indicators are used for comparison under a unified metric, as shown in Figs. 7 and 8 below, which is the recall index curve of Faster R-CNN. Two different categories “person” and “car” are calculated respectively. Therefore, the average value of both is taken when calculating the recall value of the algorithm, and the other indicators are calculated using the same method, The specific data of target recognition effect comparison between the two algorithms are shown in Table 2.
Fig. 8. Recall performance of Faster R-CNN algorithm
Table 2. Comparison of target recognition effects Using algorithms
AP (%)
Precision (%)
Recall (%)
FPS
Faster R-CNN
77.1
49.5
89.4
47
YOLO V4
89.2
92.6
86.5
54
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In conclusion, compared with Faster R-CNN, YOLO-V4 has great advantages in all aspects except its large model structure. Especially in terms of accuracy, Faster RCNN, as a two-stage model, sacrifices the detection speed of intrusion targets to improve the detection accuracy. Although the detection effect recall rate is good, the high error detection rate causes the imbalance between the two, YOLO V4 algorithm achieves a good balance in real-time, accuracy and recall, and can well meet the requirements of high-speed railway perimeter remote small intrusion target recognition on real-time and accuracy. Therefore, when building the far and small intrusion target recognition system for the high-speed railway perimeter, we choose to integrate YOLO V4 algorithm to design the system.
5 Remote and Small Intrusion Target Detection System for High Speed Railway Perimeter Click the “Select Image” button, jump out of the folder and select the image. The selected image file will appear in the left box. Click the “Start Identification” button, and call the trained YOLO V4 algorithm to identify the intrusion. The identification results are shown in Fig. 9. The types of intrusion will be displayed under the “Target Identification Results” at the bottom right, It will also frame the position of the entry and exit objects in the image to be identified and mark the type of intrusion at the location.
Fig. 9. Display of image target recognition results
First, click the “Select Video File” button, jump out of the folder directory and select the video file, as shown in Fig. 10 below. The QTimer timer starts, the background will process the video file into an image format, and call the trained YOLO V4 algorithm to identify the intruders in the image. The identification results will be dynamically displayed in Fig. 10, and the types of intruders will be dynamically displayed under the “Target Identification Results” at the lower right. In addition, the location of the objects in and out of the frame in the identified video and the type of the intrusion at the mark will be changed from the original “Select Video File” button to the “Stop Video Detection” button. Clicking the “Stop Video Detection” button will stop the intrusion target identification of the selected video file and restore the initial interface.
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Fig. 10. Recognition results of video target recognition
Click the “Open Camera” button to automatically connect to the camera of the computer, and display the image monitored by the camera in the left box. The identification results will be displayed dynamically. As the camera attached to the computer is connected, there is no way to detect the high-speed railway perimeter image.
6 Summary In this paper, a video analysis system for high-speed railway peripheral monitoring based on deep learning method is proposed to improve the recognition accuracy of far and small intrusion objects around the perimeter and the real-time performance of target recognition. Through the high-speed railway perimeter long-distance intrusion target recognition experiment, adjust the parameters of the algorithm, according to the established unified evaluation criteria, analyze and optimize the test data to achieve the best target recognition effect. Finally, the target detection algorithm with the best target recognition performance selected is combined with the software to build a high-speed railway perimeter far small intrusion target recognition system, and functional modules of the system are introduced in detail. Acknowledgments. This work was supported in part by the National Key Research and Development Program of China under Grant 2020YFF0304104.
References 1. Salmane, H., Khoudour, L., Ruichek, Y., et al.: A video-analysis-based railway-road safety system for detecting hazard situations at level crossings. IEEE Trans. Intell. Transp. Syst. 16(2), 596–609 (2015) 2. Li, H., Achim, A., Bull, D.R.: GMM-based efficient foreground detection with adaptive region update, 2009: 3181–3184 3. Nguyen, T.B., Van Nguyen, T., Chung, S.T.: A real-time pedestr ian detection based on agmm and hog for embedded surveillance. J. Korea Multimed. Soc., 18(11), 1289–1301 (2015) 4. Ciresan, D., Meier, U., Masci, J., et al.: Multi-column deep neural network for traffic sign classification. Neural Netw. 32, 333–338 (2012)
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5. Liu, Y.: Study on an improved monitoring scheme for foreign matter intrusion into railway. Railw. Commun. Signal Eng. Technol., 10(2), 30–32 (2013) 6. Jianming, Q., Zhijing, L., Wenhua, H.: Directed weighted adaBoost target detection combined with scene motion mode. J. Xidian Univ. 42(3), 67–72 (2015) 7. Huang, L., Mao, X., Hang, D. etc.: Research on star catalog unstructured rock target identification method based on deep learning network. Space Control. Technol. Appl., 47(6), 27–33 (2021) 8. Aiping, Y., Shangyang, S., Simeng, C.: Lightweight adaptive feature selection target detection network. J. Northeast. Univ. (Nat. Sci. Ed.) 42(9), 1238–1245 (2021) 9. Jiang, J., Fu, X, Qin, R. et al.: High-speed lightweight ship detection algorithm based on yolo-v4 for three-channels RGB SAR image. Remote Sensing, 13(10), (2021) 10. Tao, Z., Sun, S., Luo, C.: Research on peanut pest image recognition based on Faster RCNN. Jiangsu Agric. Sci., 47(12), 247–250 (2019) 11. Zhang, Y., Du, H., Sun, Y. etc.: Remote sensing image target detection based on improved SSD algorithm. Comput. Eng., 47(9), 252–258, 265 (2021) 12. Gao, B., Zheng, K., Zhang, F., Su, R., Zhang, J., Wu, Y.: Research on multi-target tracking method based on multi-sensor fusion. Smart Resilient Transp. 4(2), 46–65 (2022) 13. Jia, L., et al.: On autonomous transportation systems. Smart Resilient Transp. 4(2), 66–77 (2022) 14. Zhao, R., Ma, X., Zhang, H., Dong, H., Qin, Y., Jia, L.: Enhanced densely dehazing network for single image haze removal under railway scenes. Smart Resilient Transp. 3(3), 218–234 (2021)
Facial Expression Recognition Algorithm Based on Multi-source Information Fusion Xun Xiao1,2,3,4 and Zhengyu Xie1,2,3,4(B) 1 School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
[email protected]
2 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University,
Beijing 100044, China 3 Key Lab of Proactive Safety and Risk Control in Railway Operation, Beijing 100044, China 4 Beijing Research Center of Urban Traffic Information Sensing and Service Technologies,
Beijing 100044, China
Abstract. In this paper, an expression recognition algorithm based on multisource image fusion detection is designed. The visible facial expression image and thermal facial expression image obtained by multi-sensor are used to train the expression recognition model of two channels, and the yolov5 target recognition algorithm is used to identify and classify the photos of the two modes respectively. In the part of modal fusion, decision-level fusion is used to fuse the classification results of the two channels to integrate the respective advantages of the two modes. The experimental results show that the fusion algorithm can have higher recognition accuracy and reduce the occurrence of misjudgment. Keywords: Decision layer fusion · Facial expression recognition · Object detection algorithm · Convolutional neural network
1 Introduce Urban rail transit system is an important part of urban public transport system, known as the ‘urban traffic aorta ’. As a modern rail transit, subway has gradually become the preferred travel tool for urban residents because of its convenience, speed and comfort. But because of this, the subway crowd has also become the subway needs to focus on and take care of the crowd, its abnormal behavior is worthy of further attention of the subway company, and emotional perception and recognition is one of the very important part. At present, the perception of emotion has always been a key issue in various fields of research. With the continuous development of artificial intelligence, the use of computers for emotion analysis is becoming more and more popular. Computer systems that can perceive, understand and even predict human emotions will play an invaluable role in the fields of health care, education and public transportation. In this paper, it is applied to the field of urban rail transit, and a simulated scene image data set is made to train and test the algorithm. Finally, the dual-channel detection results are fused and output. Experiments show that the detection accuracy of the fusion algorithm is higher than that of the single mode algorithm. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 946–958, 2023. https://doi.org/10.1007/978-981-99-1027-4_99
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2 Related Works At present, due to the rapid development of rail transit and the characteristics of serving a large population, the use of intelligent and big data technology to allow computers to deal with problems has become the focus of research in recent years. Guo et al. [1] and Yu et al. [2] introduced computer technology for data processing under the rail transit scenario, in order to better solve the original rail transit problems. 2.1 Facial Expression Recognition Facial expression is the most direct manifestation of human emotions. The research on facial expression recognition and detection began in the 1970 s. As early as 1971, Ekman et al. proposed six basic expressions of happiness, sadness, anger, disgust, surprise and fear based on the relationship between different facial expressions, and identified the basic categories of facial expressions. In 1978, Ekman et al. proposed a facial action coding system, which divided the muscles of the face into multiple motion units, and linked the muscle activity of the face to the basic expression category through the coding of each motion unit. Opened the research direction of facial expression recognition by detecting facial action units. After entering the 21st century, more people have realized the significance of facial expression recognition, thus promoting the development of facial expression recognition research. In the first decade of the 21st century, researchers tend to design hand-crafted features to distinguish expression categories according to the response value of face images to hand-crafted features, and then predict the expression of face images. But because the features are extracted manually, the generalization ability is not strong enough. And in the case of the increasing amount of data and the more complex image data, the cost of manually designing and extracting features is even greater. In recent years, due to the maturity of deep learning methods, deep learning methods are used to solve the problem of facial expression recognition. The deep learning method can use the end-to-end training method to adaptively extract deep high-dimensional features, without the need to manually design features and extract features with stronger robustness and generalization ability. Traditional artificial extraction features are gradually replaced by deep high-dimensional features or combined with deep features. Many complex and excellent deep learning networks are also applied to facial expression recognition. The recognition effect of various expression data sets is also gradually improved. Deep learning method has become the main method of facial expression recognition. Ran et al. [3]designed an expression recognition model based on facial key feature extraction. The model uses Resnet18 as the backbone network, adds attention mechanism and Dropout regularization, achieves the training effect of integrating multiple network models, and can further improve the generalization ability of the model. Finally, the feasibility of the method is verified by experiments. Based on the residual network ResNet18, Lan and Li et al. [4] combined filter response regularization (FRN), batch regularization (BN), instance regularization (IN) and group regularization (GN) into the network respectively to balance and improve the distribution of feature data and improve the performance of the model.
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Based on the position information of facial feature points, Wang et al. [5] used a multi-layer attention mechanism to assign different weights to different regions of the image after cutting and aligning the face image. The depth features of the original image and the images of each region are weighted and merged with the depth features of each region, and then the second layer of weighted fusion is performed on the features of each group after stitching to eliminate the influence of pose changes and occlusion problems in the image and improve the recognition effect. Hu et al. [6] proposed a facial expression recognition algorithm that is robust to pose diversity by using multi-instance learning method, and achieved an accuracy of 67.44% on the BU-4DFE dataset, which is 2.41% higher than that of directly extracting LBP features. Since the subway industry entered the 21st century, as the subway plays an increasingly important role in the travel activities of urban people, the emerging group of subway people has emerged. It is precisely because the subway crowd is so important, and there are few studies on the emotional aspects of the subway crowd. This will affect the long-term development of the subway industry, affecting social harmony and stability. Therefore, it is of great theoretical and practical significance to carry out research on subway crowd emotion detection. Wei [7] of Jinan University carried out research on the security monitoring system of subway, and designed a monitoring system based on facial feature analysis to monitor whether passengers’ behavior is abnormal. Through the analysis of various facial features (such as: static expression recognition, brow area wrinkles chaotic degree evaluation, mouth area left and right half of the similarity comparison, etc.) to complete the monitoring of passengers abnormal emotions. 2.2 Multi-source Information Fusion Multi-Source Information Fusion (MSIF) is a comprehensive and interdisciplinary subject. At present, the types of data and the means of data detection are becoming more and more diversified and complicated, which adds difficulty to the information fusion of multi-source data. Information fusion is to summarize and synthesize multiple information sources, which can obtain more accurate and clear inferences than from a single information source. The information fusion of thermal imaging and visible image has become an important research direction in the field of multi-source information fusion. Due to the different imaging principles, the focus and characteristics of the images taken by the two cameras are different. The thermal imaging image is obtained by collecting the infrared ray emitted by the object through the infrared sensing device. The characteristic is that the temperature attribute of the object is distinguished by the color photo when the image is obtained. It is sensitive to the target and area of the thermal characteristic and is not affected by the external light environment. Visible light images have higher spatial resolution, richer texture structure and better readability. Both have a considerable scale of application in their respective fields, and have important application value. With the development of deep learning technology, new breakthroughs have been made in the methods of thermal imaging and visible light fusion. Xia Han [8] proposed an infrared and visible light image fusion method using deep learning technology, and
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proposed an image fusion method based on generative adversarial and siamese networks, using the global semantic information of the image as a priori knowledge to drive fusion. Chen [9] proposed a supervised deep learning image fusion technology based on attention mechanism. By adding attention mechanism, it can adaptively refine the mapping of intermediate features and strengthen important features, thereby enhancing the quality of fused images. Li et al. [10] proposed a new deep learning architecture for infrared and visible image fusion. The coding network consists of a convolutional layer, a fusion layer and dense blocks, and two fusion layers (fusion strategy) are designed to fuse these features. Finally, the fused image is reconstructed by the decoder. On this basis, Li [11] further proposed a network model based on nested links for infrared and visible image fusion, which can store the information of two channels from a multi-scale perspective. Experiments show that this method has better fusion performance than other existing methods. Hao [12] applied the target detection algorithm to the dual-channel fire detection, used the thermal imaging image to supplement the deficiency of visible light for image detection, and established the transformation model of thermal imaging mapping to visible light image, so as to achieve the fusion of thermal imaging image and visible light image. Facial expression recognition can be well applied in public safety fields such as subways and subway stations. It can be used to assist subway security personnel to understand and evaluate the mental state of passengers. It plays an important role in preventing safety accidents and maintaining the safety of subway operation. However, most of the current expression recognition relies on visible light cameras to capture human expressions. In some scenes with dark lights or ambient light, it may be misleading to use visible light cameras to capture and recognize expressions. In order to eliminate the influence of light on the recognition of expressions by visible light cameras, this paper proposes an expression recognition method based on multi-source information fusion, which can improve the detection accuracy through the fusion of two channels.
3 Methodology Visible light is the part that the human eye can perceive in the electromagnetic spectrum, and the visible light sensor is based on the reflection of the visible light by the object. It is sensitive to the color and brightness information in the environment. The obtained image content is more easily understood by people, contains more detailed texture information, and the image background information is more detailed. The photos taken by the visible light camera have high resolution and can clearly identify the faces and expressions of the characters. The thermal imaging image is an image formed according to the level of thermal radiation of the detected object. It has obvious distinction for heat, has good information collection ability for heat emission target, is not easily affected by light and other conditions, and has good recognition ability for objects.
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In general, visible light images will be more significant for human facial features. Most of the current expression recognition algorithms rely on visible light images to complete the recognition and judgment of expressions. However, it is difficult to complete the recognition and judgment of facial expressions simply relying on visible images when the light conditions are special or blocked by rain and fog.
Fig. 1. Facial expression recognition in visible light images is difficult when light conditions are dark
As shown in Fig. 1, the human face is difficult to distinguish in visible light images when the light is dark. But in this environment, the recognition of thermal imaging photos is not affected, still be able to clearly identify the person’s facial features. Therefore, it is concluded that the thermal imaging image has obvious advantages in identifying the expression of people in weak light Fig. 2. In this paper, we use visible light camera and thermal imaging camera to collect image data, expand the channel of expression recognition, and propose a dual channel expression recognition model based on depth learning. In order to provide visible light and thermal imaging photos, this paper adopts the method of overlapping visible light cameras and thermal imaging cameras to capture people’s expressions at the same time, and uses the algorithm to call two cameras at the same time for synchronous shooting. The weight of the two detection models is obtained by training the visible light photos and thermal imaging photos taken respectively. After the images are input, the output results of the two detection models are fused at the decision-making level, and finally the expression judgment is completed. 3.1 Dataset At present, there are few studies on facial expression recognition using visible light + thermal imaging, especially when one-to-one correspondence between visible light photos and thermal imaging photos is required, and there is a lack of publicly available data sets. Therefore, this paper establishes a data set by means of fixed-point shooting and live performance, which is stored separately from visible light camera shooting photos and thermal imaging camera shooting photos. In this paper, facial expressions are divided into six categories: frown, neutral, surprise, mask-frown, mask-neutral and mask-surprise.
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Fig. 2. Algorithm procedure
The data set is divided into two parts: training set and test set. The training set photos are composed of 5400 visible light and 5400 thermal imaging photos, both of which are taken by two cameras at the same point and at the same time. The infrared thermal imaging data and visible light image data are paired with each other, 5400 for each, including 900 for each type of expression (Tables 1 and 2) Table 1. Train dataset: Facial expression classification and the number of visible light images (The composition of the thermal image dataset is the same as that of the visible image dataset) Class
The number of images
Frown
900
Neutral
900
Surprise
900
Mask-frown
900
Mask-neutral
900
Mask-surprise
900
Make Sense website is used to mark all the photos collected, and the position of the face in the figure is marked and the category is marked. The marking position includes
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the complete face of the participant, which is more conducive to the training of the algorithm and the convergence result. The test image data set is divided into visible light photos and thermal imaging photos, each part of a total of 168 photos. Table 2. Test dataset: Facial expression classification and the number of visible light images (The composition of the thermal image dataset is the same as that of the visible image dataset) Class
The number of images
Frown
28
Neutral
28
Surprise
28
Mask-frown
28
Mask-neutral
28
Mask-surprise
28
3.2 Data Preprocessing The size of the thermal imaging photograph taken is 512 * 640. The thermal imaging photos obtained by the thermal imaging camera need to be preprocessed, because there is no way to train the direct thermal imaging photos, so the thermal imaging photos can be converted into grayscale images for training. (Gamma transform is used after grayscale processing. The coefficient of gamma transform in this paper is 1.5, which has a strong expansion effect on the high grayscale part of the image. This processing can enhance the contrast of the image and prevent the occurrence of over brightness.). It can be seen that the facial features of the photos after grayscale processing are more obvious, which is more conducive to the recognition and detection of expressions Fig. 3.
Fig. 3. Thermal imaging image features more pronounced after preprocessing
Visible light photos and thermal imaging photos are acquired through video frame extraction, and the input image size is uniformly changed to 640 * 640 before training.
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3.3 Training In this paper, the target detection algorithm-yolov5 algorithm [13] is used to train two single-mode expression recognition models to obtain the weight of the corresponding channel model. The yolov5 algorithm is a relatively new target detection algorithm with fast operation speed and is more conducive to deployment on various lightweight devices. After weighing the performance and speed, this paper selects the smallest model yolov5 s in yolov5 for training to speed up its operation. Yolov5s comes with data augmentation methods that complete the data augmentation of the training set, such as mosaic data augmentation, HSV and other data augmentation methods. Data augmentation is very important in the training of target detection models. Its role generally includes: (1) Enrich the training data set and enhance the generalization ability of the model; (2) Increase data changes, improve the robustness of the model; (3) Alleviate the uneven distribution of small targets. Yolov5s model uses FPN and PAN structure to fuse multi-scale features. This is because the low-level network has less loss of target location information, while the semantic information of the high-level network is stronger. Therefore, it is necessary to perform feature fusion at different scales, so that feature maps of different sizes contain strong semantic information and strong location information to ensure accurate prediction of targets of different sizes. The output of the yolov5s model is divided into two parts. One part is the value of the regression part, which is the coordinate value of the prediction box. It is usually represented by the horizontal and vertical coordinates of the upper left corner and the lower right corner, so the regression part should be the vector of batch * 4. The other part is the value of the classification part, that is, what category the prediction box belongs to and the probability that it belongs to that category. In this article, because the twochannel classification part needs to be merged later, the output classification result of the original yolov5s model is changed to the prediction box for each of all categories. The probability of each category, so the classification part should be a vector of batch * num_class, where num_class is the number of categories that need to be identified. After completing the training of the dual-channel yolov5 s model, the next step is to perform an information fusion on the two channels. There are many methods of information fusion, including pixel-level fusion, feature-level fusion and decision-level fusion. Because the decision-level fusion has a great advantage in operation speed, this paper adopts the method of decision-level fusion. Since the feature information obtained by the expression recognition model of visible light and thermal imaging in different situations has its own advantages, the classification results obtained by the two channels are extracted at the decision-making level, and then the classification results of the two channels are fused by using the iterative fully connected layer of the two parameters. The final output is the posterior probability of each expression category after the fusion of visible light and thermal imaging. The classification part of the output result of the Yolov5 s model is in the form of category name + probability, and the output form needs to be appropriately changed
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to fuse. In this paper, the classification part of the output of the original algorithm is changed from the form of ’ category name + probability ’ to the form of corresponding probability for each category, that is, the number of vector columns of the detection result is num_class, and the categories are arranged from front to back, which is convenient for the next decision-making level fusion. In order to solve the problem that the results of the two channels are one-to-one correspondence of the same picture, this paper adopts the form of numbering, and adds the serial number after the results of the two channels to ensure that the two channels simultaneously analyze and fuse the same point picture. In order to solve the problem that a photo has multiple predicted objects, this paper uses the method of sorting the coordinate points of multiple prediction boxes in a picture to make the information not confused when the prediction boxes of the two channels are fused. The sorted classification data is extracted and sorted out to build a fully connected layer (linear layer), and two fully connected layer weights are trained to achieve a good fusion prediction result (Fig. 4).
4 Experimental Results and Analysis In this paper, experiments are carried out in the environment of python-based deep learning framework PyTorch. The experimental environment is: Ubuntu18.0 system. In order to evaluate the expression recognition performance of the fusion visible light image and thermal imaging image proposed in this paper, the following experiments are carried out: (1) Visible light image expression recognition and thermal imaging image expression recognition, as a single-mode expression recognition control group, are compared with the fused expression recognition results. (2) Fusion expression recognition experiments to verify the effectiveness of fusion expression recognition method of two images. 4.1 Single-Mode Expression Recognition Experiment Single-mode expression recognition refers to the expression recognition and detection using a certain type of photo of visible light photos or thermal imaging photos alone, because this article is to train the visible light photos and thermal imaging photos separately, forming two non-interference models. The single-mode expression recognition training uses the training part of the data set constructed in the third chapter. The training set is used to train the infrared thermal imaging expression recognition detection model and the visible light expression recognition model respectively. The weights of the visible light expression recognition model and the thermal imaging expression recognition model are obtained respectively, and then the model is tested and verified. In order to verify the recognition effect of separate visible light photos and thermal imaging photos and the contribution of the fusion of the two to expression recognition, the single-mode verification of the two models and the verification of the fusion model are performed respectively, and the test set after data preprocessing is used for verification (Fig. 5).
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Fig. 4. Structure of Multi—source Information model
It can be seen from the experimental results in the table that the visible light image has a more obvious effect on expression recognition, and the accuracy rate is 79.2%. It can be seen from the table that the visible light image has a better effect on frown and mask-frown expression recognition, while the recognition effect on surprise and maskneutral is relatively poor. Thermal imaging images also play a role in facial expression recognition and can recognize some expressions (Tables 3 and 4) 4.2 Single-Mode Expression Recognition Experiment As shown in Table 5, the fusion expression recognition experiment verifies the effectiveness of the fusion of two channels of visible light and thermal imaging for expression recognition. The average accuracy rate reaches 87.5%, which is higher than that of single visible light expression recognition and thermal imaging expression recognition. By
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Fig. 5. Comparison of experimental results of visible image and thermal image expression recognition
Table 3. Visible image facial expression recognition results Class
Labels
P(Predict)
R(Recall)
Acc(Accuracy)
All
168
0.849
0.518
0.792
Frown
28
0.955
0.464
Neutral
28
1
0.679
Surprise
28
0.651
1
Mask-frown
28
0.966
1
Mask-neutral
28
0.909
0.357
Mask-surprise
28
0.614
0.964
comparing the experimental results of single mode and fusion expression recognition, the advantages of fusion mode can be seen more intuitively: when the two channels are fused, the accuracy and recall rate of the expression of wearing masks are improved to a certain extent, so as to obtain the improvement of the overall recognition accuracy. It shows that both visible light and thermal imaging channels contribute to fusion recognition, and the information expressed can be complementary to a certain extent. Combining visible light and thermal imaging channels can improve the ability and reliability of facial expression recognition (Table 6).
5 Conclusion In this paper, an expression recognition method combining visible light channel and thermal imaging channel is designed. The two models are used to train their respective
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Table 4. Thermal image facial expression recognition results Class
Labels
P(Predict)
R(Recall)
Acc(Accuracy) 0.518
All
168
0.629
0.875
Frown
28
0.722
0.464
Neutral
28
0.484
0.536
Surprise
28
0.314
0.393
Mask-frown
28
1
0.464
Mask-neutral
28
0.818
0.321
Mask-surprise
28
0.433
0.929
Table 5. Fusion model facial expression recognition results Class
Labels
P(Predict)
R(Recall)
Acc(Accuracy) 0.875
All
168
0.879
0.875
Frown
28
0.917
0.786
Neutral
28
0.929
0.929
Surprise
28
0.844
0.964
Mask-frown
28
0.866
1
Mask-neutral
28
0.864
0.679
Mask-surprise
28
0.758
0.893
Table 6. Comparison of precision, recall and accuracy between single mode model and fusion model Mode
Labels
P(Predict)
R(Recall)
(Accuracy)
Visible light
28
0.849
0.792
0.791
Thermal
28
0.629
0.518
0.517
Visible light + Thermal
28
0.879
0.875
0.875
model weights, and finally the fusion and classification are carried out at the decisionmaking level. Experiments show that although in most cases, the ability of visible light photos to recognize expressions is better than that of superheated imaging photos However, when the light is dim or the light color is abnormal during shooting, the ability of the model to recognize visible light photos is weakened, while the thermal imaging photos are not affected. This fusion method can improve the recognition rate to a certain extent. This paper also shows that the use of deep learning method for automatic image feature extraction method is effective.
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Most of the expression data sets created in this paper are close-range photos, so it is difficult to achieve the expected effect in long-distance recognition. And most of them only include the front face of the character, and the number of photos of the top and bottom view is very small, so it will cause some angle expression recognition rate is not high. This is the next problem to be solved. Acknowledgments. This work was supported in part by the National Key Research and Development Program of China under Grant 2020YFF0304104.
References 1. Guo, H., Bai, Y., Hu, Q., Zhuang, H., Feng, X.: Optimization on metro timetable considering train capacity and passenger demand from intercity railways. Smart Resilient Transp. 3(1), 66–77 (2021). https://doi.org/10.1108/SRT-06-2020-0004 2. Yu, C., Li, H., Xu, X., Sun, Q.: Estimating left behind patterns in congested metro systems: a Bayesian model. Smart Resilient Transp. 3(2), 149–161 (2021). https://doi.org/10.1108/SRT09-2020-0008 3. Ran, R., Weng, W., Wang, N., Peng, S.: Facial expression recognition based on key facial feature extraction. Comput. Eng, 1–11 (2022). (in Chinese) 4. Lingqiang, L., Xin, L., Liu Qiyuan, L., Shuhua.: Facial expression recognition method based on joint regularization strategy. J. Beijing Univ. Aeronaut. Astronaut. 46(09), 1797–1806 (2020). (in Chinese) 5. Wang, K., Peng, X., Yang, J., Meng, D., Qiao, Y.: Region attention networks for pose and occlusion robust facial expression recognition. IEEE Trans. Image Process., 29, 4057-4069 (2020). https://doi.org/10.1109/TIP.2019.2956143 6. Hu, Q., Peng, X., Yang, P., Yang, F., Metaxas, D. N. (2014). Robust multi-pose facial expression recognition. In 2014 22nd International Conference on Pattern Recognition (pp. 1782-1787). IEEE 7. Wei, Z.: Research on subway security monitoring system based on facial feature analysis technology. Jinan University, Master (2016). (in Chinese) 8. Han, X.: Research on infrared and visible image fusion methods based on deep learning. Tianjin University, Master (2020). (in Chinese) 9. Zhijie, C.: Research on supervised deep learning image fusion algorithm based on attention mechanism. Tianjin Normal University, Master (2022). (in Chinese) 10. Li, H., Wu, X.J.: DenseFuse: A fusion approach to infrared and visible images. IEEE Trans Image Process (2018). https://doi.org/10.1109/TIP.2018.2887342 11. Li, H., Wu, X., Durrani, T.: NestFuse: An infrared and visible image fusion architecture based on nest connection and spatial/channel attention models. IEEE T Instrum Meas 69(12), 9645–9656 (2020). https://doi.org/10.1109/TIM.2020.3005230 12. Hao, X.: Research on cruise ship fire detection technology based on multi-sensor information fusion. Jiangsu University of Science and Technology, MS (2020). (in Chinese) 13. yolov5, https://github.com/ultralytics/yolov5. Last Accessed 10 Jan 2022
Optimization of Township Logistics Distribution Route Based on Simulated Annealing Algorithm Dongying Li and Li Wang(B) School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China {21120841,liwang}@bjtu.edu.cn
Abstract. With the development of the economy, the demand for township logistics has greatly increased. As the end link of the transportation process, the efficiency of logistics distribution directly affects the transportation cost and customer satisfaction. Compared with urban logistics, township logistics has the characteristics of fewer distribution centers, more decentralized logistics demands, and longer distribution distances, making it difficult to achieve point-to-point distribution. Meanwhile, there is less traffic congestion on the way of township logistics distribution, and the linear relationship between distribution distance and distribution time is more significant, so shortening the distribution time can be simplified as optimizing the distribution path. This paper collects the data of the distribution center in a township and the villages under its service, and uses the simulated annealing algorithm to optimize the distribution path. The optimization results show that the optimized path is 4.3% shorter than the original path, and the optimization effect is obvious. Keywords: Logistics distribution · Vehicle routing problem · Simulated annealing algorithm · Integer programming
1 Introduction In recent years, the express delivery industry has developed rapidly, the demand for logistics has continued to increase, and the requirements of logistics centers for distribution have also continued to increase. Logistics distribution is the end link of the entire logistics process, which refers to the distribution of goods from the logistics center to the users according to the users’ requirements. However, with the increase of goods in the logistics center, there are some problems that need to be solved, among which the optimization of the distribution path is an urgent problem to be solved. If the distribution path cannot be reasonably arranged, the distribution time and distribution cost will be increased, and both users and logistics centers will be affected to some extent. The optimization of distribution route is a typical VRP (Vehicle Routing Problem) problem [1], that is, for a series of delivery points and receiving points, organizing certain vehicles, arranging appropriate distribution routes, and making vehicles pass through them in an orderly manner. Under the specified constraints, such as demand limit of goods, delivery time limit, vehicle capacity limit, mileage limit, travel time © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 959–966, 2023. https://doi.org/10.1007/978-981-99-1027-4_100
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limit, aim to achieve certain goals, such as the shortest total mileage of vehicles empty, the lowest cost of transportation, the vehicles arrive at a certain time, the number of vehicles used is the smallest. At present, the optimization algorithms for solving VRP problems are mainly divided into exact solution algorithms and heuristic algorithms such as simulated annealing algorithms, genetic algorithms, ant colony algorithms, and tabu search algorithms. The exact algorithm is suitable for solving small-scale problems and can obtain the exact optimal solution, while for large-scale VRP problems, it is necessary to obtain approximate optimal solutions through heuristic search [2].
2 Mathematical Model 2.1 Problem Description and Model Assumptions In the township logistics distribution scenario, a distribution center is set up in the town, and the distribution center is equipped with several vehicles. The distribution center must complete the distribution tasks to the villages every day. The VRP problem is to find an optimal distribution plan, including vehicle allocation and distribution route selection [3]. According to the characteristics of township logistics distribution, the following assumptions are made for the model: (1) (2) (3) (4)
Unlimited vehicle capacity; Unlimited vehicle travel distance; Customer does not specify service time window; Each customer point is only served once.
2.2 Modeling In order to facilitate the reader to understand the model, the notations involved in this article are shown in the following Table 1. Table 1. Notations used in this paper. Notations
Meaning
O
Distribution center
P
Set of customer points
N
Set of all points
K
Set of vehicles
dij
Distance from point i to point j
Decision variables are 0–1 variables: 1 vehicle k completes the distribution task from point i to point j xijk = 0 otherwise
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According to the analysis of the problem, an integer programming model aiming at minimizing the delivery distance is established: min Z =
k
i
k
j
i
xihk −
i
j
dij xijk
k
xijk = 1 ∀j ∈ P
(1)
xijk = 1 ∀i ∈ P
(2)
xhjk = 0∀k ∈ K, h ∈ P
(3)
j
xojk ≤ 1 ∀k ∈ K
(4)
j
xijk ∈ {0, 1} ∀i ∈ N , j ∈ N , k ∈ K
(5)
Constraints (1) and (2) indicate that each customer point only accepts one vehicle for service. Constraint (3) is a traffic balance constraint. Constraint (4) indicates that each vehicle only arranges one delivery route. Constraint (5) is 0–1 decision variable.
3 Solution Algorithm The VRP problem is a typical NP-hard problem, and it is difficult to obtain its exact solution through an exact algorithm, so the heuristic intelligent optimization algorithm is generally chosen to solve it [4]. Among them, the simulated annealing algorithm can effectively avoid falling into the local optimum by giving the search process a time-varying probability that eventually tends to zero, and finally tends to the global optimum [5]. 3.1 Simulated Annealing Algorithm Theory At temperature Ti , after many transfers, reducing the temperature leads to Ti+1 < Ti , and repeating the above process under Ti+1 . Therefore, the whole optimization process is an alternating process of constantly finding new solutions and slowly cooling down. The final solution is the result of optimizing the problem. Under each Ti , a new state x(k + 1) is completely dependent on the previous state x(k), and can be independent of the previous state x(0), · · · x(k − 1), so this is a Markov process. To analyze the above steps of simulated annealing using the Markov process, and the results show that the probability of generating a new solution from any state x(k) is uniformly distributed in N (x(k)), and the probability that the new solution is accepted according to the Metropolis criterion. If the state of the material is defined by the energy of the particles, the Metropolis algorithm describes the annealing process with a simple mathematical model. Assuming that the energy of the material under the state i is E(i), the material will enter the state j from the state i at the temperature T following the rules below:
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a. If E(j) ≤ E(i), accept the state j. b. If E(j) > E(i), accept the state j with a probability of formula (6). e
E(i)−E(j) KT
(6)
where K is the Boltzmann constant and T is the material temperature. It can be seen that as the material temperature T decreases, the acceptance probability gradually decreases, indicating that the algorithm gradually tends to be stable. At a certain temperature, after sufficient conversion, the material will reach thermal equilibrium. At this time, the probability that the material is in state i follows the Boltzmann distribution: E(i)
e− KT PT (x = i) = E(j) e− KT
(7)
j∈S
where x represents the random variable of the current state i of the material, and S represents the set of state space. Calculate the limit for the above formula (7) to get: E(i)
e− KT 1 lim E(j) = T →∞ |S| e− KT
(8)
j∈S
where |S| denotes the number of states in the set S. This shows that all states have the same probability at high temperature. When the temperature drops: E(i)−Emin
E(i)−Emin
e− KT e− KT lim E(j)−Emin = lim E(j)−Emin − E(j)−Emin T →0 T →0 KT e− KT e− KT + e j∈S
= lim
T →0
j∈S / min
j∈Smin
e
E(i)−Emin − KT
e−
E(j)−Emin KT
=
⎧ ⎨ ⎩
1
(9)
if i ∈ Smin
|Smin | 0 otherwise
j∈Smin
where Emin = minj∈S E(j) and Smin = {i|E(i) = Emin }. Formula (9) shows that when the temperature drops to a very low level, the material will enter the minimum energy state with a high probability, that is, to find the optimal solution of the optimization problem. 3.2 Encoding Method Due to the particularity of the feasible solutions of the VRP problem, this article adopts the natural number coding of chromosome coding, that is, each chromosome is composed of natural numbers representing distribution centers and customer points. In the
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distribution network, the distribution center is coded as 0, and the customer points are coded as (1 − 2 − · · · − m). If there are k vehicles used, inserting (k − 1) 0 into the chromosome. For example, the chromosome coded (0-1-2-3-4-0-5-6-7-8-0) represents a feasible solution, where vehicle 1 travels on a path of (0-1-2-3-4-0), vehicle 2 travels on a path of (0-5-6-7-8-0) [6]. 3.3 Neighborhood Search This paper uses 2-opt operator to generate a new solution of the simulated annealing algorithm. 2-opt operator is that selecting 2 positions and exchanging the encoded information of these two position. 3.4 Cooling Function The initial temperature of this algorithm is set as T0 , and the cooling process of annealing adopts exponential cooling function Tk+1 = α · Tk , where α is the temperature reduction coefficient and can be randomly selected in the interval [0.8, 1.0). 3.5 Algorithm Termination Criterion The termination criterion adopted by this algorithm is to set the end temperature Tf . The algorithm flow is shown in the following Fig. 1.
4 Case Analysis The township has 21 villages under its jurisdiction. At present, there is a distribution center in the town to receive and send express delivery. Collect the latitude and longitude coordinates of distribution centers and customer points, and draw a scatter plot (Fig. 2). The distribution center is equipped with a vehicle, and the current distribution route is from the distribution center through Village 6, Village 13, and back to the distribution center through Village 2 and Village 10. 4.1 Model Solving According to the characteristics of example and algorithm, select the initial temperature T0 = 1, the cooling coefficient α = 0.99, the end temperature t = 0.110 , the Markov chain length L = 20, and use the simulated annealing algorithm to solve the model. 4.2 Solution Result Using matlab to implement the designed algorithm, the following solution results are obtained. Figure 3 is the optimal delivery route found. Figure 4 is a diagram of the convergence process of the algorithm. It can be seen that the convergence of the algorithm is great, and
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Calculate the
f between the new solution and the old solution
Y
N
Δf≤0?
Accept new solution
N
Metropolis judgement
Markov chain length? Y
N
Termination condition? Y
Output optimal solution
Fig. 1. Algorithm flowchart. 36.39
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36.38 36.37 36.36
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36.35
9
1
4
19
36.34
14 11
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20
17 21
10 6
13
115.48
115.49
115.5
115.51
115.52
115.53
115.54
115.55
longitude
Fig. 2. Scatter plot of distribution center and village coordinates.
there is a reverse optimization phenomenon in which the value of the objective function increases during the optimization process, which is caused by the Metropolis criterion.
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Fig. 3. Road map after optimization. 110 100
objective value
90 80 70 60 50 40 30
0
500
1000
1500
2000
2500
iterations
Fig. 4. Algorithm convergence diagram.
The following table shows the comparison of the delivery route and delivery distance before and after optimization. The total journey is 32.3351, which is about 4.3% shorter than the current journey of 33.7799 (Table 2). Table 2. Path comparison table before and after optimization. Distribution route
Distribution distance
Initial route
Depot→6→13→21→17→5→16→20→4→1→9→3 →18→12→8→19→15→14→11→7→2→10→Depot
33.7799
New route
Depot→2→10→6→13→21→17→5→16→20→4→1→9 →3→18→12→8→19→15→14→11→7→Depot
32.3351
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5 Conclusions (1) In terms of model establishment, township logistics distribution does not consider the “last mile” problem. The distance between express delivery points in each village is relatively far, so the model established is relatively simple, and the optimization space is relatively limited. To achieve door-to-door delivery, it is necessary to add several times the number of vehicles to complete the distribution task, but the cost will increase significantly. (2) In terms of algorithm design, theoretically, the cooling process should be slow enough to achieve thermal equilibrium at each temperature. In computer implementation, if the cooling speed is too slow, although the performance of the obtained solution will be more satisfactory, the algorithm convergence will be too slow, so it has no obvious advantage over the simple search algorithm. If the cooling rate is too fast, it is very likely that the global optimal solution cannot be obtained in the end. Therefore, it is necessary to comprehensively consider the performance of the solution and the speed of the algorithm, and take a compromise between these two aspects.
Acknowledgments. This work was funded by the Joint Funds of the National Natural Science Foundation of China (No.U2034208) and the Major Program of Fundamental Research Funds for the Central Universities (No.2021JBZ106).
References 1. Dantzig, G.B., Ramser, J,H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91(1959) 2. Jiang, H., Guo, T., Yang, Z.: Research progress of vehicle routing problem. Acta Electron. Sin. 50(02), 480–492 (2022). (in Chinese) 3. Li, Y., Fan, W.: Bi-level optimization of long-term highway work zone scheduling considering elastic demand. Smart Resil. Transp. 3(2), 118–130 (2021) 4. Hashemi, L., Mahmoodi, A., Jasemi, M., et al.: Modeling a robust multi-objective locatingrouting problem with bounded delivery time using meta-heuristic algorithms. Smart Resil. Transp. 3(3), 283–303 (2021) 5. Yu, V.F., Susanto, H., Jodiawan, P., et al.: A Simulated annealing algorithm for the vehicle routing problem with parcel lockers. IEEE Access 10, 20764–20782 (2022) 6. Ge, X., Li, Z., Ge, X.: Research on logistics distribution route optimization with time window considering flexible charging strategy. Contr. Theory Appl. 37(6), 1293–1301 (2020) (in Chinese)
Study and Experimental Verification of the Effect of Assembly Pressure on the Electrical Efficiency of PEM Fuel Cells Bao Lv1 , Kai Han1,2(B) , Xiaolong Li1 , and Xuanyu Wang1 1 School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100074, China
{3220195042,autosim,lixiaolong,3120225262}@bit.edu.cn 2 Chongqing Innovation Center, Beijing Institute of Technology, Chongqing 401120, China
Abstract. Assembly pressure is one of the main factors affecting the internal charge, heat, and mass transfer of proton exchange membrane (PEM) fuel cells. It causes the deformation of the components to change the electrical and gas transport characteristics of the internal contact interface of the fuel cell, and affects the overall performance of the cell. In this paper, a three-dimensional finite element model of a single cell considering the surface topography of the component and the contact behavior of the asperities is firstly established, and the contact pressure and diffusion layer porosity of the contact interface of each component of the fuel cell are obtained; Then, the total contact resistance of the cell and the effective diffusivity of the gas in the diffusion layer were established; Finally, a detailed voltage model considering different losses of the fuel cell was established based on the MATLAB platform. The results show that the contact resistance decreases with the increase of the assembly pressure, and the maximum error between the calculated contact resistance and the experimental value is 1.7%, which meets the accuracy requirements; when the clamping pressure is 0.75MPa, the sum of the ohm internal resistance and the concentration difference internal resistance is the smallest, the fuel cell output power is the largest, which can provide guidance for the assembly of fuel cells in practical applications. Keywords: Proton exchange membrane fuel cell · Assembly Pressure · Electrical Efficiency · Resistance Test
1 Introduction In recent years, proton exchange membrane fuel cells (PEMFC) have attracted much attention in the field of new energy as a clean energy conversion device with high efficiency, zero emissions and low noise [1, 2]. PEMFC is assembled from multiple components and its performance is not only affected by the operating conditions, but also the clamping pressure is one of the important factors affecting the performance [3]. On one hand, unsuitable clamping pressure causes the deformation of components and uneven interfacial contact pressure. Accordingly, the leakage gap and leakage of gases increases. On the other hand, the big assembly pressure will increasing mass © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 967–974, 2023. https://doi.org/10.1007/978-981-99-1027-4_101
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transfer resistance and shorting fuel cell’s life [4]. Among them, the contact resistance and mass transfer resistance correspond to the ohmic and concentrated overpotential in the internal resistance of PEMFC polarization, so it is necessary to study the effect of assembly pressure on the electrical efficiency of PEMFC. In PEM fuel cell operation, the loss of output power is caused by the presence of polarization internal resistance, which is mainly composed of two parts: body resistance and contact resistance, and some studies [5–7] have shown that about 60% of the output performance loss in PEMFC is caused by the contact resistance between the bipolar plate and the GDL. The study of fuel cell clamping mechanics focuses on the effect of loading on gas transport and performance. For example, Liang et al. [8] proposed an efficient method to reduce the contact resistance of fuel cells. Sun et al. [9] used the finite element method to analyze the effect of different flow fields on the contact pressure of the gas diffusion layer. Irmscher et al. [10] designed three combinations of clamping pressure and materials of gas diffusion layer, and scanned the topography by an electron microscope. Zhou et al. [11] used Open Foam open source software to calculate the gas-liquid two-phase flow transport process inside the pressurized GDL, obtained the effect of GDL parameters on the water transport law. Abovementioned studies demonstrated the significant effect of clamping pressure on PEMFC performance. How to improve the electrical efficiency by changing the operating conditions is important for the development and application of fuel cell stacks. Zhang et al. [12] studied the effects of temperature and humidity on the electrical efficiency of fuel cells under different experimental conditions. Wang et al. [13] presented a theoretical analysis of efficiency and investigated the formation of contact internal resistance and its effect on electrical efficiency. Liu et al. [14] took voltage loss as the research objective and firstly analyzed the causes of internal resistance of fuel cells during operation. Previous studies only focus on the one way interactions of clamping pressure, surface topography, and operating parameters. The coupled interactions among three factors, i.e., clamping pressure, surface topography, operating parameters is blank and worthy to investigate. In this work, establishes a three-dimensional finite element encapsulation model of PEMFC considering the surface morphology of the seal to refine the interface contact behavior. Then combines the finite element data to obtain the relationship between assembly pressure and contact resistance, GDL effective diffusivity. Moreover, the establishes each polarization loss model and conducts experimental verification to provide reference for the actual assembly of PEMFC.
2 Methodology 2.1 W-M Fractal Function In PEM fuel cell assembly, in order to prevent internal blow-by gas and gas leakage, it is necessary to place a sealing ring at the plate for sealing, and its surface roughness affects the safety and performance of the fuel cell. In this paper, the three-dimensional W-M fractal function is used to characterize the rough surface morphology of the sealing ring,
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and the three-dimensional surface of the sealing ring is constructed by Python script (as shown in Fig. 1), and its mathematical model expressed as follows: Z(x, y) = ((ln γ)/M )1/2 × cos(φm,n )(k0 γn )D−3 ×
M m=1
Am
∞ y 1 − cos(k0 γn (x2 +y2 )1/2 cos(arctan( )) − αm ) x n=−∞
(1)
where Z(x, y) is the height of rough surface profile, M is the number of superimposed peaks when reconstructing a surface, n is the frequency index, γn is the discrete frequency spectrum of the surface roughness, Am is the surface amplitude, φm,n is the random bits uniformly distributed in the range [0, 2π], k0 is the amount of horizontal change.
(a) surface topography of seal
(b) 3D model of rough surface
Fig. 1. Surface morphology distribution of seal
2.2 Electrical Efficiency Model In fuel cells, the ratio of the total fuel enthalpy to the output energy is defined as the thermoelectric conversion efficiency, Combined with the laws of thermodynamics, the electrical efficiency expression is derived as follows: fPEMFC =
G V It IVt = · f g = fT fV fI fg H H G f nF nF g
(2)
where H is the overall enthalpy of the fuel, IV t is the actual output power, fg is the fuel utilization rate, fT is the thermodynamic efficiency, fV is the voltage efficiency, fI is the current efficiency. According to the above analysis, the current efficiency is generally taken as 1, and the thermal efficiency and fuel utilization rate are fixed values, so the electrical efficiency of the fuel cell depends on the voltage loss. When the current is constant, the polarization internal resistance determines the voltage loss, so a detailed voltage loss model needs to be established.
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2.3 Experiment For PEMFC assembly structures, thermoelectric potentials are generated when in contact with each other due to the different materials of the components. In order to reduce the measurement error caused by the thermoelectric potential, the assembly structure (shown in Fig. 2a) is established, the total electrical resistance of the PEM fuel cell assembly may be seen to be a summation of the bulk resistance and the contact resistance. The expression for the total resistance for the two assemblies is denoted as R1/R2: R1 = 2REP + 2RCP + 2REP/CP + 2RCP/GDL + RGDL R2 = 2REP + 2RCP + 2RGDL + 2REP/CP + 2RCP/GDL + 2RBPP/GDL + 2RBPP
(3) (4)
Based on the result of the total resistance R1/R2, the contact resistance between GDL and BPP is defined as follows: R2 − R1 − RGDL −RBPP (5) RBPP/GDL = 2 where REP , RCP , RGDL , RBPP represent the bulk resistance of end plate, cooper plate, gas diffusion layer, and graphite bipolar plate, respectively; REP/CP , RGDL/CP , RGDL/BPP represent the contact resistances between end plate and cooper plate, gas diffusion layer and cooper late, graphite bipolar plate and gas diffusion layer, respectively.
(a) contact resistance
(b) experimental bench
(c) geometry model
Fig. 2. Schematic diagram of the contact resistance calculation method and experimental bench
The above parameters RGDL and RBPP are obtained from the relevant suppliers, the values of R1and R2 are obtained experimentally (see Fig. 2b), among them, the contact resistance measurements were conducted using a YK-100 press to provide a series of clamping pressure, the accuracy of the pressure sensor is 0.1%FS; A Tonghui AC low resistance tester with impedance accuracy of 0.1%; A Gamry’s electrochemical workstation to measure fuel cell EIS; A PEM fuel cell test bench with a measuring range of 0–100 W.
3 Fuel Cell Model Construction 3.1 Model Assumptions For the sake of simplification, the following reasonable assumptions are made for the finite element modeling, (1) The sing-cell is in steady-state. (2) The materials properties are independent of temperature. (3) Ignore the deformation of proton exchange membrane. (4) The GDL consists of an isotropic porous medium.
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3.2 Simulation Model Generally, a PEM fuel cell is composed of end plate, current collectors, bipolar plates, gasket, membrane electrodes, and other segments. In practical applications, the microporous layer and CL are laminated between the GDL and the PEM by the hot-pressing process. Their thicknesses are relatively small in the micron range, so the effect of their own stress strain on the membrane electrode can be neglected. In this paper, the modeling is based on the real data provided by the manufacturer, and the material parameters are shown in Table 1. The model in this paper mainly contains components such as bipolar plate, GDL, PEM, and gasket (see Fig. 2c), ignoring the modeling of catalytic layer and microporous layer. Table 1. Material parameters of the components Component
Material
Young’s (MPa)
Poisson’s Ratio
BPP
Graphite
134100
0.25
GDL
Carbon
11.67
0.01
MEA
–
116
0.48
GASKET
PTFE
2.65
0.48
PEN
Polyethylene naphthalate
1184
0.3
3.3 Boundary Conditions The GDL and the PEM are tied by hot pressing process, and the interface relationship between them is set as tied constraint in the model, the interface relationship between the remaining contact parts is set as contact constraint. The tangential behavior of the contact properties is constrained by penalty function, and normal behavior is calculated by using the extended Lagrangian algorithm. A uniform pressure load of 0.1-1MPa is applied along the stacking direction, and the parameters related to the deformation variables after deformation are extracted and substituted into the model, and the GDL porosity and effective diffusion coefficient are expressed as follows: 1.5 2.5 p0 T (1 − s) δ (6) δeff =ε 1.5 0 new p T0 where s is the liquid saturation, δ0 is the original diffusivity, p is the inlet pressure, δeff is the effective diffusivity, εnew is the porosity.
4 Results and Discussion 4.1 Interface Contact Characteristics Figure 3a shows the contact state of the sealing surface under 0.2 MPa, and it can be seen that the uneven surface contact distribution is due to the uneven distribution of
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the surface asperity, and the peak position is the first to contact. Uneven distribution may lead to changes in the contact state of internal components, so it is necessary to establish a fine model of the sealing ring. The contact pressure distribution between the GDL and the bipolar plate are plotted in Fig. 3b. It can be seen that the contact pressure is zero under the channels, because the area is not compressed. The contact pressure distribution between the rib is consistent, which can be used to calculate the contact resistance. Figure 3c plots the compression of GDL along the X-direction at different clamping pressures, and it can be seen that the compression displacement increases with the increase of clamping pressure, and the deformation in the middle area is smaller than the two sides. The law of change of the compression is the same as that of the porosity, which affects the effective diffusion coefficient and thus leads to the loss of concentration difference increase.
(a) contact state
(b) contact pressure
(c) compression displacement
Fig. 3. Contact characteristics of different interface
4.2 Effect of Clamping Pressure As shown in Fig. 4a, the contact resistance decreases rapidly with the increase of clamping pressure, and when the clamping pressure is greater than 0.8 MPa, the contact resistance decreases slowly. This is because the increase in pressure changes the contact area between GDL and bipolar, gradually transitioning from non-close contact to the ideal contact area, and when the pressure increases further, the change rate of contact area decreases. By comparing with the experiment, the maximum error between the two is 1.7%, which meets the error requirements. According to Eq. 6, the effective diffusivity of hydrogen is calculated, clamping pressure fluctuates in the 0.6–0.8 MPa region, and the rate of change decreases, that is, the concentration internal resistance increases with the increase of the clamping pressure, and the sum of ohmic loss and concentration loss is minimized when the clamping pressure is 0.75 MPa. In the calculation of electrical efficiency, the internal resistance is the main reason leading to the reduction of efficiency, and the clamping pressure has a direct impact on the contact resistance and concentration loss. The percentage of the total internal resistance accounted for by the clamping pressure was obtained by combining the experiment and Simulink model, the result as shown Fig. 4b. The contact resistance and concentration difference internal resistance are the main reasons for the efficiency loss. Therefore, the selection of appropriate assembly pressure is of great significance to improve the efficiency of PEMFC.
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(a) contact resistance and effective diffusivity
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(b) effective proportion
Fig. 4. The effect of clamping pressure on electrical efficiency
5 Conclusions In this paper, a three-dimensional assembly model considering the surface morphology and contact behavior of the component is established, the relationship be-tween clamping pressure and polarization internal resistance is studied, and on this basis, a detailed voltage loss model is established to analyze the influence of clamping pressure on the electrical efficiency of PEMFC, and the following conclusions are obtained: 1. With the increase of clamping pressure, the contact resistance between GDL and bipolar plate interface decreases, and the maximum error between simulation results and experimental values is 1.7%, which meets the accuracy requirements. 2. The concentration loss increases with the increase of clamping pressure. When the clamping pressure is 0.75MPa, the sum of contact resistance and concentration internal resistance is the minimum, and the output power of the battery is the maximum.
Acknowledgments. This work was supported by the Key-Area Research and Development Program of Guangdong Province (Grant number 2020B090920001).
References 1. Singh, S., Shikha, J., Venkateswaran. P.S.: Hydrogen: a sustainable fuel for future of the transport sector. Renew. Sustain. Energy Rev. 51, 623–633 (2015) 2. Sharma, S., Ghoshal, S.K.: Hydrogen the future transportation fuel: From production to applications. Renew. Sustain. Energy Rev. 43, 1151–1158 (2015) 3. Chakraborty, U.: Fuel crossover and internal current in proton exchange membrane fuel cell modeling. Appl. Energy 163, 60–62 (2016) 4. Hu, G.L., Ji, C., Xia, Y.Z., Suo, Y., Wu, X.J., Zhang, Z.G.: Assembly mechanics and it is effect on performance of proton exchange membrane fuel cell. Int. J. Electrochem. Sci. 14(2), 1358–1371 (2019)
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5. Christopher, J.N., Benjamin, D.G.: Decreasing contact resistance in proton exchange membrane fuel cells with metal bipolar plates. J. Power Sour. 227, 137–144 (2013) 6. Molaeimanesh, G.R., Nazemian, M.: Investigation of GDL compression effects on the performance of a PEM fuel cell cathode by lattice Boltzmann method. J. Power Sour. 359, 494–506 (2017) 7. Jamshid, H., Hamid, A.: A modified rough interface model considering shear and normal elastic deformation couplings. Int. J. Solids Struct. 203, 57–72 (2020) 8. Liang, P., Qiu, D.K., Peng, L.F., Ni, J.: Contact resistance prediction of proton exchange membrane fuel cell considering fabrication characteristics of metallic bipolar plates. Energy Convers. Manag. 169, 334–344 (2018) 9. Sun, A., Tan, J.Z.: Effects of bolt number and allocation on contact pressure of PEM fuel cell. Chin. J. Power Sour. 49, 1301–1304 (2020) (in chinese) 10. Irmscher, P., Qui, D., Stolten, D.: Impact of gas diffusion layer mechanics on PEM fuel cell performance. Int. J. Hydrog. Energy 44, 23406–23415 (2019) 11. Zhou, X., Wu, L., Niu, Z., Li, Y., Jiao, K.: Effects of surface wettability on two-phase flow in the compressed gas diffusion layer microstructures. Int. J. Heat Mass Transf. 151, 119370 (2020) 12. Zhang, L.H., Jie, W.P., Xie, C.G., Xu, J., Song, H.M.: Effects of temperature, pressure and humidity of electric of PEMFC stack. J. Tianjin Univ. 40, 594–598 (2007) (in chinese) 13. Wang, L.P., Zhang, L.H., Song, H.M., Jiang, J.P.: Effect of contact resistance on efficiency of PEM fuel cells. Chin. J. Power Sources 37, 761–763 (2013) (in chinese) 14. Liu, Y.: Analysis of factors influencing the power efficiency of fuel cell system and its hydrothermal management. Master’s Thesis, Jilin University (2020) (in chinese)
Design of Non-intrusive Type Load-Monitor System for Smart Grid Sun Guofu, Guan Huashen(B) , and Xin Haomiao Jiangmen Power Supply Bureau, Guangdong Power Grid Co., Ltd., Jiangmen 529000, Guangdong, China [email protected]
Abstract. In order to further improve the information analysis and mining capabilities as well as the data sharing and interaction capabilities of the smart grid, a non-intrusive load monitoring system with complete functions and strong practicability is designed. Based on the analysis of system requirements, complete the design of the system technical architecture and overall system plan. Start with the data acquisition module design, main control module design, communication module design and other aspects to complete the design of the core functiongal modules of the system. Finally, test the operating performance of the system and the online monitoring function of the clound platform. The results show that the non-intrusive load monitoring system designed in this paper runs normally, reliably and stably, and the realization of each functional module meets the relevant design requirements. Keywords: Smart grid · Non-intrusive · Power load monitoring system · Design
1 Introduction In the context of smart grid, through the design and application of non-intrusive load monitoring system, it can not only realize automatic, remote and precise monitoring of power load, but also facilitate users to fully understand and grasp the characteristics of power load, in order to ensure power load identification accuracy, improve smart grid dispatching level and provide important platform support. Therefore, in order to promote the healthy and sustainable development of the smart grid, how to design a non-intrusive load monitoring system scientifically is a problem that technicians must think about and solve.
2 Ease of Use 2.1 System Requirements Analysis System requirements analysis is the basic content of non-intrusive load monitoring system design. Before formally entering the system design, technicians should analyze the system requirements from the following two dimensions. (1) User needs analysis. The © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 975–983, 2023. https://doi.org/10.1007/978-981-99-1027-4_102
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users involved in the system mainly include business users and system users. Different user types have different system requirements. (2) Functional requirements analysis. System functions mainly include acquisition module design, main control module design, communication module and other modules. Technicians should focus on the design and implementation of these functional modules to ensure user experience. 2.2 System Technical Architecture Design In the context of smart grid, the design of non-intrusive load monitoring system mainly uses the following core technologies, namely load monitoring and identification technology, advanced information communication technology, and data deep mining technology. First, through the use of load monitoring and identification technology, a comprehensive analysis and research of power load data is realized [1]; Then, with the help of information and communication technology, the interaction between the power grid and users is ensured, so that the power grid can quickly obtain the power load data of users in the shortest time. Finally, the data mining method is used to deeply analyze and mine the user’s power load data, so as to provide users with good intelligent power consumption services. The schematic diagram of the system technical architecture design is shown in Fig. 1.
Fig. 1. Eschematic diagram of system technical architecture design.
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3 Overall System Design 3.1 Introduction to the Core Modules of the System This system mainly includes the following modules, namely data acquisition module, main control module. The schematic diagram of the overall design of the system is shown in Fig. 2. Among them, the design of data acquisition module, main control module and communication module is the focus of this research. Once the accuracy of the collected data is not high, it will directly affect the operation performance of the system. In order to avoid the occurrence of the above undesirable phenomena, technicians should prefer sampling resistors to collect power load data, because this resistor has the ability to resist magnetic field interference. In addition, the HLW8112 energy metering chip should be selected to quickly convert the power load data into corresponding electrical signals [2]. As the basic functional module of the system, the power supply module is unreasonably controlled, which will directly affect the operating state of the system. Therefore, the technicians should give priority to the switching power supply chip to convert the power load data. This is because the switch the power chip has the characteristics of safety and reliability, small size and high efficiency. The main control module is the core module of the system. In the actual development, the STM32F1.03 microprocessor should be preferred to process the power load data sent by the data acquisition module. In order to ensure that users can conduct remote, online real-time monitoring of power load data [3], in the specific design of this system, the communication module should be used to transmit power load data to the OneNET cloud platform safely and reliably.
Fig. 2. Schematic diagram of overall system design.
3.2 System Operation Process Analysis The operation process of this system is: by installing and fixing the system at the power supply inlet, at this time, the power supply module will provide the corresponding working voltage to other modules, at this time, the system will use the data acquisition module to convert the voltage and current, power and other electrical load data are converted into corresponding electrical signals, and transmitted to the HLW8112 energy metering chip, which converts these electrical signals into voltage RMS and current RMS, and stores them in the designated registers. On the basis, the main control module will automatically complete the accurate calculation of the power load data, and convert the final calculation result into the corresponding power load characteristic value. Finally,
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the communication module securely and reliably transmits and stores these power load characteristic values in the OneNET cloud platform [4]; at this time, the user can log in and access the OneNET cloud platform by means of the mobile terminal or the PC terminal, in order to ensure the power load. The real-time, effective and targeted data monitoring lays a solid foundation.
4 System Function Module Design In the context of smart grid, in order to better improve the operation performance of the non-intrusive load monitoring system, realize the automation of electricity consumption, remote intelligent analysis and detection, and precise monitoring, and meet the diverse needs of users [5], this system is now It is divided into three modules: data acquisition module, main control module and communication module. The schematic diagram of the system function module design is shown in Fig. 3.
Fig. 3. Schematic diagram of system function design.
4.1 Design of Data Acquisition Module The data acquisition module is mainly composed of two core parts: one is the HLW8112 power metering chip; the other is the sampling resistor. Among them, the HLW8112 electric energy metering chip has the characteristics of high precision, safety and reliability. It is equipped with a power supply and a crystal oscillator. On the basis of scientifically designing the peripheral power, the data acquisition module can be guaranteed to achieve the effect by writing software codes in a standard way; at the same time, With the help of the main control module [6], it is possible to accurately read and organize the power load data in each chip register. When the ratio of these data reaches 1000:1, and the measurement error between the current rms value and the voltage rms value is less than 1%, the accuracy and authenticity of the data acquisition results can be guaranteed. In addition, during the design of the data acquisition module, technicians should prefer the following two types of resistors: one is a 1 m copper-manganese resistor; the other is a 200 k alloy resistor, both of which have the advantages of low cost, simple operation, It has the characteristics of high accuracy and high accuracy. By setting it as a sampling resistor, it can realize real-time monitoring and sorting of voltage and current, and convert them into corresponding electrical signals [7] way to safely
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and reliably transmit these electrical signals to the chip registers. In order to ensure the comprehensiveness and efficiency of power load data collection, technicians should effectively connect multiple chip alloy resistors to combine them into a unified whole; Low resistance voltage level and grid voltage instability. On this basis, it is necessary to use the HLW8112 power metering chip and use the SPI communication method to provide strong hardware support for the system design to ensure the stability, reliability and safety of the power load data output. In addition, the data acquisition module is mainly suitable for the working environment of strong electricity. In order to ensure the reliability and safety of the module, the technicians need to use the optocoupler isolation chip to effectively isolate the data acquisition module from the main module. Usually, the output frequency of the HLW8112 energy metering chip is set to 7012 Hz. The highspeed optocouplers used in this link mainly include the following two types: one is the EL357NB high-speed optocoupler; the other is the PS8101 high-speed optocoupler. SIP communication performance can be improved by using two types of high-speed galvanic couples. Only in this way can the realization effect of the data acquisition module be guaranteed and a good user experience be brought to the user. 4.2 Main Control Module Design (a) In the specific design of the main control module, the SPI communication method is mainly used to obtain and organize the power load-related data in the registers of the HLW8112 electric energy metering chip; at the same time, each functional module is also initialized. When the pin 11 of the HLW8112 power metering chip is placed in a low state, the chip automatically selects the working mode; when the pin 12 of the HLW8112 power metering chip is placed in a low state [8], the chip automatically selects the SPI communication mode. In addition, when the clock signal shows a rising state, the value of the chip register needs to be set to “0”, The main control module will automatically transmit and store the 0XE5 related instructions in the chip register, which is convenient for other personnel to view and call. On this basis, the register should be opened and closed according to the relevant instructions, so as to realize the remote and automatic control of the operation state of the register. In addition, when the clock signal shows a declining trend, the main module needs to use the HLW8112 energy metering chip to accurately read and organize the power load data according to the set register storage address [9]. For the main control module, when the corresponding read and write instructions are transmitted to the data kitchen module, the instruction type should be scientifically judged and analyzed according to the 8th bit value of the register corresponding to the HLW8112 electric energy metering chip; if the 8th bit If the value is 0, it indicates that the command type is a read command; if the 8th bit value is 1, it indicates that the command type is a write command. 4.3 Communication Module Design (b) In the specific design of the communication module, the ESP8266 chip is mainly selected. This chip has the characteristics of fast networking, high transmission efficiency, safety and reliability. In order to ensure that the system can transmit data to the cloud platform safely and reliably, technicians The transparent transmission mode
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should be selected to realize the safe and efficient transmission of power load data. In addition, in order to improve the realization effect of the communication module, technicians need to use the OneNET platform, adopt long-distance communication, and use routers to effectively connect each network terminal to ensure that the communication module extends the distance. In the traditional distribution network mode, the communication module needs a new router to effectively modify and manage the routing account and password. However, this distribution network method seriously affects the application effect of this system in practical projects. In order to avoid the above problems, technicians should adopt the network distribution method through web pages to securely and reliably transmit and store the user’s account and password in the EEPROM. In the register, it is ensured that a dynamic connection can be established between each new route. When the user name and password are verified, the communication module will automatically realize the scientific configuration of the AT-related information.
5 System Test In order to better verify the reliability and effectiveness of the non-intrusive load monitoring system, this system is now applied to a power enterprise, and the system functions are realized from the system performance test and the cloud platform online monitoring test. The effect is tested. 5.1 System Performance Test There are 2 power terminals in the internal devices of this system. Among them, one power terminal is used for the connection of 220 V mains to realize the scientific simulation of the power supply situation; the other power terminal is mainly used for the connection of the socket to realize the effective simulation of the application effect of the power load. Now set the LED lights, electric fans, and liquid crystal displays as the test objects. The powers of these devices are 7, 32, and 23 W respectively; then, three different types of power loads are set and turned on respectively. There is also a certain difference in the corresponding instantaneous current RMS. Therefore, it is necessary to accurately measure the corresponding instantaneous current RMS according to the value of the power load. On this basis, the accuracy of the measurement results should be regarded as an important indicator to measure the system performance. Only in this way can the efficiency and effect of multi-load switching processing be guaranteed. In addition, during the test of system measurement accuracy, technicians should use the multimeter model VIC-TORVC890D as the comparison object, and conduct a comprehensive analysis and comparison with the accuracy of its measurement data. The resolution corresponding to this multimeter is 1/2 of the range. 000; then, use the system and the multimeter to accurately measure the working current corresponding to three different types of power loads, set the measurement times to 1, 50 and 100 times respectively, and measure the corresponding current average value. Finally, according to the relative error between the two, the measurement accuracy of the system is accurately measured. The system is compared with the measurement results of the multimeter, and the specific results are shown in Table 1.
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Table 1. Comparison of measurement results between this system and a multimeter. Testing Object
Time
This system/A
Multimeter/A
Relative error/%
Led Lights
1
0.030
0.030
0
50
0.029
0.029
0
100
0.028
0.028
0
1
0.136
0.135
0.75
50
0.135
0.134
0.76
100
0.137
0.136
0.74
1
0.111
0.109
1.80
50
0.110
0.109
0.91
100
0.109
0.108
0.89
Electric Fan
LCD Monitor
Fig. 4. Three kinds of electric load current waveform data changes.
From the data in Table 1, it can be seen that after the system has been measured for many times, the relative error between the two is less than 1% compared with the average current value of the multimeter, which shows that the measurement accuracy of the system is high, reaching 99%. It can be seen that the accuracy of power load measurement data can be maximized by using this system. In addition, during the test of other performance indicators, it is necessary to set all LED lights, electric fans, and liquid crystal displays to the on state, and then collect the instantaneous current RMS of these devices. On this basis, according to the changing trend of the current waveform, the performance of the system is tested to determine whether there is a multi-load switching phenomenon. The three kinds of power load current waveform data changes are shown in Fig. 4. It can be seen from Fig. 4 that during the monitoring of the power load, the monitored data mainly include the following two types: one is the transient process data; the other
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is the steady-state process data, which are described in detail. It provides an important basis and reference for realizing the non-intrusive identification of power loads. 5.2 Cloud Platform Online Monitoring Test As an important IoT development platform in my country, OneNET is mainly developed by domestic mobile companies. By using this platform, it can not only realize the effective connection of each load monitoring system, but also ensure the development and deployment efficiency and effect of the monitoring system. It lays a solid foundation for validating the online monitoring performance of the system. The power load data monitoring interface is shown in Fig. 5.
Fig. 5. Power load data monitoring interface.
As can be seen from Fig. 5, the discount graph on the left presents the historical load information corresponding to the power load to the user truly and effectively, and the dashboard on the right mainly displays the real-time load corresponding to the power load to the user truly and vividly. Information. After the user logs in to the cloud platform through the browser client terminal, the system will automatically jump to the monitoring interface; then, the relevant information such as voltage, resistance, current, and power related to the power load is visually and intuitively presented in front of the user, which is convenient for the user. After analyzing and comparing these data, we can fully understand and grasp the historical information of power load.
6 Epilogue To sum up, the non-intrusive load monitoring system designed in this paper has the characteristics of high accuracy, simple maintenance and strong anti-magnetic interference
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performance. It is mainly used for monitoring single-load or multi-load conditions, and the detection accuracy higher, as high as 99% or more. By using this system, not only the accurate acquisition of the load voltage value, current value and power value can be achieved, but also the relevant power parameters such as voltage peak value and waveform diagram can be fully acquired and grasped. There are 2 communication modes: one is serial communication mode; the other is WiFi communication mode, which can realize the accurate collection and printing of load power parameters, which is convenient for users to log in and access the OneNET cloud platform, remotely and remotely control the power load. Online monitoring and control provide important platform support for improving the optimal dispatching level of smart grid. It can be seen that the non-intrusive load monitoring system has very high application value and application prospects, and is worthy of further promotion and application.
