The proceedings of the 16th Annual Conference of China Electrotechnical Society: Volume II (Lecture Notes in Electrical Engineering, 890) 9811918694, 9789811918698
122 17 161MB
English Pages [1396]
Contents
Coupling Analysis of Transient Electromagnetic Field and Temperature Field in Electromagnetic Launch Rail
1 Introduction
2 Theoretical Analysis of Electrothermal Coupling of Railgun
2.1 Electrothermal Coupling Equation
2.2 Source of Thermal Load
3 Simulation Model and Parameters
3.1 Simulation Model
3.2 Relevant Material Parameters and Inputs
4 Temperature Distribution Under Different Driving Currents
4.1 Simulation Results of X-Y Section
4.2 Simulation Results of Y-Z Section
5 Rail Temperature Change During Continuous Launch
6 Conclusion
References
Theoretical Attempts to Optimize the Geometrical Shape of Simple Electromagnetic Rail Launcher
1 Introduction
2 Inductance Gradient Theory
2.1 High-Frequency Inductance Gradient
2.2 Low-Frequency Inductance Gradient
2.3 Influence of the Tail Section Size on Inductance Gradient
2.4 Influence of Separation on Inductance Gradient
3 Mathematical Model of Launch Load
3.1 Mathematical Model of Forcing on the Launch Load
3.2 Mathematical Model of Launch Load Mass
4 Discussion on the Optimal Separation
4.1 The Optimal Separation at High-Frequency
4.2 The Optimal Separation at Low-Frequency
5 Conclusions
References
Force Analysis of Armature in Induction Coil Launcher and Design of Double-Layer Armature
1 Introduction
2 Basic Principle
3 Finite Element Model
3.1 Field-Circuit Coupling Analysis Model
3.2 Coupled Analysis of Electromagnetic and Structural Field
4 Armature Design of Different Materials
5 Design and Force Analysis of Double-Layer Armature
5.1 Double-Layer Armature Model
5.2 Double-Layer Armature Design
5.3 Optimization of Double-Layer Armature Thickness
6 Conclusion
References
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil Launcher
1 Introduction
2 The Working Principle and Mathematical Model of MECL
3 Fast Modeling Program Design for MECL System
3.1 Finite Element Simulation of Field-Path Coupling in MECL System
3.2 MECL System Parametric Programming Based on MATLAB
4 Simulation Research and Verification of Ten Stage Electromagnetic Coil Launcher System Model
5 Conclusion
References
The Application of Electromagnetic Coil Launching Technology in Non-war Military Operations AC Machines
1 Principle and Classification of Electromagnetic Coil Launching Technology
1.1 Induction Coil Launching Technology
1.2 Reluctance Coil Launching Technology
2 Key Technology of Electromagnetic Coil Launch
2.1 Launcher Design Technology
2.2 Pulse Power Technology
2.3 Launch Control Technology
2.4 High-Strength Insulation Material Technology
3 Application Field of Electromagnetic Coil Launching Technology in Non-war Military Operations
3.1 Application of Electromagnetic Coil Launching Technology in the Field of Non-lethal Weapons
3.2 Application of Electromagnetic Coil Launching Technology in the Field of Refusal to Riot
3.3 Application of Electromagnetic Coil Launching Technology in the Field of Emergency Rescue
4 Conclusion
References
Research on Parameters Optimum Design of Levitation Electromagnet Based on Orthogonal Design for EMS Maglev Train
1 Introduction
2 Numerical Model
3 Simulation Results
4 Optimization Design of Levitation System
5 Conclusions
References
Research on the Formation of Erosion in Electromagnetic Launch
1 Introduction
2 Research Object
3 Simulation
3.1 Distribution of the Armature-rail Contact Pressure Under Preload
3.2 Distribution of the Current at the Beginning of the Launch
4 Experiment
4.1 High Temperature Friction Experiment
4.2 Microstructure Analysis
4.3 Micro-hardness Test
5 Conclusion
References
Circuit Analysis of Commutation Process of Saddle Secondary Helical Coil Electromagnetic Launcher
1 Introduction
2 Analyze and Simplify the Brush Commutation Process
3 Commutation Process Analysis
3.1 Section D′B: Before Rear Commutation Process Begin
3.2 Section BE′:Rear Commutation Process Begin
3.3 Section E′C: Front Commutation Process Begin
3.4 Section CF′:Rear Commutation Process End
3.5 Section F′B′:Front Commutation Process End
3.6 Result Analysis
4 Experimental Result
5 Conclusion
Appendix
References
Research on Performance Influence of External Circuit Resistance in Synchronize Induction Coil Catapult
1 Introduction
2 System Working Principle
2.1 Working Principle
2.2 Circuit Equation
2.3 Computing Efficiency
3 Simulation Analysis
3.1 Effect of Equivalent Resistance of Discharge Circuit on Emission Performance
3.2 Effect of Equivalent Resistance of Continuous Circuit on Emission Performance
4 Experimental Verification
5 Conclusion
References
Influence of Copper Wire Sectional Shape on Induction-Coil Catapult Performance
1 Introduction
2 The Design of the Copper Wire of the Driving Coil
2.1 Shape and Size Design of Copper Wire
2.2 Copper Wire Resistance Calculation
3 Simulation Calculation of Copper Wire Windings with Different Cross-Sections
3.1 Calculation Model and Parameters
3.2 Simulation Results
4 Electromagnetic Ejection Test and Finite Element Simulation Verification
5 Conclusion
References
Effect of Temperature on the Performance of Induction Coil Launcher
1 Introduction
2 Model and Parameters of Single-Stage Induction Coil Launcher
3 Comparison Between Finite Element and Circuit Model Method
4 Influence of Temperature on Launch Characteristics of Coil
4.1 Coil Heat Dissipation Analysis
4.2 Coil Stress Comparison Analysis
5 Conclusion
References
Research of Mechanical Sensitive Factors of a Electromagnetic Rail Gun Cradle
1 Introduction
2 Mechanical Simulation Model of Electromagnetic Rail Gun Cradle
3 Simulating Calculation
3.1 Changes to the Length Calculation Analysis of the Gun Breech Guide
3.2 Changes to the Analysis of the Calculation of the Material Thickness of the Neck Barrel
3.3 Changes to the Analysis of the Calculation of the Material Thickness of the Cradle Rib Plate
4 Interpretation of Result
5 Conclusion
References
Research on Nonlinear Servo Speed Identification Based on Two-Stage Electric Cylinder
1 Introduction
1.1 Modeling and Analysis of Vertical Erection Device
1.2 Kinematics Model of Vertical Erection Device
1.3 Basic Theory and Mathematical Model of PMSM
2 Control Strategy of Electric Cylinder Servo System
2.1 PI Control
2.2 Model Reference Adaptive Speed Identification Control
2.3 Definition of Sliding Mode Variable Structure Control
2.4 Rotation Speed Identification by Sliding Mode Observation Method
3 Simulation Results
3.1 Characteristic Simulation Under Step Speed and Load Disturbance
3.2 Simulation of the Motion Characteristics of the Electric Cylinder
3.3 Motion Characteristics Under Actual Working Conditions
4 Conclusion
References
The Continuous High Precision Measurement Technique of Bore Spacing About Rail-Gun
1 Introduction
2 The Principle of Bore Spacing Measurement
3 System Measurement Error Analysis
3.1 Error Analysis of Measurement Principle
3.2 Analysis of Errors Introduced by System Machining Precision
4 Systematic Error Measurement
5 Prototype Adaptability Verification
6 Engineering Measurement of Bore Spacing
7 Conclusion
References
Research on Armature Loading Control Accuracy Based on Cloud Model Algorithm
1 Introduction
2 Design of the System
3 Design of the Control System
3.1 Theory of Cloud Model
3.2 Control Strategy of the Cloud Model
3.3 The Propulsive Force Control System
3.4 Software Implementation
4 Experimental Results
5 Summary
References
Model Predictive Control for Electromagnetic Launcher of UAV
1 Introduction
2 Model Predictive Control Method for Electromagnetic Launcher of UAV
3 Simulation Analysis
4 Conclusion
References
Research on Control Strategy of the Electromagnetic Launch System for Fixed Wing UAV
1 Introduction
2 Key Control Technology of UAV Electromagnetic Boost Launch System
2.1 Mathematical Model of Linear Motor
2.2 Field-Oriented Control
3 100 kg UAV Electromagnetic Boost Launch System
4 Conclusion
References
Torque Ripple Suppression Strategy of High-Speed Square Wave Permanent Magnet Motor Based on Direct Torque Control
1 Introduction
2 High-Speed Square Wave PMSM Control System
2.1 Motor Mathematical Model
2.2 Motor DTC Block Diagram
3 Torque Ripple Suppression Strategy for High-Speed Square Wave PMSM
3.1 DTC Without Flux Hysteresis
3.2 Torque Ripple Suppression Strategy
4 Simulation
5 Conclusion
References
Distribution of Breakdown Positions in Conditioning Progress Between Plane-Plane Electrodes in Vacuum Under Lightning Impulse Voltage
1 Introduction
2 Experimental Setup
3 Experimental Results
4 Simulation
5 Discussion
6 Conclusion
References
Vulnerability Analysis of Distribution Network Considering the Uncertainty of Source and Load
1 Introduction
2 Analysis of Distribution Network Structure
2.1 Model of DG
2.2 Load Characteristics of Electric Vehicles
3 Distribution Network Node Vulnerability Assessment Index
3.1 Improved Nodal Degree
3.2 Improved Nodal Betweenness
3.3 Load Capacity Vulnerability Index of Distribution Network Nodes Based on FVSI
4 Analysis of Calculation Examples
4.1 Setting of Calculation Case
4.2 Simulation Results
5 Conclusion
References
A Novel Efficiency-Improved LLC-Buck Isolated Power Processing Circuit
1 Introduction
2 Comparison of BOOST-LLC and LLC-BUCK Topology
2.1 Boost Circuit Design
2.2 Buck Circuit Design
2.3 LLC Circuit Design
2.4 Efficiency Comparison Between Boost-LLC and LLC-Buck
3 Experimental Results
3.1 Steady State Waveform and Analysis
3.2 Dynamic Waveform and Analysis
4 Conclusion
References
Research on Component Parameter for a Dual-Motor Coaxial Propulsion System Used in an Electric Bus
1 Introduction
2 System Configuration and Modeling
3 Methodology
3.1 Analysis Process
3.2 Dynamic Programming
4 Results and Discussion
4.1 Economic Performance Analysis
4.2 Dynamic Performance Analysis
4.3 Feasible Region Analysis of Dual-Motor Power
5 Conclusion
References
Influence of Winding Placement on the Motor Copper Losses with High Frequency Power Supply
1 Introduction
2 Copper Losses
3 Finite-Element Modelling
3.1 Conductor Modeling
3.2 Simplified Rotor Model
3.3 One-Slot Model
3.4 Winding Placement
4 Simulation Results
5 Conclusion
References
The Effect of Temperature on the Distribution Characteristics of Spatial Electric Field in Oil of Oil-Pressboard Insulation Under Impulse Voltage
1 Introduction
2 Electric Field Measuring Platform
2.1 Measurement System Composition
2.2 Kerr Electro-optic Effect for Electric Field Measurement Under Impulse Voltage
2.3 Test Model and Applied Voltage
3 The Effect of Temperature
4 Conclusion
References
A MTPA Control Strategy for Permanent Magnet/Reluctance Hybrid Rotor Dual-Stator Motor
1 Introduction
2 MTPA Control Principle of PM/RHR-DSM
2.1 PM/RHR-DSM Modeling
2.2 MTPA Control System of PM/RHR-DSM
3 Simulation
4 Conclusion
References
Interaction Between Atmosphere Pressure Plasma Jet and Substrate with Micro-hole
1 Introduction
2 Model Description
3 Results and Discussion
3.1 Characteristics of Neutral Gas Flow
3.2 Characteristics of Plasma Discharge
4 Conclusions
References
Simulation and Experiment Analysis of Opening Characteristics for High-Current Fast Switch Based on Double-Acting Mechanism
1 Introduction
2 Working Principle
3 Multi-physical Field Simulation Analysis
3.1 Geometric Model
3.2 Simulation Mathematical Model
3.3 Dynamic Characteristics Simulation and Experimental Analysis
3.4 Parameter Simulation Analysis of Double-Spring Permanent Magnet Operation-Electromagnetic Repulsion Mechanism
4 Conclusion
References
Reduced-Order and Full-Order Models of the Active-Switched-Capacitor/Inductor Quasi Z-Source Converter in Discontinuous Conduction Mode
1 Introduction
2 Reduced-Order Averaged Models
3 Equivalent Circuit Model
4 Full-Order Averaged Models
5 Experimental Verification
5.1 Steady-State Experiments
5.2 Frequency Responses
6 Conclusion
References
Small-Signal Modeling and Analysis of the Active-Switched-Capacitor/Inductor Quasi Z-Source Converter Working in Continuous Conduction Mode
1 Introduction
2 DC Steady-Status and AC Small-Signal Equations
3 Equivalent Circuit Mode
4 Small-Signal Models Characteristic Analysis
4.1 Non-minimum Phase Behavior
4.2 Input and Output Impedance Characteristics Analysis
5 Experimental Verification
5.1 Steady-State Experiments
5.2 Frequency Responses
6 Conclusion
References
A Novel Deep Flux Weakening Control Strategy for IPMSM
1 Introduction
2 Operating Constraint of IPMSM
2.1 Mathematical Model and Working Constraints of PMSM
2.2 Working Characteristics and Analysis of the Out-of-Control Flux Weakening Areas
3 Proposed Flux Weakening Control Strategy
3.1 Approximation of the MTPV Curve
3.2 Design of the Deep Flux Weakening Control Strategy
3.3 Voltage Closed-Loop Feedback q-axis Current Incremental Method
4 Simulation Research
4.1 Speed Response
4.2 Current Trajectory
5 Conclusion
References
Research on Micro-grid Regulation Strategy Formulation Based on Semi-supervised Learning Neural Network Model
1 Introduction
2 Labelling Classification Algorithm for Microgrid Operating State Based on Semi-supervised Learning
2.1 Tri-training Network Model Construction
2.2 Structure of Classification Model Based on BP Neural Network
2.3 Microgrid Operating State Labeling Classification Algorithm Flow Based on Semi-supervised Learning
3 The Similarity Evaluation Index of the Running State
4 Discussion
4.1 Performance Testing of Similarity Matching Algorithm Model Based on Semi-supervised Learning
4.2 Analysis of Optimization Results and Numerical Examples
5 Conclusion
References
Day-Ahead PV and EVs Power Forecasting of Distribution Network Based on LSTM
1 Introduction
2 LSTM Prediction Method
2.1 Recurrent Neural Network (RNN)
2.2 LSTM Unit Structure
2.3 Forecasting Model Based on LSTM
3 Calculation Example Results
3.1 Data of EVs and PV
3.2 Day-Ahead EVs and PV Forecasting Based on LSTM
4 Conclusion
References
Study on the Effect of Thermal Degradation on the Morphology Characteristics of Composite Insulator Mandrel Under Vacuum Condition
1 Introduction
2 Thermal Degradation Test
2.1 Test Samples and Instruments
2.2 Test Process
3 Macroscopic Morphology Analysis
3.1 Surface Color Analysis
3.2 Section Crack Analysis
4 Microscopic Morphology Analysis
4.1 Two-Dimensional Micro-topography Analysis
4.2 Three-Dimensional Micro-topography Analysis
5 Conclusion
References
Research on Distributed Cross-Bay Busbar Protection Based on Ring Network
1 Introduction
2 Research Content
3 Setting Operation
4 Setting Area Operation
5 Switch Operation
6 Conclusion
References
A Refined Model of On-Board Electric Power System for Turboprop Regional Aircraft
1 Introduction
2 Modeling Method
2.1 System Architecture
2.2 System Modeling
3 Simulation Results
3.1 Normal Operation Scenario
3.2 Fault Reconstruction Scenarios
4 Conclusions
References
Study of Voltage and Current Inner Control of Voltage-Controlled Converters in High Permeability Environment
1 Introduction
2 Modeling of Voltage-Controlled Mode Converters
2.1 Basic Structure of Voltage-Controlled Mode Converters
2.2 Control Structure of Voltage-Controlled Mode Converters
2.3 Inner-Loop Modeling of Voltage-Controlled Mode Converters
3 Comparison of Characteristics of the Four Control Schemes
3.1 Comparison of Control Loop Gain
3.2 Comparison of Stability Margin Range
3.3 Comparison of Control Bandwidth
3.4 Comparison of Anti-disturbance Performance
4 Simulation and Experiment Results
4.1 Platform
4.2 Verification of the Effect of Regulators Gain on System Stability
4.3 Verification of Tracking Performance
4.4 Verification of Anti-disturbance Performance
5 Conclusion
References
Study on the Morphology Change of Acid-Resistant Core Rods of Composite Insulators Under Acid-Heat Condition
1 Introduction
2 Experimental Procedure
2.1 Test Specimen
2.2 Experiment Method
3 Topography Analysis Based on Direct Observation and SEM
3.1 Morphology Analysis of Acid Etching Core Rod
3.2 Analysis of Acid-Heat Deterioration Morphology
3.3 Morphology Analysis of Decay-Like Core Rod
4 Analysis of Three-Dimensional Microscopic Topography Based on CLSM
5 Conclusion
References
Research on Optimal Dispatching of Multi-region Integrated Energy System Considering Electric Load Price Based Demand Response
1 Introduction
2 Multi-region IES
3 Price-Based Demand Response Model
4 Optimal Dispatch of Multi-region IES Considering Demand Response
4.1 Objective Function
4.2 Constraints
4.3 Problem Solving Method
5 Case Analysis
5.1 Impact of Demand Response on Electrical Load
5.2 Optimal Dispatch of Multi-region IES Considering Electric Load Demand Response
6 Conclusions
References
A Deep Adversarial Diagnosis Method for Fault Line Detection with Imbalanced Small Sample Scenarios
1 Introduction
2 Fault Line Detection Method
2.1 Data Preprocess
2.2 Data Augmentation
2.3 Feature Extraction and Classification
2.4 Fault Line Detection Process
3 Algorithm Verification
3.1 Simulation Model and Parameters
3.2 Synthetic Signal Visualization
3.3 Adaptivity Analysis
4 Conclusion
References
Experimental Investigation on Magnetic Field Controlled One-Dimensional Plasma Jet Array in He
1 Background
2 Experimental Equipment and Measurement Method
2.1 Experimental Equipment
2.2 Measurement Method
3 Results and Discussion
3.1 Electrical Characterization
3.2 Optical Characterization
4 Conclusions
References
Inspection Text Classification of Power Equipment Based on TextCNN
1 Introduction
2 Classification Framework and Data Pre-processing
2.1 Characteristics of Inspection Text
2.2 Pre-processing Process
3 Model Building
3.1 Data Augmentation
3.2 Evaluation Metrics
4 Example Analysis
4.1 Comparison of Different Models
4.2 Effect of Data Augmentation
5 Conclusion
References
Research on Reactive Power Compensation Site Selection Method for Reducing Commutation Failure Risk of MIDC System
1 Introduction
2 Mechanism Analysis of Commutation Failure
3 Simulation Analysis of Henan Power Grid
4 Reactive Power Compensation Site Selection Optimization Method
4.1 Identify the Voltage Weakness Area of the Receiving Power Grid
4.2 Identify Reactive Power Compensation Sites
5 Simulation Verification
6 Conclusion
References
Intelligent Power Transmission and Transformation Technology for PIoT
1 Introduction
2 Overview of Smart Grid
3 PIoT Architecture
3.1 Sensing Layer
3.2 Network Layer
3.3 Platform Layer
3.4 Application Layer
4 PIoT Applications
4.1 Substation Applications
4.2 Transmission Line Applications
5 Development Trend of PIoT
6 Conclusion
References
Study on the Blocking Capability Decreasing of SiC MOSFET After Short-Circuit Gate-Source Failure
1 Introduction
2 Gate-Source Failure Determination Method
2.1 Mechanism of Gate-Source Short-Circuit
2.2 Determination Method of Gate-Source Failure
3 Short-Circuit Experiment
3.1 Short-Circuit Experimental Setup
3.2 Experimental Results
4 Leakage Current Analysis
4.1 Leakage Current Measurement
4.2 Mechanism Analysis of the Increase of Leakage Current
5 Conclusion
References
A Transmission Line Multi-parameter Monitoring System Based on FBG Sensors
1 Introduction
2 Principle and Sensor Design
2.1 Sensing Principle of FBG
2.2 Design of FBG Anemometer
2.3 Design of FBG Tension Sensor
3 Design of the Sensing System
3.1 Overall System Structure
4 Conclusion
References
Reconstruction of Open-Circuit Voltage for Aging Lithium-Ion Batteries Based on Big Data
1 Introduction
2 Data Acquisition
2.1 Aging Tests
2.2 OCV Data Cloud Generation
3 Proposed Method
4 Results and Discussions
5 Conclusion
References
A Switched-Capacitor-Based Multilevel Converter for Photovoltaic Systems Suffering from Power Mismatch
1 Introduction
2 Proposed Multilevel Converter
3 Operation Principle
3.1 The Principle of Voltage Self-balancing
3.2 Control Strategy
3.3 Modulation Strategy
4 Simulation Results
4.1 Case 1: A PV DC Port Interats with the Converter
4.2 Case 2: Two PV DC Ports Interact with the Converter
4.3 Case 3: Three PV DC Ports Interact with the Converter
4.4 Case 4: Four PV DC Ports Interact with the Converter
5 Conclusion
References
Difficulty Analysis and Test Method Research on Performance Test of Medium Voltage Photovoltaic Power Generation Unit
1 Introduction
2 Difficulties in Performance Test of MV-PGU
3 Research on Test Verification Method
4 Empirical Test Cases
5 Conclusion
References
Digital Twin System for Service Performance Evaluation of Anti-vibration Device
1 Introduction
2 Modeling of Digital Twin System
3 Experiment
4 Discussion
5 Conclusion
References
Research on Fiber Channel Message Recording Scheme Based on Data Statistics
1 Introduction
2 Current Status of Fiber Channel Applications
2.1 Fiber Channel Topology
2.2 Problems and Detection Methods During Operation
3 Key Technical Solutions
3.1 Message Collection Unit
3.2 Message Analysis Unit
3.3 Message Statistics Unit
3.4 Message Storage Unit
3.5 Hardware Implementation
4 Test Verification
5 Conclusion
References
Research on Control Strategy of Energy Storage System to Improve Wind Power Smoothing Ability
1 Preface
2 Wind Power Output Model
2.1 Wind Frequency Characteristics of Wind Power Plant
3 Energy Storage System Model
3.1 Structure of Wind Power Plant Energy Storage System
3.2 Energy Storage System Cost Model
3.3 Constraints of Energy Storage System
4 Optimization of Energy Storage System Configuration Based on Genetic Algorithm
4.1 Basic Principles of Genetic Algorithm
5 Control and Configuration of Energy Storage System Based on Two-Layer Model
5.1 Bilevel Optimization Model
5.2 Example Analysis
6 Conclusion
References
Analysis and Calculation of the Capacitor Current and Voltage Ripples for Z-Source Inverters
1 Introduction
2 ZSI Capacitor Current and RMS Value
3 Capacitor Voltage Ripple Calculation
4 Experimental Results
5 Conclusion
References
Feasibility Analysis of Using the Normal Vector to Determine the Most Dangerous Power Increasing Direction of the Small-Signal Stability
1 Introduction
2 Static Voltage Stability Analysis
2.1 Static Voltage Stability Analysis Method
2.2 Difficulties in Solving the MDPID of Small-Signal Stability
3 Boundary Conditions of Small-Signal Stability
3.1 The Mathematical Model of the Power System Small-Signal Stability
3.2 Boundary Conditions
4 Model of the Most Dangerous Power Increasing Direction of Small-Signal Stability
4.1 The Relationship Between the Normal Vector and the MDPID
4.2 Normal Vector Construction and Determination of the MDPID
4.3 The Most Dangerous Power Increasing Direction Model
4.4 Model Solution Analysis
5 Conclusion
References
Design of Main Wiring Diagram Drawing System of Relay Protection Device
1 Introduction
2 System Architecture
3 Module Design
3.1 System Protocol Module
3.2 System Protocol Module
3.3 Main Wiring Diagram Drawing Module
4 System Application
5 Conclusion
References
Monitoring and Management Technical Research for Battery Energy Storage
1 Introduction
2 System Architecture
3 Module Design
3.1 BIMU
3.2 BCMU
3.3 BMU
3.4 External Communication Unit
4 System Application
5 Conclusion
References
Analysis of Lightning Impulse Response of Ground Network Based on a Distributed π Model
1 Introduction
2 Theory of Modeling
3 Simulation and Analysis
3.1 Voltage Transient Characteristics
3.2 Voltage Transient Characteristics
4 Conclusion
References
High-Resistance Fault Transient Line Selection Method Based on Ground Parameter Identification
1 Introduction
2 Principle of Line Selection for Transient Energy Based on Identification of Ground Parameters
3 Simulation
3.1 Analysis of Partial Results of Line Selection by Transient Energy Method
3.2 Validation of Simulation Line Selection Results
4 Conclusion
References
Research on MMC Circulation Suppression Strategy Based on Improved Active Disturbance Rejection and Virtual Impedance Composite Control
1 Introduction
2 Topological Structure and Circulation Generation Mechanism of MMC
3 MMC Circulation Suppression Strategy
3.1 Extraction of the Second Harmonic Circulation
3.2 Improved Linear Active Disturbance Rejection Control
3.3 Circulating Current Suppression Controller Design
4 Simulation
5 Conclusion
References
Simulation and Verification of the Temperature Field of 220 kV Natural Ester Insulating Oil Transformer
1 Introduction
2 Simulation of Temperature Field of Natural Ester Insulating Oil Transformer
2.1 Simulation Model
2.2 Setting of Model Parameters and Boundary Conditions
2.3 Simulation Results
2.4 Comparison of the Influence of Natural Ester Insulating Oil and Mineral Insulating Oil on the Temperature Field Distribution of Windings
3 Comparison of Simulation Results and Test Data
4 Conclusion
References
Design of AC Air Arc Generator Power Supply
1 Introduction
2 Structure of Power Supply Module
3 Simulation of Rectifier Circuit
4 Boost Circuit
4.1 Boost Circuit Open-Loop Characteristics Analysis
4.2 Boost Open-Loop Circuit Simulation
4.3 Boost Circuit Closed-Loop Control and Simulation
5 Inverter Circuit
5.1 Inverter Circuit Open-Loop Characteristic Analysis
5.2 Open-Loop Simulation of the Inverter Circuit
5.3 Closed-Loop Control and Simulation of the Inverter Circuit
6 Power Module Overall Simulation
7 Conclusion
References
A Compact Capacitive Power Transfer System Based on Planar Inductors
1 Introduction
2 Circuit Topology
3 Design of Capacitive Coupler
4 Experimental Results
5 Conclusion
References
Optimization Design of a Novel Partitioned Stator Hybrid Excited Permanent Magnet Vernier Machine with DC-Biased Sinusoidal Current
1 Introduction
2 Basic Principle of Proposed PSHE-PMVM Drive System
2.1 Configuration of Proposed PSHE-PMVM
2.2 Main Drive Circuit
2.3 Operation Principle
3 Simulation and Optimization
4 Conclusion
References
Image Recognition of Bird Pecking Defects in Composite Insulators Based on Improved HED Network
1 Introduction
2 Image Processing Process
3 Methods
3.1 Image Filtering
3.2 Image Enhancement
3.3 Semantic Segmentation
4 Experimental Results and Analysis
4.1 Experimental Results and Subjective Comparison Analysis of Improved HED Algorithm
4.2 Quantitative Comparative Analysis of Improved HED Algorithm
5 Conclusion
References
Prediction on the Induced Magnetic Signature of Ships Using Genetic Neural Network
1 Introduction
2 Genetic Neural Network Model
3 Simulation Analysis
3.1 Data Generation
3.2 Simulation Results
3.3 Error Analysis
4 Experimental Results
5 Conclusions
References
Reduced-Dimensionality Modeling of Azimuthal-Symmetric Structures UnderNon-symmetric Excitation in Electrostatics
1 Introduction
2 Theory and Numerical Methods
2.1 Reduced Dimensional Modeling
2.2 Weak Formulation of the Governing Equation
3 Numerical Results and Discussions
4 Conclusions
References
Study on Temperature Recognition of Metal Materials by Video Image in Sunlight Environment
1 Introduction
2 Experimental Device and Method
2.1 Experimental Device
2.2 Experimental Method
3 Data Processing
3.1 Reading Image Data
3.2 Extracting Image Features
3.3 Machine Learning
4 Result and Discussion
4.1 Effect of Sunlight Intensity on Training Results
4.2 Influence of Shooting Distance on Training Results
4.3 Training Effect of Model with Wide Range Variation of Sunlight Intensity
4.4 Comparison of Training Results Between Video Images and Mobile Phone Photos
5 Conclusion
References
Application of Electromagnetic Emission Technology in In-Situ Subsea Dynamic Penetration Test
1 Introduction
1.1 Marine Geological Exploration
1.2 Dynamic Penetration Test
1.3 Electromagnetic Emission Technology
2 Research Method
2.1 Equivalent Design of Electromagnetic Acceleration for DPT
2.2 Single-Stage Electromagnetic Acceleration Design
2.3 Multistage Electromagnetic Acceleration
3 Conclusion
References
Pressurized Air with Vacuum Breaking is the Best Alternative to SF6
1 Introduction
2 Dielectric Withstand as a Function of Pressure
3 Pressurized Air Tank is Robust
4 Pressurized Air Tank is Safe
5 Leakage Rate of Pressurized Air Tank is Similar to SF6
5.1 Permeation
5.2 Leakages at Interfaces
5.3 Example of Pressure Loss Calculation
6 Internal Arc of Pressurized Air Tank is Similar to SF6 Tank
7 Leakage Detection on Site with Acoustic System
7.1 Nominal No-Leak (0.1% P.A.) Example
7.2 Non-intended Leakage level > 1 10–3 mbarl/s