References 1. Zhou, X., Li, Y., Xie, L.: Non-intrusive power load monitoring device based on HLW8112. Bonding 48(6), 605–610 (2020) 2. Sun, Y., Cui, C., Zhang, L., et al..: Research on non-intrusive load monitoring system of intelligent electricity consumption. Bonding 34(2), 155–160 (2019) 3. Wang, K., Geng, Y., Zhou, Y., et al..: Design and implementation of non-intrusive load monitoring terminal. Comput. Knowl. Technol. 10, 50–52 (2020) 4. Wu, W„ Peng, L„ Gan, G., et al.: Laboratory load intelligent monitoring device based on SOPC. Lab. Res. Explor. 39(6), 78–82 (2020) 5. Rong, A.: Research on non-intrusive load identification algorithm of scene adaptation. Wuhan: Huazhong Univ. Sci. Technol. 26(14), 21–22 (2020) 6. Cai, Z.: Research on non-intrusive load identification algorithm based on smart meter. Tianjin: Tianjin University 33(17), 45–46 (2019) 7. Han, L.: Research on Non-intrusive Residential Load Intelligent Identification Algorithm. North China Electric Power University, Beijing (2019) 8. Wang, W., Huang, Y., Zhang, Z.: A monitoring and identification method based on non-invasive electrical equipment. Household Appliances 1, 106–109 (2021) 9. Yao, X.: Research on Non-intrusive Identification Technology of Low-voltage Power Load. Southeast University, Nanjing (2016)
Application of Digital Twin Model in Monitoring the Steady State Operation of DC Bus Capacitor Bank Mingshuo Zhu, Yi Liu, Meng Huang(B) , and Xiaoming Zha Wuhan University, Wuhan 430072, China [email protected]
Abstract. The concept of digital twin provides a new solution for the condition monitoring of DC bus capacitor bank. In this paper, a condition monitoring method of DC bus capacitor bank based on digital twin model is established. Firstly, based on the analysis of the physical characteristics of the capacitor, the digital twin model framework of the DC bus capacitor bank is constructed. After that, the application details of the proposed digital twin model in the condition monitoring of the DC bus capacitor bank are analyzed from five steps, which include digital modeling, synchronous operation, accuracy judgment, parameter calibration and condition monitoring application. Finally, the proposed method is verified by simulation. Keywords: Condition monitoring · DC bus capacitor bank · Digital twins · Electrothermal model
1 Introduction With the rapid development of the new energy vehicle industry, the DC bus capacitor has become the core component of the high-efficiency motor control inverter for new energy vehicles. The reliability of DC bus capacitor is closely related to the operation safety of the whole power electronic system [1]. The fault statistics of the converter show that the failure rate of the DC bus capacitor bank in the converter is one of the highest, accounting for 30% of the converter failure [2]. Therefore, it is of great significance to monitor the current operating state of the DC bus capacitor and predict the operating trend in the future, so as to realize the accurate evaluation of the operating state of the DC bus capacitor, and to ensure the safe and reliable operation of the converter. In engineering applications, various sensing devices are often installed in the DC bus capacitor equipment to obtain a variety of state variables in real time to indirectly reflect the operation of the equipment, so as to timely replace the aging capacitors to ensure the safe and reliable operation of the converter. Reference [3] measured the capacitance and equivalent series resistance(ESR) of the capacitor by using the discharge law of the capacitor, and the measurement error is about 1%. Reference [4] calculates the equivalent series resistance ESR of the DC bus capacitance by obtaining the short-circuit current © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 984–992, 2023. https://doi.org/10.1007/978-981-99-1027-4_103
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of the switch tube and the change of the DC bus voltage during the short-circuit test. Reference [5] analyzes the expression of ripple voltage of DC bus and establishes the monitoring model of ESR by using the ripple voltage at the switching time. Reference [6] proposes a method for monitoring the capacitance state of MMC DC bus based on an adaptive observer of capacitor voltage ripple to derive the parameter difference between the capacitor and its nominal value assumed in the observer model. However, in the current practical application process, there are still some problems. First, in the new energy vehicle, since the withstand voltage of the electrolytic capacitor is not high and the ripple current passed by the electrolytic capacitor is generally low, in order to meet the application requirements, It is often necessary to adopt a series or parallel structure of multiple capacitors to improve the withstand voltage and increase the capacity [7]. On the other hand, the new energy vehicle is often at a very high temperature during operation. High temperature will not only accelerate the aging of the capacitor, but also affect the operating state parameters of the capacitor [8]; Due to the mutual influence of heat generation between capacitors, the operating temperature of different capacitors is different. Therefore, it is necessary to detect the state of each capacitor in the capacitor bank, which greatly increases the number of sensors. In addition, due to the influence of factors such as the detection accuracy, stability and environmental noise of the sensor, there are often differences between the data collected on the site and the actual operating data of the equipment, which will also directly affect the accuracy of the state detection. Digital twin integrates many cutting-edge information technologies and realizes the virtual reflection of the whole life cycle state of physical entities and the improvement of industrial operation performance through virtual and real interaction. It is becoming a powerful driving force for the development of digitalization, networking and intelligence in various industries [9, 10], and also provides a new idea for online monitoring of power electronic equipment. In this paper, the digital twin model of DC bus capacitor bank is built based on the analysis of the physical characteristics of DC bus capacitor bank. In the second section, the physical characteristics of DC bus capacitor bank are analyzed and the mathematical model is established. In the third section, the digital twin model of DC bus capacitor bank is established, and the application of the digital twin model in the condition monitoring of DC bus capacitor bank is summarized. In the fourth section, the monitoring effect of digital twin model is verified by using Simulink-COMSOL joint simulation. The conclusions are drawn in the fifth section.
2 Digital Twin Model of DC Bus Capacitor Bank Digital twin is a multi-disciplinary, multi physical quantity and multi-scale simulation process that makes full use of physical model, sensor update, operation history and other data. Digital twin is actually a digital mirror image of physical entities. The difference between digital twin and traditional simulation is that traditional simulation and actual equipment are independent of each other, and there is no direct interaction between them; The digital twin makes full use of various sensor data of the actual equipment and the historical operation data of the equipment, and combines machine learning, parameter identification and other analysis algorithms to establish a real-time updated
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digital twin that can accurately reflect the current and future operation status of the actual equipment. There is information interaction between the digital twin model and the actual equipment. Some previous studies on the digital modeling of DC bus capacitor banks, including the equivalent circuit and thermal network model of DC bus capacitor banks have been done, which have been presented in [11]. The equivalent circuit is used to reflect the electrical operation state of the DC bus capacitor bank, and the thermal network model is used to reflect the thermal behavior of the DC bus capacitor bank. Combined with the equivalent circuit model and the equivalent thermal network model, the digital twin of DC bus capacitor bank is constructed in this paper, as shown in Fig. 1. The digital twin model consists of six parts: physical entity, sensor, digital model, data, analysis algorithm and model information and application. Wherein the physical equipment is the physical equipment of the DC bus capacitor bank; The sensor includes PCB integrated Rogowski coil (for measuring the current flowing through each capacitor), Hall voltage transformer (for measuring the DC bus voltage), thermocouple (for measuring the temperature); The digital model is the equivalent circuit and thermal network model established in the second part; The data includes sensor data, digital model data and historical operation data; The analysis algorithm includes a parameter identification algorithm for updating the parameters of the digital model and an electrothermal coupling iterative algorithm for calculating the operating temperature of the capacitor bank; Model information and application are various services realized on the basis of digital twin model, including operating temperature monitoring, condition monitoring and health assessment.
Fig. 1. Frame of DC bus capacitor bank digital twin
3 Digital Twin Model of DC Bus Capacitor Bank and Its Application in Condition Monitoring The established digital twin model can be used to realize the state monitoring of DC bus capacitor bank. The state monitoring process is shown in Fig. 2. Step 1: Digital modeling and parameters initialization. The equivalent circuit and thermal network model of DC bus capacitor bank are constructed according to Sect. 2. The
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parameters in the equivalent circuit and the thermal network model are initialized using the capacitor data book and the temperature response test.
Fig. 2. Condition monitoring method based on digital twin
Step 2: Synchronous operation of the physical equipment and the digital model. The input matrix Ek and the operation state matrix Xk of the DC bus capacitor bank are constructed by using the voltage, current and temperature data of the capacitor bank sampled by the sensors; Input Ek into the digital model to obtain the state matrix Yk of the digital model under the same operating conditions. Where Ek , Xk and Yk are defined as: Ek = [u Ta ]Tk
(1)
Xk = [i1 i2 · · · iN Tc1 Tc2 · · · TcN ]Tk
(2)
Yk = [i1∗ i2∗ · · · iN ∗ Tc1∗ Tc2∗ · · · TcN ∗ ]Tk
(3)
where u is the operating voltage of the DC bus; T a represents the ambient temperature; i1 , i2 … in and T c1 , T c2 … T cn represent the current and case temperature of each capacitor in the capacitor bank respectively; i1* , i2* … in* and T c1* , T c2* … T cn* represent the current and case temperature of each capacitor in the digital model respectively; subscript k represents the k-th sampling. Step 3: Model accuracy judgment. Calculate the error between the state data matrices Xk and Yk . When the error is less than the error determination threshold, that is, when the condition (4) is satisfied, it can be considered that the reflection of the digital model to the physical device is accurate within the tolerable error range. At this time, go to step 5. If the condition (4) is not satisfied, it indicates that the digital model cannot accurately reflect the operating state of the physical equipment, then it needs to go to step 4 to calibrate the parameters of the digital model. |Xk − Yk | < ε
(4)
Step 4: Model parameters calibration. When the digital model cannot accurately reflect the operating state of the physical equipment, it indicates that the equipment has been
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aging to a certain degree during the long-term operation, resulting in changes in equipment parameters. At this time, the parameters of the digital model need to be calibrated. According to the operating state data of the physical equipment collected by the sensor, taking (5) as the objective function, the parameters of the digital model are identified using optimization algorithms such as particle swarm optimization algorithm, genetic algorithm and least square algorithm, etc. And the parameter identification results are taken as the updated parameters of the digital model. After the parameter is updated, return to step 2. min|Xk − Yk |
(5)
Step 5: Condition monitoring application. When the digital model can accurately reflect the operating state of the physical equipment, the digital model can be used to realize the state monitoring of the DC bus capacitor bank. (1) The state matrix of the digital model Yk is used to monitor the operation state of the DC bus capacitor bank. As mentioned above, noise interference often exists in sensor data, Since Yk in the digital twin is the result of a series of mathematical operations, the influence of noise interference is much smaller than Xk , and can more accurately reflect the operating state of the equipment. (2) Monitoring of operating temperature of capacitor bank. The power loss of each capacitor is calculated from the equivalent circuit parameters, then input the power loss into the thermal network model to calculate the internal temperature of each capacitor.It should be noted that the ESR of the capacitor has a temperature characteristic, which leads to a coupling relationship between the equivalent circuit and the thermal network model. That is, the temperature change of the capacitor in the thermal network causes the change of ESR value in the equivalent circuit, which leads to the change of the power loss of the capacitor, as shown in formula (6), and the change of the power loss will affect the temperature of the capacitor in return, as shown in formula (7). It is not difficult to find that in the nonlinear equation system composed of these two formulas, temperature is not only an independent variable but also a quantity to be solved. Therefore, Newton iterative algorithm is needed to solve the temperature. Ploss,i (Tcore,i ) = Ici2 (k)Rci (Tcore,i ) Tcore,i = (Rcore,i + Rcase,i )Ploss,i +
N −1
Rcp,ij Ploss,j + Ta
(6)
(7)
j=1,j=i
(3) Health assessment of capacitor bank. The digital twin model information includes not only the ESR and capacitance values, but also the real-time operating temperature of each capacitor. Integrating these information can realize the health status evaluation of the capacitor bank. For instance, taking capacitance as the evaluation index, since the capacitance of the capacitor has a linear relationship with the temperature, which can be expressed as C = a + bT, where a and b are temperature
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characteristic coefficients. The remaining capacitance percentage of the capacitor after temperature normalization can be expressed as: D=
Cm − b1 (Tm − T0 ) Cm_T 0 = C0 a0 + b0 T0
(8)
where, a0 and b0 are the temperature coefficients without aging, C 0 is the initial rated capacity, and T 0 is the rated operating temperature. After a period of operation, the temperature characteristic coefficient changes to a1 and b1 , and the monitored capacitance value changes to C m , and the operating temperature at this time is T m . With the degradation of the capacitor, the capacitance will gradually decrease. Therefore, the remaining capacitance percentage of the capacitor can indirectly reflect the degradation degree of the capacitor. The temperature normalization of the remaining capacitance percentage can eliminate the temperature influence on the capacitance value, and make the health state assessment more accurate.
4 Verification Simulink-COMSOL joint simulation is used to verify the result of condition monitoring using digital twin model. The single-phase inverter system commonly used in new energy vehicles is selected as the external circuit and built in Simulink as shown in Fig. 3. Three capacitors are connected in series to form a DC bus capacitor bank. The inverter is controlled by open-loop control strategy. COMSOL is used to simulate the thermal behavior of the capacitor bank. The major simulation parameters are shown in Table 1. The data interaction between Simulink and COMSOL is performed with a time step of 60s, and the temperature characteristics of the capacitor are modeled by modifying the capacitor bank parameters in Simulink according to the temperature simulation results in COMSOL.
Fig. 3. Simulink simulation circuit diagram
The digital twin model of DC bus capacitor bank is constructed by the method proposed in this paper. Take the current of one capacitor as the state monitoring object. The waveform comparison between digital twin and simulation is shown in Fig. 4. It can be seen that the digital twin waveform basically coincides with the simulation waveform, which indicates that the digital twin model can accurately reflect the operating state of the DC bus capacitor bank.
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Parameter
Value
Parameter
Value
DC voltage
150 V
Ambient temperature
25 °C
Grid frequency
50 Hz
Switching frequency
1000 Hz
C1, C2, C3
470 µF
Rc1 , Rc2 , Rc3
90 m
Thermal conductivity of capacitor shell
238 W/(m·K)
Thermal conductivity of capacitor core
1.2 W/(m·K)
Specific heat capacity of capacitor shell
900 J/(kg·K)
Specific heat capacity of capacitor core
752 J/(kg·K)
Density of capacitor shell
2700 kg/m3
Density of capacitor core
1784 kg/m3
15 Digital twin waveform Simulation waveform
10
5
0
-5
-10 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Time(s)
Fig. 4. Comparison between digital twin and simulation waveform
The operating temperature of capacitor bank calculated by digital twin and COMSOL simulation results are shown in Table 2. It can be seen that the error between the digital twin calculation results and the simulation results is within 2%, so the internal temperature monitoring of each capacitor in the DC bus capacitor bank can be realized by using the digital twin model. Table 2. Temperature calculation results Temperature
Simulation result (°C)
Digital twin result (°C)
Error (%)
Internal temperature
34.11
34.47
1.05
Case temperature
29.29
29.64
1.19
Increase the ESR of the capacitor and reduce the capacitance in Simulink to simulate the aging of the capacitor. Take capacitance as the evaluation index, and use the digital twin model to realize the health status evaluation of the capacitor bank. The results are shown in Table 3. It can be seen that the digital twin model can synthesize the
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model parameters and the operating temperature to achieve temperature normalization of parameters, which eliminates the influence of the capacitor temperature characteristic, and makes the health state assessment result more accurate. Table 3. Health status evaluation result Aging degree
Parameters under 25 °C
DT monitoring results
Capacitance
ESR
Capacitance
Temperature
DT normalized capacitance (25 °C)
Unaged
470 µF
90 m
493 µF
34.47 °C
472 µF
Slight
450 µF
110 m
479 µF
36.55 °C
454 µF
Middle
430 µF
150 m
471 µF
39.92 °C
437 µF
Severe
400 µF
190 m
441 µF
43.83 °C
397 µF
5 Conclusion In this paper, the physical characteristics of capacitors are analyzed and the digital twin model frame of DC bus capacitor banks is constructed. After that, a state monitoring method of DC bus capacitor bank based on digital twin model is proposed. This method can not only reduce the influence of environmental noise, but also realize the noninvasive measurement of the operating temperature of the capacitor bank, and can use the measured operating temperature to normalize the parameters of the capacitor bank, eliminate the influence of temperature change on the capacitor parameters, and realize the accurate evaluation of the health state of the capacitor bank.
References 1. Zhang, B., Wang, M., Su, W.: Reliability analysis of power systems integrated with highpenetration of power converters. IEEE Trans. Power Syst. 36(3), 1998–2009 (2021) 2. Liu, S., Shen, Z., Wang, H.: Safe operating area of DC-link film capacitors. IEEE Trans. Power Electron. 36(10), 11014–11018 (2021) 3. Tu, C., Chai, M., Yu, X., et al.: ESR and capacitance monitoring method based on discharge law of aluminum electrolytic capacitor. Power Autom. Equip. 40(7), 108–113 (2020). (in Chinese) 4. Sun, P., Gong, C., Du, X., et al.: An on-line monitoring method for equivalent series resistance of DC bus capacitance of high-power AC converter. Chin. J. Electr. Eng. 37(17), 5134–5142 (2017). (in Chinese) 5. Duan, X.: Research on Reliability Evaluation Technology of Aluminum Electrolytic Capacitor in Switching Power Supply. South China University of technology (2020) (in Chinese) 6. Rodriguez, E., Liang, G., Farivar, G.G., et al.: Capacitor condition monitoring based on an adaptive observer of the low-frequency capacitor voltage ripples for modular multilevel converters. In: IEEE 4th International Future Energy Electronics Conference (IFEEC), pp. 1– 6. IEEE (2019)
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7. Chen, Y., Lv, G., Geng, Y.: Research on the volume optimization of support capacitor in EV driver. Electron. Des. Eng. 26(12), 139–143 (2018) (in Chinese) 8. Cui, S., Lei, H., Chao, Z., et al.: Research on temperature characteristic of DC-link capacitors applied in electric vehicles. In: IEEE Conference and Expo Transportation Electrification Asia-Pacific (ITEC Asia-Pacific), pp. 1–5. IEEE (2014) 9. Tao, F., Zhang, M., Liu, Y., et al.: Digital twin driven prognostics and health management for complex equipment. CIRP Ann. 67(1), 169–172 (2018) 10. Jain, P., Poon, J., Singh, J.P., et al.: A digital twin approach for fault diagnosis in distributed photovoltaic systems. IEEE Trans. Power Electron. 35(1), 940–956 (2020) 11. Zhu, M., Liu, Y., Huang, M., et al.: Digital twin system of capacitive DC bank considering the electrothermal coupling effect. In: IEEE Energy Conversion Congress and Exposition (ECCE), IEEE (2022)
Improve the Temperature Stability of PVDF/PMMA Energy Storage Performance by Crosslinking Zhengwei Liu, Yongbin Liu, Jinghui Gao(B) , and Lisheng Zhong State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an710049, China [email protected]
Abstract. With the development of science and technology, energy storage capacitors are gradually developing towards miniaturization and high temperature. Recently, polyvinylidene fluoride (PVDF) has attracted wide attention due to its high dielectric contant and high energy storage density. However, the problems of high dielectric loss and low temperature stability restrict the application of polyvinylidene fluoride. In this paper, it is proposed to optimize the dielectric loss and breakdown strength of polyvinylidene fluoride-based energy storage materials by blending polymethyl methacrylate (PMMA) with high glass transition temperature and high breakdown strength performance. On this basis, the crosslinking agent 1,6-hexanediamine was used to realize the crosslinking of PVDF and PMMA to improve the temperature stability of the material. Through this scheme, the finally obtained crosslinked PVDF/PMMA (40/60) film has an energy storage density of 10.4–11.9 J/cm3 at 30–90 °C, and efficiency of 79–88%, which are better than most dielectric polymers. Our work provides a solution for optimizing the temperature stability of the energy storage properties of polymer ferroelectric materials to achieve higher energy storage densities at higher temperatures. Keywords: Polyvinylidene fluoride · Crosslink · Energy storage · Temperature stability
1 Introduction With the development of science and technology, high performance capacitors occupy an increasingly important position in the defense industry, new energy field and other aspects [1–3], electrostatic energy storage depends on the polarization process of dielectric materials dipoles, which requires dielectric materials to have high dielectric constant, low dielectric losses and high breakdown strength. Due to the high breakdown strength, excellent processability and scalability of polymers, polymers have become one of the most widely used media materials. Nowadays, the demand for capacitors is gradually developing in the direction of miniaturization and high temperature, which poses a higher challenge for the preparation of polymer dielectric materials with high energy storage performance and high temperature stability. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 993–1001, 2023. https://doi.org/10.1007/978-981-99-1027-4_104
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The energy storage density (U e ) of a dielectric material can be calculated by the following formula: Ue = EdD where E is the electric field strength and D is the electric displacement intensity [4]. Therefore, the energy storage performance of dielectric materials at high temperatures is mainly determined by the breakdown strength and polarization response of dielectric materials at high temperatures. Therefore, in order to realize the application of polymer dielectric materials at high temperatures, it is necessary to improve their dielectric constant and breakdown strength at high temperatures. At present, the commonly used methods to improve the properties of polymer materials mainly include: chemical grafting, nano-doping, blending, crosslinking and so on. Zhang et al. [5] SO2 -PPO25 materials obtained by polymer post-functionalization have energy storage densities and efficiencies of ~2 J/cm3 and ~80% at temperatures of 160 °C and electric field strengths of 300 kV/mm, respectively, but the chemical grafting process is more complex is not conducive to large-scale use; He et al. [6] PVDF/Nd-BaTiO3 @Al2 O3 nanocomposites were obtained by doping NdBaTiO3 @Al2 O3 nanoparticles with core shell structure in the PVDF matrix, and the energy storage density and efficiency of the composite materials at 80 °C were 7.46 J/cm3 and ~50%, respectively, but the nanoparticles in the nanocomposites may have aggregation phenomena, affecting the performance of the composites. Liu et al. [7] The polymer film obtained by using PVDF and PMMA fused blending has an energy storage density of 9.8 J/cm3 and an efficiency of ~70% at 70 °C, which effectively improves the temperature stability of the material, but the blending method is limited by the compatibility problem between materials, and serious phase-splitting phenomenon will occur for material blending with poor compatibility. Therefore, achieving high energy storage density and high temperature stability of polymers at high temperatures is still a huge challenge. In this paper, a scheme is proposed to optimize the dielectric loss and high temperature stability of polyvinylidene fluoride energy storage material by blending polymethyl methacrylate (PMMA) with high glass transition temperature and high breakdown performance, and then use the crosslinker 1,6-hexanediamine to crosslink PVDF and PMMA to further improve the energy storage performance of the material at high temperature. The results show that the Blending and crosslinking can improve the maximum electric field strength of the material at high temperature to a certain extent, and thus improve its energy storage performance at high temperature.
2 Experimental 2.1 Materials Polyvinylidene fluoride (PVDF, No.44080) from Alfa Aesar and polymethyl methacrylate (PMMA) from Alfa Aesar; 1,6-Hexanediamine purchased from Aladdin; N,NDimethylformamide (DMF) was purchased from Aladdin.
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2.2 Preparation Principle and Process of Crosslinked PVDF/PMMA Film As shown in Fig. 1, the amine group may react with the ester group in PMMA to generate an amide bond [8, 9], while the amine group can also react with PVDF to generate a C = N double bond [10–13]. The 1,6-hexanediamine chain contains an amine group at each end, so crosslinking between PVDF and PMMA can be achieved by introducing an appropriate amount of 1,6-hexanediamine. Crosslinked PVDF/PMMA films are prepared by solution casting. First, weigh the powder samples with PVDF/PMMA ratios of 100/0, 80/20, 60/40, 40/60, 20/80, and dissolve them in DMF solvent at 10 wt%, and then add 3 wt% of 1,6-hexanediamine at room temperature and stir evenly, then use the casting method to form a film in a 60 °C vacuum oven for 1h, and then place the sample in a 180 °C oven for 1 h. Finally, the samples were placed at 200 °C for 15 min and then quenched in ice water to obtain PVDF/PMMA crosslinked blended film.
Fig. 1. PVDF/PMMA crosslinking schematic
2.3 Characterization SEM (Gemini SEM 500) is used to obtain the surface topography and distribution of O, F and N elements of crosslinked samples after crosslinking; TGA (METTLER TOLEDO) is used to measure the thermal weight loss curve between 30 °C and 800 °C at a temperature rise rate of 10 K/min; FTIR (NICOLET6700) and XRD (Bruker Advance D8) are used to analyze the crystal structure of samples; LCR (HIOKI IM3536) is used to measure the dielectric temperature spectrum of specimens at −100–110 °C at 100 Hz, 1 kHz, 10 kHz, 100 kHz, in which the specimen is sprayed with a circular gold electrode with a diameter of 10 mm; PolyK Technologies is used to measure the D-E hysteresis loop and then determine its energy density and efficiency with temperature, the measurement signal is a unipolar triangular signal of 1 kHz, and the sample is sprayed with a circular gold electrode with a diameter of 3 mm; Finally, the gel content of the conjugated crosslinking sample is measured using DMF solvent.
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3 Results and Discussion 3.1 Surface Topography and Energy Spectroscopy Analysis As shown in Fig. 2, for the SEM and EDS images of the crosslinked PVDF/PMMA film, where F is the endemic element of PVDF, O is the endemic element of PMMA, and N is only present in the bond with amide bond, and C = N bond. It can be seen from the figure that the PVDF and PMMA in the film are evenly distributed, and at the same time, the distribution of the N element can be seen that the crosslinking bond in the film is more uniformly distributed within the observed film range, but because the crosslinker 1,6-hexadiamine is used in less content, the overall content of the crosslinking bond is also less. DMF is the solvent of PVDF and PMMA, so the use of DMF to test the gel content of the crosslinked blended sample, as shown in Fig. 3, it can be seen that the blended sample is crosslinked under the action of 1,6-hexanediamine, but because the crosslinking reaction partially occurs in 10 wt% of the solution, so that the gel content of the sample after crosslinking is low.
Fig. 2. Cross-linked PVDF/PMMA thin film SEM and EDS diagrams, a SEM image; b F distribution; c O distribution; d N distribution
3.2 Thermal Properties As shown in Fig. 4a–e, the TGA curve of crosslinked samples with different PMMA contents, the thermal decomposition process of the sample is divided into two stages, of which the stage with a temperature range of 300–420 °C is the thermal decomposition stage of PMMA; The thermal decomposition stage of PVDF is the thermal decomposition stage of PVDF with a temperature range of 420–500 °C [14, 15]. From
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50
Gel content(%)
40 30 20 10 0
0
20 40 60 the Content of PMMA(%)
80
Fig. 3. Curve of the gel content with PMMA content
Fig. 4f. The maximum thermal decomposition rate temperature of the crosslinked sample changes with the PMMA content, it can be seen that the temperature corresponding to the maximum thermal decomposition rate of PMMA in the crosslinked sample is relatively increased by about 10 °C compared with the normal sample. For the PVDF thermal decomposition stage, when the PVDF content is greater than 60%, the temperature corresponding to the maximum thermal decomposition rate is also increased by 10–20 °C, which means that the stability of the blended sample at high temperature can be effectively improved by 1,6-hexanediamine crosslinking. At the same time, due to the cross-linking between PVDF and PMMA, the transition area of the two thermal decomposition stages is smoother.
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3.3 Crystal Structure Properties of Crosslinked Samples Regarding the crystallization characteristics of the crosslinking blended samples, as shown in Fig. 5a, b, where Fig. 5a shows the FTIR curve of the crosslinked samples, wherein there are absorption peaks of 613 cm−1 , 762 cm−1 , 795 cm−1 , 975 cm−1 in the pure PVDF, which represent the α phase crystallization peaks of PVDF, It can be seen from the figure that with the addition of PMMA, α phase crystallization peak gradually decreases; The absorption peak of 840 cm−1 and 1270 cm−1 is the β phase crystallization peak of PVDF [16–18], and with the addition of PMMA,β phase crystal peak shows a tendency to increase first and then decrease, which is because on the one hand, with the addition of PMMA, the orientation of PVDF crystals is promoted, the relative content of β phase crystallization in PVDF is improved. On the other hand, the addition of PMMA, an amorphous polymer, plays a diluting effect on PVDF and inhibits the crystallization of PVDF. This phenomenon can also be observed from the XRD plot of the crosslinked blended sample in Fig. 5b, which is mainly absent for samples with PMMA content greater than 40%. Although no significant crosslinking bond peaks were observed in FTIR, the gel content test in Fig. 3 shows that crosslinking PVDF with PMMA was achieved using the crosslinker 1,6-hexanediamine [11]. C-O
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3.4 Dielectric Properties of Crosslinked Samples In order to obtain the dielectric properties of the crosslinked blended samples with temperature, the dielectric temperature spectra at different frequencies in the temperature range of −100–110 °C were obtained by using LCR with the variable temperature test platform, and it can be seen from the figure that compared with the pure PVDF crosslinked film, the dielectric constant of the PVDF/PMMA crosslinked film decreased to a certain extent due to the introduction of PMMA, but due to the high glass temperature of PMMA, make the dielectric constant change trend with temperature more flat; In terms of dielectric loss, due to the introduction of PMMA and the influence of crosslinking, the dielectric loss of the crosslinked blended film does not occur suddenly (above 75 °C) compared with the pure PVDF crosslinked film at higher temperatures, and the dielectric loss at 1 kHz and the temperature range of −100–110 °C can be maintained below 0.1 to
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ensure the stability of the energy storage performance of the film at high temperatures; at the same time, due to the low content of the added crosslinking agent, the degree of crosslinking is relatively low, so the dielectric performance of the crosslinked blended film does not decrease significantly compared with the normal film, and can still be maintained at the original level (Fig. 6).
Fig. 6. Dielectric temperature spectrum at −100–110 °C, where a PVDF/PMMA (100/0); b PVDF/PMMA (80/20); c PVDF/PMMA (60/40); d PVDF/PMMA (40/60); e PVDF/PMMA (20/80)
3.5 Variable Temperature Energy Storage Performance of Crosslinked Samples Through the ferroelectric workstation with the temperature control system, the variable temperature energy storage performance of the crosslinked blended film is obtained as shown in Fig. 7a–e, The PVDF after crosslinking by 1,6-azaidiamine is shown in Fig. 7a Even when the temperature rises to 70 °C, its maximum electric field strength can still reach 400 kV/mm, but its efficiency is reduced to less than 60%; Therefore, by mixing crosslinking PMMA to adjust its maximum electric field strength, energy storage density and efficiency at high temperature. As shown in Fig. 7d, taking crosslinked PVDF/PMMA(40/60) as an example, when the temperature is in the range of 30 °C to 90 °C, its maximum electric field strength can always reach more than 490 kV/mm, at this time its energy storage density is 10.4–11.9 J/cm3 , charge and discharge efficiency up to 79–88%, which is far better than most ferroelectric polymers.
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4 Conclusion In this paper, the dielectric properties of PVDF were optimized by blending PMMA with high glass transition temperature and high breakdown performance, and then the crosslinking agent 1,6-hexanediamine was used to crosslink PVDF and PMMA, and the scheme to further improve the energy storage performance of the material at high temperature was obtained, and the different proportions of PVDF/PMMA were mixed crosslinked films, and the distribution of N in the EDS image showed that the crosslinking bonds were uniformly distributed in the crosslinked blended films. The TGA test results show that the stability of the samples after crosslinking is improved compared with that of normal samples. At the same time, the energy storage density of the crosslinked blended film with PMMA content of 60% in the temperature range of 30–90 °C is 10.4– 11.9 J/cm3 , and the efficiency can reach 79–88%, which is better than most ferroelectric polymers. This paper provides a method for obtaining polymers with high energy storage density and high temperature stability at high temperatures. Acknowledgments. This work was funded by basic scientific research business expenses of Xi’an Jiaotong University (No.xzy012021022).
References 1. Tan, D.Q.: Review of polymer-based nanodielectric exploration and film scale-up for advanced capacitors. Adv. Func. Mater. 30(18), 1808567 (2020) 2. Zhou, Y., Wang, Q.: Advanced polymer dielectrics for high temperature capacitive energy storage. J. Appl. Phys. 127(24), 240902 (2020)
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3. Li, Q., Yao, F.Z., Liu, Y., et al.: High-temperature dielectric materials for electrical energy storage. Annu. Rev. Mater. Res. 48, 219–243 (2018) 4. Chu, B., Zhou, X., Ren, K., et al.: A dielectric polymer with high electric energy density and fast discharge speed. Science 313(5785), 334–336 (2006) 5. Zhang, Z., Wang, D.H., Litt, M.H., et al.: High-temperature and high-energy-density dipolar glass polymers based on sulfonylated poly (2, 6-dimethyl-1, 4-phenylene oxide). Angew. Chem. 130(6), 1544–1547 (2018) 6. He, L., Wang, J., Yang, Z., et al.: Dielectric and energy storage properties of PVDF/NdBaTiO3@ Al2O3 composite films. Funct. Mater. Lett. 12(3), 1950034 (2019) 7. Liu, Y., Gao, J., Wang, Y., et al.: Enhanced temperature stability of high energy density ferroelectric polymer blends: the spatial confinement effect. Macromol. Rapid Commun. 40(21), 1900406 (2019) 8. Hussein, M.A., El-Shishtawy, R.M., Abu-Zied, B.M., et al.: The impact of cross-linking degree on the thermal and texture behavior of poly (methyl methacrylate). J. Therm. Anal. Calorim. 124(2), 709–717 (2016) 9. Hussein, M.A., Albeladi, H.K., El-Shishtawy, R.M., et al.: Cross-linked PMMA-based bifunctional amino derivatives. J. Therm. Anal. Calorim. 134(3), 1715–1728 (2018) 10. Taguet, A., Ameduri, B., Boutevin, B.: Crosslinking of vinylidene fluoride-containing fluoropolymers. Crosslinking in Materials Science, 127–211 (2005) 11. Shin, Y.J., Kang, S.J., Jung, H.J., et al.: Chemically cross-linked thin poly (vinylidene fluorideco-trifluoroethylene) films for nonvolatile ferroelectric polymer memory. ACS Appl. Mater. Interf. 3(2), 582–589 (2011) 12. Taguet, A., Ameduri, B., Dufresne, A.: Crosslinking and characterization of commercially available poly (VDF-co-HFP) copolymers with 2, 4, 4-trimethyl-1, 6-hexanediamine. Eur. Polymer J. 42(10), 2549–2561 (2006) 13. Van Goethem, C., Magboo, M.M., Mertens, M., et al.: A scalable crosslinking method for PVDF-based nanofiltration membranes for use under extreme pH conditions. J. Membr. Sci. 611, 118274 (2020) 14. Hirata, T., Kashiwagi, T., Brown, J.E.: Thermal and oxidative degradation of poly (methyl methacrylate): weight loss. Macromolecules 18(7), 1410–1418 (1985) 15. Nguyen, T.: Degradation of poly [vinyl fluoride] and poly [vinylidene fluoride]. Polym. Rev. 25(2), 227–275 (1985) 16. Cai, X., Lei, T., Sun, D., et al.: A critical analysis of the α, β and γ phases in poly (vinylidene fluoride) using FTIR. RSC Adv. 7(25), 15382–15389 (2017) 17. Bormashenko, Y., Pogreb, R., Stanevsky, O., et al.: Vibrational spectrum of PVDF and its interpretation. Polym. Test. 23(7), 791–796 (2004) 18. Elashmawi, I.S., Hakeem, N.A.: Effect of PMMA addition on characterization and morphology of PVDF. Polym. Eng. Sci. 48(5), 895–901 (2008) 19. Namouchi, F., Smaoui, H., Fourati, N., et al.: Investigation on electrical properties of thermally aged PMMA by combined use of FTIR and impedance spectroscopies. J. Alloy. Compd. 469(1–2), 197–202 (2009)
Research on the Main Motor Preand Post-switchable Configuration Based on DCT Hybrid Vehicle Zhengfeng Yan1 , Linzi Hou1 , Bingbing Wu1(B) , and Bo Zhang2 1 School of Automotive and Transportation Engineering, Hefei University of Technology,
Hefei 230009, China [email protected], [email protected], [email protected] 2 Tri-Ring Automotive Clutches Co. LTD, Huangshi 435000, China [email protected]
Abstract. At present, pure electric vehicle technology is still in an immature developmental stage. As a transitional technology, hybrid vehicle technology is still of great research significance. In this research, the configuration and modeswitching of a dual-clutch transmission (DCT) hybrid electric vehicle were deeply studied, and a pre- and post-switchable configuration with better comprehensive performance was proposed. A traditional DCT fuel vehicle model and pre- and post-switchable configuration vehicle model were built using the CRUISE software. MATLAB’s SIMULINK software was used to design a rule-based modeswitching control strategy and complete a joint simulation with CRUISE. Using the ISIGHT software, the multi-island genetic algorithm was used to develop a mathematical model to optimize the parameters of the transmission system, and a joint simulation was conducted again. Two simulation results show that the preand post-switchable configuration could significantly improve vehicle economy compared with the traditional fuel vehicle configuration. Keywords: Hybrid vehicle · Dual-clutch transmission · Front and rear switchable type · Configuration analysis · Parameter optimization
1 Introduction Hybrid electric vehicles (HEVs), as new energy vehicles with multiple power sources, have the advantages of high efficiency and high specific power and energy like pure electric vehicles, as well as low emission levels and low petroleum fuel requirements. They also significantly improve fuel economy and emission characteristics when compared with traditional vehicles and ensure the vehicle mileage [1]. Since the 1990s, Audi and Toyota have introduced their first hybrid cars. After more than 20 years of development, hybrid car technology has made great progress in both top design and bottom components, forming a hierarchical topology including design layer, configuration layer and part layer. The design layer primarily includes the control strategy design and the parameter design for the hybrid vehicles. The control strategy © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1002–1013, 2023. https://doi.org/10.1007/978-981-99-1027-4_105
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can be divided into rule-based, optimization-based, and intelligence-based methods. The principal control goal is to optimize the economy, power, and emission of hybrid vehicles. The parameter design methods primarily include theoretical derivations and modeling analyses, or a combination of both [2]. The main objective of parameter design is to meet the requirements of power performance, fuel economy, and mixing degree for a vehicle. The configuration layer, i.e., the configuration of a vehicle’s transmission system, is principally classified according to the combination mode and positioning of the different power sources in a hybrid car. The main classification methods are series, parallel, and hybrid methods [3–5], and the parallel configuration can be divided into P0, P1, P2, P2.5, P3, and P4 sub-configurations, among others, according to the motor’s position. The topology’s part layer mainly refers to the principal parts of a hybrid car, such as the engine, the gearbox, the motor, and the battery, and each part has a different classification. According to the layered topology, the mechanical structure of a hybrid vehicle is composed of a component layer and a configuration layer. The same mechanical structure can be designed using different methods to achieve different performance goals. Considering factors such as the transformation cost, size, and fuelsaving potential, the P2 and P2.5 solutions, combined with gearboxes, have become two of the mainstream solutions for self-developed models [6]. Currently, the types of transmissions commonly used in automobiles are the manual transmissions (MTs), the mechanical automatic transmission (AMT), the automatic transmission (AT), the continuously variable transmission (CVT), and the dual-clutch transmission (DCT) [7]. The DCT was developed along the basis of the MT because it uses an innovative design of two clutches and an even-odd shaft input, which gives it a unique shifting principle. The DCT transmission has the advantages of high transmission efficiency, continuous shifting power, good shifting comfort, and low production cost [8]. Currently, many different topologies are designed with different transmission technologies such as automated manual transmission (AMT) and continuously variable transmission (CVT). The choice of topology determines the energy-flow efficiency between the hybrid system, the engine, and the vehicle wheels. Correlational research have compared AMT (high efficiency) and a push-belt CVT (moderate efficiency) [9]. In addition, a controlled switching is introduced as a benchmark, where controlled coupling with additional clutches of the electric machine before or after the transmission minimizing transmission losses and improving hybrid performance is investigated. This study proposes a switchable configuration, based on the characteristics of the DCT, with better comprehensive performance for analysis and research. The whole vehicle simulation platform AVL/CRUISE was used to build a simulation model of a DCT traditional fuel vehicle and a pre- and post-switchable hybrid configuration. Next, the research status of the hybrid vehicle control strategy was analyzed, and a rule-based mode-switching control strategy was built using MATLAB’s SIMULINK software. Then economic and dynamic simulations using the joint model were conducted. By comparing the simulation results for the pre- and post-switchable configuration of the traditional fuel vehicle and the motor, the feasibility of the control strategy was verified. The model achieved the expected control objectives, a result which provides a reference for the further development of hybrid electric vehicles based on the DCT.
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Finally, the ISIGHT optimization software and CRUISE were used for joint simulations to establish a mathematical optimization model with dynamic constraint conditions and economy as the objective function. The multi-island genetic algorithm was used to optimize the transmission system parameters and verify the correctness of the optimization results.
2 Configuration Analysis of a DCT Hybrid Vehicle Compared with conventional fuel vehicles, hybrid vehicles have one or more power transmission lines from the source of the driving force. In terms of specific components, hybrid vehicles need at least one motor and one battery for the energy conversion of the vehicle. Therefore, hybrid electric vehicles are complex systems of electromechanical coupling. At present, there are two primary methods of studying the configuration of hybrid electric vehicles: the exhaustive method [10] and the graph theory method [11, 12]. Generally, the exhaustive method is suitable for the cases with few latent configurations, such as ordinary series-parallel structures. The graph theory method is mostly used for the cases with many latent configurations and is principally used for hybrid structures using planetary arrays as electromechanical coupling devices. The research objective of this study is based on a DCT hybrid electric vehicle for which the configuration change was relatively small, so the exhaustive method was used to analyze the configuration. 2.1 Configuration Classification Based on the investigation of domestic and foreign literature and the technical schemes of major vehicle enterprises, the possible configuration of hybrid vehicle based on DCT is analyzed and summarized, and proposed the main motor pre- and post-switchable configuration. According to the coupling form of motor and DCT and the number of motors, DCT hybrid electric vehicle can be divided into the following schemes. The configuration diagrams for each scheme are shown in Table 1. 2.2 Working Principle of Main Motor Pre- and Post-switchable Configuration The three common configurations of main motor front, main motor middle and main motor rear are not introduced in this paper. This section mainly analyzes the principle of main motor pre- and post-switchable configuration in detail. The main motor pre- and post-switchable is to realize the switching of the connection position between the motor and the gearbox through the clutch. The configuration diagram is shown in Fig. 1. According to the configuration diagram, when C3 clutch is closed and C4 clutch is separated, it is the same as the working state of the front of the main motor. When C3 clutch is separated and C4 clutch is closed, it is the same as the working state of the rear of the main motor. The advantage of this configuration is that it can combine the advantages of the front and rear of the main motor, that is, it can not only use the gearbox to realize the operation of the motor in the high-efficiency area, but also improve the efficiency of braking energy recovery. The disadvantage is that this configuration requires the coordinated work of five clutches, which increases the control
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Table 1. Schematic diagram of configurations Single motor configuration
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difficulty. At the same time, the improvement of braking energy recovery efficiency of this configuration mainly depends on the transmission efficiency of the gearbox. This configuration can also be divided into single motor type and dual motor type. Only the single-motor-mechanism type is analyzed below. The common working modes of HEVs are the hybrid mode, the driving charging mode, the pure engine mode, the pure electric mode, the brake energy recovery mode, the common brake mode, and the parking mode. The single motor type scheme can also realize 7 working modes from the perspective of achievable working conditions.
3 Model Building and Control Strategy Optimization 3.1 Development of the Vehicle Model Based on CRUISE The forward simulation software AVL CRUISE was used for simulation during this research, and the forward simulation logic was consistent with the actual information flow [13]. In addition to the engine, motor, battery, and gearbox modules, the vehicle model had many other components, such as clutch, brake, main deceleration, and differential modules. All the modules previously mentioned were correctly connected mechanically
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Fig. 2. DCT traditional fuel vehicle model (left) and pre- and post-switchable model (right)
3.2 Rule Based Control Strategy Design Because hybrid electric vehicles involve coordination between two power sources and a switch between complicated driving modes, the full realization of their fuel saving potential depends on correct cooperation between the components. A mode-switching control strategy is the key to stable and efficient operation of the vehicles, and it plays a key role in improving fuel economy and reducing emissions. The energy control strategies based on optimization and intelligence require many calculations and extensive signal collection, and their real-time performances are poor. Hardware and software for the vehicle controller are also required. Rule-based control
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strategies have the advantages of less control, fewer calculations, and better real-time performance. Therefore, a rule-based method was adopted to complete the design of the switchable configuration for this research. 3.2.1 Mode-switching Conditions and Torque Allocation According to the analysis in the Sect. 2, the possible working modes for the whole vehicle could be divided into seven types: the parking mode, the pure electric mode, the driving charging mode, the pure engine mode, the hybrid drive mode, the braking energy recovery mode, and the mechanical braking mode. The relationships between these modes are shown in Fig. 3.
Fig. 3. Relationships between different working modes
The potential running states for the whole vehicle can be divided into three types: the driving state, the braking state, and the parking state. These states can also be divided into different sub-modes according to how the engine participates in running the vehicle. The braking state can be divided into a braking energy recovery mode and a mechanical braking mode based on whether the motor is involved. The labels between modes in Fig. 3 indicate the conditions required for switching between them. The mode-switching conditions corresponding to each label are shown in Table 2. In Table 2, T _req represents the vehicle demand torque, which is determined based on the vehicle’s driving state and target conditions. Te_min is engine starting torque, equal to 50 N-m for this simulation. Te_opt is the optimal torque, which can be determined from the optimal working curve of the engine, and Te_max is the maximum torque of the engine, which can be determined from the engine’s external characteristic curve. SOC_high is the maximum charge state of the battery, selected to be 0.8 for this simulation, SOC_target represents the target charge state of the battery, chosen to be 0.6 for this simulation, and SOC_low is the lowest charge state of the battery, set equal to 0.3 for this simulation. 3.2.2 Development of a Control Model Based on SIMULINK The general method is to use MATLAB’s SIMULINK to write the model, and then use the MATLAB DLL module in CRUISE to perform the joint simulation. The SIMULINK
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control model was primarily divided into four parts: an input and output module, a demand torque calculation module, a mode-switching control logic module, and a torque distribution module. When establishing the demand torque calculation module, the fuel economy of the whole vehicle is generally simulated by using the standard cycle condition as the input to the simulation model, and the cycle condition generally does not contain slope information. In SIMULINK, there is a Stateflow module to solve the problem of switching between multiple states. The core theory of this module is the finite state machine (FSM) theory. Stateflow’s modeling centers around determining the actions that different states need to perform and the switching conditions between the states. The Stateflow module is divided into three sub-modules according to the actual state of the vehicle: Stop, Driving, and Braking. Of the three, Stop is the starting module.The initial judgment conditions are judged from this module. Driving is the driving module, which has five sub-modules of its own: pure electric driving state, engine starting state, pure engine state, hybrid driving state, and driving charging state. The Braking module is a braking module consisting of two sub-modules: the mechanical braking module and the braking energy recovery module. Based on the torque distribution for each mode, the torque distributions and control quantities for each mode were established. Finally, the C CODE compiler of SIMULINK was used to compile the control model, generate the DBF and DLL files, import them into the CRUISE software, establish the corresponding signal connection, and finally configure the joint CRUISE and SIMULINK simulation model.
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3.3 Transmission Parameter Optimization Based on Isight ISIGHT is a computer-aided engineering software that, after years of development, has been widely used to solve various optimization problems [14]. It can quickly couple all kinds of simulation software packages and combine simulation processes, optimization algorithms, and corresponding models together, and then automatically run the simulation software to achieve optimization. It can also modify the models, and then optimize the whole process. It eliminates the drawbacks of traditional design processes and achieves digitalization and automation of the whole design process. The input parameters and optimization parameters were defined through configuration steps, and the upper and lower allowable limits for each gear were ± 10%. The multi-island genetic algorithms is an improvement on the parallel distributed genetic algorithm, and it is suitable for the global optimization design of a single variable function and has better global solving ability and computing efficiency than the traditional genetic algorithm [15, 16]. Therefore, the multi-island genetic algorithm was chosen to solve the model in this research.
4 Simulation Analysis and Optimization To prove whether the pre- and post-switchable vehicle configuration could improve the whole vehicle’s economy, a traditional DCT fuel vehicle was compared with the pre- and post-switchable vehicle. After the optimization of transmission parameters, it is compared to verify whether the optimization results are helpful to improve fuel economy. 4.1 Simulation Analysis When simulating the fuel economy, the cyclic condition simulation method was the primary method used. This research employed the NEDC cyclic condition to simulate the fuel economy of the whole vehicle. The simulation speeds for the two models were basically consistent with the required speeds, indicating that the simulation model and control strategy were appropriate. One of the main reasons why hybrid vehicles can improve fuel economy is that they can change the engine’s working point. Therefore, the distribution of the engine’s operating points directly reflects the effects of the control strategy. Most of the working points for traditional fuel vehicles are concentrated in the areas with low fuel consumption rates, and that the economy and emissions are poor. The engine operating points of the pre- and post-switchable configuration essentially work along the optimal engine efficiency curve, and that the economy is better. According to the simulation results, the fuel consumption of the prototype vehicle was 8.53 L/100 km, an increase of 29.9% from the fuel consumption of the motor, which was 5.98 L /100 km. Figure 4 shows that the climbing degree of the whole vehicle at 30 km/h was about 40%, which meets the requirements for the climbing performance. Figure 5 shows 0– 100 km/h acceleration performance curve. It takes 10.5 s to accelerate to 100 km/h, which meets the acceleration performance requirements. When it reaches 100 km/h, it is the fourth gear.
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Fig. 4. Climbing curve at different speeds
Fig. 5. 0~100 km/h acceleration performance curve
4.2 Optimization Analysis of Transmission Parameters The model is solved by multi Island genetic algorithm. For the optimization, the selector population size was 5, the number of islands was 10, the algebra was 5, the crossover rate was 1, the mutation rate was 0.01, the migration rate was 0.1, and the number of iterations was 250. The optimal values of each index and the corresponding gear parameters are summarized in Table 3. Since the main objective of hybrid cars is to save fuel, the transmission ratio for each gear at the lowest fuel consumption for one hundred kilometers was selected as the optimization result. The fuel consumption for the first hundred kilometers was 8.53 L, higher by 16.7% from the optimized transmission value of 7.1L. Optimization was performed for the final drives and the transmission gears, as shown in Table 4.
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Table 3. Optimization results Optimizing parameters
Optimization Results Value of each gear i0
ig1
ig2
ig3
ig4
ig5
ig6
Fuel consumption per 100 km
7.1 L/100 km
3.51 3.97 2.67 2.02 1.48 1.11 0.80
0–100 km/h acceleration time
10.3 s
4.26 4.22 2.98 2.03 1.61 1.15 0.93
Maximum speed
202 km/h
3.5
Maximum gradeability in 204% first gear
4.31 2.63 2.16 1.55 1.08 0.77
4.50 4.37 2.87 2.00 1.43 1.20 0.86
Table 4. Comparison of main deceleration and gearbox gear parameters before and after optimization i0
ig1
ig2
ig3
ig4
ig5
ig6
Before optimization
3.94
3.97
2.91
2.13
1.56
1.15
0.84
After optimization
3.51
3.97
2.67
2.02
1.48
1.11
0.80
5 Conclusions In this study, a pre- and post-switchable configuration with better comprehensive performance was proposed. According to the performance requirements, the parameter matching and control strategy design are carried out, and the transmission system parameters are optimized. The main content and conclusions of this paper can be summarized in five points: 1. By considering the connection type between the motor and the DCT and whether there was a BSG motor, 10 vehicle configurations were summarized. Then, chose five states, which were most important to the hybrid vehicle, and analyzed the ease for each configuration to achieve these five states. According to the comprehensive comparison results, the pre- and post-switchable configuration was proposed and modeled. 2. The working principle of main motor pre- and post-switchable configuration was analyzed, and the working process of the pre- and post-switchable configuration hybrid vehicle under seven common working modes was introduced in detail. At the same time, the mathematical analysis of dynamics and fuel economy was carried out in the hybrid mode. The five most important states for hybrid vehicles were selected to analyze the difficulty of each configuration to realize these five states, and the pre- and post-switchable configuration was simulated and the control strategy was designed.
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3. The forward simulation software CRUISE was used to model a DCT conventional fuel vehicle and a pre- and post-switchable hybrid vehicle, and a rule-based control strategy was designed.The simulation results showed that compared with the traditional DCT fuel vehicle, the fuel economy of the pre- and post-switchable configuration was improved by 29.9%, and the feasibility of the rule-based control strategy was also verified. 4. Using the ISIGHT optimization software and CRUISE, the parameters of the traditional system were optimized using the multi-island genetic algorithm. The optimized results showed that the fuel economy was improved by 16.7%. 5. The advantage of this configuration is that it can combine the advantages of the front and rear of the main motor, that is, it can not only use the gearbox to realize the operation of the motor in the high-efficiency area, but also improve the efficiency of braking energy recovery. At the same time, it can greatly improve the power and fuel economy of the vehicle, which has great reference value for research and development.
References 1. Xu, C., Li, W.C.: Classification of new energy vehicles. Foreign Electron. Measur. Technol. 36(5), 1–3 (2017) 2. Li, G.: Parameter Matching and Optimization of Power Source for Parallel Hybrid Passenger Vehicles. Beijing University of Technology (2016) (in Chinese) 3. Sabri, M.F., Danapalasingam, K.A., Rahmat, M.F.: A review on hybrid electric vehicles architecture and energy management strategies. Renew. Sustai. Energy Rev. 53, 1433–1442 (2016) 4. Chan, C.C., Bouscayrol, A., Chen, K.: Electric, hybrid, and fuel-cell vehicles: architectures and modeling. IEEE Trans. Veh. Technol. 59(2), 589–598 (2010) 5. Ça˘gatay, B.K., Gözüküçük, M.A., Teke, A.: Acomprehensive overview of hybrid electric vehicle: Powertrain configurations, powertrain control techniques and electronic control units. Energy Convers. Manag. 52(2), 1305–1313 (2011) 6. Kim, K., Dong, H.S., Cha, S.W., et al.: Analysis fuel economy and dynamic performance of DCT hybrid system. In: 2017 IEEE Vehicle Power and Propulsion Conference (VPPC). IEEE (2017) 7. Zhao, Z.G., Wu, C.C., Yang, Y.Y., et al.: Optimal robust control of shifting process for hybrid electric car with dry dual clutch transmission. J. Mech. Eng. 52(18), 105–117 (2016) 8. Zhang, X.M., Wang, X.Y.: Development status and trend analysis of dual clutch transmission. Automotive Technol. 3, 22–27 (2019) 9. Hofman, T., Ebbesen, S., Guzzella, L.: Topology optimization for hybrid electric vehicles with automated transmissions. IEEE Trans. Veh. Technol. 61(6), 2442–2451 (2012) 10. Wang, Q., Zhao, Z.G., Chen, N., et al.: Configuration analysis of hybrid electric vehicle equipped with dual clutch transmission. Automob. Technol. 5, 29–33 (2013) 11. Zheng, Z.W.: Graphical Modeling and Comprehensive Design of Dual Planet EVT Hybrid Power Transmission System. Chongqing University (2017) (in Chinese) 12. Yang, Y.L., Mi, J., Hu, X.S., et al.: Graph theory modeling and dynamics analysis on the coupled planetary transmission system of HEV. Automot. Eng. 37(1), 9–15 (2015) 13. He, A.Q., Sun, K.H., Shen, L.F., et al.: Comparison and analysis of vehicle power performance based on CRUISE forward-facing and ADVISOR backward-facing simulation softwares. Bus Coach Technol. Res. 40(2), 1–4 (2018)
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14. Liu, A.G.: Research on PHEV Fuzzy Control Strategy Based on Driving Awareness Recognition. Hefei University of technology (2019) (in Chinese) 15. Zhan, C.S., Wang, Q.: Design and optimization of transmission parameters of electric vehicles based on improved genetic algorithm. J. Chongqing Univ. Technol. (Natural Science) 34(2), 1–5 (2020) 16. Zeng, X.H., Wang, Z.W., Song, D.F., et al.: Parameter optimization of dual-mode power-split hybrid electric bus based on MIGA algorithm. J. Mech. Eng. 56(2), 98–105 (2020)
Application of Lane Detection Based on Point Instance Network in Autonomous Driving Jialin Liu, Quanqing Yu(B) , and Pengyu Zhu Harbin Institute of Technology, Weihai 264200, China [email protected]
Abstract. Lane detection is the core problem of autonomous driving. After completing lane recognition, the autonomous driving system can realize the active safety and control function of vehicle lateral movement. However, the existing methods cannot adapt well to various environments and generate many unnecessary points, resulting in low detection accuracy. In this paper, Point Instance Network (PINet) based on key points estimation and instance segmentation is used, which is composed of several stacked hourglass networks that are trained at the same time. Compared with existing algorithms, PINet achieves ideal accuracy and false positive rate on CULane, especially in night and dazzle light. Keywords: Lane detection · Autonomous driving · Point Instance Network
1 Introduction As urban traffic and image processing develop dramatically fast, the auxiliary visual functions applied in vehicles are gradually maturing. Autonomous vehicles have turned into the latest trend in the progression of the automobile industry. Lane detection is a process in which an autonomous vehicle adjusts the direction of the vehicle by calculating the position of the lane line. It can provide a reference for vehicle navigation, help vehicles to make trajectory planning and offset decisions, ensure the safety of unmanned vehicles, and play an important role in vehicle assistance systems such as lane departure warning, lane keeping assistance and other functions. At present, there are two mainstream methods for lane detection, namely the traditional image detection and processing methods and the deep learning methods. The conventional lane detection model are usually based on visual information to solve the lane detection problem. The main idea of these methods is to use visual cues through image processing to segment the lane line area through edge detection and filtering, and then combine the Hough transform [1–3], RANSAC [4, 5] and other algorithms to detect the lane line. The traditional lane detection method can be divided into feature-based lane detection methods and model-based lane detection methods. Compared with traditional detection methods, the detection algorithm based on deep learning shows higher accuracy and stronger robustness. At present, there are two types of lane line detection methods based on depth learning: detection based methods [6, 7] and segmentation based methods [8, 9]. The detection-based method will divide © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1014–1022, 2023. https://doi.org/10.1007/978-981-99-1027-4_106
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the scene picture into small grid areas of the same size, and then use the target detector to detect the grid area of each row to determine whether it belongs to the lane line. Finally, the grid belonging to the lane line is fitted to the lane line. The method based on segmentation is to classify each lane line pixel of the scene image and judge whether the pixel belongs to the lane line or the background. The advantages of the detection based method are fast speed and strong ability to deal with straight lanes. However, when the environment is complex and there are many lines, the detection effect is not very good [10]. In general, the detection effect of the method based on segmentation is better than that based on detection, but the speed is slightly lower. All the current methods have some problems. The semantic segmentation method needs to be labeled or preprocessed at the pixel level for training, which increases the workload. At the same time, the prediction accuracy of these methods is not high, and there will be additional points. In addition, the existing methods are not adaptable to different environments. In order to overcome these limitations, a model called stacked hourglass networks can be employed to predict several key points on a traffic line. In Stacked hourglass networks, multi-scale features are commonly used to identify the pose. The hourglass network is actually an encoder-decoder structure. The encoder maximizes the features and spatial information of each scale. The decoder synthesizes the features extracted by the network at different resolutions and finally obtains a heat map that is consistent with the size of the input image. Unlike many networks, the hourglass network uses a convolution layer instead of a full connection layer in order to allow the network to accept inputs from different dimensions. The prediction accuracy can be improved by stacking the hourglass network. At the same time, because each subhourglass network of a stacked hourglass network will have a heat map as a prediction, the heat map of each hourglass output will be included in loss to improve the prediction accuracy. Each key point is divided into separate instances using a simple method inspired by the segmentation of point cloud instances [11].
2 Methodology 2.1 Traditional Methods Most classical lane detection methods are on the basis of manual features, and employ predefined curve models such as line models or parabolic models to match line features. Zhu Hongyu et al. [12] came up with a method on the basis of cascade Hough transform, using region of interest selection, filtering, edge detection, non-maximum suppression and other preprocessing, to overcome the traditional Hough transform needs to transform each point in the mapping process, make the calculation simpler. Tian et al. [13] proposed an ADAS lane detection and tracking method based on line segment detector (LSD), adaptive angle filter and dual Kalman filter. Firstly, the region of interest (ROI) in the input image is converted into a gray image, and then the gray image is preprocessed by median filtering and image thresholding. Then LSD algorithm is applied to ROI, and adaptive angle filter is used to eliminate incorrect lane lines more effectively.
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2.2 Deep Learning Methods In the detection methods based on deep learning, Qin et al. [6] achieved the goal of lane detection by selecting rows, which provides a good solution to the lane-line detection problem without visual cues. However, this method is not effective in the detection of curves. Chen et al. [14] proposed it by constructing the line representation as learnable points and then used the object detection network to detect these points and obtain lane lines. Tabelini et al. [7] performed feature extraction of the input images and used a polynomial to pair lane line candidate markers and then directly output lane line curves. Ji et al. [15] improves the detection effect and speed by improving the YOLO network and determining different detection scales according to the lane line distribution. In general, detection based methods focus on improving the processing speed, and are not sure about the accuracy. In the segmentation-based approach, Neven et al. [16] and Liu Bin et al. [8] treat the process as an instance segmentation problem by combining the segmentation method and the clustering algorithm. However, this method can not achieve real-time performance. Tian Jin et al. [9] instance-segmented the lane lines based on the instance segmentation method Mask-RCNN, and proposed an adaptive fitting method to fit the lane line feature points in different visual fields through polynomial fitting. Pan et al. [17] came up with the SCNN to improve the problem of no visual cue by replacing ordinary convolution with segment-by-fragment convolution. However, SCNN is not suitable for scenarios containing any number of lanes. 2.3 Stacked Hourglass Network In the hourglass network, a large number of bottleneck residual modules are used to extract the deep scale feature information of the image [18]. The structure of the residual module can well solve the problems of gradient disappearance and training difficulties caused by the network depth, and make the network performance better. The heat map estimation results obtained at each stage of the stacked hourglass network structure only rely on the multi-scale structure of the hourglass network to extract the features, which are then processed by residual modules and convolution layers. Considering that the heat map estimation result obtained in the previous stage is a valuable global feature information, which can be used to estimate the heat map in the next stage. Therefore, this paper sends the heat map result in the previous stage to the back of the convolution layer in the next stage for feature transfer, so as to obtain a more accurate heat map estimation result in the next stage. In addition to the first stage, the input of the hourglass network in the other three stages includes three channels: the input data of the hourglass network in the previous stage, the output data of the hourglass network in the previous stage, and the prediction results of the hourglass network in the previous stage. The input data, as the underlying feature, contains detailed local information. As high-level features, the prediction results contain global semantic information, which can improve the recognition performance of complex backgrounds. These data with different scales are fused by concatenation and addition. The output of the network is a group of response heat maps. In addition to the first stage, the input of the response heat map includes two paths: the output data of the network in the current stage and the prediction result of the hourglass network in the previous stage.
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2.4 Key Points Estimation Key points estimation techniques select some key points from the input image. The stacked hourglass network [19] is composed of several hourglass modules that are trained at the same time. Hourglass network includes convolutional layers, pooling layers, residual layers, bottleneck layers and upsampling layers. The function of the convolution layer is to extract the feature map of the input image and decompose the input RGB image. The function of the maximum pooling layer can be understood as the selection of places in the feature map that are important for prediction and places that are not. After passing through the pooling layer, the picture becomes smaller. The residuals layer is an important part of the hourglass network, which is largely based on the residuals module. The role of the residual layer is to pass back the output of the layer in front of the network. And then the bottleneck layer is actually a residual in nature. The bottleneck layer, however, changes the form of the convolution by changing two 3x3 cores into a combination of 1x1,3x3, and 1x1. Using a smaller core can save a lot of computer memory. The final upsampling layer uses the nearest neighbor technique to fill the image that has been reduced to a preset value until the image is the same size as the original input image. Not only has the network architecture or loss function been developed, but the method of optimizing the current network has been developed [20]. A supervision method that can be used for other multi-stage feature methods is proposed [21]. An improved network is proposed to improve the results of other existing models. We train a neural network consisting of several hourglass modules, which is called Point Instance Network (PINet). It generates points on the lane and separates the predicted points into a single instance. Figure 1 shows the structure of model for traffic line detection.
Fig. 1. Structure of PINet with three main parts.
3 Model Evaluation 3.1 Confidence Loss We predict the confidence value of each unit in the model. If there is a key point in the cell, the confidence value is close to 1. If there is no key point, the confidence value is close to
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0.The output of the confidence branch has 1 channel, which is fed to the next hourglass module [22]. The loss of confidence includes two parts: existence loss and non-existence loss. The existence loss is applied to cells containing key points; Nonexistence loss is used to reduce the confidence value of each background cell. The nonexistent loss was calculated at cells with predicted confidence values higher than 0.01. Because cells far from the key point converge quickly, this technique helps focus training on cells closer to the key point. The loss function of the confidence branch is shown below: Lexist =
1 ∗ (cc − cc )2 Ne
(1)
cc ∈Ge
Lnon_exist =
1 Nn
(cc∗ − cc )2 + 0.00001 ·
cc2
(2)
cc ∈Gn
cc ∈ Gn cc > 0.01
where Ne represents the number of cells containing key points, Nn represents the number of cells without any key points, Ge represents the key points composed of a group of cells, Gn represents the points composed of a group of cells, cc represents the predicted value of each cell, and cc∗ represents the ground truth. The ground truth of a cell with a key point is 1 and 0 otherwise. In reasoning, if the confidence value is greater than a predefined threshold, we believe that there is a critical point in the cell. The second term in which Lnon_exist is a regularization term [22]. 3.2 Offset Loss During offset processing, PINet predicts the exact position of key points according to each output unit. Each cell corresponds to a value representing the location associated with the corresponding cell. The offset branch has two channels for predicting the offset in the X and Y axes, respectively. The loss function is as follows: Loffset =
1 ∗ 1 ∗ (cx − cx )2 + (cy − cy )2 Ne Ne cx ∈Ge
(3)
cy ∈Ge
3.3 Embedding Feature Loss The goal of network training is to make embedded features belonging to the same instance closer. Similarly, only cells with key points are calculated. In a grid output, the embedding feature of each cell and the embedding feature of the remaining cells should be calculated for loss, and the loss of the whole grid is formed after traversal. For the loss of each cell, if two cells belong to the same instance, minimize the loss of the embedded features of these two cells ||Fi − Fj ||2 ; Otherwise, minimize max(0, K − ||Fi − Fj ||2 ), and K is a constant. The operations of max() and K here can be understood as regular
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constraints. Embedding feature loss can also be considered as a distance based clustering. The loss function is shown below: Lfeature l(i, j) =
Ne Ne 1 = 2 l(i, j) Ne i
(4)
j
||Fi − Fj ||2 if Iij = 1 max(0, K − ||Fi − Fj ||2 ) if Iij = 0
(5)
3.4 Distillation Loss Indeed, it may be understood that the output feature map of each hourglass network structure (“cut layer”) will first be summed of squares on the channel to yield G. Softmax of the spatial dimension of G gives F. Indeed, a stacked (series) cut with each hourglass network structure will be cut with a square sum of features maps and a full-size hourglass grid structure to obtain the current hourglass network structure (“cut loss”). The loss function is as follows: Ldistillation =
M
D(F(AM ) − F(Am ))
(6)
m
F(AM ) = S(G(Am )), S : spatial softmax G(Am ) =
C
|Ami |2 , G : RC×H ×W → RH ×W
(7) (8)
i=1
Ltotal = γe Lexist + γn Lnon_exist + γo Loffset + γf Lfeature + γd Ldistillation
(9)
4 Experimental Results 4.1 Dataset Our model is trained on CULane, which is a large scale challenging dataset for academic research on traffic lane detection. More than 55 h of videos were collected and 133,235 frames were extracted. We use the official evaluation index [23] to evaluate the data set. We calculate the intersection-over-union (IoU) between the prediction of the evaluation model and the actual ground conditions. In the CULane dataset, relevant evaluation indicators are defined as follows. TP (10) Precision = TP + FP TP Recall = (11) TP + FN 2 ∗ Precision ∗ Recall F1_measure = (12) Precision + Recall TP is a true positive, FP is a false positive and FN is a false negative [22].
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4.2 Results Table 1 and Fig. 2 show the detailed results of PINet on the CULane dataset. We observed three characteristics. First of all, the false positive rate of PINet is relatively low, which proves that this method is safer than the existing model. Secondly, when the three hourglass networks are stacked, the distillation effect is the best. Finally, our method has better detection effect and accuracy compared with the traditional method in the harsh environment such as dark, strong light and other conditions. Table 1. Evaluation results for CULane dataset. Category
PINet (1H)
PINet (2H)
PINet(3H)
PINet(4H)
SCNN[23]
R-101-SAD[24]
No line
44.6
48.9
49.6
49.9
43.4
43.5
Shadow
62.8
67.2
68.5
68.5
66.9
67.0
Night
61.5
67.1
67.8
67.9
66.1
66.3
Dazzle light
59.5
65.4
66.5
66.4
58.5
59.9
Total
57.1
62.2
63.1
63.2
58.7
59.2
Fig. 2. Results of CULane dataset.
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5 Conclusion This paper uses PINet for lane detection, one of the advantages is that it can work in real time. In addition, PINet has high performance and low false positive rate. The low false positive rate ensures the safety performance of autonomous vehicles. Compared with other algorithms, PINet shows its superiority in poor lighting conditions. But when the lane is covered or unclear, the accuracy decreases and the speed is slow, which will be improved in subsequent studies.