8 Switchgear Can Be Operated Down to Atmospheric Pressure
9 No Cost to Recover Gas at End of Life
10 Low Cost Impact of Pressurized Air Tank
11 Conclusion
References
Optimal Operation of Regional Energy Internet Considering Distributed Resource Aggregation
1 Introduction
2 Mathematical Model of Distributed Resource Aggregation and Optimization
2.1 Distributed Resource Aggregation Modeling
2.2 Objective Function
2.3 Constraints
3 Simulation Results and Analysis
3.1 Example Analysis
4 Conclusion
References
Charging Network Capacity Planning Equipped with Flexible Charging Facilities Considering User Waiting Time
1 Introduction
2 EV User Waiting Time Modeling by Flexible Charging Facilities
2.1 Power Allocation Model of Multi-plie Flexible Charging Facilities
2.2 Charging Waiting Time Model with User Preferences
3 Charging Network Capacity Planning
3.1 Multi-objective Planning Considering User Waiting Time
3.2 Process for Solving the Multi-objective Planning Problem
4 Case Study
4.1 Case Setup
4.2 Result Analysis
5 Conclusion
References
Active Power Support for Fast Frequency Response: An Economic Perspective
1 Introduction
2 Risk Assessment of Frequency Regulation Uncertainty
2.1 Conditional Value at Risk
2.2 WG Frequency Regulation Risk Cost
2.3 RDR Frequency Regulation Risk Cost
3 Calculation of Frequency Regulation Cost
3.1 Thermal Power Unit
3.2 Wind Generation
3.3 Residential Demand Response
4 Calculation Example Design
4.1 Two Calculation Results of CVaRα
4.2 Offline Optimization Algorithm
4.3 Comparison of Frequency Regulation Costs
5 Conclusion
References
Hierarchically Coordinated Optimal Schedule for Virtual Power Plant and Distribution Network Under Multiple Uncertainties
1 Introduction
2 Hierarchically Coordinated Schedule Model
2.1 Optimal Dispatch Model of VPP
2.2 Optimal Schedule Model of Distribution Network
3 Solution Method of Stochastic Programming
4 Case Study
5 Conclusion
References
Multi-armed Bandit Based Load Aggregation for Power System Frequency Regulation
1 Introduction
1.1 HVAC Load Modeling with User Behavior
1.2 Frequency Regulation Strategy
2 Multi-armed Bandit Based Load Aggregation
3 Case Study
3.1 Introduction to Test System
3.2 Results and Comparisons of the Frequency Regulation
3.3 Impacts of Changes in Users’ Behavior
4 Conclusion
References
Slow/Fast Charging Pile Configuration in Multi-areas Based on Time-Space Transfer Characteristics of EV
1 Introduction
2 Travel Chain Simulation Method
3 Charging Pile Demand Model
3.1 Charging Demand Simulation
3.2 Charging Pile Demand Simulation
4 Example Analysis of Charging Pile Demand Figures
4.1 Travel Chain Characteristics
4.2 Charging Load Curve Analysis
4.3 Analysis of Charging Pile Configuration Requirements
4.4 Suggestions for Charging Pile Mode Configuration
5 Conclusion
References
Electric Vehicle Charging Facilities Control Interoperability Testing Technology
1 Introduction
2 Interaction Mode of V2G
2.1 Distributed Access V2G
2.2 V2G Based on a Centralized Control System
2.3 V2G Based on Microgrids
2.4 V2G Based on Replacing Battery Packs
3 Charging Control Interoperability Test Method
3.1 Information Interpretation
3.2 Information Interpretation
3.3 Safety Protection and Anti Islanding Experiment
4 Electric Vehicle Charging Facility Control Interoperability Fault Simulation Device Design
5 Conclusion
References
Multi-time Scale Interactive Trading Strategy of Source Grid Load and Storage
1 Introduction
2 The Multi-time Scale Inter-bundle Trading Framework of SGLS
3 Multi-time Scale Interactive Trading Strategy of SGLS
3.1 Key Equipment Modeling of SGLS Interactive Transaction
3.2 Multi-time Bundling Transaction Strategy of SGLS
4 Solution Flow
5 Example Analysis
5.1 Basic Data
5.2 Effectiveness Analysis of Numerical Examples
5.3 Analysis on Multi-time Scale Market Transaction Results of Bundling Alliances
5.4 Comparative Analysis of Transaction Strategies in the Source Grid Load Storage Interactive Trading Market of Each Bundling Alliance
6 Conclusion
References
Study on Stress Mechanism of Filter Capacitor for HVDC Transmission
1 Introduction
2 Mechanism of Capacitor Noise
3 Core Vibration Mechanism
4 Simulation
5 Conclusions
References
Intelligent Test Scheme of Electromechanical System Based on Digital Instrument Panel
1 Introduction
2 Scheme Composition
3 Scheme Composition
3.1 Low Speed Data Control Board
3.2 High Speed Data Control Board
4 Design of Real Time Test System for Electromechanical System
5 Design of Offline Test System for Electromechanical System
5.1 Real Time Data Acquisition
5.2 Data File Collection Function
5.3 Data Analysis and Processing
5.4 Fault Reasoning and Prediction Function
5.5 Prediction Function
6 Conclusions
References
Monitoring and Analysis of AC Sampling Based on LabVIEW
1 Introduction
2 Development of the Sampling Monitoring and Analysis Tool
2.1 Overall Scheme
2.2 Message Analysis and Data Extraction
2.3 Waveform Analysis and Distortion Discrimination
3 Application Examples
4 Conclusions
References
Parameter Optimization Design of Axial Permanent Magnet Spherical Magnetic Bearingless Flywheel Machine
1 Introduction
2 Machine Topology and Operating Principle
2.1 Machine Topology
2.2 Working Principle
3 Optimized Design
3.1 Selection of Optimization Objectives and Optimization Variables
3.2 Response Surface Model
3.3 Response Surface Experimental Arrangement
3.4 Model Regression and Model Evaluation
3.5 Multi-objective Optimization Based on NSGA-II Algorithm
3.6 NSGA-II Algorithm
3.7 Pareto Optimal Solution Set
3.8 Pareto Solution Set Selection Based on Fuzzy Set Theory
4 Analysis of Optimization Results
5 Conclusion
References
The Adsorption Characteristics of HfS2for Air Partial Discharge Component CO Based on the First Principle
1 Introduction
2 Calculation Method
2.1 A Subsection Sample
3 Results and Discussion
3.1 Metal Doping Method Selection
3.2 Adsorption Performance Analysis
4 Conclusion
References
Parameter Design and Optimization Method of LCL Filter for Grid-Connected Inverter
1 Introduction
2 Structure and Mathematical Model of LCL Grid-Connected Inverter
2.1 Main Circuit Topology
2.2 Mathematical Model of LCL Filter
3 THD Estimation Model
3.1 Analysis of Output Harmonic Voltage of LCL Grid-Connected Inverter
3.2 Design of the Controller
4 LCL Filter Parameter Optimization Design
4.1 General Design of LCL Parameters (Selection Range of the First Parameter)
4.2 The Influence of LCL Filter Parameters on Performance (the Second Parameter Selection Range)
4.3 Particle Swarm Algorithm Parameter Selection (the Third Parameter Selection)
5 Experimental Verification
6 Conclusion
References
Research on Rheological Properties of Epoxy Casting Dielectric Functionally Graded Insulating Slurries and Thermal Expansion Characteristics of Composite Materials
1 Introduction
2 Experimental Materials and Methods
2.1 Experimental Materials
2.2 Sample Preparation
2.3 Test Sample
3 Results and Discussion
3.1 Rheological Analysis
3.2 Thermal Expansion Performance Analysis
4 Conclusion
References
A Method of Fault Diagnosis and Location for Train MVB Communication Network
1 Introduction
1.1 System Topology
1.2 MVB Physical Waveform Feature Extraction
1.3 Support Vector Machine
2 Test Analysis
2.1 MVB Fault Diagnosis Test
2.2 MVB Fault Location
3 Conclusion
References
Rapid 3D Modeling Method for Overhead Transmission Channel from LiDAR Data
1 Introduction
2 3D Reconstruction Technology
2.1 Technology Roadmap
2.2 Data Preprocessing
2.3 Automatic Vectorization of Key Elements of Line Tower and Channel
2.4 Elaborate Modeling and Texture Attachment with 3Ds Max
2.5 Data Quality Inspection and Achievement Handover
3 Experiment and Analysis
3.1 Experimental Data and Platform
3.2 Experimental Analysis
4 Conclusion
References
Sliding Mode Model-Free Predictive Current Control of PMSM with Direct Selection of Optimal Voltage Vector
1 Introduction
2 DM-MPCC Strategy and Parameter Sensitivity Analysis
2.1 Predictive Current Model of PMSM
2.2 Duty Cycle Modulation Based Model Predictive Current Control
2.3 Parameter Sensitivity Analysis
3 Sliding Mode Model-Free Predictive Current Control
3.1 Ultralocal Current Prediction Model of PMSM
3.2 Sliding Mode Observer for Estimating F
3.3 Model Free Predictive Current Control Based on SMO
4 Simulation and Experimental Results
5 Conclusion
References
Design of High-Power Converter for Hydrogen Production
1 Introduction
2 Topological Structure and Parameter Design of High-Power Hydrogen Production Converter
3 Two-Stage Control Algorithm for Hydrogen Generation Power Supply
3.1 The Process of Start Up—Constant Voltage Control
3.2 The Process of Operation—Tracking Renewable Energy
4 Experimental Verification
4.1 Operation Tests
4.2 Analysis of Output Ripple and Efficiency of Hydrogen Production Power Supply
5 Conclusion
References
Insights into the Fungicidal Activity of Low-Temperature Plasma Against the Pathogen of Navel Orange Fruit Mildew
1 Introduction
2 Materials and Methods
2.1 Generation of Low-Temperature Plasma
2.2 Collection of Pathogenic Spores of Fruit Mildew and Microscopic Observation
2.3 Low-Temperature Plasma Treatment and Pathogenic Spore Staining
2.4 Identification of Mildewing Activity of Pathogenic Spores
2.5 Determination of Fruit Quality
3 Results
3.1 Lethal Effect of Low-Temperature Plasma Produced by Different Gases on Pathogenic Spores of Navel Orange Mildew
3.2 Low-Temperature Plasma Inhibits Activity of Pathogenic Spores of Fruit Mildew
3.3 Physical Characteristics of Low-Temperature Plasma Produced by Oxygen Ionization
4 Conclusion and Discussion
References
Research on Smart Collaborative Optimal Control Technology of Distributed Safety and Stability Control System
1 Introduction
2 Feasibility Analysis of Emergency Control for Smart Electrical Equipment
2.1 Analysis on Emergency Control Mechanism of Intelligent Electrical Equipment
2.2 Intelligent Electrical Equipment Emergency Control Engineering Foundation
3 Smart Collaborative Optimal Control Scheme for Distributed Safety and Stability Control System
3.1 Analysis of Applicable Conditions
3.2 The Overall Framework and Information Flow of Intelligent Collaborative Control
3.3 Intelligent Collaborative Control Strategy
4 Example Analysis
5 Conclusion
References
Study on Integrated Modelling of Tower-Line System for UHV Transmission Lines and Weak Spot Distribution of Towers
1 Introduction
2 Modeling Method of Tower-Line System
2.1 Basic Theory of Finite Element Structural Analysis
2.2 Tower-Line System Modeling Element
2.3 Finite Element Modeling of Tower-Line System
3 Study on Weak Spot Distribution of Towers
3.1 Load Application and Solution
3.2 Weak Spots and Failure Analysis of Tower
3.3 Analysis of Influence of Ice Thickness and Wind Speed on Nodal Displacement
4 Conclusion
References
An Impedance Model of the High-Density Cultured Cells in a Bioreactor and the Cellular Impedance Detection Method
1 Introduction
2 Impedance Model of the High-Density Cultured Cells in a Bioreactor
2.1 Single-Cell Impedance Model
2.2 Impedance Model of the Bioreactor Solution Without Cells
2.3 Impedance Model of the Bioreactor with Cells in the Solution
3 Impedance Measurement Method for a Bioreactor
4 Impedance Measurement Platform for the Bioreactor
4.1 Electrode Configuration for Impedance Measurement
4.2 Impedance Measurement System
4.3 Results
5 Conclusions
References
Matching and Selection of Drive Motor Controller IGBT
1 Introduction
2 Analysis of IGBT Application
3 IGBT Matching Selection
3.1 Selection of Nominal Voltage
3.2 Selection of Nominal Current
4 IGBT Protection Measures
5 Conclusion
References
Study on Electromechanical Performance of Factory-Composited Cap and Pin Ceramic and Glass Insulators
1 Introduction
2 Sample Information
3 Electric Field Simulation of Factory-Composited Cap and Pin Ceramic and Glass Insulators
3.1 Simulation Model
3.2 Material Parameters and Boundary Conditions
3.3 Simulation Results
4 Test and Analysis of Factory-Composited Ceramic and Glass Insulators
4.1 Electrical Body Resistance Test
4.2 SF6Puncture Withstand Test
4.3 Thermal Mechanical Performance Test
4.4 Impulse Puncture Test in Air
4.5 Thermal Shock Test
5 Conclusions
References
Model Simulation of Lithium-Sulfur Battery Based on Different Discharge Rates and Sulfur Content
1 Introduction
2 Electrochemical Reaction of Lithium-Sulfur Battery
3 One-Dimensional Electrochemical Model of Lithium-Sulfur Battery
3.1 Matter Transport Equation
3.2 Proton and Electron Conservation Equation
3.3 Electrochemical Kinetic Equation
4 Simulation Analysis of Kinetic Model of Lithium-Sulfur Battery
5 Conclusion
References
Influence of Electromagnetic Launch Rail Structure on Current Distribution
1 Introduction
2 Electrothermal Coupling Model of Railgun
2.1 Electrothermal Coupling Equation
2.2 Simulation Model
2.3 Relevant Material Parameters and Inputs
3 Rectangular Rail Current Distribution
3.1 Influence of Rectangular Rail Parameters on Current Distribution
3.2 Influence of Chamfer on Current Distribution
4 Arc Rail Current Distribution
4.1 Double Elliptical Arc Rail Current Distribution
4.2 Single Elliptical Arc Rail Current Distribution
5 Discussion
6 Conclusion
References
Ride Through Strategy of Doubly-Fed Pumped Storage Generator-Motor
1 Introduction
2 The System Transient Analysis
3 The Cooperative Control Method
3.1 IEC (Inductance Emulating Control) of Rotor-Side Converter
3.2 DC Bus Side Control Strategy
4 Simulation Result Analysis
4.1 Comparison of Rotor Side Control Methods
4.2 Comparison of Overall Control Methods
References
Fast Neutral-Point Balance and Zero-Sequence Circulation Suppression for a T-Type Three-Level Inverter Parallel System
1 Introduction
2 Overview of T-type Three-Level Inverter Parallel System
3 Modeling Analysis of Neutral-Point Potential and Zero Sequence Circulation
3.1 Neutral-Point Potential Modeling Analysis
3.2 Modeling and Analysis of Zero Sequence Circulation
4 Neutral-Point Potential Balance Control and Zero-Sequence Current Suppression for Parallel Systems
4.1 Circulation Suppression Scheme
5 Simulation Results
6 Conclusion
References
Platform Software Scheme Based on SoftPLC Technology for New Generation of Autonomous and Controllable Protection and Measuring-Control Devices
1 Introduction
2 System Architecture
3 Platform Software Architecture
3.1 Logic Diagram Software Model
3.2 Logic Diagram Software Model
4 Logic Diagram Compilation
4.1 Element Name Definition
4.2 The Definition of Element Output Variables
4.3 The Definition of Internal Variables
4.4 Implementation of Element Logic
4.5 Assignment of Output Variables
4.6 Association of Input Variables
5 Conclusion
References
Characteristics of High-Frequency Resonance for Long-Distance Offshore Wind Farm Integration via MMC-HVDC System Considering the Distributed Parameter of Submarine Cable
1 Introduction
2 Impedance Modeling of the Grid-Connected System
2.1 Equivalent Topology of Grid-Connected System
2.2 Impedance Modeling of the Offshore Wind Farm
2.3 HSS-Based Small-Signal Impedance Modeling of the MMC
2.4 Simulation Verification
3 Stability Analysis of the Grid-Connected System
3.1 Analysis of Submarine Cable Distributed Parameter
3.2 Analysis of Submarine Cable Length
4 Conclusion
References
Interleaved High Step-Down Ratio DC-DC Converter with Coupled Inductor
1 Introduction
2 Analysis of Working Principle
3 Characteristic Analysis
3.1 Voltage Gain
3.2 Voltage Stress of Switches and Diodes
3.3 Converter Performance Comparison
4 Simulation Experiments
5 Conclusion
References
Numerical Investigations of Electric Vehicle Wireless Charging Systems Under the Interference of Metallic Foreign Objects
1 Introduction
2 The Influence of Metallic Foreign Objects on WPT Systems from a Circuit Perspective
3 Finite Element Analysis of Metallic Sheets’ Influence on the WPT Systems
3.1 Comparison of the Influence of the Metallic Sheets of Different Materials on the WPT Systems
3.2 Discussion Regarding the Positions of Metallic Sheets
3.3 Influence of the Metallic Sheets on the Equivalent Circuit Parameters on the WPT Systems
3.4 Loss Analysis
4 The Influence of Two Practical Metallic Foreign Objects on the WPT System
4.1 Clip
4.2 Aluminum Can
5 Conclusions
References
Development of Experimental Platform for Low-Power Photovoltaic Energy Storage Inverter System
1 Introduction
2 System Architecture and Composition
3 Experimental Platform Design and Development
3.1 Photovoltaic Input Side Converter
3.2 AC Side Inverter
3.3 Energy Storage Side Electric Energy Conversion
4 Experimental Platform Design and Development
5 Experimental Test Analysis
5.1 Photovoltaic MPPT Control Experiment
5.2 Experimental Research on Start-Up of Energy Storage Inverter
5.3 Grid-Connected/off Grid Control Experiment
5.4 Efficiency Test Experiment
6 Conclusion
References
Research on Short Circuit Failure Mechanism of Press Pack IGBT Device Based on Al-Si Diffusion Molecular Dynamics Simulation
1 Introduction
2 Al-Si Interface MD Simulation of IGBT Chip
2.1 Structure of IGBT Chip
2.2 MD Model of Al-Si Interface
2.3 Validity of MD Model
3 Influence of Different Conditions on Al-Si Diffusion
3.1 Influence of Interface Temperature
3.2 Influence of Interface Stress
3.3 Influence of Combined Stress
4 SCFM Analysis of PP-IGBT Device
4.1 FEM Model of PP-IGBT Device
4.2 Weak Point of PP-IGBT Device
5 Conclusion
References
Maintenance Optimization Strategy of Modular Multilevel Converter
1 Introduction
2 Reliability Model of MMC
2.1 Reliability Model of MMC SM
3 Reliability Model of MMC
4 Reliability Model of MMC
4.1 Maintenance Strategy
4.2 Maintenance Cycle Optimization Model
5 Case Study
6 Conclusion
References
Transient and Steady-State Parameters of the Synchronous Condenser Based on Field-Circuit-Network Finite Element Method
1 Introduction
2 Time-Step Finite Element Model of Field-Circuit-Network Coupling for Machine-Network System
2.1 The Field-Circuit Time-Step Finite Element Model of the SC
2.2 Excitation Control Model of the SC
2.3 Field-Circuit-Network Coupling Time-Step Finite Element Model
3 Transient Characteristics of HVDC Transmission System Under Fault
3.1 Simulation Analysis of Commutation Failure of Receiving AC System
4 Transient Steady State Parameters of the SC in Case of HVDC System Failure
4.1 Frozen Permeability Calculation Method
4.2 Transient Steady State Parameters of the SC
5 The Variation Law of Transient Steady State Parameters of the SC
6 Conclusion
References
Research on the Voltage Balance Ability of Platinum Electrode in Valve Water Cooling System Based on Leakage Current Ripple Factor
1 Introduction
2 Corrosion and Scaling Electrode Reaction Analysis
2.1 Converter Valve Cooling System Structure
2.2 Electrochemical Reaction Mechanism
3 Secondary Current-Flow-Mass Transfer Coupling Model
3.1 Governing Equations for Current Distribution
3.2 Finite Element Model and Boundary Conditions
4 Validation of Proposed Method Cation
5 Voltage Balance Ability Based on Ripple Property
5.1 Analysis of Influence Law of Scale Deposition on Pressure Equalizing Electrode
5.2 Characterization Parameters of Voltage Balance Capacity
5.3 Replacement/Cleaning Strategy of Platinum Electrode
6 Conclusion
References
Transmission Line Galloping Test System Based on Adaptive Excitation
1 Introduction
2 Introduction of the Galloping Test System
2.1 Mechanism
2.2 Establishment of Finite Element Model
3 Study on Excitation Method
3.1 Excitation with Fixed Intervals
3.2 Excitation with Adaptive Intervals
4 Conclusions
References
Investigation of Radial Electromagnetic Bearing with Shielding Shell
1 Introduction
2 Analytical Model of Shielded Electromagnetic Bearing
3 Dynamic Electromagnetic Force Response Characteristics Analysis
4 Suspension Control Experiment
5 Conclusion
References
A Wind Power Scenario Simulation Method Considering Trend and Randomness
1 Introduction
2 Scene Simulation Algorithm Based on Improved Prediction Box
2.1 Improved Prediction Box Modeling
2.2 Multivariate Standard Normal Distribution Matrix and Inverse Transformation Sampling Method
2.3 Backward Scene Reduction Algorithm
3 Evaluation Index of Scene Construction Method
4 Case Analysis
4.1 Improved Prediction Box Model Results
4.2 Effectiveness Analysis of Scenario Simulation Methods
5 Conclusion
References
Establishment of Time-Domain Mathematical Model of Suspension Force for Bearingless Multi-sector Motor Based on Maxwell Stress Tensor Method
1 Introduction
2 Time Domain Mathematical Model of Suspension Force of Bearingless Multi-sector Motor
3 Verification of Suspension Force Time-Domain Model
4 Conclusion
References
Effect of Cold Sintering Process on Performance of Tantalum Doped Lithium Lanthanum Zirconium Oxygen (Li6.4La3Zr1.4Ta0.6O12) Solid Electrolyte
1 Introduction
2 Experimental Preparation
3 Results and Discussion
3.1 Density
3.2 XRD and SEM
3.3 Lithium-Ion Conductivity
4 Conclusion and Prospect
References
Early Stage of Bubble Dynamics via Electrical Explosion in Water
1 Introduction
2 Experimental Setup
3 Experimental Results and Discussion
4 Conclusion
References
The Evaluation of Electric Power Emergency Plan Exercise Based on EMD Method
1 Introduction
2 Power Emergency Assessment Index System Based on Different Time Scales System
2.1 Electric Power Emergency Demonstration
2.2 Short Time Scale Evaluation Indicators
2.3 Medium and Long Time Scale Evaluation Indicators
2.4 Long Time Scale Evaluation Indicators
3 Standardization of Index Data Based on EMD
3.1 Introduction to EMD Methods
3.2 Application of EMD Method
4 Evaluation Model of Electric Power Emergency Deduction
4.1 The Weight of Evaluation Index is Determined
4.2 Variable Weight Correction Coefficient
4.3 Comprehensive Evaluation Model
5 The Example Analysis
6 Conclusion
References
Stability Enhancement Strategy for Low-Voltage Multi-terminal DC System Using MPC Based Additional Control
1 Introduction
2 Low-Voltage Multi-terminal System
2.1 System Structure
2.2 Typical Structure for VSC
2.3 Control Strategy of Low Voltage MTDC System
3 Small-Signal Model for Low Voltage MTDC System
3.1 Small-Signal Modeling for VSCs Under Master-Slave Control
3.2 Small Signal Modeling for DC Network
3.3 Completed Small Signal Model of Low-Voltage MTDC System
4 MPC Based Additional Control Strategy
4.1 The Design of MPC Based Additional Control Strategy
5 Simulation Verification
6 Conclusion
References
Research on Fast Location Method of Fault Line Based on Intelligent Power Emergency Plan Mode
1 Introduction
2 APTS Simplified Model
2.1 Basic Principles of the Model
2.2 APTS Simplify the Implementation Process
3 Improvement of Genetic Algorithm
3.1 Genetic Algorithm
3.2 Improvement of Similarity Coefficient
3.3 Probability Function Reconstruction
4 Fast Location of Faulty Lines Under Smart Plans
4.1 Genetic Coding
4.2 Model Switch Function
4.3 Multi-objective Fitness Function Based on Pareto Optimal
5 Case Analysis
6 Conclusion
References
Design of Active Power Control Parameters Based on Real-Time Rain-Flow Counting Method
1 Introduction
2 The Principle of Active Power Control
2.1 The Traditional Active Power Control Methods
2.2 The Filter Parameters Design Method of Active Power Control Based on Real-Time Rain-Flow Counting Method
3 Rain Flow Counting Method
4 Simulation Verification
5 Conclusions
References
Oscillation Suppression Strategy of MMC-HVDC in Weak AC Grid
1 Introduction
2 Oscillation Analysis of Weak AC Grid
3 Improved Phase Locked Loop Strategy
4 Sub synchronous Damping Control
5 Semi-physical Experimental Results
6 Conclusion
References
Research on Hybrid Control Strategy of PMSM-IM Dual Motor System
1 Introduction
2 Current Control Strategy of PMSM-IM Dual Motor System
2.1 Current Control Strategy of Induction Motor
2.2 Current Control Strategy of PMSM
3 Design of Hybrid Control Strategy for Dual-Motor System
4 Verification via Simulation
5 Conclusion
References
Design and Research of Swinging Magnetic Field System Suitable for Biological Experiment
1 Introduction
2 Development of Main Circuit of Swing Magnetic Field System
2.1 Composition of Swing Magnetic Field System
2.2 Basic Circuit Theory of Main Circuit Design
2.3 Field Coil Design
3 The Simulation Verification
4 Experimental Prototype Building and Analysis
5 Conclusion
References
Research on Design Method of Radial Magnetized Linear Voice Coil Motor
1 Introduction
2 The Magnetic Circuit Analysis
3 Study on the Parameter Design Method
3.1 Design of Permanent Magnetic Material Parameters
3.2 Current Stiffness Determines the Coil Assembly Parameters
3.3 Parameter Design Results
4 Electromagnetic Simulation of Voice Coil Motor Based on FEM
5 Prototype and Experimental Test
6 Conclusion
References
Application Analysis of New Type of Soft Magnet in High Speed and Low Loss Permanent Magnet Motor
1 Introduction
2 Motor Core Loss
2.1 A Subsection Sample
2.2 Eddy Current Loss
3 Soft Magnetic Material Testing and Analysis
3.1 Soft Magnetic Material Testing
3.2 Analysis of Test Results
4 Finite Element Simulation Experiment of Motor
5 Conclusion and Prospect
References
Electric Vehicle Charging Strategy Based on Nonlinear Droop Technology
1 Introduction
2 Composition of Power Supply Structure
3 Control Mode of Each Module
3.1 Control Mode of Bidirectional AC/DC Converter
3.2 Control Mode of Unidirectional DC/DC Converter
3.3 Battery Module Control Mode
3.4 Control Mode of Photovoltaic Power Generation Module
4 Simulation
5 Conclusion
References
Single Carrier Three Mode Modulation Method of Four Switch Converter
1 Introduction
2 Working Principle of Four-Switch Converter
2.1 Four-Switch Converter Circuit Topology
2.2 Traditional Three-Mode Modulation Strategy for the Four-Switch Converter
3 Single Carrier Three-Mode Modulation Strategy
4 Experimental Verification
5 Conclusion
References
Research Progress of High-Performance Graphene Electromagnetic Shielding Materials
1 Introduction
2 Principle of Electromagnetic Shielding
3 Graphene Electromagnetic Shielding Materials
3.1 Pure Graphene Shielding Material
3.2 Graphene/Other Carbon Nanostructure Composites
3.3 Graphene/Conductive Metal Composite
3.4 Graphene/Magnetic Metal Composite
3.5 Graphene/Ceramic Composite
3.6 Graphene/Conductive Polymer Composite
4 Challenges and Prospects
5 Conclusion
References
Multi-stage AC Low-Temperature Heating Strategy for Lithium-Ion Battery
1 Introduction
2 Consider the Multi-stage AC Heating Strategy for Lithium Plating
2.1 Electrochemical-Thermal Model Considering Lithium Evolution
2.2 Consider the Heating Strategy for Lithium Plating
2.3 Multi-stage Heating Strategy
3 Simulation
4 Conclusion
References
Prediction of Health Status and Fault of Electrical Equipment Based on the Concept of Digital Twin
1 Introduction
2 The Concept of Digital Twin
2.1 Main Characteristics of Digital Twin Model
2.2 Main Functions of the Digital Twin Model
3 Key Issues and Technical Routes in the Realization of Fault Prediction for Electrical Equipment Based on the Concept of Digital Twin
3.1 First Determine Which Equipment Faults Are Suitable for Prediction by the Digital Twin Model
3.2 Build the Mathematical-Physical Model that Describe Fault or Health Status and Its Development Characteristics
3.3 Determine the Required Equipment State Characteristic Measurement Parameters
3.4 Build the Digital Twin Model
3.5 Growth of Digital Twin Based on Actual State Characteristic Parameters
3.6 Use the Digital Twin Model for Fault Prediction and Operation Decision-Making
4 Conclusion
References
Traveling Wave Protection of Medium Voltage DC Distribution Network
1 Introduction
2 Analysis of Travelling Wave Protection
2.1 Feasibility of Fault Traveling Wave Extraction
2.2 Time Difference Calculation Principle
3 Calculation Steps
4 The Simulation Verification
5 Conclusion
References
Harmonic Suppression of Charging Station Based on Harmonic Superposition
1 Introduction
2 Harmonic Characteristics of Chargers
2.1 Principle Analysis of Chargers
2.2 Harmonic Analysis in Charging Process
3 Principle of Harmonic Superposition
4 Simulation
4.1 Simulation Analysis of Harmonic Superposition
4.2 Harmonic Suppression of Charging Station
5 Conclusion
References
Review of Transmission Line Icing and Anti-icing Technologies
1 Introduction