References 1. Shi, L.A., Yu, S.: Hough transform lane detection method based on multiple constraints. Comput. Meas. Control 26(9) 2018. (in Chinese) 2. Fan, C., Di, S., Hou, L.: Research on lane recognition algorithm based on line model. Comput. Response Appl. Res. 29(l) (2012). (in Chinese) 3. Wang, J., Hu, J.-h., NIU, Y.-t.: Vehicle and lane detection under dynamic background. Guilin Univ. Electron. Technol. Chin. J. Sci. 31(2), 111–114 (2011). (in Chinese) 4. Li, T.: Research on Lane Detection and Tracking Algorithm Based on Illumination Invariance [D] Xi’an: Chang’an University (2017). (in Chinese) 5. Xu, Y., Shan, X., et al.: A lanc detection method combincd fuzzy control with RANSAC algorithm[C]. In: HONGKONG, the 7th International Conference on Power Electronics Systems and Applications, 2017, pp. 170–175 6. Qin, Z.Q., Wang, H.Y., Li, X.:: Ultra fast structure-aware deep lane detection[C]. In: 16th European Conference on Computer Vision, 2020, pp. 276–291 7. Tabelini, L., Berriel, R., Paixão, T.M., et al.: PolyLaneNet: lane estimation via deep polynomial regression[C]. In: 2020 25th International Conference on Pattern Recognition (ICPR), 2021, pp. 6150–6156 8. B Liu HZ Liu 2020 Lane detection algorithm based on improved Enet network Comput Sci 47 4 142 149 (in Chinese) 9. J Tian JZ Yuan HZ Liu 2020 Instance segmentation based lane line detection and adaptive fitting algorithm J Comput Appl 40 7 1932 1937 (in Chinese) 10. Chong, Z., Yingping, H., Zhiyang, G. and Jingyi, Y.: Real-time lane detection method based on semantic segmentation. Opto-Electron. Eng. 222,49(05), 26–37. (in Chinese) 11. Wang, W., Yu, R., Huang, Q., Neumann, U.: Sgpn: similarity group proposal network for 3d point cloud instance segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2569–2578 (2018) 12. HY Zhu F Yang XQ Gao 2021 A fast lane detection algorithm based on cascade Hough transform Comput. Technol. Dev. 31 1 88 93 (in Chinese) 13. J Tian SW Liu XY Zhong 2021 LSD-based adaptive lane detection and tracking for ADAS in structured road environment Soft Comput. 25 7 5709 5722 14. Chen, Z.P., Liu, Q.F., Lian, C.F.: PointLaneNet: efficient end-to-end CNNs for accurate realtime lane detection[C]. In: 2019 IEEE Intelligent Vehicles Symposium (IV), pp. 2563–2568 (2019) 15. Ji, G.Q., Zheng, Y.C.: Lane line detection system based on improved Yolo V3 algorithm[Z]. Res. Sq. (2021). https://doi.org/10.21203/rs.3.rs-961172/v1 16. Neven, D., De Brabandere, B., Georgoulis, S., et al.: Towards end-toend lane detection: an instance segmentation approach[C]. In: 2018 IEEE Intelligent Vehicles Symposium (IV), pp. 286–291 (2018)
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17. Pan, X.G., Shi, J.P., Luo, P., et al.: Spatial as deep: spatial CNN for traffic scene understanding[C]. In: Thirty-second AAAI conference on artificial intelligence, pp. 7276–7283 (2018) 18. Qiao, W., Liu, H.: Attitude estimation of traffic police based on improved stacked hourglass network. Inf. Technol. (04), 17–23+29 (2021). https://doi.org/10.13274/j.cnki.hdzj. 2021.04.004. (in Chinese) 19. Newell, A., Yang, K., Deng, J.: Stacked hourglass networks for human pose estimation. In: European Conference on Computer Vision, pp. 483–499. Springer 20. Li, W., Wang, Z., Yin, B., Peng, Q., Du, Y., Xiao, T., Yu, G., Lu, H., Wei, Y., Sun, J.: Rethinking on multi-stage networks for human pose estimation. arXiv:1901.00148 (2019) 21. Moon, G., Chang, J.Y., Lee, K.M.: Posefix: model-agnostic general human pose refinement network. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7773–7781 (2019) 22. Ko, Y., Lee, Y., Azam, S., Munir, F., Jeon, M., Pedrycz, W.: Key points estimation and point instance segmentation approach for lane detection (2020) 23. Pan, X., Shi, J., Luo, P., Wang, X., Tang, X.: Spatial as deep: spatial CNN for traffic scene understanding. In: Thirty-Second AAAI Conference on Artificial Intelligence (2018) 24. Hou, Y., Ma, Z., Liu, C., Loy, C.C.: Learning lightweight lane detection cnns by self- attention distillation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1013–1021 (2019)
Effect of Lithium Rich Manganese Based Materials Coated Carbon Nanotubes Graphene Hybrid Chuangxin Ye, Weijing Yang, Haijuan Pei, and Jingying Xie(B) State Key Lab Space Power Sources Technol, Shanghai 200245, China [email protected]
Abstract. Li-rich Layered Oxide Cathodes materials (LLOs) are attractive to researcher by reason of their high specific capacity and low cost. But LLOs has poor rate performance and cycling performance due to its poor dynamic performance and low conductivity. In order to improve the rate performance and cycling performance of LLOs, the lithium rich materials were synthesized by coprecipitation method and solid-phase method. Then coating carbon nanotube graphene hybrid on the surface of LLOs, and the alternating vertical multi-level conductive paths were realized on the surface of the materials. The average capacity at 5C high magnification was 142 mAh/g, which is better than that of the uncoated one of 117.3 mAh/g; Accordingly, the capacity ratio of high and low magnification is increased from 48.85% to 54.6%. The multi-stage conductive path constructed by coated carbon nanotube graphene hybrid accelerates the electrochemical reaction kinetics of the electrode, which is beneficial to improving the ion transmission of lithium ions and electrons. This will effectively improve the electrochemical performance of LLOs. Keywords: LLOs · Coated · Nanotubes graphene hybrid
1 Introduction Lithium rich manganese based material is composed of Li2 MnO3 and LiMO2 structures. It has the characteristics of low material cost, large specific capacity and low pollution. It is a very up-and-coming cathode material for lithium ion batteries. But at the same time, there are also some problems with LLOs. For example, its disadvantages include poor cycle performance and rate performance, obvious voltage attenuation, and poor safety performance [1], which limit the further commercial application of LLOs. The existing research found that the poor performance of LLOs in the cycle process is due to the poor structural stability of this material in the cycle process [2]. At the same time, the ion diffusion ability of the material is poor [3], and the kinetics and conductivity of the active material are low [4], so the magnification performance is also relatively poor. And the side reactions of electrode materials and electrolyte [5] make for serious capacity attenuation. At the same time, it will also reduce the reversible Li+ [6] in the electrolyte, and generate irreversible compounds on the surface of the LLOs electrode, © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1023–1028, 2023. https://doi.org/10.1007/978-981-99-1027-4_107
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which will hinder the migration of Li+ from the face of the electrode material to the inside, making the rate performance of LLOs worse. Because of the above reasons, researchers proposed to modify LLOs by means of acid treatment of precursor surface [7], morphology control [8], coating [9], doping [10], crystal surface control [11] and surface integrated structure [12]. Surface coating is an effective modification method among many modification methods. Surface coating is to cover active materials with other materials. There are usually several types of coated substances [13], such as conductive polymers, fast lithium ion conductors, oxides, fluorides and phosphates. The coating can effectively guard against the escape of oxygen in the material, inhibit the oxidation of electrolyte, cut down the decompose of transition metals, and improve the conductivity of the material, So as to maintain the structural stability of the material and improve the rate performance during the cycle [14]. The surface coating is modified by two ways to upgrade the rate capability of materials, namely, improving the ionic conductivity and electronic conductivity of materials. The use of coatings with high ionic conductivity can increase the ionic conductivity, make the structure of materials more stable under high voltage, and reduce or eliminate the influence of Li+ transfer on the structure of materials. Similar to improving the ionic conductivity of materials, materials with better electron conductivity can also be adopted as coating agents to create channels conducive to electron transport, so as to increase the electronic conductivity. In addition, the surface coating can also effectively inhibit the average discharge voltage attenuation of materials. In this study, carbon nanotube graphene hybrid was coated on the face of LLOs, and the alternating vertical multi-level conductive paths were realized on the surface of the materials, which provided theoretical basis and experimental ideas for the application of Li-rich layered oxide cathodes materials in high magnification scenes, and provides a feasible technical route for the commercial production and application of materials..
2 Experiment 2.1 Preparation of Lithium Rich Manganese Based Materials MnSO4 ·H2 O, NiSO4 ·6H2 O and CoSO4 ·7H2 O were prepared into a solution with a total metal ion concentration of 2 mol/L according to the molar ratio of Mn2+ : Ni2+ : CO2+ of 4:1:1. After reacting with 2 mol/L Na2 CO3 solution at 50 °C, pH = 8, and rotating speed of 120 r/min for 20 h, a filter cake was obtained by suction filtration. The obtained filter cake was fully purged by deionized water and bakeout at 105 °C for 5 h. After that, the filter cake was screened with a 300 target sieve to acquire a lithium rich manganese based precursor. Then the precursor and Li2 CO3 were weighed according to stoichiometric ratio, mixed evenly in a mixing tank, roasted at 850 °C for 10h in air atmosphere, wait for the sample when its temperature drops to the environment, crushed and sieved, and finally the target Li-rich Layered Oxide Cathodes materials(Li[Li0.2 Mn0.54 Ni0.13 Co0.13 ]O2 ) was obtained.
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2.2 Preparation of LLOs Coated with Carbon Nanotube Graphene Hybrid A water-soluble polymer such as polyacrylamide (PAAM) or polyvinyl pyrrolidone is soluble in delionized water. Then, evenly dispersed carbon nanotube graphene hybrid (GNH) was dispersed in the polymer crosslinked aqueous solution. After a certain period of magnetic stirring, a certain amount of the above synthesized lithium rich material was weighed into the GNH mixed solution, and continued to be uniformly stirred by magnetic stirring. Finally, the obtained solution is subjected to suction filtration (centrifugation), water washing and other steps. Finally, the obtained solid is placed in a blast oven for drying, and then placed in a muffle furnace for low-temperature heat treatment in an air atmosphere to obtain the final target coating product. By adjusting the coating amount of GNH, the heat treatment temperature and the heat treatment time, the Lirich Layered Oxide Cathodes materials coated with the best modified carbon nanotube graphene hybrid can be obtained. 2.3 Preparation of LLOs Coated with Carbon Nanotube Graphene Hybrid Weigh the active material, superconducting conductive carbon black (super P) and polyvinylidene fluoride (PVDF) in a weight ratio of 8:1:1. After grinding for a certain period of time, fully mix with an appropriate amount of N-methylpyrrolidone (NMP), stir for 12 h. After forming a uniform slurry, coat it on the aluminum foil, put it in an oven, dry it at 100 °C, and then press and cut it into a positive electrode rounds with a diam of 14mm. CR2016 button cell is packaged in the glove box filled with argon, The assembly sequence is positive shell, positive material, diaphragm, lithium sheet, negative shell, and 1.2mol/L LiPF6 /EC+EMC as the electrolyte. At 25 °C, use the battery test system to test the assembled button cell, and the voltage test range is 2.0 ~ 4.6V.
3 Results and Discussion 3.1 Effect of Carbon Nanotube Graphene Hybrid Coating on Material Structure Figure 1 is a SEM image of a surface coated carbon nanotube graphene hybrid lithium rich manganese group. It can be seen that after coating, a multi-level structure of alternating vertical carbon nanotube graphene was created on the surface of the material. In addition, there were a great quantity of voids between the particles of the material and the graphene with a sheet structure. 3.2 Effect of Carbon Nanotube Graphene Hybrid Coating on Material Structure In order to study the influence of different coating weight on the electrochemical function of Li-rich Layered Oxide Cathodes materials. The magnification property of the LLOs is tested, and the results are shown in Fig. 2. Magnification characteristic curve within the voltage range of 2.0 ~ 4.6V. With the increase of the coating amount of carbon nanotube graphene hybrid, at 5 °C high magnification, with the increase of carbon nanotube graphene, the average capacity of the LLOs increases first, and then as the coating weight increase, it will decrease. Carbon nanotube graphene-3% has the highest
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Fig. 1. SEM images of of modified by carbon nanotube graphene hybrid.
Fig. 2. Rate characteristics of modified by carbon nanotube graphene hybrid.
capacity (142 mAh/g), which is better than the capacity of the uncoated one (117.3 mAh/g); Correspondingly, when the content of carbon nanotube graphene coating is increased, the ratio of 5 °C capacity to 0.1 °C capacity of each sample also showed a trend of first increasing and then decreasing, which were 48.85% (carbon nanotube graphene hybrid—0%), 54.6% (carbon nanotube graphene hybrid—3%), 51.6% (carbon nanotube graphene hybrid—5%) and 50.3% (carbon nanotube graphene hybrid—10%). It is proved that the coating significantly improves the rate capability of Li-rich Layered Oxide Cathodes materials, and makes their capacity play better at high rate. 3.3 Effect of Carbon Nanotube Graphene Hybrid Coating on Capacity and Magnification Properties of Materials Figure 3 is a cycle performance diagram of carbon nanotube graphene hybrid coated samples with different ratios at 0.2 °C. It can be seen that after 60 cycles, the carbon nanotube graphene hybrid-3% and carbon nanotube graphene hybrid-5% groups have the highest capacity (225 mAh/g), which is higher than the capacity of the uncoated LLOs after 60 cycles (205 mAh/ g, respectively); However, the capacity of carbon nanotube graphene hybrid-10% material after 60 cycles is lower than that of the raw material, because the amount of active material is relatively reduced when the coating amount is too large.
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Fig. 3. Comparison of Cyclic Properties of Materials before and after Modification
4 Conclusions Summary and Prospect Lithium ion cathode materials restrict capacity the performance of the cell, and the performance and cycling capacity of cathode materials are an important part of the application of lithium-ion cathode cell. The advent of LLOs with high specific capacity has aroused great interest. LLOs also have the advantages of wide operating voltage range, cheaper and environmental friendliness. However, LLOs cycle performance needs to be improved and rate performance restrict the extensive use of LLOs. Therefore, this paper mainly studies the modification of LLOs. In this paper, the precursors of LLOs were synthesized by the traditional coprecipitation method, and lithium rich materials were synthesised by combining the solid-phase method with lithium sintering. Then, carbon nanotube graphene hybrid was coated on the surface of LLOs, and the change of the surface structure of the coated carbon nanotube graphene hybrid material was studied by observed the surface structure by using SEM, and the change of the capacity and cycling performance of LLOs after coating was studied by electrochemical test. The coating of carbon nanotube graphene hybrid improves the low conductivity of LLOs, improves the electrochemical reaction rate of electrodes, and improve the charge/discharge capacity of materials. This is on account of the construction of alternating vertical multi-level electron transport paths of carbon nanotube graphene on the surface of materials, and the formation of a composite three-dimensional conductive network with super P, which improves the electron transmission at the interface and the lithium ion permeate ability in cathode. Secondly, there are a lot of gaps between lithium rich manganese based material particles and graphene with sheet structure, which can accommodate electrolyte, making the permeate path of lithium ions in the LLOs shorter; In addition, the electrode polarization of the coated Li-rich manganese based material is low, which can cut down the occurrence of irreversible negative reactions at the LLOs-electrolyte interface, so that the reversibility and cycling performance of the electrochemical reaction are better. Due to the lack of cobalt resources, the cost of traditional cathode materials has increased significantly. LLOs have the potential to become the main cathode materials
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for the next generation of cell. The work in this paper improves the reversibility and cycle stability LLOs, and lays a foundation for the further application of LLOs. Acknowledgments. The work was funded by the Natural Science Foundation of China (NSFC 2021 No. 04963).
References 1. Liu, S., Liu, Z.P., Shen, X.: Surface doping to enhance structural integrity and performance of Li-rich layered oxide. Adv. Energy Mater. J. 8(31), 1802105–1802112 (2018) 2. Weibin, G., Yinggan, Z., Liang, L.: Enhancing cycling stability in Li-rich Mn-based cathode materials by solid-liquid-gas integrated interface engineering. Nano Energy J. 97, 107201– 107211 (2022) 3. Duh, J., Wang, Z., Yu, F.: Dual conductive surface engineering of Li-Rich oxides cathode for superior high-energy-density Li-Ion batteries. Nano Energy J. 59, 527–536 (2019) 4. Hongfei, Z., Chenying, Z., Yinggan, Z.: Manipulating the Local Electronic Structure in LiRich Layered Cathode Towards Superior Electrochemical Performance. Adv. Funct. Mater. J. 31(30), 2100783–2100796 (2021) 5. Wenzheng, N., Shaojiu, Y., Jixian, W.: Effect of conductive agent on electrochemical performance of lithium rich manganese based materials. Power technology. Journal 44(3), 308–311 (2020). (in chinese) 6. Guo, W., Zhang, C., Zhang, Y.: A universal strategy toward the precise regulation of initial coulombic efficiency of Li-rich Mn-based cathode materials. Adv. Mater. J. 33(38), 2103173 (2021) 7. Xiaoxia, L., Xiaoyu, H., Jingyan, C.: Improvement of electrochemical performance of lithium rich manganese based cathode materials by acid steam treatment. New chemical materials. Journal 49(03), 192–196 (2021) (in chinese) 8. Zhen, Y., Ying, L., Peihua, M.: Effect of precursor drying temperature on morphology and electrochemical properties of lithium rich manganese based cathode materials. J. Eng. Sci. J. 43(08), 1019–1023 (2021) 9. Hao, Y., Li, X., Liu, W.: Interfacial Mn vacancy for Li-Rich Mn-based oxide cathodes. ACS Appl. Mater Interfaces. Journal 14(19), 22161–22169 (2022) 10. Wei, Z., Yanxiao, C., Xiaodong, G.: Aluminum doped lithium rich manganese based cathode material Li_(1.2)Ni_(0.2)Mn_(0.6)O_2. Inorganic salt industry. Journal 53(06), 128–133 (2021). (in chinese) 11. Jianfeng, Z., Xinhua, Z., Panpan, Z.: Research progress in structure optimization and crystal plane control of lithium rich manganese based cathode materials. Mater. Guide J. 35(11), 11057–11066 (2021). (in chinese) 12. Luu, N., Lim, J.M., Castanedo, C.: Elucidating and mitigating high-voltage interfacial chemomechanical degradation of nickel-rich lithium-ion battery cathodes via conformal graphene coating. Journal 4(10), 11069–11079 (2021) 13. Zhao, L., Zhong, W., Liqing, B.: Research progress on surface modification of lithium rich manganese based cathode materials. Acta Chem. J. 77(11), 1115–1128 (2019). (in chinese) 14. Lei, C., Diandian, W., Haibin, C.: Effect of coating modification on properties of lithium rich manganese based materials. New chemical materials. Journal 49(02), 223–226 (2021). (in chinese)
State of Health Prediction of Lithium Battery Based on Extreme Learning Machine Optimized by Genetic Algorithm Changshan Bai, Kui Chen(B) , Kai Liu, Yan Yang, Guoqiang Gao, and Guangning Wu School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611731, China [email protected]
Abstract. Accurate prediction of the capacity of lithium battery is of great significance for the failure prediction and health management. At present, the prediction accuracy of machine learning cannot meet the demand, so this paper proposes a prediction model based on genetic algorithm (GA) to modify extreme learning machine (ELM). Firstly, the characteristic quantities related to degradation of battery are extracted from the cycle life test; then, the aging characteristic parameters of the battery are analyzed using the correlation coefficients; finally, a GA-ELM neural network model is established and the input weights and implicit layer bias of the extreme learning machine are optimized using the genetic algorithm. The proposed model is validated with the experimentally obtained battery data and compared with a single ELM neural network model prediction method. The results show that: the method proposed in this paper can effectively predict the state of health (SOH) with better prediction accuracy than the single ELM model. Keywords: Lithium Battery · State of Health · Genetic Algorithm · Extreme Learning Machine
1 Introduction Lithium batteries have become the mainstream choice for electric vehicles and energy storage systems because of their high energy density, low self-discharge, long service life, and lack of environmental pollution [1]. The aging of lithium batteries is a long-term gradual and irreversible process, and factors such as temperature, charge and discharge current ratio, charge/discharge depth, and charge/discharge cycle interval all have an impact on the performance of lithium batteries [2]. At present, the research and modeling analysis of battery state of health (SOH) have been achieved, and the related research includes the analysis of battery degradation mechanism and aging factors, battery health management, battery state monitoring and estimation, battery life prediction, etc. However, the research on the prediction of SOH is not yet perfect. How to accurately predict the SOH is of great importance for the management, maintenance and economic evaluation of battery [3]. The single hidden layer feedforward neural network (SLFN) has the problems of long training time and low learning efficiency, for which Guangbin Huang proposed an © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1029–1039, 2023. https://doi.org/10.1007/978-981-99-1027-4_108
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extreme learning machine (ELM) algorithm with fast learning speed and good generalization performance [4]. However, since the input weights and implicit layer thresholds are randomly assigned and cannot be adjusted during training, it has a great impact on its classification performance, and to some extent, it also leads to poor structural stability of the network [5]. To address the common problems of ELM, this paper tries to combine genetic algorithm with ELM to optimize the input weights and implicit layer bias, and compares the prediction results with those of a single ELM algorithm, and verifies the excellence of GA-ELM model in predicting lithium battery SOH through experimental data.
2 Correlation Coefficient The correlation coefficient is a quantity to study the degree of linear correlation between variables, and three common correlation coefficients by Pearson [6], Spearman [7] and Kendall [8] are presented below. 2.1 Pearson Correlation Coefficient The Pearson correlation coefficient describes a linear correlation which is calculated as follows: cov(x, y) (1) ρ(x, y) = σx σy where cov(x, y) is the covariance, σx , σy is the standard deviation. The value range is [−1, 1]. A negative number indicates a negative correlation and a positive number indicates a positive correlation. Under the premise of significance, the larger the absolute value, the stronger the correlation. If the absolute value is 0, there is no linearity and an absolute value of 1 means perfect linear dependence. 2.2 Establishment of Finite Element Model The Spearman, often also called the Spearman rank correlation coefficient, is a type of rank correlation coefficient. For two sets of samples x and y with a capacity of n, n raw data are converted into rank data and the correlation coefficient is calculated as follows: n di2 6 i=1 (1) rs = 1 − n(n2 − 1) where di is the grade difference between xi and yi , the ith sample value in samples x and y. The value range of Spearman is as follows: [−1,1].The larger the absolute value, the stronger the correlation. When rs is positive, it is considered that there is a positive rank correlation. When rs is negative, it is considered that there is negative rank correlation. In the absence of repeated data, if a variable is a strictly monotone function of another variable, the Spearman rank correlation coefficient is + 1 or −1, which is called complete Spearman rank correlation of variables.
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2.3 Kendall Correlation Coefficient Kendall is also known as the Kendall rank correlation coefficient. N similar statistical objects are ordered by a specific attribute, and other attributes are usually disordered. The ratio of the difference between same-ordered pairs and opposite-ordered pairs to the total number of pairs n*(n − 1)/2 is defined as the Kendall coefficient. It uses calculated correlation coefficients to test the statistical dependence of two random variables. The value ranges from −1 to 1. When the value is 1, it indicates that the two random variables have consistent rank correlation. When the value is −1, it means that two random variables have completely opposite rank correlation. A value of 0 indicates that the two random variables are independent of each other.
3 Build SOH Prediction Model 3.1 Extreme Learning Machine Algorithm The ELM has a relatively simple structure and is a feedforward neural network containing only a single hidden layer [9], as shown in Fig. 1.
Fig. 1. Structure of ELM.
Given N sets of training data (xi , yi ), xi = [xi1 , xi2 , . . . , xin ]T
(3)
where xi is the input value of the sample and yi is the output value of the sample. It is assumed that there are n neurons in the input layer, k neurons in the implicit layer, and the activation function of the implicit layer is g(xi ), bi is the bias of the implicit layer. ωi = [ωi1 , ωi2 , . . . , ωin ]
(4)
The output of the network is shown below, Where ωi is the weight connecting the input layer to the hidden layer and βi is the weight connecting the hidden layer to the output layer. yi =
k i=1
βi gi (ωi xj + bi ), j = 1, 2, . . . , N
(5)
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Equation (5) can also be expressed in a simplified matrix form: Hβ = Y
(6)
H is the output matrix of the hidden layer and the specific form of it is: ⎛ ⎞ g(ω1 x1 + b1 ) . . . g(ωk x1 + bk ) ⎜ ⎟ .. .. .. H =⎝ ⎠ . . . g(ω1 xn + b1 ) · · · g(ωk xn + bk
(7)
n×k
β is determined by the resolution of the generalized inverse operation of the hidden matrix. β = H +Y
(8)
where H + is the generalized Moore inverse matrix of H . 3.2 ELM Optimized by Genetic Algorithm Genetic algorithm is an efficient search algorithm based on natural selection and genetic mechanism. It simulates the law of survival of the fittest in the process of biological evolution and the random information exchange mechanism of chromosomes in the population to search for the optimal solution of a problem. The algorithm encodes the problem parameters and b as chromosomes and uses iterations for selection, cross-variance and other operations to exchange chromosomal information to continuously optimize the population and thus seek to its optimal value [10]. The steps based on ELM and genetic algorithm are as follows [11]. (1) Determine the basic structure of ELM. Set the parameters of the GA, including the number of chromosomes, the number of iterations, the coding length, the crossover probability and the mutation probability. (2) Initialize the population and encode the input weights and implicit layer bias of ELM with binary encoding. (3) To calculate the fitness of individuals, some samples from the training samples are selected as validation samples, and the correct diagnosis rate of the validation samples is used as the fitness. (4) Selection. Based on the fitness value of each chromosome, a roulette wheel method is used to select the better individual from the current population into the next generation. (5) Crossover. A crossover point is randomly selected in the individual code and a partial exchange is made at that point for two paired individual genes to produce two new individuals. (6) Mutation. Two mutation sites are randomly selected on a chromosome, and the genes at the two sites are switched to produce a new individual. (7) Repeat steps 3 to 6 until the number of generations of evolution is satisfied. When the optimal search meets the termination condition, the optimal individual is obtained. By decoding the optimal individual, the optimal parameters are obtained and used to train the ELM model. Finally, the improved ELM model based on genetic algorithm is obtained.
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3.3 The Prediction Model of SOH The data used in this paper are from the NASA Prediction Center [12], and the charge/discharge aging tests were performed on 18650 lithium batteries with a nominal capacity of 2 A·h. The dataset contains data for four batteries: B0005 (B5), B0006 (B6), B0007 (B7), and B0018 (B18). The battery was cyclically tested for charging and discharging under the same room temperature (24 °C) environment. Constant current charging at 1.5A was first performed until the voltage reached 4.2 V, then continue charging the battery at constant voltage mode until the charging current dropped below 20mA. The discharge test is performed in 2A constant current mode and the experiment is stopped when the battery degrades to the point of dropping to end of life, in other words, the voltage of B5, B6, B7 and B18 are decreased to 2.7 V, 2.5 V, 2.2 V and 2.5 V, respectively. During this process, the rated capacity degraded by 30% (from 2 A·h to 1.4 A·h). Capacity is an important characterization of SOH, and the feature quantities extracted from the factors affecting SOH of lithium batteries represent, to a certain extent, the decay trend of SOH over the whole cycle life cycle, which has a certain correlation with capacity. In order to better understand the mapping relationship between the selected characteristic quantities and capacity, three correlation coefficient including Pearson, Spearman and Kendall are used in this paper to jointly verify. Taking battery B5 as an example, Fig. 1 shows the voltage curve of its partial cycle charging stage, and Fig. 2 shows the voltage-capacity change rate curve of its charging stage smoothed by sgolay.
Fig. 2. The charging voltage curve.
The charging process of lithium battery includes two stages of constant current and constant voltage, in which the duration of constant current charging directly affects the capacity charged in the constant current charging stage and represents the polarization phenomenon of the battery. From Fig. 2, it can be seen that with the increase of charge/discharge cycles, the moment when the lithium battery charging voltage first reaches 4.2V gradually shifts to the left, i.e., the time used for constant current charging shows a gradual decrease, so the time when the charging voltage first reaches 4.2V is extracted as the characteristic quantity and recorded as F1 . In addition, it is also observed
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Fig. 3. The voltage and capacity variation rate curves of lithium battery.
that the time used for medium-voltage charging in the constant current charging stage decreases continuously with the cycle life experiment. And the difference between the selected charging stages with equal voltage drop varies between charging cycles, which to some extent indicates the decline of lithium battery charging capacity and the main decline interval. In order to include all cycle data in the charging time analysis, this paper extracts the characteristic quantities starting from 3.8V, where the 3.8 ~ 4.2V stage is selected as F2 , and the 4.0 ~ 4.2V stage is selected as F3 . Capacity incremental analysis (ICA) is an important method to analyze the material characteristics of lithium batteries and the mechanism of decline, and its core is the battery capacity incremental curve, and the IC curve can well infer the characteristics of the internal chemical changes of lithium batteries with the characteristics and laws of SOH [13]. However, the original IC curve is not smooth due to sampling error or noise interference, which hinders the discovery of graphical laws and the extraction of characteristic quantities. To solve this problem, the sgolay function is used to smooth the original IC curve in this paper. By comparing the IC curves of different cycles, the peak gradually decreases and moves toward the high voltage as the number of cycles keeps increasing. This change implies that the peak IC value and the corresponding voltage can effectively characterize the decline of the battery, so the peak IC and the corresponding voltage are selected as the characteristic quantities, which are noted as F5 and F4 , respectively. In summary, five characteristic quantities are extracted from the battery charging stage to predict the SOH of the battery, which are the time F1 when the charging voltage first reaches 4.2 V, the charging time F2 (3.8 ~ 4.2 V), the charging time F3 (4.0 ~ 4.2 V), the peak of the IC curve F5 and the corresponding voltage F4 , and then calculate their correlation. The data analysis of the three correlation coefficients found that the five selected characteristic quantities have excellent correlation compared with the capacity, among which the Spearman coefficient has the best correlation, so the Spearman coefficients between SOH of each cell and the selected characteristic quantities were obtained as shown in Table 1. It can be seen that the eigenvalues show different trends as the number
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of cycles increases, with F4 showing a strong negative correlation with SOH, while F1 , F2 , F3 and F5 show a strong positive correlation. The correlation between these characteristic quantities and SOH reflects to some extent that the decreasing of constantcurrent charging time, charging time with equal voltage drop, IC peak, and the increasing of the voltage corresponding to IC peak will lead to the decreasing of the lifetime of lithium battery with the increasing of the cycle times. Table 1. Correlation coefficient analysis between characteristic quantity and SOH. Battery
Characteristic quantities and correlation coefficients F1
F2
F3
F4
F5
B5
0.9828
0.9951
0.9902
−0.9363
0.9804
B6
0.9951
0.9485
0.9877
−0.9779
0.9583
B7
0.9951
0.9926
0.9804
−0.8775
0.9804
B18
0.9868
0.9868
0.9956
−0.8154
0.9868
Figure 3 shows the prediction model of SOH based on the GA-ELM algorithm proposed in this paper [14].
Fig. 4. The prediction model of SOH based on GA-ELM.
First of all, the parameters of the prediction model are determined. From Table 1, it can be seen that the five selected feature quantities have very high correlation that used as input parameters to train the model, and the capacity is used as the output parameter. Then the GA-ELM structure is established, and the parameters of the topology need to be set when using the genetic algorithm to optimize the extreme learning machine, as shown in Table 2. 3.4 Criteria for Assessment In order to evaluate the prediction effect of the model, this paper select the mean absolute error and mean square error. Error(Prediction error of capacity):
(9) Error = yˆ − y
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Parameter
The numerical size
Population size
20
Maximum genetic algebra
100
Number of bits in a variable
10
Probability of crossing
0.7
Probability of mutation
0.01
Generation gap
0.95
MAE(Mean absolute error):
1
yˆ − y
n
(10)
1 (ˆy − y)2 n
(10)
n
MAE =
i=1
MSE(Mean square error): n
MSE =
i=1
4 Experiment and Analysis In this experiment, a set of data was extracted from NASA battery data every 10 charge/discharge cycles as test samples, in which B5, B6 and B7 batteries included 168 charge/discharge cycles and a total of 17 sets were selected, and B18 included 132 charge/discharge cycles and a total of 14 sets were selected (Fig. 8). The first 50% of the samples are selected for training and the remaining samples were used for prediction. The error evolution curves and prediction curves of the four batteries were obtained as shown in Figs. 4, 5, 6 and 7, and the prediction error pairs are shown in Table 3. As can be seen in Figs. 4, 5, 6 and 7, the error evolves to the minimum value before setting the end condition, which satisfies the experimental requirements. Then the optimized input weights and implied layer thresholds are brought to the extreme learning machine model for predicting the SOH of the test samples. In addition, in order to verify that the prediction model based on the GA-ELM has better prediction accuracy, a single ELM model is also used as a comparison. From the comparison table of prediction curves and prediction errors, it can be seen that both the ELM model and the GA-ELM model have relatively good learning effects in the training phase. However, in the prediction stage, the prediction error of the ELM model for battery SOH tends to increase gradually with the increase of prediction generations except for battery B6, and the prediction effect is poor, while the prediction of the GA-ELM model for SOH of the four batteries always maintains very small errors. And through data comparison, the two error criteria of the GA-ELM model are better than the single ELM model, so the GA-ELM model proposed in this paper has good prediction ability and can predict the SOH of lithium batteries more accurately.
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Fig. 5. The error evolution and SOH prediction of B5.
Fig. 6. The error evolution and SOH prediction of B6.
5 Conclusion In this paper, a SOH prediction model for lithium batteries based on GA-ELM algorithm is proposed by combining genetic algorithm and limit learning machine. Compared with the traditional limit learning machine model, GA-ELM optimizes the input weights and hidden layer bias to improve the prediction accuracy. In the experimental part, the performance of the proposed model is verified using the original battery degradation data from NASA. The experimental results show that the GA-ELM-based prediction model exhibits good prediction performance for different battery data, and has a significant advantage in prediction accuracy compared with a single ELM.
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Fig. 7. The error evolution and SOH prediction of B7.
Fig. 8. The error evolution and SOH prediction of B18.
Table 3. The Comparison of SOH prediction errors between different batteries. Battery
ELM
GA-ELM
MAE
MSE
MAE
MSE
B5
0.38374
0.008662
0.011572
7.8778 × 10−6
B6
0.12653
0.00094182
0.056114
1.8522 × 10−4
B7
0.19552
0.0022487
0.023572
3.2684 × 10−5
B18
0.098337
0.00069073
0.011436
9.3415 × 10−6
During the experiments, when optimizing the input weights and implied layer thresholds using the GA-ELM model, the optimal solution was found only after passing a larger number of genetic generations. The prediction accuracy of this model for B5, B7 and
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B18 was high, but the prediction effect for B6 was slightly insufficient. Therefore, how to adjust the GA setting parameters to achieve higher prediction accuracy is the focus of the next research. Acknowledgments. This work was funded by State Grid Corporation of China Headquarters Management Technology Project (SGTYHT/19-JS-215).
References 1. Zhou, J., Hua, Y.H., Liu, K., Lan, H., Fan, C.: Research on a high-precision modeling scheme for lithium-ion battery. Proc. CSEE 39(21), 6394–6403 (2019). (in Chinese) 2. Ji, C.W., Pan, S., Wang, S.F., Wang, B., Jiejie, S., Pengfei, Q.: Experimental study on effect factors of aging rate for power lithium-ion batteries. J. Beijing Univ. Technol. 46(11), 1272– 1282 (2020). (in Chinese) 3. Yao, F., Tian, J.Y., Huang, K.: Review of state of health calculation method for lithium battery. Chin. J. Power Sources 42(01), 135–138 (2018). (in Chinese) 4. Huang, G.B., Zhu, Q.Y., Siew, C.K.: Extreme learning machine: theory and applications. Neurocomputing 70(1–3), 489–501 (2006) 5. Li, F.T., Yao, Q.: Wind power capacity based on matlab and genetic algorithm. Trans. China Electrotech. Soc. 24(03), 178–182 (2009). (in Chinese) 6. Xiaofeng, L., et al.: A probabilistic explanation of Pearson’s correlation. Teach. Stat. 41(3), 115–117 (2019) 7. Shaikh, M., et al.: Wiener-Hammerstein system identification: a fast approach through spearman correlation. IEEE Trans. Instrum. Meas. 68(5), 1628–1636 (2019) 8. Liebscher: Eckhard.Kendall regression coefficient. In: Computational Statistics & Data Analysis, p. 157 (2021) 9. Suresh, S., et al.: Performance enhancement of extreme learning machine for multi-category sparse data classification problems. Eng. Appl. Artif. Intell. 23(7), 1149–1157 (2010) 10. Minhas, R., Mohammed, A.A., Wu, Q.J.: A fast recognition framework based on extreme learning machine using hybrid object information. Neurocomputing, 73(10–12), 1831–1839 (2010) 11. Cui, J., Tang, J.X., Zhang, Z.R., et al.: Fast fault classification method research of aircraft generator rotating rectifier based on extreme learning machine. Proc. CSEE 38(8), 2458– 2466+2555 (2018). (in Chinese) 12. Goebel, K., Saha, B., Saxena, A., et al.: Prognostics in battery health management. IEEE Instrum. Meas. Mag. 11(4), 33–40 (2008) 13. Chen, Z., Gu, Q.F., Shen, S.Q., et al.: State of health prediction for lithium-ion batteries based on health feature extraction and PSO-RBF neural network. J. Kunming Univ. Sci. Technol. 45(6), 92–103 (2020). (in Chinese) 14. Shi, Y., Hong, Y., Ding, E., Shi, M., Ou, Y.: The state of health estimation of lithium-ion battery based on improved extreme learning machine. Chin. J. Electron Devices 43(03), 579–584 (2020). (in Chinese)
Suppression Technology of Thrust Fluctuation for Long-Stroke Segmented Linear Motor Mingyi Wang, Kai Kang(B) , Chengming Zhang, and Liyi Li Harbin Institute of Technology, Harbin 150001, China {wangmingyi,cmzhang,liliyi}@hit.edu.cn, [email protected] Abstract. For long-distance linear motion fields, such as rail transit, electromagnetic ejection, material transmission and automatic industrial manufacturing line, PMLSM is irreplaceable due to the superiority of direct drive. In this paper, in order to suppress the thrust fluctuation of discontinuous segmented linear motor (DSPMLSM), the thrust fluctuation model of DSPMLSM is obtained. Then, an experimental platform is built to verify the theory analysis, the thrust fluctuation data is collected at low speed. In order to analyze the thrust fluctuation appropriately, the regional fast Fourier transform (FFT) is proposed which can effectively reduce the harmonic number of thrust fluctuations. Through Fourier analysis, the harmonic characteristics of the thrust fluctuation is achieved and the results are in good agreement with thrust fluctuation model. Finally, the positioning error of DSPMLSM is effectively reduced by adopting the thrust fluctuation suppression method proposed in this paper, which is of great significance to the further industrial application of DSPMLSM. Keywords: DSPMLSM · Driver and control technology · Thrust fluctuation analysis
1 Introduction In the field of long-stroke linear motion, segmented permanent magnet linear synchronous motor (SPMLSM) has many advantages, such as higher efficiency and higher thrust density, so it has been gradually studied and applied, such as TR series maglev trains in Germany and high-speed maglev trains in China, in which the structure with long primary stators and short secondary magnet is adopted, the primary segments laid along the track and the secondary magnet installed on the vehicle [1]. With the application of long-stroke SPMLSM, the structural design [2–4] and the research of drive and control technology are essential. The research on drive control technology of SPMLSM mainly includes driver and control strategy of segmented primary [5–7], multi-stage primary power supply strategy and winding switching research [8, 9], long-stroke position detection technology research [10], multi-stage primary drive efficiency optimization design and system reliability design [11]. In this paper, the thrust fluctuation characteristics of DSPMLSM is analyzed firstly, the regional-dependent feature is revealed. In order to reduce the influence of thrust fluctuation on position control accuracy, the thrust fluctuation data is collected, and feed-forward control is adopted to compensate the thrust fluctuation. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1040–1049, 2023. https://doi.org/10.1007/978-981-99-1027-4_109
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2 The Thrust Fluctuation Characteristics of DSMPMLSM Detent force and ripple force are main components of thrust fluctuation, the detent force consist of cogging force and end force. Compared with conventional PMLSM, the detent force of DSPMLSM will vary with the movement of the mover. As shown in Fig. 1, the variation of detent force can be divided into two conditions during the movement of mover. The first condition, as shown in Fig. 1a, is that the mover is coupled with a single primary stator in which the detent force is mainly the cogging force and the left and right end forces of the segmented primary. The second condition, as shown in Fig. 1b, the detent force includes the end forces and cogging force of the two primary stators, the left and right end forces of the mover. It can be seen that the end forces of the mover are different when the mover locates on two adjacent primary stators (between-segment) or locates on one primary stator (within-segment). Next, the positioning forces in the two cases in Fig. 1 are analyzed in detail.
Fig. 1. Detent force variation of DSPMLSM. (a) the mover locates on one primary stator. (b) the mover locates on two adjacent primary stators.
2.1 Cogging Force Analysis Based on the principle of minimum reluctance, the cogging force of a single tooth should have a periodicity about pole pitch, which can be expressed as the sum of a series sinusoidal functions, as shown in (1), where fi is the amplitude of the ith harmonic, x is the displacement of the mover, x0 is the initial phase and τ is the pole pitch. Fi =
∞ i=1
2π i(x + x0 ) fi sin τ
(1)
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Then the cogging force of a Ns slot 2p pole DSPMLSM can be expressed as (2), where τs is the slot pitch. Fcog =
Ns ∞
fi sin
k=1 i=1
2π i(x + τs (k − 1)) τ
(2)
Using trigonometric function formula to simplify (2), and obtain the total cogging force as shown in (3). ∞ sin(2pπ i) 2π xi 2pπ i Fcog = − sin( fi ) (3) τ Ns sin( 2pπ i ) i=1
Ns
It can be seen from (3) that the harmonic and amplitude of the total cogging force are determined by the pole pair p and the number of slots Ns . 2.2 End Force Analysis For DSPMLSM, the situation shown in Fig. 1a is equivalent to the situation of short primary and long secondary. The expressions of the left and right end forces FR (x) and FL (x) are shown in (4), where γn is the initial phase angle of each harmonic, and χ is the phase difference between the left and right end forces determined by the primary length. Its expression is shown in (5), where Ls is the primary length. ⎧ ∞ ⎪ ⎪ fei sin( 2iπ ⎨ FR (x) = f0 + τ x + γn ) i=1 (4) ∞ ⎪ ⎪ fi sin( 2iπ ⎩ FL (x) = −f0 + τ x + γn +χ ) i=1
χ =2π
mod (Ls , τ ) τ
(5)
The total end force of the mover obtained by adding the left and right end forces is shown in (6). It can be seen that the harmonic amplitude of the end force is related to the primary size, pole pitch and other motor parameters. Fend =
∞ i=1
2iπ χ χ x + γi + ) 2fei cos( )sin( 2 τ 2
(6)
2.3 Detent Force Analysis for Between-Segment When the mover moves to the between-segment, the harmonic components of the detent force are complex, mainly including the left and right end forces caused by the open slot iron core of primary windings. At the same time, because the mover overlaps the two segments of primary windings, it also includes the left and right end forces caused by the open iron core of the mover, this phenomenon can be defined as “double end effect”.
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To analyze the thrust fluctuation about double-ended effect, the superposition principle can be used. The end force produced by two adjacent primaries is same as (4), then for the end force produced by open iron core of mover, a virtual primary winding can be assumed in the two-adjacent primary region to avoid the end force of the primary stators, and thus can be regarded as a long primary and short secondary PMLSM. For this condition, the fundamental period of the detent force is mainly one tooth pitch, the expression of detent force can be obtained as shown in (7), where fci is the amplitude of each harmonic, γci is the initial phase of each harmonic. Fcog =
∞ i=0
2π ix fci sin + γci τs
(7)
By using the superposition principle, the detent force of between-segment can be the sum of (3), (4) and (7). Then the analysis of detent force in two cases is completed, and the detent force expression is achieved in (8). It can be seen that one pole pitch is the fundamental frequency for detent force of within-segment, while for between-segment, the detent force includes two fundamental frequency which are one tooth pitch and pole pitch. ⎧∞
χ 2iπ i) i ⎪ χ 2π xi ⎪ + 2f − 2pπ cos x + γ + fi sin(2pπ sin ⎨ ei i 2pπ i sin τ N 2 τ 2 s sin Ns within − segment Fd = i=1
∞ ⎪ χ 2π ix ⎪ fci sin τs + γci + 2fei cos χ2 sin 2iπ ⎩ τ x + γi + 2 between − segment i=1
(8)
3 Experimental Evaluation 3.1 Experimental Setup The structure of DSPMLSM consists of four primary stators and one mover, as shown in Fig. 2. Four distributed grating reading heads of absolute linear encoders are installed in the whole motion range, and the movers are supported by guide rails. The interval distance of each primary stators is 420 mm, and the pole slot ratio is 8 poles and 6 slots. The primary stators adopt Akribis linear motor module (AKM100-B2).
Fig. 2. The picture of experimental DSPMLSM
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The drive and control system of DSPMLSM includes two driver modules, two sampling modules and a microprocessor unit. The experimental platform contains four primary stages, but in the view of experimental research, only two primary stages are needed to analyze the thrust fluctuation characteristics for between-segment and withinsegment, at the same time, the proposed suppression method of thrust fluctuation can be verified. The drive system is divided into two parts: the control board and the driver board. The control board composed of DSP and FPGA. The DSP adopts the fourth-generation high-performance dual-core chip TMS320F28379D, and the FPGA adopts the Spartan-6 series of Xilinx. The main frequency of TMS320F28379D can reach 200 MHz. Dual-core synchronous operation, with very strong real-time signal processing capability, is mainly responsible for trajectory planning, position loop control operation, current loop control operation, vector control calculation, current sampling, filtering and communication with CAN host computer, etc. In the experiment, the current loop frequency is 10 kHz, and the position loop frequency is 2 kHz. The control board is shown in Fig. 3.
Fig. 3. The control board of DSMPSM
The FPGA is mainly responsible for position detection, communicating with four Heidenhain grating reading heads, and calculation the absolute position of the mover in the whole motion range. The communication between DSP and FPGA adopts EMIF interface. The designed power board includes two sets of three-phase voltage source inverters connected in parallel with DC buses, corresponding driving circuits, phase current sampling circuits and protection circuits, etc. As shown in Fig. 4, the driver board mainly includes the IGBT IPM and current sampling modules of three-phase two-level inverters. The specific names of relevant parts are given in Fig. 4.
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Fig. 4. The driver board of DSPMLSM
3.2 Experimental Results The control strategy adopts position-current double closed-loop controllers. Select the parameters of motion trajectory as follows: speed is 10 mm/s, acceleration is 200 mm/s2 , and a motion range is 420 mm to 840 mm. The CAN communication is used to collect data, and the collection frequency is 5 kHz. The detent force data of between-segment (region two) and within-segment (region one) with the position can be obtained, as shown in Fig. 5.
Fig. 5. The acquired thrust fluctuation waveform
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According the theory analysis of detent force in Sect. 2, the FFT is carried out on the collected thrust fluctuation in single region, and the obtained harmonic components are shown in Figs. 6 and 7, where Fig. 6 is the harmonic component within-segment, Fig. 7 is the harmonic component between-segment. From the Figs. 6 and 7, when the mover state is within-segment, the detent force takes the pole pitch as the fundamental period, while when the mover state is betweensegment, the detent force takes the tooth pitch and the pole pitch as the fundamental period. The experimental results are consistent with theoretical analysis.
Fig. 6. The harmonic components of thrust fluctuation (within-segment)
Fig. 7. The harmonic components of thrust fluctuation (between-segment)
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3.3 Thrust Fluctuation Suppression Look-up table compensation is a simple feed-forward compensation method. In this paper, the thrust fluctuation data is collected and stored in FLASH. The thrust fluctuation compensation value is read from FLASH every 0.1 mm, and add it as feed-forward component to current feed-forward compensation. The control diagram of DSMPMLSM system is shown in Fig. 8. Three experimental groups are set to verify the compensation validity in different speed conditions, set the speed of the S trajectory as v1 = 20 mm/s, v2 = 200 mm/s, v3 = 400 mm/s, the corresponding acceleration a1 = 500 mm/s2 , a2 = 4000 mm/s2 , a3 = 5000 mm/s2 , and the motion range is 420 mm to 840 mm. The position control error obtained is shown in Fig. 9.
Fig. 8. The control diagram of DSPMLSM system
From the position error waveform in Fig. 9, it is known that the feed-forward compensation is useful for improving the position control accuracy at low speed and high speed condition. But we can see that the position error increase when the speed increase. It can be explained that,at high speed, the friction force will increase, while the thrust fluctuation is acquired at low speed, so the thrust fluctuation compensation error based on look-up table will further increase at high speed.
4 Conclusion In this paper, the harmonic characteristics of detent force for long-stroke DSPMLSM are studied, and the thrust fluctuation difference characteristics of between-segment and within-segments are pointed out. Then, the experimental platform of DSPMLSM is built, the thrust fluctuation data of DSPMLSM is collected by the position controller, and the theoretical analysis of the harmonic characteristics of thrust fluctuation between segments and within segments is verified by FFT analysis. Finally, the thrust fluctuation of DSPMLSM is compensated through feed-forward control. The experimental results show that the feed-forward compensation can effectively restrain the influence of thrust fluctuation at full range speed.
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Fig. 9. Position error waveform without and with feed-forward compensation
Acknowledgments. This research was partially funded by National Natural Science Foundation of China (Grant No. 52077041) and the Key Laboratory of Special Machine and High Voltage Apparatus (Shenyang University of Technology) , ministry of Education (KFKT202108).
References 1. Zigang, D., Zongxin, L., Haitao, L., Weihua, Z.: Development status and prospect of Maglev train. J. Southwest Jiaotong Univ. 57(03), 455–474 (2022). (in Chinese) 2. Kim, Y., Dohmeki, H.: Cogging force verification by deforming the shape of the outlet edge at the armature of a stationary discontinuous armature PM-LSM. IEEE Trans. Magn. 43(6), 2540–2542 (2007) 3. Kim, Y., Hwang, S., Jeong, Y.: Cogging force reduction of a stationary discontinuous armature PM-LSM by magnet segmentation. IEEE Trans. Magn. 45(6), 2750–2753 (2009) 4. Ma, M., Li, L., Zhang, J., Yu, J., Zhang, H.: Investigation of cross-coupling inductances for long-stator PM linear motor arranged in multiple segments. IEEE Trans. Mag. 51(11), 1–4 (2015) 5. Li, L., Zhu, H., Chan, C.C.: Investigation of the inter-stator current control for long primary winding segmented PMLSM used in electromagnetic launch system. In: 17th International Symposium on Electromagnetic Launch Technology, pp. 1–6. La Jolla, CA, USA (2014)
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6. Suzuki, K., Kim, Y., Dohmeki, H.: Driving method of permanent-magnet linear synchronous motor with the stationary discontinuous armature for long-distance transportation system. IEEE Trans. Ind. Electron. 59(5), 2227–2235 (2012) 7. Wang, M.Y., Kang, K., Zhang, C.M., Li, L.Y.: A driver and control method for primary stator discontinuous segmented-PMLSM. Symmetry-Basel 13(11), 1–13 (2021) 8. Zhang, M., Ma, W.M., Xu, X., Zhang, Y., Wang, Y.: A block feeding strategy for linear motor considering switching at current-crossing point. J. Nav. Univ. Eng. 31(4) (2019) (in Chinese) 9. Liu, J., Shi, L., Guo, K., et al.: A low current fluctuation switching strategy for long primary linear motors. In: 2021 13th International Symposium on Linear Drives for Industry Applications (LDIA), pp. 1–4. Wuhan, China (2021) 10. Leidhold, R., Mutschler, P.: Speed sensorless control of a long-stator linear synchronous motor arranged in multiple segments. IEEE Trans. Industr. Electron. 54(6), 3246–3254 (2007) 11. Perreault, B.M.: Optimizing operation of segmented stator linear synchronous motors. Proc. IEEE 97(11), 1777–1785 (2009)
A Uniformity Sorting Strategy for Lithium-Ion Batteries Based on Impedance Spectroscopy Miao Bai, Chao Lyu(B) , and Tong Liu School of Electrical Engineering and Automation, Harbin Institute of Technology, Heilongjiang, China [email protected]
Abstract. In the context of the energy revolution, the research and application of energy storage technology have been paid more and more attention. As one of the main energy storage devices, lithium-ion batteries are usually put into use in the form of battery packs in practice. Due to the inconsistency between battery cells, the battery pack cannot play the best performance. Moreover, there is a lack of sorting means in the recycling of battery cells. To solve this problem, a battery uniformity sorting method based on electrochemical impedance spectroscopy is presented. Seventy commercial batteries of the same type were sorted and grouped by this strategy. The capacity decay of the battery pack before and after sorting and the dispersion degree of the battery voltage curve were tested. It is proved that this method can achieve fast and effective sorting of batteries and has practical application prospects. Keywords: Lithium-ion battery · Uniformity sorting · Impedance spectrum
1 Introduction When lithium-ion batteries are used in electric vehicles and energy storage power stations, they need to form battery packs in series and parallel to meet the requirements of the system for high voltage and high current. There will be inconsistencies in the manufacturing process and when the battery is put into use [1]. These inconsistencies will lead to differences in the performance of the battery, which will affect the performance of the battery pack and accelerate the aging of the battery pack. Therefore, when building the battery pack, it is necessary to conduct uniformity sorting on the battery cells first. At present, battery sorting is mainly based on the voltage and current data of deep charge and discharge [2–4]. Xie Leiqiong and others of Tsinghua University found that the voltage difference of the battery at the end of discharge was large by charging and discharging the series battery pack composed of 80 cells, and proposed a battery sorting method using the voltage at the end of discharge as the battery sorting index [5]. Li Honglei of Dalian University of technology extracted multiple features on the battery capacity increment curve, analyzed the correlation between these features and capacity degradation, and finally proposed a lithium-ion battery sorting method based on the capacity increment curve [6]. Zhou Yafu of Dalian University of technology © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1050–1058, 2023. https://doi.org/10.1007/978-981-99-1027-4_110
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developed a method to analyze the consistency of batteries based on ohmic resistance [7]. The existing methods have the disadvantages of unreliable sorting results, long time consumption and capacity loss. Battery impedance spectrum is a collection of impedance of batteries under different frequency excitation. Because it can describe the different electrochemical processes within batteries, it is considered as a powerful tool for comprehensive analysis of the health and safety of batteries [8]. However, the application research of this technology in battery uniformity sorting is relatively few. A uniformity sorting strategy for lithium-ion batteries based on impedance spectroscopy is proposed. This strategy extracts the parameters related to the aging degree of the battery by measuring the impedance spectrum of the battery and building an equivalent circuit model, and clusters them based on these parameters to achieve uniformity sorting. The experimental results show that this strategy has practical application prospects.
2 Impedance Spectrum Measurement of Lithium-Ion Battery Firstly, an experimental device which can realize the rapid measurement of impedance spectrum is developed. The principle of the device is to inject multiple sinusoidal overlapped current excitation signals into the battery and collect the battery voltage response. The frequency components of the excitation signal and response signal are separated by Fast Fourier Transform (FFT), and the impedance spectrum of the battery in this frequency range is obtained by calculating the excitation signal and response signal of each frequency. The device is mainly composed of a signal acquisition card, a VI conversion circuit and a computer. In the process of measurement, the voltage signal sent by the card is converted into a current excitation signal through the VI conversion circuit and amplified. The frequency of the excitation signal designed in this research is 0.1 ~ 1000 Hz. The frequency components of the overlapped signal are shown in Table 1. Compared with using high time-cost deep charging and discharging method to obtain battery characteristics, this method only takes 52s. In order to verify the accuracy of the measurement method, the measurement results of this method are also compared with those of the electrochemical workstation (see Fig. 1). It can be seen that the measurement results are basically consistent. Table 1. The harmonic frequency contained in the excitation signal. Frequency band (Hz)
Frequency points (Hz)
0.1 ~ 1
0.1, 0.14, 0.18, 0.24, 0.32, 0.42, 0.56, 0.74
1 ~ 10
1, 1.4, 1.8, 2.4, 3.2, 4.2, 5.6, 7.4
10 ~ 100
10, 14, 18, 24, 32, 42, 56, 74
100 ~ 1000
100, 140, 180, 240, 320, 420, 560, 740, 1000
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In order to study the correlation between aging degree and battery impedance spectrum, the cyclic aging experiment of battery cells was designed. UR14500AC ternary lithium battery is selected as the test object. The battery was cyclically charged and discharged at 1C current rate, and the impedance spectrum were measured at every 30 cycles. After 7 times measurements, the impedance spectrum of the battery changes (see Fig. 2). It can be seen that with the battery aging, the shape of the Nyquist plot of the impedance spectrum changes significantly, which proves that there is a strong correlation between the impedance and the state of health.
Fig. 1. Comparison of measurement results.
0.02 0.018
-Zim(Ω )
0.016 0.014
Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7
0.012 0.01 0.008 0.006 0.004 0.002 0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
Zre(Ω )
Fig. 2. Impedance spectra of batteries with different aging degrees
3 Feature Extraction and Analysis of Lithium-Ion Battery Sorting After measuring the impedance spectrum of the battery, the equivalent circuit model of the battery is built to fit the impedance spectrum [9]. Then, the model parameters are extracted to select the feature quantity for filtering. The third-order fractional order equivalent circuit model shown in Fig. 3 is selected, which can describe the impedance characteristics of lithium-ion batteries at various aging degree well.
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In order to identify the model parameters quickly and accurately, the identification method is divided into two steps. Firstly, combined with the impedance spectrum morphology, the initial value of the fractional model is obtained by using the geometric relationship. Then, based on the initial value identification results, the final fractional order model parameters of the battery are obtained by using the nonlinear least square method. The theoretical impedance spectrum of fractional order model used in this paper is shown in Fig. 4. Charge transport
SEI Ohmic resistance
Inductance
Warburg
CPEdl
CPESEI
CPEW
L
Rohm
RSEI
Rct
Fig. 3. Fractional order equivalent circuit model.
For the impedance spectrum at a certain aging stage, the model fitting results after initial value identification and nonlinear least square optimization are shown in Fig. 5. Formula 1 is used to describe the error, the error between the calculated fitting result and the actual impedance spectrum is only 0.4601%. The results show that the model and parameter identification strategy used can effectively describe the characteristics of battery impedance. N ZRe (ωi |P ) − ZRe (ωi |P 0 ) 2 1 ZIm (ωi |P ) − ZIm (ωi |P 0 ) 2 + σi = (1) N ZRe (ωi |P 0 ) ZIm (ωi |P 0 ) i=1
)
ω→0
− v1
1/ω m2 = ( Rct Qdl )
− v2
k= tan
1/ω m1 = ( RSEIQSEI )
( v3 π
/2
-ZIm
v3π 2
o
Rohm+RSEI
ω→∞ Rohm
ZRe
P1 P2
Fig. 4. Theoretical impedance spectrum of model.
During the research, we found that for UR14500AC battery, when the aging degree is low, it is difficult to separate Rohm and Rsei because the solid electrolyte interface (SEI) impedance is small. Therefore, when analyzing characteristic parameters, Rohm + Rsei is considered as a united characteristic. The model parameters of lithium-ion battery in different aging degree are identified, and the changes of various parameters with the aging of the battery are obtained. On this basis, Spearman’s correlation coefficient was used to measure the correlation between parameters and battery SOH. The results are shown in Table 2.
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-Zim(Ω)
0.02
0.015
0.01
0.005
Measured data Fitting data
0 0.08
0.1
0.12
0.14
0.16
Zre(Ω)
Fig. 5. Measured data and model fitting data.
After evaluating the correlation coefficient between model parameters and battery SOH, it is also needed to examine the sensitivity between these parameters and impedance spectrum. The specific method is to expand each parameter to 1.1 times of the original. When different parameters are changed, the relative error between the model impedance and that before the change is calculated. The greater the error is, the higher the sensitivity of the parameter is. The sensitivity of each model parameter is shown in Table 2. It is considered that high sensitive parameter if the relative error of impedance spectrum of more than 4.5% before and after the change. The influence of two high sensitivity parameters on impedance spectrum morphology before and after change is shown in Fig. 6. After analysis, Rohm + RSEI , Rct , solid electrolyte interface CPE index v1 and load transfer structure CPE index v2 were finally selected as sorting health characteristic.
4 Classification Method and Effect Verification K-medoids clustering algorithm is used to realize battery uniformity sorting. Because the dimensions of each parameter are different, normalization is carried out first to eliminate the influence of dimensions on the final result. K-medoids clustering algorithm takes the Euclidean distance from each point to the cluster center as the classification basis. Sum of square error (SSE) is defined by Euclidean distance to judge the clustering effect, as shown in Formula 2: SSE =
n i=1
c k=1
xi − vk =
c i=1
n i=1
dik
2
(2)
where vk represents the kth cluster center, and d ik is the Euclidean distance between battery xi and cluster center vk .
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Table 2. Correlation coefficient and sensitivity of model parameters. Parameter
Correlation coefficient
Relative error (%)
Sensitivity
Rct
−1
11.1026
High
Rohm + RSEI QSEI
−0.8571
7.7403
High
−0.9643
0.8138
Low
Qdl
0.75
4.1057
Low
Qw
−0.6071
2.2857
Low
0.9643
11.9783
High
v2
0.8929
14.4887
High
v3
−0.8929
1.6830
Low
L
−0.5357
1.2828
Low
v1
9
-3 10
8 Initial parameter Changed parameter
8
7 6.5
-Zim(Ω )
7
-Zim(Ω )
10-3
7.5
6 5
6 5.5 5 4.5 Initial parameter
4
4
Changed parameter
3.5
3 0.07 0.075
0.08
0.085
0.09 0.095
0.1
0.105
3
0.07 0.075
0.08 0.085 0.09 0.095
0.1 0.105
Zre(Ω )
Zre(Ω )
(a)Rct
(b) Rohm+RSEI
0.11
Fig. 6. Effect of two high sensitivity parameters on impedance spectrum.
The number of cluster centers has a great influence on the clustering effect. The number of cluster centers has been adjusted several times during the research process. SSE changes with the number of cluster centers as shown in Fig. 7. It can be seen that when the number of cluster centers is more than 6, SSE changes little with the number of cluster centers, so 6 cluster centers are selected. After grouping 70 batteries, three four-series battery groups were set up for aging experiment. Group A consists of randomly selected batteries. Group B consists of batteries filtered by impedance spectroscopy and Group C consists of batteries filtered by traditional sorting methods. Seven parameters, such as battery capacity, discharge curve area, constant current constant voltage capacity ratio, platform efficiency, median voltage, ICA curve phase transition point, DC internal resistance, are selected as features in traditional sorting methods [10]. The cell voltage of each group is monitored during cycling. If the cell voltage is greater than 4.25 V or less than 2.95 V, the battery pack jumps out of the current step and proceeds to the next step. The capacity decay of the three groups of batteries are shown in Fig. 8. It can be seen that the capacity decay of group A is significantly faster than that of group B and group C. The sorting scheme is important for prolonging the life of the battery pack.
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The charging and discharging voltage curves of batteries, representing the uniformity of cells within the group, are also studied. 8 7
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As can be seen from Fig. 9, when group A is being charged and discharged, battery 26 has the fastest rate of charging and discharging, which also results in overcharging and discharging. This provides an explanation for the fast decay of the battery life of group A. Charging and discharging curves of individual units of group B batteries are shown in Fig. 10. It is easy to see that the charging and discharging rates of the cells are equal, and there is no obvious overcharging and over discharging cell, which proves that the sorting strategy is effective. Charging and discharging curves of individual cells of group C batteries are shown in Fig. 11. As can be seen from the diagram, the charging and discharging rates of battery 19 and battery 5 are significantly faster than those of other batteries after sorting by traditional sorting methods.
5 Conclusions A battery uniformity sorting strategy based on battery impedance spectrum is proposed, including rapid measurement, parameter identification, sorting feature selection, sorting
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clustering and so on. The effectiveness of the proposed method is verified by experiments on 70 UR14500AC batteries. The results show that compared with the traditional sorting method, this method has the advantages of fast speed and good consistency in the whole life cycle (Table 3).
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Number
Average deviation Charging voltage (mV)
Group A
7.6220
Standard deviation Discharging voltage (mV)
Charging voltage (mV)
Discharging voltage (mV)
38.0890
10.3467
46.6879
Group B
6.2483
7.7660
8.4464
10.5795
Group C
20.9349
30.4754
23.7866
35.7607
References 1. Diouf, B., Pode, R.: Potential of lithium-ion batteries in renewable energy[J]. Renew. Energy 76, 375–380 (2015) 2. Li T, Wang D, Wang H.: New method for acquisition of impedance spectra from charge/discharge curves of lithium-ion batteries[J]. J. Power Sources 535 (2022) 3. Middlemiss, L.A., Rennie, A.J., Sayers, R., West, A.R.: Characterisation of batteries by electrochemical impedance spectroscopy[J]. Energy Rep. 6(Supl.5) (2020) 4. Weng, C., Cui, Y., Sun, J., et al.: On-board state of health monitoring of lithium-ion batteries using incremental capacity analysis with support vector regression[J]. J. Power Sources 235, 36–44 (2013) 5. Xie, L., Wang, L., Tian, G., He, X: A new method for consistency screening of lithium ion batteries – series charge discharge screening [j]. Power Technol. 44(02), 149–152+226 (2020) 6. Li, H.: Capacity estimation and consistency screening of retired batteries based on IC curve [d]. In: Dalian University of technology (2021) 7. Zhou, Y., Liu, Y., Sun, X., Lian, J.: Local consistency analysis based on battery internal resistance [j]. In: Automotive Practical Technology (2020) 8. Lyu, C., Liu, H.Y., Luo, W.L., Zhang, T.: A fast time domain measuring technique of electrochemical impedance spectroscopy based on FFT[C]. In: Prognostics and System Health Management Conference (PHM-Chongqing), 26–28 Oct. 2018, pp. 450–455 9. Fairweather, A.J., Foster, M.P., Stone, D.A.: Battery parameter identification with Pseudo Random Binary Sequence excitation (PRBS)[J]. J. Power Sources 196(22), 9398–9406 (2011) 10. Liu, E.: Lithium ion battery screening grouping based on internal health characteristics [d]. In: Harbin Institute of Technology (2018)
Integrated Dynamics Control for Path Tracking and Obstacle Avoidance of Four-Wheel Intelligent Distributed Drive Vehicles Based on Time-Varying Predictive Control Bowen Wang1(B) , Cheng Lin1 , Peiyuan Lyu1 , Xinle Gong1,2 , and Sheng Liang1 1 National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology,
Beijing 10081, China {wangbowen,lincheng,liangsheng}@bit.edu.cn 2 School of Vehicle and Mobility, Tsinghua University, Beijing 10084, China
Abstract. The four-wheel intelligent distributed drive vehicle (4WIDEVs) has been attracted a great attention in dynamics control due to its inherent actuation flexibility recently. However, frequent variation of vehicle speed in dynamic control is usually ignored or simplified. To enhance the driving safety in the extreme path tracking and obstacle avoidance maneuvers, this paper proposed an integrated dynamic control method. We first design the time-varying predictive model comprehensively considering velocity variation and yaw stability. Compared with the traditional speed constant model, by analyzing the mechanism of multi-degree of freedom nonlinear adaptive time-varying characteristics of four-wheel independent vehicles model, the influence of frequently changing speed on model accuracy is reduced. For ensuring the tracking accuracy, a linear adaptive timevarying predictive based control method (LATV-MPC) is developed to compute optimal front wheel steering angle and longitudinal tire force, where the predictive model is updated in each time horizon with the changing speed, eliminating the errors accumulation between the prediction model and real state. Simulation results based on MATLAB and CarsSim platform demonstrates that the proposed integrated dynamics control strategy allows the yaw stability to perform better and the tracking error to decrease in both double lane change and random obstacle avoidance scenario. Keywords: Dynamics control · Path tracking · Obstacle avoidance · Time-varying predictive control
1 Introduction As autonomous driving technology advances, many researches focus on improving the integrated electric vehicle driving ability based on 4WIDEVs [1, 2]. The four wheels in 4WIDEVs can give a rapid motor torque response independently, which can bring better dynamic control performance to guarantee the driving stability [3]. However, due to the © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1059–1066, 2023. https://doi.org/10.1007/978-981-99-1027-4_111
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high dynamics and nonlinear characteristics of the 4WIDEVs model, the vehicles safety extremely relies on the control strategy. An appropriate control scheme (including vehicle model and control strategy) for 4WIDEVs to ensure both longitudinal and lateral safety is a challenged task. Some researches discussing the strategy of 4WIDEVs stability and tracking control in different driving maneuvers [4–6]. In them, the vehicle model below three degrees of freedom is often used [7]. In [8], a linear-parameter-varying model is employed. Chen et. al applied an enhanced piecewise affine tire model to approximate the nonlinear properties of tire force [9]. Although the three degrees model performs well in most scene, but the velocity variation and vehicle continuous time-varying properties are not fully considered. The dynamics control method for 4WIDEVs can be classified into the following different categories including the Active Front Steering method (AFS) [10], Direct Yaw Control method (DYC) [8] and Integrated Coordination method [11]. The optimization control scheme such as model predictive control (MPC) is commonly applied to solve the optimal input [12, 13] in coordinated control problem. Zi et al. proposed a MPC-based framework for coordinated control to make sure the stability is in a good range, where the velocity variation is considered a disturbance [14]. Zhao et. al proposed an integrated controller by coordinating both 4WIDEVs motor and tire slip energy in MPC scheme to achieve consuming-efficient [15]. Cairano et. al used the hybrid model predictive control strategy with piecewise affine (PWA) function to substitute for the wheel force model to achieve active front wheel steering and differential braking coordinated control [16]. In [17], speed and steering angle are optimized to avoid obstacles at high speed scenario. In order to sufficiently consider the linear adaptive time-varying and longitudinallateral features of the vehicle model, and adapt it into coordinated control scheme, we proposed an integrated dynamics control for path tracking and obstacle avoidance of 4WIDEVs to obtain high-quality trajectory tracking and stability control effects.
2 Vehicle System Model The vehicle velocity is regarded as the important time-varying parameter to influence the control performance. The four-wheel vehicle nonlinear model is proposed to characterize the properties with speed variation of 4WIDEVs. The following nonlinear differential equations is derived by analyzing the 4WIDEVs’ longitudinal, lateral and yaw moments in the inertial coordinate system, which is given by ⎧ 1 ⎪ ⎪ x¨ = ϕ˙ y˙ + Fxlf + Fxlr + Fxrf + Fxrr ⎪ ⎪ m ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎪ ⎨ y¨ = −ϕ˙ x˙ + m Fylf + Fylr + Fyrf + Fyrr d (1) 1 ⎪ lf Fyfr + Fyfl − lr Fyrr + Fyrl + −Fxlf − Fxlr + Fxrf + Fxrr ϕ¨ = ⎪ ⎪ ⎪ Iz 2 ⎪ ⎪ ⎪ ⎪ X˙ = vx cos ϕ − vy sin ϕ, Y˙ = vx sin ϕ + vy cos ϕ ⎪ ⎪ ⎪ ⎩ ϕ˙ = ϕ, ˙ vx = x˙ , vy = y˙ where x and y are the displacement according to the vehicle coordination system respectively, ϕ represents the vehicle yaw, X and Y are the displacement in global coordination
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system respectively. d represents the vehicle width. lf and lr are the distance which are from front and rear axis to center of gravity. Fx∗· and Fy∗· represent tire forces in the vehicle coordination system respectively, where ∗ ∈ {l, r} denotes left and right, · ∈ {f , r} T and F T represent the tire forces in the tire coordination denotes front and rear. Let Fx∗· y∗· system, and then the tire force can be written as ⎧ T cos δ − F T sin δ Fx∗f = Fx∗f ⎪ y∗f ⎪ ⎪ ⎨ F = F T sin δ + F T cos δ y∗f x∗f y∗f (2) T ⎪ Fx∗r = Fx∗r ⎪ ⎪ ⎩ T Fy∗f = Fy∗f where δ is the steering angle. T and δ are considered as the control input in the following part. F T In this paper, Fx∗· y∗· can be calculate by the Pacejka tire model, which is expressed as T Fy∗· (3) = fTire Dy∗· , Cy∗· , By∗· , Ey∗· , α∗·
where Dy∗· , Cy∗· , By∗· , Ey∗· are the constant coefficients, α∗· represents the sideslip angle, which can be described as
v˙ +l ϕ˙ α∗f = −δ + y v˙ x f (4) v˙ −l ϕ˙ α∗r = y v˙ x r
3 Integrated Dynamics Control 3.1 Time-Varying Predictive Model Model predictive control is applied on a large scale to the path tracking portion of the autonomous driving vehicles because of its advantages in predicting the future state of the system and great capability to handle with the control problem of multiple inputs and constrains. We design the time-varying predictive control algorithm based on the MPC scheme. We first design the vehicle state and input are presented as ⎧ ⎪ ⎨ ξ˙ = h(ξ, p) ξ = [˙x, y˙ , ϕ, ˙ X , Y , ϕ]T (5) ⎪ ⎩ p = δ, F , F , F , F T xrr xlf xlr xrf In general, the state matrix and control input matrix of linear system are always constant matrices. To cope with the nonlinear system, the model will be linearized firstly, but the obtained Jacobian matrix will change with the time step. It may cause large control errors and even lead to algorithm failure in high-risk condition while the matrix of system is deemed to be a constant value. As results, the linear adaptive time-varying (LATV) model predictive control is adopted to obtain a better control performance. We linearize and expand the formular (1) to the form of (6) as follows ξ˙ (t) ≈ h ξ , p + ∂h ξ , p ∂ξ ξ − ξ + ∂h ξ , p ∂p(p − p) + o(ξ, p) (6)
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where h(·) represents vehicle formula of (1) ~ (4), the p and ξ are the input of vehicle i and the nominal state. The detail of how to calculate p and ξ will describe later. Based on the (6), the Jacobian matrix Actrl and Bctrl can be obtained. In the next, we defined the deviation variables of ξ = ξ − ξ , p = p − p, then the continuous-time linear system can be expressed as follows
where Actrl =
d (ξ ) = Actrl · ξ + Bctrl · p (7) dt ∂h = ∂p ξ ,p , and they can be updated when ξ and p change.