2 Transmission Line Ice-Covering Mechanism and Characteristics
2.1 Relationship Between Temperature and Wire Ice Covering
2.2 Effect of Wind Speed on Wire Ice
2.3 Effect of Wire Diameter
2.4 The Characteristics of Ice Covering and Ice Disasters in China
3 Anti-ice Technology
3.1 Anti-ice Wires
3.2 Anti-ice Materials
3.3 Other Anti-ice Technologies
3.4 Prospects for Anti-ice Technology
4 Conclusion
References
Current Transformer Excitation Current Calculation Method and Current Wave Characteristics Analysis
1 Introduction
2 Non-linear Model Establishment
2.1 Basic Structure and Related Variables of CT
2.2 CT Calculation Model Establishment
2.3 Model Expressed with Inductive Excitation Current
3 Excitation Current Model Solution Process and Implementation Method
3.1 CT Nonlinearity Expression Method
3.2 Iterative Scheme and Solution of Nonlinear Differential Equations
4 Simulation and Calculation Examples
5 Conclusion
References
Summary of Research on Control Technology of Pulsed Power Supply in Electromagnetic Launch System
1 Introduction
2 Brief Introduction to the Development Status of Pulse Power Supply in Electromagnetic Launch System
3 Development Status and Trend of Pulse Power Supply Control Technology
3.1 Research on Control System Hardware
3.2 Research on Control System Software
3.3 Research on Centralized Control of Distributed System
4 The Development Direction of Pulse Power Supply and Its Control Technology in the Field of Electromagnetic Emission
5 Conclusion
References
Review on Application of Infrared Detection Technology in State Detection of Electrical Equipment
1 Introduction
2 Overview of Infrared Detection Technology
2.1 Advantages of Infrared Detection Technology
3 Common Methods of Infrared Detection
4 Application of Infrared Detection of Electrical
4.1 New Infrared Image Edge Detection Technology
4.2 Thermal Fault Detection System Based on Infrared Image Analysis
4.3 Infrared Image Registration Technology
4.4 Infrared Temperature Measurement and Line Inspection Robot System
5 Summary and Prospect
References
Review of Wind Power Grid Connection Technology
1 Introduction
2 Grid Connection Mode of Wind Power
2.1 Grid Connection Mode of Constant Speed and Constant Frequency Wind Turbine System
2.2 Grid Connection Mode of Variable Speed Constant Frequency Wind Turbine System
2.3 Grid Connection Mode of Offshore Wind Farm
3 Problems and Solutions in Wind Power Grid Connection
3.1 Problems Affecting Power Quality
3.2 Island Effect Problem
3.3 Problems Affecting System Stability
4 Summary and Prospect
References
Mathematical Model and Working Characteristics Analysis of Alkaline Electrolyzer
1 Introduction
2 Working Principle of Alkaline Electrolyzer
3 Modeling of Alkaline Electrolyzer
4 Working Characteristics of Alkaline Electrolyzer
4.1 U-I Characteristics of Alkaline Electrolyzer
4.2 Hydrogen Production of Alkaline Electrolyzer
4.3 Energy Efficiency of Alkaline Electrolyzer
5 Conclusion
References
Overview of Research on SiC Power Devices
1 Introduction
1.1 A Subsection Sample
2 SiC MOSFET Device Structure and Development
2.1 Basic Structure of SiC MOSFET
2.2 Development History of SiC MOSFET
2.3 Research Status of SiC MOSFET Products
3 Main Technical Problems of SiC MOSFET
3.1 Difficulties in Modeling SiC MOSFETs
3.2 Problems in SiC MOSFET Driving
3.3 EMI Problems of SiC MOSFET
4 Main Application Areas of SiC Switching Devices
4.1 SiC MOSFET for Motor Drive
4.2 SiC MOSFETs Used in Photovoltaic Inverters
4.3 SiC MOSFETs Used in Power Systems
5 Conclusion
References
Experimental Study on the Effect of the Stress on the Magnetic Field of the Submarine Steel
1 Introduction
2 Ferromagnetic Theory of the Magnetomechanical Effect
3 Experiment of the Steel Specimen
4 Experiment of the Simple Submarine Model
5 Conclusion
References
Structural Optimization Design of Rotor Magnet of Large High Temperature Superconducting Condenser
1 Introduction
2 Design of Magnets Structure
2.1 Introduction of Basic Principles
2.2 Model of Magnets Structure
3 Finite Element Model of Electromagnetic Simulation
3.1 Establishment of Finite Element Model of Electromagnetic Simulation
3.2 Post-processing of Finite Element Simulation Results
4 Simulation Results and Analysis
5 Conclusion
References
Electromagnetic Performance of the Nickel-Iron Alloy in High Frequency
1 Introduction
2 Experimental
3 Results and Discussion
3.1 Morphology and Crystal Structure of Milled Nickel-Iron Powder
3.2 Electromagnetic Characteristics of Milled Nickel-Iron Powder
3.3 Anti-electromagnetic Interference Characteristics of Milled Nickel-Iron Powder/Epoxy Composite
4 Conclusions
References
Study on the Influence of Skin Effect on AC Loss of YBCO Tape
1 Introduction
2 YBCO Tape Structure Analysis
3 AC Loss Calculation
3.1 Critical State Model
3.2 H-formulation
4 Results and Analysis
4.1 The Influence of Transmission Current Frequency on AC Loss
4.2 The Influence of Superconducting Tape Reinforcement Layer on AC Loss
5 Conclusion
References
Simulation and Comparative Analysis of Permanent Magnet Motor with Rectangular-Wire and Circular-Wire
1 Introduction
2 Analysis and Calculation of AC Loss
2.1 Theoretical Analysis
2.2 Simulation Analysis of AC Copper Loss
3 Characteristic Simulation
4 Comparative Study and Analysis
5 Conclusion
References
A Power Distribution Control Strategy for the Cascaded H-Bridge Energy Storage System
1 Introduction
2 Working Principle of Cascaded H-bridge Converter Topology
3 Simulation Model
4 Control Strategy
4.1 Power Voltage Control
4.2 Sub-module Capacitor Voltage Equalization Control
4.3 Super Capacitor Charging and Discharging Control in the DC-DC Link
5 Simulation Verification
6 Conclusion
References
Research on a New Intelligent Transformer Integrating SVG and DVR
1 Introduction
2 The Topology and Working Principles of HDT
3 The Control Strategy of HDT Rectifier Stage
3.1 Control Strategy of Outer Voltage Loop
3.2 Control Strategy of Inner Current Loop
4 The Control Strategy of HDT Inverter Stage
4.1 Detection Process of Grid Connection Point Voltage
4.2 Compensation Control Strategy of Inverter Stage
5 Simulation Results and Analysis
5.1 Simulation Results of Rectifier Stage Converter
5.2 Simulation Results of Inverter Stage Converter
6 Conclusions
References
Open-Circuit Fault Diagnosis of Quasi-Z-Source Inverter Based on Cloud Model
1 Introduction
2 Principle of Fault Diagnosis of Quasi-Z Source Inverter
2.1 Fault Classification
2.2 Single IGBT Open Circuit Fault Diagnosis
2.3 Fault Diagnosis of Open Circuit of Two IGBTs in the Same Bridge Arm
2.4 Fault Diagnosis and Location Based on Cloud Model
3 Simulation
3.1 Simulation Environment
3.2 Single IGBT Open Circuit Fault Simulation
3.3 Simulation of Two IGBT Open Circuit Faults in the Same Bridge Arm
3.4 Simulation of Open-Circuit Faults of IGBTs on Different Sides of Two Bridge Arms
3.5 Simulation of Open-Circuit Faults of IGBTs on the Same Side of Two Bridge Arms
4 Conclusion
References
Real-Time Demand Response Interactive Behavior Model of Electric Vehicle Cluster
1 Introduction
2 Real-Time Demand Response Interactive Behavior Model of Electric Vehicles
2.1 Physical Model of Charging and Discharging of Electric Vehicle Battery
2.2 Demand Response Interactive Model of Electric Vehicle
3 Real-Time Demand Response Interactive Behavior Model of Electric Vehicle Clusters
4 Simulation Example Analysis
4.1 Example Analysis of Electric Vehicle
4.2 Example Analysis of Electric Vehicle Clusters
5 Conclusion
References
Author Index
Recommend Papers
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Lecture Notes in Electrical Engineering 890
Xidong Liang Yaohua Li Jinghan He Qingxin Yang Editors
The proceedings of the 16th Annual Conference of China Electrotechnical Society Volume II
Lecture Notes in Electrical Engineering Volume 890
Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, 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, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany 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, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, 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 Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Luca Oneto, Dept. of Informatics, Bioengg., Robotics, University of Genova, Genova, Genova, Italy Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Walter Zamboni, DIEM - Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA
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Xidong Liang Yaohua Li Jinghan He Qingxin Yang •
•
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Editors
The proceedings of the 16th Annual Conference of China Electrotechnical Society Volume II
123
Editors Xidong Liang Department of Electrical Engineering Tsinghua University Beijing, Beijing, China Jinghan He Beijing Jiaotong University Beijing, Beijing, China
Yaohua Li Institute of Electrical Engineering Beijing, Beijing, China Qingxin Yang Tianjin University of Technology Tianjin, Tianjin, China
ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-19-1869-8 ISBN 978-981-19-1870-4 (eBook) https://doi.org/10.1007/978-981-19-1870-4 © Beijing Paike Culture Commu. Co., Ltd. 2022 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
Coupling Analysis of Transient Electromagnetic Field and Temperature Field in Electromagnetic Launch Rail . . . . . . . . . . . . . . . . Yifan Ge, Shihong Qin, and Lixue Chen
1
Theoretical Attempts to Optimize the Geometrical Shape of Simple Electromagnetic Rail Launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shaohui Chen and Hongyan Sun
12
Force Analysis of Armature in Induction Coil Launcher and Design of Double-Layer Armature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Yang, Yanming Li, Shasha Wang, Yazhou Zhang, and Chengfei Zheng
24
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil Launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pengfei Zhao, Zhiye Du, Yadong Zhang, and Gen Li
34
The Application of Electromagnetic Coil Launching Technology in Non-war Military Operations AC Machines . . . . . . . . . . . . . . . . . . . . Zhiyuan Li, Jingchao Wang, and Xiaojuan Zhang
42
Research on Parameters Optimum Design of Levitation Electromagnet Based on Orthogonal Design for EMS Maglev Train . . . Xiwen Yu, Yu Wang, Kai Bo, Junquan Chen, and Dong Wang
50
Research on the Formation of Erosion in Electromagnetic Launch . . . . Wenping Cheng, Weidong Xu, Zhizeng Wang, and Ping Yan
59
Circuit Analysis of Commutation Process of Saddle Secondary Helical Coil Electromagnetic Launcher . . . . . . . . . . . . . . . . . . . . . . . . . Zhiming Cui, Housheng Wang, Jianchao Wang, and Bendong Ma
69
Research on Performance Influence of External Circuit Resistance in Synchronize Induction Coil Catapult . . . . . . . . . . . . . . . . . . . . . . . . . Yanwei Chen, Pinghui Li, Qi Li, Wei Yang, and Yawei Wang
79
v
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Influence of Copper Wire Sectional Shape on Induction-Coil Catapult Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qingzhao Liu, Qi Li, Shuguo Pan, and Changbo Wang
90
Effect of Temperature on the Performance of Induction Coil Launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Yadong Zhang, Mingzhi Zhu, Kaixiang Li, Xiong Lin, and Ao Zhou Research of Mechanical Sensitive Factors of a Electromagnetic Rail Gun Cradle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Jun Xu Research on Nonlinear Servo Speed Identification Based on Two-Stage Electric Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Pengfei Li and Danfeng Wang The Continuous High Precision Measurement Technique of Bore Spacing About Rail-Gun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Pengchao Pei, Bin Cao, Mingtao Li, and Xia Ge Research on Armature Loading Control Accuracy Based on Cloud Model Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Xue Han, Dongdong Zhang, Zhiqiang Wang, Guofeng Li, and Jingshong Li Model Predictive Control for Electromagnetic Launcher of UAV . . . . . 147 Guanglei Xie, Jun Wu, Yunzhou Zhang, and Yu Yang Research on Control Strategy of the Electromagnetic Launch System for Fixed Wing UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Yao Li, Donghuai Zhang, Xinyu Zhang, Xiaoxiao Ma, Hongwei Yao, and Yanming Li Torque Ripple Suppression Strategy of High-Speed Square Wave Permanent Magnet Motor Based on Direct Torque Control . . . . . . . . . 170 Shi Jin, Shuai Liu, Wuhen Jin, and Jianqiao Wang Distribution of Breakdown Positions in Conditioning Progress Between Plane-Plane Electrodes in Vacuum Under Lightning Impulse Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Yu Du, Dianyu Chi, Jingyu Shen, Hui Ma, Jing Yan, Zhiyuan Liu, and Yingsan Geng Vulnerability Analysis of Distribution Network Considering the Uncertainty of Source and Load . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Wenbin Hao, Xiaoping Su, Bo Xie, Peng Zeng, Zhigao Meng, Jing Xue, and Lingyun He
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A Novel Efficiency-Improved LLC-Buck Isolated Power Processing Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Danni Yang, Yan Zhang, Boyang Yu, and Jinjun Liu Research on Component Parameter for a Dual-Motor Coaxial Propulsion System Used in an Electric Bus . . . . . . . . . . . . . . . . . . . . . . 208 Cheng Lin, Yue Su, and Xiao Yu Influence of Winding Placement on the Motor Copper Losses with High Frequency Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Yuqing Wang, Guangwei Liu, Deming Xiong, Jianqiao Wang, and Fengge Zhang The Effect of Temperature on the Distribution Characteristics of Spatial Electric Field in Oil of Oil-Pressboard Insulation Under Impulse Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Juzhen Wu, Qing Yuan, Congcong Chen, Chunjia Gao, Bo Qi, and Chengrong Li A MTPA Control Strategy for Permanent Magnet/Reluctance Hybrid Rotor Dual-Stator Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Shi Jin, Wang Jiang, Wuhen Jin, and Yujiang Sun Interaction Between Atmosphere Pressure Plasma Jet and Substrate with Micro-hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Xianghao Kong, Shuang Xue, and Ruixue Wang Simulation and Experiment Analysis of Opening Characteristics for High-Current Fast Switch Based on Double-Acting Mechanism . . . . 249 Wei Zhao, Bing Zhao, Yanjun Zhao, Zhiwen Xie, Wei Wang, and Ning Xie Reduced-Order and Full-Order Models of the Active-SwitchedCapacitor/Inductor Quasi Z-Source Converter in Discontinuous Conduction Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Shuai Dong, Baichuan Zhang, Rengui Lu, Chunbo Zhu, and Qianfan Zhang Small-Signal Modeling and Analysis of the Active-SwitchedCapacitor/Inductor Quasi Z-Source Converter Working in Continuous Conduction Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Shuai Dong, Yifan Gao, Kai Song, Chunbo Zhu, and Qianfan Zhang A Novel Deep Flux Weakening Control Strategy for IPMSM . . . . . . . . 279 Renxin Xiao, Shuai Peng, and Zhiqiang Huang Research on Micro-grid Regulation Strategy Formulation Based on Semi-supervised Learning Neural Network Model . . . . . . . . . . . . . . 291 Li Qian, Huanna Niu, Zongsheng Li, and Wei Dou
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Day-Ahead PV and EVs Power Forecasting of Distribution Network Based on LSTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Xiaoping Su, Wenbin Hao, Zhigao Meng, Peng Zeng, Bo Xie, Pan Peng, and Zhizhuo Liang Study on the Effect of Thermal Degradation on the Morphology Characteristics of Composite Insulator Mandrel Under Vacuum Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Xiang Cai, Chao Gao, Dandan Zhang, Ming Lu, Junzhe Peng, Zehui Liu, Wenwu Pan, and Zhiyu Wan Research on Distributed Cross-Bay Busbar Protection Based on Ring Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Bei Dong, Zhong Xue, and Yao Zhang A Refined Model of On-Board Electric Power System for Turboprop Regional Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Yuyang Song and Xi Xiao Study of Voltage and Current Inner Control of Voltage-Controlled Converters in High Permeability Environment . . . . . . . . . . . . . . . . . . . 336 Changzhou Yu, Haizhen Xu, Qinglong Wang, Meimei Sun, and Xing Zhang Study on the Morphology Change of Acid-Resistant Core Rods of Composite Insulators Under Acid-Heat Condition . . . . . . . . . . . . . . . 347 Junzhe Peng, Ming Lu, Dandan Zhang, Chao Gao, Wenwu Pan, Yupeng Zhang, Xiang Cai, and Zhiyu Wan Research on Optimal Dispatching of Multi-region Integrated Energy System Considering Electric Load Price Based Demand Response . . . . . 360 Hui Hui, Wei Liu, and Ning Ma A Deep Adversarial Diagnosis Method for Fault Line Detection with Imbalanced Small Sample Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Yifan Wang, Junqi Zhang, Yiping Wu, Ye Tian, and Yunting Shao Experimental Investigation on Magnetic Field Controlled One-Dimensional Plasma Jet Array in He . . . . . . . . . . . . . . . . . . . . . . . 383 Changquan Wang and Haiyun Luo Inspection Text Classification of Power Equipment Based on TextCNN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Jianning Chen, Yuanxiang Zhou, and Jiamin Ge Research on Reactive Power Compensation Site Selection Method for Reducing Commutation Failure Risk of MIDC System . . . . . . . . . . 399 Limin Ma, Jun Wen, Xiangkun Meng, and Minxiao Han
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Intelligent Power Transmission and Transformation Technology for PIoT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 Guangyong Xie, Xiaorui Xu, Shuqin Zhang, Fei Geng, and Hailu Jin Study on the Blocking Capability Decreasing of SiC MOSFET After Short-Circuit Gate-Source Failure . . . . . . . . . . . . . . . . . . . . . . . . 416 Jiaoyang Peng, Peng Sun, Yumeng Cai, Haoran Zhang, and Zhibin Zhao A Transmission Line Multi-parameter Monitoring System Based on FBG Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 Sihan Wang, Rongbin Shi, Weiqi Qin, Kunpeng Ji, Xuehong Lin, and Guoming Ma Reconstruction of Open-Circuit Voltage for Aging Lithium-Ion Batteries Based on Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Deshun Wang, Haikun Wei, Jinhua Xue, and Lei Pei A Switched-Capacitor-Based Multilevel Converter for Photovoltaic Systems Suffering from Power Mismatch . . . . . . . . . . . . . . . . . . . . . . . . 445 Hui Fang, Yongtao Chen, Jingsen Zhou, Te Zhu, He Peng, and Cheng Wang Difficulty Analysis and Test Method Research on Performance Test of Medium Voltage Photovoltaic Power Generation Unit . . . . . . . . . . . . 454 Zhilei Chen, Lie Xia, Qingbin Yang, and Lianghui Xu Digital Twin System for Service Performance Evaluation of Anti-vibration Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 Jianli Zhao, Zhexing Chen, Yong Liu, Yilin Wang, Yisheng Zhang, and Liang Wang Research on Fiber Channel Message Recording Scheme Based on Data Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Jin Li, Tao Zhang, Hao Zhang, Yuping Li, and Mingjun Xue Research on Control Strategy of Energy Storage System to Improve Wind Power Smoothing Ability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 Jianlin Li, Yaxin Li, Zedong Zhang, Rongpei Wang, and YiWen Wu Analysis and Calculation of the Capacitor Current and Voltage Ripples for Z-Source Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Shuai Dong, Chen Lin, Tuopu Na, Qianfan Zhang, and Chunbo Zhu Feasibility Analysis of Using the Normal Vector to Determine the Most Dangerous Power Increasing Direction of the Small-Signal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Mengru Chen, Kewen Wang, Jiatong Yu, Zheng Huang, Songfang Jiang, and Jian Chen
x
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Design of Main Wiring Diagram Drawing System of Relay Protection Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Chunfeng Luo, Zhong Xue, Lihui Wu, Zilan He, Daopin Chen, and Dong Liu Monitoring and Management Technical Research for Battery Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Zhong Xue, Bei Dong, and Yao Zhang Analysis of Lightning Impulse Response of Ground Network Based on a Distributed p Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Ruming Feng, Tianyu Liu, Lei Zhao, Chuanqiang Che, Qiong Wang, Jun Zhao, and Jiali Chong High-Resistance Fault Transient Line Selection Method Based on Ground Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Zunxian Wang, Shouyuan Wu, and Xiaoming Luan Research on MMC Circulation Suppression Strategy Based on Improved Active Disturbance Rejection and Virtual Impedance Composite Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 Zhi Qiao and Guo Wang Simulation and Verification of the Temperature Field of 220 kV Natural Ester Insulating Oil Transformer . . . . . . . . . . . . . . . . . . . . . . . 552 Youqin Zhang, Jinhui Man, Haoyong Song, Qingdan Huang, Kun Li, Jiahui Zhang, and Shuhong Wang Design of AC Air Arc Generator Power Supply . . . . . . . . . . . . . . . . . . . 560 Zexin Yan, Chi Ma, Boyu Zhang, Zihan Sun, and Jiangtao Li A Compact Capacitive Power Transfer System Based on Planar Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 Haiwen Sun, Xinyun Zhang, and Liang Huang Optimization Design of a Novel Partitioned Stator Hybrid Excited Permanent Magnet Vernier Machine with DC-Biased Sinusoidal Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 Liangliang Wei, Dongqing Liu, Xiaojun Tan, and Jiaxin Yuan Image Recognition of Bird Pecking Defects in Composite Insulators Based on Improved HED Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Bing Zhang, Huijian Wu, Bin Zhang, Houxu Li, Jian Zhao, and Yujiao Zhang Prediction on the Induced Magnetic Signature of Ships Using Genetic Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 Yi Wang, Guohua Zhou, Kaisong Wang, and Xuelian Zhu
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Reduced-Dimensionality Modeling of Azimuthal-Symmetric Structures Under Non-symmetric Excitation in Electrostatics . . . . . . . . 606 Lu Zhang, Siyuan Ma, Zhiyao Luo, Yinan Wu, Haibao Mu, and Tianyu Dong Study on Temperature Recognition of Metal Materials by Video Image in Sunlight Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Xiaofei Nie, Qizheng Ye, Zhe Yuan, and Mengting Han Application of Electromagnetic Emission Technology in In-Situ Subsea Dynamic Penetration Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628 Hai Zhu, Jia Wang Chen, Xue Yu Ren, Jin Guo, Hao Nan Li, Peng Zhou, and Tao Liang Pressurized Air with Vacuum Breaking is the Best Alternative to SF6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636 Christophe Preve, Raimund Summer, Jack Wang, Michel Perrone, Haifeng Lu, and Romain Maladen Optimal Operation of Regional Energy Internet Considering Distributed Resource Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648 Dian Yuan, Haohui Ding, Qinran Hu, Zaijun Wu, and Rushuai Han Charging Network Capacity Planning Equipped with Flexible Charging Facilities Considering User Waiting Time . . . . . . . . . . . . . . . 657 Zhenya Ji, Lixing Chen, Hao Li, and Yuqing Bao Active Power Support for Fast Frequency Response: An Economic Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 Weichun Zhang, Zhuolin Cao, Xinyi Chen, and Qinran Hu Hierarchically Coordinated Optimal Schedule for Virtual Power Plant and Distribution Network Under Multiple Uncertainties . . . . . . . . . . . . 678 Xinyuan Liu, Ke Feng, Qian Zhang, Huiping Zheng, Mengzan Li, and Peishuai Li Multi-armed Bandit Based Load Aggregation for Power System Frequency Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 Yufeng Yang, Xianliang Teng, Kang Chen, Wei Cheng, Yunqiang Si, and Junjun Xu Slow/Fast Charging Pile Configuration in Multi-areas Based on Time-Space Transfer Characteristics of EV . . . . . . . . . . . . . . . . . . . 694 Yiwei Xu, Wenxuan Shu, Jiaming Chen, Linwei Sang, Qinran Hu, and Rushuai Han Electric Vehicle Charging Facilities Control Interoperability Testing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Bin Zhu, Zhi Li, and Binbin Zang
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Multi-time Scale Interactive Trading Strategy of Source Grid Load and Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Xun Dou, Yingchun Feng, Ping Shao, and Xiaojun Cao Study on Stress Mechanism of Filter Capacitor for HVDC Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Guojun Ding, Yang Liu, Honglu Guan, Wei Yao, Dong Wang, and Lei Guo Intelligent Test Scheme of Electromechanical System Based on Digital Instrument Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Tingting Wu, Daocan Wang, Yiqi Li, and Mengyao Li Monitoring and Analysis of AC Sampling Based on LabVIEW . . . . . . . 747 Shuai Li, Shimin Gong, Liangliang Cai, Bin Tang, and Ying Hong Parameter Optimization Design of Axial Permanent Magnet Spherical Magnetic Bearingless Flywheel Machine . . . . . . . . . . . . . . . . . . . . . . . . 755 Zhiying Zhu, Linjing Shao, Yuhui Ni, and Bingyu Cong The Adsorption Characteristics of HfS2 for Air Partial Discharge Component CO Based on the First Principle . . . . . . . . . . . . . . . . . . . . . 765 Guochao Qian, Jin Hu, Shan Wang, Weiju Dai, Wenjun Hou, and Qu Zhou Parameter Design and Optimization Method of LCL Filter for Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773 Haihong Huang and Shaohua Yang Research on Rheological Properties of Epoxy Casting Dielectric Functionally Graded Insulating Slurries and Thermal Expansion Characteristics of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . 785 Yijia Fu, Chao Wang, Wendong Li, and Guanjun Zhang A Method of Fault Diagnosis and Location for Train MVB Communication Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794 Jiaren Wang Rapid 3D Modeling Method for Overhead Transmission Channel from LiDAR Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803 Yi Wu, Wei Hu, Xiaoqian Meng, Zan Li, Chuntian Ma, and Maojie Tian Sliding Mode Model-Free Predictive Current Control of PMSM with Direct Selection of Optimal Voltage Vector . . . . . . . . . . . . . . . . . . 813 Lin Jiang, Jun Deng, Yang Wang, Lu Han, and Pingyuan Li Design of High-Power Converter for Hydrogen Production . . . . . . . . . . 824 Wenqiang Yang, Xiaowen Xing, Xun Sun, and Sihan Wang
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Insights into the Fungicidal Activity of Low-Temperature Plasma Against the Pathogen of Navel Orange Fruit Mildew . . . . . . . . . . . . . . . 834 Ying Sun, Yu Xiang Wang, Yu Xu, Hai Lun Lu, Ya Li Sang, Jin Ping Li, Rui Xu, Qing Wang, Yuan Yuan Li, Xing Quan Wang, and Zhi Qiang Gao Research on Smart Collaborative Optimal Control Technology of Distributed Safety and Stability Control System . . . . . . . . . . . . . . . . 844 Ke Feng, Wang Wang, Xiong Chen, Shiguang Xu, Weidong Xu, and Kaiyang Zhu Study on Integrated Modelling of Tower-Line System for UHV Transmission Lines and Weak Spot Distribution of Towers . . . . . . . . . . 859 Huipeng Li, Daochun Huang, Yuangen Xu, Li Zhang, and Jiangjun Ruan An Impedance Model of the High-Density Cultured Cells in a Bioreactor and the Cellular Impedance Detection Method . . . . . . . 867 Changzhe Wu, Guanghao Zhang, Cheng Zhang, and Xiaolin Huo Matching and Selection of Drive Motor Controller IGBT . . . . . . . . . . . 877 Wenhui Zhang, Weifeng Kong, Song Zhao, Changhe Wei, Zhidong Qin, Jihong Liu, Ruzhi Qi, and Hailong Wang Study on Electromechanical Performance of Factory-Composited Cap and Pin Ceramic and Glass Insulators . . . . . . . . . . . . . . . . . . . . . . 886 Hu Zhang, Wenhua Wu, Rui Zhang, Jinxiang Liang, Yujia Gong, Lei Yang, and Sida Xu Model Simulation of Lithium-Sulfur Battery Based on Different Discharge Rates and Sulfur Content . . . . . . . . . . . . . . . . . . . . . . . . . . . 897 Yangyang Liu, Chenglin Liao, and Wenjie Zhang Influence of Electromagnetic Launch Rail Structure on Current Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906 Yifan Ge, Shihong Qin, and Lixue Chen Ride Through Strategy of Doubly-Fed Pumped Storage Generator-Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917 Yu Zhang, Yutian Sun, Shumei Cui, Jinming Hu, and Jiahong Liu Fast Neutral-Point Balance and Zero-Sequence Circulation Suppression for a T-Type Three-Level Inverter Parallel System . . . . . . 926 Tianyu Yue, Alian Chen, Zhiyuan Chen, Qicai Ren, Nan Wang, and Tong Liu Platform Software Scheme Based on SoftPLC Technology for New Generation of Autonomous and Controllable Protection and Measuring-Control Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936 Bei Dong, Yao Zhang, Yi Ding, Feng Yue, and Changsong Qin