∂h ∂ξ ξ ,p , Bctrl
The discrete form of nominal state vector ξ can be obtained by adapting the Forward Euler (FE) method. With regard to the nominal input p, it can be approximately by applying the value of forward step. Thus, the recursive nominal state sequence ξ (τ ) in a discrete form is written as (7). p(τ ) is obtained by the previous calculated optimal value. ξ (τ + 1) = h ξ (τ ), p(τ ) · T + ξ (τ ) (8) The discrete form of (8) can be concluded in a solid form which is shown as e ξ (τ + 1) = Aectrl (τ )ξ (τ ) + Bctrl (τ )p(τ )
ξ (τ ) = ξ (τ ) − ξ (τ ) p(τ ) = p(τ ) − p(τ ) e Aectrl = T · Actrl + I , Bctrl = T · Bctrl
(9)
3.2 Linear Adaptive Time-Varying Predictive Control Our control target is that the vehicle should accurately track the lateral displacement computed according to the current and predictive longitudinal displacements, while the yaw stability is enhanced by given the desired yaw rate reference. The displacement and vehicle yaw angle rate reference are described as
τ +1|τ Yref = X τ +1|τ
(10)
δ τ +1|τ
· δ τ +1|τ < vτμg τ +1|τ +1|τ ϕ˙ref = μg μg sign · δ τ +1|τ · δ k+1|t ≥ vτ +1|τ v τ +1|τ where K =
m(lf Cf −lr Cr )
and =
v
(lf +lr )(1+kv2 ) τ displacement reference policy related to X +1|τ . Cf Cr (lf +lr )
2
, (·) represents the lateral
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Based on the given reference, the optimization problem in adaptive time-varying MPC scheme is written as N −1 τ |τ 2 τ +1|τ τ +1|τ τ +1|τ 2 τ +1|τ 2 min ψ = min − Yref + ϕ˙ − ϕ˙ref + p Y R Q2
k=1
Q1 τ |τ τ |τ τ +1|τ τ |τ τ |τ s.t. ξ = T · Actrl + I · ξ + T · Bctrl · p
τ +1|τ τ |τ τ |τ ξ = h ξ , pτ |τ · T + ξ pτ |τ = pτ +1|τ −1 , pNp |τ = pNp |τ −1 τ +1|τ ξ τ +1|τ = ξ τ +1|τ + ξ pτ +1|τ = pτ +1|τ + pτ +1|τ pmin ≤ pτ |τ ≤ pmax pmin ≤ pτ |τ ≤ pmax τ = 0, 1, 2, · · · , Np (11) where ξ τ +1|τ is the state of vehicle at time τ in (τ + 1)th predictive horizon. pτ |τ and pτ |τ are the input and deviation of input at k th sample time respectively. Q1 , Q2 ,R e,τ |τ e,τ |τ denote the weighting matrix. Actrl and Bctrl are the adaptive time varying state space τ +1|τ
and pτ |τ are the τ th vector of predictive nominal state and input based matrix. ξ on (8), where pτ |τ applies the solved previous optimal input pτ +1|τ −1 at forward step. In addition, we define pNp |τ = pNp |τ −1 when predictive horizon τ = Np . ξ τ +1|τ and uτ +1|τ denote the predictive state and input of vehicles related to (11). The constrains of input and the deviation of input are given by pmin , pmax , pmin , pmax , respectively. The 0|τ initial state ξ is defined as the actual feedback of vehicle state ξ τ −1 at the previous time step τ . The overall integrated dynamics control scheme is shown in Fig. 1.
Ffl
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Fig. 1. Integrated dynamics control schem
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4 Simulation Results Sine curve obstacle avoidance scenario test scenario is conducted in the MATLAB together with CarSim to testify the proposed integrated dynamics control method, where The hybrid control strategy and linear model predictive control proposed in [18] are utilized for comparison. To guarantee control accuracy and real-time ability, the FORCES Pro [19] is adopted to generate the solver code for computing.
Fig. 2. Tracking performance (a) and the vehicle states variation (b)–(e)
The tracking trajectory and reference trajectory of the three controllers are given in Fig. 2a to compare the effect of three different control methods in tracking the sine curve, and it is observed that the tracking trajectory with the time-varying MPC control strategy can basically fit the given reference trajectory perfectly with minimal error, and the tracking trajectory with the hybrid MPC control strategy can basically follow the reference trajectory with relatively small error. However, when using the linear MPC control strategy, there is a huge error between the tracking trajectory and the reference trajectory, and the tracking effect is poor. The tracking process of the whole sine curve requires the speed to rise from a certain value close to 0 to 40 km/h within 5s, and keep it around 40 km/h. As shown in Fig. 2, only the time-varying MPC controller can do adaptive adjustment of the speed to achieve better tracking. Figure 2c and d show the yaw rate curves and steering angle plots of the three methods respectively. As can be seen, the time-varying MPC test method has the optimal yaw rate curve with the smallest assignment and frequency, and the steering angle curve performs well, although it is slightly worse than the linear MPC, but the tracking effect of the time-varying MPC control strategy is much better than that of the linear MPC control strategy. The longitudinal force of each tire during the time-varying
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MPC test is shown in Fig. 2e, and it can be seen that they are all within a reasonable range, which proves that the method is feasible practical. The simulation results are summarized in Table 1, where the time-varying MPC presents the greater computing efficiency and smaller tracking errors. In conclusion, the time-varying MPC control strategy, as the method with the smallest error among the three tracking control strategies, can not only perform speed adaptive adjustment according to the given reference trajectory, but also greatly reduce the amplitude of yaw rate and steering angle, and the proposed framework is validated by analyzing the four tires’ forces, which further proves the superiority of the method. Table 1. Simulation in Obstacle Avoidance Scenario Testing method
Computing time ratio
Tracking Error
Solver code
Linear MPC
24.27
2.9778
Hybrid Toolbox
Hybrid MPC
27.82
0.6070
Hybrid Toolbox
Time-varying MPC
16.54
0.0583
FORCES Pro
5 Conclusion In this paper, we propose an integrated dynamics control scheme for vehicles 4WIDEVs based on time-varying predictive control. The first contribution of this paper is that we design a time-varying model for prediction by linearizing and discretizing the nonlinear continuous-time vehicle dynamical model, particularly, the longitudinal velocity variation and lateral tire force are both taken into account. Secondly, a time-varying predictive control algorithm is proposed. During each horizon of the MPC processing, the predictive model is updated by using the computed input sequence in the last step, and the path tracking and obstacle avoidance stability are characterized in the cost function. Finally, the algorithm calculates the optimal control input yielding desired steering angle and four tire forces. Sine curve obstacle avoidance is conducted in MATLAB together with CarSim for verification, which shows that the proposed method can achieve smaller tracking error and faster calculation. Acknowledgments. This work was supported in part by the National Natural Science Foundation of China under Grant 51975049.
References 1. Zhao, H., Gao, B., Ren, B., Chen, H.: Integrated control of in-wheel motor electric vehicles using a triple-step nonlinear method. J. Franklin Inst. 352, 519–540 (2015) 2. Guo, J., Luo, Y., Li, K.: An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles. IEEE Trans. Intell. Transp. Syst. 19, 2482–2492 (2018)
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3. Hang, P., Xia, X., Chen, X.: Handling stability advancement with 4WS and DYC coordinated control: a gain-scheduled robust control approach. IEEE Trans. Veh. Technol. 70, 3164–3174 (2021) 4. Ataei, M., Khajepour, A., Jeon, S.: Model predictive control for integrated lateral stability, traction/braking control, and rollover prevention of electric vehicles. Veh. Syst. Dyn. 58, 49–73 (2019) 5. Zhang, J., Sun, W., Du, H.: Integrated motion control scheme for four-wheel-independent vehicles considering critical conditions. IEEE Trans. Veh. Technol. 68, 7488–7497 (2019) 6. Li, X., Xu, N., Guo, K., Huang, Y.: An adaptive SMC controller for EVs with four IWMs handling and stability enhancement based on a stability index. Veh. Syst. Dyn. 1–24 (2020) 7. Yangyan, G., Timothy, G., Mathias, L.: Optimal control of brakes and steering for autonomous collision avoidance using modified Hamiltonian algorithm. Veh. Syst. Dyn. 57, 1224–1240 (2019) 8. Zhang, L., et al.: Model predictive control for integrated longitudinal and lateral stability of electric vehicles with in-wheel motors. IET Control Theory Appl. 14, 2741–2751 (2020) 9. Chen, W., Yan, M., Wang, Q., Xu, K.: Dynamic path planning and path following control for autonomous vehicle based on the piecewise affine tire model. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 235, 881–893 (2020) 10. Na, X., Cole, D.J.: Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver–AFS interactive steering control. Veh. Syst. Dyn. 51, 165–198 (2013) 11. Hang, P., Chen, X., Luo, F.: LPV/H ∞ controller design for path tracking of autonomous ground vehicles through four-wheel steering and direct yaw-moment control. Int. J. Automot. Technol. 20, 679–691 (2019) 12. Cabaco, A.S., Choi, S.B.: Model predictive control for vehicle yaw stability with practical concerns. IEEE Trans. Veh. Technol. 63, 3539–3548 (2014) 13. Cheng, S., Li, L., Guo, H.-Q., Chen, Z.-G., Song, P.: Longitudinal collision avoidance and lateral stability adaptive control system based on MPC of autonomous vehicles. IEEE Trans. Intell. Transp. Syst. 21, 2376–2385 (2020) 14. Li, Z., Wang, P., Liu, H., Hu, Y., Chen, H.: Coordinated longitudinal and lateral vehicle stability control based on the combined-slip tire model in the MPC framework. Mech. Syst. Signal Process. 161 (2021) 15. Zhao, B., Xu, N., Chen, H., Guo, K., Huang, Y.: Design and experimental evaluations on energy-efficient control for 4WIMD-EVs considering tire slip energy. IEEE Trans. Veh. Technol. 69, 14631–14644 (2020) 16. Di Cairano, S., Tseng, H.E., Bernardini, D., Bemporad, A.: Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain. IEEE Trans. Control Syst. Technol. 21, 1236–1248 (2013) 17. Liu, J., Jayakumar, P., Stein, J.L., Ersal, T.: Combined speed and steering control in highspeed autonomous ground vehicles for obstacle avoidance using model predictive control. IEEE Trans. Veh. Technol. 66, 8746–8763 (2017) 18. Wang, B., Lin, C., Liang, S., Gong, X., Tao, Z.: Hierarchical model predictive control for autonomous collision avoidance of distributed electric drive vehicle with lateral stability analysis in extreme scenarios. World Electr. Veh. J. 12 (2021) 19. https://www.embotech.com/products/forcespro/overview/. Accessed 10 Sept 2022
Research on Communication Mechanism of Cloud-Edge-End Distributed Energy Storage System Jiabao Min, Yuhang Song, and Xin Jiang(B) School of Electrical and Information Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected]
Abstract. In view of the characteristics of distributed energy storage system with “large number and scattered distribution” of terminal devices, this paper proposes a star and chain two-layer networking mode. For devices with a long communication distance, they can connect to edge iot agent through sink nodes, and for devices with a short communication distance, they can directly communicate with edge iot agent. This networking mode can effectively enhance the reliability of system communication. According to the semantic rules of the Internet of Things, the iot terminal model of battery energy storage system is constructed from three aspects of static attributes, dynamic attributes and services, and it is combined with the traditional IEC61850 model. The IEC61850 model is responsible for the communication between edges, and the iot model is responsible for the communication between cloud edges. It not only solves the problem of information model heterogeneity between systems, but also breaks the situation of chimney system. Based on this, puts forward the MQTT protocol in the cloud - edge - end information interaction mechanism, from the themes of the communication architecture, interaction topic and protocol mapping specification design, makes the energy storage system has more standardized communication mechanism, effectively solve the current energy storage system terminal equipment communication protocol and networking mode difference big problem. Finally, taking an energy storage power plant system as an example, the MQTT client software is used to interact with the cloud for information, and the reliability and timeliness of this communication mechanism is verified through information interaction tests and time delay analysis. Keywords: Iot terminal model · Networking mode · MQTT · Information interaction
1 Introduction With the deep reform of the energy supply-side structure, the proportion of clean energy access continues to increase [1], distributed power sources and energy storage terminal devices are increasing, and fundamental changes in energy forms are occurring [2]. The © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1067–1075, 2023. https://doi.org/10.1007/978-981-99-1027-4_112
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“14th Five-Year Plan” Implementation Plan for the Development of New Energy Storage released in March 2022 emphasizes the need to accelerate the construction of energy storage system information collection, sensing, processing, and application [3, 4], and to promote the integration of new energy storage with all aspects of the power system [5]. Processing, and application [3, 4], promote the integration of new energy storage with all aspects of the power system, and strive to build a leading international energy Internet by 2025 [5]. In recent years, more and more research has been conducted at home and abroad on communication technology and information technology in the construction of new energy storage systems. The literature [6] introduced the standard system framework of smart IOT sensing technology for new power systems, including common communication networking methods and so on, but did not explain the application of energy storage system scenarios; the literature [7] proposed an information interaction architecture for energy storage systems, but its networking method was too simple and only applicable to traditional chimney-type systems. Literature [8, 9] modeled the information of energy storage system terminals based on IEC61850 and proposed different IEC61850 to CIM model mapping methods; literature [10, 11] studied the communication mechanism between energy storage system terminals and cloud master station based on IEC60870– 104 protocol, but the models and communication protocols used in the above literature did not consider IoT technology, which is not conducive to promote the integration of new energy storage with all aspects of the power system. In view of the current problems that the communication protocols in the energy storage system are not yet unified, the networking methods differ greatly, and the data models are not unified, this paper focuses on the communication mechanism of the cloud-side -end distributed energy storage system.
2 Distributed Energy Storage System Communication Networking Method The cloud-edge-end energy storage system system mainly includes all kinds of terminals of the energy storage system, edge agent gateway, and human-computer interaction platform, and its architecture is shown in Fig. 1. Sensing terminal: the sensing unit in the architecture of the energy storage system, including various collection terminals for fire fighting, flood control, equipment status, electrical quantity monitoring, etc. Aggregation node: core equipment with strong data collection capability, with the function of enhancing signal strength [12]. In view of the large number of terminal devices in the distributed energy storage system and the different communication methods, setting the aggregation node can improve the reliability of the communication at the edge [13]. “Edge” edge agent gateway: It is a central terminal that integrates the core capabilities of network communication, edge computing, data storage and protocol conversion on the edge side of the network near the source of things or data. HMI platform: deployed in the “cloud”, from the platform you can see the data of the energy storage system, including current, voltage, temperature and humidity of
Research on Communication Mechanism of Cloud-Edge-End HCI Platform
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Fig. 1. Cloud-edge-end energy storage system architecture.
the environment and alarm events, etc., mainly to achieve the function of equipment management and data management.
3 Distributed Energy Storage System Information Model 3.1 IEC61850-Based Virtual Logic Device Modeling With the updated iteration of IEC61850 standard, IEC61850–7-420 defines the relevant logical nodes of distributed power supply so that they can meet the functional needs of the devices related to distributed energy storage systems [14]. This section introduces the battery energy storage system as an example. The Intelligent Electronic Device (IED) model of the battery energy storage system generally includes logical devices such as energy converters, battery systems, circuit breakers, etc. The logical devices and key logical nodes are shown in Fig. 2. Energy storage terminal virtual logic device LD1 LLN0
LD3
LPHD
XSWI
LLNO
LPHD
ZRCT
ZINV
CSWI LD2
LLN0
LPHD
ZBAT
ZBTC
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Fig. 2. Information model of battery energy storage system
From Fig. 2, LD1 is a monitoring and protection logic device whose main function is to control and monitor switchgear such as circuit breakers and environmental gases,
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where the CSWI logic node is responsible for controlling the switchgear and CSWI.Pos is able to report the switchgear control status to the edge agent, and the XSWI logic node is responsible for encapsulating the DC switch interface and XSWI.Pos is able to report the switch closure Pos is able to report the switch closure status. LD2 is a battery system monitoring logic device whose main function is to monitor the operation status and working characteristics of BESS. ZBTC logic node is responsible for recording physical information such as charger charging voltage and charging current, and ZBAT is responsible for monitoring and recording the internal physical quantities of the battery, including the operation status of the energy storage battery, battery temperature and other information, where ZBAT.Vol.mag Beh.stVal can report other physical quantities such as battery temperature to the edge agent; SIMG is responsible for monitoring gas status, and SIMG.Pres can report gas concentration data such as hydrogen and carbon monoxide. LD3 is a measurement and monitoring logic device, whose main function is to monitor the operation status of the DC converter. ZRCT qualifies the status information of the DC converter, including the isolation type, current and voltage setting values, etc. ZINV characterizes some control information of the DC converter, including output power and other data, and MMXU is responsible for the measurement function of various non-electrical quantities, such as ambient temperature and humidity. MMDC is responsible for the information reading function, which mainly reads the physical information related to BESS measured by the MMXU logic node in the electric power measurement LD. 3.2 IOT Terminal Model The IOT terminal model is the information description of distributed energy storage terminal attributes, events and services based on the semantic rules of IOT, and the model built is an ISON format information description file. The structure of the IOT terminal model is shown in Fig. 3. Model identifier Model description Terminal model of energy storage system
Static properties
Dynamic properties
News
Device type Ă Equipment manufacturer Total current of battery pack ... Total battery voltage Grid voltage too high ... AC short circuit fault
Static attribute identifier Static property name Data type Dynamic attribute identifier Dynamic property name Data type Message identifier Message Description/ Type Message call method
Fig. 3. Structure of iot model of energy storage system
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As shown in Fig. 3, the structure of the energy storage system IOT model contains model identifier, model description, static attributes, dynamic attributes, and message subject fields. Firstly, we sort out the static attributes of energy storage terminal such as “device type”, “device manufacturer”, “device address”, etc.; dynamic attributes such as Total battery pack current”, “Total battery pack voltage”, etc.; message domain “High grid voltage”, “AC short circuit fault”, etc. Then add the description id, description identifier and other corresponding values to the JSON object according to the “National Grid IOT Terminal Unified Modeling Specification”.
4 Cloud-Side Interaction Mechanism Based on MQTT Protocol 4.1 Distributed Energy Storage System Communication Model The communication model based on IEC61850 adopts the publish-subscribe communication method, and the communication model between the distributed energy storage system terminal and the cloud master station is shown in Fig. 4. HCI platform IEC61850 communica tion m odel
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IEC61850 model
ACSI
SCS M
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Fig. 4. Communication model between distributed energy storage terminal and human-computer interaction platform
From Fig. 4, it can be obtained that the distributed energy storage terminal first aggregates data in the IED information model, and then provides communication services for data file transfer through Abstract communication service interface (ACSI), and since ACSI is not really a communication protocol, it is necessary to then convert the corresponding data and services to other communication protocols through Specific Since ACSI is not really a communication protocol, the corresponding data and services need to be converted to other communication protocols through Specific Communication Service Mapping (SCSM). Depending on the type of data, the mapping protocols may also vary, and generally include 104 protocol, MMS protocol, MQTT protocol, etc. 4.2 IEC61850-MQTT Protocol Conversion The IEC61850 to MQTT protocol conversion is essentially a mapping of the IEC61850 standard definition related objects to JSON format, and the data objects and related services are transmitted and implemented using the MQTT protocol [15], and the IEC61850
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to MQTT protocol mapping process and the structure of the MQTT statute are shown in Fig. 5.
IEC61850.7-3 Public data class
IEC61850.7-4 Logical node class
IEC61850.7-2 ACSI
IEC61850.8-2 SCSM
MQTT
Fig. 5. Mapping process from IEC61850 to MQTT
From Fig. 5, we can see that at the application layer the virtual logical devices, abstract communication services and interface services under the IEC61850 standard are converted into data objects and services of the MQTT protocol; at the representation layer the code is written using the JSON data format; at the session layer the communication entities are controlled, the associated identity codes are established and SSL is used to encrypt the message transmission; at the transport layer, the MQTT protocol encapsulates the messages into the corresponding Topic (subject) for transmission based on the differences in the service approach, and the identity verification of the message transmission object is performed at the application layer; the mapping of the protocol is completed by close cooperation between the layers. 4.3 Cloud-Side Interaction Architecture The information interaction architecture between the edge agent gateway and the HCI platform is shown in Fig. 6. The edge agent gateway is equipped with a model mapping and data conversion device, and its converted data information is sent to the HCI platform through port 1. Figure 6 shows that the MQTT protocol uses the client/server-side model, and there are three identities in the MQTT protocol: publisher (Publish), agent (Broker), and subscriber (Subscribe) where the message agent is the HCI platform, which can subscribe to the messages published by the edge agent gateway, and the edge agent gateway is the publisher, which can publish messages to the The message transmitted by MQTT contains two parts: the topic is the type of the message, which mainly includes two categories of device management and business interaction in the energy storage system, and the load is the content of the message, which refers to the specific content to be used by the subscriber.
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Information Model Library Cloud master station
HCI platf orm˄MQTTBROKER˅ AccessP oint2
MQTT
Subscribe
Publish
AccessP oint1 Model mapping and data conversion device Edge proxy gateway(MQTT-PUBLISH) Information plug and play interfac e(IED) IEC61850 information model
Fig. 6. Cloud edge information interaction architecture
5 Example Analysis This section takes an energy storage power plant in Henan Province as an example to test and verify the system as a whole, mainly including communication delay analysis. The communication delay is an important indicator of the reliability of the communication mechanism, so two calculation equations are introduced in this section. Average communication delay: H Z=
1
Ti
H
(1)
where: H denotes the number of packets, Ti denotes the communication delay in grabbing the ith packet, and Z denotes the average communication delay. Delay jitter: D=
H 2
(Ti − Ti−1 )2 H
(2)
where: H denotes the number of packets, Ti denotes the communication delay in grabbing the ith packet, and D denotes the delay jitter. Here the delay time indicates the total time of communication completion, including the return time of the acknowledgement message. For example, Fig. 7 shows the delay time for the system to grab 100 packets. From Fig. 7, we can see that the data delay of the system is mainly distributed in 50ms to 240ms, and the average delay is 181ms according to Eq. (1), and the delay jitter is 54.2ms according to Eq. (2). Reference [16] shows that the data delay in the traditional cloud computing system is mainly distributed in 70ms to 250ms the average delay is 324ms, and the delay jitter is 282.8ms compared to the better latency of the cloud side end energy storage system.
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TIME DELAY/MS
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0 DATA PACKETS/A
Fig. 7. Data delay
6 Conclusion This paper firstly proposes a star + chain two-layer networking method, which has the advantages of simple structure, easy management, small network delay and low transmission error of star networking, and the advantage of simplified path control of ring networking to effectively enhance the reliability of system communication. Based on the semantic rules of IoT, the IoT terminal model of battery storage system is constructed from static attributes, dynamic attributes and services, and combined with the traditional IEC61850 model, which not only solves the problem of information model heterogeneity among systems, but also breaks the situation of chimney system. The cloud-side-end information interaction mechanism of MQTT protocol is proposed, and the communication architecture, interaction topics, protocol mapping and other aspects are standardized and designed to make the energy storage system have a more unified and standardized communication mechanism. Finally, taking an energy storage power plant system as an example, the MQTT client software is used to interact with the cloud for information, and the reliability and timeliness of this communication mechanism is verified through information interaction tests and time delay analysis.
References 1. Li, X., Zhao, S., Hui, D.: Development trend analysis and prospect of key technologies of large-scale energy storage power station for new power system. Power Supply Electr. 39(07), 2–8+24 (2022) (in Chinese) 2. Wang L.: Application of new energy storage system in power supply of communication base station. Mod. Build. Electr. 13(05), 58–62 (2022) (in Chinese) 3. Wu, Z., Jia, C., Chen, L., et al.: Research on the innovation direction of energy storage in new power system. Acta Energiae Solaris Sin 42(10), 444–451 (2021) (in Chinese) 4. Murty, V.V.S.N., Kumar, A.:Multi-objective energy management inmicrogrids with hybrid energy sources andbattery energy storage systems. Prot. Control Mod. Power Syst. V5(1), 1–20 (2020) 5. Zhu, N., Qu, Z., Li, S.: Thinking of DC power supply system and new energy storage system. Mod. Build. Electr. 11(09), 31–34 (2021) (in Chinese)
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6. Lv, S., Ding, J., Zhang, H., et al.: Research and thinking on intelligent IoT sensing technology standard system of new power system. Electr. Power Inf. Commun. Technol. 19(08), 39–46 (2021) (in Chinese) 7. Vishal, K., Gayatri, S., Chandra, S.: WSN and IoT based smart city model using the MQTT protocol. J. Discret. Math. Sci. Cryptogr. 22(8), 1423–1434 (2019) 8. Chen, H., Wang, X., Li, Z., Chen, W., Cai, Y.: Distributed sensing and cooperative estimation/detection of ubiquitous power internet of things. Prot. Control Mod. Power Syst. 4(1), 1–8 (2019). https://doi.org/10.1186/s41601-019-0128-2 9. Kuntschke, R., Winter, M., Glomb, C., Specht, M.: Message-oriented machine-to-machine communication in smart grids. Comput. Sci. Res. Dev. 32(1–2), 131–145 (2016). https://doi. org/10.1007/s00450-016-0314-7 10. Senthil, K., Bwandakassy, E.B.: IEC61850 standard-based harmonic blocking scheme for power transformers. Prot. Control Mod. Power Syst. 4(2), 121–135 (2019) 11. Xie, J., Ye, Q., Lu, Y., et al.: Research on plug-and-play information interaction mechanism of distributed power supply. Power Supply Electr. 36(10), 52–60 (2019) (in Chinese) 12. Xie, Z., Wang, M., Cao, W.: Network algorithm of power line communication based on multi-factor weighting. Radio Eng. 52(08) 1482–1489 (2022) (in Chinese) 13. Song, W., Wang, K., Cao, W., et al.: Time delay measurement and adjustment strategy in underwater ring network. Electron. Prod. World 28(12), 45–48+86 (2021) (in Chinese) 14. Xi, Y., Chen, B., Yuan, Z., et al.: Research on modeling and testing requirements of distribution automation terminal based on IEC61850. Electr. Meas. Instrum. 57(07), 41–47 (2020) (in Chinese) 15. Xi, Y., Chen, B., Guo, X., et al.: Function analysis and modeling of distribution system automation based on IEC61850. Electr. Meas. Instrum. 57(05), 32–36 + 43 (2020) (in Chinese) 16. Zheng, G., Yu, X.: Design and application of intelligent power management and control system based on edge computing. Electr. Meas. Instrum. 58(08), 28–35 (2021) (in Chinese)
Predictive Cruise Control Algorithm Design for Commercial Vehicle Energy Saving Based on Quadratic Programming Xianning Li1 , Tingting Lv2 , Hanqi Yue3 , Shuangping Liu2 , Xiaoxiang Na4 , Hong Chen5 , and Bingzhao Gao1(B) 1 School of Automotive Studies, Tongji University, Shanghai, China
{li_xianning,gaobz}@tongji.edu.cn
2 Dongfeng Commercial Vehicle CO., LTD, Wuhan, Hubei, China
{LvTingting,liusp}@dfcv.com.cn
3 BYD AUTO CO., LTD, Xi’an, Shanxi, China
[email protected]
4 Department of Engineering, University of Cambridge, Cambridge, UK 5 College of Electronic and Information Engineering, Tongji University, Shanghai, China
[email protected]
Abstract. In this paper, a layered control algorithm for energy-efficient predictive cruise control (PCC) algorithm of commercial vehicles that can optimize engine torque and gear in real time is proposed. The predictive cruise upper layer controller constructs a quadratic programming (QP) problem incorporating forward road information to optimize the vehicle driving force in the Model Predictive Control (MPC) framework. The predictive cruise lower layer controller optimizes the gear by finding the offline optimized gear MAP based on the overall vehicle driving force and current vehicle speed obtained from the upper layer controller. The predictive cruise algorithm is validated under highway conditions with slope changes. Compared with the traditional cruise control (CC) algorithm, it can save more than 4% fuel, and can better balance fuel economy, time economy, and driving comfort compared with the PCC algorithm based on indirect method solving. As for its solution speed, it is only twice as fast as the indirect method, which can meet the demand of real-time control. Keywords: Energy saving · Predictive cruise control (PCC) · Quadratic programming (QP) · Model predictive control (MPC)
1 Introduction By 2018, industrialization has caused global warming of 1°C, and the Intergovernmental Panel on Climate Change (IPCC) has pointed out that in order to avoid serious effects of climate change, global warming must be controlled within 1.5 °C between 2030 and 2052 [1], so energy saving and carbon reduction has become an issue that all industries must confront. In the whole industrial field, the energy consumption and emissions generated © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1076–1088, 2023. https://doi.org/10.1007/978-981-99-1027-4_113
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by transportation account for a huge proportion, and the liquid fuel consumed by trucks alone accounts for more than 20% of the whole industrial field [2, 3], so the research on the energy saving of trucks is of urgent practical significance. At the current stage, predictive cruise control (PCC) with the objective of energy saving is easier to achieve than fully driverless, and therefore has been widely studied [4]. Model predictive control (MPC) benefits from its rolling optimization framework, which allows the continuous incorporation of future information into the control system, while being applicable to multi-objective and multi-constrained control problems, and is the basic framework for PCC [4, 5]. In the framework of MPC, there are generally three ways to solve the PCC optimization problem: one is the direct method, using the programming method to solve [6, 7], which can guarantee the optimality of control to a greater extent, but the solution speed of optimization problems with large complexity is slow; another is the indirect method, which uses the variational method or the Pontryagin minimax principle (PMP), etc. to transform the optimization problem and then solves it using numerical methods [8, 9], which is not conducive to imposing constraints on some state quantities; in addition is the dynamic programming method [10], which can guarantee the optimality of the control, but is difficult to optimize in real time, so it is often calculated in the cloud as a reference for the vehicle. In this paper, a quadratic programming (QP) approach is used to reduce the complexity of the optimization problem as much as possible while ensuring performance. Real-time optimization of discrete gear for PCC is a complex problem, and there are two main methods to solve it. One is to use the default gear position known in the prediction horizon to deal with the problem [6], which will inevitably lose certain control optimality; the other is to use the mixed integer programming (MIP) approach to integrate the gear optimization directly into the speed planning [11], which can ensure the control optimality but has the disadvantage of slow solution speed. In this paper, a hierarchical control approach is used to achieve real-time optimization of gears while avoiding gear optimization and speed planning simultaneously. In this paper, a hierarchical control approach is adopted, in which the lower layer controller searches for an offline optimized gear table based on the vehicle driving force and vehicle speed to achieve real-time optimization of gear, and the upper layer controller achieves real-time optimization of speed by solving a QP problem based on a linearized vehicle model. The structure of the later paper is as follows: the second section describes the way of gear optimization by the lower layer controller; the third subsection describes the design of the upper layer controller in MPC framework in detail; in the fourth section, the hierarchical controller is simulated and verified under typical road and real road scenarios respectively, and the results is analyzed; the fifth section summarizes the whole paper.
2 Lower Layer Gear Optimization Controller Design In the PCC algorithm considering gear optimization, engine torque and gears need to be optimized simultaneously. In order to avoid solving complex MIP problems, it is necessary to separate the gear optimization from the engine torque optimization in a layer. In this section, the design of the lower layer gear optimization controller is briefly described, and for more details, please refer to the previous work.
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2.1 Gear Optimization Map Design The essence of the vehicle design with different gears is to make the engine work in the proper engine speed and torque range when the vehicle is driven at different speeds and driving forces. The design of the gear optimization map in this paper is to select the most energy-saving gears for vehicles operating at different speeds and driving forces with the goal of saving fuel, and to establish a single mapping relationship from speed and driving force to gears. The specific selection method is to calculate the engine torque and engine speed at different gears for a fixed operating point of vehicle speed and driving force, and then find the engine fuel consumption rate map to get the corresponding fuel consumption rate at different gears (The gears that are out of the engine operating range must be excluded), and select the gear with the lowest fuel consumption rate as the optimal gear at the operating point of the vehicle. (At a certain speed, the minimum fuel consumption rate is equivalent to the minimum fuel consumption in 100 km.) The optimal gears for different vehicle speeds and driving forces are aggregated to obtain the gear optimization map shown in Fig. 1.
Fig. 1. Gear optimization map.
It should be noted here that frequent gear changes should be avoided in the actual vehicle driving process, so a certain shift interval should be set, and the optimal gear map cannot be connected to consider only the shift interval, but it can be constrained at the output end. 2.2 Fuel Consumption Model Fitting The fuel consumption rate of an engine can usually be expressed as a higher-order polynomial of engine torque and engine speed. When the gears of the vehicle operating points at different vehicle speeds and driving forces are determined, their corresponding engine fuel consumption rates are also fixed, so a higher-order polynomial of vehicle
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speed and driving force can be tried to fit the fuel consumption rate of the engine. m ˙ f (v, Ft ) = (h03 v2 + h11 Ft + h13 v2 Ft + h21 Ft2 )v
(1)
m ˙ f is fuel consumption rate, v is vehicle speed, Ft is driving force, and others are fitting coefficients. The choice of different order matching of vehicle speed and drive force is mainly considered for the construction of the subsequent QP problem. The least squares based fitting of fuel consumption rate is very effective (see Fig. 2), so it is used as the energy consumption model in this paper.
Fig. 2. Fuel consumption rate fitting result.
3 Upper Layer PCC Controller Design In this section, the design of the upper-level predictive cruise controller is described in detail. First, the conventional vehicle longitudinal dynamics model is transformed to obtain a linear vehicle model. After that, the objective function of the PCC optimization problem is established in the MPC framework, the system constraints are specified, and the optimization problem is organized into a normalized QP problem by derivation. Finally, the solution method and effect of the optimization problem are briefly explained. 3.1 Vehicle Model Conversion The vehicle model usually used in the study of longitudinal control of vehicle is based on Newton’s second law. Ft (k) − Farg (k) v(k + 1) − v(k) = t δmv
(2)
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δ is the equivalent rotating mass conversion factor, mv is the overall vehicle mass, and Farg is the sum of air resistance, rolling resistance, and hill climbing resistance during driving. For commercial vehicle, their rotating mass is small compared to the overall vehicle mass, and their δ is close to 1. Therefore, the effect of rotating mass will be ignored in the subsequent contents of this paper. In order that the optimal control problem in the MPC framework can be subsequently transformed into a QP problem, the kinetic energy theorem is applied to obtain the longitudinal vehicle model by using Eulerian dispersion. E(k + 1) − E(k) =
1 2 mv v (k + 1) − v2 (k) = Ft (k) − Farg (k) s 2
(3)
After that, vehicle kinetic energy and driving force are selected as state quantities, and the rate of change of driving force is used as the control quantity, which is convenient for the establishment of QP problem and also for imposing comfort constraints on the vehicle, and the final state equation of vehicle longitudinal dynamics is obtained as follows. x(k + 1) = Ax(k) + Bu u(k) + Bd d (k), y(k) = Cc x(k)
(4)
T 1 x(s) = E(s) Ft (s) ; u(s) = F˙ t (s) = F˙ t (t); y(s) = x(s) v −mv s(f cos α(s) + g sin α(s)) d (s) = ; 0
C A ρ 0 10 10 1 − dmvf s s A= ; Bd = ; Cc = . ; Bu = s 01 01 0 1 Cd is air resistance coefficient, Af is windward area, ρ is air density, f is rolling resistance coefficient, g is gravitational acceleration, and α is road slope. In this paper, the distance domain discretization is used, which can well introduce the forward road information into the state equation as a known disturbance term. 3.2 Optimized Problem Establishment The optimization problem in this paper will be constructed in the MPC framework with a mathematical expression that is discrete over the distance domain. Objective Function Establishment. For the design of energy-saving PCC for commercial vehicles, the primary goal is fuel economy, but it is also necessary to consider time economy and driving comfort, so the design objective function is as follows. J =
n
m ˙ f (v(k + i|k), Ft (k + i|k)) v(k + i|k) i=1
+ωr (E(k + i|k) − Er (k + i))2 + q0,i F˙ t2 (k + i − 1) s
(5)
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Er is the reference kinetic energy, calculated from the reference vehicle speed. In the objective function, fuel economy is expressed in the form of cumulative fuel consumption, time economy is expressed as the squared speed tracking error, and comfort is expressed as the squared rate of change in drive force. The coefficients in front of each term are weighting factors, all of which can be adjusted. System Constraint Selection. The system constraints include mainly the physical constraints of the vehicle, the physical constraints of the road as well as the safety constraints, and the driver comfort constraints. Powertrain Constraints. The powertrain constraints are mainly engine output torque range limits related to engine speed, which can be translated into vehicle drive range limits related to vehicle speed after fixing the gear optimization map. Ft,min (v(k)) ≤ Ft (k) ≤ Ft,max (v(k))
(6)
Under most vehicle driving conditions, the change of vehicle speed within the prediction horizon will not be very significant and basically will not reach the boundary of the driving force, so the upper and lower boundaries of the driving force at the current vehicle speed can be used as the limit within the whole prediction horizon. Road Adhesion Restraint. The maximum and minimum drive force available to a vehicle under a given road is determined not only by the powertrain, but also by the road’s adhesion limits. |Ft (k)| ≤ mv gϕ
(7)
ϕ is road adhesion coefficient. Road Security Restraint. In the case of highways, the main consideration for the safety restraint of vehicles is the speed limit. The speed limit of the vehicle is usually determined by two aspects, which depend on the speed limit specified by the road on one hand and on the curvature of the road on the other hand. For car-following conditions, the safety distance or time gap constraint can also be transformed into a speed constraint. vmin (k) ≤ v(k) ≤ vmax (k)
(8)
Driving Comfort Constraints. The comfort constraint, usually considered as a constraint on the jerk, is considered here as a constraint on the rate of change of the vehicle drive. In the case of small changes in slope, the constraints on the rate of change of driving force are equivalent to the constraints on the jerk. F˙ t (k) ≤ F˙ t,max (9) QP Problem Establishment. The optimal control problem built in the MPC framework needs to be transformed into the following normalized QP problem after a series of transformations in order to be solved conveniently by existing solvers. min U T (k)HU (k) + G(k + 1|k)U (k)
U (k)
s.t.Cu U (k) ≥ b(k + 1|k)
(10)
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First, the relationship between the observed sequence and the initial state quantity, the control sequence and the measurable disturbance in the whole prediction horizon needs to be expressed in the form of a matrix calculation equation. Yp (k + 1|k) = Sx x(k) + Su U (k) + Sd D(k)
(11)
⎡
⎤ y(k + 1|k) ⎢ y(k + 2|k) ⎥ ⎢ ⎥ Yp (k+1|k) ⎢ ⎥ .. ⎣ ⎦ . ⎡ ⎢ ⎢ U (k) ⎢ ⎣ ⎡ ⎢ ⎢ D(k) ⎢ ⎣ ⎡ ⎢ ⎢ ⎢ Sx = ⎢ ⎢ ⎣
⎡
⎤
Cc A Cc A2 ⎥ ⎥ Cc A3 ⎥ ⎥ .. ⎥ . ⎦ Cc An
⎢ ⎢ ⎢ ; Su = ⎢ ⎢ ⎢ ⎣
;
y(k + n|k) n×1 ⎤ u(k) u(k + 1) ⎥ ⎥ ⎥ ; .. ⎦ .
u(k + n − 1) d (k) d (k + 1) .. .
⎤
n×1
⎥ ⎥ ⎥ ⎦
d (k + n − 1) Cc Bu 0 Cc ABu Cc Bu Cc A2 Bu Cc ABu .. .. . .
;
n×1
0 0 Cc Bu .. .
··· ··· ··· .. .
0 0 0 .. .
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
Cc An−1 Bu Cc An−2 Bu Cc An−3 Bu · · · Cc Bu ⎤ 0 ··· 0 Cc Bd 0 0 ··· 0 ⎥ Cc ABd Cc Bd ⎥ ⎥ Cc Bd ··· 0 ⎥ . Cc A2 Bd Cc ABd ⎥ .. .. ⎥ .. .. .. . . . ⎦ . . Cc An−1 Bd Cc An−2 Bd Cc An−3 Bd · · · Cc Bd n×n
n×1
⎡
⎢ ⎢ ⎢ Sd = ⎢ ⎢ ⎢ ⎣
After that, the objective function is written in a quadratic form. n T 2 J = y (k + i|k) Qi y(k + i|k ) + q y(k + i|k ) + q0,i u (k + i − 1) s
n×n
(12)
i
i=1
Qi =
q1,i = ωr,i ; q2,i =
;
q1,i q2,i /2 ; q = q4,i q5,i ; q2,i /2 q3,i i
2h13 2h03 ; q3,i = h21 ; q4,i = − 2ωr,i Er (k + i); q5,i = h11 , q0,i . Mv Mv
The objective function of the optimization problem is then transformed into a pure matrix expression by associating Eqs. (11) and (12). Considering that the discrete steps
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within the prediction horizon should be treated equally, the same values are used for the weights at different control steps, which will similarly the expressions. 2 (13) J = y Yp (k + 1|k) + u U (k)2 + y Yp (k + 1|k) ⎡√ ⎤ ⎤ R 0 ··· 0 q0 s 0 ··· 0 √ ⎢0 R ··· 0⎥ ⎢ 0 q0 s · · · 0 ⎥ ⎢ ⎢ ⎥ ⎥
y = ⎢ . . . ⎥ ; ⎥ ; u = ⎢ . .. .. ⎣ .. .. . . 0 ⎦ ⎣ .. . . 0 ⎦ √ 0 0 · · · R n×n 0 0 · · · q0 s n×n
y = q · · · q s; RT R = Qs. 1×n ⎡
It should be noted that when the matrix Q is non-positive it should be made positive by adjusting the parameters associated with it and the energy model fitting coefficients. Then, the objective function is transformed into a quadratic form about the control sequence through an equivalent transformation to obtain the objective function matrix of the normalized QP problem (see Eq. (10)). H = SuT yT y Su + uT u (14) G(k + 1|k) = −2EpT (k + 1|k) yT y Su + y Su Ep (k + 1|k) −Sx x(k) − Sd D(k) After that the constraint of the control quantity is normalized and its upper and lower bound is determined by Eq. (9).
−In×n −Umax (k) U (k) ≥ (15) Umax (k) In×n T T Umax (k) = F˙ t,max · · · F˙ t,max 1×n ; Umax (k) = − F˙ t,max · · · F˙ t,max 1×n . The constraints on the state quantities are normalized as follows, with the upper and lower bounds determined by Eqs. (6)–(8).
−Su (Sx x(k) + Sd D(k)) − Ymax (k) U (k) ≥ (16) −(Sx x(k) + Sd D(k)) + Ymin (k) Su T (k|k + 1) · · · y T (k|k + n) ]T ; Ymax (k) = [ ymax max T (k|k + 1) · · · y T (k|k + n) ]T . Ymin (k) = [ ymin min
Summarizing Eqs. (15) and (16), the inequality constraints for the QP problem is obtained as follows. ⎡ ⎡ ⎤ ⎤ −Umax (k) −In×n ⎢ ⎢ I ⎥ ⎥ Umax (k) ⎢ ⎢ n×n ⎥ ⎥ (17) ⎢ ⎥U (k) ≥ ⎢ ⎥ ⎣ (Sx x(k) + Sd D(k)) − Ymax (k) ⎦ ⎣ −Su ⎦ Su
−(Sx x(k) + Sd D(k)) + Ymin (k)
At the above point, the PCC problem in the MPC framework has been completely transformed into a QP problem.
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3.3 Optimization Problem Solving There are numerous well-established solvers available for the normalized QP problem. In this paper, MATLAB’s own quadprog solver is used to solve the PCC optimization problem established in the previous paper, and the average computational speed of a single optimization is 2.05ms on a computer configured with an i7-10875H CPU @ 2.30GHz, which can satisfy the real-time optimization. Table 1. Table captions should be placed above the tables. Parameter name
Symbol
Parameter value
Overall vehicle mass
mv
49000 kg
Final drive ratio
I0
2.87
Transmission ratio
Ig
[16.41,13.16,11.13,8.92,7.16,5.74, 4.68,3.75,2.97,2.3,1.91,1.53,1.25,1]
Mechanical efficiency
ηt
0.98
Rolling resistance coefficient
f
0.00743
Wheel radius
rw
0.5267 m
Air resistance coefficient
Cd
0.5
Vehicle windward area
Af
4.2 m2
Air density
ρ
1.225 kg/m3
Road adhesion coefficient
φ
0.85
Discrete distance
s
20 m
Predicted step size
N
50
Weighting factor
ωr
3 × 10–11
q0
0.01
4 Simulation In this section, the PCC algorithm designed in this paper is compared with the PCC based on indirect method solving in classical road scenario and real road scenario respectively by SIMULINK simulation, and the effectiveness of the algorithm is proved. Some vehicle parameters and controller parameters are shown in Table 1. 4.1 Simulation Results Typical Road Scenario Simulation Result. The typical road Scenario uses a combination of flat, uphill and downhill road scenarios with a continuous downhill hazard scenario. The reference speed used for the simulation is 60km/h. The road information
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Fig. 3. Gear optimization map.
and the vehicle speed curve, drive force curve, shift curve and fuel consumption curve during the simulation are shown in Fig. 3. The cumulative fuel consumption using the QP solution is 2003.51 g, the 100 km fuel consumption is 31.88L, and the average speed is 60.06 km/h; the cumulative fuel consumption using the indirect method is 2009.88 g, the 100 km fuel consumption is 31.96L, and the average speed is 59.02 km/h. Real Road Scenario Simulation Result. Real road scenario uses the real road data from Yicheng service area to Zhongxiang toll station of 33 km on G55 highway with the same reference speed of 60 km/h. The curve of road information and simulation results are shown in Fig. 4. The cumulative fuel consumption using the QP solution is 7687.51 g, the 100 km fuel consumption is 31.45 L, and the average speed is 60.59 km/h; the cumulative fuel consumption using the indirect method is 7689.22 g, the 100 km fuel consumption is 31.46 L, and the average speed is 59.68 km/h.
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Fig. 4. Gear optimization map.
4.2 Analysis of Simulation Results The simulation results will be analyzed from four perspectives: fuel economy, time economy, driving comfort, and computational speed. Fuel Economy. Compared with the indirect method, the QP solution can save 0.32% of fuel under typical road scenario and 0.022% of fuel under real road scenario. Considering the simulations of both conditions, it can be concluded that the QP-based PCC algorithm is slightly more fuel-efficient than the indirect method-based PCC algorithm, and considering that the latter can save at least 4% of fuel compared with the conventional CC algorithm in previous studies [8, 9], it can be concluded that the PCC algorithm proposed in this paper can achieve 4% fuel savings. Time Economy. Compared with the indirect method, the QP solution can save 1% of time under typical road conditions and 2% of time under real road conditions, which can achieve the improvement of time economy without reducing the fuel economy.
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Driving Comfort. Comparing the speed and drive curves of the two algorithms, it can be seen that both curves of the QP-based PCC algorithm change more gently, which means that the acceleration and jerk are smaller, i.e., the driving comfort of the vehicle is improved. Computational Speed. As mentioned in the previous section on solving optimization problems in the MPC framework, the average speed of a single optimization computation using the QP method is 2.05 ms. The average speed of a single optimization computation using the indirect solution method in the previous work is related to the number of iterations of the algorithm, and the minimum speed of a single optimization computation is 0.95 ms. The computational speed of both algorithms is in the order of milliseconds, and both can achieve real-time optimization. To conclude, the PCC algorithm proposed in this paper can achieve the improvement of time economy and driving comfort compared with the algorithm based on the indirect method of solving, while ensuring the fuel economy and real-time optimization.
5 Summary and Future Work In this paper, a hierarchical control approach is used to achieve simultaneous real-time optimization of vehicle speed and gear. The lower layer controller optimizes the gears offline with the goal of energy saving, avoiding the problem of slow solution of complex mixed integer programming problems; the upper layer controller, using vehicle kinetic energy and driving force as state quantities, linearizes the nonlinear vehicle model and constructs a quadratic programming mathematical problem, which can take into account the fuel economy, time economy and driving comfort of the vehicle, and can be constrained for both state and control quantities, and can be solved by a well-developed method. In the future, the method can be applied to electric vehicles with gearbox, using the characteristics of motor braking energy recovery to uniformly fit the energy consumption of drive and brake when the motor brake can meet the braking demand, and combine the drive and braking force into one control quantity for optimization. In addition, the speed prediction of the previous vehicle can be imported and transformed into a reference vehicle speed and speed constraint to achieve the car-following condition.
References 1. Masson-Delmotte, V., Zhai, P., Pörtner, H.O., et al.: Global warming of 1.5 °C. In: An IPCC Special Report on the Impacts of Global Warming of 8, 1(5) (2018) 2. Van Fan, Y., Perry, S., Klemeš, J.J., et al.: A review on air emissions assessment: transportation. J. Clean. Prod. 194, 673–684 (2018) 3. Dudley, B.: BP energy outlook. In: Report–BP Energy Economics (2020) 4. Sciarretta, A., Nunzio, G.D., Ojeda, L.L.: Optimal ecodriving control: energy-efficient driving of road vehicles as an optimal control problem. IEEE Control Syst. Mag. 35(5), 71–90 (2015) 5. Nie, Z., Farzaneh, H.: Role of model predictive control for enhancing eco-driving of electric vehicles in urban transport system of Japan. Sustainability 13(16), 9173 (2021) 6. Yoon, D.D., Ayalew, B., Ivanco, A., et al.: Predictive kinetic energy management for an add-on driver assistance eco-driving of heavy vehicles. IET Intel. Transport Syst. 14(13), 1824–1834 (2020)
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7. He, C.R., Alan, A., Molnár, T.G., et al.: Improving fuel economy of heavy-duty vehicles in daily driving. In: Proceedings of the 2020 American Control Conference (ACC) (2020) 8. Chu, H., Guo, L., Gao, B., et al.: Predictive cruise control using high-definition map and real vehicle implementation. IEEE Trans. Veh. Technol. 67(12), 11377–11389 (2018) 9. Chen, H., Guo, L., Ding, H., et al.: Real-time predictive cruise control for eco-driving taking into account traffic constraints. IEEE Trans. Intell. Transp. Syst. 20(8), 2858–2868 (2019) 10. Liu, J., Pattel, B., Desai, A.S., et al.: Fuel efficient control algorithms for connected and automated line-haul trucks. In: Proceedings of the 2019 IEEE Conference on Control Technology and Applications (CCTA) (2019) 11. Shao, Y., Sun, Z.: Vehicle speed and gear position co-optimization for energy-efficient connected and autonomous vehicles. IEEE Trans Control Syst Technol 1–12 (2020)
Charge Transport and Energy Accumulation Breakdown Probability Distribution Characteristics of Polyimide Gao Ziwei1
, Min Daomin2(B) , Yang Lingyu1 , Duan Yanan1 , Wu Qingzhou2 , Zhu Shenlong3 , and Qin Shaorui3
1 Xi’an Jiaotong University, Xi’an 710049, China {gaoziwei,3121104192,ynduan}@stu.xjtu.edu.cn 2 Institute of Fluid Physics, Academy of Engineering Physics, Mianyang 621022, China [email protected], [email protected], [email protected] 3 Anhui Electric Power Research Institute, Hefei 230031, China [email protected], [email protected]
Abstract. Polyimide (PI) has excellent electrical insulation properties and is widely used in pulsed power devices and new energy vehicles. It is of great significance to study the breakdown characteristics and mechanism of insulating materials to ensure the safe and reliable operation of electrical equipment. The key problem is to establish the correlation between the spatial dispersion of polyimide charge transport parameters and the breakdown probability distribution characteristics. In this paper, polarization, trap distribution, carrier mobility and breakdown Weibull distribution of polyimide were studied. Then, considering the physical processes such as charge transport, molecular chain displacement and charge energy accumulation, the breakdown probability model of space charge and energy accumulation modulation was established. The breakdown probability distribution characteristics of polyimide were calculated by simulation, which follows Weibull distribution, and the relationship between characteristic breakdown strength and sample thickness follows inverse power function. The breakdown Weibull distribution curves with different shape parameters were obtained by adjusting the dispersion of charge transport parameters. By comparing the simulation results with the experimental results, the variances of four characteristic parameters of charge transport, such as carrier mobility, attempted escape frequency, trap energy level and trap density, are obtained by inversion. The dispersion of trap levels is a key factor affecting the shape parameters of breakdown Weibull distribution. The probability distribution of the breakdown strength is caused by the difference of charge trapping effect of traps in different spatial locations. With the increase of sample thickness, the dispersion of trap energy level increases, and the Weibull distribution shape parameter decreases gradually. The correlation between the spatial dispersion of trap energy levels and the breakdown probability distribution is revealed, which provides theoretical basis and model support for the design and risk assessment of high voltage power equipment. Keywords: Weibull distribution · Size effect · Charge transport · Breakdown strength · Polyimide © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1089–1107, 2023. https://doi.org/10.1007/978-981-99-1027-4_114
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1 Introduction Energy is the main driving force for economic and social development and civilization progress. In response to fossil energy shortages and climate change, it is urgent to develop renewable energy [1–3]. The corresponding development of high-voltage direct current transmission, electric vehicles, wind power generation and other fields has promoted the development and utilization of renewable energy. Polyimide (PI) has excellent electrical insulation, high temperature resistance, dielectric energy storage and mechanical properties, so it has been widely used in AC and DC power systems, electronic equipment and electric vehicles and other fields [4, 5]. The breakdown of polymer insulation is the key factor that determines the stable operation of power equipment. It is generally believed that the breakdown of polymer medium under strong electric field is related to the physical processes such as charge accumulation, electric field distortion, current multiplication and energy accumulation [6–8]. Under DC voltage, the charge is injected into the medium and accumulates near the electrode-medium interface. The accumulated charge causes the electric field distortion and finally leads to the breakdown phenomenon. The breakdown of polymer is affected by many factors, so is difficult to analyze. In the early stage, through statistical research on the breakdown strength of polypropylene and aromatic polymers, it is found that the strong dependence of breakdown strength in polymers decreases with the increase of thickness, and the inverse power function relationship between breakdown strength and thickness in aromatic polymers is found [9–11]. In more sophisticated experiments, the researchers founded the same pattern on PI [12] films and Biaxially oriented polypropylene (BOPP) [13] films. Tanaka [14, 15] tested the distribution of space charge, electric field and external circuit current density of Low-density polyethylene (LDPE) and crosslinked polyethylene under strong electric field. It is founded that the electric field distortion affected the breakdown of polyethylene, but the reason of breakdown was attributed to heat accumulation. Chen [16] considered the space charge injection, transport and conduction processes in LDPE, and established a polymer breakdown model based on space charge accumulation and electric field distortion and calculated the inverse power function relationship between the breakdown strength and the thickness. Pitike [17] believed that in the initial situation there were randomly distributed conductive channels in the medium. The conductive channels would release energy and extend. When the conductive channels in the medium is through, the medium is broken down. Based on this phenomenon, the breakdown model of phase field method was established. Then they calculated the relationship between dielectric breakdown strength and thickness. The results show that the breakdown strength of the dielectric has an inverse power function relationship with the thickness close to -0.5. In addition, Wang [18] discovered the new mechanism of dielectric breakdown caused by conductive particles, Schneider’s [19] Griffith type energy release rate dielectric breakdown model based on space charge-limiting conductance, and Sun’s [20] theoretical analysis of dipole scattering and phonon scattering. We has established the breakdown model of charge transport and molecular chain energy accumulation modulation (CTMD). By quantitative experiments on commercial
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PI film samples, the charge transport parameters controlled by the polymer chain structure the characteristic parameters of the dielectric itself were extracted. Meanwhile, the characteristic breakdown field intensity and probability distribution were recorded in detail. Based on the CTMD model, the simulation results were similar to the experimental results. Combined with the time and space distribution characteristics of each physical quantity in the model, the reason for the probability distribution characteristics of polyimide was revealed. The causes of the thickness scale effect of PI thin films were analyzed from the perspective of the change of free volume in the medium caused by carrier transport and molecular chain displacement. In this paper, the accuracy of CTMD model in breakdown Weibull distribution simulation was verified, and this model provided a new simulation method for dielectric breakdown Weibull distribution. This model can reasonably predict dielectric insulation breakdown performance, and provide theoretical basis and model support for the structural design, safe operation and risk assessment of high voltage equipment.
2 Experiment 2.1 The Sample Processing The model 6501 PI samples with 30–100 µm thickness were all from Baoying, Yangzhou Jinggong Insulation Material Limited Company. Before the experiment, the samples of each thickness should be dried and gold spraying. The samples were heated and dried for 12 h in an incubator at 100 °C. After that, both sides of the sample were sprayed with 15 mm gold electrodes using an ion sputtering coater. The thickness of each sample was the thickness before gold spraying. 2.2 Characterization and Performance Testing The broadband dielectric spectrum testing was performed using Concept 80 from Novocontrol Technologies, Frankfurt, Germany. The dielectric spectrum of 100 µm thickness samples was measured from 10 to 90 °C at the 10–1 –106 Hz frequency and 1Vrms voltage. The surface potential and carrier mobility of 100 µm thickness PI samples were tested using Surface Potential Decay (SPD) experiments. The needle electrode of SPD conducts corona discharge on the surface of the samples to generate positive and negative charges. The charges move to the surface of the sample and deposit under the action of the gate electric field. Then, the surface potential was measured using the high voltage electrostatic meter (P0865, Trek, Lockport, NY, USA) and the non-contact probe (3453ST, Trek, Lockport, NY, USA). And the carrier mobility was calculated. The positive corona discharge voltages of the needle electrode and grid in this paper were 12 kV and 8 kV, and the negative corona discharge voltages were −12 kV and −8 kV. Thermally stimulated depolarizing current (TSDC) experiments were performed using a Concept 90 from Novocontrol Technologies, Frankfurt, Germany. Before the experiment, the 100 µm sample was placed under 180 °C and 1000 V for 30 min. After the polarization, cooled the sample to −100 °C with liquid nitrogen and short-circuited for 10 min. During the experiment, the heating was heated to 290 °C at 3 °C min−1
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heating rate. The pico-ammeter was used to measure the depolarization current in the experiment. The samples of each thickness were tested for DC breakdown respectively. The breakdown device used was HJC-100 kV from Yangzhong, Huayang Instrument Limited Company. Under the experimental conditions of 30 °C transformer oil (Karamay 25# of China National Petroleum Corporation), the DC breakdown experiment was carried out using a spherical copper electrode with 25 mm diameter and 1000 Vs−1 boosting rate. 2.3 A Subsection Sample Figure 1 shows the variation of relative complex permittivity relative to frequency for the 100 µm sample at 10–90 °C. In the logarithmic coordinate, the real part ε and the imaginary part ε" of the complex relative permittivity show a certain law with frequency and temperature. As the frequency increases, the real part decreases slightly. The increase of temperature also decreases the real part significantly. The imaginary part changes little when the frequency is lower than 102 Hz, and increases significantly with the increase of frequency. The increase in temperature shifts the inflection point of the dielectric constant toward high frequencies. Taking the sample at 30 °C as an example, as the frequency increases from 10−1 Hz to 106 Hz, the real part decreases from 3.35 to 3.28. When the frequency is lower than 5 × 102 Hz, the dielectric loss tangent value is less than 3 × 10–3 . According to the dielectric loss formula ε"/ε , under the action of DC voltage, the temperature rise caused by dielectric loss can be ignored. (b)
10-1
3.4 3.3 3.2
Loss tangent
Relative permittivity
(a)
3.1 3.0 2.9 2.8 10-1
10oC 50oC 90oC 100
30oC 70oC 101
102 103 104 Frequency(Hz)
105
106
10-2
10-3 -1 10
10oC 30oC 50oC 70oC 90oC
100
101
102 103 104 Frequence(Hz)
105
106
Fig. 1 The relationship of PI complex permittivity varying with frequency at different temperatures
Figure 2 shows that the experimental results of the surface potential of the 100 µm sample changes with time under positive and negative corona discharges. During the charging process, the high-energy ions emitted by the needle tip electrode will collide with air molecules to generate ionization, and a large number of positive and negative charges will be deposited on the surface of the material, forming the electric field inside the material. During the experiment, the surface charges migrate to the ground electrode causing the potential to decay. Figure 2 shows that the surface charge decay rate is variable, and the maximum value of the potential decay rate corresponds to the carrier arrival time at the ground electrode. Since the times at which positive and negative
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charges correspond to the maximum decay rate are not the same, the mobilities of positive and negative charge carriers are different. The transit time t T is defined when the carriers reach the ground electrode, and the carrier mobility under the influence of shallow traps can be obtained by comparing the extreme values of the potential decay curve curvature. Fit the experimental results of potential decay with the exponential function, as shown in Fig. 2, the relationship between the tdϕ s /dt and time t can be obtained. The time corresponding to the peak value is the transit time t T . The carrier mobility can be calculated in the expression [21], (1) μ0(e,h) = d 2 ϕs0 tT where μ0(e,h) is the carrier mobility, in m2 V−1 s−1 , (e) and (h) represent electrons and holes; d is the thickness, in m; ϕ s0 is the surface potential at the initial moment, in V. Figure 2 shows that the initial potentials after positive and negative corona charging are 4769.95 V and 6601.38 V, and the transit times are 84s and 38s. According to formula (1), the electron mobility under the influence of shallow traps is 3.92 × 10–14 m2 V−1 s−1 , and the hole carrier mobility is 2.48 × 10–14 m2 V−1 s−1 . negative charge positive charge
6000 5000 4000 3000 2000
1000 800
Transit time tN=38 s tP=84 s
t|dφs/dt| (V)
Absolute surface potential (V)
7000
1000 0 100
600 400 200 0 0
200
400
Time(s)
101
600
Time(s)
102
103
Fig. 2 Time variation of surface potential of 100µm thickness PI sample
Figure 3 shows the TSDC experimental and fitting results of 100µm PI samples. It is observed that there is an obvious relaxation peak at 70 °C and may have other relaxation peaks around 120 °C, which proves the existence of the relaxation process in this experimental temperature range. Using the TSDC theory [22], 1 EA − jTSDC (T ) = B exp[− kB T βτ0
T
T0
EA dT ] exp − kB T
(2)
where jTSDC is the thermally stimulated depolarization temperature, in Am−2 ; B is a constant, in Am-2; E A is the activation energy of relaxation, in eV; τ 0 is the relaxation time constant, in s; β is the heating rate, in o Cs−1 ; k B is the Boltzmann constant; T 0 , T’ represent the initial temperature and final temperature, in o C. The TSDC fitting results show that there are peaks at 69 °C, 87 °C, 109 °C and 135.5 °C. In the peak temperature, we obtained the activation energy and relaxation time of the corresponding relaxation. With the relaxation temperature increases, the
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Current density (Am-2)
3.5x10-7 3.0x10-7 2.5x10-7
Experiment Fitting 1 Fitting 2 Fitting 3 Fitting 4 Sum of 1, 2, 3, and 4
2.0x10-7 Epoling=2.5 kV/mm o 1.5x10-7 Tpoling=180 C
1.0x10-7 5.0x10-8 0.0 -90 -60 -30
0 30 60 90 120 150 Temperature (oC)
Fig. 3 Experimental results and fitting results of thermal stimulation depolarization current for 100 µm PI sample.
corresponding activation energies show an increasing trend. The peaks at 69 °C, 87 °C and 109 °C may correspond to the process of shallow trap-assisted carrier migration in PI. And the peak at 135.5 °C may correspond to the process of deep traps trapping carriers to form space charges in PI. The breakdown process was simulated with the 0.83 eV activation energy of the relaxation peak at 135.5 °C as the deep trap parameter (Table 1). Figure 4 is the DC breakdown Weibull distribution of different PI samples at 30 °C. The two-parameter Weibull distribution [23] is widely used in dielectric breakdown performance and reliability analysis, and its expression is: Pi = 1 − exp[−(Ebi /α)β ], (i = 1, 2, ..., n)
(3)
where E bi and Pi represent the ith breakdown strength and its breakdown probability. Using a set of numbers to sort the data from small to large; α is the characteristic breakdown strength (the probability occurs 63.2%), in kVmm−1 ; β is the shape distribution parameter, which characterizes the dispersion degree of breakdown strength and is negatively correlated with the dispersion degree. The Fig. 4 shows that the characteristic breakdown strengths of the 30, 40, 50, 75 and 100 µm PI samples are 625, 574, 542, 457 and 382 kVmm−1 , and the shape parameters are 61.65, 26.51, 26.01, 15.09, and 15.89. With the thickness increases, the DC breakdown strength of the PI sample gradually decreases. And the dispersion of PI breakdown strength increases gradually, which is expressed as the decrease of shape parameter.
3 Modeling and Simulation of CTMD 3.1 Charge Transport and Molecular Chain Energy Accumulation Modulation Model Figure 5 is the charge transport and molecular chain energy accumulation modulation (CTMD) model’s schematic diagram under DC voltage. The upper and lower ends are
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Probability (%)
90 63.2 50
10 5 30μm
1 300
40μm
50μm
75μm
100μm
400 500 600 Breakdown strength (kVmm-1)
Fig. 4 Fitting results of DC breakdown Weibull distribution and inverse power function of different PI samples.
the cathode and anode of the electrode; and the middle is the high-molecular polymer dielectric material which the thickness is d. When applying a high field, electrons and holes must overcome the injection barrier between the electrode and the medium, and are injected from the metal electrode into the dielectric [24]. The electrons and holes are transported inside the medium. Due to the presence of a large number of polar groups (traps) inside the polymer dielectric, the traps trap charges and limit the charges migration. The trapped charges are called trap charges, which are driven by the Coulomb force to drive the displacement of the molecular segments, resulting in the expansion of the free volume. The increase of free volume causes free charges to accumulate more energy. Breakdown of the polymer dielectric occurs when the charge energy exceeds the trapping capability of the deep trap. e
e e
migration
e
e e
e
e
e
e
recombination
h h h
h
h
e
trapping
h e
e
e
h
e
e
h
h
h
e
e
trap
h
de-trapping
h
h
h
The molecular chain segments are displaced by Coulomb forces
h
h h
Fig. 5. Schematic diagram of DC voltage CTMD model
According to the energy band theory, physical and chemical defects on the molecular chain will form localized state energy levels near the conduction band, valence band or Fermi level, resulting in shallow traps or deep traps. During the migration process of free electrons or holes, trapping, de-trapping, and recombination will occur. Trap is a phenomenon in which free charges are captured by traps. The trapping charges on molecular chains can cause steric accumulation of charges. Under the action of the Coulomb force, the charge will drive the molecular chain to undergo local displacement, resulting in an increase in the local free volume, making it easier for the free charge to accumulate energy. At the same time, the electric field inside the medium will be
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distorted due to the accumulation of electric charges, so that the maximum electric field strength inside the medium will gradually increase with the accumulation of electric charges. When the energy of the trap charge itself is higher than the trap barrier, it can be de-trapped through the thermal excitation process and re-migrate on the molecular chain. Meanwhile, charge recombination behavior occurs when holes and electrons in the material meet. k ramp is the ramp voltage rising rate. It was applied between the two poles as the boundary condition of the CTMD model. When the cathode potential is set to zero, the voltage at the anode is the applied voltage. After the voltage is applied, the anode potential or the applied voltage satisfies the integral equation, ϕ(d , t) = Vappl (t) = kramp tramp
(4)
where V appl , in V; k ramp , in Vs−1 , t ramp is the ramp voltage action time, in s. Under the applied electric field, the electrodes inject electrons and holes into the medium through Schottky thermal emission [24]. The current density of charge injection is determined by the injection barrier between the dielectric and the electrode, the temperature at the interface, and the electric field strength, ⎧
⎪ ⎨ jin(e) (t) = AT 2 exp −ϕin(e) kB T × exp eE(0, t)/4π ε0 εr kB T
(5)
⎪ ⎩ jin(h) (t) = AT 2 exp −ϕin(h) kB T × exp eE(d , t)/4π ε0 εr kB T where jin(e) (t) and jin(h )(t) represent the current densities of electrons, in Am−2 ; ϕ in(e) and ϕ in(h) are the electron and empty the effective injection barrier of the hole, in eV; A is Avogadro’s constant (=1.20 × 106 Am−2 K−2 ); e is in C; ε0 is the vacuum dielectric constant; εr is the material the relative permittivity of; E(0, t) and E(d, t) are the electric fields at the x = 0 and x = d interfaces. Due to the electric field distortion created by the space charge, the electric field inside the dielectric cannot be completely shielded. The free charge in the material will migrate to the corresponding electrode under the electric field force, then form the conduction current. Therefore, the current density of electrons and holes in the dielectric material is related to the carrier mobility, charge density and electric field. It satisfies the constitutive equation [25–27], jc(e) (x, t) = qfree(e) (x, t)μ0(e) E(x, t) (6) jc(h) (x, t) = qfree(h) (x, t)μ0(h) E(x, t) where jc(e) and jc(h) are the conduction current densities, in Am−2 ; qfree(e) and qfree(h) are the densities of free electrons and free holes, in Cm−3 ; E is in kVmm−1 . The probability of free charges being trapped by deep traps while migrating within the medium is positively related to the carrier mobility and deep traps’ density [28, 29], also inversely proportional to the dielectric constant. That is, Ptr(e,h) = eN T(e,h) / ε0 εr . The escape probability of the trapped charge at the center of the deep trap is jointly determined by the trap energy level and temperature, Pde(e,h) = vATE exp(-uT(e,h) /k B T ). Where the vATE is the frequency of the carrier tries to escape, in s−1 .
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The accumulation of space charges will lead to the distortion of the electric field inside the dielectric material, so the electric potential inside the material needs to be recalculated to obtain the electric field at each position [30]. The relationship between the potential ϕ and the space charge q satisfies the Poisson equation [27, 28]. qfree(e) (x, t) + qtrap(e) (x, t) qfree(h) (x, t) + qtrap(h) (x, t) − (7) ∂ 2 ϕ(x, t) ∂x2 = − ε0 εr ε0 εr The equation boundary conditions ϕ(0) = 0V, ϕ(d,t) = V appl (t)V. In the equation, e is the amount of elementary charge, in C. In polymers, molecular chains and polar groups are connected by covalent bonds, and the deep traps mostly exist in polar groups. When the trapped charge stays in the trap, it will be affected by the continuous Coulomb force to drive the displacement of the molecular chain [26, 31]. Molecular segments containing electron traps move toward the anode, and molecular segments containing hole traps move toward the cathode, resulting in an expansion of the free volume. The size of the trap energy level determines how long the trap charge is trapped. The deeper the trap level, the stronger the ability to trap the charge, the longer the charge stays in the trap, and the longer the molecular chain moves under the influence of the Coulomb force. Under the influence of the electric field, the equation of motion is: (8) dλ dt = μ0 E − λ τmol where λ is the molecular chain displacement, in m; μmol is the molecular chain mobility, which decreases with the increase of the deep trap energy level, in m2 V−1 s−1 ; τ mol is the molecular chain relaxation time constant, in s. The τ mol is equal to the residence time of the charge in the trap, which is related to the trap energy level and temperature, τ mol = τ 0 exp(uT /k B T ). The free charge in the free volume will be accelerated by the electric field to accumulate energy, so the energy of the carrier depends on the strength of the local electric field and the length of the free volume. The continuously expanding free volume will make it easier for free charges to accumulate energy, and when the energy is large enough, the carriers will continue to migrate in a direction and cause breakdown [32]. Assuming that the length of the free volume is equal to the displacement of the molecular chain, λfv (t) = λmol (t), the breakdown criterion of the CTMD model is expressed as [eλfv (t)E(t)]max ≥ uT . When the energy is not enough to break down the medium, a part of the energy will be transferred to the molecular chain in the charge capture process, resulting in energy dissipation. This process is beneficial to the improvement of the dielectric breakdown strength. 3.2 Parameter Extraction According to the analysis of the DC breakdown process of the dielectric, it is found that the transport of charge carriers and the energy accumulation in free volume are the key leading to the breakdown of the dielectric material. Four characteristic parameters of charge transport were extracted from the carrier transport and molecular chain displacement breakdown process: attempted escape frequency, carrier mobility, trap energy level and trap density.
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The decrease of the attempted escape frequency and the increase of the charge injection barrier will reduce the number of carriers injected into the medium across the barrier, and reduce the density of mobile carriers in the medium, then increase the resistivity of the dielectric material. At the same time, due to the reduction of the carrier density inside the medium, the space charge accumulation effect will be reduced, and the breakdown strength of the material will be improved. The decrease in carrier mobility will reduce the internal current density and increase the resistivity and breakdown performance of the dielectric. The increase of trap energy level and trap density will enhance the trapping effect of traps, reduce the mobility and current density of carriers, then increase the internal resistivity of the medium; at the same time, the number of trapped carriers will increase and they will be more difficult to escape. The space charge of the same polarity formed near the electrode will greatly weaken the electric field at the surface of the electrode/dielectric, and limit the charge injection process. The carrier energy will be dissipated in the trap trapping process, and the reduction of electric field distortion will also slow down the energy accumulation process of carriers. Finally, it will improve the breakdown performance of the material. In simulation, the change of each transport parameter will cause the change of the molecular chain displacement characteristics of the medium itself and the change of the transport characteristics of carriers in the medium, thereby influence the breakdown strength of the material. The four charge transport parameters were set as expected values (from the experimental results) as shown in Table 2, and the 15-dimensional parameters obeying the Gaussian distribution were used as random parameters. The carrier transport and fluctuations in molecular chain displacement and free volume expansion can be simulated when the variance of the random variable is non-zero. The standard deviation of the variance was adjusted separately until it was consistent with the experimental results. Table 1. TSDC parameter fitting results E A (eV)
B (Am−2 )
τ 0 (s)
69
0.60
1.60 × 10–4
4.88 × 10–7
87
0.63
1.40 × 10–4
4.89 × 10–7
109
0.65
1.35 × 10–4
1.04 × 10–6
135.5
0.83
1.00 × 10–4
2.01 × 10–8
Peak temperature (o C)
Based on the CTMD model, the Matlab uses high-order precision discontinuous Galerkin method and finite element method to numerically solve the charge continuity equation and Poisson equation. It is used to simulate the change of the breakdown strength of polyimide under the influence of different thickness samples and different transport parameters. In the simulation, the temperature was set to 303 K, the same as the experiment, and the boost rate was set to 1000 Vs−1 .
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Table 2. Parameter setting Parameter
Unit
Expectation
Standard deviation range
Attempted escape frequency(υ ATE )
s−1
3.24 × 107
0–0.6
Electron mobility(μe )
m2 V−1 s−1
3.92 × 10–14
0–0.64
Hole mobility(μh )
m2 V−1 s−1
2.48 × 10–14
0–0.64
Electron and hole trap levels(uT )
eV
0.83
0–0.005
Electron and hole trap densities(eN T(e,h) )
Cm−3
95
0–0.16
Electric field strength(V/m) 8x108 30
position(µm)
10
20
5x10
4x108
-5.8x102 10
3x108
0
5
(e) 100
2.1x10-10
position(µm)
5.6x103
0 0 10 15 0 time(s) (g) Electric field strength(V/m) 8 100 8x10
2.8x10
3
1.5x103 1.0x10 0
10
20 time(s)
30
3x10
8.5x10
8
2x108
20
10x10 0
0 0
10
20 time(s)
30
0.00 10 time(s)
15
Electron energy (eV) 0.83 0.73
80
0.62 0.52
1.1x10-9 60
4x108 40
0.10 5
1.3x10-9
5x108 60
60
0.21
0 0.0 0 10 15 time(s) (h) Molecular displacement (m) 1.7x10-9 100
80
6x108
2
-1.3x103
0
5
1.5x10-9
7x108 80
4.2x103
20
0.31
10x107 5
0.52 0.41
2x10
7.0x103
40
0.62
8.5x10-10
-4.7x103
8.3x103
60
0.73 20
-2.6x10
10
8
-6.8x103 0 0 10 15 time(s) (f ) Space charge density(C/m3) 9.7x103 100
80
1.1x10
-9
6.4x10-10 10 4.3x10-10
3
0
20
8
1.5x103
-9
1.3x10-9
6x108
5.6x103 3.5x103
1.5x10
7x10
7.6x10
Electron energy(eV) 0.83
Molecular displacement (m) 1.7x10-9 30
8
3
20
(d)
(c)
Space charge density (C/m3) (b) 9.7x103 30
(a)
30
0.41
-10
40
6.4x10-10
40
0.31 0.21
20
4.3x10-10 20 2.1x10-10
7
0.0
0 0
10
20 time(s)
30
0.10 0.00
0 0
10
20 time(s)
30
Fig. 6. The space charge density (a), electric field (b), molecular chain displacement (c), electrostatic energy distribution (d) of the 30 µm sample; and the same as the 100 µm sample (e, f, g, h)
3.3 Simulation and Results Analysis Figure 6 is the CTMD model simulation results of 30 and 100 µm PI specimens. Taking the 30 µm PI as an example, in the first 4 s, the applied electric field has not yet reached the critical electric field for charge injection, and the charge injection in the medium is relatively small; after 4 s, the applied electric field reaches a certain value, and the charge injection speed increases significantly. Figure 6a shows that with the continuous increase of the applied voltage V appl , more charges were injected into the medium and captured by the traps to form space charges of the same polarity, which accumulated near the electrodes. A large accumulation of the same polarity charges prevented the migration of charge carriers to the interior of the medium. With the extension of the pressurization time, the accumulation of space charge near the electrode became more and more obvious. The space charge densities near the anode of the dielectric at 5, 10, 15 and 18 s were 1441.36, 3897.72, 7023.97 and 9148.66 Cm−3 . Since the space charge gradually developed to the inside of the medium, the positive and negative charges would meet and neutralize each other in the middle
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of the medium, so the accumulation of space charges in the middle of the medium was less. Also taking the above medium as an example, the space charge densities near the anode, the middle and the cathode of the medium at 15s were 7023.97, −4.19 and − 4855.37 Cm−3 . Figure 6b is the electric field distribution diagram along the electric field direction inside the sample. In the first 4s, the space charge accumulation was less, the distortion to the electric field is smaller, and the electric field inside the medium was lower; increase, the electric field inside the medium was obviously enhanced. At 5, 10, 15 and 18s, the highest field strength inside the medium was 219.43, 418.70, 630.81 and 758.13 kVmm−1 . When the applied electric field was very large, the electric field inside the medium would be obviously distorted, and the electric field strength would gradually increase from the position close to the electrode to the middle of the medium. The maximum value of the electric field strength appeared in the middle part of the medium. This change in electric field strength is closely related to the accumulation of space charges. Where the dielectric is close to the electrode, a large amount of the same polarity space charges accumulate. According to the Poisson equation, the same polarity space charges will establish an electric field opposite to the applied electric field, weakening the equivalent electric field near the electrode. At the same time, the electric field inside the medium will be stronger than the applied electric field due to the superposition of the space electric field, and it will become stronger with time and charge accumulation. At 15s, the electric field strengths near the anode, the middle, and the cathode of the dielectric were 127.13, 630.81, and 122.39 kVmm−1 . Figure 6c shows that the molecular chain displacement changed with time. When the space charge was captured by the traps in the medium, the captured charges would be directionally displaced by the electric field force, thereby pulling the connection with the polar group. The molecular chain moved, resulting in the expansion of the free volume inside the dielectric medium. Since the glass transition temperature of PI is much lower than room temperature, the length of free volume is extremely small at this temperature, and the free volume length can be equal to the displacement value of molecular chain. Figure 6d is the spatial distribution of electron energy inside the medium, since the electron energy is related to the electric field and the free volume length. The increase of the electric field strength and the free volume length make it easier for the carriers to accumulate energy in the electric field. When the maximum energy umax = (eEλ)max of the electron carrier exceeds the trap energy level uT , the local current will multiply, which will lead to a sharp increase in the temperature of the medium and eventually lead to electrical breakdown. Figure 6e, f, g, h shows the CTMD model simulation results of the 100µm PI specimens. Compared with the 30 µm sample, it can be seen that the DC breakdown strength decreases gradually with the increase of thickness. When the sample thickness is 30 µm, the DC breakdown strength is 626.18 kVmm−1 , and when the sample thickness is 100 µm, the DC breakdown strength is only 380.21 kVmm−1 , which is almost consistent with the experimental results 625.11 kVmm−1 and 382.87 kVmm−1 . In the CTMD model, after the carriers trapped by the molecular chains with deep traps, they were displaced under the action of the electric field, resulting in an increase in the free volume and a gradual increase in the ramp voltage with time. The increase in the electric
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field and length of the free volume will allow the carriers to accumulate more energy. When the carrier energy was large enough, it would cross the trap barrier and eventually break down the medium. 3.4 Discussion on Simulation Results of Weibull Distribution Under each of the thickness PI sample, we adjusted the variance of each charge transport parameter random variable individually, and obtained a set of calculation results of breakdown strength. Then it was fitted with Weibull distribution. Figure 7 is the breakdown strength calculation results obtained by changing the random variable standard deviation σ of the four charge transport parameters of carrier mobility, attempted escape frequency, trap energy level, and trap density for the 30 µm sample.
Fig. 7. Weibull distribution of charge transport parameters in carrier mobility (a), attempt to escape frequency (b), trap energy level (c), trap density (d).
In Fig. 7a, when the carrier mobility standard deviation σ (μ0 ) are 0.01, 0.2, 0.43, 0.5, 0.6, and 0.7, their Weibull shape parameters are 3588.22, 108.77, 76.87, 50.19, 27.51, and 20.58. In Fig. 7b, when the standard deviation σ (ν ATE ) of the attempted escape frequency are 0.01, 0.025, 0.05, 0.1, 0.2, 0.3, 0.4, their Weibull distribution shape parameters are 489.44, 139.28, 54.20, 35.56, 20.86, 11.98, 8.79. In Fig. 7c, when the standard deviation σ (E T ) of trap energy levels are 0.0001, 0.001, 0.003, 0.004, 0.005, 0.007, 0.008, the Weibull shape parameters are 1208.94, 81.54, 30.97, 44.20, 21.93, 15.27, 12.79. In Fig. 7d, when the standard deviation of trap density σ (N T ) are 0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.25, the Weibull shape parameters are 208.97, 81.22, 46.88, 51.02, 24.01, 30.18, 16.60. The results have shown that, based on this model, if the four charge transport parameters of carrier mobility, carrier attempted escape frequency, trap energy level, and trap
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density are set as random parameters obeying Gaussian distribution, the obtained simulation results obey Weibull distributed. When the standard deviation of the Gaussian distribution increases, the dispersion of random parameters in the model will increase, so that the slope of the Weibull distribution curve decreases and the shape parameters decrease. In order to better explore the effect of the standard deviation σ of the transport parameter random variable on the shape parameter, a curve of the shape parameter changing with the standard deviation σ of the transport parameter was drawn. Extracted the Weibull shape parameters from Fig. 7. Then plot the shape parameter versus the standard deviation of the charge transport parameters. Since the Weibull shape parameter is the embodiment of the breakdown dispersion of the dielectric material, the larger the shape parameter, the weaker the dispersion, which means that the dielectric material is more uniform and more stable. In the experiment shown in Fig. 4, with the increase of the thickness of the PI sample, the breakdown strength and shape parameters gradually decreased.
Fig. 8. (a) Relationship between Weibull characteristic voltage and the standard deviation of charge transport variables; (b) 30 µm PI trap energy level standard deviation 0.003 breakdown probability curve.
Figure 8a shows the relationship between the Weibull shape parameters of the 30 µm PI sample and the standard deviation of the four charge transport parameters, and the comparison between the simulation and experimental results when only the standard deviation σ (E T ) of the trap energy level is adjusted to 0.003. As the standard deviation σ increased, the shape parameters of the simulation results decreased. This is because the parameters of charge transport parameters regulate the transport behavior of carriers in the dielectric. The increase of the standard deviation will increase the control range of the parameters of charge transport, increase the volatility of the action on carriers, and expand the breakdown time. The range of possible voltages, resulting in an increase in the dispersion of the breakdown simulation results and a decrease in the shape parameters. Comparing the downward trend of the four transport parameter curves, it is found that with the increase of the standard deviation of the Gaussian distribution, the shape parameters all show a trend of rapid decline at first and then a gentle decline. The decreasing trend of the shape parameters of the Weibull distribution obtained by the simulation calculation slows down near the experimental value, which proves that with the increase of the standard deviation, the difficulty of regulating the carrier transport with only a single transport parameter will increase. It represents in the actual working conditions,
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due to the different processing technology and environment, the carrier transport in the dielectric is jointly affected by the distribution of many parameters, and finally shows the dispersion change of the breakdown Weibull distribution. Comparing the decline speed of the transport parameter curve, it is found that the variable of trap energy level has the fastest decline speed; the two parameters of attempted escape frequency and trap density have similar decline trends, and the decline speed is in the middle; the variable curve of trap density has the slowest decline speed. It also can be seen from the decreasing speed of the curve that the Weibull distribution of the PI breakdown strength has the strongest dependence on the trap energy level, and the trap energy level has the strongest modulation effect on the medium. Since this model controls the breakdown Weibull distribution by adjusting the standard deviation of the transport parameters, within a reasonable standard deviation range, the simulation results are basically similar with the experimental results, and almost with no error. Figure 8b shows the comparison between the simulation results and the experimental results when the standard deviation of the trap energy level is set to 0.003. It is shown that within a reasonable range, it is feasible to use this model for Weibull simulation analysis of dielectric materials, and the breakdown strength of the dielectric can be obtained more accurately.
Fig. 9. The simulation and experimental results of samples with different thicknesses are shown as the expected values in the trap energy level.
The relationship between the PI breakdown strength and thickness obtained by the CTMD model is changed to logarithmic coordinates, as shown in Fig. 9. It can be seen that the four simulation results are consistent with the experimental results, and are consistent with the predicted inverse power function phenomenon. The coefficient n is −0.398. When the displacement of the molecular chain is not very large, according to the molecular chain dynamics formula (6), when the influence of the second term of the molecular chain relaxation time constant on the motion of the molecular chain is not considered, only the first term on the right side is retained. The formula (6) can be simplified is dλ/dt = μmol E. If the electric field distortion effect caused by the accumulation of space charges is ignored, namely E = k ramp t/d, and we can get the λ = (k ramp μmol /2d)t 2 .
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Molecular chain displacement or free volume length is proportional to the inverse of the thickness and the time’s square. Since the squared change in time is significantly faster than the change in thickness, the molecular chain displacement or free volume length increases gradually with increasing sample thickness. Since the applied electric field increases linearly with time, and the trap energy level can be regarded as the same when the same medium breaks down. When the maximum electron energy (the product of the maximum free volume length and the maximum electric field strength) exceeds the trap energy level, the breakdown phenomenon occurs. The relationship between the breakdown strength and the thickness is an inverse power function relationship with the exponent term of −0.5. Therefore, the breakdown strength of the sample decreases gradually with the increase of the thickness of the sample as an inverse power function. However, due to the preparation process, test conditions and other reasons, there will be certain errors in the index term. The results show that the CTMD breakdown model explains the reason for the formation of the breakdown scale effect of the PI film from the perspective that the force-directed displacement of the molecular chain increases the free volume and changes the dielectric breakdown properties.
Fig. 10. The transport parameter standard deviation changes with the thickness curve
Figure 10 shows the variation curves of the standard deviations of the four transport parameters with thickness when the simulated Weibull distribution is consistent with the experimental values. When the thickness of the PI samples increased from 30 µm to 100 µm, the standard deviations of the parameters showed an increasing trend. The attempted escape frequency standard deviation σ (ν ATE ) increases from 0.54 to 0.65. The carrier mobility standard deviation σ (μ0 ) increases from 0.43 to 0.65. The trap level standard deviation σ (E T )increases from 0.003 to 0.0055. And the trap density standard σ (N T ) increases from 0.112 to 0.15. Comparing the upward trend of the four transport parameter curves, it is found that the standard deviation and variation range of the transport parameters are quite different. The carrier mobility standard deviation σ (μ0 ) is the largest, while the trap level standard deviation σ (E T ) is the smallest. In the simulation, the variation of the trap energy level is the smallest among the four parameters, and the carrier mobility changes the most. It indicating that the change of thickness has different effects on the dispersion of a single transport parameter. Due to the mutual influence of transport parameters, the change of PI thickness will change the dispersion of each
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transport parameter. However, a slight increase in the very small dispersion of the trap level itself will significantly change the Weibull distribution affecting the breakdown. That is, there is a strong correlation between thickness and trap level. This is the same conclusion as the strong dependence of the PI Weibull distribution on trap energy levels obtained in Fig. 7. It means that in actual working conditions, even if the materials, processing technology, environment and other factors are the same, only the difference in thickness can affect the dispersion of the breakdown Weibull distribution by changing the dispersion of the material’s charge transport parameters.
4 Conclution In this paper, the breakdown model of charge transport and molecular chain energy accumulation modulation for PI was established. By adjusting the standard deviation of the charge transport parameters, this paper studied the key parameters that affect the characteristics of the PI breakdown probability distribution, and drew the following main conclusions: (1) Adjust the dispersion of charge transport parameters separately, the obtained curves have different shape parameters and obey the Weibull distribution. By comparing with the experimental results, the inversion obtained the standard deviation of the Weibull distribution shape parameters controlled by the carrier mobility, attempted escape frequency, trap energy level and trap density. (2) According to the standard deviation range corresponding to the experimental results and the variation law of shape parameters and standard deviations under the single thickness, the dependence of the CTMD breakdown model on the four parameters is determined. It is found that the trap level dispersion is the key factor affecting the shape parameters of the breakdown Weibull distribution. As the thickness of the sample increases, the dispersion of the trap energy levels of the sample increases, and the shape parameter of the Weibull distribution decreases gradually. The difference in the trapping effect of traps at different spatial positions results in the probability distribution of the breakdown strength. (3) Based on the CTMD breakdown model, the reason why the breakdown strength of the sample changes with the thickness as an inverse power function is analyzed. The correlation between the spatial dispersion of trap levels and the breakdown probability distribution is revealed.
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State of Health Estimation for Lithium-Ion Batteries Using Random Charging Data Xing Shu1
, Zheng Chen1(B) , Hongqian Zhao1 , Jiangwei Shen1 , and Yongang Liu2
1 Faculty of Transportation Engineering, Kunming University of Science and Technology,
Kunming 650500, China {shuxing92,chen,shenjiangwei6}@kust.edu.cn, [email protected] 2 State Key Laboratory of Mechanical Transmissions & College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China [email protected]
Abstract. Precise state of health (SOH) estimation is pivotal for reliable operations of lithium-ion batteries in electric vehicles. However, the collected charging data is usually incomplete, which makes it difficult to generate health features and brings great challenges to SOH estimation. To conquer this defect, Gaussian process regression (GPR) is developed using random partial charge segment to estimate battery SOH. Firstly, a voltage fitting process is proposed to reconstruct the constant charging voltage trajectories from random partial charging data. Then, the charging time is inferred to characterize battery deterioration. Correlation analysis is conducted and high correlation between SOH and health feature is verified. Following this endeavor, GPR is presented to effectively predict SOH with the input of charging duration. The proposed method can extend the random partial charging segment to complete charging data, thereby relieving the pain there is little chance that the drivers charge the battery from a predefined voltage data. Train and validation are executed on four battery cells, highlighting that the developed approach can maintain the SOH within 2% error. Keywords: Lithium-ion battery · State of health · Random charge segment · Voltage matching · Gaussian process regression
1 Introduction Lithium-ion battery has become the mainstream energy source of electric vehicles since its excellent performance in long lifetime [1]. Nonetheless, with the increment of cycle numbers, the remaining capacity of battery will deteriorate [2]. Generally, the state of health (SOH) is applied to describe this degradation behavior. Accurate SOH estimation is critical for safe operations of electric vehicles [3]. Extensive researches have been carried out on SOH estimating, these methods include measurement methods, filter methods and machine learning methods [4]. The first group uses the measured resistance or capacity to characterize the battery SOH [5]. Although © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1108–1116, 2023. https://doi.org/10.1007/978-981-99-1027-4_115
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these methods are sample and easy to implement, they are difficult to be applied online and are usually implemented to calibrate SOH under laboratory conditions. Filter-based methods apply a physical or chemical model to describe the internal electrochemical reaction of batteries. Then, the advanced filter methods are hired to reckon the battery capacity, so as to achieve SOH. Sliding observer [6] and particle filter (PF) [7] have been frequently employed to mimic the battery model and, consequently, estimate SOH. These methods feature the advantage of online application. Nevertheless, their estimation fidelity and reliability highly depend on the modeling accuracy and robustness[8]. Recently, machine learning-based SOH estimation methods have received wide attention [9]. The nuclear ideal of these methods is to excavate the potential functional relationship between health features and SOH [10]. In [11], four types of health features are generated to characterize battery aging behavior, and the SOH is estimated via long short-term memory (LSTM) algorithm. In [12], artificial neural network (ANN) is established to efficiently reveal the latent association between health features and SOH. In addition to the above mentioned machine learning approaches, such as random forest (RF) [13], support vector regression (SVR) [14], gated recurrent unit (GRU) NN [15], Gaussian process regression (GPR) [16] have been attentionally exerted for SOH reckoning. Considering that the battery discharge process is a random process, and its discharge current is determined by the user’s driving habits and driving cycles, inversely, the charging procedure is usually fixed and it is decided by chargers [17]. Most of the health features are generated from the charging process in the existing literature. However, there are still some shortcomings. For example, external interference leads to discontinuous sampling data, or the user’s charging process does not cover the voltage range of feature extraction, which results in the feature cannot be extracted. To solve these problems, a pragmatic SOH estimation framework for lithium-ion batteries via random charging data is devoted in this study. Concretely, to acquire complete charging voltage data, a voltage fitting method based on polynomial function is developed to reconstruct the constant charging voltage trajectories using random partial charging data. Then, the charging time is excavated as input and the GPR is deduced to effectively estimate the SOH with the input of charging duration. Experimental tests are conducted on four cells and validated the feasibility of the developed method for SOH estimation using random sampling data.
2 Voltage Fitting and Feather Extraction To extend the random partial charging data to the complete voltage curve, a polynomial model is exercised to match the correlation relationship, as: f (x) = a0 + a1 · x + · · · + an · xn
(1)
where x defines as the time slot, ai represents the fitting coefficient, n is the order of polynomial function. From the above process, it can be seen that as long as part of the charging data is collected, the above formula can be used to fit and obtain the complete charging voltage data. After obtaining the complete charging voltage data, the health feature is extracted. Generally, health feature should be easy to acquire and avoid complex calculations. In
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this study, the health feature is extracted from the charging procedure and four battery cells, named as Cell 1 to 4, are tested to collect the degradation data. The nominal capacity and voltage are 4 Ah and 3.6 V, respectively. First, the CC-CV scheme is addressed to charge the cells until voltage extends to 4.15 V. After resting 5 min, CC strategy applied to discharge the cells. The charging and discharging current are 2 A and 4 A. Figure 1 plots the charging voltage, as can be seen, the time during CC charging procedure decreases with the increment of cycle number. Thus, it can be considered as the health feature to characterize battery deterioration. To quantize the correlation, Pearson correlation coefficient is calculated. When the voltage range is set [3.4, 4.15], the Pearson correlation coefficient is 0.9993. When the voltage range is narrowed to [3.7, 4.15] and [3.7, 4.1], the Pearson correlation coefficients decrease to 0.89 and 0.87, respectively. Considering these results and the voltage fitting method, the charging duration for [3.4, 4.15] is extracted as the health feature.
Fig. 1. Flowchart of the GPR-based SOH estimation method.
3 State of Health Estimation Framework The implementation process of the developed SOH prediction is demonstrated in Fig. 2. First, the random partial charging data such as voltage and time are sampled. Then, the polynomial function is hired to fit the sampling points and acquire the complete charging data. Derived from the correlation analysis, health features are excavated from the fitting voltage curves. Next, the health features as inputs and SOH as output are exploited to train the GPR model. Finally, error analysis is performed to authenticate the reliability and accuracy of the developed model using test dataset.
Data sampling
Voltage fitting
Feature extraction
Model training via GPR
Fig. 2. Framework of the SOH estimation method.
Model testing via GPR
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The GPR is a nonparametric approach, which applies probabilistic framework to portray the regression function. The GPR executing processes are summarized, as: ⎧ fg (x) ∼ G(m(x), k(x, x )) ⎪ ⎪ ⎪ ⎪ ⎪ y = fg (x) + ζ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ K(x, x) + σn2 In K(x, x∗ ) y ⎪ ⎪ ∼ N 0, ⎪ ⎨ y∗ K(x, x∗ )T K(x∗ , x∗ )
(2) ∗
∗ ⎪ p(y x, y, x ) = N (y∗ y∗ , cov(y∗ ) ) ⎪ ⎪ ⎪ −1 ⎪ ⎪ ∗ ∗ T 2 ⎪ ⎪ K(x, x) + σ y = K(x, x ) I y n n ⎪ ⎪ ⎪ ⎪ −1 ⎪ ⎪ ⎩ cov(y∗ ) = K(x∗ , x∗ ) − K(x, x∗ )T K(x, x) + σ 2 In K(x, x∗ ) n where m(x) and kf (x, x ) represent the mean and covariance functions, ζ indicates the noise and subjects ζ ∼ N (0, σn2 ), K is symmetric positive definite matrix, σn2 In signifies the matrix of noise covariance. y, y∗ and y∗ are prior distribution, prediction and the average of the prediction, p refers the prior distribution.
4 Validation and Discussion 4.1 Voltage Fitting Validation Since the order of the polynomial function and sampling points will affect the voltage fitting effect, these two parameters are discussed first. The statistical error, including AAE, MAE and RMSE, with different sampling numbers and orders are shown in Fig. 3. In this study, the sampling points are randomly selected 500 times and the average fitting results and errors are calculated. It can be observed that the statistical errors do not decrease with the increasement of order, inversely, increasing the sampling points will improve the fitting accuracy. However, the cost of increasing the sampling points is to waste the computational complexity, and the potentiality of meeting the required sampling points is reduced. Through comparison, it can be found that when the sampling points and polynomial orders are 30 and 4, a relatively small fitting error can be obtained. Moreover, the precision enhancement caused by increasing sampling point is restricted. After determining the order and number of sampling point, voltage fitting results for the four cells at different cycle numbers are depicted in Fig. 4. The fitting results are very close to the reference ones, and the aging of the battery does not affect the voltage fitting error. The maximum fitting error occurs in the initial state, which is less than 74 mV (about 2% of the nominal voltage). Eliminating the initial error, the maximum error is less than 1% of the nominal voltage. The comparison results exhibit that the developed voltage fitting approach can achieve an acceptable voltage data. 4.2 SOH Estimation Results After voltage fitting and feature extraction, the GPR is trained and the estimations are depicted in Fig. 5, it also compares the estimations with complete charging data. Note
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(a)
(b)
(c)
Fig. 3. Statistical error of SOH with different sampling numbers and orders: (a) RMSE; (b) MAE; (c) AAE.
that the training set of GPR and the selection of model parameters are consistent when using the complete data and random data for SOH estimation. It can be found from Fig. 5 that the SOH profiles feature nonlinear degradation trends with the increment of cycle number. The estimation results with complete and random data track the reference curves within reasonable error scope. The estimation results revel that the proposed health feature extraction method and GPR model have the excellence performance to trace the deterioration characteristics with satisfactory fidelity. The MAE for the four cells with complete charging data are respectively 1.27%, 0.75%, 1.75% and 1.64%. For the case of random charging data, they are 1.65%, 0.78%, 1.78% and 2.65%. To assess the estimation performance, RMSE and AAE are calculated to analyze the error and shown in Table 1. The maximum RMSE and AAE are 0.41% and 0.29% for the case of complete charging data. Similarly, the worst case for the random charging data are 0.43% and 0.3%, which are only 0.02% and 0.01% higher than that of the complete charging data. This can be ascribed to the fact that the proposed voltage fitting method, albeit confirmed to be trusty, still confront some unpredictability, compared to ideal situation where the complete charging data are securable. Nevertheless, the estimation RMSE of 0.43%, MAE of 2.65% and AAE of 0.3% are acceptability from the engineering perspective. In summary, the developed approach can extend the 30 random sampling points to complete charging data, and guarantee the estimation error is less than 3%, indicates the feasibility of the developed method.
5 Conclusion In this study, a SOH prognosis framework for lithium-ion batteries using random charging data is developed. The proposed method uses polynomial function to fit the voltage
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
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Fig. 4. Voltage fitting results: (a), (b) Voltage fitting and errors for Cell 1; (c), (d) Voltage fitting and errors for Cell 2; (e), (f) Voltage fitting and errors for Cell 3; (g), (h) Voltage fitting and errors for Cell 4.
curve during the charging process based on random partial sampling points. Then, the charging time is deduced as health feature and GPR is engaged to effectively estimate the SOH. The influence of polynomial function order and sampling number on voltage fitting is analyzed and discussed. The comparison results show that the 4-order polynomial and 30 sampling points can ensure the voltage fitting error is less than 2%. Furthermore, benefitting from the voltage fitting and GPR model, the developed method can achieve an accurate SOH estimation, within an error of 2% for only using 30 sampling points.
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 5. SOH estimation results for different battery cells: (a) SOH for Cell 1; (b) SOH error for Cell 1; (c) SOH for Cell 2; (d) SOH error for Cell 2; (e) SOH for Cell 3; (f) SOH error for Cell 3; (g) SOH for Cell 4; (h) SOH error for Cell 4.
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Table 1. Statistical results for different cells. Cell number
Complete data
Random data
RMSE
MAE
AAE
RMSE
MAE
AAE
1
0.17
1.27
0.12
0.19
1.65
0.14
2
0.18
0.75
0.13
0.19
0.78
0.14
3
0.41
1.75
0.29
0.43
1.78
0.30
4
0.37
1.64
0.26
0.42
2.65
0.29
Acknowledgments. This work was supported in part by the National Natural Science Foundation of China (Grant No. 52162051, and 52172400).
References 1. Bian, X., Wei, Z., He, J., Yan, F., Liu, L.: A novel model-based voltage construction method for robust state-of-health estimation of lithium-ion batteries. IEEE Trans. Industr. Electron. 68, 12173–12184 (2021) 2. Tian, J., Xiong, R., Shen, W., Lu, J., Sun, F.: Flexible battery state of health and state of charge estimation using partial charging data and deep learning. Energy Storage Mater. 51, 372–381 (2022) 3. Shu, X., Li, G., Shen, J., Yan, W., Chen, Z., Liu, Y.: An adaptive fusion estimation algorithm for state of charge of lithium-ion batteries considering wide operating temperature and degradation. J. Power Sources 462, 228132 (2020) 4. Shu, X., Shen, J., Li, G., Zhang, Y., Chen, Z., Liu, Y.: A flexible state-of-health prediction scheme for lithium-ion battery packs with long short-term memory network and transfer learning. IEEE Trans. Transp. Electrification 7, 2238–2248 (2021) 5. Fu, Y., Xu, J., Shi, M., Mei, X.: A fast impedance calculation-based battery state-of-health estimation method. IEEE Trans. Industr. Electron. 69, 7019–7028 (2022) 6. Hashemi, S.R., Mahajan, A.M., Farhad, S.: Online estimation of battery model parameters and state of health in electric and hybrid aircraft application. Energy 229, 120699 (2021) 7. Lyu, Z., Gao, R., Chen, L.: Li-Ion Battery state of health estimation and remaining useful life prediction through a model-data-fusion method. IEEE Trans. Power Electron. 36, 6228–6240 (2021) 8. Gou, B., Xu, Y., Feng, X.: An ensemble learning-based data-driven method for online stateof-health estimation of lithium-ion batteries. IEEE Trans. Transp. Electrification 7, 422–436 (2021) 9. Shu, X., Shen, S., Shen, J., Zhang, Y., Li, G., Chen, Z., Liu, Y.: State of health prediction of lithium-ion batteries based on machine learning: advances and perspectives. iScience 24, 103265 (2021) 10. Meng, J., et al.: An automatic weak learner formulation for lithium-ion battery state of health estimation. IEEE Trans. Industr. Electron. 69, 2659–2668 (2022) 11. Ma, Y., Shan, C., Gao, J., Chen, H.: A novel method for state of health estimation of lithiumion batteries based on improved LSTM and health indicators extraction. Energy 251, 123973 (2022)
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12. Driscoll, L., de la Torre, S., Gomez-Ruiz, J.A.: Feature-based lithium-ion battery state of health estimation with artificial neural networks. J. Energy Storage 50, 104584 (2022) 13. Lin, C., Xu, J., Shi, M., Mei, X.: Constant current charging time based fast state-of-health estimation for lithium-ion batteries. Energy 247, 123556 (2022) 14. Shu, X., Li, G., Shen, J., Lei, Z., Chen, Z., Liu, Y.: A uniform estimation framework for state of health of lithium-ion batteries considering feature extraction and parameters optimization. Energy 204, 117957 (2020) 15. Chen, Z., Zhao, H., Zhang, Y., Shen, S., Shen, J., Liu, Y.: State of health estimation for lithiumion batteries based on temperature prediction and gated recurrent unit neural network. J. Power Sources 521, 230892 (2022) 16. Deng, Z., Hu, X., Li, P., Lin, X., Bian, X.: Data-driven battery state of health estimation based on random partial charging data. IEEE Trans. Power Electron. 37, 5021–5031 (2022) 17. Shu, X., Li, G., Zhang, Y., Shen, J., Chen, Z., Liu, Y.: Online diagnosis of state of health for lithium-ion batteries based on short-term charging profiles. J. Power Sources 471, 228478 (2020)
Capacity Estimation of Lithium-Ion Batteries Based on an Optimal Voltage Section and LSTM Network Qianyuan Dong, Xiaoyu Li, Jindong Tian, and Yong Tian(B) College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China [email protected]
Abstract. Accurate capacity estimation is the cornerstone of attaining the state of health and remaining useful life of lithium-ion batteries. However, most of existing methods for battery capacity estimation are developed based on the fully charging/discharging condition, which is limited for onboard applications. This paper proposes a capacity estimation method based on an optimal voltage section. Firstly, the feasibility of capacity estimation based on sectional voltage data is demonstrated by correlation analysis between the voltage section-based health factors and the complete capacity. Secondly, the quantum particle swarm optimization algorithm is employed to determine the optimal voltage section. Thirdly, a mapping model between health factors and battery capacity is constructed using a long short-term memory neural network. Finally, validation results on public data sets show that the proposed method can realize accurate capacity estimation with an average root mean square error of 1.53%. Keywords: Capacity Estimation · Voltage Section Optimization · LSTM neural network
1 Introduction Lithium-ion batteries have been widely used to be the energy storage systems in electric vehicles (EVs), consumer electronics, aerospace industry, and other fields because of their high energy and power densities, high efficiency, and long lifespan [1]. With the increase in life cycle, the performance of a lithium-ion battery gradually declines, often reflected in rising of internal resistance and decreasing of available capacity. If the battery is not replaced in time as its capacity degrades to a particular stage, e.g., 80% of the rated capacity, serious consequences such as thermal runaway, may occur because of the significant increase in internal resistance and thermal generation. Accordingly, accurate estimation of the battery capacity is of great significance to its operation safety and reliability. Currently, a number of capacity estimation methods have been proposed. Amongst model-based methods [2, 3] and data-driven methods [4, 5] are commonly concerned. Each of these two methods has its own advantages and disadvantages. In particular, the © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1117–1127, 2023. https://doi.org/10.1007/978-981-99-1027-4_116
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data-driven methods that have good applicability to different battery types and require little professional knowledge about the lithium-ion battery, have attracted extensive attention in recent years. Most of existing data-driven capacity estimation methods are developed on the basis of full charging/discharging data. However, in practical applications, the batteries usually are charged and discharged incompletely due to safety concerns and range anxieties. Consequently, it is crucial to estimate the capacity based on partial charging/discharging data. In Ref. [6], the charging capacity in a fixed voltage range of 3.95–4.15 V was used as the health factor (HF), and the least square algorithm is employed for state of health (SOH) estimation. In Ref. [7], the length of voltage section and estimation error were considered simultaneously, and the non-dominated sorting genetic algorithm II (NSGAII) was used to optimize the multi-voltage sections. However, the used mapping model is too simple to estimate battery capacity accurately. Aiming to address the aforementioned issues, a data-driven capacity estimation method based on the optimal voltage section is proposed in this paper. Three HFs are extracted from a voltage section, and the quantum particle swarm optimization algorithm (QPSO) is introduced to find the optimal voltage section, which achieves the highest correlation between the HFs and the capacity. A long short-term memory (LSTM) neural network model is constructed to output capacity based on the input HFs. The remainder of the paper is organized as follows: Sect. 2 introduces the dataset and analyzes the feasibility of capacity estimation based on sectional voltage. Section 3 details the proposed method for capacity estimation. Experimental results are discussed in Sect. 4. Finally, the paper are concluded in Sect. 5.
2 Battery Dataset and Feasibility Analysis 2.1 Battery Dataset In this paper, the lithium cobalt oxide (LiCoO2 ) battery datasets from the center for Advanced Life Cycle Engineering (CALCE) of the University of Maryland are used. Battery cell CS2_33 is severed as test data, battery cells CS2_34 and CS2_35 are used as training data, and battery cells CS2_36 as well as CS2_37 are used as test data. The rated capacity of the battery is 1.1 Ah. The experimental steps are as follows: (1) Charging the battery with a constant current of 0.55 A until the upper cut-off voltage of 4.2 V; (2) Charging the battery with a constant voltage of 4.2 V until the current lowers than 20 mA; (3) Discharging the battery with a constant of 0.55 A for CS2_33 and CS2_34, and 1.1 A for CS2_35, CS2_36 and CS2_37, until the lower cut-off voltage of 2.7 V. (4) Repeating steps (1)–(3) until the battery capacity degradation is more than 20%. Capacity degradation curves are shown in Fig. 1a, and the charging voltage and current profiles versus operating cycle are plotted in Fig. 1a and b, respectively.
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Fig. 1. The used dataset: (a) capacity degradation curves, (b) charging voltage profiles, (c) charging current profiles.
2.2 Feasibility Analysis and HF Extraction The voltage sections of 3.8–3.9 V and 3.85–3.95 V are taken as examples to analyze the feasibility of capacity estimation based on sectional voltage. The capacity degradation curve in these two voltage sections and complete capacity are shown in Fig. 2, and it can be seen that the three curves show a uniform trend towards similarly reduced capacity. The Pearson coefficient is utilized for quantitative analysis, which can be formulated as n (xi − x)(yi − y) n (1) r = n i=1 2 2 i=1 (xi − x) i=1 (yi − y) where x and y are two variables, x and y are the average of x and y, respectively.
Fig. 2. The complete capacity and sectional capacity.
The calculated Pearson correlation coefficients are 0.959 and 0.988, respectively, which both further demonstrate the high correlation between the sectional capacity and the complete capacity. Thus, it is feasible to estimate the complete capacity based on the sectional data. High-quality HFs that well characterizes the capacity degradation are very important for the data-driven methods to improve estimation accuracy. To enrich the HFs and enhance their robustness, this paper extracts HFs from the time-voltage and increment
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capacity (IC) curves [8], as shown in Fig. 3. It can be seen from Fig. 3a that charging time corresponding to a fixed voltage range decreases with the increase in cycle, meaning that the charging capacity also decreases. Therefore, in this paper charging capacity is selected as an HF. The IC curve can enlarge the slow-rising process of the voltage curve. From Fig. 3b, it is clear that with the increase in cycle, the peak of the IC curve decreases, and the peak position shifts to the higher voltage side.
Fig. 3. Examples of HF extraction: (a) sectional time-voltage curve, (b) IC curve.
Table 1 summarizes the Pearson correlation coefficients between the three HFs and the capacity. It is indicated that the correlation coefficients differ obviously for the two sections, even though they are the same in length. In other words, HFs extracted from different voltage sections perform differently in representing the capacity degradation. Consequently, the selection of an optimal voltage section is key to capacity estimation. Table 1. Correlation coefficients between HFs and capacity for two different voltage sections. HF
3.8–3.89 V
3.85–3.94 V
Charging capacity
0.93
0.98
IC peak value
0.86
0.96
−0.23
−0.90
Voltage of IC peak
In addition, it is clear from Table 1 that all the absolute correlation coefficients in the section of 3.85–3.94 V exceed 0.90. Then, it can be concluded that as long as a voltage section is selected appropriately, the HFs extracted from the sectional data can capture the law of capacity degradation very well. Therefore, estimating the complete capacity based on an optimal voltage section is feasible.
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3 Proposed Method Usually, EV users would like to recharge the battery when its SOC is about 10–20% rather than till its full discharge due to range anxiety, and stop charging before the full charge of the battery because of safety concerns or urgent use of the EVs. In other words, the battery likely experiences incomplete charging and discharging. Accordingly, this paper proposes a capacity estimation method based on a charging voltage section. The proposed method is illustrated in Fig. 4, and it includes three steps: (1) HF extraction, (2) voltage section optimization, and (3) model construction.
Fig. 4. Flowchart of the proposed method.
3.1 Voltage Section Optimization with QPSO To select the optimal voltage section, it is important to set an optimization objective and constraints appropriately. Here, the optimization objective is set to maximize the sum of Pearson coefficients, that is 3 |ri | max F = (2) i=1
where r i denotes the Pearson coefficient between the ith HF and the complete capacity. Additionally, it is necessary to consider the limited charging range and the length of the voltage section to ensure the rationality in practical applications, so corresponding constraints are set as 10% ≤ SOC ≤ 60% (3) 0.05 V ≤ Vb − Va ≤ 0.25 V
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where V a and V b indicate the lower and upper limits of the voltage section, respectively. In this paper, the QPSO algorithm is introduced to solve the nonlinear programming problem in Eqs. 2 and 3. The QPSO algorithm proposed by Coelho [9] is an improved version of the PSO algorithm in order to avoid falling into a local optimization and reduce the number of parameters to configure. It regards all particles as quantum particles, and introduces a wave function to represent the particle state. The principle of the QPSO algorithm is summarized as follows: (1) The average history best position of particles (mbest) is calculated by 1 pbesti mbest = n n
(4)
i=1
where n is the number of particles, and pbest i denotes the individual optimal position of the ith particle. (2) Particle position update ⎧ ⎪ ⎨ Pi = · pbesti + (1 − ) · gbest
1 ⎪ | × ln = p ± α|mbest − x x i i ⎩ i+1 u
(5)
where Φ and u are two random variables between 0 and 1, x i stands for the position of the ith particle, α is a compression expansion coefficient to regulate the convergence rate of the QPSO algorithm, which is set to 0.8 in this paper. 3.2 Estimation Model Construction This paper establishes the capacity estimation model using a LSTM network [10]. Nowadays, LSTM network has been successfully applied in many fields, and it is good at time series prediction and estimation. It has been also introduced for estimation of battery SOC [11] and SOH [12]. An LSTM cell is plotted in Fig. 5, where it , f t , and Ot denote input gate, forget gate and output gate, respectively. The forget gate is used to determine how much information from the previous cell state C t-1 will be forgotten, and it is formulated as
ft = sigmoid(Wf ht−1 , Xt + bf ) (6) The input gate it and state value C˜ t are used to save and update the cell information, and they are
it = sigmoid(Wi ht−1 , Xt + bi ) (7)
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Fig. 5. The structure of the LSTM cell.
C˜ t = tanh(WC ht−1 , Xt + bC )
(8)
Then, the LSTM cell can determine information to forget or save as follows Ct = ft · Ct−1 + it · C˜ t The output gate Ot determines the final state of the cell, ht , as follows
Ot = tanh(WO ht−1 , Xt + bO ) ht = Ot · tanh(Ct )
(9)
(10) (11)
The LSTM network is configured as: Learning rate-0.01, Epochs-1000, hidden size128, LSTM layers-2, and time step-5. More details can be found in [3].
4 Experimental Validation and Discussion In this section, the root mean square error (RMSE), the mean absolute percentage error (MAPE) and R2 are used as evaluation indicators to verify the feasibility and accuracy of the proposed method, and they are formulated as N 1 (qi − qˆ i )2 N i=1
× 100% q N 1 qi − qˆ i MAPE = q × 100% N i i=1 N (qi − qˆ i )2 R2 = 1 − i=1 N 2 i=1 (qi − q)
RMSE =
(12) (13) (14)
where qi and qˆ i stand for the real and estimated battery capacity, respectively, q represents the average capacity, and N is the number of data.
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4.1 Validation for the Voltage Section Optimization The optimized voltage sections for each battery are detailed in Table 2, where score is calculated by Eq. 2, and time proportion denotes the ratio of the sectional charging time to the full charging time. From Table 2, it is evident that the optimal voltage sections are mostly concentrated to the range of 3.86–4.02 V, which is slightly different for each battery. Considering that setting an individual optimal section for every battery is difficult, it is necessary to unify the optimal voltage section for a same battery type. Herein, the optimal voltage section is unified to 3.88–4.01 V, and the corresponding details for each battery are presented in Table 3. Table 2. The results of voltage section optimization. Battery cell
Optimal section
Score
Start SOC
End SOC
Time proportion
CS2_33
3.89 V-4.01 V
2.91
22.7%
56.9%
47%
CS2_34
3.88 V-4.02 V
2.80
13.2%
50.8%
39%
CS2_35
3.86 V-3.98 V
2.89
15.3%
48.5%
39%
CS2_36
3.87 V-4.02 V
2.93
17.8%
58.8%
48%
CS2_37
3.87 V-4.01 V
2.91
17.0%
55.9%
46%
Table 3. Details of the unified optimal voltage section (3.88–4.01 V). Battery cell
Score
Start SOC
End SOC
Time proportion
CS2_33
2.90
19.8%
56.9%
41%
CS2_34
2.77
13.2%
48.3%
36%
CS2_35
2.87
18.8%
55.3%
42%
CS2_36
2.89
20.1%
56.8%
42%
CS2_37
2.91
19.2%
55.9%
40%
Based on the results in Table 3, the average correlation reaches a high level of 0.959, which provides a good foundation for subsequent capacity estimation. Furthermore, the average charging time only accounts for 40% of the full charging time, reducing the amount of data required for capacity estimation obviously. To verify the effectiveness of the optimal voltage section, herein 3.95–4.08 V is taken as an example of non-optimal voltage section for comparison study, and the results are detailed in Table 4. It can be seen from Table 4 that although the non-optimal voltage section has the same voltage increment with the optimal voltage section, the score decreases obviously, meaning that the HFs extracted from this non-optimal voltage section have lower correlation with the capacity than that extracted from the optimal voltage section. Particularly, the average correlation coefficient reduces to 0.682, while the average time proportion increases to about 55%.
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Table 4. Details of a non-optimal voltage section (3.95–4.08 V). Battery cell
Score
Start SOC
End SOC
Time proportion
CS2_33
2.33
42.6%
69.4%
57%
CS2_34
1.12
29.9%
63.5%
49%
CS2_35
2.07
40.6%
68.1%
55%
CS2_36
2.20
42.7%
69.2%
57%
CS2_37
2.50
41.5%
68.6%
56%
4.2 Validation for Capacity Estimation HFs extracted from the full charging curve (Exp. 1), the optimal section (Exp. 2) and a non-optimal section (Exp. 3) are compared. The HFs extracted from batteries CS2_34, and CS2_35 are used to train the LSTM neural network, while HFs extracted from batteries CS2_33, CS2_36 and CS2_37 are employed to test the LSTM model. The results are shown in Figs. 6, 7 and 8. More details about the capacity estimation results are presented in Table 5.
Fig. 6. Capacity estimation results of CS2_33: (a) Exp. 1, (b) Exp. 2, (c) Exp. 3.
From Figs. 6, 7 and 8 and Table 5, it is evident that the estimation results with the optimal voltage section are very close to that with the full charging curve, and they both can well represent the law of capacity degradation. The estimation errors with the non-optimal voltage section are relatively large. Then, it can be concluded that as long as a voltage section and HFs are selected appropriately, the battery capacity still can be estimated accurately only using a voltage section.
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Fig. 7. Capacity estimation results of CS2_36: (a) Exp. 1, (b) Exp. 2, (c) Exp. 3.
Fig. 8. Capacity estimation results of CS2_37: (a) Exp. 1, (b) Exp. 2, (c) Exp. 3.
Table 5. Comparison results of capacity estimation. Battery cell
Exp. 1
Exp. 2
Exp. 3
RMSE
MAPE
R2
RMSE
MAPE
R2
RMSE
MAPE
R2
CS2_33
1.30%
1.09%
0.992
1.27%
1.06%
0.991
3.14%
3.16%
0.954
CS2_36
1.59%
1.41%
0.982
1.63%
1.36%
0.985
2.66%
2.29%
0.961
CS2_37
1.54%
1.30%
0.988
1.70%
1.46%
0.986
5.04%
4.10%
0.875
5 Conclusions This paper proposes a capacity estimation method based on an optimal voltage section for lithium-ion batteries. Three health factors are extracted from a voltage section. The quantum particle swarm optimization algorithm is utilized to determine the optimal voltage section. The nonlinear relationship between the HFs and the battery capacity is modeled by a long short-term memory neural network. The CALCE battery datasets are adopted to verify the effectiveness of the proposed method. Experimental results indicate that the optimized voltage section only accounts for about 40% of the full charging time,
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thus obviously improving the availability of the required data, and it is more in accord with the real-world scenarios. In addition, the proposed method performs good accuracy and generalization ability. Acknowledgements. This work was supported by the open research fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (No. GML-KF-22–19).
References 1. Hannan, M.A., Lipu, M.S.H., Hussain, A., Mohamed, A.: A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: challenges and recommendations. Renew. Sustain. Energy Rev. 78, 834–854 (2017) 2. Jie, L., Ad, E.K., Yagin, N.L., et al.: A single particle model with chemical/mechanical degradation physics for lithium ion battery state of health (SOH) estimation. Appl. Energy 212, 1178–1190 (2018) 3. Tian, Y., Dong, Q., Li, X., et al.: Capacity estimation of lithium-ion batteries based on optimized charging voltage section and virtual sample generation. Appl. Energy 332, 120516 (2023) 4. Sui, X., He, S., Vilsen, S., et al.: A review of non-probabilistic machine learning-based state of health estimation techniques for Lithium-ion battery. Appl. Energy 300, 117346 (2021) 5. Zhu, J., Wang, Y., Huang, Y., et al.: Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation. Nat. Commun. 13, 2261 (2022) 6. Yang, Q., Xu, J., Cao, B., et al.: State-of-health estimation of lithium-ion battery based on interval capacity. Energy Procedia 105, 2342–2347 (2017) 7. Meng, J., Cai, L., Stroe, D., et al.: Lithium-ion battery state-of-health estimation in electric vehicle using optimized partial charging voltage profiles. Energy 185, 1054–1062 (2019) 8. Jiang, B., Dai, H., Wei, X.: Incremental capacity analysis based adaptive capacity estimation for lithium-ion battery considering charging condition. Appl. Energy 269, 115074 (2020) 9. Coelho, L.: A quantum particle swarm optimizer with chaotic mutation operator. Chaos Solitons Fractals 37(5), 1409–1418 (2008) 10. Hochreiter, S., Schmidhuber, J.: Long Short-Term Memory. Neural Comput. 9(8), 1735–1780 (1997) 11. Tian, Y., Lai, R., Li, X., Xiang, L., Tian, J.: A combined method for state-of-charge estimation for lithium-ion batteries using a long short-term memory network and an adaptive cubature Kalman filter. Appl. Energy 265, 114789 (2020) 12. Tan, Y., Zhao, G.: Transfer learning with long short-term memory network for state-of-health prediction of lithium-ion batteries. IEEE Trans. Industr. Electron. 67(10), 8723–8731 (2020)
Enhancing Specific Capacitance and Structural Durability of VO2 Through Rationally Constructed Core-Shell Heterostructures Minghua Chen(B) , Nianbo Zhang, Jiawei Zhang, and Yu Li Key Laboratory of Engineering Dielectric and Applications (Ministry of Education), Harbin University of Science and Technology, Harbin 150080, China [email protected]
Abstract. The widespread applications of supercapacitors are greatly restricted by their inferior energy density. Developing advanced electrode materials with high capacitance and large voltage windows has been regarded as a promising way to conquer the above challenge. Considering this, VO2 @NiO core-shell heterostructures were constructed by a facile and controllable hydrothermal reaction combined with the atomic layer deposition technique. The NiO coating layer can buffer the hydrolyzed reaction of VO2 , improving the chemical/electrochemical stability of VO2 . Moreover, heterogeneous interfaces between NiO and VO2 can effectively regulate the charge distribution around the phase boundaries, which can render additional active sites and enhance the intrinsic electronic conductivity of two building blocks. as a result, the as-prepared VO2 @NiO heterostructure exhibits extremely high specific capacitance of 1265 F/g at 1 A/g and remains 80.6% of initial capacity after 5000 cycles at 10 A/g. The assembled asymmetric supercapacitors employing the VO2 @NiO heterostructure materials as the negative electrode and the commercial nickel-cobalt-aluminum oxides as the positive electrode exhibit an attractive energy density (39.81 Wh/kg) and superior cycling lifespans. This work may guide the development of core-shell heterostructure as advanced electrodes for electrochemical energy storage. Keywords: Supercapacitor · Heterostructure · Vanadium oxides · Nickel oxide · Core-shell
1 Introduction The rising concern about the global energy crisis and its impact on the environment implies a transition from the current development paradigm to a sustainable one, which remains a significant challenge for scientists, industries, and governments to make reasonable energy and environmental policies to save energy and reduce environmental impact as well as carbon emission during the managing and controlling process at each level of the concerning ecosystems [1–3]. There is already plenty of discussion about these problems, along with an abundance of journals with disciplinary territories and sharp boundaries on the intellectual landscape, some of which may prove to be valuable © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1128–1136, 2023. https://doi.org/10.1007/978-981-99-1027-4_117
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[4]. However, we need a problem-oriented forum, not a discipline-based one, for putting the pieces together, and promoting intelligent discussion of an integrated vision of the human and natural world. In recent years, supercapacitors have attracted much attention due to their high power density and long lifespan [5]. However, the main challenges driving the development of supercapacitor technology are the low energy density, so the development of new materials for supercapacitor electrodes is one of the most important approaches [6]. Currently the most popular supercapacitors are carbon materials with high specific surface area, which charges based on EDLC mechanism [7]. Compared with pseudocapacitive supercapacitors deliver higher specific capacitive through Faraday processes [8]. The capacity of an electrode to achieve the pseudocapacitive effect depends on the chemical affinity of the material for ions adsorbed on the electrode surface, as well as the structure and size of the electrode pores. Traditional pseudocapacitive materials include transition metal oxides compounds [9] and conductive polymers [10]. Conventional capacitors are generally low in capacity and therefore not suitable for future applications [11]. As a result, a series of new materials have emerged to improve the performance of supercapacitor electrodes, covalent organic frameworks (COFs) [12], metal organic frameworks (MOFs) [13], MXenes [14], etc. The heterostructure, due to the existence of a large number of heterophase interfaces, will cause a large number of lattice defects, distortions and dislocations, which can adjust the electronic structure and enhance the interface charge transfer, thereby accelerating the electrochemical kinetics [15]. Moreover, the synergistic effect between different components in the heterophase interface can effectively accelerate the diffusion/transfer of electrolyte ions and electrons, providing favorable conditions for fast charge-discharge, enabling the electrode to exhibit high rate capability and excellent cycle life [16]. In addition, the construction of unique core-shell structures is also a promising means to improve the electrochemical performance of electrode materials. The structure possesses an open structure for easy ion/electron transport and excellent surface permeability, which is beneficial to improve the electrochemical kinetics of electrode materials. Herein, VO2 @NiO heterostructure electrode was prepared by the hydrothermal synthesis method and atomic layer deposition technology. NiO is a traditional supercapacitor material with stable structure, easy preparation and high specific capacity. Therefore, the existence of the NiO layer can effectively prevent the hydrolysis of VO2 during the electrode reaction process, thereby improving the cycle stability of the material. In addition, VO2 @NiO heterogenous The structure uses foamed nickel as the current collector, which can speed up the electron transfer, and at the same time fully exert its advantages of light weight and high strength. In addition, the micropores in the VO2 @NiO heterostructure are conducive to the diffusion of the electrolyte, which can accelerate the water system. The ions in the electrolyte diffuse to the electrode surface. VO2 @NiO electrode material has extremely high electrical conductivity and good cycling stability as the anode of supercapacitor. The electrode material greatly improves the conductivity of the electrode and the diffusion of ions, which provides a new idea for the design of supercapacitor electrodes.
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2 Experimental Section The detailed synthesis route of VO2 @NiO heterostructure is as follows: 5 mmol of oxalic acid and 1.5 mmol of vanadium pentoxide were added to 30 ml of deionized water, which was stirred for 30 min, then 30 ml of absolute ethanol and 1.5 ml H2 O2 was added with stirring for 5 min. The mixture was transferred into a Teflon-lined stainless steel autoclave and maintained at 180 °C for 5 h in an oven. Then the samples were collected and rinsed with deionized water and ethanol three times in a turn. The samples were placed in a vacuum oven and dried at 60 °C for 6 h to obtain the VO2 precursor. Finally, NiO were deposited on the surface of the VO2 substrate by atomic layer deposition to obtain VO2 @NiO heterostructure materials.
3 Results and Discussion Figure 1a, b and d, e are the SEM images of VO2 and VO2 @NiO heterostructures. The morphology of the VO2 @NiO heterostructure after ALD treatment is well maintained compared with pure VO2 . The diameter is about 1 µm, and the dispersibility is good without agglomeration. The microscopic morphology and structure of the VO2 @NiO heterostructure were further characterized by TEM and HRTEM, as displayed in Fig. 1c and 1f. It can be seen that the layer of NiO is uniformly coated around VO2 to form a VO2 @NiO core-shell heterostructure, which is consistent with the result of SEM. From Fig. 1f, the interface between NiO and VO2 and the lattice fringes of VO2 can be observed. It is determined that the interplanar spacing of VO2 is 0.352 nm, which corresponds to the (110) crystal planes of VO2 . The NiO deposited by ALD is in an amorphous state, so its lattice fringes are not observed. The element distribution of VO2 @NiO was analyzed by the energy spectrum analysis function of SEM. As illustrated in Fig. 1g–j, it is suggested that V, Ni, and O coexist in VO2 @NiO heterostructure, and the content of Ni is much less than V and O elements. Figure 2a shows the XRD patterns of VO2 and VO2 @NiO. It can be seen that the characteristic peaks of various VO2 @NiO and pure VO2 are consistent, indicating the introduction of the NiO layer does not influence the crystal structure of VO2 . Since the NiO deposited on the surface of VO2 by atomic layer deposition technology is amorphous, the characteristic peaks of NiO cannot be found in the XRD spectrum, which is very good with the TEM image. Figure 2b shows the Raman spectrum of VO2 @NiO and VO2 . The Raman peaks of NiO were observed in VO2 @NiO samples, revealing the successful deposition of the NiO layer. To further characterize the successful synthesis of VO2 @NiO, the X-ray photoelectron spectroscopy (XPS) of VO2 @NiO was carried out. Figure 2c shows the full spectrum of XPS of VO2 @NiO, demonstrating the existence of Ni, V, and O elements. Figure 2d shows the high-resolution spectrum of V 2p. After peak fitting, the V 2p3/2 signal peak at the binding energy of 516.1 eV and the V 2p1/2 signal peak at 523.6 eV corresponds to the V4+ element [17]. Figure 2e is the O 1s spectrum. The signal peaks at the binding energy of 529.4 and 531.7 eV represent the formation of Ni-O and V-O bonds, respectively. Figure 2f is the Ni 2p spectrum, in which the characteristic peak of Ni 2p3/2 at 855.2 eV and Ni 2p1/2 at 873.1 eV correspond to Ni element with +2 valence [18]. The characteristic peaks located at 862.1 and 879.8 eV
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Fig. 1. (a, b) SEM images of VO2 . (c) TEM images of VO2 @NiO. (d, e) SEM images of VO2 @NiO. (f) High-resolution TEM image of VO2 @NiO. (g–j) Mapping spectra of different elements of VO2 @NiO.
are Satellite peaks. The XPS spectra can show that the VO2 @NiO heterostructure was successfully prepared and the product is pure and without other impurities.
Fig. 2. (a) XRD patterns. (b) Raman spectra of VO2 and VO2 @NiO. (c, f) XPS spectra of VO2 @NiO
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Figure 3a shows the CV curves of VO2 and VO2 @NiO in the voltage range from −1 to −0.5 V. According to the CV curves, it can be inferred that the specific capacitance of VO2 @NiO is the highest due to it has the largest closed area of CV curve. In addition, there is no redox peak in the CV curve, indicating that the electrode reaction is typical capacitive behavior. Similarly, the GCD curves of different deposition turns (Fig. 3b) also show that VO2 @NiO has mass-specific capacitance, which is as high as 1265 F/g at a current density of 1 A/g. The high specific capacitance value is due to that the heterostructure can expose more active sites to facilitate the intercalation and deintercalation of electrolyte ions. In addition, the structure provides a considerable specific surface area, which can further improve the energy storage capacity of the electrode. It can be seen that VO2 @NiO has the best electrochemical performance. Cyclic voltammetry tests were carried out at different scan rates as shown in Fig. 3c. As the scan rate increases, the shape of the CV curve remains unchanged. Change, which indicates that VO2 @NiO has excellent stability and excellent reversibility. Besides, the shape of the GCD curve of VO2 @NiO in Fig. 3d is relatively symmetrical, and there is no obvious charge-discharge plateau and no voltage drop at different current densities, indicating that VO2 @NiO has high specific capacitance and good electrochemical reversibility.
Fig. 3. (a) CV curves of VO2 and VO2 @NiO. (b) GCD curves of VO2 and VO2 @NiO. (c) CV curves of VO2 @NiO at various scan rates. (d)GCD curves at various current densities. (e) Capacitive contribution at a scan rate of 100 mV s−1 . (f) The specific capacitance versus scan rate for the VO2 @NiO. (g) The specific capacity comparison of VO2 @NiO and VO2 at different current densities. (h) Nyquist plots in the frequency ranging from 100 kHz to 0.1 Hz. (i) Cycling stability over 5000 cycles.
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To explore the pseudocapacitive effect of VO2 @NiO electrode in the energy storage process. As plotted in Fig. 3e 70.54% of the capacitance contribution comes from the surface control process at a scan rate of 100 mV/s, which indicates that the pseudocapacitive reaction dominates the electrode reaction process. In addition, Fig. 3f shows the comparison of the diffusion contribution and the surface contribution at different scan rates. From Fig. 3f, it can be found that the surface contribution increases with the increase of the scan rate, which indicates that the pseudocapacitive reaction dominates the capacity contribution during the fast charge-discharge process. By measuring the mass-specific capacitance of VO2 @NiO at different current densities, as shown in Fig. 3g, it can be seen that the maximum specific capacitance of VO2 @NiO is 1265 F/g at the current density of 1 A/g, even if the current density reaches 7 A/g VO2 @NiO still retains a specific capacitance of 520 F/g, which exhibits surprising rate performance compared to VO2 . The extremely small horizontal intercept (only 2.7 ) of VO2 @NiO by electrochemical impedance measurement (EIS), i.e., Fig. 3h, indicates its low internal resistance and charge transfer resistance, which benefited from the formation of the interface in the heterostructure, which further proves the excellent electrochemical performance of VO2 @NiO. The cycle performance of VO2 @NiO is shown in Fig. 3i. After 5000 charge-discharge cycles, the capacity of the VO2 @NiO electrode can still maintain 80.6% of the initial capacity, which is about 30% higher than that of VO2 . It can be seen that the coating of the NiO layer can effectively inhibit the structural damage and hydrolysis of VO2 during the charging and discharging process, thereby improving the cycling stability of the VO2 @NiO electrode. The NCA oxide as the positive electrode and VO2 @NiO as the negative electrode were assembled into an asymmetric supercapacitor to explore its practical application value. The schematic diagram of the asymmetric device is shown in Fig. 4a. Among them, the cyclic voltammetry curves of NCA and VO2 @NiO are shown in Fig. 4b. Observing these two voltammetry curves, it can be found that the difference in the area surrounded by the CV curves of the positive electrode and the negative electrode is small, indicating that a better matching can be achieved. The voltage range of the asymmetric device is obtained by changing the voltage range at a scan rate of 100 mV/s, as shown in Fig. 4c. It can be seen that the voltage window of the device is as high as 1.8 V and no polarization is found during the charging and discharging process. A high voltage window corresponds to a high energy density which indicates that the performance of the device will be very good. Figure 4d shows the CV curves of the asymmetric device at different scan speeds. The shape of the CV curve remains stable at different scan speeds, indicating that the device has good capacitive performance. To further study the energy storage characteristics of the asymmetric device, the GCD test was carried out, as shown in Fig. 4e, the specific capacitance of the device can be calculated to be 63 F/g at the current density of 1 A/g. A further calculation can be obtained that the energy density of the asymmetric device energy density 39.81 Wh/kg at a power density of 833.35 W/kg. Compared with other works of the same system, as shown in Fig. 4f, [19–24] it can be seen that the device prepared based on this work has both excellent energy density and power density. To explore the reliability of the asymmetric device in practice, the cycle test was carried out at 10 A/g as shown in Fig. 4g. After 5000 charge-discharge cycles, the capacitance retention rate was 93.7%, proving that the device has excellent cycle
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stability. Long-term use is possible. In addition, connecting three devices in series can light up the LED lights for a long time as shown in Fig. 4h.
Fig. 4. (a) NCA//VO2 @NiO ASC assembly structural representation. (b) CV curves of VO2 @NiO and NCA. (c) CV curves at various potential voltage windows. (d) CV curves at various scan rates. (e) GCD curves at various current densities. (f) Ragone plot of ASC and some reference samples. (g) The cycle life at the current density of 10 A g−1 . (h) Photograph of LED powered by three serial ASCs.
4 Conclusions In summary, a VO2 @NiO heterostructure was prepared for supercapacitor applications. The structure uses VO2 as the matrix and coats a layer of NiO on its surface to form a VO2 @NiO heterostructure electrode material with a core-shell structure. The existence of the protective layer enhances the structural stability, provides a large specific surface area, and abundant electrochemical reaction active sites, which effectively improves the comprehensive performance of VO2 and expands its applications. Electrochemical performance tests show that the VO2 @NiO heterostructure has a fairly high mass-specific capacitance (up to 1265 F/g at a current density of 1 A/g) and good cycling stability (capacitance retention rate of 80.6 after 5000 charge-discharge cycles). Assembled asymmetric device testing found that the device has a large voltage window (1.8 V), high
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energy density(energy density 39.81 Wh/kg at power density 833.35 W/kg), and good cycle stability (capacitance retention rate of 93.7 after 5000 charge-discharge cycles). All of the above can prove that the VO2 @NiO heterostructure is very suitable for application in supercapacitors, and this work provides an effective solution for the design of supercapacitors. Acknowledgement. This work is supported by National Natural Science Foundation of China (Grant No. 52122702) and Natural Science Foundation of Heilongjiang Province of China (No. JQ2021E005).