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Characteristics of High-Frequency Resonance for Long-Distance Offshore Wind Farm Integration via MMC-HVDC System Considering the Distributed Parameter of Submarine Cable . . . . . . . . . 944 Qinghe Li, Hui Li, Hongtao Tan, Jiayao Wang, Zhiting Zhou, and Jie Zheng Interleaved High Step-Down Ratio DC-DC Converter with Coupled Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952 Liying Zhou Numerical Investigations of Electric Vehicle Wireless Charging Systems Under the Interference of Metallic Foreign Objects . . . . . . . . . 964 Jiawei Wang, Jinghui Shao, and Xikui Ma Development of Experimental Platform for Low-Power Photovoltaic Energy Storage Inverter System . . . . . . . . . . . . . . . . . . . . 978 Yiwang Wang, Bo Zhang, Yao Zhang, Xiaogao Chen, Jie Wang, and Jin Zhang Research on Short Circuit Failure Mechanism of Press Pack IGBT Device Based on Al-Si Diffusion Molecular Dynamics Simulation . . . . . 986 Li Hui, Yu Yue, and Yao Ran Maintenance Optimization Strategy of Modular Multilevel Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 Li Liu, Meng Huang, Liangjun Bai, and Min Qiao Transient and Steady-State Parameters of the Synchronous Condenser Based on Field-Circuit-Network Finite Element Method . . . . . . . . . . . . . 1004 Hui Li, Yunzhu Zeng, Jianfu Li, Xiao Wang, Bin Yuan, Renkuan Liu, and Yue Yu Research on the Voltage Balance Ability of Platinum Electrode in Valve Water Cooling System Based on Leakage Current Ripple Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 Zhenyu Li, Bing Gao, Biyue Cao, Yongchao Song, Zhiwei Yu, and Yongxing Zhu Transmission Line Galloping Test System Based on Adaptive Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027 Li Zhang, Jiangjun Ruan, Daochun Huang, Wei Cai, Jian Li, and Zhihui Feng Investigation of Radial Electromagnetic Bearing with Shielding Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036 Zongze Cui, Boyu Wang, Rui Zhang, Hao Wei, Liying Zhang, and Liwei Song
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A Wind Power Scenario Simulation Method Considering Trend and Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043 Xiu Ji, Cong Li, Beimin Xie, Yan Wang, and Qisu Wang Establishment of Time-Domain Mathematical Model of Suspension Force for Bearingless Multi-sector Motor Based on Maxwell Stress Tensor Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051 Yuanyang Cheng, Jingpo Shi, and Huifeng Cui Effect of Cold Sintering Process on Performance of Tantalum Doped Lithium Lanthanum Zirconium Oxygen (Li6.4La3Zr1.4Ta0.6O12) Solid Electrolyte . . . . . . . . . . . . . . . . . . 1059 Yang Yang, Shenglin Kang, Jie Liang, Jiexin Zhang, Xuetong Zhao, Lijun Yang, and Ruijin Liao Early Stage of Bubble Dynamics via Electrical Explosion in Water . . . . 1067 Yuchen Cao, Ruoyu Han, Chen Li, Wei Yuan, and Rui Liu The Evaluation of Electric Power Emergency Plan Exercise Based on EMD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075 Yongchao Song, Zhenyu Li, Zhiwei Yu, Biyue Cao, and Yongxing Zhu Stability Enhancement Strategy for Low-Voltage Multi-terminal DC System Using MPC Based Additional Control . . . . . . . . . . . . . . . . . . . . 1089 Ying Zhuang, Wei Pei, and Wei Deng Research on Fast Location Method of Fault Line Based on Intelligent Power Emergency Plan Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1100 Zhenyu Li, Biyue Cao, Jianping Gong, Yongchao Song, Zhiwei Yu, and Yongxing Zhu Design of Active Power Control Parameters Based on Real-Time Rain-Flow Counting Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115 Ziqi Liu, Tao Xu, and Feng Gao Oscillation Suppression Strategy of MMC-HVDC in Weak AC Grid . . . 1122 Hui Fang, Youqiang Zhang, Ke Zhao, Shengyi Zhu, Zhongkai Ning, and Cheng Wang Research on Hybrid Control Strategy of PMSM-IM Dual Motor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131 Tao Liu and Heping Wang Design and Research of Swinging Magnetic Field System Suitable for Biological Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142 Fan Feng and Jiansheng Xu Research on Design Method of Radial Magnetized Linear Voice Coil Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1150 Lei Yang, Yuan-zi Zhou, Zhun Li, and Qian Wu
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Application Analysis of New Type of Soft Magnet in High Speed and Low Loss Permanent Magnet Motor . . . . . . . . . . . . . . . . . . . . . . . . 1157 Yixuan Song, Xusheng Wu, and Wei Gao Electric Vehicle Charging Strategy Based on Nonlinear Droop Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1168 Erhao Su, Zhipeng Lv, and Yang Shan Single Carrier Three Mode Modulation Method of Four Switch Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177 Hongyu Li, Wei Wang, Fen Tang, Xuezhi Wu, and Yubo Yuan Research Progress of High-Performance Graphene Electromagnetic Shielding Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185 Lei Hou and Xue Ding Multi-stage AC Low-Temperature Heating Strategy for Lithium-Ion Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1193 Xuenan Zhang, Wei Shi, Tian Han, and Yangmei Zhao Prediction of Health Status and Fault of Electrical Equipment Based on the Concept of Digital Twin . . . . . . . . . . . . . . . . . . . . . . . . . . 1200 Xuan Yu, Jinkui Huang, Shipeng Liu, Guanghui Lu, and Jiansheng Yuan Traveling Wave Protection of Medium Voltage DC Distribution Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1208 Songfang Jiang, Jun Liang, Kewen Wang, Jian Chen, Mengru Chen, and Jiatong Yu Harmonic Suppression of Charging Station Based on Harmonic Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216 Jian Chen, Jun Liang, Kewen Wang, Songfang Jiang, Mengru Chen, and Jiatong Yu Review of Transmission Line Icing and Anti-icing Technologies . . . . . . 1224 Qingyuan Zhao, Zhendong Liu, Peng Yu, Liang Chen, and Feng Guan Current Transformer Excitation Current Calculation Method and Current Wave Characteristics Analysis . . . . . . . . . . . . . . . . . . . . . . 1233 Hongsen You, Yuan Chi, Dapeng Duan, Cheng Zhao, Weiqiong Song, Fengming Lv, Jinjun Xie, and Jiansheng Yuan Summary of Research on Control Technology of Pulsed Power Supply in Electromagnetic Launch System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1242 Hongyan Sun, Wanyu Liu, and Kun Liu Review on Application of Infrared Detection Technology in State Detection of Electrical Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254 Songlin Cong, Haitao Pu, and Fuqiang Yao
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Review of Wind Power Grid Connection Technology . . . . . . . . . . . . . . . 1262 Yanfang Zhao, Haitao Pu, and Fuqiang Yao Mathematical Model and Working Characteristics Analysis of Alkaline Electrolyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1270 Jiarui Wang, Dexin Li, Jiajun Zhang, Guanqun Zhuang, and Song Gao Overview of Research on SiC Power Devices . . . . . . . . . . . . . . . . . . . . . 1278 Sisi Li, Yaozong Liu, Peichang Yu, and Zhiqi Liu Experimental Study on the Effect of the Stress on the Magnetic Field of the Submarine Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1292 Guohua Zhou, Kena Wu, Yuelin Liu, Kaisong Wang, and Yufen Wang Structural Optimization Design of Rotor Magnet of Large High Temperature Superconducting Condenser . . . . . . . . . . . . . . . . . . . . . . . 1302 Zhengjun Shi, Song Meng, and Wenxu Liu Electromagnetic Performance of the Nickel-Iron Alloy in High Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1311 Shengming Zhou, Jian Zhao, Hua Zhou, Boping Su, and Jianqiang Wei Study on the Influence of Skin Effect on AC Loss of YBCO Tape . . . . . 1317 Ying Xu, Hong Xie, Zhining Lv, Zhenzi Wang, Zhe Wang, Bangzhu Wang, and Shaotao Dai Simulation and Comparative Analysis of Permanent Magnet Motor with Rectangular-Wire and Circular-Wire . . . . . . . . . . . . . . . . . . . . . . . 1326 Guanglong Jia, Ming Jing, Yeliu Xu, and Fengge Zhang A Power Distribution Control Strategy for the Cascaded H-Bridge Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1334 Tong Yu, Fanqiang Gao, and Zhixuan Gao Research on a New Intelligent Transformer Integrating SVG and DVR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345 Xi Wan, Wenqin Lu, Bo Xue, Han Yan, and Jianhua Wang Open-Circuit Fault Diagnosis of Quasi-Z-Source Inverter Based on Cloud Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1353 Jifang Li, Huishan Guo, Mengbo Guo, and Genxu Li Real-Time Demand Response Interactive Behavior Model of Electric Vehicle Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1362 Ye Yong, Yin Zhou, and Xiaobo Mao Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1373
Coupling Analysis of Transient Electromagnetic Field and Temperature Field in Electromagnetic Launch Rail Yifan Ge1 , Shihong Qin1 , and Lixue Chen2(B) 1 Wuhan Institute of Technology, Wuhan 430200, China 2 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. In the launching process of railgun, the performance degradation caused by local overheating will seriously affect the life of electromagnetic launch rail and launching efficiency. In this paper, a two-dimensional dynamic finite element model of railgun is established to analyze the distribution of rail current and temperature under different driving current and continuous firing frequency. The results show that during the launching process, the current is concentrated on the inner edge of the rail, and the penetration depth is about 1–2 mm. The highest temperature of the rail appears near the end of the current rising edge, and the temperature near the gun tail is higher. Under the case of continuous emission, the change of material properties caused by temperature rise has a great influence on the results. In this paper, the electromagnetic thermal coupling calculation method is used, which can provide a reference for the optimal design of the rail. Keywords: Railgun · Temperature field · Coupling analysis · Current distribution
1 Introduction Electromagnetic rail launch is a launch technology that generates electromagnetic force under the influence of pulse current to accelerate objects to ultra-high speed [1]. One of the main technical bottlenecks of electromagnetic rail launch is the overheating of rail and armature. The prediction of electromagnetic launch speed requires accurate simulation of electric heating [2]. In the case of continuous launch of electromagnetic gun, temperature is the main constraint on continuous launch performance. The research on electromagnetic thermal coupling of railgun is of great significance to the design of it. Scholars have carried out relevant researches on the heating phenomenon of railgun. Kerrisk et al. Was one of the first scholars to study the heating and temperature field of railgun. He applied the finite difference method to calculate the rail and armature temperature distribution [3]. Powell et al. Conducted coupling analysis of two-dimensional © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1–11, 2022. https://doi.org/10.1007/978-981-19-1870-4_1
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rail electromagnetic field and temperature field [4]. S. Fish et al. Measured the rail temperature distribution under continuous launch through thermocouples, and the results showed that the inside of the rail temperature was higher [5]. Gao Bo et al. Calculated and compared the temperature of common C-type armature and saddle C-type armature under multi field coupling situation [6]. Li Bai et al. Established the calculation model of armature melting characteristics considering the influence of roughness of armature-rail interface [7]. Chen Lixue et al. Studied the armature erosion in the rising edge stage of current during the launch of railgun. The simulation results show that the current is concentrated on the edge of armature tail wing [7]. The existing research mainly focuses on the heat transfer analysis of the armature-rail interface and the design of armature temperature constraints, and there is relatively little research on the rail temperature distribution in the transient process. Based on COMSOL multipysics finite element analysis software, a two-dimensional dynamic model on the transverse and longitudinal sections of the railgun rail is established. Considering the influence of velocity term, the rail transient temperature rise process under single launch and continuous launch is calculated, and the temperature rise calculation results of Joule heat and friction heat under electromagnetic thermal coupling are given, Combining the section results, the heat distribution characteristics under three-dimensional motion are reflected, which provides a reference for rail optimization and design.
2 Theoretical Analysis of Electrothermal Coupling of Railgun 2.1 Electrothermal Coupling Equation Figure 1 is the schematic diagram of railgun model. Electromagnetic railgun is a typical magnetic quasi-static field. Ignoring ∂D/∂T, it can be obtained from Maxwell’s equations and Ohm’s law.
Fig. 1. Schematic diagram of railgun model
Coupling Analysis of Transient Electromagnetic Field and Temperature Field
∂B ∂t
(1)
= J
(2)
=− ∇ ×E ∇×
B μ
3
+ v × B J = σ E
(3)
E is the current density, magnetic induction intensity and electric field intenWhere J , B, sity respectively, and μ, v, σ is the permeability, relative motion speed and conductivity respectively. − → Vector magnetic potential A and scalar potential ϕ are introduced =∇ ×A B
(4)
= −∇ϕ − ∂ A E ∂t
(5)
The electromagnetic field equations can be obtained − σ μv × ∇ × A = −σ μ∇ϕ σ μ ∂∂tA − ∇ × ∇ × A ∂A ∇ × σ (v × ∇ × A − ∇ϕ − ) = 0
(6)
∂t
The heat transfer equation can be obtained from Fourier theorem − →2 J ∂T ∂T → + ρ− vC = ∇ · (κ∇T ) + ρC ∂t ∂t σ
(7)
Where κ, σ, C are thermal conductivity, conductivity and specific heat respectively, and T , ρ, t are temperature, density and time respectively. 2.2 Source of Thermal Load During the launching process of railgun, the current is millisecond pulse and the armature moves at high speed. And friction heat is generated on the armature-rail interface. A large amount of Joule heat and friction heat on the rail and armature surface cannot be effectively diffused in a short time [9], and local high temperature is formed on the surface. When the excessive temperature reaches or exceeds the melting point of the material, or even reaches the boiling point, serious melting or ablation occurs at the armature-rail interface, resulting in irreversible damage to the surface of the guide rail. The incomplete contact between rail and armature at micro level forms contact thermal resistance. The contact points between the contact surfaces lead to excessive current concentration [10], so the local heat and local temperature of the contact points are high in the process of heat transfer.
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The heat generation of rail resistance during launch can be expressed as: Q1 = ∫tt21 i2 Rg dt
(8)
For the armature-rail interface of ultra-high speed sliding electrical contact, the work done by friction is converted into heat, so the sliding friction heat of armature-rail interface can be expressed as: 1 Q2 = ∫tt21 μ v( i2 L cosα + N )dt 2
(9)
For the imperfect contact state, the contact resistance heat generation at the armaturerail interface is: Q3 = ∫tt21 i2 Rc dt
(10)
3 Simulation Model and Parameters 3.1 Simulation Model In the simulation model, the rail length is 2 m, the rail size is 20 mm × 40 mm, the caliber is 40 mm, the armature is an ordinary C-type armature, and the length is 30 mm. In this paper, the X-Y section and Y-Z section of the model are taken for two-dimensional calculation respectively, Fig. 2 are the calculation models of two sections respectively, the Y-Z section adopts the 1/4 calculation model, and the shadow intersection part is the Y-Z section of the railgun.
Fig. 2. X-Y and Y-Z section model of railgun
The physical field interfaces such as magnetic field, solid heat transfer and moving grid in COMSOL multipysics finite element analysis software are used to calculate the model, and the current distribution and temperature distribution on the railgun section are obtained.
Coupling Analysis of Transient Electromagnetic Field and Temperature Field
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3.2 Relevant Material Parameters and Inputs In the simulation, rail adopts pure copper rail and the armature adopts pure aluminum armature. Table 1 and Table 2 are the material parameters of rail and armature, among which the parameters related to temperature are conductivity, constant pressure heat capacity and heat transfer coefficient. Table 1. Rail material parameters Parameter
Value
Unit
C κ ρ σ
360 + 0.1T 412–0.0787T 8900.0 1/(−0.24.596 + 0.671T)
J/(kg·K) W/(m·K) kg/m3 MS/m
Table 2. Armature material parameters Parameter
Value
Unit
C κ ρ σ
766 + 0.486T 257–0.0695T 2700.0 1/(−6.837 + 0.114T)
J/(kg·K) W/(m·K) kg/m3 MS/m
In this paper, the following assumptions are made for the calculation of heat distribution. 1) The sliding friction coefficient between armature and rail is a constant value of 0.05; 2) The contact resistance between armature and rail is a constant value of 0.5 m; 3) The sliding friction heat and contact resistance Joule heat on the X-Y section are transmitted to the rail and armature in the form of line heat source.
4 Temperature Distribution Under Different Driving Currents Input three driving currents with the same flat edge time (0.15 ms) and amplitude (500 ka), different rising edge time (0.3 ms, 0.5 ms, 0.7 ms), as shown in the figure below (Fig. 3).
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Fig. 3. Driving current waveform
4.1 Simulation Results of X-Y Section After calculation by COMSOL mlutipysics finite element calculation software, the simulation results are shown as follows. From the Fig. 4, we can observe the relatively uniform magnetic diffusion phenomenon in the rail and armature when the armature speed is low at the initial stage. With the continuous increase of armature speed, The velocity skin effect is becoming more and more obvious, and the current is concentrated on the inner edge of the rail.
Fig. 4. Current density of X-Y section at different time
Fig. 5. Maximum temperature change of X-Y section railgun
Coupling Analysis of Transient Electromagnetic Field and Temperature Field
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Figure 5 is the diagram of the maximum rail temperature at each time under different driving currents during a single launch. It can be seen from the curve that the maximum temperatures under three driving currents are 429 k, 442 k and 461 K respectively. None of them has reached the melting point of copper (1376 k) and has a similar temperature change trend. In the rising edge stage of driving current, the maximum rail temperature rises rapidly, After the rising edge, the maximum temperature of the rail rises slowly. In the initial stage of launch, the armature speed is low and the current rises rapidly. The area swept by the armature is only part of the initial stage. The friction heat and contact resistance Joule heat generated during this period are relatively concentrated, resulting in the maximum value in the initial stage. Subsequently, with the decrease of input current, the heating of the two decreases, the armature speed increases, and the contact time with the rail decreases, resulting in less subsequent heating. The maximum rail temperature appears at the beginning of armature movement, and changes rapidly at the rising edge stage. After the rising edge, it rises very slowly under the action of Joule heat of rail resistance. The temperature rise presents a gradient distribution along the rail, and the temperature rise gradually decreases from the tail to the muzzle. The initial stage of armature movement, that is, the tail is the area with the highest temperature rise of railgun, which is the key of thermal management. Figure 6 shows the temperature distribution of the rail at 1m under the action of driving current 3 at 2 ms, Combined with the two figures, it can be observed that the heat of the rail is concentrated on the rail surface, the speed skin effect causes the current to concentrate on the inner edge of the rail, and the Joule heat inside the rail is negligible compared with the Joule heat of the edge, At the same time, the launching time of the railgun is very short, the heat diffusion time in the launching process is short, and the heat is distributed at 1–2 mm on the rail surface.
Fig. 6. Rail temperature distribution at 2 ms
4.2 Simulation Results of Y-Z Section Figure 7 (a)–(d) shows the current distribution of Y-Z section at t = 0.2, 0.5, 1 and 2 ms under the influence of driving current 2. Due to the skin effect caused by the rising edge, the current is distributed around the rail, and the inner and outer edges and corners are relatively concentrated. The velocity skin effect makes the current at the inner edges and corners of the rail more concentrated, with a maximum of 11.2 GA/m2 . Over time,
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the current diffuses inward from the side and top of the rail, and the current becomes relatively uniform in the rail. Current density
(a)t=0.2ms
(b)t=0.5ms
(c)t=1ms
(d)t=2ms
Fig. 7. Current density of Y-Z section at different time
Figure 8 (a) - (d) shows the temperature change of Y-Z section at t = 0.2, 0.5, 1 and 2 ms under the influence of driving current 2. As can be seen from Fig. 8, the rail generates Joule heat under the action of current, and the temperature gradually increases.Moreover, due to the skin effect, the heat is concentrated on the inner and outer edges. Due to the velocity skin effect, the current on the inner edge is concentrated, and the temperature on the inner edge is significantly higher than that on the outer side. The heat is slowly transmitted to the interior of the rail over time, and its distribution is similar to the current density distribution. The diffusion of heat obviously lags behind the diffusion process of current, and the maximum temperature at 2 ms is 320 K. It can be seen from the comparison, The Joule heat generated by the resistance of the rail itself accounts for less of the source of rail heat. Temperature
(a)t=0.2ms
(b)t=0.5ms
(c)t=1ms
(d)t=2ms
Fig. 8. Temperature of Y-Z section at different time
Coupling Analysis of Transient Electromagnetic Field and Temperature Field
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5 Rail Temperature Change During Continuous Launch Temperature is the main limiting factor of continuous emission performance. The railgun is fired continuously, and the driving current 1 is applied for electromagnetic thermal coupling calculation. Only heat transfer calculation is carried out in the launch gap, and the heat transfer process is divided into two parts. On the one hand, it is the natural diffusion process of the heat accumulated in the rail in the launch process from the surface to the inside, and on the other hand, it is the natural cooling process of the rail in the air, in which the heat transfer coefficient is set to 10 W/(m2 °C). Figure 9 (a) shows when continuous firing, the highest temperature change of the rail under 6 launches per minute. It can be seen from the figure that in the case of 6 launches per minute, the temperature at the last firing is 571 K. During the cooling process, the temperature gradient is large at the initial stage and decreases rapidly, and the temperature change behind is relatively gentle. The thermal conductivity of the copper rail is excellent, and the diffusion of heat in the rail is the dominant process, After the inward diffusion gradually reaches the steady state, air heat transfer is dominant, but natural cooling can not effectively reduce the rail temperature, and external forced cooling is required. In the process of continuous firing, the rising temperature of firing decreases continuously. When the second firing is out of the chamber, the temperature rises by 45 k compared with the first firing, and the last temperature rise falls to 22 K. During the continuous launching of the railgun, on the one hand, the heat of the continuous launching rail is continuously accumulated, the temperature difference between the inside and outside of the rail increases each time, and the heat conduction rate is accelerated. On the other hand, under the condition of electromagnetic thermal coupling, rail resistivity increases with the increase of temperature, The current distribution is relatively uniform, which reduces the rise of rail temperature in the next launch. The combined action of the two leads to the decrease of temperature rise in each launch. Figure 9 (b) shows the maximum temperature change of the railgun under the conditions of coupling and uncoupling of material properties and temperature at 60 shots per min. Under the coupling condition, the maximum temperature after 6 shots is 605 k, which is 34 k higher than the maximum temperature under 6 shots per min. Under the electrothermal uncoupled condition of the same firing speed, the maximum temperature after 6 shots is 649 k, with an error of 7%.
Fig. 9. Maximum temperature change of rail under different firing frequency
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By adjusting the heat dissipation time, the railgun is calculated under two shots. Figure 9 (c) shows the change of the maximum temperature of the rail gun launched again after 110 s of heat dissipation. After the second launch, the maximum temperature of the rail rises to 461 K, which is the same as the maximum temperature of the first launch, then the calculation model can carry out one shot of non-stop launch every 110 s. In the uncoupled calculation, the temperature rise amplitude is the same every time, The rail needs to be cooled to room temperature, and the cooling time is obviously longer. Therefore, it is of great significance to carry out electrothermal coupling calculation under the condition of continuous firing of railgun.
6 Conclusion In the launching process of railgun, the heat accumulates rapidly in rail and armature, which makes the local temperature rise rapidly, resulting in material softening, melting and even gasification, which has an adverse impact on the life, launching efficiency and structural safety of railgun. The acquisition of the temporal and spatial distribution and evolution law of the temperature of the electromagnetic railgun is of great significance to the rail optimization design. In the calculation model of this paper, the high-speed motion conditions of armature and rail are considered. The numerical simulation of launching process is carried out through the coupling of transient electromagnetic field and temperature field in twodimensional sections of X-Y and Y-Z, and the space-time distribution of temperature driven by current with the same amplitude and different rising edges is obtained. The main conclusion are as follows: 1) During launching, the rail temperature rise mainly occurs on a section of rail around the end of the rising edge of the driving current and close to gun tail, which is the key position for rail thermal management of the railgun. 2) The high temperature area inside the rail is distributed on the inner rail edge, and only penetrates to a depth of about 1–2 mm. 3) In the case of continuous firing of railgun, forced cooling is required, and the temperature changes frequently during continuous firing. In order to obtain the accurate temperature distribution of railgun, it is of great significance to use electrothermal coupling calculation.