References 1. Jl, A., Jq, B., Kl, A.: Hydroxide ion conducting polymer electrolytes and their applications in solid supercapacitors: a review - ScienceDirect[J]. Energy Storage Mater. 24, 6–21 (2020) 2. Pang, Z., Li, G., Xiong, X., et al.: Molten salt synthesis of porous carbon and its application in supercapacitors: a review[J]. J. Energy Chem. 2021, 61 (2015) 3. Huang, Z., Li, L., Wang, Y., et al.: Polyaniline/graphene nanocomposites towards highperformance supercapacitors: a review[J]. Compos. Commun. 83–91 (2018) 4. Yaseen, M., Khattak, M., Humayun, M., et al.: A review of supercapacitors: materials design, modification, and applications[J]. Energies 14 (2021) 5. Namsheer, K.: Photo-powered integrated supercapacitors: a review on recent developments, challenges and future perspectives[J]. J. Mater. Chem. A (2021) 6. Chee, W.K., Lim, H.N., Zainal, Z., et al.: Flexible graphene-based supercapacitors: a review[J]. J. Phys. Chem. C 120(8) (2016) 7. Luo, X., Chen, Y., Mo, Y.: A review of charge storage in porous carbon-based supercapacitors[J]. Carbon 177, 427–428 (2021) 8. Wei, W., Cui, X., Chen, W., et al.: Manganese oxide-based materials as electrochemical supercapacitor electrodes[J]. Chem. Soc. Rev. 40(3), 1697 (2011) 9. Abdah, M., Azman, N., Kulandaivalu, S., et al.: Review of the use of transition-metal-oxide and conducting polymer-based fibres for high-performance supercapacitors[J]. Mater. Des. 186, 108199 (2019) 10. Snook, G.A., Kao, P., Best, A.S.: Conducting-polymer-based supercapacitor devices and electrodes[J]. J. Power Sources 196(1), 1–12 (2011) 11. Zhi, M., Xiang, C., Li, J., et al.: Nanostructured carbon–metal oxide composite electrodes for supercapacitors: a review[J]. Nanoscale 5 (2012) 12. Halder, A., Ghosh, M., Abdul, K.M., et al.: Interlayer hydrogen-bonded covalent organic frameworks as high-performance supercapacitors[J]. J. Am. Chem. Soc. (2018) 13. Yao, M., Xin, Z., Lei, J., et al.: High energy density asymmetric supercapacitors based on MOF-derived nanoporous carbon/manganese dioxide hybrids[J]. Chem. Eng. J. 322, 582–589 (2017) 14. Wang, Q.Q. Fang, Y.S., Cao, M.S.: Constructing MXene-PANI@MWCNTs heterojunction with high specific capacitance towards flexible micro-supercapacitor (2022) 15. Jabeen, N., Xia, Q., Yang, M. et al.: Unique core-shell nanorod arrays with polyaniline deposited into mesoporous NiCo2O4 support for high-performance supercapacitor electrodes [J].. Acs Appl. Mater. Interfaces 6093 (2016) 16. Zhai, X., Pan, H., Wang, F., et al.: Controlled growth of 3D interpenetrated networks by NiCo2O4 and graphdiyne for high-performance supercapacitor[J] (2022)
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17. Cheng, W.A., Hx, A., Cw, A., et al.: Preparation of VO2 (M) nanoparticles with exemplary optical performance from VO2 (B) nanobelts by Ball Milling[J]. J. Alloy. Compd. (2021) 18. Fomekong, R.L., Kamta, H., Lambi, J.N., et al.: A sub-ppm level formaldehyde gas sensor based on Zn-doped NiO prepared by a co-precipitation route[J]. J. Alloy. Compd. 731, 1188– 1196 (2018) 19. Li, H.Y., Chuang, W., et al.: Hierarchical vanadium oxide microspheres forming from hyperbranched nanoribbons as remarkably high-performance electrode materials for supercapacitors[J]. J. Mater. Chem. A 3(45), 22892–22901 (2015) 20. Chen, H.C., Lin, Y.C., Chen, Y.L., et al.: Facile fabrication of three dimensional hierarchical nanoarchitectures of VO2/graphene@NiS2 hybrid aerogel for high-performance all-solidstate asymmetric supercapacitors with ultrahigh energy density [J]. ACS Appl. Energy Mater. (2018) 21. Deng, L., Zhang, G., Kang, L., et al.: Graphene/VO2 hybrid material for high performance electrochemical capacitor[J]. Electrochim. Acta 112, 448–457 (2013) 22. Ma, X.J., Zhang, W.B., Kong, L.B., et al. VO2: from negative electrode material to symmetric electrochemical capacitor[J]. RSC Adv 5 (2015) 23. Lv, W., Yang, C., Meng, G., et al.: (B) nanobelts/reduced graphene oxide composites for high-performance flexible all-solid-state supercapacitors[J]. Sci. Rep. 24. Ndiaye, N.M., Madito, M.J., Ngom, B.D., et al.: High-performance asymmetric supercapacitor based on vanadium dioxide and carbonized iron-polyaniline electrodes[J]. AIP Adv. 9(5), 055309 (2019); Author, F.: Article title. Journal 2(5), 99–110 (2016)
Determination Method of Solid-State Diffusion Coefficient for Lithium-Ion Batteries Based on Electrochemical Impedance Model Linjing Zhang, Kefan Zhai, Xue Cai, Caiping Zhang(B) , and Weige Zhang School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China {lj.zhang,caixue,zhangcaiping,wgzhang}@bjtu.edu.cn
Abstract. The solid-state diffusion coefficient is an important parameter to characterize the kinetics performance of lithium-ion batteries. It is the basis for establishing accurate electrochemical models. In this paper, the solid-phase diffusion coefficients of positive and negative electrodes of ternary lithium-ion batteries were measured based on electrochemical impedance spectroscopy. The expressions of battery diffusion process were derived by Fick’s law, and then the impedance model of lithium-ion batteries was built. A genetic algorithm was used to fit the electrochemical impedance spectrum of lithium ion batteries. The solid-phase diffusion coefficients were obtained according to the time constant of diffusion process. The results show that the impedance model fits well with the experimental spectroscopy. At room temperature, the solid-phase diffusion coefficient of the positive electrode of the ternary lithium-ion battery increases first and then decreases with further delithiation of the electrode. The solid-phase diffusion coefficient is approximately 10–15 ~ 10–13 m2 /s. In contrast, the degree of lithium intercalation has little effect on the solid phase diffusion coefficient of negative electrode graphite, which maintains about 10–13 m2 /s. Traditionally, the Warburg impedance is used to measure the solid-phase diffusion coefficient only in the case of semi-infinite diffusion. In comparison, the proposed method in this paper takes varied diffusion conditions in consideration. It is more suitable for different types of materials, and has better application prospects. Keywords: Lithium-ion Batteries · Electrochemical Impedance Spectroscopy · Impedance Model · Solid-state Diffusion Coefficient · Genetic Algorithm
1 Introduction In recent years, lithium-ion batteries have been widely used in electric vehicles and other energy storage fields, due to their characteristics of high energy density and low self-discharge rate. The electrochemical process of lithium-ion batteries includes the diffusion of lithium ions in electrolyte, electrode interface reaction and the diffusion of lithium ions in solid phase. At room temperature, the solid phase diffusion process of Li+ in the electrode is often slower than other processes, generally considered as the control step of dynamics performance. Therefore, the diffusion rate of Li+ in the solid © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1137–1150, 2023. https://doi.org/10.1007/978-981-99-1027-4_118
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phase determines the dynamic performance of the battery. In general, the solid-phase diffusion coefficient (Ds ) describes the transport characteristics of Li+ in the solid phase under the concentration gradient. The electrode with larger diffusion coefficient has better electrochemical performance under high rates. As a result, battery manufacturers usually hope that the diffusion coefficient as large as possible to meet the power density requirements. Therefore, the solid-phase diffusion coefficient of lithium-ion batteries is an important characterization parameter of lithium-ion batteries. At present, many determination methods of solid-phase diffusion coefficient have been studied, such as Galvanostatic Intermittent Titration Technique (GITT), Potentiostatic Intermittent Titration Technique (PITT), Capacity Intermittent Titration Technique (CITT), Cyclic Voltammetry (CV), Electrochemical Impedance Spectroscopy (EIS) [1– 3]. GITT is one of the most commonly used methods to determine the solid-phase diffusion coefficient of electrode materials for lithium-ion batteries. The principle of GITT method is to use a series of constant current pulse data to decouple the diffusion process at a specific charge state. The experiment of GITT is easy to implement and has low requirements for equipment, so PITT and CITT methods with similar principles are derived. However, the boundary conditions of GITT are strict. The time of a single pulse needs to be much less than the time constant of the diffusion process. Besides, results of GITT measurement becomes to be controversial by more and more scholars. Shen et al. [4] points out that GITT ignores the influence of SOC change on the transient change of battery voltage, caused by charging or discharging pulse. The measured solid-phase diffusion coefficient is usually 1–2 orders of magnitude larger. Schied et al. [5] shows that the charge transfer impedance increases at low temperature, in hence, the double-layer capacitance effect is significant. In this case, the precondition of GITT is no longer satisfied. Nickol et al. [6] used six different GITT-based calculation methods to determine the solid-phase diffusion coefficient of Li+ in LiNi0.5 Co0.2 Mn0.3 O2 at low temperature. The measured values might differ by 1–2 orders of magnitude using different methods. In view of the limitations of traditional GITT method, Chayambuka et al. [7] combines GITT with electrochemical model to identify the dynamic parameters of electrode materials, by simulating the initial stage of GITT pulse, which extends the limited conditions of GITT and shortens the experimental time. However, the numerous electrochemical model parameters bring the problem of additional errors, and the effectiveness of this method needs to be further verified. By means of EIS, it is possible to decouple various physical-chemical processes in wide frequency ranges. The diffusion process of lithium-ion batteries corresponds to the low frequency region ( 0, charging (7) Cbat = Pbat ηdc ηfc ηbat_dsc αLHV Pbat < 0, discharging where Cbat represents the equivalent hydrogen consumption of battery, Pbat is battery power, αLHV is the low heat value of hydrogen, and ηbat_chg , ηbat_dsc , ηdc , ηfc are battery charge efficiency, battery discharge efficiency, DC/DC convertor efficiency, and PEMFC efficiency respectively.
3 Proposed EMS Approach 3.1 Description of Objective Function The objective of EMS is minimizing the total cost of hybrid power system. The total cost can be summarized from Eqs. (2) (6) (7) as Eq. (8): (8) Costtotal = Costfc + β CfcRPL (t) + Cbat
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where β is hydrogen price (4$/kg). To ensure PEMFC and battery in optimal working states, the fuel cell output power, power deferential and battery SOC should be limited as Eq. (9) shows. ⎧ ⎨ Pfc_min ≤ Pfc ≤ Pfc_max (9) SOCmin ≤ SOC ≤ SOCmax ⎩ Pfc_def _min ≤ Pfc_def ≤ Pfc_def _max
3.2 Proposed DDPG Based EMS DDPG is an off-policy based RL using policy-gradient actor-critic algorithm, as shown in Fig. 1. The actor and critic are two different deep neural networks which represent policy network and Q-value network respectively. The actor produces action according to the environment state. Then Q-value is calculated by critic network based on action and state. Each time an action is produced, a reward from environment is generated and fed to DDPG. Since the objective of DDPG is to maximize reward by updating its policy network and Q-value network, the reward can be designed as Eq. (10) to minimize total cost of FCHV. r = −Costtotal
(10)
In order to determine the optimal recovery procedure performing time, different to common used RL-based method, the action space of proposed approach has two dimension as shown in Eq. (11). Action = Pfc , δ (11) where δ represents whether to perform recovery procedure. The state space is modified as: State = [Pload , SOC, θ ]
(12)
where Pload represents the vehicle power demand and θ represents whether recovery procedure is performing. When δ equals 1, the recovery procedure illustrated in Sect. 2.3 starts to perform, thus θ is set to 1. In the duration of recovery procedure (θ = 1), whether or not DDPG choose a positive Pfc , it is set to 0. At the end of recovery procedure, set t in Eq. (6) to 0 indicating that recoverable performance loss is completely reversed. Then set θ to 0 representing recovery procedure is not performed. In this way, the optimal time to perform recovery procedure can be obtained by DDPG and the total cost can be minimized.
4 Simulation Results The power demand of fuel cell hybrid vehicle is calculated according to New European Driving Cycle (NEDC). The technical parameters of fuel cell and battery is listed in
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Fig. 1. Structure of DDPG
Table 2. More details about vehicle and experiment can be found in 2020 IEEE VTS Motor Vehicle Challenge. The power distribution among fuel cell and battery considering recoverable performance loss is shown in Fig. 2. The time performing recovery procedure is presented in Fig. 3 where recovery state equals 1 representing PEMFC is under recovery. It can be seen that with proposed EMS, appropriate recovery procedure performing time can be determined and fuel cell is under recovery state in most time to reduce recoverable performance loss. As for battery SOC, it fluctuates between 72% and 82.5% indicating the proposed EMS meets the requirement of battery working region. To further illustrate the effectiveness of proposed EMS, DDPG based EMS without considering recoverable performance loss is compared, i.e., the action only contains power of PEMFC while state only contains power demand and battery SOC. The total cost and total equivalent hydrogen consumption cost of two methods are listed in Table 3. By performing recovery procedures, PEMFC hydrogen consumption can be reduced. As a result, the total cost is reduced by about 10.36%. Therefore, from the results we can conclude that the proposed EMS is effective.
5 Conclusion In this paper, a DDPG based EMS considering PEMFC recoverable performance loss is proposed to optimize the total cost of FCHV. The recoverable performance loss is converted to equivalent hydrogen consumption firstly. Then DDPG is performed to obtain EMS. In order to study the optimal time to perform recovery procedure, the action space and state space of DDPG is modified. The effectiveness of proposed method is verified on NEDC load condition. Comparing with normal EMS, the proposed EMS can reduce the total cost of FCHV by about 10.36%. Thus, the proposed EMS is promising to be applied in practical scenarios.
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(a)
(b)
(c)
(d)
Fig. 2. Simulation results. (a) Power demand. (b) Output power of PEMFC. (c) Output power of battery. (d) SOC of battery.
Fig. 3. Time to perform recovery procedures.
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Table 2. Technical parameters of FCHV Value Fuel cell power
[0, 58] kW
Fuel cell current
[0, 370] A
Fuel cell current derivative
[−40, 40] A/s
Battery rated voltage
48 V
Battery capacity
16 Ah
Battery SOC
[0.64, 1]
Table 3. Comparison of proposed EMS and EMS without considering recoverable performance loss Cost
Considering recoverable performance loss
Without considering recoverable performance loss
Total cost
0.70030
0.78131
Total equivalent consumption cost
0.37209
0.46317
Acknowledgements. This work is supported by Key R&D Plan of Anhui Province (Grant No. 202104h04020006), National Natural Science Foundation of China (NSFC) (Grant No. 51975549), Anhui Provincial Natural Science Foundation (Grant No. 1908085ME161), Hefei Municipal Natural Science Foundation (Grant No. 2021022), and CAS Pioneer Hundred Talents Program.
References 1. Zhang, G., Chen, W., Li, Q.: Modeling, optimization and control of a FC/battery hybrid locomotive based on ADVISOR. Int. J. Hydrog. Energy 42(185), 68–83 (2017) 2. Hu, Z., Li, J., Xu, L., Song, Z., Fang, C., Ouyang, M., et al.: Multi-objective energy management optimization and parameter sizing for proton exchange membrane hybrid fuel cell vehicles. Energy Convers. Manag. 129(10), 8–21 (2016) 3. Odeim, F., Roes, J., Heinzel, A.: Power management optimization of a fuel cell/battery/supercapacitor hybrid system for transit bus applications. IEEE Trans. Veh. Technol. 65(578), 3–8 (2016) 4. Ettihir, K., Higuita, C.M., Boulon, L., Agbossou, K.: Design of an adaptive EMS for fuel cell vehicles. Int. J. Hydrog. Energy 42, 1481–1489 (2017) 5. Wu, Y., Tan, H., Peng, J., Zhang, H., He, H.: Deep reinforcement learning of energy management with continuous control strategy and traffic information for a series-parallel plug-in hybrid electric bus. Appl. Energy 247(4), 54–66 (2019) 6. Zhang, Q., Schulze, M., Gazdzicki, P., Friedrich, K.A.: Quantification of effects of performance recovery procedures for polymer electrolyte membrane fuel cells. J. Power Sources 512(3), 16:32 (2021)
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7. Zago, M., Baricci, A., Bisello, A., Jahnke, T., Yu, H., Maric, R., et al.: Corrigendum to “Experimental analysis of recoverable performance loss induced by platinum oxide formation at the polymer electrolyte membrane fuel cell cathode”. J. Power Sources 455–466 (2020) 8. Mitzel, J., Zhang, Q., Gazdzicki, P., Friedrich, K.A.: Review on mechanisms and recovery procedures for reversible performance losses in polymer electrolyte membrane fuel cells. J. Power Sources 488 (2021) 9. Li, Q., Meng, X., Gao, F., Zhang, G., Chen, W.: Approximate cost-optimal energy management of hydrogen electric multiple unit trains using double Q-learning algorithm. IEEE Trans. Ind. Electron. 69(90), 99–110 (2022) 10. Lin, L.-C., Cheng, Y.-S., Liao, W.-C., Huang, Y.-H., Pan, Y.-T.: Transient loss and recovery of platinum fuel cell cathode catalyst at high voltage efficiency regimes. J. Electrochem. Soc. 168(5), 78–110 (2021)
Collaborative Eco-Routing Optimization for Continuous Traffic Flow in a Road Network Qianyou Chen1(B) , Yitao Wu1 , Zhenzhen Lei2 , Zheng Chen3 , and Yonggang Liu1 1 College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044,
China [email protected] 2 School of Mechanical and Power Engineering, Chongqing University of Science & Technology, Chongqing 401331, China 3 Faculty of Transportation Engineering, Kunming University of Science and Technology, Kunming 650500, China
Abstract. Transportation is one of the critical factors that leads to energy crisis, and over the years there has been a lot of research around the improvement of vehicle energy efficiency. To effectively reduce the overall energy consumption of continuous traffic flow in a road network, a collaborative eco-routing optimization strategy is proposed. The strategy takes advantage of the differences in energy consumption characteristics among vehicles to coordinate the path allocation among vehicles. It improves the energy consumption of low-energy-consumption vehicles and reduces the energy consumption of high-energy-consumption vehicles more significantly, thus achieving the effect of improving the overall economy. The simulation results show that the proposed method can effectively improve the economy of all vehicles in the road network by up to 4.85% without additional time cost. Keywords: Eco-routing · Continuous traffic flow · Co-optimization
1 Introduction With the rapid development of modern industry, energy consumption and greenhouse gas emissions make significant contribution to energy and environment crisis, in which the energy consumption of the automotive industry shares a main part. Over the years, there has been a lot of research around automotive energy efficiency. In terms of energy management, Ref. [1] identifies a pair of boundary equivalence factors based on future traffic information and proposes an adaptive equivalent fuel consumption minimization strategy. An energy management strategy based on driver behavior prediction is proposed in [2], to reduce the energy consumption of hybrid buses. Reference [3] proposes an online PHEV energy management control method based on driving environment identification and genetic algorithm. An energy management strategy based on model predictive control is proposed in [4], by combining the information of V2V and V2I, the accuracy of speed prediction can be improved. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1169–1173, 2023. https://doi.org/10.1007/978-981-99-1027-4_121
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In recent years, research on vehicle energy efficiency has gradually shifted from energy management to eco-driving and eco-routing, aiming to further exploit the energysaving potential in vehicle driving. A collaborative optimization strategy for speed planning and energy management of plug-in hybrid electric vehicles is proposed in [5], using iterative dynamic planning to achieve collaborative optimization of speed planning and power allocation. An eco-driving control strategy based on model predictive control is applied in [6], which ensure safe driving in hybrid driving scenarios and effectively reduce energy consumption and emissions. The optimal eco-routing problem is solved by the A-star algorithm and the fastest path is compared in [7]. The results show that for HEVs, the eco-path has lower consumption and is easier to meet the terminal SOC constraint but increases travel time. Reference [8] presents the optimization problem of collaborative planning of eco-routing and eco-driving, and solves it with genetic algorithm. Lagrangian relaxation methods is applied to eco-routing problems with travel time constraints in [9]. However, there is a few literatures on eco-routing that considers multi-vehicle collaborative planning. If the eco-routing strategy is employed by all drivers in a certain area and the drivers take the suggested path, the route will quickly become congested, leading to increased emissions, i.e., multi-vehicle collaboration in route assignment is not considered [10]. In this paper, a collaborative eco-routing optimization strategy is proposed to effectively reduce the overall energy consumption of continuous traffic flow in a road network. We have fully considered the effect of mutual congestion between vehicles and use the difference in energy consumption levels between different vehicles for route allocation. The simulation results show that the proposed method can effectively improve the economy of all vehicles in the road network.
2 The Collaborative Eco-Routing Optimization Strategy When a continuous traffic flow passes through the road network, the path of vehicles in the flow are allowed to be different. Supposing they have the same start and end point, the problem to be solved in this study is to find a reasonable path distribution strategy to optimize the overall energy consumption while satisfying the time constraint. The optimization problem can be described as follows. wijk xijk (1) min Z = k∈Q ij∈E
tijt = tij0 [1 + α(
ntij cij
)β ]
(2)
where Z is the optimization target, which is the sum of the costs of vehicles in the road network for all considered traffic flows, Q is the set of traffic flows, xijk represents whether the kth vehicle passes through the road section ij, wijk is the cost of the kth vehicle traveling on section ij, tij0 denotes the travel time when there is only one vehicle on the road section ij (running at the maximum speed limit of the road section), α, β are constant factors, ntij is the number of vehicles on road segment ij at second t, cij
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means the rated capacity of road segment ij. The BPR function (2) is introduced to reflect the road congestion level, which shows that when the number of vehicles on the same road increases, this road becomes congested, reducing the speed of all vehicles and increasing energy consumption. We define virtual costs to accomplish path allocation, and the strategy flow chart is as follows (Fig. 1).
Fig. 1. Flow chart of routing distribution strategy
When each vehicle is planned for a path, the actual cost rijk is calculated first, then the virtual cost rijkv is calculated by considering the impact on the following vehicles, and finally the path Rkv is obtained from the virtual cost. If the path obtained from the virtual cost exceeds the time limit, the time-optimal path is selected. For example, the nearest path contains roads a-b; the current vehicle energy consumption level is y0 , and the energy consumption level of m vehicles in the following period is y1−m . The virtual kv can be calculated as: cost rab kv k rab = rab +ε
m
max(0, yi − y0 )
(3)
i=1
3 Simulation and Analysis In this study, a part of area in Chongqing city are selected to model the road network. The road network model ignores some narrower passable roads in the region and designates a total of 14 road sections between nodes as passable routes. The adjacency matrix is used to build the model, and the distances between the nodes are obtained from online map measurements, as shown in Fig. 2 (a).
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Fig. 2. The road networks and the simulation results of two strategies
Set point 6 as the starting point and point 10 as the end point, and there are 100 vehicles in total. The model of each vehicle is chosen randomly among EV, FV and HEV. An alternative strategy is set up for comparison, where each vehicle departs independently to find the fastest path, namely the independent-vehicle time-optimal strategy (TOS). The strategy proposed in this study is named the collaborative eco-routing optimization strategy (COS). The simulation results of two strategies are as follows. Table 1. Comparison of simulation results TOS
COS
Energy consumption of EV (CNY)
17.99
23.04 (+28.07%)
Energy consumption of FV (CNY)
146.59
136.90 (−6.61%)
Energy consumption of HEV (CNY)
54.25
48.27 (−11.02%)
Total consumption (CNY)
218.83
208.21 (−4.85%)
Total time (seconds)
537
524 (−2.42%)
The differences in path allocation between the two strategies are shown in the Fig. 2 (b). There is no significant difference between the vehicles in TOS, while EVs are required to travel a longer trip than HEV and FV in COS. In Table 1, It can be found that COS increases the driving cost of EV to some extent than TOS but leads to a great cost reduction of FV and HEV, thus the total cost is reduced by 4.85%, and the total time is shorter by 2.42%. The optimization results conducted by COS indicate that the proposed eco-routing strategy can effectively reduce the overall cost in a certain road network without influence on travel time efficiency.
4 Conclusion This paper investigates the path co-allocation strategy for continuous traffic flow in a local road network, which have fully considered the problem of increased energy consumption due to congestion on the same road section. The strategy takes advantage
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of the differences in energy consumption levels between different vehicles and allocates their paths rationally. The economy of low-energy-consumption vehicles is sacrificed for more economy of high-energy-consumption vehicles, which results in a reduction of overall energy consumption. The simulation results show that the proposed strategy reduces the total energy cost by 4.85% compared with the independent-vehicle timeoptimal strategy, which manifests the effectiveness of the proposed method in improving area energy economy. Acknowledgements. The work is funded by the National Natural Science Foundation of China (No. 52002046).
References 1. Liu, Y., Li, J., Lei, Z., Li, W., Qin, D., Chen, Z.: An adaptive equivalent consumption minimization strategy for plug-in hybrid electric vehicles based on energy balance principle. IEEE Access 7, 67589–67601 (2019). https://doi.org/10.1109/access.2019.2918277 2. Li, M., He, H., Feng, L., Chen, Y., Yan, M.: Hierarchical predictive energy management of hybrid electric buses based on driver information. J. Clean. Prod. 269 (2020). https://doi.org/ 10.1016/j.jclepro.2020.122374 3. Liu, T., Yu, H., Guo, H., Qin, Y., Zou, Y.: Online energy management for multimode plug-in hybrid electric vehicles. IEEE Trans. Ind. Inform. 15(7), 4352–4361 (2019). https://doi.org/ 10.1109/tii.2018.2880897 4. He, H., Wang, Y., Han, R., Han, M., Bai, Y., Liu, Q.: An improved MPC-based energy management strategy for hybrid vehicles using V2V and V2I communications. Energy 225 (2021). https://doi.org/10.1016/j.energy.2021.120273 5. Li, J., Liu, Y., Zhang, Y., Lei, Z., Chen, Z., Li, G.: Data-driven based eco-driving control for plug-in hybrid electric vehicles. J. Power Sources 498 (2021). https://doi.org/10.1016/j.jpo wsour.2021.229916 6. Wang, S., Lin, X.: Eco-driving control of connected and automated hybrid vehicles in mixed driving scenarios. Appl. Energy 271 (2020). https://doi.org/10.1016/j.apenergy.2020.115233 7. Le Rhun, A., Bonnans, F., De Nunzio, G.: An eco-routing algorithm for HEVs under traffic. IFAC-PapersOnLine 6 (2020) 8. Miao, C., Liu, H., Zhu, G.G., Chen, H.: Connectivity-based optimization of vehicle route and speed for improved fuel economy. Transp. Res. Part C: Emerg. Technol. 91, 353–368 (2018). https://doi.org/10.1016/j.trc.2018.04.014 9. Zeng, W., Miwa, T., Morikawa, T.: Eco-routing problem considering fuel consumption and probabilistic travel time budget. Transp. Res. Part D: Transp. Environ. 78 (2020). https://doi. org/10.1016/j.trd.2019.102219 10. Alam, M.S., McNabola, A.: A critical review and assessment of eco-driving policy & technology: benefits & limitations. Transp. Policy 35, 42–49 (2014). https://doi.org/10.1016/j.tra npol.2014.05.016
Lithium-Ion Battery SOC Estimation Based on OWA Operator Fusion Algorithm Aihua Tang , Jiajie Li , and Yukun Huang(B) School of Vehicle Engineering, Chongqing University of Technology, Chongqing 400054, China [email protected], [email protected], [email protected]
Abstract. The accuracy and robustness of the state of charge (SOC) estimation play an important role in the overall deployment and control of the battery management system. To maintain high accuracy and stability of SOC estimation in the whole range, the author uses OWA (ordered weighted average) operator to fuse three Kalman filter algorithms. OWA operators can assign weights to different algorithms based on values that approximately characterize the estimation accuracy. In this paper, the weights are updated based on the voltage residual and the real covariance respectively. The results show that whether it is the OWA fusion algorithm based on voltage residues or the OWA fusion algorithm based on the real Covariance, the estimated accuracy and robustness are better than the single algorithm. Keywords: SOC estimation · Kalman filter · Fusion · OWA
1 Introduction With the implementation and promotion of the “double carbon” policy, the new energy vehicle industry has developed rapidly. However, the problems of short battery life, slow charging speed, inaccurate and unstable SOC measurement seriously hinder the development of new energy vehicles, especially the accuracy and robustness of battery SOC estimation are the most urgent problems to be solved. At present, there are generally four types of common SOC estimation methods (1) the method based on Ah counting [1, 2], (2) the method based on characterization parameters [3, 4], (3) the method based on data driven [5, 6] and (4) the method based on battery model [7, 8]. The method based on Ah counting is simple and easy to achieve, but it has high dependence on accurate SOC’s initial value and it needs to be revised regularly. The method based on characterization parameters has excellent real-time performance, but it is easy to be affected by uncertain factors such as working environment, external temperature, aging degree and so on. The method based on data driven has high estimation accuracy, but it is highly dependent on the data which is used for training. The method based on battery model is the most common SOC estimation method, including Kalman filter, HIF and so on. Liu and Yu [9] uses a square root unscented Kalman filter, which has high SOC estimation accuracy. Cui et al. [10] uses an extended Kalman filter, which © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1174–1182, 2023. https://doi.org/10.1007/978-981-99-1027-4_122
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can solve the interference caused by the white noise in the system. However, most of the current studies only pay attention to the accuracy or robustness of battery SOC estimation in part of the interval. In order to guarantee the high accuracy and robustness of Kalman filter in the whole region, OWA operator is introduced in this paper.
2 Battery Modeling and Parameter Identification In this paper, Thevenin equivalent circuit model is established, as shown in Fig. 1. RD iL
Ri CD UD Uoc
Ut
Fig. 1. Thevenin model.
The battery state space equation can be written as follows: ⎧ ⎨ U˙ = iL − UD D CD CD RD ⎩ Ut = UOC − UD − iL Ri
(1)
where UD is the terminal voltage. UOC refers to the OCV of the battery, which has a specific functional relationship with the battery SOC. Ri represents ohmic internal resistance. CD is the polarization capacitance. RD is the internal resistance of polarization. iL is the circuit current. After the model is established, we need to recognize parameters. Common methods of identifying parameters include the recursive least squares, genetic algorithm and Kalman filter method. This article adopts the recursive least squares method containing genetic factor, and the identification results are shown in Table 1. Table 1. Identification results. Parameter Ri CD RD
Value 0.0114139676360643 1393.06158162959 0.129928005362772
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3 Kalman Filter 3.1 Adaptive Extended Kalman Filter This section introduces three different Kalman filter algorithms, which have their own advantages. AEKF has simple principle and high calculation efficiency. CDKF does not need to calculate Jacobian matrix. HIF has strong ability to resist the influence of model accuracy. The detailed implementation process is shown as follows. Step 1: Initialization Set initial value of algorithm: x0 , P0 , Q0 , R0 . Step 2: Priori estimate The time update equation of AEKF filter is expressed as follows: System state estimation: xˆ − k = f (xk−1 , uk−1 ). Update of covariance matrix of state estimation error: Pk− = Ak−1 Pk−1 ATk−1 + Qk−1
(2)
ek = yk − h(ˆx− k , uk )
(3)
Kk = Pk− CkT (Ck Pk− CkT + Rk−1 )−1
(4)
Step 3: Posterior estimation Innovation matrix:
AEKF gain matrix:
Adaptive noise covariance matching: Hk =
1 M
k
eieiT
i=k−M +1 Rk = Hk − Ck Pk− CkT Qk = Kk Hk KkT
(5)
xˆ + ˆ− k =x k + Kk ek
(6)
System status correction:
Update of covariance matrix of state estimation error: Pk+ = (I − Kk Ck )Pk−
(7)
xk = xˆ + ˆ k+ k , pk = p
(8)
Step 4: Time update
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3.2 The Central Difference Filter Flow of CDKF algorithm Step 1: Initialization Set the initial value of the filter algorithm: k = 1, xˆ 0 = E[x0 ] P0 = E[(x0 − xˆ 0 )(x0 − xˆ 0 )T ] Step 2: Construct 2m + 1 dimension Sigma point Xk−1 = [ˆxk−1 xˆ k−1 +(h Pk−1 )j xˆ k−1 −(h Pk−1 )j ]
(9)
(10)
Step 3: Time update Status estimation: Xk|k−1 = f(Xk−1 , uk ) + Xw k−1 xˆ − k =
2M
Wj Xj,k|k−1
(11)
j=0
Elementary estimation: Pk− =
2M
T Wj (Xj,k|k−1 − xˆ − ˆ− k )(Xj,k|k−1 − x k)
(12)
j=0
Observation estimation: yk|k−1 = g(Xk|k−1 , uk ) + Xvk|k−1 2M
yˆ k =
Wi yi,k|k−1
(13)
j=0
Step 4: Measured update Cross covariance: Pxk yk =
2M
T Wj (Xj,k|k−1 − xˆ − ˆ− k )(yj,k|k−1 − y k)
(14)
T Wj (yj,k|k−1 − yˆ − ˆ− k )(yj,k|k−1 − y k)
(15)
j=0
Auto covariance: Pyk yk =
2M j=0
Estimated gain matrix: Kk = Pxk yk Py−1 k yk Status estimation measurement update: xˆ k = xˆ − ˆ− k +Kk (yk − y k) Pk =Pk− − Kk Pyk yk KkT Step 5: Cycle When k = k + 1 repeat steps 2–4.
(16)
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3.3 H-Infinity Filter HIF algorithm flow is shown in Table 2. Step 1: Initialization Set the initial value of the algorithm: x0 , P0 , Q, R, λ, S Step 2: Priori estimate The time update equation of AEKF filter is expressed as follows: System state estimation: xˆ − k = f (xk−1 , uk−1 ). Update of covariance matrix of state estimation error: Pk− = Ak−1 Pk−1 ATk−1 + Q
(17)
Table 2. The flow of HIF algorithm. Step
Flow
1
Initialization
2
For k = 1,2,…, complete the priori estimation operation, and calculate the state and covariance estimation from the previous time to the current time
3
In this step, the measured value yk at time k is used to correct the state estimation and
4
covariance estimation. The estimation results are expressed in xˆ k+ and Pk+ respectively Take the state and covariance matrix at the time k as the final output, and prepare the state estimation at (k + 1) time
Step 3: Posterior estimation Innovation matrix: ek = yk − h(ˆx− k , uk )
(18)
Kk = Ak Pk− (1 − λSPk− + CkT R−1 Ck Pk− )−1 CkT R−1
(19)
HIF gain matrix:
System status correction: xˆ + ˆ− k =x k + Kk ek
(20)
HIF characteristic matrix correction: Pk+ = Pk− (1 − λSPk− + CkT R−1 Ck Pk− )−1 Step 4: Time update
(21)
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4 OWA Operator Fusion Algorithm In order to combine the advantages of the three algorithms, the OWA operator is proposed. The framework of the OWA operator is as follows: ωk,i =
−1
N
−1 xk,i
−1 xk,i
(22)
i=1
(1) Voltage residual The expression of voltage residual is as follows: rk,i = Uk,i − Uˆ k,i
(23)
In formula: rk,i represents the voltage residual of the filter algorithm of type i at time k. Uk,i represents the measured value of terminal voltage corresponding to the filter algorithm of type i at time k. Uˆ k,i represents the terminal voltage prediction value of the filter algorithm of type i at time k. When the voltage residual is brought into the OWA operator framework, the formula giving the algorithm weight can be obtained. ωk,i =
N
−1 −1 rk,i
−1 rk,i
(24)
i=1
(2) Real covariance The expression of real covariance is as follows: Hk,i
N 1 T = rk,i rk,i N
(25)
i=1
In formula: Hk,i represents the real covariance of the filter algorithm of type i at time k. rk,i represents the voltage residual of the filter algorithm of type i at time k. N denotes the number of filter algorithms. When the real covariance is brought into the OWA operator framework, the formula giving the algorithm weight can be obtained. ωk,i =
N i=1
−1 −1 Hk,i
−1 Hk,i
(26)
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5 Results and Discussion NMC lithium battery pack is selected as the power battery pack. AEKF filtering algorithm, CDKF filtering algorithm and HIF filtering algorithm are selected. Figure 2 is a schematic diagram of the comparison of SOC estimated value and SOC real value before and after the fusion of each filtering algorithm. It can be seen from Fig. 3 that the power battery state estimation method proposed by the invention has smoother estimation results than each single filter algorithm, and has better follow-up in the whole process of SOC estimation. Among them, the method of weight allocation and fusion based on voltage residual has the best follow-up in the whole process of SOC estimation.
Fig. 2. SOC estimation results of single algorithm and fusion algorithm
6 Conclusions In this paper, the equivalent circuit model of NMC battery is established, and the model parameters are identified through the experimental data. In order to integrate the advantages of AEKF, CDKF and HIF, OWA operator is proposed, and the three algorithms are weighted and fused by real covariance and voltage residual respectively. Three single algorithms and two forms of fusion algorithm are used to estimate the SOC of NMC battery. The results show that compared with the existing literature, this method achieves relatively high SOC estimation accuracy. With high model accuracy, the SOC estimation error of the fusion algorithm is less than 0.15%.
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Fig. 3. Mean value of error
Acknowledgments. This work was jointly supported by the National Natural Science Foundation of China (Grant No. 52277213), Natural Science Foundation of Chongqing, China (Grant No. Cstc2021jcyj-msxmX0464) and Key Project of Science and Technology Research Program of Chongqing Education Commission of China (Grant No. KJZD-K202201103).
References 1. Yang, N., Zhang, X., Li, G.: State of charge estimation for pulse discharge of a LiFePO4 battery by a revised Ah counting. Electrochim. Acta 151, 63–71 (2015) 2. Huang, H., et al.: A comprehensively optimized lithium-ion battery state-of-health estimator based on local Coulomb counting curve. Appl. Energy 322 (2022) 3. Lee, S.J., Kim, J.H., Lee, J.M., Cho, B.H.: The state and parameter estimation of an Li-ion battery using a new OCV-SOC concept. In: IEEE Power Electronics Specialists Conference, pp. 2799–2803 (2007) 4. Zhang, S., Zhang, X.: A novel non-experiment-based reconstruction method for the relationship between open-circuit-voltage and state-of-charge/state-of-energy of lithium-ion battery. Electrochim. Acta 403 (2022) 5. Fan, X., Zhang, W., Zhang, C., Chen, A., An, F.: SOC estimation of Li-ion battery using convolutional neural network with U-Net architecture. Energy 256 (2022) 6. Chaoran, L., Fei, X., Yaxiang, F., Guorun, Y., Xin, T.: An approach to lithium-ion battery SOH estimation based on convolutional neural network. Trans. China Electrotech. Soc. 35(19), 4106–4119 (2020) 7. Xile, D., Caiping, Z., Jiuchun, J.: Evaluation of SOC estimation method based on EKF/AEKF under noise interference. Energy Procedia 152, 520–525 (2018)
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8. Xu, C., et al.: Dual fuzzy-based adaptive extended Kalman filter for state of charge estimation of liquid metal battery. Appl. Energy 327 (2022) 9. Liu, Q., Yu, Q.: The lithium battery SOC estimation on square root unscented Kalman filter. Energy Rep. 8, 286–294 (2022) 10. Cui, Z., Weihao, H., Zhang, G., Zhang, Z., Chen, Z.: An extended Kalman filter based SOC estimation method for Li-ion battery. Energy Rep. 8, 81–87 (2022)
Model Predictive Control Based Frequency Regulation for Power Systems Containing Massive Energy Storage Clusters Yujun Lin , Qiufan Yang, Jianyu Zhou, Xia Chen(B) , and Jinyu Wen State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China [email protected], {yangqiufan,jinyu.wen}@hust.edu.cn, [email protected]
Abstract. A large number of small-capacity distributed energy storage (ES) systems have been introduced to take an important part in grid frequency regulation. However, the accompanying high-order optimization problem causes an inevitable issue for both centralized and distributed control methods. Accordingly, based on the reduced-order predictive model, a two-layer control strategy of frequency support for power systems is proposed in this paper, in which the frequency regulation and economic dispatch are combined. The lower layer is implemented in a distributed framework which only requires communication between adjacent ESs, and the upper layer only utilizes the reduced-order information sent from the lower layer which lessens the computation burdens. The effectiveness of the entire control method is validated under different scenarios by simulations. As indicated in the simulation results, the proposed method achieves almost the same control effect in ES clusters as that using centralized control with a shorter computing time. And the proposed method incorporates the widespread multiple small-capacity ESs effectively for power system frequency control. Keywords: Frequency Support · Model Predictive Control (MPC) · Economic Dispatch · Energy Storage
1 Introduction The increasing integration of renewable energy sources (RESs) such as wind and solar lead to undesired power fluctuations in power systems. The synchronous generators are replaced and the system frequency reserves are subsequently reduced. To cope with the frequency regulation of high RES penetrated power systems, energy storage (ES) is introduced due to its high flexibility. Distributed small-capacity ESs show some unique advantages like lower transmission loss, reduced investment and operation costs [1]. However, distributed small-capacity ESs with large amounts bring great technical challenges to the frequency control just like huge computational burden and low efficiency. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1183–1190, 2023. https://doi.org/10.1007/978-981-99-1027-4_123
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As for control schemes, centralized control methods have been proposed for ESs to help in frequency regulation. However, the centralized control method meets its limitations when implemented on distributed ESs, because a centralized controller and its communication access to every controllable ES are required. Under this infrastructure, the communication burden is heavy and the plug-and-play capability, which is desired for small-scale distributed ESs, is lacking. Therefore, distributed control scheme is of growing concern. Distributed control schemes for frequency control have been studied in [2–4]. In addition, the prediction intelligence of each individual agent is introduced in distributed control by utilizing model predictive control (MPC) to deal with the predictable uncertainties. The recent works have explored distributed MPC’s application in secondary voltage control, active power dispatch for wind farm cluster [5] and grid frequency regulation [6]. However, the aforementioned works mainly focus on centralized large-scale ESs or distributed small-scale ESs with small quantities. Problems appear when the amounts of ESs connected with utility grid become larger [7]. To deal with the problem brought by large quantities of controlled objects, an aggregator (reduced-order) model is introduced in the recent works. There are methods proposed to build the aggregator models for inverters [8], wind turbine [9–11], and microgrids [12]. The aims of the aforementioned aggregator models are mainly stability analysis for power systems. Furthermore, aggregator models are also utilized to provide system frequency regulation services [7, 13, 14]. Motivated by the discussion above, a two-layer control strategy of frequency support for power systems based on aggregator model is proposed in this paper, in which the frequency regulation among clusters and economic operation within clusters are achieved respectively. The lower layer is implemented to allocate the power reference signals from the upper layer, and the upper layer only uses the aggregate information sent from the lower layer, which reduces the computation burdens.
2 Methods 2.1 The Lower Layer The Consensus-based Economical Dispatch Method (CEDM). As shown in Fig. 1, the lower layer conducts economical dispatch problem as Fig. 1 after receiving the control signal uClu from the upper layer, with N ESs in one cluster. ⎧ Min Ui (Pi ) ⎪ ⎪ ⎪ i∈NClu ⎨ s.t. Pi = uClu ⎪ i∈NClu ⎪ ⎪ ⎩ ES Pi ∈ [P ES i , Pi ]
(1)
The operation cost of ES i can be presented by a convex linear-quadratic cost function [15] as Ui (Pi ) = ai Pi + bi Pi2
(2)
Model Predictive Control Based Frequency Regulation for Power The ith Cluster
CEDM
P1
+
u2
1 1+sT2
P2
+
uN
1 1+sTN
1+sT1
ES3
uiClu ES1
ESN
ES2
The actual model The reduced model
ESs model u1 1
GCon(s)
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PN +
GClu(s)
Fig. 1. The consensus-based economical dispatch in one cluster.
where ai and bi are cost coefficients of ES i . According to the equal incremental dispatch principle, matching the incremental costs (ICs) of ESs is the standard for the economical dispatch in one cluster. Mi (Pi ) =
dUi (Pi ) = λ∗ = ai + 2bi Pi∗ dPi
(3)
Consequently, to achieve the economic operation of cluster, a consensus control protocol is designed for satisfying lim λi − λ∗ , ∀i ∈ SClu (4) t→∞
Set Pi,k (0) = PClu /N
Pˆ˙ i =
aij (λj − λi )
(5) (6)
i∈NClu
where Pi,k (0) is the initial value of control signal to ES i during kth cycle. It’s obtained by sharing the cluster’s control signal evenly. We select ui P (t) to represent the control input of ES i . ESs Reduced-order Aggregation Model. Due to the large amount of the ESs with heterogeneous parameters, it’s hard to model the actual characteristics of each ES. So the reduced-order aggregation model of ESs is built in this subsection. As shown in Fig. 3, the reduced-order aggregation model is divided into two transfer function Gcon (s) and GClu (s). Gcon (s) stands for the inertia effect of CEDM. The proposed DMPC method could accelerate the converge speed to under 0.5 s as shown in Sect. V A, thus the inertia effect of CEDM could be ignored compared to ESs, Gcon (s) = 1. GClu (s) stands for the inertia effect of aggregated ES cluster, which can be represented as GClu (s) = 1/(1 + sT Clu ). The aggregated inertia coefficient T Clu is obtained by TClu SiES = Ti SiES (7) i∈NClu
i∈NClu
where NClu represents the set of ESs belong to the cluster. Si ES is the capacity of ESi.
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2.2 The Upper Layer The state-space model of the whole power system is express as x˙ u = Au xu + Bu uu + Fu du
(8)
yu = Cu xu
(9)
Clu ]T . where xu = [f Pt Pg,1 Pg,2 PI PClu,1 …PClu,M ]T , uu = [u1Clu …uM The state-space model is translated into discrete form by
xd (k + 1) = Ad xd (k) + Bd ud (k) + Fd dd (k)
(10)
yd = Cd xd (k)
(11)
t t where Ad = eAu td , Bd = 0d eAu td Bu dt, Cd = Cu , Fd = 0d eAu td Fu dt. With the prediction and control steps denoted as N pc and N cc , the dynamic model can be extended to N pc steps ahead as X(k + 1) = SA X(k) + SB UU (k)
(12)
Y(k) = SC X(k)
(13)
where X T (k + 1) = [xd T (k + 1), xd T (k + 2)…, xd T (k + N p )] ∈ R1×Npc N , U u T (k) = [uu T (k), uu T (k + 1)…, uu T (k + N cc − 1)], Y T (k) = [yd T (k), yd T (k + 1)…, yd T (k + N pc − 1)] ∈ R1×Npc N . JU (k) = YU (k + 1)2Q + UU (k)2R = qu
Npc k=0
(f (k))2 + ru
Ncc
uu2 (k)
(14)
k=0
where QU and RU are weighting matrices, which are selected as QU = diag(qu , qu ,…qu ) ∈ RNpc×Npc , RU = diag(r u , r u ,…r u ) ∈ RNcc×Ncc . The minimization of the cost function can be solved by MATLAB. After obtaining Clu ]T , to the optimal solution, the upper layer only sends the first item, uu = [u1Clu …uM every ES cluster until the next control step.
3 Experimental Validation and Results Comparison The effectiveness of the proposed two-layer frequency regulation strategy is tested in this section by setting a system with 10 ESs. The parameters of the system are given in Tables 1 and 2.
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Table 1. Parameters of AGC and conventional thermal plants. Item
Value
Item
Value
R
0.04
T CH
0.2 s
D
1.6
T RH
7s
M
12
F HP
0.3 s
Tg
0.2 s
Table 2. Parameters of ESs. Cluster
1
2
3
ES
Response time (s)
Power range (MW)
Ramping-rate constraints (GW/h)
Cost coefficient ai ($/MW)
bi ($/MW2 )
2.7
60
1-1
0.4
±9
±10
1-2
0.3
±10
±15
52.5
1-3
0.2
±11
±20
45
1-4
0.1
±12
±25
37.5
2-1
4
±10
±20
60
2-2
1
±9
±15
52.5
2-3
0.1
±8
±10
45
3-1
10
±10
±20
60
3-2
1
±6
±15
52.5
3-3
0.1
±3
±10
45
3.1 Case 1: Dynamic Performance In this case, the dynamic response of the system to a 150 MW step load change is investigated to illustrate the effectiveness of the two-layer frequency control strategy. Figure 2 shows the frequency response under loading transitions. The maximum frequency deviations are about 1.5 and 2.5 Hz with and without ES clusters. The maximum frequency deviation has decreased by about 40% and the overshoot is eliminated by ES clusters. The frequency nadir can be limited within the range of security operation of the power system. The clusters with smaller equivalent inertia have faster dynamic response, thus the frequency control signal for them is larger. And as shown in Fig. 2 (b), the active power of clusters is nearly synchronous with the power signals. It indicates that the ES clusters are easier to control. Taking Cluster 1 for example, the convergence of the lower layer is completed within every iteration step of the upper layer as shown in Fig. 2 (c)(d), which means the time scales of the upper and lower layer coordinate with each other.
Cluster 1 Cluster 2 Cluster 3
20 10 0
(c) Control signal to ESs (MW)
-10 0
20
40 60 Time (s)
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12
10
8
80
100
4
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0 -5 0
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(d) Output power of ESs (MW)
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20
40 60 Time (s)
15
12
10
8
80
100
4
5
00
10
20
0 -5 0
20
40 60 Time (s)
80
100
Fig. 2. The controller performance under loading transitions in case 2: (a) control signals to clusters, (b) output power of clusters, (c) control signals to ESs, (d) output power of ESs.
3.2 Case 2: Control Scheme Comparisons
1.07
1.06
1.05
1.04
1.03
1.02 1 0
1.01 0.99
0
20
5
10
40
60
Time(s) (a)
15 80
20 100
Increment cost of ESs (pu)
Increment cost of ESs (pu)
In this sub-section, the control performance of a centralized control method in [6] is compared with the proposed two-layer frequency control method. The centralized control method uses only one centralized controller to send the control signal directly to the ESs. Figure 3 illustrates that the proposed method guarantees the convergence of ICs within each cluster, while the ICs under the centralized control do not complete convergence until the frequency deviation is eliminated at nearly t = 55 s. It is the result of different control structures. The proposed method separates the frequency regulation and economic operation into two layers, while the centralized control makes a tradeoff between them. In conclusion, the proposed two-layer frequency control provides an effective method to guarantee the frequency regulation and the economic operation of ESs with an increased computational efficiency.
ES 1-1 ES 1-2 ES 2-1 ES 3-1
1.05 1.03
ES 1-3 ES 2-2 ES 3-2
ES 1-4 ES 2-3 ES 3-3
1.01 0.99
0
20
40
60
80
100
Time(s) (b)
Fig. 3. The comparison of ICs curves under (a) the proposed method, (b) the centralized control.
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4 Conclusion A frequency control strategy based on the aggregator model is proposed in this paper, in which the upper layer deals with the aggregate power signal allocation among clusters, and the lower layer decomposes the signal within clusters. The controller of the upper layer periodically samples the aggregate information of a cluster, solves an optimization problem online, and provides the power signals to the lower layer. The lower layer aims to disaggregate the power signals to individual ESs for economic dispatch. In conclusion, with the proposed control scheme, the computational burdens are lightened and the control resilience is guaranteed as indicated in the simulation results. The results show that it effectively incorporates the widespread multiple small-capacity ESs for power system frequency control. It provides a practical method to solve the challenges encountered by power systems with widespread distributed ESs. Acknowledgements. This work is supported by Science and Technology Project of State Grid Corporation of China 5419-202199551A-0-5-ZN.
References 1. Meng, L., et al.: Fast frequency response from energy storage systems—a review of grid standards, projects and technical issues. IEEE Trans. Smart Grid 11, 1566–1581 (2020) 2. Shi, M., Chen, X., Zhou, J., Chen, Y., Wen, J., He, H.: PI-consensus based distributed control of AC microgrids. IEEE Trans. Power Syst. 35(3), 2268–2278 (2020) 3. Ding, L., Han, Q., Zhang, X.: Distributed secondary control for active power sharing and frequency regulation in islanded microgrids using an event-triggered communication mechanism. IEEE Trans. Ind. Inform. 15(7), 3910–3922 (2019) 4. Wang, Z., Wu, W., Zhang, B.: A distributed quasi-Newton method for droop-free primary frequency control in autonomous microgrids. IEEE Trans. Smart Grid 1 (2018) 5. Ye, L., et al.: Hierarchical model predictive control strategy based on dynamic active power dispatch for wind power cluster integration. IEEE Trans. Power Syst. 34(6), 4617–4629 (2019) 6. Yi, Z., Xu, Y., Gu, W., Fei, Z.: Distributed model predictive control based secondary frequency regulation for a microgrid with massive distributed resources. IEEE Trans. Sustain. Energy 12(2), 1078–1089 (2021) 7. Rey, F., Zhang, X., Merkli, S., Agliati, V., Kamgarpour, M., Lygeros, J.: Strengthening the group: aggregated frequency reserve bidding with ADMM. IEEE Trans. Smart Grid 10(4), 3860–3869 (2019) 8. Purba, V., Johnson, B.B., Jafarpour, S., Bullo, F., Dhople, S.V.: Dynamic aggregation of grid-tied three-phase inverters. IEEE Trans. Power Syst. 35(2), 1520–1530 (2020) 9. Du, W., Dong, W., Wang, H., Cao, J.: Dynamic aggregation of same wind turbine generators in parallel connection for studying oscillation stability of a wind farm. IEEE Trans. Power Syst. 34(6), 4694–4705 (2019) 10. Teng, W., Wang, X., Meng, Y., Shi, W.: An improved support vector clustering approach to dynamic aggregation of large wind farms. CSEE J. Power Energy Syst. (2019) 11. Zhou, Y., Zhao, L., Matsuo, I.B.M., Lee, W.: A dynamic weighted aggregation equivalent modeling approach for the DFIG wind farm considering the Weibull distribution for fault analysis. IEEE Trans. Ind. Appl. 55(6), 5514–5523 (2019)
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12. Shuai, Z., Peng, Y., Liu, X., Li, Z., Guerrero, J.M., Shen, Z.J.: Dynamic equivalent modeling for multi-microgrid based on structure preservation method. IEEE Trans. Smart Grid 10(4), 3929–3942 (2019) 13. Wang, M., Mu, Y., Shi, Q., Jia, H., Li, F.: Electric vehicle aggregator modeling and control for frequency regulation considering progressive state recovery. IEEE Trans. Smart Grid 11(5), 4176–4189 (2020) 14. Wang, Y., et al.: Aggregated energy storage for power system frequency control: a finite-time consensus approach. IEEE Trans. Smart Grid 10(4), 3675–3686 (2019) 15. Zaery, M., Wang, P., Wang, W., Xu, D.: Distributed global economical load sharing for a cluster of DC microgrids. IEEE Trans. Power Syst. 35(5), 3410–3420 (2020)
Analysis and Application of Energy-Saving Approaches for Mining Dump Trucks Based on the Reuse of Braking Energy Yilin Wang
and Weiwei Yang(B)
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China [email protected]
Abstract. The operating characteristics of the continuous climbing time, the long downhill retarding distance, and the wide load variation range make the fuel consumption of mining dump trucks high, and the energy consumption cost can reach 1/3 of the total operating cost. The electric retarding technology with the resistance cabinet is the only way to dissipate the braking energy of large mining dump trucks. However, it cannot realize the recovery and reuse of braking energy. High instantaneous braking power, short braking time, less energy recovery, and short life of the energy storage components make the lithium battery an auxiliary energy storage hybrid technology unable to effectively adjust the engine load rate to achieve the expected energy saving and cost reduction effect. Therefore, a typical operating condition model is established based on the operational characteristics of open-pit mines. Combined with the three topology structures of motor light overload, cooling fan electrification, and reverse drag engine, four technical solutions are proposed to improve the energy utilization rate of mining dump trucks. “Energy-saving coefficient of feedback braking energy” is the evaluation index, taking a mine dump truck with a load of 150 tons as the scheme’s application object and comparing each scheme’s energy-saving effects. The results show that on the premise of ensuring the vehicle’s dynamic performance, maximizing the use of braking energy can reduce engine energy consumption by 2–11%. Keywords: Mining dump truck · Reuse of braking energy · Light overload of motor · Electrification of cooling fans
1 Introduction Large-scale mining dump trucks are the main production equipment in open-pit mines. They use long-distance heavy-load uphill, downhill electric retarding braking, loading, and unloading idling conditions. There are often accompanied by the heavy-load startup and frequent short-term braking. Unload downhill sections have long distances and frequent braking, and the gravitational potential energy of the vehicle is usually dissipated in the form of thermal energy in the resistance cabinet, resulting in lots of energy lost [1]. © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1191–1199, 2023. https://doi.org/10.1007/978-981-99-1027-4_124
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Through the organic combination, four schemes to improve the efficient utilization of braking energy of mining dump trucks are obtained. A mine dump truck with a load of 150 tons is used as the application object to compare and analyze the four technical schemes.
2 Modeling of the Transmission System and Operating Conditions The topology of the transmission system of the electric wheel mining dump truck is shown in Fig. 1. The electric drive transmission system decouples the engine from the driving wheel to ensure that the engine can work in the high-efficiency region at different speeds [2]. The engine-generator set and the energy storage power supply serve as dual energy sources to power the electric motor [3]. DC + Attachments
Engine
genera tor
controlled rectifier
fan
braking resistor
chopper
Capacitance
inverter
motor
inverter
motor
Energy storage power
DC -
Fig. 1. Layout of the electric drive system of mining dump truck
2.1 Vehicle Longitudinal Dynamics Model Considering the change in the loading mass of the mining dump truck, the longitudinal dynamics model of the whole vehicle is established as follows. F − Ff − Fi − Fw = (δm + M ) ·
dv dt
(1)
where, F, F f , F i , and F w are wheel traction, rolling resistance, slope resistance, and air resistance, respectively; m, M, δ, and v are unloaded mass, loaded mass, rotating mass coefficient, and driving speed, respectively. 2.2 Engine-Generator Model In this paper, the complex internal dynamic characteristics of the engine are ignored, and the simplified model [3] of the test data is used for calculation. Te − Te_input − Tacc = (Je + Jg + Jacc ) ·
dwe dt
(2)
where, T e , T e_input , T acc , J e , J g , J acc are the output torque of the engine, the input torque of the engine, the torque consumed by the accessories, the moment of inertia
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of the engine, the moment of inertia of the generator, the moment of inertia of the accessories, and the engine speed. The BSFC (brake specific consumption) brake fuel consumption curve [4] of the engine is shown in Fig. 2. ηfuel = f (we , Te )
(3)
where, ηfuel is the fuel consumption rate of the engine.
Fig. 2. Universal characteristic curve of the engine
2.3 Drive Motor Model The drive motor is the power component of the mining dump truck. In this paper, the complex dynamic characteristics of the motor are ignored, and a simplified motor-speedtorque model based on experimental data [5] is used to obtain the maximum stable ramp driving speed of the dump truck under full load conditions. 2.4 Operating Case Model By sorting out a large amount of data on transportation roads in some mining areas at home and abroad [6], a working condition model for evaluating the calculation of the braking energy recovery and reuse of mining dump trucks is constructed, as shown in Fig. 3. The transportation distance is 4 km, the lifting height is 139 m, and the average gradient is 3.475%. According to the speed limit requirements of most large and mediumsized open-pit mines at home and abroad [7].
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Fig. 3. Typical mine road
3 Reuse of Braking Energy In the slow downhill section with unloading, the braking power is small, the change is stable, and the time is long during the deceleration section before entering the curve with heavy load and unloading uphill and reaching the loading point or unloading point. In the previous section, the braking power was significant, and the time was short. 3.1 Motor Light Overload A vehicle’s energy consumption is integral to the fuel consumption rate over time, and reducing the fuel consumption rate of the engine is an effective energy-saving means for hybrid technology [8]. However, in addition to the curve speed limit on a heavy load uphill, the vehicle travels slowly, and both the electric motor and the engine work at the rated power state. The direct manifestation of the motor overload state is heat accumulation, so the load rate variation range corresponding to the allowable temperature rise range during the normal driving process of the vehicle can be selected through the relationship between the motor overload rate and the temperature rise. The motor efficiency varies significantly with different operating points, and the efficiency is higher in the medium torque region of the motor output power of 0.5–1.2 Pm (Table 1). 3.2 Electrification of Cooling Fans Since the engine only drives the fan, oil pump, and other accessories, its output power is small (Fig. 8). The engine load rate and efficiency are low, resulting in a low energy utilization rate of the entire vehicle. In the electric retarding braking condition, the engine can run at a low speed of 650–700 r/min. The layout of the modified electric drivetrain is shown in Fig. 4. The reduction in engine energy consumption by the electrification of the cooling fan is mainly reflected in the change in accessory power. (P +P ) Pfe + Poil + ηgfg·ηm ·ηfma (Traction) (4) Pacc = Pfe + Poil (Brake)
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Table 1. Comparison of energy-saving effects of motor light overload Slope f G (%)
Load ratio ε
Driving time t (s)
Electric motors use recovery energy E m (kWh)
Engine energy consumption E e (kWh)
E e /E m
3
1
103.26
0
33.29
0.8196
1.097
97.14
2.41
31.319
4
1
76.35
0
24.61
1.2
68.91
3.52
22.21
5 10
1
154.45
0
49.79
1.2
132.76
6.79
42.79
1
148.72
0
47.94
1.2
124.19
6.35
40.03
Engine Cooling Fan
0.6807 1.0302 1.2457
DC Bus +
Inverter Engine
Genera tors
Lifting oil pump Steering/brake oil pump
Controlled rectification
Fan
Brake Resis tance
Generator/motor cooling fan
Chop pers
Intermediate capacitor
Inverter
DC Bus -
Inv ert er
motor
Inv ert er
motor
Energy storage power supply
Fig. 4. Improved electric drive system layout
At this time, the feedback energy used by the accessory motor is shown as follows. Pfg Pfm · treta · ηbat Efgm = + (5) ηm1 · ηa1 ηm2 · ηa2 where, ηm1 , ηa1 , ηm2 , ηa2 , and t reta are the efficiency of the generator cooling fan driving motor, the generator cooling fan rectification and inverter efficiency, the motor cooling fan driving motor efficiency, the motor cooling fan rectification and inverter efficiency, and a cyclic braking delay working time. In the operating condition, the feedback energy used by the accessory motor in one working cycle is 3 kWh, accounting for 11.11% of the total feedback energy. The engine energy consumption reduces by 2.4 kWh, accounting for 0.93% of the total engine energy consumption. 3.3 Reverse Drag Engine The motor and the resistance grid need a large amount of ventilation to ensure heat dissipation. It is necessary to maintain high-speed operation to provide sufficient cooling
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power. Mining dump truck engines with slow braking run at low load rates for a long time, resulting in poor fuel economy. To realize the recovery and reuse of braking energy and reduce fuel consumption. According to the power/speed curve of the engine and accessories, the energy consumption of the motor driving the engine at the corresponding speed can be obtained as follow. EmT = PT · treta · ηmT · ηa
(6)
where, E mT , PT , and ηmT are the feedback energy used by the driving engine, the power of the driving engine, and the motor efficiency during driving, respectively.
4 Theoretical Analysis and Comparison of Energy-Saving Effect 4.1 Comparative Analysis of Energy-Saving Solutions This paper will take a mining dump truck with a load of 150 tons as the object to study the energy-saving problem of electric drive mining dump trucks. The main parameters of the truck are shown in Table 2. The formulas for solving the engine energy consumption and the braking energy utilized by the motor for the four combination schemes are shown in Table 3. Table 2. Main parameters of mining dump truck Main parameters
Numerical value
Units
Load M
145
t
Unload m
105
t
Engine power rating Pe
1193
kW
Maximum torque/speed T emax /nmax
6835@1500
N m@r/min
Generator input power Pg
1020
kW
Traction motor power Pm
460
kW
Tire size Rtire
33.00R51
–
Wheel-side reduction speed ratio iT
32.4
–
4.2 Results Comparison The schemes are compared and analyzed from the three aspects of driving time, engine energy consumption, and energy saving coefficient of regenerative braking energy, as shown in Table 3.
1203.9
1158.4
1158.4
1140.1
Option 2
Option 3
Option 4
1203.9
Separate-drive cooling fan
Option 1
1203.9
No brake energy Series cooling recovery fans
Recovery of braking energy
Driving time t (s)
Topology solutions
197.3
194.9
203.4
208.3
218.4
217.3
Heavy load uphill engine energy consumption E eu (kWh)
30.0
31.1
29.5
31.1
34.3
40.8
Unload downhill engine energy consumption E ed (kWh)
227.3
226.0
232.7
239.5
252.7
258.0
Total engine energy consumption E e (kWh)
Table 3. Comparison of energy-saving effects
0.881
0.876
0.902
0.928
0.979
0
E ei /E e1
1.01
0.96
0.92
0.83
0
0
Feed-back energy-saving factor J
11.87
12.38
9.77
7.17
2.03
0
Energy saving ratio Ω (%)
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5 Conclusion (1) Rational use of braking energy, light overload operation of the motor in the climbing section, working at a load rate of 1.1–1.2 to increase the climbing speed not only achieves the purpose of energy saving but also improves production efficiency. (2) On the premise of the same curb weight of the vehicle, the independent drive mode of the generator and the motor can save more than 1% of the energy compared with the series fan structure. Product design, especially in the design of large-tonnage products, should use the “independent drive” method as much as possible. (3) For mining dump trucks that work in long-distance and frequent uphill and downhill conditions, dragging the engine can consume part of the braking energy and reduce the capacity of the braking resistor. When the engine controlled by electronically controlled fuel injection is pulled to a high speed, it will automatically reduce the amount of fuel injection to achieve the purpose of saving fuel and meet the power system for the regular operation of the peripheral components of the engine. (4) The concept of the “evaluation index of the energy-saving effect of regenerative braking energy” is proposed to evaluate the energy-saving effect of regenerative braking energy under different utilization conditions. The energy consumption of various structural schemes and control strategies is analyzed based on the typical road conditions of open-pit mines. Due to the lack of mature experimental data support in calculating engine energy consumption, only the “steady-state response” is considered. The transition process from one power state to another power state and its influence on the solution of vehicle dynamics equations and the calculation of energy consumption should also be considered in the following research. Acknowledgment. The authors are grateful for the support from the University of Science and Technology Beijing, and the Shunde Graduate School of University of Science and Technology Beijing. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Central University Basic Research Fund of China (No. FRF-TP-20-054A1), Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515110195).
References 1. An, X., Li, Y., Sun, J., et al.: Energy management strategy of electric vehicle dual-source hybrid energy storage system based on fuzzy logic. Power Syst. Prot. Control. 49(16), 135–142. https:// doi.org/10.19783/j.cnki.pspc.201266 (in Chinese) 2. Han, T., Zeng, B., Tong, Y.: Theoretical study on energy recovery rate of regenerative braking for hybrid mining trucks with different parameters. J. Energy Storage 42(1), 103127 3. Li, F., Yang, Z., Wang, Y., et al.: Energy management strategy of hybrid energy storage tram based on Pontryagin minimum principle. J. Electrotech. Technol. 34(S2), 752–759. https://doi. org/10.19595/j.cnki.1000-6753.tces.L80191 (in Chinese) 4. Li, Y., Yang, J., Liu, R., et al.: Research on energy-saving and zero-emission technology route of large electric-wheel mining trucks. Chin. J. Coal 1–12. https://doi.org/10.13225/j.cnki.jccs. 2021.1000 (in Chinese)
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5. Lv, C., Zhang, J., Li, Y., Yuan, Y.: Mechanism analysis and evaluation methodology of regenerative braking contribution to energy efficiency improvement of electrified vehicles. Energy Convers. Manag. 92, 469–482 6. Qin, Q., Guo, T., Lin, F., et al.: Energy management and capacity allocation optimization of urban rail transit battery energy storage system based on energy transfer. J. Electrotech. Technol. 34(S1), 414–423. https://doi.org/10.19595/j.cnki.1000-6753.tces.180773 (in Chinese) 7. Qiu, M., Yu, W., Zhao, H., et al.: Braking energy recovery strategy of plug-in hybrid electric vehicle considering the coupling effect of working conditions and driving style. China Mech. Eng. 33(2), 10 (in Chinese) 8. Shen, X., Wei, H.: Research on regenerative braking energy dispatch of urban rail transit based on bypass DC circuit. J. Electrotech. Technol. 36(15), 3308–3316. https://doi.org/10.19595/j. cnki.1000-6753.tces.200688 (in Chinese)
Optimal Scheduling of Integrated Energy System Considering Gas Pipeline Leakage Failure Maosen Cao, Bo Hu(B) , Changzheng Shao, and Kaigui Xie The State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China [email protected]
Abstract. The integrated energy system (IES) has seen widespread application in the energy production as a result of the advancement of energy intelligent technology. While significantly increasing energy efficiency, small hole leakage failures of gas pipelines bring operational risks to the energy supply. Gas pipeline leakage may cause explosions, threatening people and buildings. Therefore, based on the one-dimension gas flow equation and dynamic gas flow model, a system network model that considers the change of pipeline topology caused by leakage failure is proposed. The process of gas leakage in the operation of gas pipelines is illustrated in the system network model. Then, an optimal scheduling model for IES is established, which includes the dynamic characteristics of gas system and leakage failure. The integrated gas and electricity testing systems are used to validate the suggested model. Keywords: Integrated electricity-gas energy systems · Leakage failure · Dynamic characteristics of gas system · Optimal scheduling model
1 Introduction In recent years, natural gas consumption in industrialized countries has grown steadily [1, 2]. IES is seen as a sensible option for achieving the integration of renewable energy because it is more adaptable and effective in terms of energy supply [3]. However, due to the long transmission distance of the gas pipeline network, pipeline fracture failure and small hole leakage failure often occur, causing gas leakage and reducing energy supply [4]. More seriously, gas pipeline failure may cause explosions, threatening people and buildings [5]. Although many efforts have been made in the area of the risk of gas pipeline fracture failure [6], little is known about the impact of the small hole leakage failure in the operation of IES. Pipeline failure can be divided into two types [7]: small hole leakage failure and fracture failure. After the occurrence of the fracture failure, a dispatch command is issued by the monitoring system, and the valves at both ends of the failed pipeline will be closed rapidly, thus preventing the normal transmission of gas [8]. On the contrary, the small hole leakage failure is difficult to detect because of the small effect on the © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1200–1208, 2023. https://doi.org/10.1007/978-981-99-1027-4_125
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pipeline pressure, small amounts of gas leakage unavoidably into the environment until the failure is repaired [9]. In addition, the frequency of the small hole leakage failure is 5–10 times higher than the frequency of fracture failure [10], so ignoring the small hole leakage failure may lead to large errors in the operation results. Helena et al. proposed the mathematical model, which is available for performing the prediction of the release flow rate of the small hole leakage failure. Besides, the Petri net describes the system topology well and represents the dynamic transfer process between the small hole leakage failure and fracture failure [11]. To sum up, the above research has studied the impact or mathematical analysis of the small hole leakage failure. However, they did not focus on the impact of the small hole leakage failure on the optimal dispatch in the combined power-gas model, nor did they investigate the impact of dynamic gas flow on the mathematical analysis of the small hole leakage failure. To fill this gap, firstly, based on the one-dimension gas flow equation and dynamic gas flow model, a system network model that considers the change of pipeline topology caused by leakage failure is proposed. The process of gas leakage in the operation of gas pipelines is illustrated in the system network model. Then, an optimal scheduling model for IES is investigated, which includes the dynamic characteristics of gas system and leakage failure.
2 System Network Model Gas leakage often occurs in gas pipelines, due to pipeline corrosion and artificial construction [12]. There are two ways for gas to enter the atmosphere due to accidental breakage. One is direct leakage into the atmosphere through the pipeline fracture and the other is leakage through the soil. In this paper, we only discuss the leakage calculation for the former. Gas pipeline failure may cause explosions, threatening people and buildings [5]. Therefore, a gas leakage model is needed to portray the gas leakage process. A dispatching model of IES is also needed to study the risk caused by gas leakage to the IES. 2.1 Gas Flow Model Considering the Small Hole Leakage Failure The dynamic gas energy flow model for a pipeline without a leakage failure can be expressed as 2 1 t+1 t t (P t+1 −Pxt+1 ) + (Qt+1 −Qout,xy + Qin,xy −Qin,xy ) 2Lxy y tπ D2 out,xy λxy w02 t+1 t+1 2λxy w0 t+1 t+1 (P +Px ))= 0 + sgn(Q)( (Q + Q ) − out,xy in,xy π D3 4cw2 D y 1, Q ≥ 0 sgn(Q) = −1, Q < 0
(1)
(2)
where, Lxy and D represent the length and inner diameter of the gas pipeline. P denotes t t and Qout,xy are the inflow and outflow of the gas pipeline. λxy depicts the pressure. Qin,xy the hydraulic friction factor. w0 indicates the initial speed. cw represents the sound speed.