References 1. Ma, W., Xiao, F., Nie, S.: Applications and development of power electronics in electromagnetic launch system. Trans. China Electrotech. Soc. 31(19), 1–10 (2016). (in Chinese) 2. Li, J., Yan, P., Yuan, W.: Electromagnetic gun technology and its development. High Volt. Eng. 40(4), 1052–1064 (2014). (in Chinese) 3. Kerrisk, J.F.: Electrical and thermal modeling of railguns. IEEE Trans. Magn. 20(2), 399–402 (1984) 4. Powell, J.D., Zielinski, A.E.: Ohmic heating in a double-taper sabot-armature. IEEE Trans. Magn. 39(1), 153–157 (2003)
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5. Fish, S., Phipps, C., Tang, V.: Rail heating analysis for multishot EM gun operation. IEEE Trans. Magn. 35(1), 398–402 (1999) 6. Gao, B., Qiu, Q., Qie, W.: Multi-field coupling analysis and experimental research on armature of electromagnetic railgun. Trans. China Electrotech. Soc. 35(S2), 341–345 (2020). (in Chinese) 7. Li, B., Lu, J., Sai, T., Jiang, Z., Zhang, Y.: Effect of interfacial roughness of sliding electrical contact on the melting characteristics of armature. Trans. China Electrotech. Soc. 33(07), 1607–1615 (2018). (in Chinese) 8. Chen, L., He, J., Xia, S., et al.: Influence of rail resistivity and rail height on armature edge erosion at current ramp-up in solid armature railgun. High Volt. Eng. 40(04), 1071–1076 (2014). (in Chinese) 9. Bayati M S, Keshtkar: A Novel study of the rail’s geometry in the electromagnetic launcher. IEEE Trans. Plasma Sci., 43(5), 1652–1656 (2015) 10. Ruan, J., Chen, L., Xia, S., et al.: A review of current distribution in electromagnetic railguns. Trans. China Electrotech. Soc. 35(21), 4423–4431 (2014). (in Chinese)
Theoretical Attempts to Optimize the Geometrical Shape of Simple Electromagnetic Rail Launcher Shaohui Chen1,2(B) and Hongyan Sun2 1 Institute Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
[email protected] 2 Beijing Aeronautical Technology Research Center, Beijing 100076, China
Abstract. Inductance gradient, an important parameter that affects the performance of electromagnetic rail launcher, is mainly determined by the geometrical shape of the launcher. This study therefore intends to analyze the influence of the rail’s height and width on the inductance gradient, with the area of the cross-section of the guiding rail fixed. The study finds that the maximum inductance gradient peaks when the guiding rail section is rectangular (i.e., its width is greater than height) under both the high- and low-frequency circumstances. Attempts are also made to establish arithmetic models for forcing and masses of the launch load with a pulsed current. The optimum rail separation is thereupon derived at high- and low-frequency, respectively, to maximize the initial velocity of the effective payload. The results show that the rectangular aperture launcher with rail separation greater than rail height can maximize the initial velocity of payload. Keywords: Inductance gradient · Electromagnetic rail launcher · Geometrical shape · Optimization
1 Introduction Electromagnetic railgun is a new technology that uses extremely high ampere force generated by pulsed large current flows through the rails and armature to accelerate the armature and payload to thousands of meters per second in milliseconds. It boasts of high initial speed, high cost-effectiveness ratio, high security, good controllability and good concealment, harbors great application potential in various fields ranging from military, aerospace to scientific experiment and hence draws wide attention and support from various countries [1–4]. Factors of the electromagnetic rail launcher such as its structure, size, section shape, and material are directly related to its inductance gradient value (i.e., the inductance value of the per unit length rail), which ultimately determines the force on the armature and affects both the muzzle kinetic energy and launch efficiency. The inductance gradient value of the launcher is therefore one of the most important research fields in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 12–23, 2022. https://doi.org/10.1007/978-981-19-1870-4_2
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the electromagnetic rail launch technology, and is mainly approached by analytical or numerical method. Kerrisk [5] studied the case when the magnetic field does not diffuse into the rail and the current is mainly concentrated on the surface of the rail, and gave the analytical formula for high-frequency inductance gradient. Grover et al. [6] studied the case when the magnetic field diffuses into the rail and the current diffuses completely in the rail, and gave the formula for low-frequency inductance gradient under steady state. Batteh et al. [7] proposed an analytical algorithm for inductance gradient of plasma armature electromagnetic rail launcher, which ignores the influence of rail thickness and current diffusion. Based on the skin effect and magnetic energy equivalence principle, Peng Zhiran et al. [8] proposed an analytical expression of inductance gradient considering the influence of both rail size and current diffusion. Xu Rong et al. [9] studied the influence factors of electromagnetic field distribution and inductance gradient of augmented railgun using finite element simulation method; Sun Liqiang et al. [10] used the modeling and simulation method to obtain the rail inductance gradient corresponding to different times in the actual electromagnetic launch process; Ghassemi et al. [11] obtained the inductance gradient versus time curve under a given current through transient field simulation. Keshtka et al. [12, 13] designed the armature and rail model through the finite element software, considered the existence of armature in the inductance gradient analysis, and analyzed the relationship between the rail thickness and width and the inductance gradient. Finally, it is concluded that the inductance gradient is greatly affected by the separation, and the inductance gradient increases gradually with the increase of the separation. Li Xiaojiang et al. [14] analyzed the influence of the change of rail geometry on armature muzzle velocity and muzzle kinetic energy, and thereupon optimized the rail geometry using genetic algorithm with armature muzzle kinetic energy as the objective function. Wang Zhizeng et al. [15] derived the expression of inductance gradient under two-dimensional transient condition from the perspective of magnetic energy, and obtained the diffusion behavior of electromagnetic field in rail through solving the magnetic field control expression. The aforementioned studies have deepened our understanding of inductance gradient in both theoretical and numerical simulation approaches. But their efforts to optimize the geometric dimension of electromagnetic rail launcher were not geared to maximize the initial velocity of effective payload consisting of armature and payload. This study aims to maximize the initial velocity of payload through the construction of a mathematical model of launch load force and mass based on inductance gradient theory, and hence to optimize the geometric size of electromagnetic rail launcher.
2 Inductance Gradient Theory The theoretical calculation of inductance gradient of rails can be categorized into highand low-frequency cases. 2.1 High-Frequency Inductance Gradient High-frequency inductance gradient refers to cases when the magnetic field cannot diffuse to the depth of the rail but only flow along the surface of the rail. Kerrisk calculated
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the current distribution in the rectangular rail of the square aperture rail launcher, and proposed an algebraic method to calculate the high-frequency inductance gradient (as shown in Fig. 1), which is known as “Kerrisk L” (unit is μH /m) [5]:
L = [A + B ln(F1 )] ln(F2 )
(1)
Where: F1 = 1 + A1 (w/h) + A2 (w/h)(s/h) F2 = B1 + B2 (s/h) + B3 (w/h) + B4 (s/h)(w/h) A = 0.4406 B = − 0.0777 A1 = 3.397 A2 = − 0.06603 B1 = 1.0077 B2 = 2.7437 B3 = 0.02209 B4 = 0.2637 w is the rail width, h is the rail height, and s is the separation.
Fig. 1. Rails’ cross-section: h-height, w-width, and s-separation.
2.2 Low-Frequency Inductance Gradient When the current density is evenly distributed in the rail, the inductance gradient can be considered of low-frequency. Grover proposed a simple algebraic method to calculate the low-frequency inductance gradient of the rectangular rail (see Fig. 1), as is shown below (unit is μH /m) [6]: s+w (2) + 1.5 + ln(k) L = 0.4 ln h+w where ln(k) is obtained by looking up the table according to s/h and w/h.
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2.3 Influence of the Tail Section Size on Inductance Gradient From formulas (1) and (2), the main factors affecting the inductance gradient of rectangular rail are the rail width, height and separation, in which the rail width and height determine the cross-sectional area of rail and basically determine the carrying capacity of rail. This paper assumes that the cross-sectional area of the rail is a fixed value of 450 mm2 , with the height of the rail varying between 5 mm–30 mm and the width between 90 mm–15 mm. Figures 2, 3 and 4 show the variation of high- and low-frequency inductance gradients with, respectively, rail height, width and w/h ratio when the separation is 30 mm. Both high- and low-frequency inductance gradients show increases followed by decreases with increasing rail height and width, though at different variation amplitudes. When the maximum of high-frequency inductance gradient is 0.5845 µH the height and width of the rail are 10.9 mm and 41.3 mm respectively, and the w/h value is 3.79. While when the maximum of low-frequency inductance gradient is 0.7274 µH the height and width of the rail are 11 mm and 40.9 mm respectively, and the w/h value is 3.72. It can be seen that under the assumption that the rail cross-sectional area is a fixed value, the inductance gradient is large when the rail cross-section is rectangular (i.e., width is greater than height). The differences are small in the rail height, width and w/h ratio between maximum high- and low-frequency inductance gradients. In other words, no significant differences exist for the inductance gradient calculations from the design point of view, be it of high- or low-frequency cases.
Fig. 2. Variation of the inductance gradient with the rail height
Fig. 3. Variation of the inductance gradient with the rail width
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Fig. 4. Variation of the inductance gradient with w/h
2.4 Influence of Separation on Inductance Gradient Figure 5 shows the variation of high- and low-frequency inductance gradient with separation when the rail height is set at 11 mm and the width 40.9 mm. The variation trend of high-frequency and low-frequency inductance gradient with separation is basically the same. The inductance gradient increases with the increase in the separation. The inductance gradient increases faster when the separation is narrow than wide separation.
Fig. 5. Variation of the inductance gradient with the separation of the rails
3 Mathematical Model of Launch Load The electromagnetic rail launch requires the electromagnetic force on the launch load to be directly proportional to the inductance gradient and square of the current. As the electromagnetic thrust increases with inductance gradient under the equivalent current waveform, the widening in the separation will lead to increase in the effective inductance gradient. For the electromagnetic rail launcher, however, the widening in the separation also leads to increases in the volume and mass of the launch load consisting of effective payload and armature, and hence may not always result in a maximum muzzle velocity of the payload. Separation A mathematical model considering both forcing and the mass of the launch load is therefore needed for the optimal separation to achieve the maximum muzzle velocity of payload.
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3.1 Mathematical Model of Forcing on the Launch Load A schematic map of the armature structure is shown in Fig. 6, and its force-bearing scenario is shown in Fig. 7, having ignored the air resistance, viscous resistance, ablation resistance and other factors and highlighted the effect on the armature by the electromagnetic force, rail pressure and friction. The payload is hence mainly affected by the thrust of armature and the friction of rail.
Fig. 6. The armature diagram
In Fig. 6, d0 represents the tail root thickness, d 1 the tail length, d 2 the tail end thickness, and θ the inclination angle of the tail wing. The constraint relationship between the parameters is: d0 = d2 + d1 tan θ
(3)
Among them, the electromagnetic force F acting on the side tail of the armature is given by (4):
L I 2 d1 · F= 2 X
(4)
Where X is the armature width in the x direction, with its value equivalent to the separation s. In Fig. 7, the tail wing on one side of the armature is subjected to the mechanical interference, F C, electromagnetic component, F cos θ , and tail pressure on the rail in the x direction, F r, all three summing up to zero if we assume no relative movement of the rail and armature tail in the direction during the launch. In the z direction, otherwise, the tail wings on both sides of the armature are subjected to friction, 2ƒ1 , while the armature head is subjected to electromagnetic force, L I 2 2. Meanwhile, the two sides of the payload are subjected to friction 2ƒ2 . The combination of all three forces result in the acceleration of the launch load along the z direction. The friction force on one side of the armature tail can be determined by applying Eq. (4) as follows: f1 = μ1 (FC + F cos θ) L I 2 d1 = μ1 FC + cos θ 2X where μ1 is the dynamic friction coefficient.
(5)
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Fig. 7. Cross section of the launch load
Considering X = s, the resultant force of launch load in the z direction is:
L I2 − 2f1 − 2f2 2 L I2 L I 2 d1 − 2μ1 FC + cos θ − 2f2 = 2 2X 1 μ1 d1 − cos θ − 2(μ1 FC + f2 ) =L I 2 2 s
FA =
(6)
in which the friction force 2ƒ2 on the payload is assumed to be a fixed value. 3.2 Mathematical Model of Launch Load Mass The launch load is composed of payload and armature. The mass and muzzle velocity of the payload are generally determined by the launch mission. It can be assumed that its mass does not change with the calibre. The armature mass is mainly composed of the mass of the tail wings on both sides and that of the head (Fig. 8). The armature tail wings are mainly used to ensure good contact between the armature and the rail, channel the current on the rail into the armature, or into the rail. It can be considered that its mass does not change with the separation, but changes in proportion with the height of the rail. Driven by the electromagnetic force, the armature head directly accelerates the movement of the effective payload. The payload mass thus not only has a certain structural strength, but also carries the expected current, hence is expressed as follows: M = m0 + ma = m0 + 2mtail + mtop = m0 + 2τ (h − 2h) + ρsc(h − 2h)
(7)
Where, m0 is the payload mass, mtail the mass of the armature tail on one side, mtop the mass of the armature head, τ is a constant, h − 2h the armature height, h the gap between one side of the armature and the insulating support, ρ the armature material density, s the separation, and c the armature head thickness.
4 Discussion on the Optimal Separation In the process of electromagnetic rail launch, the payload, consisting of the payload and armature, accelerates as a whole with the armature thrust. The payload, armature and
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Fig. 8. Bird’s view of the armature and rails
launch load have the same speed and acceleration, with the speed expressed as: FA dt v = adt = M
(8)
The separation corresponding to the maximum speed can be obtained by equating the derivative of s in formula (8) to zero. That is:
∂ FA M ∂v = dt = 0 ∂s ∂s (9)
∂ FMA =0 ⇒ ∂s 4.1 The Optimal Separation at High-Frequency The payload acceleration at high-frequency can be obtained from Eqs. (1), (6) and (7): ah = =
FA M
[A + B ln(F1 )] ln(F2 )I 2
1 2
−
μ1 d1 s
cos θ
m0 + 2τ (h − 2h) + ρsc(h − 2h) 2(μ1 FC + f2 ) m0 + 2τ (h − 2h) + ρsc(h − 2h)
−
(10)
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The optimum separation can be obtained by calculating the derivative of the rails’ (s) and equating it to zero at high-frequency: [A + B ln(F1 )] ln(F2 )I 2 K − M2 2ρc(μ1 FC + f2 )(h − 2h) =0 M2
(11)
Where, K=
μ1 d1 M cos θ ρc(h − 2h) μ1 d1 ρc(h − 2h) cos θ + − s2 2 s M = m0 + 2τ (h − 2h) + ρsc(h − 2h)
The application of the equation can be exemplified by a specific case. Suppose the discharge current is a pulsed current (Fig. 9) with the peak value being 200 kA, and the current rising and falling at, respectively, 4 × 108 and −8 × 107 A/s. Other input parameters are set as below, with the sectional area of the rail as 450 mm2 , the kinetic friction coefficient 0.04, the length and inclination angle of the tail wing 16 mm and 0.23 rad, respectively, the interference pressure of the armature 1000 N, the friction force on one side of the payload 100 N, the armature head 5.5 mm in thickness, the spacing between the armature and the insulating support as 2 mm, the payload mass as 12g, τ 0.167 g/mm, and the density of the aluminum armature material as 2.7 × 10−3 g/mm3 .
Fig. 9. Variation of the current with time at high-frequency
In the aforementioned case, the variations of the muzzle velocity and separation are studied under five different conditions, i.e., muzzle separation when the rail height is 14 mm, 18 mm, 22 mm, 26 mm and 30 mm, respectively (Fig. 10). Correspondingly, the maximum muzzle velocity is 1181.97 m/s, 973.50 m/s, 817.04 m/s, 695.78 m/s and 599.69 m/s respectively, the separation 66mm, 60mm, 57mm, 55mm and 55 mm respectively, and the corresponding launch load mass 25.14 g, 29.15 g, 33.25 g and 37.32 g and 41.92 g, respectively. Hence the optimal separation decreases with the increase in the rail height, and the separation is always greater than the rail height. This implies that, the muzzle velocity is the largest when generated by a launcher of rectangular calibre.
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Fig. 10. Variation of the muzzle velocity with the separation and height of rails at high-frequency
4.2 The Optimal Separation at Low-Frequency The acceleration of the launch load at low-frequency can be yielded from Eqs. (2), (6) and (7) as follows: al = =
FA M
s+w + 1.5 + ln(k) I 2 21 − 0.4 ln h+w
μ1 d1 s
cos θ
m0 + 2τ (h − 2h) + ρsc(h − 2h) 2(μ1 FC + f2 ) − m0 + 2τ (h − 2h) + ρsc(h − 2h)
(12)
When the derivative of the separation, s, is calculated from Eq. (12) and equated to zero, the optimal separation at low-frequency can be expressed as: 0.2I 2 G1 M − 0.2I 2 ρc(h − h)G2 − 2ρc(h − h)(μ1 FC + f2 ) = 0
(13)
Where, s − 2μ1 d1 cos θ s+w μ1 d1 cos θ 2 ln + 3 + 2 ln(k) + G1 = 2 s h+w s(s + w) μ1 d1 cos θ s+w s+w G2 = ln + 1.5 + ln(k) − 2 ln + 3 + 2 ln(k) h+w s h+w M = m0 + 2τ (h − 2h) + ρsc(h − 2h) The same example case as in Sect. 4.1 is adopted here to illustrate the scenarios at lowfrequency conditions. As shown in Fig. 11, when the rail height is set at 14 mm, 18 mm, 22 mm, 26 mm and 30 mm, respectively, the maximum muzzle velocity is 1378.51 m/s, 1148.57 m/s 967.09 m/s, 821.62 m/s and 703.98 m/s, respectively, the separation is 51 mm, 46 mm, 45 mm, 45 mm and 45 mm, respectively, and the corresponding launch load mass is 22.91 g, 26.24 g, 30.04 g, 34.05 g and 38.06 g, respectively. In general, the optimal separation decreases with the increase in the rail height, and the separation is always greater than the rail height, which implies the highest muzzle velocity as generated by a launcher of rectangular calibre.
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Fig. 11. Variation of muzzle velocity with the separation and height of the rails at low-frequency
From the above calculation results, it can be seen that for high-frequency and lowfrequency cases, the variation trend of launch load muzzle velocity with the separation increases first and then decreases, and there is a maximum value. Under the same conditions, the optimal separation at high-frequency is greater than that at low-frequency, and the maximum muzzle velocity at high-frequency is less than that at low-frequency.
5 Conclusions 1) Assuming that the cross-sectional area of the rail is a fixed value, the inductance gradient is the largest when cross section of the rail is rectangular (i.e., width is greater than height) at high-frequency and low-frequency, corresponding to the width-toheight ratio as 3.79 and 3.72, respectively; 2) Under the assumption of pulsed current, both high-frequency and low-frequency muzzle velocities first increase and then decrease with the separation. The optimal separation corresponding to the maximum muzzle velocity decreases with the increase of rail height. The optimal separation at high-frequency is greater than that at low-frequency, and the maximum muzzle velocity at high-frequency is less than that at low-frequency. The maximum muzzle velocity can be obtained for launchers of rectangular calibre (i.e., rail separation is greater than height).
References 1. Li, J., Yan, P., Yuan, W.: Electromagnetic gun technology and its development High Volt. Eng. 40(04), 1052–1064 (2014). (in Chinese) 2. Ma, W., Lu, J.: Electromagnetic launch technology. J. Nation. Univ. Def. Technol. 38(06), 1–5 (2016). (in Chinese) 3. Wang, Y., Xiao, F.: The Principle of Electrical Gun. National University of Defense Technology, BeiJing (1995).(in Chinese) 4. McNab, I.R.: Brief history of the EML symposia: 1980–2018. IEEE Trans. Plasma Sci. 47(5), 2136–2142 (2019). https://doi.org/10.1109/TPS.2018.2885269 5. Kerrisk, J.F.: Current Distribution and Inductance Calculations for Railgun Conductors. Los Alamos National Laboratory, New Mexico, USA (1981)
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6. Grover, F.W.: Inductance Calculations: Working Formulas and Tables. Dover Publications, New York (1962) 7. Batteh, J., Powell, J.: Analysis of plasma arcs in arc-driven rail guns. IEEE Trans. Magn. 20(2), 336–339 (1984) 8. Peng, Z., et al.: Modeling and analysis of time-varying inductance gradient for electromagnetic rail launcher. Trans. China Electrotech. Soc. 35(23), 4843–4851 (2020). (in Chinese) 9. Xun, R., et al.: Simulation and analysis of electromagnetic field for augmented railgun. High Volt. Eng. 40(04), 1065–1070 (2014). (in Chinese) 10. Sun, L., Yuan, W., Yan, P.: Study of rail inductance gradient during EM rail launch based on time-frequency analysis. Adv. Technol. Electr. Eng. Energy 27(02), 38–41 (2008). (in Chinese) 11. Ghassemi, M., Barsi, Y.M., Hamedi, M.H.: Analysis of force distribution acting upon the rails and the armature and prediction of velocity with time in an electromagnetic launcher with new method. IEEE Trans. Magn. 43(1), 132–136 (2007) 12. Keshtkar, A.: Effect of rail dimension on current distribution and inductance gradient. IEEE Trans. Magn. 41(1), 383–386 (2005) 13. Keshtkar, A., Bayati, S., Keshtkar, A.: Derivation of a formula for inductance gradient using intelligent estimation method. IEEE Trans. Magn. 45(1), 305–308 (2009) 14. Li, X., Wang, Z., Wu, H.: Characteristics analysis and optimization design of rail geometry size of electromagnetic railgun. J. Gun Launch Control. 36(02), 54–58 (2015). (in Chinese) 15. Wang, Z., Yuan, W., Yan, P.: Inductance gradient for rail-type electromagnetic launcher under transient conditions. High Volt. Eng. 43(12), 4039–4044 (2017). (in Chinese)
Force Analysis of Armature in Induction Coil Launcher and Design of Double-Layer Armature Lin Yang(B) , Yanming Li, Shasha Wang, Yazhou Zhang, and Chengfei Zheng Beijing Institute of Mechanical Equipment, Beijing 100854, China [email protected]
Abstract. During inductive coil launching, the armature is subjected to axial electromagnetic force to be accelerated and radial electromagnetic force to be compressed. If the armature lacks structural strength, plastic deformation happens and may cause abrasion of launcher bore. Electromagnetic field model coupled with circuit and structural model of single-stage coil launcher are establish. Simulation result of three different materials armature shows the thickness effect on launching performance and gives proper thickness design that meets the armature strength requirement. A new type double-layer armature is proposed and simulated. By properly choose the two layers’ thickness, the armature structure gets strengthened and achieves higher launching velocity and higher convention efficiency. Keywords: Synchronous induction launching · Double-layer armature · Armature material · Coupled simulation
1 Introduction Electromagnetic coil launch is a launch method that uses sequential pulses or alternating currents to generate a changing magnetic field to drive a projectile with a coil or a projectile of magnetic material. The current on the armature in a synchronous induction coil launcher is generated by the synchronous pulse discharge of the drive coil. This kind of launcher has the advantages of a large range of launch load quality, good controllability, no contact and no ablation. It is one of the current research hotspots in the field of electromagnetic launch [1, 2]. As a key component in the synchronous induction coil launcher, many scholars have carried out various studies on the armature because the material and structure of the armature can greatly affect the launch performance. In terms of stress analysis of armature, thin shell theory was used to analyze the elastic bulking of armature under radial and axial non-uniform electromagnetic load in coil launch. This method is mainly applicable to the case of small armature wall thickness [3]; McKinney and finite element method were used to conduct a detailed force analysis on the armature of induction coil gun. Result showed that force distribution of armature was uneven, tail of the armature should be strengthened [4]; The magnetic-structural © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 24–33, 2022. https://doi.org/10.1007/978-981-19-1870-4_3
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coupling model of single-stage synchronous induction coil gun was established and stress distribution of the armature at different moments under the peak current of 17 kA was calculated. A method of strengthening armature by heat treatment was also given [5]. In terms of armature structure, the current-carrying coil armature structure was given and compared with solid armature and coil armature [6]. Optimization of cylindrical armature structure was conducted with the total armature volume as the objective function [7]. The inner tapered armature and stepped armature structure were proposed. Simulation study showed that these kind of armature could improve the magnetic field distribution and increase the launch efficiency [8, 9]. In this paper, the circuit-electromagnetic-structural field coupled simulation model of single-stage synchronous induction coil launcher is established, and the spatial electromagnetic field distribution and the kinematic parameters of the armature are obtained. The stress and deformation of armature under radial electromagnetic force are obtained by coupled filed simulation. The armature thickness is designed to obtain higher speed and efficiency while ensuring the structural strength requirements for different armature materials. A double-layer armature structure with a high strength inner layer and a high electrical conductivity outer layer is proposed; the coupled field simulation model of double-layer armature is established and calculated. The result shows that the launch speed and energy conversion efficiency can be improved when the double-layer material design is reasonably matched.
2 Basic Principle The working principle of synchronous induction coil gun is similar to that of cylindrical linear induction motor. When the magnetic field generated by stator coil changes due to the application of pulse current, induced current is generated on the armature. The magnetic field generated by induced current interacts with the magnetic field of stator coil to generate axial force to push the armature forward [10]. The inductance method is used to analyze the acceleration force of the armature during motion. It is considered that the change rate of energy in the movement is the force, and the magnitude of the force is calculated by calculating the energy gradient in the movement direction [2]. For a single stage synchronous induction coil launcher system, the stored magnetic field energy is determined by the inductance and current of the system, and the total stored energy of the system can be expressed as: Wm =
1 1 Lp Ip2 + Ld Id2 + MIp Id 2 2
(1)
When the energy loss is not considered, the acceleration force acting on the moving direction of the armature is Fp =
dM dWz = Ip Id dx dz
(2)
Where Ip and Id respectively represent the current on the armature and coil, Lp and Ld respectively represent the self-inductance of the armature and coil, M which is the mutual inductance between the armature and the drive.
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The current on the armature is caused by the change of magnetic flux, so the induced current can be expressed as: μ dϕ 1 dH = dA (3) Ip = dt Z Z dt Where Z is the impedance of the armature, H is the magnetic induction intensity, A is the effective area surrounded by the armature, and μ is the permeability.
3 Finite Element Model 3.1 Field-Circuit Coupling Analysis Model Using Maxwell field circuit coupling analysis method, the pulse power system model is established in the external circuit simulation model, and the finite element electromagnetic field modeling of the driving coil and armature is carried out. In this model, the magnetic coupling between the external circuit driving coil and armature needs to be considered. The established simulation model is shown in Fig. 1.
Fig. 1. Electromagnetic simulation model
The simulation model is a two-dimensional axisymmetric model, where the z-axis is the axis of symmetry which is the direction of armature motion. The armature is represented by the gray area, the driving coil is represented by the brown area, the green area is the armature motion area, and the red outer frame is the air domain. Through the calculation of external circuit model and electromagnetic field model, the velocity, displacement and other kinematic parameters of armature in the launch process, as well as the distribution of current, magnetic field and electromagnetic force can be obtained. 3.2 Coupled Analysis of Electromagnetic and Structural Field The finite element model of armature structure analysis is established in the workbench. Through the load transfer between Maxwell and ANSYS Workbench, the electromagnetic force calculated by electromagnetic field is mapped to structural field simulation. It should be noted that the structural field establishes a three-dimensional model with z-direction in the axial direction of the armature, and the spatial location of the armature in the structural field should correspond to the location in the electromagnetic field in order to map the electromagnetic force effectively. In addition, the calculation of the
Force Analysis of Armature in Induction Coil Launcher
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armature strength is performed using static analysis, so the moment of force maximum is chosen for mapping the electromagnetic force. Figure 2 shows the electromagnetic force calculated by the electromagnetic field and the distribution of the electromagnetic force on the armature after mapping. Before mapping, the electromagnetic force is surface force and after mapping it is axis-symmetric body force density.
Fig. 2. EM force before and after Mapping
The boundary conditions are set in the structural analysis model to calculate the stress distribution on the armature structure under the mapped electromagnetic forces, and the result is shown in Fig. 3.
Fig. 3. v-m stress distribution
The armature material chosen for the above calculation is a common 6061 aluminum alloy, and it can be seen from Fig. 3 that the stresses at most locations on the armature are relatively small, with stress concentrations occurring only at the tail of the armature, especially at the inner layer of the tail, where the maximum stress value is 287.12 MPa.
4 Armature Design of Different Materials The maximum stress on the armature in Fig. 3 is greater than the yield strength of the material, and the armature will have plastic deformation, affecting the launch performance, so the armature must be improved. The armature strength can be improved by replacing high-strength material or increasing the armature thickness, but for general aluminum alloy materials, the higher the strength, the lower the conductivity, and the increased thickness of the structure will cause an increase in mass, thus affecting the final launch speed.
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Table 1 shows the parameters of three common aluminum alloy materials, which are widely used as armature materials for electromagnetic launch. Table 1. The parameters of three different aluminum alloys Material name
Density
Conductivity
Yield strength
Young’s modulus
Poisson’s ratio
6061-T6
2700 kg/m3
25.1 MS/m
276 MPa
68.9 GPa
0.33
6101A-T6
2700 kg/m3
33.4 MS/m
193 MPa
68.9 GPa
0.33
7075-T6
2810 kg/m3
19.4 MS/m
503 MPa
71.7 GPa
0.33
Without considering the launch load, the case when only launching the armature is calculated, and the total launch mass is equal to the armature mass. The stress of the armature of three different materials is calculated. Assuming that the shape of the armature structure remains unchanged, the armature stress is ensured to be in a safe range by designing the armature thickness. The maximum electromagnetic forces on the armature of the three materials at different thicknesses are shown in Fig. 4 below.
Fig. 4. Maximum EM acceleration force
It can be seen in Fig. 4 that the electromagnetic force on the armature gradually increases as the thickness increases, but when reaching a certain level, the increase of electromagnetic force is not significant. When armature thickness is the same, the higher the conductivity, the greater the electromagnetic force. Figure 5 shows the calculation results of the maximum armature speed. Different from the results of electromagnetic force, when the armature thickness increases, the maximum speed decreases, mainly because the armature mass increases. The ratio of outlet kinetic energy to capacitor energy storage is taken as the energy conversion efficiency. Figure 6 shows the energy conversion efficiency results of different armature materials and different thickness. As can be seen from the figure, the higher the
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Fig. 5. Maximum speed
armature conductivity, the higher the energy conversion efficiency. When the thickness is small, the energy conversion efficiency increases with the increase of thickness. When the armature thickness reaches a certain value, the energy conversion efficiency fluctuates.
Fig. 6. Convention efficiency of the System
Figure 7 shows the calculated maximum stress of armature with different thickness. According to Table 1 the yield strength of the three materials are 193 Mpa, 276 Mpa and 503 Mpa respectively. Without considering the safety factor, the armature won’t have plastic deformation when the maximum stress is less than the yield strength. The minimum thickness of the armature without plastic deformation for the three materials is calculated to be 18 mm, 11 mm and 2 mm respectively, as shown by the red symbols in Fig. 7. The results on the left side of the red symbols produce stresses that have exceeded the material limits, and the results on the right side correspond to armature stress within the material tolerance range, but according to the results in Fig. 6, the greater the thickness the smaller the velocity, so for the three armature materials, the maximum velocity that can be obtained for a given discharge condition is shown in Table 2.
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Fig. 7. Maximum v-m stress Table 2. Results of different armature materials Material
Minimum thickness
Mass
Speed
Efficiency
Al6101
18 mm
2.8 kg
67.76 m/s
13.12%
Al6061
11 mm
1.83 kg
77.28 m/s
11.15%
Al7075
2 mm
0.38 kg
93.99 m/s
3.38%
It should be noted that for the 7075-T6 material, because of its high strength, the armature thickness of only 2 mm can still meet the strength requirements, and due to the light mass, higher speed can be obtained, but the conversion efficiency of the system is very low, and according to reference [4], when the thickness to diameter ratio of the armature is too small, the armature stiffness and strength can be analyzed according to thin shell theory. When the thickness to diameter ratio is less than 0.0512, the stability cannot be guaranteed. The calculated thickness of armature outer diameter of this paper should not be less than 3 mm. When the thickness is greater than 3 mm, whether the armature can maintain stability under the combined action of radial electromagnetic force and axial electromagnetic force also needs further research.
5 Design and Force Analysis of Double-Layer Armature Through the calculation of single material armature, it is found that the maximum stress of armature mainly occurs in the inner layer of armature tail. A double-layer material armature is designed with higher strength al7075 as inner layer and better conductivity al6061 as outer layer material, so to meet the requirements of high conductivity and high strength of armature at the same time. 5.1 Double-Layer Armature Model A rigid connection between the two layers is formed by mechanical assembly or welding, and the established electromagnetic field model is shown in Fig. 8. Similar to the single
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layer armature model, the surrounding air domain and coordinate axes are not shown in this figure, and the dark gray represents the inner layer armature and the light gray represents the outer layer armature. It should be noted that a separate envelope model should be created outside the two layers, and since the two layers are rigidly connected to each other, it can be assumed that the two layers of the armature move with this envelope model as a whole.
Fig. 8. Simulation model of two-layer armature
The structural field analysis model of the double-layer armature is similar to that of the single-layer armature, with bonding contacts between two layers. 5.2 Double-Layer Armature Design According to the established double-layer armature model, Aluminum 7075 is selected for the inner armature and Aluminum 6101 is selected for the outer armature. The electromagnetic acceleration force curve on the armature after completing the electromagnetic field calculation is shown in the figure below (Fig. 9).
Fig. 9. EM acceleration force of two-layer armature
The solid line is the total acceleration force of the armature, the dash line is the force on the outer armature, and the dot line is the force on the inner armature. It can be seen that the force of the outer armature is much greater than that of the inner armature in both the acceleration stage and the deceleration drag stage, which is related to the conductivity parameters of the inner and outer materials and the thickness setting of the inner and outer layers. The maximum force difference between inner and outer armature is 128
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kN, so the rigid connection between layers must be ensured when using double-layer armature.
Fig. 10. V-m stress of two-layer armature
Mapping the electromagnetic force to the structural field to calculate the force distribution of the double-layer armature, the typical stress distribution of the double-layer armature is shown in Fig. 10. The stresses of the inner and outer armature are still mainly concentrated in the inner part of the tail, and the maximum value of the inner armature stress is greater than the maximum value of the outer armature stress. 5.3 Optimization of Double-Layer Armature Thickness As shown in Fig. 10, the maximum stress of 6101-layer armature is 294.46 Mpa, which is still greater than the material yield strength. The optimization design has been conducted to finally obtain a set of two-layer armature designs without armature yielding, as shown in the table below. The thickness of the inner layer is 2 mm, the thickness of the outer layer is 15 mm, and the total thickness of the armature is 17 mm. Compared with the single layer armature results in the previous section, higher speed and higher energy conversion efficiency can be obtained for double-layer armature (Table 3). Table 3. Comparison of double-layer armature with general armature Structure
Material
Thickness
Mass
Maximum speed
Efficiency
Single layer
Al6101
18mm
2.8kg
67.76m/s
13.12%
Double layer
Al6101
15mm
2.689kg
71.57m/s
14.05%
Al7075
12mm
6 Conclusion Using the circuit-electromagnetic-structural field coupled simulation method, through the analysis of armature of different materials, the following conclusions are obtained: With other conditions constant, the electromagnetic acceleration force on the armature gradually increases as the thickness increases, but when the thickness increases at a
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certain level, the increase in electromagnetic force is not obvious; the maximum speed decreases when the thickness of the armature increases; when the thickness is small, the energy conversion efficiency increases with the thickness, and when the thickness of the armature reaches a certain value, the energy conversion efficiency fluctuates. Given the coil structure and armature shape, for three kinds of aluminum alloy materials, the 7075 armature can theoretically obtain higher speed without plastic deformation, but the armature thickness is too thin, buckling failure may occur, and the energy conversion efficiency is very low; the 6101 armature can obtain high energy conversion efficiency, but the maximum speed of armature is low; A double-layer armature design with an inner layer of high-strength material and an outer layer of high conductivity material is used. When the thicknesses of the inner and outer layers are properly matched, the strength is increased compared to a single material armature, while higher speed and higher efficiency can be obtained.
References 1. Wang, Y., Marshall, R.A., Cheng, S.K.: Physics of Electric Launch. Science Press, Beijing (2004) 2. Wang, Y., Xiao, F.: Principle of Electric Cannon. National Defense Industry Press, Beijing (1995).(in Chinese) 3. Cao, H.J., Chen, J.J., Wang, D.M.: Bucking analysis of coil gun (cylindrical shell). Chinese J. Appl. Mech. 15(4), 40–45 (1998). (in Chinese) 4. Zhang, C.W., Li, Z.Y., Chen, F.B., Jiang, G.C.: Analysis of the force acting on the armature in induction coil gun. High Volt. Eng. 31(12), 32–34 (2005). (in Chinese) 5. Zou, B.G., Cao, Y.J., Wu, J., Wang, H., Chen, X.: Magnetic-structural coupling analysis of armature in induction coil gun. IEEE Trans. Plasma Sci. 39(1), 65–70 (2011) 6. Jin, H.J., Cao, Y.J., Wang, C.X., Wang, H.J.: Comparison of system characteristics between current and induction armature in electromagnetic coil launcher. Chinese J. High Press. Phys. 30(6), 517–525 (2016). (in Chinese) 7. Zou, B.G., Cao, Y.J., Li, R.F., Wang, M.: Optimization of geometric structure for armature in synchronous induction coilgun. Micromotors 45(10), 15–18 (2012). (in Chinese) 8. Lu, F., Wang, Y., Yan, Z., Hu, Y., Deng, H.: Investigation of the inner conical armature in synchronous induction coilgun. IEEE Trans. Plasma Sci. 47(8), 4203–4208 (2019) 9. Lu, F.: Investigation of synchronous induction coilgun with stepped coil launcher and stepped armature. IEEE Trans. Plasma Sci. 48(4), 1190–1194 (2020) 10. Kaye, R.J.: Operation requirements and issues for coilgun electromagnetic launchers. IEEE Trans. Magn. 41(1), 194–199 (2005)
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil Launcher Pengfei Zhao(B)
, Zhiye Du , Yadong Zhang, and Gen Li
School of Electrical and Automation, Wuhan University, Wuhan, China [email protected]
Abstract. Electromagnetic coil launcher is the research object that attracts more attention in the field of electromagnetic emission technology at present. However, with the increase of the series of driving coils, the more complex the factors such as power supply parameters, coil triggering sequence parameters and coil structure parameters need to be considered, and the time of manual design and modeling simulation will greatly increase. So in order to improve the multi-stage electromagnetic coil launcher system modeling and simulation of artificial design efficiency, this paper combined with multilevel structure and working principle of electromagnetic coil launcher, two-dimensional model of multistage electromagnetic coil launcher system research and the field-circuit coupling relationship, this paper proposes a fast for multi-stage electromagnetic coil launcher system modeling and simulation approach, Finally realized in the process of development on the visual interface corresponding parameters can be input to the multi-stage electromagnetic coil launcher fast automatic modeling and simulation system model, and through ten levels of electromagnetic coil launcher model proves the feasibility of parametric design program. At the same time, it provides some reference value for the automatic design optimization of multistage electromagnetic coil launcher system. Keywords: Multistage electromagnetic coil launcher · Fast modeling · Field-circuit coupling · Parameterized programming
1 Introduction Multistage Electromagnetic Coil Launcher (MECL) also known as the electromagnetic coil gun. Although many research institutions and scholars on the electromagnetic coil emitter armature outlet speed, coil temperature rise, inter-stage coupling, dynamic characteristics, efficiency improvement and other aspects of a large number of simulation and experimental verification [1–3]. However, most of them are about single-stage electromagnetic coil emitters, and only a few scholars have carried out simulation research on three-stage and above electromagnetic coil emitters [4–6]. The main reason is that the power supply parameters, coil trigger timing parameters, coil structure parameters and other factors need to be considered more complicated when the electromagnetic coil emitter series increases [7]. The time of manual design modeling and simulation will © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 34–41, 2022. https://doi.org/10.1007/978-981-19-1870-4_4
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil
35
also greatly increase, and most of the modeling and simulation research of electromagnetic coil emitter is only considered from the overall structure model of the drive coil [8]. The detailed turns of the real winding model is not deeply considered, such as how to arrange the radial layers, axial turns, layer spacing and turn spacing of the wire under the detailed turns of the driving coil. Therefore, in order to improve the efficiency of manual design modeling and simulation of MECL system, this paper focuses on the two-dimensional model and field-path coupling relationship of MECL system, considers the detailed winding structure model of MECL drive coil, and combines the modeling rule of the three-stage electromagnetic coil emitter system in Ansoft Maxwell finite element software. This paper proposes a fast modeling and simulation method for MECL system. Finally, this paper uses the written program to conduct a rapid modeling and simulation research on the ten-stage electromagnetic coil emitter model, and verifies the feasibility of the parametric program design.
2 The Working Principle and Mathematical Model of MECL MECL system is mainly composed of multistage drive coil, pulse power supply (condenser), trigger switch, the armature and duct insulation parts, such as structure diagram as shown in Fig. 1. Each level of drive coil connected with independent pulse power supply and trigger switch, begin with the first level trigger switch closed while working the drive coil conduction. While the armature in the induction of eddy current and magnetic field interact to produce to the axial of Lorentz force, promote the armature forward accelerated motion. Closing the switches in sequence gives the armature a continuous acceleration thrust in the same manner until the armature is fired away from the launch system device.
Fig. 1. Structural representation of MECL
MECL emission process is a complex motion coupling process, and its mathematical model is mostly analyzed by current wire method [9], the armature section is discretized into M pieces along the axial direction, and the induced current is approximately distributed uniformly on the section. Finally, “current wire” loops are used to equivalent
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the original armature, and its circuit equivalent model is shown in Fig. 2. According to the circuit model parameters MECL system control equation can be summarized as follows: (L + M)
dM dI = U c − RI − v I dt dx C
d Uc = −I c dt
(2)
dMpc dv Ip Ic = dt dx m
F = mp
(1)
n
(3)
p=1 c=1
dx =v dt
(4)
In the above formula, there are n driving coil currents, m current wire currents, and n capacitor voltages. U c and I c are n-order column vectors of capacitor voltage and driving coil currents. L and R represent drive coil and armature self-induction and resistance; M represents mutual inductance between drive coils or between drive coils and armature; C represents each capacitance value. S1 Ic1 Rc1 First Stage
C1
VD1
Lc1
Mc1p
M12
Lp1
Rp1
S2 Ic2
Mc2p
Rc2 Second Stage
C2
VD2
Lc2
Sn
Lp2 M2n
Rp2
M1n
Mcnp
Lpm
Rpm
Icn Rcn N-Stage
Cn
VDn
Armature
Lcn
Coils
Fig. 2. Equivalent circuit model of MECL
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil
37
3 Fast Modeling Program Design for MECL System 3.1 Finite Element Simulation of Field-Path Coupling in MECL System In order to explore the field-path coupling modeling mode of MECL system, a twodimensional finite element model and external excitation circuit design based on the field-path coupling relationship were established in Ansoft software, taking the threestage electromagnetic coil emitter as an example. The parameters of the simulation model are shown in Table 1. The two-dimensional finite element model of the threestage electromagnetic coil emitter and the applied excitation circuit of the winding is shown in Fig. 3. The symmetry axis of the model is Z axis, the boundary of the solution domain is set as the balloon boundary, the material properties of the solution domain and the moving band are set as air, the wire material is copper, the armature material is aluminum, and the material between the coil wires is epoxy resin. The initial capacitor voltage of each coil is 4 kV, the capacitance value is 13.5 mF, the initial armature speed is 0 m/s, the simulation time is 100 ms, the time step is 2 ms, and the trigger switching time is set to 0, 15 ms and 29 ms successively. Table 1. The simulation parameters of 3-stage electromagnetic coil launcher. Name
Parameter
Value
Armature
Thickness /m
0.065
Coils
Power
Length /m
0.35
Weight /kg
225
Coil spacing /m
0.03
Wire width /m
0.004
Layer spacing /m
0.004
Turn spacing /m
0.002
Wire numbers
175
Capacitance /mF
13.5
Voltage /kV
4
Resistance /m
5
Based on the simulation parameters set above, the armature electromagnetic force curve and armature velocity curve of the three-stage electromagnetic coil emitter model can be obtained. The simulation results are shown in Fig. 4. Can be seen from the diagram, the armature electromagnetic force in turn appeared three peaks, corresponding to three basic peak discharge current. At 44 ms, the maximum firing velocity of the armature is about 16.5 m/s, and the maximum electromagnetic force of the armature movement is 161.2 kN. From the armature electromagnetic force and armature velocity curve, it can be seen that the acceleration process of armature launching is approximately smooth launching, and the launching effect is basically consistent with the expectation.
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Fig. 3. Two - dimensional finite element model and external excitation circuit model
Fig. 4. Dynamic simulation results of three stage electromagnetic coil launcher
3.2 MECL System Parametric Programming Based on MATLAB As can be seen from the finite element modeling and simulation process of the three-stage electromagnetic coil emitter, the finite element model establishment process of MECL system involves many detailed wire model elements of each stage of the drive coil, and it takes a lot of time to set the excitation of the wire model and put it into the coil winding to solve the condition setting. If the MECL system is designed and modeled manually, it will inevitably consume a lot of time. In order to improve the efficiency of MECL system’s manual design modeling and make the MECL system’s drive coil model more close to the real structural design, this paper considers the detailed winding structure model of MECL’s drive coil, uses MATLAB software to carry out parametric programming of MECL system and develop visual interface. Finally, by inputting corresponding MECL system parameters on the developed visual interface, corresponding script files can be generated for automatic modeling and simulation, thus greatly improving the efficiency
Study on Fast Modeling and Simulation of Multistage Electromagnetic Coil
39
of manual design and modeling of MECL system model. The flow chart of parametric programming is shown in Fig. 5. Start Input Key Parameter Pulse power supply, coil series, coil spacing parameters˗ Each stage coil, armature, trigger timing parameters˗
Programmed Design Determine MECL system specific model; Parameters are passed to the script˗ Write modeling files programmatically in turn˗
Use Interfaces to Call Software Start the interactive interface with a command program˗ Realize the background automatically open software˗
Modify model parameters
Automatic Loading of Script Files Use the program to load the. VBS modeling file Continue SPH circuit file after model building
Complete modeling and simulation 1R Meet expectations 30Q130 > 35WW270 > 50WW800 > 1J22. For optimization scheme, the weight of the levitation electromagnet decreases by about 56.99 kg, it can be increased by more than 10% for floating-weight ratio. This study have guiding significance for optimum design of electromagnetic system of EMS maglev trains. Keywords: EMS · Levitation force · Floating-weight ratio · Orthogonal design · Soft magnetic material
1 Introduction EMS maglev train is the only one technology that has put into commercial operation. It has received increasing interest for advantages, such as high efficient, low noise, low maintenance costs, and ride comfort. Present and future applications lie in the fields such medium and long distance high speed railway transportation. Recently, there already exist some researches on electromagnetic characteristics and optimum design of the linear synchronous motor [1–5], However, there is little information about the influence of different soft magnetic materials as suspended electromagnet core on levitation force and key influence parameters on floating weight ratio, more simple and efficient optimum design method is of significant value for the reduction of the power consumption and the reliability of the EMS maglev train. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 50–58, 2022. https://doi.org/10.1007/978-981-19-1870-4_6
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In this paper, it was established that the dynamic electromagnetic FEM model of levitation electromagnet for EMS maglev train, and the influences of typical soft magnetic materials on levitation force and floating weight ratio is analyzed. The key influence parameters of the core structure affecting the floating weight ratio are determined by orthogonal experimental design method, and optimum structural parameters of the levitation electromagnetic are proposed and compared with the existing structure.
2 Numerical Model It is shown in Fig. 1 that the diagram of one standard levitation magnet and long stator. The long primary stator with concentrated wave winding and iron core, which is applied symmetrical three-phase AC current to obtain the driving force, and the winding is set as a single wire coil group according to the order of AZBXCY. The standard levitation electromagnet consists of 10 intermediate modules (integral pole) and 2 end modules (half pole), used as the secondary mover of the linear synchronous motor, which consist of DC excitation coil and lamination core. Stator winding
Exciting winding
Long stator
Levitation electromagnet
Fig. 1. Model of levitation magnet and long stator.
ia = Im cos(ωt + θ0 ) ib = Im cos(ωt + θ0 − 2π/3) ic = Im cos(ωt + θ0 − 4π/3)
(1)
while I m is the amplified value symmetrical three-phase AC current, ω is the angle frequency, θ 0 is initial phase. Details on control equations of electromagnetic field and boundary conditions are given as same as Ref. [4, 5]. The BH curve data of soft magnetic materials are from the database of magnetic materials which is built by our research group independently. All the equations are solved by the commercial code ANSYS Electronics Desktop (Table 1).
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X. Yu et al. Table 1. Parameters of levitation electromagnet and long stator
Parameters
Values
Parameters
Values
Pole pitch/mm
266.5
Stator slot distance/mm
86
Tooth width/mm
43
Air gap/mm
12.5
Core thickness/mm
170
Windings section/mm2
84 × 44.6
Core width/mm
166.5
Excitation current/A
25
Mover yoke height/mm
56
Excitation coil turns
300
Stator pole pitch/mm
258
Excitation coil material
Al99.5
Stator slot width/mm
43
Velocity m/s
25.8
Core material
M800-50A
Exciting winding material
Al
3 Simulation Results The simulated magnetic flux density and magnetic field lines at t = 0.03 s in which the I m is 1000 A with the ω of 50 Hz and the θ 0 of 89° obtained by sweeping calculation under same conditions is shown in Fig. 2. The axial component of the magnetic flux density at the center of the air gap between the long stator track and the levitation electromagnet is shown in Fig. 3. While electromagnetic force of levitation magnet was calculated by virtual displacement method and Maxwell stress tensor method [6]. Time evolution of levitation force and thrust is shown in Fig. 4. It can be found that the fluctuation of levitation force and thrust all have a trend of six times frequency due to six times relationship between the stator tooth distance and the pole distance. The calculated levitation force and thrust has the same tendency with Ref. [5], which represented the mathematical model here is reasonable and viable.
Fig. 2. Magnetic line and flux density distribution.
The soft magnetic materials are ferromagnetic or sub ferromagnetic materials with coercivity less than 1000 A/m. It mainly includes pure iron, low carbon soft steel, silicon steel, other steel, iron nickel alloy, amorphous soft magnetic materials, iron cobalt alloy, soft magnetic materials produced by powder metallurgy process and other alloys [6–8]. In this section, several typical soft magnetic materials are selected to compare the levitation force and floating weight ratio, especially the non-oriented silicon steel sheet (0.5 mm 50WW1300, 0.35 mm 35WW270), high-quality oriented silicon steel sheet (18RK070)
Research on Parameters Optimum Design of Levitation Electromagnet
53
Fig. 3. Magnetic flux density distribution in the air gap.
Fig. 4. Levitation force and thrust.
and iron cobalt alloy (1J22). It is shown that the calculated average values of dynamic levitation force has little difference for the typical soft magnetic materials. The maximum average dynamic levitation force obtained by setting 18RK070 as the iron core is about 0.83 kN higher than that of silicon steel 50WW1300. The floating weight ratio is defined as the ratio of the levitation electromagnetic force produced by the levitation electromagnet to its own weight, which reflects the levitation ability of the levitation electromagnet per unit weight. η=
Fy mg
(2)
while, F y is the levitation force, m is the mass of the suspension electromagnet. The larger the ratio η, the less the material required for levitation system of EMS maglev train. The calculation results show that the order of floating-weight ratio with typical soft magnetic materials as iron cores is 18RK070 > 30Q130 > 35WWW270 > 50WW800 > 1J22 (Table 2).
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X. Yu et al. Table 2. Parameters of typical soft magnetic materials Materials
Levitation force Fy(kN)
Floating weight ratio(η)
18RK070
44.77
8.21
30Q130
44.68
8.19
1J22
44.58
7.63
35WW270
44.18
8.10
50WW800
43.94
7.85
Therefore, the silicon steel 18RK070 has great potential for improving the floatingweight ratio of levitation electromagnet, in the next selection we will chose 18RK070 as core material. However, it should be confessed that 18RK070 belongs to the oriented silicon steel sheet, which is mostly used in power electromagnetic equipment such as transformers, and it needs further research that the application in long stator linear synchronous motor of EMS maglev train.
4 Optimization Design of Levitation System The orthogonal experimental design method realizes the investigation of multiple key factors and levels by selecting some test points with ‘uniform dispersion, neat and comparable’ characteristics in all experiments. In this section, it is determined that the orthogonal test table and the virtual prototype test is completed. Then the simulation data are analyzed by intuitive analysis method and variance analysis method to determine the influence of various factors on the optimization index. Finally, according to the significance of each factor, the primary and secondary order of the influencing factors and the best level are obtained. Without considering the interaction between various factors, we chose the orthogonal experimental design of four factors and four levels, and it was selected to arrange the numerical simulations that the orthogonal table L16 (45). lM
l1 hR h2
Fig. 5. Diagram of levitation electromagnetic Core
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Table 3. Levels table of factors. Level
Factor h2/mmA
hR/mmB
l1/mmC
lM/mmD
1
15
50
30
166.5
2
16
52
40
168.5
3
17
54
50
170.5
4
18
56
60
172.5
The factor level is shown in Table 3, and the implication of each factor is shown in Fig. 5. The test index is the float-weight ratio, the core material is 18RK070. It is analyzed by the intuitive analysis method that the float-weight ratio of levitation electromagnets were calculated under different parameters obtained from the experimental calculation as shown in Table 4. It can be seen from the range R that factor D (iron core width lM) has the greatest influence on the float-weight ratio, and the optimization level is 4, the second factor is B (yoke height hR), the preferred level is 1. The third factor is C (the length of the chamfer part l1), the optimal level is 4. The factor of A (U-shaped part of the top height h2) has less effect on the float-weight ratio, the optimal level is 3. The optimum parameters combination is A3B1C4D4. However, the optimum parameters combination is not in the orthogonal table L16 (45), we carry out additional test analysis under the condition of the optimum parameters combination, and the float-weight ratio is 9.5, which is further verifying the rationality of the above optimal scheme selection. Table 4. Data by the intuitive analysis method.
NO.
A
B
C
D
K1 36.04 37.16 35.68 34.92 K2 35.84 36.42 35.54 35.57 K3 36.19 35.5 36.11 36.04 K4 36.17 35.16 36.91 37.71 k1 9.01 9.29 8.92 8.73 k2 8.96 9.11 8.885 8.89 k3 9.048 8.88 9.028 9.01 k4 9.043 8.79 9.228 9.428 R 0.088 0.5 0.343 0.698 Order D>B>C>A Level A3 B1 C4 Combination A3B1C4D4
E 36.28 36.03 35.91 36.02 9.07 9.01 8.98 9.01 0.093 D4
It is shown in Table 5 that the results are analyzed by variance analysis, and the results are plotted as variance analysis tables. From the comparison of F value and critical value
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in the table, it can be seen that factors D and B (i.e. core width lM and yoke height hR) have a significant impact on the floating weight ratio of levitation electromagnet. Comparing the F value of each factor, it can be seen that factor D has the most significant impact on the floating weight ratio, followed by B and C (the length of the chamfer part l1). Compared with factors D, B and C, the influence of A (top height of U-shaped part h2) on the float-weight ratio is not significant.
Fig. 6. Levitation force at different factor levels
Table 5. Variance analysis table.
A B C D Error Sum
S
f
MS
F
Critical values
0.01945 0.6158 0.28495 1.06565 0.01835 2.0042
3 3 3 3 3
0.0065 0.205 0.095 0.355 0.006
1.0599 33.559 15.529 58.074
F0.01(3,3)=29.45 7 F0.05(3,3)=9.277 F0.1(3,3)=5.391
Significance ** * **
The variation curve of the levitation force of suspension electromagnet is shown in Fig. 6 which obtained by intuitive analysis method with the values of four factors. It can be seen that the levitation force increases linearly with increment of the core width. With increment of yoke height, the levitation force increases slightly. It can be seen that the levitation force decreases very slightly along with the increment of the chamfer part length, and the decreasing value is only 0.25 kN. With increment of the top height of the U-shaped part, the levitation force generally decrease slight linear. Therefore, under the premise of ensuring the levitation force, The width of the core, the length of the chamfering part and the top height of the U-shaped part are appropriately increased to reduce the height of the yoke, so as to reduce the cross-sectional area of the
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core and the amount of the core material, so as to reduce the weight of the iron core part, if the levitation force will not decrease too much or it is better to increment and finally improve the floating weight ratio of the electromagnet. Combined with the previous analysis of soft magnetic materials and the conclusion of orthogonal test optimization design, we choose 18RK070 in the optimized scheme due to its relatively high float-weight ratio as the core material. The optimum scheme of levitation magnet core is set as followings, The core width lM is 172.5 mm, the yoke height hR is 50 mm, the top height h2 of the U-shaped part is set to 18 mm, and the chamfer part length l1 is set to 60 mm. The simulation results show that the magnetic flux density of optimization is higher than the existing structure, and the low magnetic flux intensity distribution area is smaller than that before optimization, and the optimized structure is more compact, and the weight of the suspended electromagnet core is reduced by about 61.57 kg (Fig. 7).