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Due to the dynamic properties of gas [13] that allow it to be stored in pipelines, the line-pack Eqs. (3) and (4) based on the storage capacity of gas pipelines are defined. t = Mxy
π D2 Lxy t (P + Pxt ) 8ZRc T y
t+1 t+1 t+1 t Mxy =Mxy +t · Qin,xy − t · Qout,xy
(3) (4)
t is proportional to the average pressure and the pipeline characThe line-pack Mxy teristics in Eq. (3), and it follows the mass conservation (4). Rc , Z, and T represents the specific gas constant, compressibility factor, and temperature of gas.
Fig. 1. Diagram of a small hole leakage failure on pipeline
The small hole leakage failure is shown in Fig. 1. In this paper, a virtual load is assumed to replace the gas leakage failure. A pipeline is divided into two sections to calculate the energy flow separately, and the energy flow equation in the section xm of the pipeline is as follows. 2 1 t+1 t t (P t+1 −Pxt+1 ) + (Qt+1 −Qout,xm + Qin,xm −Qin,xm ) 2Lxm m tπ D2 out,xm λxm w02 t+1 t+1 2λxm w0 t+1 t+1 (P +Px ))= 0 (Q + Q ) − +sgn(Q)( out,xm in,xm π D3 4cw2 D m t = Mxm
π D2 Lxm t (Pm + Pxt ) 8ZRc T
t+1 t+1 t+1 t Mxm =Mxm +t · Qin,xm − t · Qout,xm
(5)
(6) (7)
where λ is related to the inner diameter of the pipeline and is considered unchanged because the small hole leakage failure has little effect on the size of the inner diameter of the pipeline. λxm = λxy
(8)
Similarly, we can obtain the energy flow equation for the section my of the pipeline. At the same time, the energy-flow balance equation needs to be satisfied at the virtual load. t t t Qout,xm = Qleak, m + Qin,my
(9)
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t The gas leakage load Qleak, m can be calculated as t Qleak, m
Pt = 0.25π D √ m Rc T
2
2 2 2κκ ( ) κκ−1 κκ + 1 κκ + 1
(10)
where κκ denotes the isentropic index of the gas. 2.2 The Optimal Scheduling Model for IES The IES is shown in Fig. 2. The main components of the gas system include gas pipeline, gas source and compressor. The main components of the power system include gas-fired units and coal-fired units.
Fig. 2. Integrated electricity-gas energy system
2.3 Objective Function The goal of the objective function is to lower the cost of system operation for different forms of energy. The formulation of the optimization problem is as follows. ⎛ ⎞ t cwell,x Qwell,x + cpg,k PGkt 24hour ⎟ ⎜ k∈p(k) ⎜ x∈Q(x) ⎟ (11) min ⎜ ⎟ t t⎠ ⎝+ c L + c S t=1
curl,k
k∈m(k)
curs,x
k
x
x∈m(x)
where the positive values of cwell,x and cpg,k are used to lower the production and fuel consumption of gas wells and coal-fired units. The penalty cost factors for the gas and electricity load shedding are determined as ccurs,x and ccurl,k , respectively. 2.4 Gas System Constraints PExt t t t t (Qout,xy −Qin,xy ) + Qwell,x = Sxt − Sxt + fcpt + τcp + ηgas y∈n(x)
(12)
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0 ≤ Sxt ≤ Sxt
(13)
t =fcpt τcp
(14)
t t ≤ γcp Py,cp Px,cp
(15)
t ≤ Qwell,max Qwell, min ≤ Qwell,x
(16)
Px,min ≤ Pxt ≤ Px,max
(17)
t ≤ Qxy,max Qxy,min ≤ Qxy
(18)
Equations (1)–(10). t Equation (12) is used to illustrate the gas flow balance (12). Qwell,x represents the t t gas production. Sx and Sx denote the gas demand and demand shedding, respectively. PExt and ηgas depict the generation output and conversion efficiency of a gas-fired unit, respectively. Equation (13) constrains the demand curtailment. Equation (14) shows the connection between the gas flow and the gas that is used by the compressor. is the compressor coefficient. The connection between the gas pressure at the compressor’s inlet and outlet is addressed by Eq. (15). The gas production, gas pressure, and mass flow are limited by Eqs. (16)–(18), respectively. 2.5 Power System Constraints PEkt +PGkt = Ltk − Ltk +
Fklt
(19)
l∈k
bkl Fklt = θkt − θlt
(20)
−π ≤ θk,t ≤ π
(21)
0 ≤ Ltk ≤ Ltk
(22)
t F ≤ F kl,max kl
(23)
PGk,min ≤ PGkt ≤ PGk,max
(24)
PEk,min ≤ PEkt ≤ PEk,max
(25)
where Eq. (19) guarantees power balance. The connection between the power flow Fklt and the nodal voltage phase angle θkt is addressed by Eq. (20). The voltage phase angle is restricted by Eq. (21). The variation of load curtailment and power transmission capacity is imposed by Eqs. (22) and (23). The generation of the coal-fired unit and gas-fired unit is restricted by Eqs. (24) and (25).
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3 Case Studies 3.1 System Description and Data Sources The IES shown in Fig. 6 contains the 30-bus power system and 20-node gas system (Fig. 3).
R2
W4
B8
P1
8
B9 10
9
B10 11
B11 12
G1
W5
13
B12
B15
W6 B17
B16 18
W3
2
3
B6
B5 R1
G4 7
8
6
28
B14 R3
G6
13
12
16
17
16
B4 5
4
G3 5
29
B7
B3
B2
B1 1
3 15
14
17
W2 W1
2
P2
B13 19
20
G2
1
10
14
30
11 22
19 18
27
21
20
4 7
9
G5 23
15
24
25
26
6
Fig. 3. Integrated power and gas system.
Scenarios 1–3 are discussed in relation to the impact of scheduling of IES while taking into account the leakage failure of the gas system. Scenario 1: Pipelines B13 and B14 operate normally. Scenario 2: Fracture failure occurs in pipeline B13, and B14 operates normally. Scenario 3: Fracture failure occurs in pipeline B13, and small hole leakage failure occurs in B14.
Fig. 4. Curtailed gas in scenarios 2 and 3.
Figure 4 shows the gas load shedding in scenarios 2 and 3 in a regular 24-h dispatch conducted after the failures. Figure 5 shows the generation of gas-fired and coal-fired units in the power system in three scenarios. In scenario 1, the gas load shedding is 0 because the pipelines are normal. Pipelines B13 and B14 transmit natural gas to G6 in the power system. G1, G3 and G6 are working simultaneously. In scenarios 2 and 3, due to the failure of pipeline B13, pipeline B14 consumes the line-pack to continue supplying the conventional gas load at node 15 of the gas system for a short time. Therefore, the generation of G6 is 0, and G1 and G3 increase their output (yellow dotted line) to maintain the power balance. As can be seen from Fig. 4, compared to scenario 2,
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Fig. 5. The power generation of power system in scenarios 1, 2 and 3.
there is a leakage gas load in pipeline B14 in scenario 3, increasing the consumption of line-pack. Therefore, conventional gas load shedding exists most of the time. The total conventional gas load shedding of scenario 3 is 127072.08 m3 , which is greater than the total gas load shedding of scenario 2 of 91424.88 m3 . Scenarios 4–6 are discussed in relation to the impact of scheduling of IES while considering the position of leakage failure of the gas system. Scenario 4: Fracture failure occurs in pipeline B15 and small hole leakage failure occurs at 1/10 of the length of pipelines B16 and B17. Scenario 5: Fracture failure occurs in pipeline B15 and small hole leakage failure occurs at 5/10 of the length of pipelines B16 and B17. Scenario 6: Fracture failure occurs in pipeline B15 and small hole leakage failure occurs at 9/10 of the length of pipelines B16 and B17.
Fig. 6. The line-pack of pipelines 16 and 17 for scenarios 4, 5 and 6.
Figure 6 shows the variation of line-pack for pipelines 16 and 17 in the three scenarios. It can be seen that the smallest and largest consumption of line-pack exists in scenarios 4 and 6, respectively. During the transmission of gas, the gas pressure at the starting is always higher than that at the terminal of the pipeline. We define the pipeline from the position of leakage failure to the starting of the pipeline B16 as the first section (FS). We define the section from the position of leakage failure to the terminal of pipeline B16 as the second section (SS). Since the small hole leakage failure occurs near the starting of pipeline B16 in scenario 4, the line-pack of FS bears the leakage gas load. As a result, the line-pack of FS decreases faster, reducing its supply to the conventional gas load. Then,
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the line-pack’s consumption of SS is accelerated, resulting in a rapid reduction of the terminal pressure and reaching the allowable lower pressure. Conversely, if the leakage failure occurs at the end of pipeline B16, there is more line-pack available in the pipeline to be consumed, while maintaining a short supply of conventional gas load and reducing its shedding. The same is suitable for pipeline B17. It can also be seen in Table 1 that since the leakage gas load is proportional to the pipeline pressure, the leakage gas load of scenario 4 is greater than that of scenarios 5 and 6. Meanwhile, the conventional gas load shedding gradually decreases with the increase of the failure distance. Table 1. The leakage gas load and conventional gas load shedding. Scenario
Leakage gas load (m3 )
Conventional gas load shedding (m3 )
Scenario 4
46806.84
21167.28
Scenario 5
45635.76
13645.8
Scenario 6
44935.2
5004
Acknowledgments. This study is supported by the National Natural Science Foundation of China under grant 52107072.
References 1. Zeng, Z., et al.: Reliability evaluation for integrated power-gas systems with power-to-gas and gas storages. IEEE Trans. Power Syst. 35(1), 571–583 (2020) 2. Wang, L., et al.: Optimal operation analysis of integrated community energy system considering the uncertainty of demand response. IEEE Trans. Power Syst. 36(4), 3681–3691 (2021) 3. Liu, N., et al.: Bilevel heat–electricity energy sharing for integrated energy systems with energy hubs and prosumers. IEEE Trans. Ind. Inform. 18(6), 3754–3765 (2022) 4. Shahmohammadi, A., Moradi-Dalvand, M., Ghasemi, H., Ghazizadeh, M.S.: Optimal design of multicarrier energy systems considering reliability constraints. IEEE Trans. Power Deliv. 30(2), 878–886 (2015) 5. Zhang, Z., et al.: Day-ahead optimal dispatch for integrated energy system considering powerto-gas and dynamic pipeline networks. IEEE Trans. Ind. Appl. 57(4), 3317–3328 (2021) 6. Bao, M., Ding, Y., Shao, C., Yang, Y., Wang, P.: Nodal reliability evaluation of interdependent gas and power systems considering cascading effects. IEEE Trans. Smart Grid 11(5), 4090– 4104 (2020) 7. Wang, Y., Guo, S.: Analysis of natural gas pipeline accidents abroad. Oil Gas Storage Transp. 19(7), 5–10 (2000) 8. Clegg, S., et al.: Integrated electrical and gas network flexibility assessment in low-carbon multi-energy systems. IEEE Trans. Sustain. Energy 7(2), 718–731 (2016) 9. Montiel, H., V´ıLchez, J.A., Casal, J., et al.: Mathematical modelling of accidental gas releases. J. Hazard. Mater. 59(2–3), 211–233 (1998)
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10. European Gas Pipeline Incident Data Group: Gas Pipeline Incidents: 9th Report of the European Gas Pipeline Incident Data Group (period 1970–2013)[R/OL]. [2020-12-10]. https:// www.egig.eu/startpagina/$61/$156 11. Fang, H., Fang, X., Wang, L.: Review of reliability analysis based on petri nets. Comput. Sci. 41(7), 40–44 (2014) (in Chinese) 12. Li, H., Kong, Z., Tao, C.: Reliability evaluation of electric-gas integrated energy system considering the multi-state model of natural gas pipeline network. In: Proceedings of the CSEE (2022). https://doi.org/10.13334/j.0258-8013.pcsee.211234 (in Chinese) 13. Liu, W., Li, P., Yang, W., Chung, C.: Optimal energy flow for integrated energy systems considering gas transients. IEEE Trans. Power Syst. 34(6), 5076–5079 (2019)
Multi-index Thermal Safety Warning Based on Real Vehicle Big Data Xinyu Wu1 , Zheming Chen1 , Aihua Tang1(B) , Quanqing Yu2 , Manni Zou1 , and Shengwen Long2 1 School of Vehicle Engineering, Chongqing University of Technology, Chongqing 400054,
China {wuxinyu,zoumanni}@stu.cqut.edu.cn, [email protected] 2 School of Automotive Engineering, Harbin Institute of Technology, Weihai 264209, China [email protected], [email protected]
Abstract. New energy vehicle fire accidents have raised concerns about their safety in recent years. Two indicators of maximum temperature and temperature extreme difference, which are closely related to heat, were chosen for the thermal safety of new energy vehicles. The rate of heat transfer in actual, everyday use, is, however, significantly lower than the comparable rate of voltage. As a result, indicators that express the consistency of the battery pack include voltage polarity and voltage information entropy associated with voltage. The thresholds for the four indicators were then set using a study of the literature and 3σ different techniques, and voltage clustering was performed to check for potentially dangerous single cells. Keywords: New Energy Vehicles · Thermal Safety · Cloud Data · Power Battery · Consistency
1 Introduction Development of new energy vehicles has become a global consensus and a national plan for China in response to the escalating energy problem and environmental security [1]. Battery packs, which have the benefits of high specific energy, small size, light mass, long cycle life, low self-discharge rate, no memory effect, and no pollution, power new energy vehicles [2]. However, as the use of new energy vehicles rises, the performance and safety of the battery inevitably fall. This is reflected in the rise in inconsistency between battery packs, overcharging and overdischarging of some individual cells, which can reduce the power performance, range, and safety of the vehicle and even result in thermal runaway. Because of this, battery pack safety warnings are essential to the operation of electric cars safely. Reconstruction of resistive voltages based on kernel principal component analysis for the isolation and detection of various fault types has been studied in the past [3]; while this method is useful for multi-fault detection, it is not yet ready for use in practical applications. Qiao et al. [4] were able to identify internal short circuits in 2.51 h using © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1209–1216, 2023. https://doi.org/10.1007/978-981-99-1027-4_126
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cluster analysis. Its technique can provide safety warning information in advance, but it is only usable with the same battery type and battery pack configuration. A technique based on PEARSON correlation analysis was presented in the literature [5] to monitor the internal short circuit of the battery. The single cell voltage parameter was chosen, and the correlation coefficient between neighboring single cells was calculated. In order to evaluate whether the battery is short-circuited, the correlation coefficient between two neighboring single cells is computed. In the literature [6], an analogous circuit model was utilized to detect battery internal resistance-related issues by identifying factors such ohmic internal resistance, polarized internal resistance, Chen, etc. using the local outlier factor (LOF) and Grubbs criteria (Grubbs). Although Hou et al. [7] suggested a vehicle alarm neural network for high-temperature fault diagnosis in electric cars, setting up a three-level fault, there are numerous temperature affecting elements and a relatively delayed reaction, so the detection efficacy is missing. Similar to how anomaly identification and localization of electric scooters employ statistical distribution [8]. Chang et al. [9] calculated the position of relative changes in the consistency of several charging segments of the battery, consequently detecting micro-faults in a research based on battery development. According to the literature [10], the four phases of an electric vehicle’s operation are separated into independent models, each of which is trained to anticipate voltage and identify faults. However, this technique is computationally demanding even if accuracy increases. This work offers a thorough safety warning for power batteries by focusing on four vehicle-specific safety indicators: maximum temperature, voltage polarity, temperature polarity, and voltage information entropy. Following are the remaining arrangements in this paper: The data sources and data cleaning techniques are described in Sect. 2. The multi-indicator alerting is demonstrated in Sect. 3, the anomalous single screening technique is introduced in Sect. 4, and a summary review is given in Sect. 5.
2 Data Introduction and Cleaning 2.1 Data Introduction The large data adopted in this article for the car-pile operation was collected from electric vehicle bus, which is commuting in Chongqing. The pure electric city bus operation data was logged from 2022/4/1 0:09:33 to one full month; the sampling frequency is 0.1 Hz. The automobile battery module is made up of 198 series-connected lithium iron phosphate batteries. Information on each individual battery is provided in Table 1. 2.2 Data Cleaning The GB/T32960-2016 standard is followed while data collection on the automobile pile big data platform. Read the total current, total SOC, and individual voltage of the past historical data of electric vehicles recorded by the big data platform. However, due to information loss during the transmission process, the big data recorded by the car-pile with missing values, duplicate values, and inaccurate contents cannot be used directly and data cleaning work is required. The data are completed using nearest neighbor
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Table 1. Specific information of the battery. Item
Parameters
Type
LiFePO4
Nominal capacity
271 Ah
Charge cut-off voltage
3.65 V
Dimensions
207.3*71.6*173.6 mm
Weight
j V (S) represents the set of all the sub-chains of a single voltage sequence S, which is defined in the way to make sure that the generated sub-chain contains all possible binary combinations of the original set. For example, for set S = 001, V (S) = {0, 1, 00, 01, 001}. Calculation of component number is performed in a recursive way starting with comparison between S(i, j) and V (S(1, j − 1)). If S(i, j) is in V (S(1, j − 1)), continue to compare S(i, j + 1) and V (S(1, j)). If it is not, add a • after S(i, j) to include a new component, and then continue to compare S(j + 1, j + 1) and V (S(1, j)). The whole process starts from S(1, 1) and ends when j = n. For example, for a power battery with 12 single cells, set the sequence of single voltage symbols at a given time as: S = 101101010001. After going through the calculation presented above, the sequence of single voltage symbols can be divided into: S = 1 • 0 • 11 • 010 • 100 • 01 •. 3.3 Complexity Calculation of Single Voltage Sequence The number of components of a single voltage sequence is represented by c(n), and the complexity is derived: c(n) log2 c(n) + 1 CLZ = (4) n
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3.4 Complexity Calculation for Battery Life Cycle During a charging cycle, the complexity of individual voltage sequence at each time slot is calculated. The calculated complexity values are then averaged to form a quantitative standard of the potential risk level for the battery to suffer from thermal runaway. After examing the calculated complexity over battery life cycle, a clear boundary can be derived between healthy cells and those at high risk.
4 Analysis of Fault Diagnosis Results Data used in this paper is collected in real time through China’s national electric vehicle big data platform. By the end of June 2022, more than 9 million EVs have been connected in [10]. After pre-processing, data from real-world EVs are introduced to verify effectiveness of the proposed algorithm.
Fig. 3. Voltage and complexity of a faulty vehicle (a) voltage values of cells during last five charging before thermal runaway (b) calculated complexity during vehicle life cycle.
Figure 3 (a) shows the individual voltage curve of all cells of the last five charging cycles before thermal runaway happens. We pick this vehicle because no obvious faulty cell has been detected so that traditional algorithms, including entropy-based algorithms, will not work properly. As shown in Fig. 3 (b), the complexity of the power battery pack increases from 0.875 to 1.025 with the increase of mileage throughout its lifetime. Increased complexity can be understood physically as increased discrepancies and deterioration of consistencies among battery cells, which could lead to over-charge of stronger cells and over-discharge of weaker ones. Minor damage is expert each time a cell get over-charged or over-discharged. With dangerous or abusive conditions such as overcharging, overheating, collision, etc., serious thermal runaway accidents may occur [11]. Further analysis of vehicles of the same type is presented in Fig. 4, verifying vehicles with a complexity over 1.0 are highly likely to suffer from thermal runaway.
5 Conclusion This paper presents a novel battery fault diagnosis method based on Kolmogorov complexity that is calculated through an improved LZA algorithm. Data used in this paper
Fig. 4. Voltage and complexity curve of faulty vehicles of same type (a) voltage values of cells from four vehicles during last five charging cycles before thermal runaway (b) calculated complexity of four vehicles throughout life cycle.
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are from the real fault vehicles of China’s national electric vehicle big data supervision platform, which can accurately reflect the characteristics of electric vehicles in actual operation. The analysis results show that the Kolmogorov complexity method can describe the degree of chaos in the battery pack that could not be directly achieved by observing the voltage curve. In addition, this method can also be applied to the performance evaluation system of electric vehicle battery pack. Acknowledgments. This work was supported by the Research on Safety Inspection and Law Enforcement Technology of New Energy Vehicles based on Big Data (2020YFB1600602).
References 1. Shang, Y., Zhang, Q., Cui, N., Duan, B., Zhang, C.: An optimized mesh-structured switchedcapacitor equalizer for lithium-ion battery strings. IEEE Trans. Transp. Electrif. 5(1), 252–261 (2019) 2. Lombardi, W., Zarudniev, M., Lesecq, S., Bacquet, S.: Sensors fault diagnosis for a BMS. In: 13th European Control Conference (ECC), pp. 952–957. IEEE, Univ Strasbourg, Strasbourg, France (2014) 3. Liu, L., Feng, X., Zhang, M., Lu, L., Han, X., He, X., Ouyang, M.: Comparative study on substitute triggering approaches for internal short circuit in lithium-ion batteries. Appl. Energy 259, 114143 (2020) 4. Peng, Y., Yang, L., Ju, X., Liao, B., Ye, K., Li, L., Cao, B., Ni, Y.: A comprehensive investigation on the thermal and toxic hazards of large format lithium-ion batteries with LiFePO4 cathode. J. Hazard. Mater. 381, 120916 (2020) 5. Xiong, R., Li, L., Yu, Q., Jin, Q., Yang, R.: A set membership theory based parameter and state of charge co-estimation method for all-climate batteries. J. Clean. Prod. 249, 119380 (2020) 6. Wang, J., Zhang, S., Hu, X.: A fault diagnosis method for lithium-ion battery packs using improved RBF neural network. Front. Energy Res. 9, 702139 (2021) 7. Sun, Z., Wang, Z., Liu, P., Qin, Z., Chen, Y., Han, Y., Wang, P., Bauer, P.: An online datadriven fault diagnosis and thermal runaway early warning for electric vehicle batteries. IEEE Trans. Power Electron. 37(10), 12636–12646 (2022) 8. Kolmogorov, A. N.: Three approaches to the quantitative definition of information. Prob. Inf. Transm. 1, 1–7 (1965) 9. Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Inf. Theory IT-22(1), 75–81 (1976) 10. Cui, D., Wang, Z., Liu, P., Wang, S., Zhang, Z., Dorrell, D.G., Li, X.: Battery electric vehicle usage pattern analysis driven by massive real-world data. Energy 250, 123837 (2022) 11. Wang, Q., Wang, Z., Zhang, L., Liu, P., Zhang, Z.: A novel consistency evaluation method for series-connected battery systems based on real-world operation data. IEEE Trans. Transp. Electrif. 7(2), 437–451 (2021)
Power Capability Prediction and Energy Management Strategy of Hybrid Energy Storage System with Air-Cooled System Li Wang1
, Ji Wu1(B)
, Ying Du2 , Yadong Liu2 and Duo Yang3
, Xiuchen Jiang2
,
1 School of Automotive and Transportation Engineering, Hefei University of Technology,
Hefei 230009, China {wangli,wu.ji}@hfut.edu.cn 2 State Energy Smart Grid (Shanghai) R&D Center, Shanghai Jiao Tong University, Shanghai 200240, China {duying,lyd,xcjiang}@sjtu.edu.cn 3 School of Electrical and Information Engineering, Zhengzhou University, Zhengzhou 450001, People’s Republic of China [email protected]
Abstract. Hybrid energy storage systems (HESSs) are playing an increasingly important role in smart mobility platforms including electric vehicles. The design of the energy management strategy is the core of making the system rationalize the power distribution and stable operation. The power state and temperature state directly affect the determination of safe operating boundaries in the energy management strategy. In this paper, based on the equivalent circuit model of HESS, a thermoelectric coupling model of battery pack considering air-cooled system is established. In addition, a power capability prediction method considering the constraints of temperature, current, voltage and SOC is proposed and the power capability prediction method is embedded in the energy management strategy based on model predictive control. The experimental results show that the proposed algorithm can further improve the system performance and reduce the system energy consumption. The energy management strategy can provide the optimal power distribution at different air-cooled wind speeds and guarantee the maximum temperature of both the battery pack and the supercapacitor pack are in the normal operating range. Keywords: Hybrid Energy Storage System · Energy Management Strategy · Power Capability Prediction · Air-cooled
1 Introduction Energy reversibility is one of the key indicators for judging the value of energy storage technologies in many energy saving applications today. Lithium batteries are limited by their inherent properties, and their inherent electrochemical side reactions inevitably © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1224–1234, 2023. https://doi.org/10.1007/978-981-99-1027-4_128
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cause problems such as low reversibility and capacity degradation. Unlike lithium batteries, supercapacitors (SCs), a rapidly emerging and increasingly popular application technology, are highly reversible. It is capable of charging and discharging at ultra-fast speeds and extremely high efficiencies [1]. As a high power buffer, SC has the characteristics of ultra-low internal resistance, extremely high power density and million cycles, which can precisely make up for the defects in the performance of lithium battery. More importantly, the low temperature performance of SC is much higher than that of lithium battery. Therefore, it can guarantee the normal operation of vehicles under extreme conditions. With its many advantages, SC are now widely used in thousands of different types of energy systems. However, they still have defects such as expensive and low energy density, which make SC as auxiliary energy in systems that need to work continuously [2]. The combination of lithium batteries and SCs can build a long-life hybrid energy storage system (HESS) that can absorb and release power instantaneously. The HESS composed of the battery and SC has been used in new energy electric vehicles, rail transportation, utility grid or smart grid, instrumentation and forklift equipment. The thermal model of the battery and SC is the basis for the study of the HESS temperature state and power state estimation, and is a prerequisite for the design of the HESS energy management system. From the modeling principle, the thermal behavior models of Li-ion batteries can be divided into two categories: Electrochemical-thermal model and Electro-thermal coupling model. Wang et al. [3] developed an electrochemical thermal model to study the series and parallel lithium battery pack with series and parallel connections to investigate the inhomogeneity of electrochemical reactions and temperature distribution. However, such models require solving a large number of partial differential equations, which is difficult to be applied to practical engineering. The electro-thermal coupling model is based on the equivalent circuit model, which directly reflects the thermal characteristics of the cell by calculating the heat conduction, heat convection and heat radiation equations, ignoring the electrochemical reaction process. Chen et al. [4] developed a multilayer electrical-thermal coupling model. This approach can accurately characterize the thermal behavior of the battery without consuming a large amount of computational resources. Hijazi et al. [5] expressed the heat production behavior as a current source, which is related to the SC current, and modeled the heat transfer process as an equivalent thermal resistance. In HESS, the batteries are usually connected in series and parallel with air-cooled system, so it is important to study the thermal characteristics of the battery pack with cooled system. Lin et al. [6] designed a core temperature adaptive observer and considered the effect of surface wind speed on the thermal resistance of the cell. Xie et al. [7] proposed to consider the effect of uneven cooling of the battery pack on the temperature model for a battery pack consisting of 4 series and 3 parallel, and verified the electrical and thermal model parameters under different operating conditions. State of Charge (SOP) is one of the key states to monitor in HESSs. It provides a quantitative assessment of the maximum chargeable power inside the battery and SC. SOP estimation methods can be divided into three categories: experimental test methods, data-driven methods, and multi-constraint methods [8]. Multi-constraint methods are the most common methods used in engineering. Because these methods do not require
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complex calculations and accurate data sets and can calculate the maximum available power for batteries and SCs in real time [9]. However, in the SOP estimation of HESS, it is important to consider not only the effects of charge state, current and voltage on the power available to the battery and SC, but also the effects of temperature on them. At the same time, it is crucial to consider the power state and temperature state in real time during energy management process. In this paper, a thermoelectric coupling model of battery pack considering air-cooled system is established. The power state estimation with temperature constraint is also considered. In particular, the effect of temperature state and power state on power distribution is considered in the energy management strategy.
2 System Model The HESS adopts a semi-active topology with an equivalent circuit model for both the battery and SC. An efficiency model for the bidirectional DCDC. The configuration of battery and SC is shown in Table 1. Table 1. The configuration of battery and SC Parameters
Battery
SC
Type
ANR26650M1B
BCAP3000
Rated parameters
3.3 V/2.5 Ah
2.7 V/3000 F
Maximum discharge current
5C
170 A
Maximum charging current
−4 C
−170 A
Sizing
39s15p
28s5p
2.1 Battery Model Due to the resistance of lithium batteries, their heat generation is inevitable during operation. The Joule heat generated inside the battery is transferred from the inside of the battery to the case in the form of heat conduction. Moreover, it is diffused to the surrounding environment through thermal convection. Unlike the universality of the electrical model, the thermal model is related to the shape of the cell. ⎧ Cpb · V˙ pb = ib − Vpb /Rpb ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ Vb = mb Vocv − Vpb − ib Rsb t ⎪ ⎪ ⎪ ⎪ zb = zb0 − ib (τ )d τ/CNb ⎪ ⎩ t0
(1)
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Tb
Rpb Rsb
Tavg Cpb
Vocv ib
Vb
Ts Core Surface
Qb Rin
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Tb Ts Rs (vair)
Teˈvair
(a)
(b)
Fig. 1. (a) Battery equivalent circuit model, (b) battery electro-thermal coupling model.
where, zb is the SOC of the battery. mb is the series of the battery. Cpb and Rpb are the equivalent polarization capacitance and the resistance of battery. Rsb is the ohmic resistance, Vpb is the polarization voltage, and Vb is the terminal voltage of battery. This paper addresses the modeling of the thermal behavior of cylindrical lithium batteries. Based on the first-order equivalent circuit model (see Eq. 1), the battery electrothermal coupling model is considered with the effect of air-cooled wind speed. As shown in Fig. 1, assuming that the parameters such as the internal material density, thermal conductivity, and specific heat capacity of the cell are equal everywhere, then the average cell temperature is approximately equal to the average cell radial temperature [10], and the following equation can be obtained. Tb = 2Tavg − Ts
(2)
Based on the principle of conservation of energy, the heat control equation can be established by [11]. 2(Tavg − Ts ) Te − Ts + Cs T˙ s = Rs (vair ) Rin
(3)
Cs Cin − Cs Te − Ts + Cs T˙ avg = (Tavg − Ts ) + Qb Rin Cin 2Rs (vair ) 2Cin
(4)
where Cs denote the surface heat capacities and is related to the heat capacity of the battery case, Cin is the core heat capacities. Rin is the heat conduction resistance. Rs (vair ) is the convection resistance and is related to the ambient air-cooled speed vair . Ts represents the surface temperature, Te is the ambient temperature, Tavg denotes the averaged cell temperature, and Tb denotes the core temperature of battery. The battery heat generation is expressed by the following equation [12] Qb = |ib (Vb − Vocv )|
(5)
where ib is the current of battery, Vb denotes the terminal voltage, and Vocv represents the open-circuit voltage of battery. The total power generated by the current through the ohmic internal resistance and the polarized internal resistance, ignoring the energy dissipated by electrode over-potentials.
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2.2 SC Model Similarity, we can obtain the construction method of SC equivalent circuit model and electro-thermal coupling model [13], as shown in Fig. 2. ⎧ Csc · V˙ psc = isc − Vpsc /Rpsc ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ Vsc = msc Vpsc + isc Rssc (6) t ⎪ ⎪ ⎪ ⎪ z = zsc0 − isc (τ )d τ/CNsc ⎪ ⎩ sc t0
where, zsc is the SOC of the SC. msc is the series of the SC. Rssc and Rpsc are the equivalent resistance of the SC, Vpsc is the voltage of the capacitor Csc , and Vsc is the is voltage of SC. Since the temperature adaptation capability of SC is much higher than that of lithium battery, and for simplifying the system model, the effect of wind speed on the temperature model of SC is not considered. Rth Cth T˙ sc = Te − Tsc + Rth Qsc
(7)
where, Qsc represents the heat generation of SC, Tsc denotes the SC operating temperature, Rth is the equivalent thermal resistance and is related to the conduction material, surface area and radius of SC, Cth denotes the thermal capacitance. According to the equivalent electrical model of the SC, we can obtain the heat production equation as follows. 2 Rssc + Qsc = isc
2 Vpsc
(8)
Rpsc
Rpsc Qsc Rssc
Csc
Vsc
Qn
Tsc Rth Qenv Te
Cth isc (a)
(b)
Fig. 2. (a) SC equivalent circuit model, (b) SC electro-thermal coupling model.
2.3 Battery Pack Electro-thermal Model Based on the previously established electro-thermal coupling model of a single cell, we established the electro-thermal coupling model of the battery pack. Assuming that a
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battery group consists of five cells connected in parallel, and then connect such a battery group in parallel three times to form a 15-parallel pack as shown in Table 1. The battery group is arranged in the form of five cells in a row, and the battery pack structure is shown in Fig. 3(a). Tb Db
Lb
Rin
vair
. . .
. . .
. . .
. . .
. . .
B1
B2
B3
B4
B5
Tb
Qbb
Qb1
Ts
Qb2 Rin
Rs (vair) vair
(a)
Ts Rs (vair)
Te (b)
Fig. 3. (a) Battery pack structure, (b) energy transfer between adjacent cells
From Fig. 3(b), the expression for each individual temperature can be obtained by (3) and (4). To simplify the battery pack model, the cell-to-cell heat transfer can be ignored [14].
Cs (vair )T˙ avg,i Te,i =
2(Tavg,i − Ts,i ) Te,i − Ts,i Cs T˙ s,i = + Rs (vair ) Rin Cs (vair ) Cin − Cs (vair ) Te,i − Ts,i + = (Tavg,i − Ts,i ) + Qb Rin Cin 2Rs (vair ) 2Cin Te , ikb S 0.37 +ik S (Tb,1 2ρcSvair b
+
0.37 −ik S 2ρcSvair b Tb,i )+ 0.37 +ik S Te , 2ρcSvair b
i=1 i = 2, 3, 4, 5
(9) (10) (11)
Db vf Db Lb , Nu = qRem Pr0.36 , Re = , vf = vair (12) hNuS Lb − Db where Te is the ambient temperature, the change in temperature of each cell row along the direction of air fluid motion is approximated as an equal amplitude increment. ρ is the density of air, c is the specific heat capacity of the air, kb is a fixed value in the heat transfer coefficient. Db is the diameter of the battery, Lb denotes the center distance between cells, S is the surface area of the battery. h is the thermal conductivity of the coolant, Nu means the Nusselt number, Re means the Reynolds number, Pr means the Prandtl number, and the thermophysical parameters q and m are obtained from [15]. is the kinematic viscosity, vf is the maximum wind speed of the battery surface and vair is the inlet air speed. Rs is related to the inlet air speed, other parameters can be found in the literature [16]. Rs =
3 SOP Estimation Under Temperature Constraints In order to accurately predict and estimate the available battery power, a study based on the electro-thermal model proposed above is required. The SOP estimation methods
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based on voltage, current and charge state constraints are specified in the literature [12]. In this paper, we focus on the effect of considering the maximum temperature constraint of the monomer on SOP estimation. The temperature limit is the power limit caused by the maximum and minimum of the cells operating temperatures. The higher the temperature, the tighter the limits are due to electro-thermal coupling. The temperature is limited by the maximum temperature of the monomer, so the temperature of the 5th cell is used as the state variables. The HESS integrated thermal model is obtained by (2)–(11), XT (k + 1) = AT XT (k) + BT UT (k) + ξ(k) YT (k) = CT XT (k)
(13)
where, XT , UT , YT , AT , BT and CT can be expressed by ⎤ ⎡ ⎤ 0 0 Ts,5 (k) Qb (k) Tb,5 (k) ⎢ t 0 ⎥ , YT (k) = , BT = ⎣ 2C XT (k) = ⎣ Tavg,5 (k) ⎦, UT (k) = ⎦, in Qsc (k) Tsc (k) 0 Ctth Tsc (k) ⎡ tTe,5 (k) ⎤ ⎤ ⎡ 2t − R2t 0 1 − Rt Rs Cs Rin Cs s Cs in Cs ⎢ ⎥ ⎢ (Cs −Cin )t t e,5 (k) ⎥ in )t ξ(k) = ⎣ tT , AT = ⎣ (CRsin−C 0 ⎦, Cin Cs − 2Rs Cs 1 − Rin Cin Cs 2Rs Cs ⎦ t tTe,5 (k) 0 0 1 − Rth Cth ⎡
Rth Cth
⎡
⎤T −1 0 CT = ⎣ 2 0 ⎦ 0 1 The maximum heat production when the maximum temperature is reached in the next Lt moment can be obtained by recurrence of (13). UT,max (k) =
L−1 i=0
−1 CT AiT BT
Tmax − CT ALT XT
−
L−1
CT AiT ξ T (k)
(14)
i=0
where, ξ (k) = max{ξ(k), ξ(k + 1), ..., ξ(k + L)}, UT,max (k) = [Qbmax ; Qscmax ], Tmax = [Tbmax ; Tscmax ], Tscmax and Tbmax are the rated upper and lower temperature limits allowed in the user manual. Using the heat production equation of battery and SC, (5) and (8), the effect of the temperature limit on the current can be obtained. ⎧ 2 + 4R Q 2 ⎪ −Vpb − Vpb sb bmax Vpsc ⎪ Qscmax ⎪ T T ⎪ , Ichg,scmin = − − ⎪ ⎨ Ichg,bmin = 2Rsb Rssc Rpsc Rssc (15) ⎪ 2 + 4R Q ⎪ 2 −V V + ⎪ pb sb bmax Vpsc pb Qscmax ⎪ T T ⎪ ⎩ Idcg,bmax = , Idcg,scmax = − 2Rsb Rssc Rpsc Rssc
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4 Energy Management Strategy An energy management strategy based on the AMPC algorithm is applied in this paper. The exact algorithmic procedure is shown in our previous work [12]. In (16), the optimization objective function considers minimizing the energy loss on the HESS, and maintaining the SC capacity fluctuating around the median value. min : J = Jy +Ju = + +
P i=1 P
i=1 P
wVsc [Vscref (k + i|k) − Vsc (k + i|k)]2 2 wib rssc isc (k + i|k) +
wib rsb ib2 (k + i|k) +
i=1
P wVpsc
i=1 P
rpsc
wVpb
i=1
rpb
2 Vpsc (k + i|k)
2 Vpb (k + i|k)
(16)
The results of power prediction based on multiple power constraints are used as constraints for optimization objectives in energy management. ⎧ Vbmin ≤ Vb ≤ Vbmax ⎪ ⎪ ⎪ ⎪ ⎪ Vscmin ≤ Vsc ≤ Vscmax ⎪ ⎪ ⎪ ⎨z bmin ≤ zb ≤ zbmax (17) st. ⎪ zscmin ≤ zsc ≤ zscmax ⎪ ⎪ ⎪ ⎪ ⎪ Pbmin ≤ ib Vb ≤ Pbmax ⎪ ⎪ ⎩ Pscmin ≤ isc Vsc ≤ Pscmax The parameters of the HESS electro-thermal coupling model can be obtained experimentally, and then the relevant state parameters can be obtained by the above state space expressions.
5 Simulation Results In order to verify the validity of the proposed thermoelectric coupling model for the battery pack, simulations were conducted for each cell ambient temperature, core temperature and surface temperature, as shown in Figs. 4, 5, and 6. At this time the battery is at an ambient temperature of 25 °C and is located in a constant temperature chamber (Te = 25 ◦ C, vair ≤ 0.15 m/s). From the results, it can be seen that the surface and core temperatures of each individual cell are approximately increasing in equal magnitude. The farther away from the air inlet, the higher the cell temperature is, with a maximum temperature difference of about 0.2 °C. In addition, we also compared the core temperature of each cell at different wind speeds under high temperature conditions, as shown in Fig. 7. The results of current
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Ambient temperature ( )
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Time (s)
Core temperature (
)
Fig. 4. Ambient temperature in the vicinity of each battery cell.
Time (s)
Surface temperature (ć)
Fig. 5. Core temperature of each battery cell.
Time (s)
Fig. 6. Surface temperature of each battery cell.
limitation under battery operating current and temperature constraints during energy management are shown in Fig. 8. As can be seen from the figure, the temperature constrained discharge current limit dominates in the late operating period. The battery current in the first stage of operation is limited by the rated current constraint.
Core temperature ( )
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Vair=1m/s
Vair=0.5m/s
Time (s)
Current of battery (A)
Fig. 7. Comparison results of core temperature at different wind speeds.
Time (s)
Fig. 8. Current of battery cell and the current limit under temperature constraint during energy management.
6 Conclusion In this paper, based on the HESS equivalent circuit model, a thermal model of the battery pack considering the air-cooled system is constructed. The power state estimation method and the energy management strategy based on the model predictive control are combined to guarantee that the battery and SC are in the safe working area in real time. The effectiveness of the proposed method is verified under UDDS operating conditions. The results show that the peak battery operating current can be reduced and the SC absorbs and releases high power current to achieve the effect of extending the battery life, and the
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performance of the power state estimation method in the energy management strategy is verified. Our future work is to build the CFD model of HESS on ANSYS software, perform joint MATLAB–ANSYS simulation, and verify the effect of temperature control of each individual cell of the battery pack during energy management.
References 1. Alkhulaifi, Y.M., Qasem, N., Zubair, S.M.: Improving the performance of thermal management system for electric and hybrid electric vehicles by adding an ejector. Energy Convers. Manage. 201, 112133 (2019) 2. Zhang, L., Hu, X., Wang, Z.: Overview of supercapacitor management techniques in electrified vehicle applications. J. Mech. Eng. 53(16), 13 (2017) 3. Wang, B., Ji, C., Wang, S., et al.: Study of nonuniform temperature and discharging distribution for lithium-ion battery modules in series and parallel connection. Appl. Therm. Eng. 168, 114831 (2019) 4. Chen, M., Bai, F., Lin, S., et al.: Thermal performance of battery module based on multilayer electro-thermal coupling model. Energy Procedia 158, 2617–2622 (2019) 5. Hijazi, A., Kreczanik, P., Bideaux, E., et al.: Thermal network model of supercapacitors stack. IEEE Trans. Ind. Electron. 59(2), 979–987 (2011) 6. Lin, X., Perez, H.E., Siegel, J.B., et al.: Online parameterization of lumped thermal dynamics in cylindrical lithium ion batteries for core temperature estimation and health monitoring. IEEE Trans. Control Syst. Technol. 21(5), 1745–1755 (2012) 7. Xie, Y., Li, B., Hu, X., et al.: Improving the air-cooling performance for battery packs via electro-thermal modelling and particle swarm optimization. IEEE Trans. Transp. Electrif. 7(3), 1285–1302 (2021) 8. Wang, Y., Tian, J., Sun, Z., et al.: A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems. Renew. Sustain. Energy Rev. 131, 110015 (2020) 9. Hu, X., Xiong, R., Egardt, B.: Model-based dynamic power assessment of lithium-ion batteries considering different operating conditions. IEEE Trans. Ind. Inform. 10(3), 1948–1959 (2014) 10. Zou, C., Klintberg, A., Wei, Z., et al.: Power capability prediction for lithium-ion batteries using economic nonlinear model predictive control. J. Power Sources 396, 580–589 (2018) 11. Mohan, S., Kim, Y., Stefanopoulou, A.G.: Estimating the power capability of li-ion batteries using informationally partitioned estimators. IEEE Trans. Control Syst. Technol. 24, 1643– 1654 (2016) 12. Wang, L., Li, M., Chen, Z.: An energy management strategy for hybrid energy storage systems coordinate with state of thermal and power. Control Eng. Pract. 122(2), 105122 (2022) 13. Berrueta, A., Martin, I.S., Hernandez, A., et al.: Electro-thermal modelling of a supercapacitor and experimental validation. J. Power Sources 259, 154–165 (2014) 14. Wang, H., Ma, L.: Thermal management of a large prismatic battery pack based on reciprocating flow and active control. Int. J. Heat Mass Transf. 115, 296–303 (2017) 15. Zukauskas, A.: Heat transfer from tubes in crossflow. Adv. Heat Transf. 8, 3–160 (1972) 16. Ma, Y., Ru, J., Yin, M., Chen, H., Zheng, W.: Electrochemical modeling and parameter identification based on bacterial foraging optimization algorithm for lithium-ion batteries. J. Appl. Electrochem. 46(11), 1119–1131 (2016). https://doi.org/10.1007/s10800-016-0998-1
Signaling Game Approach for Energy Scheduling in the Community Microgrid Ruilong Xu, Yujie Wang, and Zonghai Chen(B) University of Science and Technology of China, Hefei 230027, Anhui, China [email protected]
Abstract. The community microgrid is a potential solution to integrate distributed energy resources into the main grid. The Stackelberg game is widely used to solve the energy dispatch problem for the community microgrid, where the utility functions of prosumers have to be publicly available. However, such a scheduling strategy is challenged due to the increased prosumer privacy awareness and the difficulty of accurately describing the utility. In this paper, we propose a signaling game-based energy scheduling strategy for a community microgrid with shared energy storage. The utility functions of prosumers are private and unavailable to others. An improved Bayesian optimization algorithm (BOA) with a sliding window is proposed for game equilibrium acquisition. In addition, the existence and uniqueness of the game equilibrium solution are proven, and the effectiveness of the BOA algorithm is demonstrated. The superiority of the proposed method is verified by simulation experiments using the Stackelberg game as the benchmark. The utility of the shared energy storage provider is increased by 17.4%, while the utilities of the prosumers are guaranteed to remain almost constant. In addition, the impact of the community microgrid on the main grid is reduced by approximately 20%. Keywords: Microgrid · Energy scheduling · Signaling game · Bayesian optimization algorithm
1 Introduction With the increasingly prominent global energy crisis and environmental pollution problem, distributed energy resources (DERs) have attracted widespread attention. However, they have the characteristics of randomness, fluctuation, and intermittency. With their increasing penetration, the reliability and stability of the traditional grid suffer from tremendous impacts. The community microgrid is widely considered to be a potential solution, which integrates local DERs, and energy storage, and connects to the grid as a whole entity [1]. An efficient energy scheduling strategy for community microgrids is urgently needed to both fully utilize DERs and reduce their adverse impacts. Energy storage, as an energy buffer, can alleviate the imbalance between energy supply and demand on a time scale [2]. An energy management strategy for a grid-tied microgrid with an energy storage system was studied in Ref. [3]. The operational electricity cost minimization problem was portrayed as a nonlinear programming problem © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1235–1248, 2023. https://doi.org/10.1007/978-981-99-1027-4_129
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under multiple constraints, and a two-step energy management strategy was proposed. To make full use of distributed energy storage systems to alleviate the load balancing issues in power networks, Ref. [4] proposed the construction method of an energy grand coalition based on cooperative game theory, which effectively reduced the variability of a local network load profile. Demand response management plays an important role in peer-to-peer energy markets. Reference [5] established a blockchain-empowered community P2P energy trading system composed of heterogeneous participants. Based on this, a non-cooperative game-based demand response mechanism was proposed and smart contract technology was utilized to effectively reduce the net peak load. Real-time pricing is an effective method for demand-side management. Reference [6] formulated real-time pricing as a noncooperative game and proposed an online distributed algorithm to obtain the Nash equilibrium. To effectively utilize the information of residential units, a central hybrid approach using stochastic programming and the Stackelberg game was proposed in Ref. [7]. Reference [8] developed a community-oriented distributed energy trading system for demand-side management of residents. A linearized branch flow model was used to develop a Stackelberg game under voltage constraints. The game equilibrium ensured the maximum revenue for the community energy storage provider and the minimum energy cost for the users. Reference [9] proposed a threelevel Stackelberg game-based power dispatching method for the community microgrid, which effectively addressed the impact of the uncertainty of housing users on system dispatching. Reference [10] described the interaction between aggregators, consumers, and the day-ahead electricity market as a Stackelberg game and designed a bilevel optimization framework. An efficient capacity scheduling and decision-making method was developed in Ref. [11] to maximize the benefits to storage providers. First, LSTM recurrent neural network was used for net load prediction. Then, a rolling horizon approach was used to achieve multi-timescale capacity scheduling. Finally, a Q-learning algorithm was applied for dynamic price design. Simulation experiments showed that the proposed method could promote community energy sharing, increase the utilities of participants, and reduce the impact of renewable energy resources on the grid. Games are widely used in electricity markets, especially Stackelberg games [12]. The Stackelberg game is a kind of dynamic game of complete and perfect information. The private local load demands and renewable energy generations need to be open. However, evaluating one’s utility function is impossible for others [13]. Considering incomplete information, an energy scheduling scheme between residential communities was proposed in Ref. [14]. The interaction of participants was formulated as a static Bayesian game, where the decision of whether the community participates in demand response was private information, and the other communities were agnostic. Markov chain was used to describe the probabilistic behavior of residential community decisions. In addition, the assumption of bounded rationality was used instead of absolute rationality to better describe the imitation and randomness of human behavior. The interaction between the participants within the community should be formulated as a dynamic game. As a non-complete information dynamic game, the signaling game has been widely employed in cybersecurity [15], where the sender’s private information is unavailable to the receiver but can only be deduced from observed messages [16]. From this perspective, the signaling game is an excellent candidate to describe participant
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interactions in a community microgrid when prosumer privacy is taken into account. In this paper, a signaling game-based energy scheduling strategy for the community microgrid is proposed, where an improved Bayesian optimization algorithm (BOA) is taken to obtain the game equilibrium. The uncertainty of the prosumer utility function is described as a Gaussian process. A sliding window is introduced to update historical information. The rest of the paper is organized as follows. The system model of a community microgrid with shared energy storage is given in Sect. 2, including the system scheduling structure and utility models of participants. Section 3 presents the scheduling strategy based on the signaling game. Then, Sect. 4 conducts case studies to evaluate the performance of the proposed strategy. Finally, the conclusion is drawn in Sect. 5.
2 System Model of the Community Microgrid 2.1 Scheduling Structure for the Community Microgrid
Community microgrid Producer set
Shared energy storage provider (SESP)
Prosumer p1 Prosumer pn
gt
gt
pn
pn
xt
gt
p1 g t
p1
xt
qt
Energy shared by producers
b t
qt
c1
Shared energy storage (SES)
b t
Surplus energy sold to grid
trt
Consumer set
Prosumer c1
p1
p
pn
Energy provided to consumers
Directly shared Provided by the SES
trtSESP+
s t
p
c1
xt
gt
cn
cn
xt
Insufficient energy brought from grid
b t
trtSESP-
s t
Prosumer cn
gt
c1
trt
PCC
Grid
gt
cn
gt
s t
Power Information
Fig. 1. Bilevel scheduling structure for the community microgrid.
The bilevel scheduling structure for the community microgrid is shown in Fig. 1. The microgrid under study consists of a single shared energy storage (SES) system and a large number of prosumers with load demands and renewable energy generations, such as photovoltaic (PV) devices. Prosumers usually have inconsistent usage patterns, which means they can play the role of producer, consumer, or self-reliant actor. If the p p PV generation capacity is larger than the local load demand (gt n > xt n ), prosumer pn is called a producer. If the PV generation capacity cannot meet the local load demand (gtcn < xtcn ), prosumer cn is called a consumer. Otherwise, it is called a self-reliant actor. In the community microgrid, producers can sell their spare generation capacity qt+ = {qtn > 0} to the SES provider (SESP), and consumers can buy energy qt− = {qtn < 0} from the SESP, which is directly shared by producers or stored in the SES. The SESP will set and broadcast the internal feed-in and selling prices (ptb , pts ). Outside the
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n community microgrid, prosumers can also sell energy tr+ t = {trt > 0} to or buy energy − n trt = {trt < 0} from the grid. If the SES is overcharged or insufficient, the SESP can sell energy trtSESP+ = {trtSESP > 0} to or buy energy trtSESP− = {trtSESP < 0} from the grid as well. Moreover, the grid will also broadcast the grid feed-in and selling prices (λbt , λst ). Hence, the overall electricity trading is free, and it is the electricity prices that affect the volume of electricity traded. The energy traded between the microgrid and grid will be gathered at the point of common connection (PCC), the net load of which implies the impacts of the microgrid on the grid. Two basic assumptions need to be listed as follows: (1) All involving parties are rational, which means they try to take action to maximize their own utilities. (2) The grid prices (λbt , λst ) change during the day.
2.2 Utility Model of the Shared Energy Storage Provider The utility of the SESP consists of the profits/costs of energy transactions with prosumers and the grid. When considering the short-term utility, we ignore the aging costs and initial investment costs. Thus, the utility of the SESP can be given by: qtn − ptb qtn + λbt max(trtSESP , 0) + λst min(trtSESP , 0) (1) UtSESP = −pts n∈Bt
n∈St
where t is the time slot. The prosumer set is defined as N = Bt ∪ St ∪ Mt , where Bt = {n ∈ N|qtn < 0} is the consumer set, St = {n ∈ N|qtn > 0} denotes the producer n = 0} represents the self-reliant actor set. tr SESP = n = {n ∈ N|q set, and M t t t n∈St qt + n − δe denotes the energy that the SESP trades with the grid, which is positive q t n∈Bt t when selling to and negative when buying from the grid. δet is the energy charged to the SES, which is positive when charging and negative when discharging. Although the market is free, the SESP set internal tariffs to be more favorable to encourage consumers to share energy within the microgrid, that is, λbt ≤ ptb < pts ≤ λst . To determine δet , , we need to carefully consider the state of energy (SOE), which can be defined as: SOEt + δet · ηc /EN , δet ≥ 0 (2) SOEt+1 = SOEt + δet /ηd /EN , δet < 0 where ηc and ηd are the charging and discharging efficiency, respectively, which are both assumed to be 0.95. EN is the rated available energy of the SES. To extend the SES lifetime, the SOE should be limited between SOEmin and SOEmax . Further considering the power limit, the charge/discharge energy in one time slot will be limited between Rated,max and Ratec,max . Thus, we can derive that: ⎧
n ⎪ max Rated,max , EN (SOEmax − SOEt−1 )ηd δet1 , qt < δet1 ⎪ ⎪ ⎪ n∈N ⎨
n 2 qt > δet2 δet = min Ratec,max , EN (SOEmin − SOEt−1 )/ηc δet , (3) n∈N ⎪ ⎪ n ⎪ ⎪ qt , other(trtSESP = 0) ⎩ n∈N
Hence, the utility of the SESP (UtSESP ) can be considered as a function of variables (qt , ptb , pts ). To ensure the next day energy sharing service, the initial SOE needs to be kept above a given threshold of 0.5.
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2.3 Utility Model of Prosumers The utility of the prosumer consists of three components: (1) the profits/costs of energy transactions with the SESP or grid, (2) the additional utility of energy consumption, and (3) the policy subsidy. Then, the utility of prosumer n is given by: Utn = ktn ln(xtn ) + γ gtn + Qtn + Trtn
(4)
where xtn is the energy consumed, and ktn is the coefficient of consumption preference. The natural logarithm function ln(·) has been widely used in economics to design the utility of power consumers [17]. Assume that each consumer has a critical load xtn,min that cannot be scheduled. Therefore, there is the following load constraint: xtn ≥ xtn,min . gtn is PV generation, and γ is the policy subsidy coefficient, which is set to 0.08 yuan/kWh. Qtn and Trtn are the profits/costs of energy transactions with the SESP and grid, respectively, which are specified as follows: b n n b n n pt qt , qt ≥ 0 λt trt , trt ≥ 0 n n , Trt = (5) Qt = pts qtn , qtn < 0 λst trtn , trtn < 0 where qtn +trtn = gtn −xtn . Due to the strong uncertainty of solar radiation, PV generation (gtn ) is portrayed as a Gaussian process. That is, gtn = g˜ tn + δtn
(6)
where δtn ∼ N (0, ν 2 ), and ν is the standard deviation of PV generation prediction. g˜ tn is the prediction value.
3 Scheduling Strategy Based on a Signaling Game 3.1 Formulation of Signaling Game A signaling game is a dynamic game of incomplete information involving two players: the sender and the receiver. The sender sends a message based on privacy, and the receiver takes action based on the historical observed messages. It is crucial that the privacy of the sender affects the receiver’s utility, but the receiver does not know the privacy and can only update his belief through messages. Consider prosumers as senders who send messages of shared energy quantity based on the private PV generations and consumption preferences, and take the SESP as a receiver who sets the internal prices based on the historical transaction information. The signaling game can be formally stated as follows: (7) = {N, SESP}, H, f , T, p(st ), {Ut }, UtSESP where {N, SESP} is the player set. H is the historical information set, whose elements are divided as Dt,1 = (pkb∗ , pks∗ , qk∗ , UkSESP∗ )tk=t1 for the SESP and Dt,2 = ∗ , U SESP∗ )t (pkb∗ , pks∗ , qk−1 k−1 k=t1 for prosumers. Prosumers and the SESP will take actions sequentially. f is the player function, which decides the order of decision-making. Specifically, f (Dt,1 ) = SESP, f (Dt,2 ) = N. T is the type set of senders, which is private and
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unavailable to the SESP. The element of T is st = (gt , kt ), where gt = {gt1 , gt2 , . . . , gtN } and kt = {kt1 , kt2 , . . . , ktN }. p(st ) is the prior probability of st , which is assumed to obey the Gaussian distribution. {Ut } = {Ut1 , . . . , UtN } and UtSESP are the utilities of prosumers and the SESP, respectively. Definition 1 Consider the signaling game defined above. A pure-strategy perfect Bayesian equilibrium (PBE) (qt∗ , ptb∗ , pts∗ ) in the game must satisfy the following four requirements: (1) Receiver’s belief of sender’s privacy based on massages, the posterior probability p(st |qt∗ ), must satisfy that p(st |qt∗ ) > 0 and st ∈T p(st |qt∗ ) = 1. (2) The receiver is rational, and the action must maximize his expected utility under the given belief p(st |qt∗ ). (3) Senders are rational, and their messages must maximize their expected utilities. (4) If qt∗ is decided by st , the belief p(st |qt∗ ) must follow Bayesian rules and the sender’s strategies.
pts M tj
A
s t
λ
P3 P2 M tk 0
P1
B
M ti
C
λbt
ptb
Fig. 2. Illustration of the strategy set.
Theorem 1 A unique PBE can always be achieved in the proposed game . Proof 1 Since λbt ≤ ptb < pts ≤ λst , rational prosumer n will set trtn = 0 and Trtn = 0. According to Eq. (4), to maximize Utn , the optimal action qtn∗ can be derived as follows: n b n k /p , x˜ ≤ gtn x˜ tn = tn ts tn (8) kt /pt , x˜ t > gtn
x˜ tn∗ = max xtn,min , x˜ tn (9) qtn∗ = gtn − x˜ tn∗
(10)
there exists a critical decision point for each prosumer n at time slot t: Mtn = n Then, n n kt /gt , kt /gtn . We can illustrate the strategy set of SESP (φt ) as the red triangle area (AB-C) in Fig. 2. Depending on the location of the decision point, there are three different
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scenarios. Decision point Mti divides the strategy set φt into three regions (P1 , P2 , P3 ). Under the premise of satisfying the critical loads, prosumer i will become a generator, consumer or self-feeding actor when the internal prices are set in region P1 , P2 , P3 . Decision point Mtk is quite low, which means prosumer k has high gtk or small ktk , and can always be a generator for any possible internal prices. Similarly, prosumer j can always be a consumer. Thus, the strategy set φt can be divided into at most (N + 1)(N + 2)/2 (N +1)(N +2)/2 i ϕt . Without loss in generality, ϕti subsets for N prosumers, that is, φt = ∪i=1 can be considered as a closed subset, as the continuity of UtSESP . For ∀ϕti ∈ φt , the utility of SESP UtSESP can be calculated as follows: ⎧
b ⎪ λbt − pts gtn − ktn /pts + λt − ptb gtn − ktn /ptb − λbt δet , trtSESP ≥ 0 ⎪ ⎨ n∈Bt n∈S t UtSESP =
⎪ λs − ps g n − k n /ps + λs − pb g n − k n /pb − λs δe, tr SESP < 0 ⎪ t t t t t t t t t t t t ⎩ n∈Bt
(11)
n∈St
The Hessian matrix of UtSESP can be derived as: ⎧⎡ ⎤ n b 3 ⎪ −2λbt kt /(pt ) 0 ⎪ ⎪ ⎢ ⎪ n∈St ⎪ n s 3⎥ ⎪ ⎣ ⎦ < 0, trtSESP > 0 b ⎪ ⎪ kt /(pt ) 0, −2λ ⎨ t n∈Bt ⎤ n b 3 H= ⎡ s ⎪ −2λ k /(p ) 0 ⎪ t t t ⎪ ⎪⎢ n∈St ⎪ n s 3⎥ ⎪ ⎣ ⎦ < 0, trtSESP < 0 ⎪ ⎪ kt /(pt ) 0, −2λst ⎩
(12)
n∈Bt
Obviously, H is negative definite for trtSESP > 0 and trtSESP < 0, and UtSESP is continuous at trtSESP = 0. Therefore, there exists a unique optimal value when trtSESP ≥ 0 b∗ , ps∗ ) and (pb∗ , ps∗ ). The optimal decision or trtSESP < 0, which can be referred as (pt,1 t,1 t,2 t,2 point in the closed subset ϕti is: b∗ s∗ SESP b∗ s∗ (pt,ϕ (pt,j , pt,j ) i , pt,ϕ i ) = arg max Ut t
t
(13)
j=1,2
The optimal decision point in the strategy set φt can be obtained as follows, which is the unique PBE: b∗ s∗ (ptb∗ , pts∗ ) = arg max UtSESP (pt,ϕ i , pt,ϕ i ) ϕti ∈φt
t
(14)
t
3.2 Solution for Game Equilibrium The BOA is a powerful tool for unknown objective function optimization [18]. An improved BOA with a sliding window is designed to obtain the game equilibrium, as shown in Table 1. The acquisition function facq (·) guides the search for the optimum value. Typically, it is a measure of the objective function UtSESP improvement probability. The Upper-Confidence-Bound (UCB) criteria is chosen here. Specifically, facq (pt ) =
√ μ(pt ) + vτt σ (pt ), where pt = ptb , pts , v = 1, τt = 2 log t 2 2π 2 /(3λ) and λ ∈
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Table 1. The implementation of a distributed BOA-based energy management strategy. − → s∗ ∗ ∗ Initialization: Initialize (ptb∗ , pts∗ ) = (λb∗ t1 , λt1 ), qt1 −1 = qt1 = 0 , and 1 1 = UtSESP∗ = 0. Dt1 −1,1 = Dt1 −1,2 = {} UtSESP∗ 1 1 −1 1. For t = t1 ; t < t2 ; t + + do 2. The SESP broadcasts (ptb∗ , pts∗ ) decided in time slot t − 1; ∗ , U SESP∗ ) ; 3. Update Dt,2 = Dt−1,2 , (ptb∗ , pts∗ , qt−1 t−1 4. Prosumers offer the best responses qt∗ ; 5. The SESP samples utility UtSESP∗ (qt∗ , ptb∗ , pts∗ , ω); 6. Update Dt,1 = Dt−1,1 , (ptb∗ , pts∗ , qt∗ , UtSESP∗ ; 7. Update facq according to Eqs. (15–21); 8. The SESP decides the optimal internal prices for the next time slot t + 1: b∗ , ps∗ ) = arg max f ((pb , ps )|D ); (pt+1 acq t,1 t+1 t+1 t+1
9. PBE: (qt∗ , ptb∗ , pts∗ ); 10. End for
(0, 1). The prediction error is assumed to obey a Gaussian distribution, and there exists Gaussian noise ω ∼ N (0, ε2 ) in the samples. The posterior probability of the SESP utility SESP |{D , p p(Ut+1 t,1 t+1 }) is subject to a Gaussian process, with mean μ(pt+1 ), covariance cov(pt+1 , pτ ), and variance σ 2 (pt+1 ), which can be denoted as follows: μ(pt+1 ) = k(pt+1 )T (Kt + ε2 I)−1 UtSESP∗
(15)
cov(pt+1 , pτ ) = k(pt+1 , pτ ) − k(pt+1 )T (Kt + ε2 I)−1 k(pτ )
(16)
σ 2 (pt+1 ) = cov(pt+1 , pt+1 )
(17)
2 k(pi , pj ) = exp(−pi − pj /2θ 2 ), t1 ≤ i, j ≤ t + 1
(18)
UtSESP∗ = [UtSESP∗ , UtSESP∗ , . . . , UtSESP∗ ]T 1 1 +1
(19)
k(pt+1 ) = [k(pt+1 , pt1 ), k(pt+1 , pt1 +1 ), . . . , k(pt+1 , pt )]T
(20)
Kt = [k(pi , pj )]t1 ≤i,j≤t
(21)
where θ is a single hyperparameter, which controls the width of the kernel function k(·). The utility functions of prosumers could be time-varying. Hence, a sliding window with a width of sw is introduced to select the latest effective historical samples.
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Theorem 2 The above BOA is always guaranteed to achieve the PBE. Proof 2 Here, we just need to prove that the proposed BOA satisfies the four requirements in Definition 1. First, since the SESP decides internal prices for the next time slot based on historical transaction information (step 8), the shared energy qt∗ determines the SESP’s decision p∗t+1 . In addition, qt is a variable of UtSESP . Thus, qt∗ determines (p∗t+1 , UtSESP∗ ). Further considering the observable history, qt∗ determines (Dt,1 , p∗t+1 ) = ((pkb∗ , pks∗ , qk∗ , UkSESP∗ )tk=t1 , p∗t+1 ). Second, the optimal shared energy of prosumers qt∗ is based on privacy st . After receiving the message qt∗ , the SESP will b∗ , ps∗ ) to achieve the highest utility U SESP∗ . Thus, set the optimal internal prices (pt+1 t+1 t+1 SESP∗ is determined by the privacy s . To conclude, the prior probability p(U SEPS∗ ) Ut+1 t t+1 SESP∗ ) corresponds to p(q∗ |s ), corresponds to p(st ). The likelihood p((Dt,1 , p∗t+1 )|Ut+1 t t SESP∗ |(D , p∗ )) means the which represents the strategy of senders (prosumers). p(Ut+1 t,1 t+1 belief in privacy p(st |qt∗ ). According to the Bayes theorem, we can express that:
p(st |qt∗ ) ∝ p(qt∗ |st ) · p(st ) SESP∗ |(D , p∗ )) ∝ p((D , p∗ )|U SESP∗ ) · p(U SEPS∗ ) p(Ut+1 t,1 t+1 t,1 t+1 t+1 t+1
(22)
SESP∗ |(D , p∗ )) is Thereby, requirement (4) is satisfied. Due to the fact that p(Ut+1 t,1 t+1 ∗ subject to GP, p(st |q ) naturally meets requirement (1). In addition, step 4 means that the senders (prosumers) rationally send messages to maximize their expected utility, which satisfies requirement (3). Moreover, the acquisition function facq represents the improvement probability of objective function UtSESP , and step 8 means the SESP takes action that can maximize the expected utility. Thus, requirement (2) is satisfied. In conclusion, the proposed distributed BOA fully meets the four requirements in Definition 1.
4 Performance Evaluation A community microgrid with six prosumers and SES is demonstrated in this paper. Based on a publicly available Ausgrid dataset [19], we choose six typical residential prosumers in Little Jilliby, New South Wales (2259). The configurations are listed in Table 2. The original loads, actual PV generations and netloads of prosumers are shown in Fig. 3. The negative part of netloads represents the original spare generation capacity of each prosumer. We can observe that different prosumers have different consumption patterns but similar PV generation patterns due to the close geographical location in a community. The grid prices are from Ref. [7]. The simulation process is carried out on a computer (OS: Win10, 64-bit, Memory: 8 GB, CPU: Inter Core i7-8750H @2.20 GHz) with MATLAB 2018b. The initial SOE is set to 0.5 at 7 a.m. SOEmin and SOEmax are set to 0.2 and 0.8, respectively. To evaluate the proposed community microgrid scheduling strategy based on the signaling game model, it is compared with the Stackelberg game model, where a simulated annealing algorithm [20] is used to obtain the Stackelberg equilibrium. The electricity prices in the two scheduling models are shown in Fig. 4. Note that before 7 a.m.,
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Prosumer index
1
2
3
4
5
6
Prosumer ID in dataset
2
20
38
106
169
184
Solar system equipment (kWp)
1.62
1.57
1.05
1.5
2.04
1.05
SES capacity (kWh)
60
(a)
(b)
(c)
Time (h)
Fig. 3. (a) Original loads. (b) Actual PV generations. (c) Netloads of prosumers.
prosumers have insufficient spare generation capacity, so energy sharing cannot be implemented. Thus, we focus on the service phase after 7 a.m. The internal prices in the two game models are within grid prices to encourage prosumers to participate in the community market. However, they differ from each other. The internal prices in the Stackelberg game model coincide with the grid prices after 20:30. This means that the SES is no longer able to provide shared energy storage under this scheduling strategy. However, the SES in the signaling game model is still working at that time. The main reason lies in the fact that the SESP can obtain the utility functions of prosumers and is greedy to
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make use of the SES as much as possible in each time slot to achieve profits. This makes the SOE lower and leads to a premature end of service, as shown in Fig. 5.
b t s t
ptb(Stackelberg) pts(Stackelberg)
ptb (signaling) pts (signaling)
Fig. 4. Electricity prices in different scheduling models.
Fig. 5. The SOE of the SES in different scheduling models.
Energy scheduling for a community microgrid with shared energy storage has two purposes: (1) enhance the benefits for all participants and (2) reduce the impact on the grid. Here, the performance will be evaluated from the two aspects. The utility of the players is shown in Fig. 6, including the SESP utility and the prosumers utility improvement. The detailed numerical results are presented in Table 3. The unit of values in the table is CNY. Compared with the community grid without the SES, the prosumers and SESP can achieve more utilities. This means that SES plays an important role in the community microgrid. The utilities of prosumers do not change much in the two scheduling models. However, the signal game improved SESP utility by 17.4%, from 21.33 to 25.04. Actually, according to the leader-follower assumption of the Stackelberg game, the SESP is fully aware of the utility functions of prosumers, which are not
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available in the signaling game. This results from the premature end of service in the Stackelberg game formulation. Compared with the Stackelberg game model, the signaling game model obtains lower SESP utility before 20:30 but higher utility after that. In addition, the social utility (the summation of utilities of all players) is improved by 9.1% and 10.2% in Stackelberg and signaling game models, respectively. (a)
(b)
Fig. 6. The utility of players: (a) the SESP utility, (b) the prosumers utility improvement. Table 3. Utility of prosumers and the SESP. Prosumer
1
2
3
4
5
6
Prosumer utility
SESP utility
Social utility
Original
84.01
55.50
72.34
23.53
26.79
125.00
387.17
0.00
387.17
Stackelberg
86.25
57.36
75.65
24.15
27.44
130.32
401.16
21.33
422.48
Signaling
86.97
58.01
74.94
24.29
27.85
129.43
401.49
25.04
426.53
The influence of the community microgrid on the grid can be expressed in terms of the magnitude of the PCC net load deviation from zero and the degree of fluctuation. The net load of PCC is shown in Fig. 7. It can be found that the net load of the PCC with SES is almost zero during the daytime, both in the Stackelberg and signaling game models. The numerical statistics of the net load of PCC are listed in Table 4. The mean absolute value
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Fig. 7. Net load of PCC.