Fig. 7. Comparison of dynamic levitation forces
5 Conclusions The order of the floating-weight ratio with different soft magnetic materials is 18RK070 > 30Q130 > 35WW270 > 50WW800 > 1J22, the difference between different typical soft magnetic material is tiny under the fixed contracture. For optimization scheme, the weight of the levitation electromagnet decreases by about 61.57 kg, and the levitation force increases by 1.93 kN. It can be increased by more than 16% for floating-weight ratio through adjustment of core material and optimization of structure parameters. This study have guiding significance for optimum design and reliability enhancement of electromagnetic system of EMS maglev train.
References 1. Gang, L.: Review of the application and key technology in the linear motor for the rail transit. Proc. CSEE 40(17), 5665–5675 (2020)
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2. Kim, J., Ha, C.-W., King, G., et al.: Experimental development of levitation control for a high-accuracy magnetic levitation transport system. ISA Trans. 101, 358–365 (2020) 3. Li, L., Zhang, J., Lu, Q.: Investigation of electromagnetic coupling field of traction and levitation systems in high speed maglev train. In: The 22nd International Conference on Electrical Machines and Systems (ICEMS), pp.1–6, Harbin, China, August 2019 4. Bo, K., Xiong, Y., Yu, X., et al.: Study on transient electromagnetic characteristics based on typical soft magnetic material for EMS Maglev train. In: The 13th International Symposium on Linear Drives for Industry Application, pp. 891–894, Wuhan, China, July 2021 5. Chen, D., Pan, M., Luo, F., et al.: Electromagnetic field analysis and measurement for high speed attraction type magnetic levitation vehicle systems. Key Eng. Mater. 295–296, 655–660 (2005). https://doi.org/10.4028/www.scientific.net/KEM.295-296.655 6. Xie, Y., Wang, Y.: Local electromagnetic force calculation on the rotor of squirrel-cage induction motors with broken bar faults. Proc. CSEE 33(27), 127–134+18 (2013) 7. Chen, J., Wang, D., Chen, Z., et al.: Review of precise modeling technology of electrical soft magnetic material applied in vessel equipment. Trans. China Electrotech. Soc. 32(22), 1–29 (2017) 8. Guoxin, Z., Decai, K., Xiaolin, G.: Performance difference study on permanent magnet synchronous motor based on soft magnetic composite material and silicon steel sheet. Trans. China Electrotech. Soc. 33(S1), 166–175 (2018)
Research on the Formation of Erosion in Electromagnetic Launch Wenping Cheng1 , Weidong Xu1 , Zhizeng Wang1 , and Ping Yan1,2(B) 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
[email protected] 2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract. In electromagnetic launch, the erosion phenomenon usually appears on the sides of the rail after repeated launches, and the erosion distribution corresponds with the tail edges of the armature. The erosion grooves are severe at the initial segment of the rail, and become shallow along the direction of the armature movement. The appearance of erosion will degrade the armature-rail contact performance, and at the same time the degradation of the armature-rail contact performance will aggravate the extent of the erosion. As a result, the performance and efficiency of the launch will be severely degraded. In this paper, the formation mechanism of erosion is discussed with simulations and experiments. The research shows that initial erosion is the result of the comprehensive effect of force and heat, Joule heat generated by large pulse current is the dominate factor. After the appearance of erosion grooves, gaps appear between the erosion grooves of rail and the tail of armature, which will lead to miniature arc when the large pulse current flows through the launch system. In repeated launches, the repeated action of current and arc makes the erosion grooves become deeper and wider. Keywords: Electromagnetic launch · Erosion · Contact performance
1 Introduction In electromagnetic launch, the device requires a power supply of more than one billion watts to provide several mega joules of electricity in a few milliseconds [1]. The drive current in the device can reach several MA, and the contact pressure between the armature and rail can reach several hundred MPa. As a result of comprehensive actions of large current, great pressure and high-speed friction, some damages will appear after repeated launches, such as erosion, ablation, and so on. Among of these damages, erosion damage is long groove occurring at the beginning of the rail, and the groove extends along the rail length [2]. Erosion has accumulative effect, and the higher the current, the severer the erosion [3]. The depth of the erosion grooves can usually reach several millimeters after repeated launches when the drive current is large enough. Erosion will affect the contact performance of the armature-rail, reduce the efficiency of the launch, and has a serious effect on the life of the launch device. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 59–68, 2022. https://doi.org/10.1007/978-981-19-1870-4_7
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The erosion grooves are located on both sides of the rail, and the position is corresponding with the edges of the armature tail. Experiments of T. Watt under different conditions show that on the rail the position of erosion is corresponding with the position where the current is largest and the contact time with the armature is the longest [3]. At the same time, the erosion position is corresponding with the area on the armature tail where the damage is strongest. The formation mechanism of erosion is not yet clear, but contact pressure and Joule heat are regarded as the main factors at present [4, 5]. R. M. Gee et al. discovered the erosion grooves first, and attributed them to plastic deformation of the material and chemical corrosion of the liquid metal film [6]. Simulation results of Kuo-Ta Hsieh showed that erosion might be formed by softening and yield of the material caused by local high temperature [7]. T. Watt et al. suggested that erosion was caused by molten aluminum on the rails [3]. Shengguo Xia et al. thought the erosion depends upon both current distribution and flow of liquid aluminum [8]. In this paper, the formation mechanism of erosion is discussed through simulations and experiments.
2 Research Object 20 launch experiments were carried out on an electromagnetic launcher. Then the bore of the launcher was disassembled, and the rails were analyzed. Current of the experiment is shown in Fig. 1.
Fig. 1. Current of the experiments
There are obvious erosion grooves at both sides of the rails after repeated launches. The erosion grooves appear at the beginning of the armature movement where the groove depth is the maximum, become shallow gradually along the direction of the armature movement, and last to the end of the flat top of the current. Figure 2 shows the rail sections before and after the launch experiments. Erosion grooves can be seen, and the depth is about 1 mm meanwhile the width is about 2.5 mm. The position of the grooves is nearly corresponding with the edges of the armature tail, but the center of the erosion groove is closer to the rail than the edges of the tail. In order to study the formation process and mechanism of erosion, the distributions of stress, current and temperature of the contact surface were simulated, and experiments of high temperature friction, SEM and Micro hardness were carried out.
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Fig. 2. Sections of the rail before and after repeated launches
3 Simulation 3.1 Distribution of the Armature-rail Contact Pressure Under Preload The armature tail must keep a close contact with the rail, in order to ensure the electrical contact performance. The armature-rail contact pressure is provided by the interference of the armature tail before being electrified, and mainly the electromagnetic force after being electrified. The initial contact state before electrified affects the current distribution directly, and then affects the distribution of the subsequent electromagnetic force. So the distribution of the armature-rail contact pressure under preload was simulated. Figure 3 shows the model used in the simulation. The tail of armature has a certain interference compared to the bore in free constrain condition, and will deform when the armature is pushed into the bore. The elastic deformation provides force to press the tail of armature and the rail.
Fig. 3. Simulation model of the armature-rail
The contact pressure distribution on the tail of the armature is shown in Fig. 4, which is equivalent to that on the rail. It can be seen that the contact area is a small part of the tail, and the value of pressure is larger at the edges of the tail. The reason that causes this phenomenon may due to lack of constrain on the edges of the tail, which means that the pressure will be more concentrated on the edges when the tail is affected by electromagnetic force. Figure 5 shows the contact pressure distribution of the armature tail tested by sensing paper under preload. The red area indicates that there is contact pressure here, and the darker the color is, the larger the pressure is. In this figure, the dark red area on the left side is the result of pressure accumulation caused by the compression method during the experiment, which should be ignored. Pressure distribution of the rest area is corresponding with the simulation. The contact pressure concentrates on the edges of the tail, and distributes in an arc at the front of the contact area.
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Fig. 4. The distribution of contact pressure on the tail
Fig. 5. The contact pressure distribution tested by sensing paper
3.2 Distribution of the Current at the Beginning of the Launch Relative researches show that the current concentrates on the edges of the armature tail at the beginning of the launch, which will cause ablation of the tail. The distribution of the current has a great effect on the distribution of the Joule heat and electromagnetic force. Therefore, the distribution of the current at the beginning of the launch should be simulated combined with the position of the erosion grooves. In actual launches, it will take some time to start its movement for the armature after the system is electrified, because of the friction generated by the preload. Since the erosion is the severest at the beginning of the armature movement, and in order to exclude the effect of friction, the time when the armature stays stationary was chosen, the distribution of current in this time was simulated and analyzed. Determination of the Beginning of the Launch. The forward electromagnetic force on the armature F: F = 1/2I 2 L .
(1)
I is the current that flows through the armature, L’ is the inductance gradient of the device. The acceleration of the armature a: a = (F − f )/m
(2)
f is the friction between the armature and the rail, m is the weight of the armature.
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The displacement of the armature s:
t
s=
atdt
(3)
0
Figure 6 shows the displacement-time curve of the armature based on the above formulas. The armature starts to move at about 0.3 ms according to the displacement curve. The distribution of current and temperature on the contact surface at 0.3 ms was simulated and analyzed.
Fig. 6. The displacement-time curve of the armature
Distribution of Current on the Contact Surface. Only the middle part of the armature tail contacts with the rail under preload, and surfaces of the armature and rail are uneven in microcosmic state. As a result, there is a relatively large contact resistance between the contact surfaces. An object was inserted between the contact surfaces as contact resistance in the simulation. The shape and dimension of the object referred to the actual contact are shown in Fig. 4, with a depth of 0.2 mm. The value of contact resistance Rj (m) was calculated by the following formula [9]: k Rj = n 0.102Fj
(4)
k is a coefficient which is related to the contact materials, and its value is 0.98 when the contact materials are Al and Cu. F j is the contact force between the armature and rail, and its value is 15500 N in this research. n is another coefficient which is related to the contact form, and its value is 1 when the contact is face-to-face. The contact resistance is about 0.6 µ by calculation, the resistivity of the contact object was set according to the calculation result. The distribution of current at 0.3 ms was simulated, which is shown in Fig. 7. The current concentrates at the edges of the contact surface, especially at the corners.
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Fig. 7. The distribution of current on the contact surface
Distribution of Temperature on the Contact Surface. The temperature rise of the contact surface is entirely due to Joule heat generated by the current before the armature starts to move [10]. The temperature of the contact surface at 0.3 ms was simulated based on the previous simulation of the current distribution. The simulation result is shown in Fig. 8.
Fig. 8. The distribution of temperature on the contact surface
It can be seen that the temperature in multiple areas is higher than the melting point of Al which will cause ablation to the armature tail. And the temperature at the corners is higher than the melting point of Cu which may cause local melting to the rail even if the phase transformation latent heat is considered. The areas where the temperature is higher than the melting point of Cu are at the edges of the armature tail, and the positions are corresponding with the erosion grooves on the rail. Combining the above simulation results, several conclusions can be given. Due to the skin effect of the current, the concentration of current on the edges of the contact surface is obvious at the beginning of the launch. At the same time, since the contact pressure on the edges is larger under preload, the contact resistance on the edges is smaller than that on the center part of the contact surface, which will aggravate the current concentration on the edges. The contact edges of the rail will be effected by concentrated Joule heat and electromagnetic force, caused by the concentrated current. The armature moves very slowly at the beginning of the launch, the Joule heat and electromagnetic force will act on the initial part of the rail for a long time. As a result, the temperature of the edges will be higher than the melting point of Cu, both Cu and Al materials start to melt. As
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the continuing role of electromagnetic force on the molten Cu and Al, erosion grooves appear.
4 Experiment 4.1 High Temperature Friction Experiment A high temperature friction experiment was designed according to the simulations. C18150 (material of the rail) plates and Al6061 (material of the armature) pins were machined for the experiment. The samples are shown in Fig. 9. Heated the plates and pins to a certain temperature (The heat of friction would increase the temperature of the surface by 150–200 °C more). A force was applied to press the plate and pin, making the average contact pressure up to 50 MPa. Started the experiment machine to make the pin move around the plate in a circular motion. Stopped the machine when the rotation speed reached 300 r/min. Figure 10 shows the states of the plate and pin after repeated experiments at different temperatures. In each experiment, there is a large amount of fusion and abrasion with the aluminum pin, and meanwhile there is no obvious damage with the copper plate.
Fig. 9. Samples of the high temperature friction experiment
4.2 Microstructure Analysis The rail after repeated launches was sliced along the length direction, and two samples with and without obvious erosion grooves were selected to study. The sections of the samples were polished and chemically corroded. Then the contact surface of the sample and armature was observed by scanning electron microscopy. Figure 11(a) shows the grain structure of the erosion groove, and Fig. 11(b) shows the grain structure of the rail without obvious change. It can be seen that grain refinement occurs on the surface of the erosion groove. Grain refinement is usually caused by high temperature, but the depth of grain refinement on the surface of groove is very small, only about 200 µm, which indicates that the action time of the high temperature is very short.
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(a) 20䉝
(c) 400䉝(7 times)
(b) 200䉝
(d) 500䉝(4 times)
Fig. 10. States of the plate and pin after repeated experiments
(a)
(b)
Fig. 11. States of the plate and pin after repeated experiments
4.3 Micro-hardness Test A rail sample with erosion grooves was selected. Five test points are selected near the contact surface, and positions of the five points are shown in Fig. 12. The HV hardness was tested three times near each point, and the average value was calculated. The test results are shown in Fig. 13. There is no obvious difference in the HV values, which shows that there is no significant difference in temperature, stress and other conditions at each test point.
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Fig. 12. Test points on the section of the rail
Fig. 13. Micro hardness of the test points
5 Conclusion Simulation results show that both contact pressure and skin effect lead to the current concentration on the edges of the contact surface, and current concentration leads to the contact pressure larger on the edges of the contact surface in turn. Besides, current concentration also leads to local extremely high temperature at the corners of the contact surface which will melt copper. The high temperature friction experiments show that aluminum sample has been melted while no obvious damage appears on cooper sample from the room temperature to the melting point of cooper, SEM and micro-hardness of the rail section indicates the surface of the erosion groove is heated by a transient extremely high temperature. Combining the simulations and experiments, it is deduced that initial erosion is caused by local melting of the cooper rail, then the melting copper is taken away by the high-speed armature and a pair of very shallow erosion grooves appear. The appearance of shallow grooves will make the current concentration move towards the center of the rail which will widen the groove, and lead to the appearance of arc which will deepen the groove. During the latter part of the launch, erosion grooves disappear since more melting aluminum improves the contact performance and the high-speed armature makes the acting time of heat much shorter.
References 1. Marshall, R.A., Wang, Y.: Railguns: Their Science and Technology. China Machine Press, Beijing, pp. 3–24 (2004). (in Chinese) 2. Li, S., Cao, R., Zhou, Y., et al.: Performance analysis of electromagnetic railgun launch system based on multiple experimental data. IEEE Trans. Plasma Sci. 47(1), 524–534 (2018)
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3. Watt, T., Stefani, F., Crawford, M., et al.: Investigation of damage to solid-armature railguns at startup. IEEE Trans. Magn. 43(1), 214–218 (2007) 4. Li, C., Chen, L., Xu, J., et al.: Causes of damage at electromagnetic railgun’s initial position and corresponding improvement measures. IEEE Trans. Plasma Sci. 48(8), 2932–2938 (2020) 5. Zhang, Q., Li, J., Li, S., et al.: Experimental studies on melt erosion at rail-armature contact of rail launcher in current range of 10–20 kA/mm. IEEE Trans. Plasma Sci. 47(8), 4184–4188 (2019) 6. Gee, R.M., Persad, C.: The response of different copper alloys as rail contacts at the breech of an electromagnetic launcher. IEEE Trans. Magn. 37(1), 263–268 (2001) 7. Kuo-Ta, H.: Numerical study on groove formation of rails for various materials. IEEE Trans. Magn. 41(1), 380–382 (2005) 8. Xia, S., Yuyang, H., Chen, L., et al.: Experimental studies on melt erosion at rail-armature contact of rail launcher in current range of 10–20 kA/mm. IEEE Trans. Plasma Sci. 47(3), 1674–1680 (2019) 9. Jun, X., Kun, L.: The research on resistance of electrical contact. Electr. Eng. Mater. 1, 10–13 (2011). (in Chinese) 10. Xing, Y., Lv, Q., Lei, B., et al.: Research on melting erosion law of a multiturn series-parallel railgun during launching period. IEEE Trans. Plasma Sci. 46(8), 3008–3016 (2018)
Circuit Analysis of Commutation Process of Saddle Secondary Helical Coil Electromagnetic Launcher Zhiming Cui1,2 , Housheng Wang1,2(B) , Jianchao Wang1 , and Bendong Ma1 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
[email protected] 2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract. The commutation process of the saddle secondary helical coil electromagnetic launcher is studied, and the theoretical analysis model is established. The working principle of the electromagnetic launcher is clarified, and a simplified model of the launcher is proposed on this basis. According to Kirchhoff’s law, the transient equations of the circuit are written to analyze the changes of the circuit parameters in the process of asynchronous commutation of the launcher. The saddle secondary helical coil electromagnetic launcher experiment platform was built, and the experiment was compared to verify the reliability of the theoretical analysis. This theoretical analysis model provides an effective method for studying the arc generation and elimination during the commutation process of the helical coil electromagnetic launcher. Keywords: EM launcher · Coil launcher · Brush commutation · Arc-suppression
1 Introduction Helical coil electromagnetic launcher (HCEL) is one of the coil launchers, mainly divided into the brush commutation HCEL and brushless HCEL. The brush commutation HCEL is mainly composed of the primary coil, secondary coil, two power supply rails, two rail brushes and two coil brushes [1]. Compared with the orbital electromagnetic launcher, HCEL has obvious advantages: first, the structure of the helical coil enables it to have a higher inductance gradient, so can work with a smaller current and reduce the requirement of high-power pulse power [2–5]. Second, HCEL has higher energy conversion efficiency. HCEL secondary and the primary coil excitation zone move synchronously, so that the force of secondary acceleration is always maximum, which is more efficient than ordinary coil type launchers [6–9]. During the commutation process of the HCEL, arc discharge occurs between the brush and the coil electrode. Arc provides an important channel for energy release in the circuit, but it will cause the commutation process to take longer time and reduce efficiency. And the high-temperature and high-energy arc will ablate the electrode thus © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 69–78, 2022. https://doi.org/10.1007/978-981-19-1870-4_8
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the service’s life was seriously reduced [10]. Therefore, some necessary measures must be taken to shorten the arc burning time, and improve the commutation effect. The saddle secondary HCEL studied in this paper is different from the conventional HCEL. The secondary is designed to be saddle-shaped and puts the primary at the center of the secondary coil. It looks like a saddle riding on the primary. In this paper, the theoretical analysis model of the launcher is established by simplifying the analysis of the launcher, and a lumped equivalent circuit is established based on this model. Writing the circuit equations for different states in the commutation process, and using MATLAB to calculate the current of the commutation coil and the main circuit of the launcher during the commutation process. The correctness of the analysis is verified by comparing and analyzing the waveform of the experimental results. It provides an effective method for analyzing the arc generation and elimination during the commutation process of the helical coil electromagnetic launcher.
2 Analyze and Simplify the Brush Commutation Process To facilitate the analysis of the commutation process of the launcher, the launcher model needs to be simplified and then establishing the lumped equivalent circuit. (1) The power supply guide rail and the guide rail brush are in close contact during the operation of the launcher, which has no effect on the commutation process and can be ignored in the model. (2) The primary coil is only partially excited during the operation of the launcher and which synchronized with the secondary, so only the excited section and the commutation coil are retained in the model. (3) Assuming an ideal contact between the commutation brush and the coil electrode and the contact resistance is constant. (4) The secondary and commutation brushes of the launcher move from left to right at a speed V. The simplified launcher model, as shown in Fig. 1, includes: power supply DC, primary excited section coil L2, front and rear commutation coils L1, L3, secondary coil L4, front and rear commutation brushes 1, 2. (5) The commutation process of the launcher is the same when it is powered by a DC power and a pulse power source, so the commutation process is only analyzed when it is powered by a DC power. S1
L4
S2 Brush 1
Secondary
1
2
3
10
L2
L1
Primary
9
11
L3
Brush2 V
AB D' E'
C B' F'
S4
S3 D E
Fig. 1. Simplified model of helical coil electromagnetic launcher
F
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In the commutation process, the movement of the brush leads to a process of contact and disconnection between it and the commutation coil electrode. This process can be regarded as the conduction and disconnection of the circuit, so can use an equivalent switch to represent it. S1–4 shown in Fig. 1, is the equivalent switch position. The equivalent circuit diagram of the launcher is shown in Fig. 2. S2
R6
I0
R2
S1 R0
R5
L1
R1
S4
R8
S3
R7
L2 L3
R3
I3
I1
DC R4
L4
Fig. 2. The equivalent circuit of the helical coil electromagnetic launcher
where: DC: power, and voltage is U 0 . R0 : internal resistance of the power. R1 , R2 , R3 , R4 : internal resistance of the coil. R5 , R6 , R7 , R8 : internal resistance of the brush and contact resistance. L 1 : inductance of the rear commutation coil. L 2 : coil inductance of the primary excited section. L 3 : inductance of the front commutation coil. L 4 : secondary coil inductance. L 12 , L 13 , L 23 : mutual inductance between the primary excited section and the commutation coil.
3 Commutation Process Analysis The switch state in the equivalent circuit of the launcher is determined by the relative position of the brush and the electrode of the primary coil. Then the transient equation of the circuit during the commutation process can be written and the current and voltage waveform of the commutation process can be obtained by calculation. In Fig. 1, the position of point A indicates that the rear commutation brush 1 leaves the previous coil electrode and only contacts the coil electrode 1. The position of point B indicates that the rear commutation brush 1 is about to contact the coil electrode 2. The position of point C indicates that the rear commutation brush 1 is about to leave the coil electrode 1, and the rear commutation coil is disconnected from the primary excitation section. The position of point D indicates the front commutation brush 2 leaves the previous coil electrode and only contacts the coil electrode 10. The position of point E indicates that the front commutating brush 1 is about to contact the coil electrode 11. The position of point F indicates that the front commutation brush 2 is
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about to be disconnected from the coil electrode 10, and the front commutation coil will be connected to the primary excitation section. The installation position of the commutation brushes will affect whether the front and rear commutation processes are synchronized. When the commutation brush installation position satisfies: (1) The distance between section AB and DE is equal. When brush 1 reaches the position of point B and brush 2 reaches point E at the same time, the front and rear commutation process is synchronized, S2 and S3 are closed at the same time. (2) The distance between section AB and DE is not equal. When brush 1 reaches the position of point A and brush 2 doesn’t reach point E, the front and rear commutation process is not synchronized. S2 is closed before S3. This article only analyzes the changes of various state quantities in the system for the asynchronous commutation process. The relative position of brush 1, 2 and the coil in Fig. 1 determine the commutation process and the state of the equivalent circuit. 3.1 Section D B: Before Rear Commutation Process Begin In section D B, brush 1 is in close contact with the commutation coil electrode 1, and brush 2 is in close contact with the commutation coil electrode 10. The switch state in the equivalent circuit is that S1 and S4 are closed, S2 and S3 are opened. The currents I1 and I3 are equal to the launcher current I0. In the equivalent circuit, the voltage function of the circuit can be deduced according to Kirchhoff’s law: dI0 U0 = R + 2M v(t) I0 + (L + 2M ) dt
(1)
Where R is the total resistance in series in the circuit, M is the sum of L 12 , L 14 (x) and L 24 (x), M is the sum of the mutual inductance gradient of L 14 (x) and L 24 (x). 3.2 Section BE: Rear Commutation Process Begin In section BE , brush 1 is in close contact with the commutation coil electrode 1 and starts to contact with the primary coil electrode 2. And brush 2 is in close contact with the commutation coil electrode 10. In the equivalent circuit, the switch state of S1, S2, and S4 are closed, S3 is opened. The current I1 in the commutation coil L1 begins to decrease and finally decreases to R1 +RR65 +R6 ·I0 . At this time, the equivalent circuit voltage equation is Eq. (2): ⎧ ⎨ U0 = Rs1 + M v(t) I0 + (L + M2 ) dI0 + Rs2 + dL14 (x) v(t) I1 + (L1 + M1 ) dI1 3 dt dx dt ⎩ 0 = dL14 (x) v(t) − R6 I0 + M1 dI0 + Rs3 I1 + L1 dI1 dx dt dt (2)
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3.3 Section E C: Front Commutation Process Begin In section E C, brush 1 is in close contact with the commutation coil electrode 1, and the contact area with the primary coil electrode 2 gradually increases. brush 2 is in close contact with the commutation coil electrode 10. In the equivalent circuit, the switch state of S1–S4 is all closed. The current in the commutation coil L1 decreases. And the current I3 in L3 begins to increase, and finally increases to R3 +RR87 +R8 · I0 . At this time, the equivalent circuit voltage equation is: ⎧ (x) ⎪ U0 = Rs1 + M1 v(t) I0 + M1 dIdt0 + Rs2 + dL14 v(t) I1 ⎪ ⎪ dx ⎪ ⎪ ⎪ (x) ⎨ + M2 dIdt1 + Rs3 + dL34 v(t) I3 + M3 dIdt3 dx (3) (x) ⎪ 0 = Rs4 I1 + L1 dIdt1 + L13 dIdt3 + dL14 v(t) − R6 I0 + M4 dIdt0 ⎪ ⎪ dx ⎪ ⎪ ⎪ ⎩ 0 = Rs5 I3 + L3 dI3 + L13 dI1 + dL34 (x) v(t) − R8 I0 + M5 dI0 dt dt dx dt
3.4 Section CF: Rear Commutation Process End In section CF , brush 1 leaves the commutation coil electrode 1 and is in close contact with the primary coil electrode 2. At this time, the rear commutation process end, the commutation coil L1 is disconnected from the primary excitation section. The switch state in the equivalent circuit is that S1 is opened and S2–S4 is closed. At this time, the equivalent circuit voltage equation is: ⎧ dI0 ⎪ U0 = Rs1 + M3 v(t) I0 + ⎪ M1 dt ⎨ (x) + Rs2 + dL34 I3 + (L3 + M2 ) dIdt3 (4) dx v(t) ⎪ ⎪ ⎩ 0 = Rs3 I3 + L3 dI3 + dL34 (x) v(t) − R8 I0 + M2 dI0 dt
dx
dt
3.5 Section F B: Front Commutation Process End In section F B , brush 1 is in close contact with the commutation coil electrode 2 and brush 2 leaves the commutation coil electrode 10. At this time, the front commutation process end, and the commutation coil L3 is connected to the primary excitation section. The switch state in the equivalent circuit is that S1 and S4 are opened, S2 and S3 are closed. At present, the equivalent circuit voltage equation is: dI0 U0 = R + 2M v(t) I0 + (L + 2M ) dt
(5)
Where R is the total resistance in series in the circuit, M is the sum of L 23 , L 24 (x) and L 34 (x), M is the sum of the mutual inductance gradient of L 24 (x) and L 34 (x).
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3.6 Result Analysis The parameters in Eqs. (1)–(5) are obtained by measuring and calculating the launcher experimental platform. And using MATLAB software to calculate the current waveform of the commutation coil and the main loop of the launcher during the commutation process, as shown in Fig. 3. It can be seen from Fig. 3 that the current in the commutation coil L1 is in the BC section start to drop from I0 and eventually reach R1 +RR65 +R6 · I0 . At point C, the current in the coil quickly decreases to zero, rear commutation process end. There is no significant change in the current of the main circuit of the launcher. In section E F , the current of the commutation coil L3 rises from zero and finally increases to R3 +RR87 +R8 · I0 . At point F , the current of the coil L3 increases rapidly, but doesn’t increase to I0. At the same time, the main circuit current of the launcher is also decreasing rapidly. In section F B (the front commutation coil is fully connected to the primary excitation section), the current of the launcher and the current of the commutation coil L3 eventually both increase to I0.