Table 4. Numerical statistics of the net load of PCC. Indicator
Original
Stackelberg
Signaling
Mean absolute value (kWh/0.5 h)
1.401
0.914 (−34.7%)
0.734 (−47.6%)
Standard deviation (kWh/0.5 h)
1.523
1.198 (−21.3%)
0.952 (−37.4%)
of the net load of PCC is reduced by 34.7 and 47.6% in the Stackelberg and signaling models, and the standard deviation is reduced by 21.3 and 37.4% in the Stackelberg and signaling models. Compared to the Stackelberg game model, the mean absolute value and standard deviation of the net PCC load in the signaling game model are reduced by 19.7% and 20.5%, respectively. This illustrates that the proposed signaling game-based scheduling strategy can effectively reduce the adverse impacts of the microgrid on the grid.
5 Conclusion This paper proposes an efficient energy scheduling strategy based on a signaling game for a community microgrid with shared energy storage. The interaction between participants in a community microgrid is formulated as a signaling game. The signaling game effectively avoids the situation in which the private utility functions of prosumers have to be obtained, which is necessary in the Stackelberg game. The improved BOA with a sliding window is designed to acquire the game equilibrium. In addition, the existence and uniqueness of the equilibrium are demonstrated. The superiority of the proposed strategy is verified by case simulation. The utility of the shared energy storage provider is improved by 17.4% without compromising prosumer utility. Moreover, the overall power fluctuations of the community microgrid decreased by approximately 20%. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant No. 91848111, 61803359).
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References 1. Luo, X., Shi, W., Jiang, Y., et al.: Distributed peer-to-peer energy trading based on game theory in a community microgrid considering ownership complexity of distributed energy resources. J. Clean. Prod. 351, 131573 (2022) 2. Shen, Y., Hu, W., Liu, M., et al.: Energy storage optimization method for microgrid considering multi-energy coupling demand response. J. Energy Storage 45, 103521 (2022) 3. Wu, J., Xing, X., Liu, X., et al.: Energy management strategy for grid-tied microgrids considering the energy storage efficiency. IEEE Trans. Ind. Electron. 65(12), 9539–9549 (2018) 4. Han, L., Morstyn, T., McCulloch, M.: Incentivizing prosumer coalitions with energy management using cooperative game theory. IEEE Trans. Power Syst. 34(1), 303–313 (2018) 5. Zhang, M., Eliassen, F., Taherkordi, A., et al.: Demand-response games for peer-to-peer energy trading with the hyperledger blockchain. IEEE Trans. Syst., Man, Cybern.: Syst. 52(1), 19–31 (2021) 6. Tao, L., Gao, Y.: Real-time pricing for smart grid with distributed energy and storage: a noncooperative game method considering spatially and temporally coupled constraints. Int. J. Electr. Power Energy Syst. 115, 105487 (2020) 7. Liu, N., Cheng, M., Yu, X., et al.: Energy-sharing provider for PV prosumer clusters: a hybrid approach using stochastic programming and Stackelberg game. IEEE Trans. Ind. Electron. 65(8), 6740–6750 (2018) 8. Mediwaththe, C.P., Blackhall, L.: Network-aware demand-side management framework with a community energy storage system considering voltage constraints. IEEE Trans. Power Syst. 36(2), 1229–1238 (2020) 9. Qiu, H., Gu, W., Wang, L., et al.: Trilayer Stackelberg game approach for robustly power management in community grids. IEEE Trans. Ind. Inform. 17(6), 4073–4083 (2020) 10. Bruninx, K., Pandži´c, H., Le Cadre, H., et al.: On the interaction between aggregators, electricity markets and residential demand response providers. IEEE Trans. Power Syst. 35(2), 840–853 (2019) 11. He, L., Liu, Y., Zhang, J.: Peer-to-peer energy sharing with battery storage: energy pawn in the smart grid. Appl. Energy 297, 117129 (2021) 12. Erol, Ö., Filik, Ü.B.: A Stackelberg game approach for energy sharing management of a microgrid providing flexibility to entities. Appl. Energy 316, 118944 (2022) 13. Dong, G., Chen, Z.: Data-driven energy management in a home microgrid based on Bayesian optimal algorithm. IEEE Trans. Ind. Inform. 15(2), 869–877 (2018) 14. Liu, X., Tang, D., Dai, Z.: A Bayesian game approach for demand response management considering incomplete information. J. Mod. Power Syst. Clean Energy 10(2), 492–501 (2021) 15. Shen, S., Huang, L., Zhou, H., et al.: Multistage signaling game-based optimal detection strategies for suppressing malware diffusion in fog-cloud-based IoT networks. IEEE Internet Things J. 5(2), 1043–1054 (2018) 16. Oprea, S.V., Bâra, A.: A signaling game-optimization algorithm for residential energy communities implemented at the edge-computing side. Comput. Ind. Eng. 108272 (2022) 17. Maharjan, S., Zhu, Q., Zhang, Y., et al.: Dependable demand response management in the smart grid: a Stackelberg game approach. IEEE Trans. Smart Grid 4(1), 120–132 (2013) 18. Zhang, Y., Zhou, G., Jin, J., et al.: Sparse Bayesian classification of EEG for brain–computer interface. IEEE Trans. Neural Netw. Learn. Syst. 27(11), 2256–2267 (2015) 19. Ratnam, E.L., Weller, S.R., Kellett, C.M., et al.: Residential load and rooftop PV generation: an Australian distribution network dataset. Int. J. Sustain. Energy 36(8), 787–806 (2017) 20. Dababneh, F., Li, L.: Integrated electricity and natural gas demand response for manufacturers in the smart grid. IEEE Trans. Smart Grid 10(4), 4164–4174 (2018)
Lithium-Ion Battery Fast Charging Strategy Based on Reinforcement Learning Algorithm in Electric Vehicles Aihua Tang1
, Jinyuan Shao1(B) , Tingting Xu2 , and Xiaorui Hu2
1 School of Vehicle Engineering, Chongqing University of Technology, Chongqing 400054,
China [email protected], [email protected] 2 State Grid Chongqing Electric Power Company Marketing Service Center, Chongqing 400014, China [email protected], [email protected]
Abstract. The quality of the Lithium-ion battery charging performance straight affects clients’ awareness and acceptance of the electric vehicles. Researching on the optimization of the charging methods is critical for the evolution of more intelligent battery management systems and smart electric vehicles in the future. This paper first introduces the types of simple charging methods and the existing shortcomings, and then describes the characteristics of various optimized charging methods and compares them, then proposes a fast charging strategy based on the DDPG (deep deterministic policy gradient) algorithm. By balancing the charging speed, battery life and safety, the minimum penalty target function is established by Zhong et al. 1699–1704, 2004. Combining the model-based state observer with the general algorithm framework of the optimizer based on deep reinforcement learning, a context-aware deep deterministic policy gradient algorithm with priority experience playback is proposed. Compared with the traditional charging methods, the optimized charging method can shorten the charging time, improve the charging performance, prolong the battery cycle life, and perform a clever compromise between the charging speed and the compliance with physical constraints. Keywords: Fast charging · DDPG · Battery life · Thermal management
1 Introduction At present, due to the energy crisis and environmental problems, electric vehicles have developed very quickly, especially blade electric vehicles, in which the battery is one of the most critical components. There are many outstanding features in the Lithiumion battery such as high energy density and power density, long cycle life, low self discharge and good safety performance [2]. It is currently considered to be the preferred battery of electric vehicles. Fast charging of power batteries is considered to be the key technology for the prosperity of electric vehicles in the future. Many studies have shown © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1249–1255, 2023. https://doi.org/10.1007/978-981-99-1027-4_130
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that the key challenge for fast charging is the battery. Blindly increasing the charging current will increase the charging speed, but also shorten the life of the battery, It’s a dilemma. The serious consequences of pursuing the maximum charging speed include SEI membrane growth, electrode particle cracking, graphite material falling off, and even safety accidents in extreme cases. Therefore, in order to charge the battery as quickly as possible without excessively affecting the battery life, it is necessary to find an optimal fast charging strategy. Charging control has always been an extensive and intensive research field, and many kinds of charging methods have been produced. The first is based on charging waveform control including constant current constant voltage (CC–CV) [3], trickle charging constant flow constant voltage (TC-CC–CV), multi-level constant current charging based on the upper cut-off voltage displacement conditions and the SOC interval shifting conditions, Pulse charging that can add a period of rest or short-term discharge during the charging process to reduce the polarization voltage, and AC charging can be obtained from the electrochemical impedance spectrum to obtain the best charging current frequency and minimize impedance [4]. Although these methods have low complexity and less computation, they are based on experience and do not have enough understanding of the dynamic characteristics and internal mechanism of the battery. Therefore, People have found that in terms of both charging speed and battery safety life, such a charging strategy is far from reaching the best results. The second is the model-based charging strategy, including the charging strategy based on electrochemistry and equivalent circuit model, and an optimized MCC charging strategy based on electro-thermal coupling (CET) model is proposed, which can limit the adverse effects caused by polarization and thermal effects [5]. The model-based charging strategy has better optimality guarantee and stronger robustness, but due to the need for many nonlinear calculations, the amount of calculation will be large. Therefore, there is an urgent need for finding a fast charging method which has the advantages of online tractability and multi-objective optimization [6]. The characteristics of different charging methods are shown in Table 1 [7]. Table 1. Comparison of the characteristics of various charging methods Charging methods
Time
Efficiency
Complexity
Cycle life
Constant current
Medium
Large
Large
Large
Constant voltage
High
Large
Large
Large
CC–CV
Medium
Medium
Medium
Medium
Multi-stage CC
Large
Medium
Medium
High
Current-pulse charging
Medium
Medium
Medium
Large
Voltage-pulse charging
Medium
Medium
High
Large
ECM-based
Medium
High
High
High
EM-based
Large
High
High
High
Alternating charging
Medium
High
High
High
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2 Introduction of the Fast Charging Strategy 2.1 Model Establishment Establish electrothermal coupling model and aging model for the battery studied. The model consists of a second-order RC model and a two-state thermodynamic model. In terms of equivalent circuit model, the voltage source represents the open-circuit voltage linearly related to SOC, Rs is the ohmic internal resistance, Ts is the cell surface temperature and Ta is the cell internal temperature. The two RC simulate polarization effects, charge transfer, diffusion and passivation layer effects on the electrode, respectively. Vt (t) = Voc (SOC, t) + Vp1 (t) + Vp2 (t) + Rs (t)I (t) dTa (t) = dt
Tf Cs − Cc 1 Cs − Cc H (t) Ts (t) + − Ta (t) + + Rc Cc Cs 2Ru Cs Rc Cc Cs 2Cc 2Ru Cs
(1) (2)
A model based on energy throughput is used to determine the remaining life of lithium-ion batteries. The throughput model refers to the flow of charge emitted or charged into a lithium-ion battery before it fails at the end of its life, which is equivalent to the loop of charging and discharge. The degree of decline in battery life (SOH) under multiple influencing factors is given by the following formulas. The designed model according to above principle is shown in Fig. 1 [8]. 1 dSoH (t) =− dt 2N (c, Ta )Cn
t |I (τ )|d τ
(3)
0
|Ik |t SoHk = − 2Nk (c, Ta )Cn
Fig. 1. Electro-thermal model of Lithium-ion battery.
(4)
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3 State Observer Adopt the expansion of the Karman filtering method, and use the electric heating model to establish a state space model with polarization voltage, SOC and internal temperature of the battery as state variables. The calculated surface temperature and terminal voltage of the battery are compared with the real values measured by the sensor, and the feedback control is carried out to obtain the required state variables. Ft =
∂f (x(t − 1), u(t − 1)) ∂h(x(t), u(t)) , Gt = ∂x ∂x
(5)
x(t) = f (x(t − 1), u(t − 1))
(6)
Pt = Ft Pt−1 FtT + w
(7)
Kt = Pt GtT (Gt Pt GtT + v )
−1
(8)
x(t) = x(t) + Kt (z(t) − g(x(t), u(t)))
(9)
Pt = (I − Kt Gt )Pt
(10)
4 Establishment of Target Function In order to achieve the best balance between charging speed, battery life and safety, this paper establishes the minimum penalty target function: Jt = w1 Csoc + w2 Cvolt + w3 Cheat + w4 Csoh + w5 Csmooth
(11)
where w1 , w2 , w3 , w4 , w5 represents the weight of the importance of different goals, which are the increase of SOC, the increase of terminal voltage, the increase of internal temperature of battery, the decline of battery life, and the smoothness of charging current. Csoc = |SoC tar − SoC t | ⎧ ⎨ 0 if Vtar_low Vtar_upp ⎩ τ1 Vt − Vtar_low if Vt < Vtar_low 0if Ta,t < Ttar Cheat τ2 Ta,t − Ttar if Ta,t > Ttar
(12)
(13)
(14)
Csoh = τ3 |SoHt |
(15)
Csmooth = |It − It−1 |
(16)
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5 DDPG Algorithm Battery Fast Charging Reinforcement learning is agent in a “trial and error” approach to learning, through the guidance and environment interact to obtain the reward behavior, it belongs to a field of machine learning that emphasizes how to act based on the environment to maximize the expected benefits [9]. Its inspiration comes from the behaviorism theory in psychology, that is, how the organism, under the stimulus of the reward or punishment given by the environment, gradually forms the expectation of the stimulus and produces the habitual behavior that can obtain the maximum benefit [10]. This method is universal. This algorithm designs two deep neural networks—value network Q and strategy network μ. The essence of reinforcement learning is to enter the value network by inputting the current environment. The value network judges the corresponding value according to each possible action, and then the strategy network selects an action with the highest total reward value according to the value obtained by the value network, and then enters the next state to start a new cycle and constantly update the network. At the same time, each action will have a corresponding reward. In the fast charging of power battery, the environmental state is the SOC terminal voltage, internal temperature obtained by the state observer, the action is the charging current, and the reward is the target function. The larger the reward value is, the more beneficial this action is. The designed system according to above principle is shown in Fig. 2.
Fig. 2. Reinforcement learning algorithm fast charging model.
The value network parameter Q is updated through the temporary difference learning algorithm, that is, the value estimated in step t + 1 is multiplied by the learning rate γ , Then add the reward of step t and compare it with the estimated value of step t. Finally, use the gradient descent method to update the parameters, because yt includes the reward value obtained in step t, so it is closer to the real value. yt = rt + γ Q(St+1 , at+1 ; w) Loss : Lt =
1 (Q(st , at ; w) − yt )2 2
(17) (18)
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wt+1 = wt − α
∂Lt |w=wt ∂w
(19)
The strategic network parameter θ is updated through the Policy-Based Learning algorithm, and the action value of each step is multiplied by the probability of the action, and then sum to obtain Vπ (s; μ), that is, the quality of the environment S. The higher the value of Vπ (s; μ), the better. Then use the gradient rising method to update the network parameters [11]. Vπ (s; μ) = a π (a|s; μ) · Qπ (s, a) g(at , μ) ≈
∂Vπ (s; μ) ∂μ
μt+1 = μt + β · g(at , μ)
(20) (21) (22)
6 Conclusions This paper proposes a fast charging strategy based on the DDPG algorithm for fast charging of lithium-ion batteries. By punishing the overheating and decay of lithiumion batteries, a multi-objective optimization problem is established. Compared with the charging strategy based on charging waveform control, the fast charging strategy based on this algorithm has higher accuracy and faster calculation speed than the model-based charging strategy. The charging strategy has cleverly weighed between the charging speed and the compliance with physical constraints, which raises the possibility for future applications in real life. Acknowledgements. This work is sponsored by Natural Science Foundation of China (Grant No. 52277213), key project of science and technology research program of Chongqing Education Commission of China (Grant No. KJZD-K202201103), Natural Science Foundation of Chongqing, China (Grant No. Cstc2021jcyj-msxmX0464), Scientific Research Foundation of Chongqing University of Technology (Grant No. 2021ZDZ004) and Science and Technology Project of State Grid Chongqing Electric Power Company (Grant No. 5220002000C0).
References 1. Zhong, H., He, H., Wei, Z.: Stress-constrained fast charging of lithium-ion battery with predictive control. In: 2021 IEEE energy conversion congress and exposition (ECCE), pp. 1699–1704 (2021) 2. Dung, L.R., Yen, J.H.: ILP-based algorithm for Lithium ion-battery charging profile. In: IEEE International Symposium on Industrial Electronics, pp. 2286–2291. IEEE (2010) 3. Bhatt, M., Hurley, W.G., Wolfle, W.H.: A new approach to intermittent charging of valveregulated lead-acid batteries in standby applications. IEEE Trans. Industr. Electron. 52(5), 1337–1342 (2005)
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4. Li, J., Murphy, E., Winnick, J., Kohl, P.A.: The effects of pulse charging on cycling characteristics of commercial lithium-ion batteries. J. Power Sources 102(1–2), 302–309 (2001) 5. Ouyang, Q., Chen, J., Zheng, J., Fang, H.: Optimal multiobjective charging for lithium-ion battery packs: A hierarchical control approach. IEEE Trans. Ind. Inform. 14(9), 4243–4253 (2018) 6. Tian, N., Fang, H., Wang, Y.: Real-time optimal lithium-ion battery charging based on explicit model predictive control. IEEE Trans. Ind. Inform. p. 1 (2020) 7. Lin, Q., Wang, J., Xiong, R., et al.: Towards a smarter battery management system: a critical review on optimal charging methods of lithium-ion batteries. Energy 183, 220–234 (2019) 8. Wei, Z., Quan, Z., Wu, J., et al.: Deep deterministic policy gradient-drl enabled multiphysicsconstrained fast charging of lithium-ion battery. IEEE Trans. Industr. Electron. 69(3), 2588– 2598 (2021) 9. Dabbaghjamanesh, M., Moeini, A., Kavousi-Fard, A.: Reinforcement learning-based load forecasting of electric vehicle charging station using q-learning technique. IEEE Trans. Ind. Inform. 17(6) 4229–4237 (2020) 10. Cao, J., D. Harrold, Z. Fan, T. Morstyn, D. Healey, and K. Li.: Deep Reinforcement LearningBased Energy Storage Arbitrage With Accurate Lithium-Ion Battery Degradation Model. IEEE Trans. Smart Grid 11(5), 4513–4521 (2020) 11. Wei, Z., Zhao, J., Ji, D., Tseng, K. J.: A multi-timescale estimator for battery state of charge and capacity dual estimation based on an online identified model. Appl. Energy 204(6), pp. 1264–1274 (2017)
Differential Drive Based Cooperate Steering Control Strategy Considering Energy Efficiency for Multi-axle Distributed Vehicle Yonghua Wu(B) , Junqiu Li, and Weichen Wang School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China [email protected], [email protected], [email protected]
Abstract. This chapter presents a differential drive based cooperate steering control strategy considering energy efficiency for multi-axle distributed drive vehicle. Apart from used as a fault-tolerant control method of Steer-by-Wire (SBW) system to keep stability and performance of the vehicle, the differential drive steer (DDS) can also be combined with SBW by reasonable torque allocation with considering the efficiency distribution of drive motors during normal driving. Firstly, the dynamic models of multi-axle vehicle including the front SBW system are established. Then, the upper layer path follow controller is designed based on model predictive control (MPC) with measurable disturbance to obtain the generalized steer torque. According the drive motor efficiency map, the lower layer steer axles optimal torque allocation strategy is proposed to balance the contribution of SBW motor torque and differential torque. Finally, the strategy is validated through close-loop simulation in MATLAB/Simulink. The result shows that the proposed strategy can adaptively adjust differential torque of steer axles and SBW motor torque to track the target path with better energy efficiency. Keywords: Distributed vehicle · Differential drive steer · Model predictive control · Cooperate steering control
1 Introduction As electric drive and automated became a general trend of vehicle development, many advantage technologies has been developed to improve vehicle performance and energy efficiency. The distributed drive different from traditional centralized drive is regarded as one of the main means to enhance vehicle handling performance by controlling torque of each individual motor drive wheels [1]. According to this, the differential drive torque of steer axle wheels can generate a novel steering mechanism without extra steer power unit (e.g., motor). It needs to be noted that differential drive steer (DDS) is different from differential speed steer (DSS) which depends on skid steer. In most situations, DDS is used as a fault-tolerant control method of Steer-by-Wire (SBW) system to keep stability and performance of the vehicle [2]. The study in [3] designed two different slide-mode based controller corresponding to DDS and DSS © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1256–1265, 2023. https://doi.org/10.1007/978-981-99-1027-4_131
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respectively with considering a SBW failure, where the result shows the advantages of DDS in target tracking stability and robustness. The study in [4] proposed a faulttolerant control method based on the coordination of differential steering and direct yaw moment to solve the problem of trajectory tracking and yaw stability when the actuator of steering-by-wire system fails. Except for SBW and DDS working separately, Wang [5] proposed a differential drive coordination active steering (DDCAS) control system to combine their contribution to steering with corresponding to steer angle correction and torque correction, respectively. From another perspective, energy consumption is an unavoidable issue for electric drive vehicles. Since the energy efficiency of electric drive vehicles is mainly depend on the motors and their drive controllers, for distributed vehicle, the longitudinal control basically focuses on the torque allocation between axles [6–8]. Furthermore, the torque allocation between the left and right wheels of the steering axles can be an essential factor to improve vehicle energy efficiency in differential steering. Shen proposed DDS mode of distributed-drive articulated vehicle to reduce energy consumption of its hydraulic steering system [9]. And Du developed an energy efficient pivot steering control algorithm for skid steering vehicle by optimizing the front-middle and front-rear force factors of three-axle vehicle [10]. Despite this, there is not much research on the combination of SBW and DDS for multi-axle vehicles with considering energy efficiency. In this chapter, a steering control strategy combining DDS and SBW is proposed for the multi-axle distributed electric vehicle to improve energy efficiency in path tracking mission. The dynamic model of six-axle distributed vehicle including steer system model and tracking error model is built in Chap. 2. In Chap. 3, with the idea of hierarchical control, a MPC based path tracking controller is proposed in the upper layer to obtain the generalized steer torque required for path tracking, then by analyzing the efficiency map of drive motor system, the torque allocation is transformed into a real-time solved optimal control problem (OCP) in lower layer. Finally in Chap. 4, the close-loop simulation in MATLAB/Simulink is used to validate the proposed strategy.
2 Modeling of Vehicle System 2.1 2DOF Dynamic Model In this research, with ignoring the pitch, roll, and vertial motion, and keeping the vehicle drive at a constant speed, a 2DOF dynamic model of 6-axle distributed drive vehicle is established as follows: m(˙vy + vx r) = 6j=1 Fyj (1) Iz r˙ = 2j=1 Fyj Lj − 6j=3 Fyj Lj where m, Iz , vy , vx , r represents the total mass of vehicle, the yaw inertial of vehicle, the lateral and longitudinal velocity in vehicle coordinate system, vehicle yaw rate, respectively; Lj (i = 1, 2, …, 6) represents the distance from each axle to the center of gravity (CG); Fyj represents the lateral force of each axle.
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Assuming quite small tire slip angles and wheel steer angles, the lateral force Fyj can be expressed as v +L r Cαj (δj − y vx j ), j = 1, 2 (2) Fyi = −vy +Lj r Cαj vx , j = 3, 4, 5, 6 where Cαj , δj represents the tire cornering stiffness, the wheel steer angle of front axles, respectively. 2.2 Steering System Model
Tm
δ11 Fx11
Rd
SBW motor
Fx12
Steer Machine
δ 21 Fx 21
Fx 22
Fig. 1. Steer system of front-double-axle
A typical front-double-axle SBW system is structured in Fig. 1, which include SBW motor, steer machine, steer rods, etc. The dynamic equation of the steer system can be expressed as Is δ¨ + Bs δ˙ = Tm + Mzw + τf + Tdiff
(3)
where δ represents the steer angle of steer column; Is , Bs , τf represents the equivalent rotational inertial, equivalent rotational damping and friction torque, respectively; Mzw represents the equivalent self-align moment of wheel, with small slip angle assumption, it can be obtained from Mzw =
1 l2 (Cα1 α1 + pCα2 α2 ) N 3
(4)
where l, N , p denotes the tire trail, gear ratio of steer machine and fixed steer angle ratio of the front two axles p = δ2 /δ1 , respectively.
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As Tm and Tdiff are the main drive torque of steer system, where Tm is the torque of SBW machine without considering a gear box, and Tdiff is the converted differential torque obtained from Tdiff = −
TRd (1 + p) Rw N
(5)
where Rd , Rw represents the scrub radius and wheel roll radius, respectively; T represents the differential drive torque of each axle between left and right wheel, and it takes a positive value when the left is larger, vice versa. 2.3 Tracking Error Model Without regard to the input of driver, the whole vehicle is controlled by controller to track target path. eϕ is defined as the yaw angle deviation between vehicle and target path, and ed is defined the normal distance from vehicle to target path, it takes a positive value when vehicle is on the left side of the road. Then, the tracking error model can be expressed as e˙ ϕ = r − vx ρ (6) e˙ d = vy + vx eϕ where ρ represents the curvature of target path.
3 Strategy of Cooperate Steering Control In this chapter, the differential torque and SBW torque are considered to have the same effect on vehicle steering, which means the additional yaw moment brought by differential torque is ignored since it has relatively small impact on this heavy vehicle. Meanwhile, the robustness of MPC can ensure the accuracy of path tracking even with such additional yaw moment to some extent. 3.1 MPC Based Path Tracking Control From Eqs. (1)–(6), the states of vehicle in path tracking mission are described by x = T vy r δ δ˙ eϕ ed . Define the manipulate variable u = [Ta ], the measurable variable v = [ρ], the continuous state space model can be given as x˙ = Ax + Bu + Bv v (7) y = Cx
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Y. Wu et al.
−
6
j=1 Cαj
mvx − Iaz v1x
a1 − mv − vx x
−
a2 mN a3 Iz N
2
2 j=1 Lj Cαj
Iz vx
0
0
l 2 a2 3Is vx N
l 2 a3 3Is vx N
0 1
1 0
0 2 − 3Il aN42 s 0 0
C = diag[ 1 1 1 1 1 1 ], a1 =
2
⎤
0 0 1 − Bs Is 0 0
Lj Cαj −
j=1
⎡ ⎤ ⎤ ⎡ 0 0 ⎥ ⎢0⎥ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎥ ⎢ 0⎥ ⎢0⎥ ⎥ ⎥ ⎢ 0 ⎢ ⎥ ⎥ ⎢ ⎥ 0 ⎥, B = ⎢ 1 ⎥, Bv = ⎢ ⎥ ⎢ Is ⎥ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎥ ⎢ 0⎥ ⎥ ⎣0⎦ ⎣ −vx ⎦ ⎦ 0 0 0 0
0 0 0 0 0 0 vx
6
(8)
Lj Cαj
j=3
a2 = Cα1 + pCα2 , a3 = L1 Cα1 + pL2 Cα2 , a4 = L1 Cα1 + p2 L2 Cα2 . To design the MPC based controller, Eq. (8) is discretized with the method of zeroorder holder, then we can get x(k + 1) = Ad x(k) + Bd u(k) + Bdv v(k) (9) y(k + 1) = Cx(k + 1) T T where Ad = eAT , Bd = 0 eAτ d τ B, Bdv = 0 eAτ d τ Bd , T denotes sample time of system. Then, with introducing the slack variables ε, soft constrains are used for tracking error and hard constrains are used for dynamic states and steer angle. The path tracking problem is written in the form of MPC: min J =
u,x,ε
Np c −1 2 N
Su u(h)2R + Su u(h)2E + ς ε2 Sx y(h) - yref (h) + k=1
Q
k=0
⎧ x(k) = Ad x(k − 1) + Bu,d u(k) + Bv,d v(k) ⎪ ⎪ ⎨ −Kε + ymin ≤ y(k) ≤ ymax + Kε s.t. ⎪ umin ≤ u(k) ≤ umax ⎪ ⎩ umin ≤ u(k) ≤ umax
(10)
where the cost function above includes the penalty for the output target tracking error, the penalty for the control quantity and its change of rate. Sx , Su are corresponding normalized weights, and Q, R, E, ς are corresponding weight matrix or scalar. The generalized steer torque Ta then can be obtained from above MPC problem solving by method for Quadratic Programming (QP). 3.2 Optimal Torque Allocation Generally speaking, the high efficiency area of permanent magnet synchronous motor has a high degree of coincidence with the actual operating conditions of the vehicle. As shown in Fig. 2, the high-efficiency area of the drive motor is mainly concentrated in
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Fig. 2. Drive motor efficiency map
the middle area of speed and torque, and the efficiency sharply reduced in relatively low (or high) speed and torque. According to the previous assumption, the motor speed is regarded as constant positive value n. To clearly represent the relationship between drive torque T and power consumption. The power loss PL is defined as follow Tn η ,T > 0 PL = 9550Tn1−η (11) − 9550 η, T < 0 where η represents the power efficiency of motor driving system; the negative PL means drive motor is working in braking mode. With Eq. (11), PL can be obtained from discrete points of motor test data. Through curve fitting methods of smooth cubic spline, we can get PL (T ) = f (T , n)
(12)
where f represents the fitted function; n is the motor speed at current vehicle speed. To improve energy efficiency, the cost function to be optimize is expressed in the form of total energy power consumption at the current moment J = Psteer + Pdrive
(13)
where Psteer represents the power consumption of SBW motor and Pdrive represents the power consumption of front axles drive motors. They are expressed as Psteer = |Tm ns /(9550ηs )| Pdrive = 2PL (Tp + T ) + 2PL (Tp − T ) + 4Tp n/9550
(14)
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where Tp , ns , ηs represents torque pre-allocated to each wheel, equivalent rotating speed of steering column and power efficiency of SBW system. The relationship between SBW torque and differential torque is Ta = Tm + kdiff T
(15)
with kdiff = − RRwdN (1 + p), according to Eq. (5). After ignoring the constant term in the cost function, the OCP of torque allocation can be structed as min J = |Psteer | + 2|PL (T + T )| + 2|PL (T − T )| T ⎧ ⎨ |T + T | ε
(5)
where d(x i , yj ) is the difference value between x i in sequence X and yj in sequence Y, ε denotes the set threshold. Suppose that the real sequence Y is used as a template to perform delete, insert, and replace operations on the real sequence X. (1) Deletion: delete an element in the real sequence X (equivalent to inserting an element into Y ), and add 1 to d EDR (i − 1, j). (2) Insertion: insert an element into the real sequence X (equivalent to deleting an element in Y ), and add 1 to d EDR (i, j − 1). (3) Replacement: If d(x i , yj ) is larger than ε, add 1 to d EDR (i − 1, j − 1); if d(x i , yj ) is smaller than ε, there is no operation. After operating on all elements in X and Y, the result d EDR (m, n) is the edit distance between sequence X and sequence Y [11]. And if edit distance is larger, it means that the similarity between X and Y is lower.
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3 Data Acquisition and Introduction The data are sampled from an NCM LIB pack in one electric vehicle. The LIB pack suffered a thermal runaway. According to post-incident report, the thermal runaway was caused by the battery pack.The data are collected from May 24, 2020, to September 14, 2020, and include 9 cycles and one more charging segment (the first one is the charging segment). The voltage and temperature values of cells in the battery pack before thermal runaway are in the normal operating range. The local cell voltage curves before thermal runaway and during thermal runaway are respectively shown in Fig. 2(a) and (b). In Fig. 2(a), the voltages of cell A (red line) are significantly lower than other cell voltages. However, both faults and voltage inconsistency may cause this anomaly, making it difficult to identify cell A as a faulty cell. And from Fig. 2(b), we can know that during thermal runaway, cell A’s voltage was down to 0.514 V at sampling moment 13388, which exceeds the discharge cut-off voltage of NCM batteries. Besides, the voltages of cells B and C respectively rose to 5.374 V and 4.674 V, and both of them exceed the set charge cut-off voltage of NCM batteries. After that, the voltages of some cells are also disordered, and the changes in voltages of cells B and C increase the difficulty to identify the real faulty cell from the voltage abnormality during thermal runaway. Considering the difficulty in determining the real cause of voltage anomaly of cell A before thermal runaway, it is necessary to apply the method proposed in this paper for further analysis. (13388, 5.374)
(13388, 4.674)
(13388, 0.514)
(a) Voltage curves before thermal runaway. (b) Voltage curves during thermal runaway. Fig. 2. Voltage curves in thermal runaway case.
4 Results and Discussion 4.1 Results Figure 3 presents the edit distances between cell #1 and the rest cells in 10 charging segments and 9 discharging segments. The threshold of edit distance is set to 0.004 both in charging and discharging segments, and the voltage intervals in charging and discharging are 3.915–4.117 V and 4–4.05 V, respectively. From the 1st cycle to the 7th discharge segment, the edit distances of cell A, both in charging segments and discharging segments, deviate from the other cells, which may be caused by voltage inconsistency. From the 8th charging segment to the 10th charging segment (the 8th
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charging - 8th discharging - 9th charging - 9th discharging - 10th charging), two editing distance curves of cell A present an upward trend and further deviate from others. Considering the continuity of battery charging and discharging, the curves well indicate that the abnormality of cell A is gradually serious, which may be the evolution of the voltage abnormality brought by the fault from occurrence to seriousness. After the 10th charging segment, the battery pack suffered from thermal runaway, which is probably caused by the gradual seriousness of the fault of cell A. Some other cells need to be analyzed to avoid misdiagnosis. The edit distance curve of cell D (green line), the same as that of cell A, deviates from other cells before the 8th discharge segment. Although the trend is rising in the 8th discharge and 9th discharge segments, the edit distance curve of cell D does not increase in the 9th and 10th charging segments. Considering that the fault should have abnormal performance both in the charging and discharging process, the abnormality in discharging segments indicates that there may only be a certain voltage inconsistency, rather than a fault. And cells B and C always have no abnormality. After excluding cells B, C, and D, we can identify cell A as the faulty cell combined with its abnormal performance of editing distance.
(a) Charging.
(b) Discharging.
Fig. 3. Edit distances in charging and discharging segments.
4.2 Clustering with DBSCAN In this paper, the unsupervised DBSCAN [12] is employed to achieve automatic fault identification. As the core parameters in DBSCAN, Radius ε and Minimum number minPts need to be determined. The algorithm randomly selects a point and counts other points in the radius ε of this point. If the number is not less than the set minPts, the points within the radius belong to a cluster; if the number is less than minPts and the point is not within the radius of other points, the point is regarded as an outlier. After that, unsupervised clustering is achieved by traversing all target points. Figure 4 presents the clustering results during charging and discharging. Under parameter radius of 18 and minPts of 1, we can know from Fig. 4(a) and (c) that the DBSCAN algorithm identifies anomalies (red points) in the 9th charging segment, the 9th discharging segment and the 10th charging segment. Although it is later than the 8th charging segment analyzed above, the results are acceptable considering the accuracy and false alarm rate. And in Fig. 4(b) and (d), the number of clustering is 1 until the
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9th charging segment, indicating that no false positive occurs. After the 9th charging segment, the cells are classified as 2 clusterings (fault and normal), indicating that no false negative occurs. So far, based on the DBSCAN algorithm, this paper has identified the abnormality of cell A in the 9th charging segment at the earliest and realized the early warning of thermal runaway 10 days in advance.
(a) Clustering results in charging segments. (b) Number of clustering in charging segments.
(c) Clustering results in discharging segments. (d) Number of clustering in discharging segments.
Fig. 4. Clustering results in charging and discharging segments.
4.3 Comparison The edit distance is compared with the voltage mean-normalization (MN) [13], to describe the superiority of the proposed feature and the innovation of this paper. And Fig. 5 presents the results of MN. The MN can only detect the deviation of cell A at the approximate sampling moment 11000 (in the 10th charging segment), while there is no obvious abnormality in the previous moments. It is only 6 h ahead of the thermal runaway, which is too short to achieve an effective warning. In contrast, the edit distance can achieve the fault warning 10 days in advance of thermal runaway, which is significantly more effective than MN.
5 Conclusion This article presents a fault diagnosis method based on VMD and edit distance combined with an actual battery thermal runaway case. The main work is shown below.
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Fig. 5. Results of MN
(1) The voltages of all cells during discharging are decomposed by VMD to obtain the static components. Then the edit distances between cells are extracted from the charging curves and discharging static components in certain voltage intervals. Finally, the unsupervised DBSCAN algorithm is employed to realize the automatic identification of faulty cell 10 days ahead of thermal runaway. (2) The edit distance is compared with MN and its superiority is verified. This paper further complements the feature parameter system of battery safety. And the proposed method can achieve battery fault warning with high accuracy and long warning time, which has a certain application value. In the future, more thermal runaway battery data will be considered for verification. Acknowledgments. This work is supported by science and technology project of State Grid Corporation of China (5400-202111166A-0-0-00).
References 1. Hu, X., Zhang, K., Liu, K., Lin, X., Dey, S., Onori, S.: Advanced fault diagnosis for lithiumion battery systems: a review of fault mechanisms, fault features, and diagnosis procedures. IEEE Ind. Electron. Mag. 14(3), 65–91 (2020) 2. Zheng, Y., Luo, Q., Cui, Y., Dai, H., Han, X., Feng, X.: Fault identification and quantitative diagnosis method for series-connected lithium-ion battery packs based on capacity estimation. IEEE Trans. Ind. Electron. 69(3), 3059–3067 (2022) 3. Xiong, R., Sun, W., Yu, Q., Sun, F.: Research progress, challenges, and prospects of fault diagnosis on battery system of electric vehicles. Appl. Energy 279, 115855 (2020) 4. Xiong, R., Yang, R., Chen, Z., Shen, W., Sun, F.: Online fault diagnosis of external short circuit for lithium-ion battery pack. IEEE Trans. Ind. Electron. 67, 1081–1091 (2020) 5. Rezvanizaniani, S., Liu, Z., Chen, Y., Lee, J.: Review and recent advances in battery health monitoring and prognostics technologies for electric vehicle (EV) safety and mobility. J. Power Sources 256, 110–124 (2014) 6. Hu, J., He, H., Wei, Z., Li, Y.: Disturbance-immune and aging-robust internal short circuit diagnostic for lithium-ion battery. IEEE Trans. Ind. Electron. 69(2), 1988–1999 (2022) 7. Jiang, L., Deng, Z., Tang, X., Hu, L., Lin, X., Hu, X.: Data-driven fault diagnosis and thermal runaway warning for battery packs using real-world vehicle data. Energy 234, 121266 (2021) 8. Tan, F.: Fault diagnosis and implementation of electric vehicle lithium-ion battery system. Beijing Institute of Technology (2015) (in Chinese)
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9. Dragomiretskiy, K., Zosso, D.: Variational mode decomposition. IEEE Trans. Signal Process. 62(3), 531–544 (2014) 10. Jiang, J., Cong, X., Li, S., Zhang, C., Zhang, W., Zhang, L.: A hybrid signal-based fault diagnosis method for lithium-ion batteries in electric vehicles. IEEE Access 9, 19175–19186 (2021) 11. Biswas, S.K., Milanfar, P.: One shot detection with Laplacian object and fast matrix cosine similarity. IEEE Trans. Pattern Anal. Mach. Intell. 38(3), 546–562 (2016) 12. Bryant, A., Cios, K.: RNN-DBSCAN: a density-based clustering algorithm using reverse nearest neighbor density estimates. IEEE Trans. Knowl. Data Eng. 30(6), 1109–1121 (2017) 13. Qiao, D., et al.: Toward safe carbon–neutral transportation: battery internal short circuit diagnosis based on cloud data for electric vehicles. Appl. Energy 317, 119168 (2022)
Joint Estimation of State-of-Charge and State-of-Health for Lithium-Ion Batteries Based on OLS-UKF Algorithm Xin Lai(B) , Ming Yuan, Jiahui Weng, Yi Yao, and Yuejiu Zheng School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China {laixin,yuejiu.zheng}@usst.edu.cn, [email protected], [email protected], [email protected]
Abstract. Aiming at the problem that the change of capacity during the aging process of lithium-ion batteries affect the accurate estimation of state-of-charge (SOC) and state-of-health (SOH), this paper proposes a joint estimation method combines Ordinary Least Squares (OLS) and Unscented Kalman Filter (UKF) algorithm. First, OLS algorithm is used to estimate SOH online to improve the prior accuracy of SOC. Then, the SOC is estimated by UKF algorithm. The experimental results indicate that the joint SOC-SOH algorithm can realize the accurate estimation of SOC and SOH during battery aging. The SOH estimation error is within 1.5%, and the SOC estimation error is within 2%. Keywords: Lithium-ion batteries · Joint estimation · Ordinary Least Squares · Unscented Kalman Filter
1 Introduction In the face of increasingly serious energy and environmental problems, electric vehicles (EVs) have been developing rapidly in the world due to their environmentally friendly advantages [1, 2]. As the only power source of EVs, lithium-ion batteries (LIBs) have significant strengths such as high energy density and low self-discharge rate [3]. State estimation is one of the most critical functions of battery management system (BMS). Accurate SOC and SOH estimation can monitor the health status of batteries, effectively estimate the vehicle mileage, improve the safety and service performance of LIBs [4]. The accuracy of SOC estimation is affected by capacity and temperature. Therefore, it is an effective technical scheme to estimate SOH and SOC considering temperature. Common methods of SOC estimation include the current integration method, opencircuit voltage (OCV) method, data-driven method, and model-based method [5]. Ampere hour integral method has been widely used in practical engineering because of its simple calculation. Still, it cannot solve the cumulative error caused by initial SOC and current and voltage measurement errors. The simple OCV method requires long-time standing of LIBs to ensure that LIBs reach a stable state, which is challenging © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, pp. 1314–1320, 2023. https://doi.org/10.1007/978-981-99-1027-4_137
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to realize SOC estimation online. The method of real-time estimation of OCV based on the voltage model [6] and then obtaining SOC estimation value is easy to complete, but current noise, voltage noise, and model error have impact on OCV estimation, so the accuracy is not high. The data-driven methods, such as neural networks (NN) [7], are suitable for all types of LIBs with self-learning functions. However, it requires a lot of training data to ensure estimation accuracy. The method based on the electrochemical model [8] contains rich internal information on LIBs, but it is challenging to be used for online application. The method based on the equivalent circuit model (ECM) [9] is to estimate SOC and then use the filtering algorithm to provide feedback and correct the SOC estimation according to battery model. Common filtering algorithms include Extended Kalman Filter (EKF) algorithm [10] and Unscented Kalman Filter (UKF) algorithm [11, 12]. SOC and SOH estimation will affect each other, and the change of SOH will cause SOC estimation error. In recent years, joint SOC-SOH estimation frameworks have been proposed. Shen et al. [13] used the RLS algorithm with a forgetting factor to identify battery parameters online, then the SOH was estimated according to the identified parameters. In this work, a joint estimation method that combines Ordinary Least Squares (OLS) algorithm and UKF algorithm is proposed. In this method, the current SOH is calculated by OLS algorithm. Based on model parameters and current capacity, the SOC is estimated by UKF algorithm. Finally, the aging experiment is designed to verify the effectiveness of our proposed method.
2 Joint SOC-SOH Estimation 2.1 SOH Estimation With the aging of LIBs, the capacity will gradually decline. As an essential parameter in the prior estimation of SOC, the update of capacity is the basis of accurate SOC estimation. At present, “Two-Point” [14] is the most used method in SOH estimation. The calculation formula of this method is as follows: t2 ηI (t) t1 3600 dt (1) Cap = SOC(t2 ) − SOC(t1 ) where SOC(t1 ) and SOC(t2 ) are the SOC value at two points of time, t1 and t2 , respectively, and η is coulomb efficiency, which is usually taken as 1. Due to the significant error of the “Two-Point” method, the OLS algorithm [15] is used to estimate the capacity. Equation (1) can be re-written as follows: 1 SOC(t2 ) − SOC(t1 ) = Cap
t2
ηI (t) dt 3600
(2)
t1
Marking xi =
t2
ηI (t) t1 3600 dt,
and yi = SOC(t2 ) − SOC(t1 ), we can obtain Eq. (3): yi = β1 + β2 xi + vi
(3)
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where β1 , β2 and vi are estimated constant, estimated coefficient and noise. Vector form and matrix form are as follows: ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ 1 x11 v1 y1 ⎢ y2 ⎥ ⎢ 1 x21 ⎥ ⎢ v2 ⎥ ⎥ β1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎢ .. ⎥ ⎢ .. .. ⎥ β + ⎢ .. ⎥ ⎣ .⎦ ⎣ . ⎦ ⎣. . ⎦ 2 1 xn1
yn
(4)
vn
Y =X ·H +V
(5)
H can be calculated by OLS algorithm: H = (X T X )−1 X T Y
(6)
CapOLS = 1/H (2)
(7)
SOH =
CapOLS Cap0
(8)
where Cap0 is the capacity of the fresh battery. 2.2 SOC Estimation UKF algorithm [12, 16, 17] uses the idea of probability distribution to deal with nonlinear systems. When estimating SOC based on UKF algorithm, SOC is the state vector, and voltage is the observed value. The discrete equation of SOC estimated by the current integration method is written as Eq. (9), and the terminal voltage of the observed value is written as Eq. (10). The polarization voltage needs to be calculated by state transition iteration, and it is written as Eq. (11). ηIk + w1,k 3600CapOLS
(9)
Ut,k = OCV (SOCk ) − Ik R0 − U1,k + vk
(10)
SOCk+1 = SOCk +
U1,k+1 = U1,k exp(−
t t ) − R1 (1 − exp(− )) · Ik + w2,k τ1 τ1
(11)
State vectors xk , observation value yk , and system excitation uk are shown in Eqs. (12)–(14), respectively. With these definitions, Eqs. (12) and (14) can be re-written as Eq. (15).
SOCk xk = (12) U1,k yk = Ut,k
(13)
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uk = Ik
xk+1 = Axk + Buk + Q
η
(14) (15)
w1,k 1 0 3600·CapOLS . ,B= , and Q = t t 0 exp(− τ1 ) −R1 · (1 − exp(− τ1 )) w2,k The state equation and observation equation can be written in Eqs. (16) and (17):
with A =
xk+1 = f (xk , uk ) + wk
(16)
yk = g(xk , uk ) + vk
(17)
The iterative process is listed in Table 1.
3 Results In our work, aging experiments considering temperature are designed to verify the proposed method. To verify the effectiveness of OLS algorithm in SOH estimation, 15 groups of NEDC test data after each aging cycle are selected. The SOH estimation trajectories and their errors during battery aging are shown in Fig. 1. It can be observed from Fig. 1(b) that the SOH estimation error is less than 1.5%, showing high estimation accuracy. To verify the effectiveness, NEDC test data of two batteries which in the same batch after the first aging cycle is selected. SOC estimation results are shown in Fig. 2. To simulate the actual situation, initial error, current error and voltage error are set, which are 5%, ±0.01 and ±0.01, respectively. It can be intuitively seen that OLS-UKF algorithm has fast convergence speed. Before SOC reaches 95%, the error has converged to less than 2%. During the estimation, the error is kept within 2%. It can be concluded that the proposed scheme based on OLS-UKF algorithm can greatly improve the SOC estimation accuracy during battery aging.
4 Conclusions In the actual operation of EVs, battery aging is inevitable, affecting not only the performance of LIBs but also the accuracy of SOC estimation, making drivers misjudge the mileage. To reduce estimation error affected by the change of battery capacity caused by battery aging, a joint estimation method based on the OLS-UKF algorithm is proposed. Conclusions are drawn: (1) An online SOH estimation method based on OLS algorithm is proposed. The results indicate that the estimation error is within 1.5%, showing high estimation accuracy. (2) The OLS-UKF algorithm can improve the accuracy of SOC estimation. The experimental results indicate that OLS-UKF algorithm can maintain a faster convergence. The error is kept within 2% even if there are initial, current, and voltage measurement errors.
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(1) Initialization: P = 10−6 ∗
10
01
(2) Iterative calculation,k = 1, 2, 3, . . . , N : (a) State transition: (i),−
(i),−
= f (xk−1 , uk−1 ) + wk−1 (18)
xk
(b) The updated state vector xk− and error covariance matrix Pk− : 2n (i) (i),− ωm xk (19)
xk− =
i=0
Pk− =
2n (i) (i),− − (i),− T ωc [xk− − xk ][xk − xk ] + Q (20)
i=0
(c) Sigma points are brought into Eq. (16): (i)
(i),−
yk = g(xk
, uk ) + vk (21)
(d) The mean value of yk and error covariance Pyk yk ,Pxk yk are obtained. Here R is noise yk =
2n (i) (i) ωm yk (22)
i=0
Py k y k = Px k y k =
2n (i) (i) (i) ωc [yk − yk ][yk − yk ] + R (23)
i=0
2n (i) (i),− (i) ωc [xk − xk− ][yk − yk ] (24)
i=0
(e) Calculating the Kalman gain Kk : P (25) Kk = Py−1 k yk xk yk (f) Updating xk+ and Pk : xk+ = xk− + Kk (Ut,k − yk ) (26) Pk = Pk− − Kk Pyk yk KkT (27)
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(a)
98 96 94 92
0.5 0 -0.5 -1
90 88 1
(b)
1
Error/%
SOH/%
1.5
Reference OLS
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-1.5 1
15
5 9 11 13 15 3 7 Standard Capacity Tests/n
Fig. 1. SOH estimation. (a) Results; and (b) errors.
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1
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4
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Reference OLS-UKF
(c)
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(d)
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(a)
2 0
-2
1
2
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10
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Fig. 2. SOC estimation. (a) Result of battery 1; (b) error of battery 1; (c) result of battery 2; and (d) error of battery 2
Acknowledgments. This work is supported by the National Natural Science Foundation of China (Grant Nos. 51977131 and 51877138), the Natural Science Foundation of Shanghai (Grant No. 19ZR1435800), the State Key Laboratory of Automotive Safety and Energy under Project No. KF2020, and Shanghai Science and Technology Development Fund (Grant No. 19QA1406200).
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References 1. Lai, X., et al.: Critical review of life cycle assessment of lithium-ion batteries for electric vehicles: a lifespan perspective. eTransportation 12, 100169 (2022) 2. Lai, X., et al.: Co-estimation of state-of-charge and state-of-health for lithium-ion batteries considering temperature and ageing. Energies 15(19), 7416 (2022) 3. Zheng, Y.J., Lu, Y.F., Gao, W.K., Han, X.B., Feng, X.N., Ouyang, M.G.: Micro-short-circuit cell fault identification method for lithium-ion battery packs based on mutual information. IEEE Trans. Ind. Electron. 68(5), 4373–4381 (2021) (in English) 4. Hu, X.S., Feng, F., Liu, K.L., Zhang, L., Xie, J.L., Liu, B.: State estimation for advanced battery management: key challenges and future trends. Renew. Sustain. Energy Rev. 114(13), 109334 (2019) (in English) 5. Xiong, R., Cao, J.Y., Yu, Q.Q., He, H.W., Sun, F.C.: Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access 6, 1832–1843 (2018) (in English) 6. Wu, G., Lu, R., Zhu, C., Chan, C.C.: State of charge estimation for NiMH battery based on electromotive force method. In: 2008 IEEE Vehicle Power and Propulsion Conference (VPPC), p. 5 (2008) (in English) 7. Dang, X.J., Yan, L., Xu, K., Wu, X.R., Jiang, H., Sun, H.X.: Open-circuit voltage-based state of charge estimation of lithium-ion battery using dual neural network fusion battery model. Electrochim. Acta 188, 356–366 (2016) (in English) 8. Han, X.B., Ouyang, M.G., Lu, L.G., Li, J.Q., Zheng, Y.J., Li, Z.: A comparative study of commercial lithium ion battery cycle life in electrical vehicle: aging mechanism identification. J. Power Sources 251, 38–54 (2014) (in English) 9. Guo, X.W., Kang, L.Y., Yao, Y., Huang, Z.Z., Li, W.B.: Joint estimation of the electric vehicle power battery state of charge based on the least squares method and the Kalman filter algorithm. Energies 9(2), 16 (2016) (in English) 10. Plett, G.L.: Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs - part 3. State and parameter estimation. J. Power Sources 134(2), 277–292 (2004) (in English) 11. He, H.W., Xiong, R., Peng, J.K.: Real-time estimation of battery state-of-charge with unscented Kalman filter and RTOS mu COS-II platform. Appl. Energy 162, 1410–1418 (2016) (in English) 12. Meng, J.H., Luo, G.Z., Gao, F.: Lithium polymer battery state-of-charge estimation based on adaptive unscented Kalman filter and support vector machine. IEEE Trans. Power Electron. 31(3), 2226–2238 (2016) (in English) 13. Shen, P., Ouyang, M.G., Lu, L.G., Li, J.Q., Feng, X.N.: The co-estimation of state of charge, state of health, and state of function for lithium-ion batteries in electric vehicles. IEEE Trans. Veh. Technol. 67(1), 92–103 (2018) 14. Einhorn, M., Conte, F.V., Kral, C., Fleig, J.: A method for online capacity estimation of lithium ion battery cells using the state of charge and the transferred charge. IEEE Trans. Ind. Appl. 48(2), 736–741 (2012) (in English) 15. Jiang, Y., Jiang, J.C., Zhang, C.P., Zhang, W.G., Gao, Y., Li, N.: State of health estimation of second-life LiFePO4 batteries for energy storage applications. J. Clean. Prod. 205, 754–762 (2018) (in English) 16. Julier, S.J., Uhlmann, J.K.: Unscented filtering and nonlinear estimation. Proc. IEEE 92(3), 401–422 (2004) (in English) 17. He, W., Williard, N., Chen, C.C., Pecht, M.: State of charge estimation for Li-ion batteries using neural network modeling and unscented Kalman filter-based error cancellation. Int. J. Electr. Power Energy Syst. 62, 783–791 (2014) (in English)
Author Index
A Ai, Xuhua, 667
B Bai, Changshan, 1029 Bai, Miao, 1050 Bao, Lianwei, 1285 Bao, Zhengyi, 588 Bian, Xinran, 1296 Bi, Jiangang, 479
C Cai, Xue, 778, 1137 Cao, Kan, 786 Cao, Linfeng, 598 Cao, Maosen, 1200 Cao, Yuan, 720 Cao, Ziqing, 281 Chai, Yi, 107 Chang, Junhao, 420 Chang, Yongle, 833 Chaomurilige,, 310 Chen, Bin, 32 Chen, Bowen, 420 Chen, Fujia, 610 Cheng, Chunlei, 506 Cheng, Shuai, 547 Cheng, Xin, 79 Chen, Hong, 1076 Chen, Hu, 809 Chen, Huimin, 1305 Chen, Kui, 68, 448, 494, 1029 Chen, Lvquan, 833 Chen, Minghua, 1128 Chen, Qianyou, 1169 © Beijing Paike Culture Commu. Co., Ltd. 2023 F. Sun et al. (Eds.): ICEIV 2022, LNEE 1016, 2023. https://doi.org/10.1007/978-981-99-1027-4
Chen, Sheng, 536 Chen, Siqi, 1266 Chen, Xia, 1183 Chen, Xinying, 389 Chen, Yifeng, 459 Chen, Yu, 119 Chen, Yuanyuan, 361, 514 Chen, Yuxin, 926 Chen, Zhaoli, 667 Chen, Zheming, 1209 Chen, Zheng, 206, 1108, 1151, 1169 Chen, Zhuo, 361, 514 Chen, Zonghai, 1235
D Dai, Keren, 617 Daomin, Min, 1089 Deng, Haonan, 408 Ding, Haohui, 536 Dong, Huajun, 389 Dong, Jinting, 918 Dong, Qianyuan, 1117 Dong, Yun, 667 Duan, Xinyu, 262 Du, Shaohua, 1305 Du, Xuelong, 22 Du, Ying, 1224
F Fang, Rengcun, 579 Fang, Yu, 216 Fan, Libing, 127 Feixiang, Chen, 250 Feng, Fei, 107 Feng, Shuai, 809 1321
1322 Fu, Dehui, 479 Fu, Hao, 809 Fu, Jiacheng, 667 Fu, Lei, 857 Fu, Lijuan, 809
G Gao, Bingzhao, 1076 Gao, Chengzhi, 206 Gao, Furong, 1276 Gao, Guoqiang, 68, 448, 494, 1029 Gao, Jinghui, 161, 993 Gao, Mingyu, 588 Gao, Shengpu, 644 Gao, Tieyu, 809 Geng, Qiao, 310 Ge, Zhengzheng, 536 Gong, Jiayuan, 1296 Gong, Peng, 381 Gong, Xinle, 1059 Gong, Yanpeng, 479 Gong, Zhaofeng, 289 Guofu, Sun, 975
H Haitao, Liu, 350 Hanan, Abdul Hadi, 32 Han, Kai, 865, 967 Han, Wei, 119 Han, Xuebing, 1266 Haomiao, Xin, 975 He, Hongwen, 152 He, Kai, 186, 1160 He, Ting, 696 Hongkun, Ma, 310 Hou, Hui, 579 Hou, Lintao, 778 Hou, Linzi, 1002 Hou, Tingting, 579 Hou, Yanjiao, 361 Huang, Chaochan, 737 Huang, Feng, 635 Huang, Guosheng, 635 Huang, Haihong, 558 Huang, Meng, 984 Huang, Shengxu, 1217 Huang, Xiaochuan, 119 Huang, Yukun, 1174 Huashen, Guan, 975 Hu, Bo, 79, 1200 Hu, Changyi, 373
Author Index Huo, Yongchen, 506 Hu, Qinran, 536 Hu, Sile, 598 Hu, Xiaorui, 171, 381, 802, 1249 Hu, Xinzhu, 873 Hu, Yixin, 857 Hu, Zezhou, 242
J Jackson, Lisa, 186 Jia, Hongjie, 770 Jia, Li, 262 Jiang, Jinpeng, 479 Jiang, Xin, 52, 1067 Jiang, Xiuchen, 1224 Jiang, Yihan, 802 Jia, Yuqiao, 730 Jilei, Ye, 250 Jin, Chu, 566 Jing, Haoran, 745 Jin, Yang, 52, 487 Jin, Yu, 770 Jin, Yuan, 1305 Ji, Zhenya, 262 Junjie, LiGao, 300 Ju, Yuyan, 216
K Kang, Jingyue, 225 Kang, Kai, 547, 1040 Ke, Chang, 865 Ke, Song, 300 Kong, Shengli, 119 Ku, Zhaoyu, 389
L Lai, Chenguang, 809 Lai, Xin, 1276, 1314 Lei, Mingyu, 361 Lei, Zhenzhen, 1169 Lian, Gaoqi, 61 Liang, Sheng, 1059 Liang, Yiheng, 536 Liang, Zeyu, 536 Liao, Jiaxin, 881 Liao, Qiang, 68 Liao, Shuangle, 547 Li, Dahu, 786 Li, Danyang, 289 Li, Dongying, 959 Li, Hailong, 1
Author Index Li, Jia, 745 Li, Jiajie, 1174 Li, Jianlin, 225 Li, Jinfu, 778 Li, Jinzhong, 234 Li, Jun, 32 Li, Junqiu, 1256 Li, Liyi, 1040 Li, Mao, 471 Li, Meng, 435 Li, Menglin, 152 Li, Na, 262, 547 Lin, Cheng, 824, 1059 Lin, Chengrong, 79 Lin, Fei, 10 Ling, Jiang, 350 Lingyu, Yang, 1089 Lin, Huipin, 588 Lin, Ni, 1217 Lin, Yujun, 1183 Li, Pengfei, 678 Li, Qi, 194 Li, Qinghao, 161 Li, Shuowei, 1305 Li, Siqi, 178 Liu, Baolei, 707 Liu, Candong, 435 Liu, Fang, 627, 688 Liu, Fen, 92 Liu, Guangjun, 547 Liu, Haitao, 225 Liu, Haoran, 152 Liu, Jialin, 1014 Liu, Jilin, 272 Liu, Kai, 68, 448, 494, 1029 Liu, Qishan, 178 Liu, Shengchun, 1 Liu, Shifei, 330 Liu, Shuangping, 1076 Liu, Tong, 1050 Liu, Yadong, 1224 Liu, Yanchao, 778 Liu, Yanli, 100 Liu, Yi, 984 Liu, Yongang, 1108, 1151 Liu, Yongbin, 993 Liu, Yonggang, 206, 1169 Liu, Zhengwei, 993 Liu, Zhongyong, 186, 1160 Li, Weizhan, 79 Li, Xianglong, 1305 Li, Xianning, 1076 Li, Xiaolong, 865, 967
1323 Li, Xiaoyu, 850, 1117 Li, Xuejin, 408 Li, Xueqiang, 1 Li, Yalun, 1266 Li, Yan, 61, 688 Li, Yaxin, 225 Li, Ying, 659 Li, Yu, 1128 Li, Yuanfeng, 754 Li, Zheng, 730 Long, Shengwen, 1209 Lu, Jin, 310 Lu, Jintao, 140 Lu, Languang, 1266 Lu, Mengting, 935 Luo, Shuxin, 566 Lu, Runge, 737 Lu, Shouxiang, 186 Lu, Sizhao, 178 Lu, Xiaotian, 833 Lu, Xingrui, 389 Lu, Yanbing, 92 Lv, Bao, 865, 967 Lv, Qiang, 140 Lv, Tingting, 1076 Lyu, Chao, 1050 Lyu, Nawei, 487 Lyu, Peiyuan, 1059
M Ma, Chuangming, 558 Ma, Kai, 688 Ma, Lijun, 696 Ma, Mingyu, 300 Ma, Shichang, 340, 471 Ma, Shiqian, 770 Ma, Simin, 340 Ma, Wensai, 206 Man, Jingbin, 610 Mao, Lei, 186, 234, 1160 Ma, Xingyuan, 289 Mei, Bing-Ang, 272 Meng, Jinhao, 107 Meng, Qi, 667 Min, Jiabao, 52, 1067 Mu, Yunfei, 770
N Na, Xiaoxiang, 1076 Nie, Zipan, 320 Ni, Yulong, 44
1324 O Ouyang, Minggao, 1266
P Pan, Chaochong, 547 Pang, Fangyuan, 408 Pan, Qifeng, 610 Pei, Haijuan, 1023
Q Qi, Haojin, 194 Qi, Nanjian, 617 Qingzhou, Wu, 1089 Qin, Ruyi, 194, 696 Qin, Yu, 398 Qin, Yue, 408 Qi, Taoyi, 1285 Qi, Teli, 330 Qiu, Qingquan, 320 Qiu, Qunxian, 678
R Ran, Anjie, 10 Rao, Zhuyi, 659 Ren, Chunguang, 408 Ren, Wenbo, 1296 Ren, Zewen, 127 Rui, Fu, 350
S Sha, Donglei, 10 Shan, Zhilin, 459 Shao, Changzheng, 79, 1200 Shao, Jinyuan, 1249 Shaorui, Qin, 1089 Sheng, Zhou, 250 Shen, Jiangwei, 206, 1108, 1151 Shen, Jinpeng, 300 Shenlong, Zhu, 1089 Shen, Yongpeng, 754 Shi, Jianbo, 1 Shi, Nian, 547 Shiye, Yan, 250 Shu, Xing, 1108, 1151 Song, Jie, 809 Song, Kai, 44 Song, Kaiyang, 598 Song, Yuhang, 52, 1067 Sun, Bingxiang, 340, 471 Sun, Kaibin, 79
Author Index Sun, Songnan, 754 Sun, Yichao, 281 Sun, Ying, 598 Sun, Yue, 79 Sun, Yuning, 186 Su, Weixing, 627 Su, Xiaojia, 340, 471 T Tang, Aihua, 171, 381, 762, 802, 1174, 1209, 1249 Tang, Jinrui, 579, 833 Tang, Sai, 688 Tang, Xiaopeng, 1276 Tan, Keliang, 635 Tao, Sihan, 881 Tian, Jindong, 850, 1117 Tian, Peigen, 720 Tian, Shiming, 140 Tian, Yong, 850, 1117 Tian, Yu, 420 Tu, Lingying, 398 W Wang, Bo, 745 Wang, Bowen, 1059 Wang, Chengyou, 435 Wang, Chun, 857 Wang, Dajiang, 730 Wang, Guangzhen, 479 Wang, Haifeng, 906 Wang, Haixin, 558 Wang, Hewu, 1266 Wang, Hongli, 300 Wang, Hu, 234 Wang, Jianfeng, 92 Wang, Jiasong, 525 Wang, Jiayi, 881 Wang, Jihua, 194 Wang, Jing, 1285 Wang, Junyi, 100 Wang, Li, 873, 890, 898, 918, 926, 959, 1224 Wang, Mingyi, 1040 Wang, Qiao, 61 Wang, Shaokun, 32 Wang, Shishun, 178 Wang, Shunli, 107 Wang, Shuping, 459 Wang, Wei, 262 Wang, Weichen, 1256 Wang, Weida, 22
Author Index Wang, Xiaofei, 216 Wang, Xiaofeng, 617 Wang, Xuanyu, 865, 967 Wang, Yabo, 1 Wang, Yang, 161 Wang, Yibo, 361, 514 Wang, Yifan, 408 Wang, Yilin, 1191 Wang, Yuan, 598 Wang, Yujie, 1235 Wang, Ze, 617 Wang, Zecheng, 890, 898 Wang, Zengqing, 906 Wang, Zhihua, 579 Wang, Zhiming, 1 Wei, Meng, 61 Weiyu, Deng, 310 Wei, Zhichuan, 32 Weng, Jiahui, 1314 Wen, Jinyu, 566, 745, 786, 1183 Wu, Bingbing, 1002 Wu, Guangning, 68, 448, 494, 1029 Wu, Ji, 1224 Wu, Xiaobo, 10 Wu, Xinyu, 1209 Wu, Yan, 720 Wu, Yitao, 1169 Wu, Yonghua, 1256
X Xia, Jilu, 330 Xiao, Qian, 770 Xiao, Xi, 720 Xiaoxia, Chen, 250 Xiao, Xun, 946 Xia, Wei, 707 Xia, Yufeng, 547 Xie, Changjun, 579 Xie, Hong, 1285 Xie, Hongbing, 127 Xie, Jiale, 107 Xie, Jingying, 1023 Xie, Junchao, 754 Xie, Kaigui, 79, 1200 Xie, Wenzhuo, 737 Xie, Xianfei, 525 Xie, Yuexi, 873 Xie, Yuguang, 234 Xie, Zhengyu, 881, 906, 935, 946 Xu, Guo, 250 Xu, Hongyang, 152 Xu, Huan, 841
1325 Xu, Jianhua, 610 Xu, Jianing, 44 Xu, Jinli, 707 Xu, Menglong, 32 Xu, Qiushi, 745 Xu, Ruilong, 1235 Xu, Tao, 737 Xu, Tingting, 171, 381, 802, 1249 Xu, Yuan, 479 Xu, Yuhang, 890, 898 Xu, Zhihong, 373
Y Yanan, Duan, 1089 Yang, Aoling, 420 Yang, Chao, 22 Yang, Deng, 250 Yang, Duo, 1224 Yang, Hongqing, 1305 Yang, Jiaqiang, 598 Yang, Jun, 300 Yang, Kai, 281 Yang, Lin, 762 Yang, Liuquan, 22 Yang, Qiufan, 1183 Yang, Shaobing, 514 Yang, Weijing, 1023 Yang, Weiwei, 1191 Yang, Wenyao, 506 Yang, Xusheng, 547 Yang, Yajie, 610 Yang, Yan, 68, 566, 1029 Yang, Yang, 627 Yang, Yanju, 506 Yang, Yueping, 194, 696 Yang, Zhile, 841 Yang, Zhongping, 10 Yan, Mei, 152 Yan, Xuexiang, 635 Yan, Zhengfeng, 1002 Yao, Jianqi, 696 Yao, Wei, 745, 786 Yao, Yi, 1314 Ye, Chuangxin, 1023 Ye, Hu, 610 Ye, Min, 61 Ye, Xiaming, 194, 696 Ye, Xin, 140 Ying, Fangyi, 194, 696 Yin, Hongpeng, 107 Yin, Yuan, 667 You, Zheng, 617
1326 Yuan, Ming, 1276, 1314 Yuan, Shuai, 479 Yue, Hanqi, 1076 Yu, Haiyue, 1285 Yu, Haolin, 770 Yu, Jiajie, 194, 696 Yu, Jianshun, 127 Yu, Kexun, 525 Yulong, Ding, 310 Yu, Lu, 720 Yu, Ming, 786 Yu, Quanqing, 1014, 1209 Yusheng, Bao, 250 Yu, Shengjia, 881 Yu, Xiao, 824 Yu, Xintong, 850 Yu, Zhongan, 242 Z Zeng, Chong, 506 Zeng, Junxiong, 809 Zeng, Tao, 762 Zhai, Kefan, 1137 Zhang, Bo, 1002 Zhang, Caiping, 778, 1137, 1305 Zhang, Changkun, 373 Zhang, Chengming, 1040 Zhang, Gang, 289 Zhang, He, 44, 617 Zhang, Heng, 1160 Zhang, Jiande, 330 Zhang, Jiawei, 1128 Zhang, Jinghan, 1217 Zhang, Junling, 242 Zhang, Junzhi, 824 Zhang, Li, 216 Zhang, Linjing, 1137 Zhang, Nianbo, 1128 Zhang, Qian, 1305 Zhang, Qiankai, 161 Zhang, Qixing, 459 Zhang, Shengming, 506 Zhang, Shuo, 635 Zhang, Weige, 1137 Zhang, Wenfei, 487 Zhang, Wentao, 272 Zhang, Xixiang, 667 Zhang, Yixing, 107 Zhang, Yongmin, 459 Zhang, Yu, 506
Author Index Zhang, Yuan, 471 Zhang, Yunxiang, 644, 652 Zhang, Zhaosheng, 1217 Zhang, Zhihang, 1266 Zhang, Zhiyong, 140 Zhang, Zicheng, 330 Zhan, Sha, 171 Zhao, Bingquan, 22 Zhao, Guangjin, 119 Zhao, Hongqian, 1108, 1151 Zhao, Hongsheng, 745 Zhao, Jingbo, 730 Zhao, Manqing, 161 Zhao, Mingjie, 824 Zhao, Yifan, 786 Zhao, Yong, 361, 514 Zhao, Yongming, 320 Zhao, Yuchan, 598 Zhao, Yuetao, 610 Zhao, Yuming, 1285 Zhao, Zhichao, 140 Zha, Xiaoming, 984 Zheng, Shanpi, 850 Zheng, Yuejiu, 1314 Zheng, Yun, 652 Zhong, Lisheng, 993 Zhou, Ande, 127 Zhou, Bangyu, 841 Zhou, Bowen, 420 Zhou, Jianyu, 1183 Zhou, Jun, 161 Zhou, Luoyan, 873 Zhou, Shuyuan, 448 Zhou, Xingzhen, 340 Zhou, Yuanqiang, 1276 Zhou, Yujiu, 610 Zhou, Zhuobei, 737 Zhu, Chunbo, 44 Zhu, Chunxiang, 588 Zhu, Jiamin, 494 Zhu, Jiang, 310 Zhu, Mingshuo, 984 Zhu, Pengyu, 1014 Zhu, Qingdong, 161 Zhu, Xiaoning, 918, 926 Zhu, Xinyao, 730 Zibo, Huang, 310 Ziwei, Gao, 1089 Zou, Manni, 1209 Zuo, Zhengmin, 566