Fig. 3. Current changes in the commutation coil in a commutation cycle
When the launcher is powered by a pulsed power capacitor, the commutation process analysis is the same as the DC power supply, and only the capacitor discharge formula (6) needs to be supplemented in Eqs. (1)–(5). Since a commutation process is very short, the current of the launcher can still be analyzed as shown in Fig. 3. Where C is the power capacitor capacity, and Uc is the capacitor voltage. Ic = C
dUc dt
(6)
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4 Experimental Result The parameters of the saddle secondary HCEL experimental platform are shown in Table 1. The front and rear commutation brushes are installed in front of the secondary movement direction. The rear commutation brush is installed directly below the arc section of the secondary front end (Fig. 4). Table 1. Parameters of saddle secondary helical coil electromagnetic launcher. Parameter Primary coil
Saddle-secondary coil
Value
Materials
Rectangular enameled copper wire
Turns
8
Outer diameter/mm
80
Inner diameter/mm
60
Thickness/mm
8
Total number of coils
150
Materials
Rectangular enameled copper wire
Turns
10
Outer diameter/mm
120
Inner diameter/mm
96
Arc angle/deg
218
Axial length/mm
170
Fig. 4. Capacitor power and HCEL with saddle secondary experimental platform
The launcher is powered by a power capacitor with a capacity of 16 mF. When the capacitor charging voltage is 0.2 kV and 0.5 kV respectively, obtained the voltage and
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current waveforms of the launcher during operation. The results are shown in Fig. 5 and 6. In the figure, the yellow curve is current and the blue is voltage. When the charging voltage is 0.2 kV, the secondary moving distance less than the thickness of a primary coil, so no commutation process occurs. The current and voltage waveforms are smooth and few fluctuation. When the charging voltage is 0.5 kV, the secondary has moved a distance of 5 primary coil thicknesses. The voltage and current waveforms have small fluctuations in the second half (red rectangle in Fig. 6).
Fig. 5. Current and voltage waveforms when charging voltage is 0.2 kV
Fig. 6. Current and voltage waveforms when charging voltage is 0.5 kV
The power source used in the experiment is a power capacitor, so the actual current of the launcher is different from the DC source used in the theoretical analysis. When using power capacitors, the current of the launcher’s main circuit drops rapidly after rising to the peak value. While using DC power, the current waveform of the launcher’s main circuit is relatively stable. By comparing Fig. 5 and 6, the reason for the current waveform fluctuation in Fig. 6 is that the commutation process occurred when secondary moves forward. During the
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commutation process, when the commutation coil is disconnected or connected, the current waveform of the launcher fluctuates significantly. Only focusing on the current fluctuations during the commutation process, the launcher’s circuit current fluctuations are similar to section F B in Fig. 3 (when the front commutation coil is connected to the primary energized section). The fluctuation trend of current waveforms can reflect the brush commutation situation, so the commutation process analysis is in good agreement with the experimental results right.
5 Conclusion In this paper, the equivalent circuit of the launcher is established by simplifying the HCEL, and the circuit equations of the launcher commutation process are deduced. The current and voltage waveform of the main circuit of the launcher are obtained through experiments, which verified the correctness of the analysis. The simplified model and circuit equation of the launcher in this paper provide an effective method for analyzing the arc generation and elimination of HCEL. Acknowledgment. This work was supported in part by the National Natural Science Foundation of China under Grant 51907189 and in part by the Institute of Electrical Engineering, CAS under Grant E1551501.
Appendix Variables in Eq. (2): Rs1 = R0 + R2 + R4 + R8 Rs2 = R1 + R5 Rs3 = R1 + R5 + R6 L = L2 + L4 M1 = L12 + L14 (x) M2 = L12 + L14 (x) + 2L24 (x) (x) (x) M3 = dL14 + 2 dL24 dx dx Variables in Eq. (3): Rs1 Rs2 Rs3 Rs4 Rs5 M1 M2 M3 M4 M5
= R0 + R2 + R4 = R1 + R5 = R3 + R7 = R1 + R5 + R6 = R3 + R7 + R8
= L2 + L4 + L12 + L23 + L14 (x) + 2L24 (x) + L34 (x) = L1 + L12 + L13 + L14 (x) = L3 + L13 + L23 + L34 (x) = L12 + L14 (x) = L23 + L34 (x)
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Variables in Eq. (4): Rs1 = R0 + R2 + R4 + R6 Rs2 = R3 + R7 Rs3 = R3 + R7 + R8 M1 = L2 + L4 + L23 + 2L24 (x) + L34 (x) M2 = L23 + L34 (x) (x) (x) M3 = 2 dL24 + dL34 dx dx
References 1. Wang, Y., Xiao, F.: The Principle of Electrical Gun, pp. 93–109. National Defense Industry Press, Beijing, China (1995). (in Chinese) 2. Engel, T.G., Nunnally, W.C., Neri, J.M.: Development of a medium-bore high-efficiency helical coil electromagnetic launcher. IEEE Trans. Plasma Sci. 32(5), 1893–1895 (2004) 3. Engel, T.G., Surls, D., Nunnally, W.C.: Prediction and verification of electromagnetic forces in helical coil launchers. IEEE Trans. Magn. 39(1), 112–115 (2003) 4. Engel, T.G., Nunnally, W.C., Neri, J.M.: High-efficiency, medium-caliber helical coil electromagnetic launcher. IEEE Trans. Magn. 41(11), 4299–4303 (2005) 5. Li, J., Yan, P., Yuan, W.: Electromagnetic gun technology and its development. High Voltage Eng. 40(04), 1052–1064 (2014). (in Chinese) 6. Engel, T.G., Nunnally, W.C., Gahl, J.M., Nunnally, W.C.: Medium-Bore helical coil electromagnetic launcher with a liquid nitrogen cooled armature. In: 15th IEEE Pulsed Power Conference, June 2005, pp. 87–90 (2005) 7. Engel, T.G., Nunnally, W.C.: Design and operation of a sequentially-fired pulse forming network for non-linear loads. IEEE Trans. Plasma Sci. 33(6), 2060–2065 (2005) 8. Wang, Q., Wang, H., Li, X., Chen, S.: Review of coaxial coil electromagnetic propulsion technology. High Voltage Eng. 41(08), 2489–2499 (2015). (in Chinese) 9. Xiong, L., Cheng, J., Wang, Q., Wang, H.: Effect of armature position on efficiency of asynchronous coil-propeller. J, Ordnance Equip. Eng. 40(04), 105–108 (2019). (in Chinese) 10. Yang, D.: Research on energy conversion technologies of the helical coil electromagnetic launcher [Ph.D]. National University of Defense Technology (2018). (in Chinese)
Research on Performance Influence of External Circuit Resistance in Synchronize Induction Coil Catapult Yanwei Chen, Pinghui Li(B) , Qi Li, Wei Yang, and Yawei Wang Zhengzhou Electromechanical Engineering Institute, Zhengzhou, People’s Republic of China [email protected]
Abstract. The external circuit of synchronize induction coil catapult can be equivalent to R-L-C circuit with freewheeling diode, the resistance directly affects the current and efficiency. In order to improve the performance of the catapult, the final launching speed can be increased in a certain range by the means of reducing the resistance of discharge circuit or increasing the resistance of freewheeling circuit. In this paper, Maxwell two-dimensional transient simulation model and single-stage coil ejection test of two kinds of coils with different turns was used to verify the influence of the external circuit. The research show that, the driving coil current and the electromagnetic force on armature can be increased effectively by reducing the resistance of discharge circuit, the launch speed which the armature is separated from the load is improved; the armature drag effect can be reduced by putting resistance in freewheeling circuit according to coil resistance, the final speed which the armature is connected to the load is improved, so the ejection performance is optimized. Keywords: Induction coil catapult · Discharge circuit · Freewheeling circuit · Launching performance
1 Introduction The synchronous induction coil ejector has the characteristics of no mechanical contact between the projectile and the drive coil, and has the advantages of large propulsion mass range, high propulsion efficiency, long service life and good controllability under the same current condition. It is one of the effective ways to achieve medium-high speed propulsion at present, and has a very broad application prospect in military and aerospace [1–3]. At present, the volume and weight of the power supply system are larger because of the efficiency of the ejection system is lower than the theoretical value, which once became the restriction condition of the electromagnetic ejection weapon production. The factors affecting the performance of the ejection system include the structural parameters of the drive coil and the armature, the relative position between the armature and the driving coil, the electrical parameters of the energy storage power supply, etc. A © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 79–89, 2022. https://doi.org/10.1007/978-981-19-1870-4_9
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number of domestic universities and institutions have carried out relevant research on the coupling effects of single parameter and multiple parameters and the optimization of magnetic field configuration [4–10], the research on the influence of power supply parameters mainly focuses on the voltage and capacitance value, and the research on the influence of external circuit on performance is less. In this study, the finite element simulation software is used to model the induction coil gun, and the effective method to improve the firing speed is explored through simulation analysis, and verified by experiments.
2 System Working Principle 2.1 Working Principle Coil ejection system is composed of energy storage power supply, driving coil, launching component (including armature and projectile), high-voltage trigger switch and other components [9]. During the launch, the driving coil is fixed and the armature is initially located at the right of the driving coil center. Switch on the high voltage trigger, charging capacitor bank feed pulse high current to driving coil. The current flowing through the driving coil generates a strong pulsed magnetic field, and induces a large pulsed current in the armature. The current is in opposite direction between the driving coil and the armature, which generates a mutually exclusive electromagnetic force. The driving coil is stationary, and the armature propels the projectile into accelerated motion until it reaches a predetermined speed, so the launch is complete. 2.2 Circuit Equation In the transmitting process, the uneven distribution current along its axial direction of aluminum armature is ignored, and the single-stage induction coil coupling circuit is established, as shown in Fig. 1C is pulse power supply capacitance; D is continuous diode; S is the thyristor and its control assembly; Rc is the resistance of capacitor; RD is the continuous loop resistance, which including the diode resistance and series consumption resistance; R1 is the resistance of the discharge circuit, including the resistance of the cable and the connecting interface; Rd is the resistance and Ld is the inductance of the driving coil. M is mutual inductance between driving coil and armature [11]. S
A
R1 Id
RC
Rd
RD
M Ip Ld
Lp
D
C
B
Fig. 1. Coupled circuit of single-stage
Rp
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1) When discharging the coil, the voltage UAB ≥ 0 which from point A to point B, and the equivalent circuit equation is as follows: dId (t) d + (Rc + R1 + Rd )Id (t) + [MIp (t)] = UB dt dt t Among them UB = U0 − 0 Id (t)dt, In the formula Ld
Rp Ip (t) + Lp
dIp (t) d + [MId (t)] = 0 dt dt
(1)
(2)
2) After discharge, the driving coil is continued through the diode, and the equivalent circuit equation is as follows: Ld
dId (t) d + (RD + R1 + Rd )Id (t) + [MIp (t)] = 0 dt dt
(3)
According to the magnetic flux coupling and mutual inductance law, Id M = IP LP , substitute the expression of armature current IP into Eq. (3) get: (Rd + R1 + RD − Rp
M2 M 2 dId (t) =0 )Id (t) + (Ld − ) 2 Lp Lp dt
(4)
Solving the equation results in: M2 Id (t) = c exp[−(Rd + R1 + RD − 2 )t Lp
(Ld −
M2 )] Lp
(5)
3) The force F on the armature in the process of movement is: Fp = Id Ip
dM M dM = Id2 dx Lp dx
(6)
In order to improve the performance of the catapult, it is necessary to increase the force in the coil discharge stage and reduce the armature drag force in the continuation stage. According to the force formula (6), the current should be increased or decreased under the corresponding circumstances. The current can be increased when the equivalent resistance of the discharge circuit is reduced, corresponding to the increasing of the thrust peak value. The current of the loop during the continuous flow can be reduced when the equivalent resistance of the continuous loop is increased, correspondingly reduce the peak value of the armature drag force, which can increase the efficiency of the catapult to a certain extent.
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2.3 Computing Efficiency During the launching process, the total energy of the system remains unchanged, including the electrical energy of the capacitor bank, electromagnetic energy in the coil, kinetic energy of the load, and thermal loss of the resistance, etc. The efficiency of the system is defined as the ratio of the kinetic energy acquired by the load and armature to the initial energy of the capacitor bank. η=
1 2 2 2 m(v2 − v1 ) 1 2 2 CU
(7)
In the formula, m is the mass of armature and load, V2 is fire velocity,V1 is initial velocity, C is the capacitance value of the circuit outside the coil, U is the initial voltage of the capacitor.
3 Simulation Analysis The external circuit of coil ejector has great influence on the ejection performance, among which the resistance value of the discharge loop affects the highest launching speed, and the resistance value of the continuation loop affects the final launching speed. In order to analyze the influence of resistance value on transmission efficiency, Ansoft Maxwell was used for transient simulation calculation for two kinds of coils with different turns. The capacitance of the pulse capacitor is 4.2 mF, and the initial voltage is 7.5 kV. The projectile armature is an aluminum cylindrical entity with external radius of 184 mm, thickness of 18 mm, axis length of 340 mm, and mass of 8 kg. The mass of armature and load is 110 kg, initial speed is zero, the initial trigger position is the axial center of the coil. The simulation model is shown in Fig. 2.
Fig. 2. Simulation model of single stage coil catapult
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Table 1. The simulation parameters of coil Parameter
coil1
coil2
Turns
140
70
Inner diameter/mm
186
186
Eternal diameter/mm
260
230
Axial length/mm
100
100
3.1 Effect of Equivalent Resistance of Discharge Circuit on Emission Performance The equivalent resistance of the drive coil discharge circuit includes coil resistance, modulated inductance resistance, cable resistance and contact connection resistance. Since the resistance of the drive coil is obtained by combining the number of turns, current carrying capacity, strength and other factors, it is not within the scope of this study. This paper mainly studies the line resistance of other parts of the circuit, which is 10 m, 50 m, 100 m and 200 m in sequence, conducts transient simulation calculation for them. It can be seen from Fig. 3 and 4 that, with the decrease of the resistance of the discharge circuit, the peak time of the current and thrust of the driving coil is advanced, and the value of the peak velocity increases significantly. For the ejection system composed of coils with different turns, the speed and efficiency change to different degrees. The load speed of the catapult of coil 1 increases from 10.32 m/s to 13.47 m/s, and the speed increases by 30.5%, the efficiency increases from 4.96% to 8.45%, and the efficiency increases by 70.36%. The load speed of coil 2 catapult increases from 8.91 m/s to 17.17 m/s, the speed changes 92%, the efficiency changes from 3.70% to 13.73%, and the efficiency increases 271%. On the whole, it can be seen that the equivalent resistance of the discharge circuit has a great influence on the performance of the catapult, and the resistance with fewer turns has a higher degree of influence under the condition of the same discharge resistance.
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Fig. 3. Transient simulation Results of coil1 with different discharge resistance
3.2 Effect of Equivalent Resistance of Continuous Circuit on Emission Performance According to the impedance value of the coil itself, the resistance of coil 1 continuous loop is 0 , 0.1 , 0.8 and 10 , and the resistance of coil 2 continuous loop is 0 , 0.03 , 0.5 and 10 . Transient simulation calculation is performed. Figure 5 and 6 show that the value of the continuation resistance does not affect the current waveform and thrust waveform at the discharge stage. With the increase of circuit resistance, the current attenuation speed is accelerated, and the time of negative force on the armature is shortened. When the continuous loop resistance reaches a certain value, the driving coil current is reversed and the thrust changes from negative to positive, which is conducive to the acceleration of the armature. The speed can be increased by 13%, and the efficiency can be increased by 26.06% or even higher. However, in this case, the capacitor is reverse charged, which affects the life of the pulse capacitor.
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Fig. 4. Transient simulation Results of coil2 with different discharge resistance
Therefore, the selection of the resistance of the continuation circuit combined with the value of the resistance of the discharge circuit itself, it is not the larger the better. The speed of the armature is 11.42 m/s when the resistance of the discharge circuit of coil 1 is zero, and the speed is 11.93 m/s when the resistance is 0.8 , the speed is increased by 4.5% and the efficiency is increased by and 9.23%. When the resistance of the discharge circuit of coil 2 is 0, the speed of the armature is 12.42 m/s, and when the resistance is 0.5 , the speed is 12.73 m/s, the speed is increased by 2.5% and the efficiency is increased by and 5.15%. The serial resistance of the continuous loop can reduce the armature drag effect to a certain extent and improve the final speed, especially for the coil with larger resistance value.
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Fig. 5. Transient simulation results of coil1 with different freewheeling resistance
4 Experimental Verification In order to verify the accuracy of the theoretical and simulation results, two kinds of coil specimens were processed according to the parameters in Table 1, and a single-stage coil catapult was built. The pulse power parameters were capacitance value 4 mF, voltage 7.5 kV, and resistance of the optimized external circuit discharge circuit was 20 m. The mass of armature is 8 kg and the mass of load is 100.4 kg. During the test, the armature is placed in the middle axial position of the coil, and the armature and load contact is placed without fixed connection. After charging the pulse capacitor to the required voltage with a high voltage charger, control signals are sent to the thyristor drive circuit through the optical fiber, so that the pulse capacitor discharges the driving coil and the armature is emitted. During the launching process, infrared laser velocity measurement is placed at the tail for the speed test of the armature, and a scale is laid under the front end of the load to complete the load speed test through high-speed photography (Fig. 7 and Table 2).
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Fig. 6. Transient simulation results of coil2 with different freewheeling resistance
Fig. 7. Single-stage coil catapult
For the two coil parameters, the discharge resistance was set as 0.8 and 0.5 respectively. It can be seen from the results that after adding the resistance of the continuation loop, the exit velocity of the armature is improved, but the actual velocity is lower than the simulation due to ignoring the influence of friction and other factors during
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Parameter/
The highest speed m/s
The drum speed m/s
Speed up%
Efficiency up%
coil1
0
13.247
11.04
4.6
9.5
0.8
12.78
11.55
0
14.29
12.25
3.2
6.67
0.5
13.56
12.65
coil2
launching. The speed of coil 1 with higher resistance is promoted greater than that of coil 2 with lower resistance, which is consistent with the results of simulation analysis.
5 Conclusion In this paper, through theoretical analysis and simulation to calculate the discharge circuit and loop resistance change, on the influence of catapult performance including discharge current, electromagnetic thrust, maximum speed and the final speed, and two kinds of different specifications of a single-stage coil ejection experiments, the results coincide with the results of simulation, the results of the study has reference function to the catapult optimization. (1) With the decrease of the resistance of the coil discharge circuit, the efficiency of the catapult is improved, and the effect of the coil catapult with fewer turns is greater. The loop resistance value can be further reduced from the following aspects, such as coil wire material selection, modulated inductance optimization, cable selection and interface design, so as to improve the transmission efficiency of coil ejection system. (2) As the resistance value of coil continuation loop increases, the armature speed increases, but its value needs to be matched with the coil impedance design. When the current resistance reaches a certain value, the current will reverse to charge the capacitor. Considering capacitor safety, the value of the current resistance has a certain limit. The matching resistance value of coil continuation loop with large impedance is also larger, and the speed improvement effect is larger. If the pulse capacitor can withstand reverse charging, the final launch speed of the catapult can be greatly improved. (3) The external circuit should be optimized according to the coil loop and the firing demand. When the armature and load are separately, the smaller the resistance of the continuation loop is the better. At this time, the load complete the firing at the highest speed, and the armature can be discharged or even recovered at a lower speed with the help of the armature dragging effect. In the integrated of armature and load, appropriate resistance should be connected in the continuous loop to weaken the influence of armature drag force and improve the final launch speed.
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References 1. Author, F.: Article title. Journal 2(5), 99–110 (2016) 2. 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) 3. Author, F., Author, S., Author, T.: Book title. 2nd edn. Publisher, Location (1999) 4. Author, F.: Contribution title. In: 9th International Proceedings on Proceedings, pp. 1–2. Publisher, Location (2010) 5. Niu, X., Liu, K., Zhang, Y.: Research on adaptive design of multi-stage synchronous induction coil launcher. Trans. Chin. Electrotech. Soci. 33(15), 3644–3650 (2018) 6. Yu, J., Li, W., Guo, D.: Modeling and simulation of electromagnetic torpedo launching. Mar. Electr. Electron. Eng. 37(3), 5–12 (2017) 7. Liu, K.-P., et al.: Key design parameters and optimum method of medium- and high-velocity synchronous induction coilgun based on orthogonal experimental design. Chin. Phys. B 28(2), 024102 (2019) 8. Abdalla, M.A., Mohamed, H.M.: Asymmetric multistage synchronous inductive coilgun for length reduction, higher muzzle velocity and launching time reduction. IEEE Trans. Plasma Sci. 27(1), 1–25 (2016) 9. Li., Z.: Analysis effects of parameters in pulsed power supplier system on the accuracy of muzzle velocity. Nanjing University of Science Technology, Nanjing (2017) 10. Li, Z., Ma, Y., Lu, M.: Design and study of electromagnetic launch system for unmanned aerial vehicle. Adv. Technol. Electr. Eng. Energy 37(8), 68–74 (2018) 11. Zhang, W., Qi, C., Quan, Y.: Design of three-stage coil gun launching system. Elctr. Measur. Instrum. 54(14), 93–98 (2017) 12. Guo, W., Su, Z., Cao, B.: Muzzle velocity and efficiency performance of single-stage induction coilgun. J. Gun Launch Control 37(2), 1–4 (2016) 13. Wang, X., Yu, C., Zhao, S.: An optimization method of magnetic field configuration for electromagnetic coil launch. Ordnance Ind. Autom. 37(8), 1–5 (2018) 14. Liu, H., Zhang, P., Luo, W.: Influence of single-stage inductive coil guns peripheral circuit on armature capture effect. J. High Press. Phys. 29(6), 449–454 (2015) 15. Xiong, S., Lu, J., Zheng, Y.: Modeling and analysis of discharge of pulsed power supply for electromagnetic launch. J. Nat. Defense Univ. Sci. Technol. 41(4), 53–59 (2019)
Influence of Copper Wire Sectional Shape on Induction-Coil Catapult Performance Qingzhao Liu(B) , Qi Li, Shuguo Pan, and Changbo Wang Zhengzhou Electromechanical Engineering Research Institute, Zhengzhou 450000, China [email protected]
Abstract. Firstly, according to the parameters of orthogonal optimization and engineering constraints, two kinds of windings with the same number of turns and copper wire cross section area are designed, and the copper wire cross section shape is rectangular and circular respectively. Then, based on the Maxwell transient solver, a two-dimensional axisymmetric model was established, and the influence of the rectangular section and circular section driving coil on the performance of the single-stage coil catapult was simulated an analyzed. Finally, the singlestage coil catapult is designed and tested. The test results are consistent with the simulation results, which proves the correctness of the simulation method and model. The results show that the shape of copper wire affects the performance of single-stage coil catapult. And the ejection performance of rectangular copper wire winding is better than that of circular section. Keywords: Induction coil catapult · Copper wire winding · Rectangular section · Emission efficiency
1 Introduction The coil type electromagnetic launching device is essentially a launcher that can convert electrical energy into the kinetic energy needed to launch objects. Many of its performances are far better than mechanical energy launchers and chemical energy launchers [1], During the ejection process, there is no mechanical contact between the mover and the driving coil, which has huge application prospects in artillery, aerospace launching and other technical fields [2, 3]. At present, the research on induction coil catapult at home and abroad is mainly based on engineering test prototypes and finite element simulation [4, 5], and it has not really entered the engineering stage. The drive coil is the core component of the coil ejector. Its structural design will directly affect the launch efficiency of the coil ejector [6, 7]. The larger the diameter of the drive coil winding, the smaller the resistance loss, but it will also cause winding and The coupling between the armatures becomes smaller, thereby reducing the transmission efficiency. The selection of the copper wire of the winding, and the difference in insulation between turns and layers will cause changes in the overall coil magnetic field and electromagnetic force distribution. If the design is unreasonable, it will affect the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 90–102, 2022. https://doi.org/10.1007/978-981-19-1870-4_10
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ejection performance of the coil ejector and even cause electrical breakdown or structural damage between the turns and layers of the wire. In recent years, researchers have done many researches on driving coils to induction coil catapults. In 2014, Zhang Yadong of Wuhan University and others conducted research on the coil stranded wire model, compared and analyzed the advantages and disadvantages of the coils made by the litz wire model and the strip wire model, and pointed out that the litz wire production is more suitable for the production of high-strength coils than the ribbon coil [8]. In 2018, Yu Chengbo and others used ANSYSY simulation software to analyze the distribution of the magnetic field strength of the transmitting coil, and analyzed the factors affecting the magnetic field strength by changing the design parameters [9]. The driving coil works in a high voltage, high current, and strong magnetic field environment. Pulsed high current discharge will generate strong electromagnetic force on the coil, so its structural design will directly affect the performance of the coil catapult. This article first optimizes the design of the basic parameters of the coil catapult. According to the design parameters and engineering constraints, two drive coil copper wires with rectangular and circular cross-sections are selected, and then the twodimensional transient model of the Maxwell finite element analysis software is used to compare the two A coil ejector with a copper wire cross-section is simulated and calculated. Finally, a driving coil wound with a rectangular cross-section copper wire is processed and tested. The test results are compared with the simulation results to verify the accuracy of the simulation model and method.
2 The Design of the Copper Wire of the Driving Coil 2.1 Shape and Size Design of Copper Wire The induction coil catapult involves many parameters, and each parameter will affect its launch efficiency. The design method of induction coil catapult is to optimize the design of these parameters. At present, there are common optimization methods such as genetic algorithm, ant colony algorithm, simulated quenching method, and orthogonal experiment method. Among them, the orthogonal test method is a theoretically simple optimization method for multiple factors and multiple levels, and it is also a relatively widely used design method in engineering. In 2016, Zhang Yadong of Wuhan University and others used the orthogonal experiment method to design the three-stage coil catapult model, and obtained a more ideal launcher parameter design [10]. In this paper, orthogonal experiment method is used, according to the design requirements [11, 12], the exit speed of the armature is taken as the target, the parameter level value is determined, the orthogonal experiment table is constructed, and the Ansoft Maxwell software is used for simulation calculation according to the orthogonal experiment table. Get a relatively ideal set of parameter values. Whether the data obtained after optimization can meet the engineering constraints requires further verification. The driving coil is made of a copper wire with a rectangular cross-section, and the copper wire is composed of a copper core and an insulating layer. As shown in the figure, an insulating layer is attached to the surface of the copper wire,
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and the surface of the insulating layer is uniform. There are: x1 − x2 = y1 − y2
(1)
formula: x 1 —length of copper core plus insulation layer; x 2 —length of copper core; y1 —copper core plus insulation layer width; y2 —copper core plus insulation layer length copper core width. The driving coil is wound layer by layer by a wire, and the length of the winding is represented by a. The number of coil turns that can be wound on each layer is: a (2) n1 = x1 The number of driving coil layers n2 is: n2 =
r2 − r1 y1
(3)
The total number of turns N of the drive coil is: N = n1 × n2
(4)
The driving coil can be approximated as a hollow cylindrical coil, regardless of the influence of the insulating layer, the inductance L of the driving coil is: L = 2π μ0 n2c r15 T (q, p)
(5)
In the formula, nc —the number of turns per unit area in the section of the driving coil; p—the thickness-to-diameter ratio of the driving coil; u0 —vacuum permeability; T(q, p)—the shape factor of the hollow cylindrical coil. After the equivalent inductance is calculated, the maximum peak current I max in the drive coil is approximately calculated: C (6) Imax = U × L Through formulas (1)–(6), the maximum current that the wire of the drive coil must bear can be obtained. At present, scholars at home and abroad have established the current-carrying characteristic quantity SAM of different materials through experiments. The unit is the square of the current density multiplied by the time in seconds. When the core of the wire section is a copper core, the SAM value is 80490 (A/mm2 )2 s. Discharge cycle T of the discharge current of the drive coil: √ (7) T = 2π LC Since the discharge current of the drive coil with freewheeling diode is mainly concentrated in the first half of the cycle, the maximum current carrying capacity I of the copper wire per unit cross-sectional area can be calculated: SAM (8) I= T /2
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Therefore, the cross-sectional area w of the copper core of the wire should meet the following conditions: ω = x2 × y2
(9)
The optimized design parameters r 1 = 90 mm, r 1 = 115 mm, a = 90 mm, N = 90, U = 8000 V, C = 4 mF. Substituting the above conditions into Eqs. (1)–(8), we can get: Lrectangle = 1.67 mH
Lround = 1.89 mH
Irectangle = 2226.96 A
Iround = 2158.86 A
ωrectangle ≥ ωround ≥
Imax rectangle = 5.6 mm2 I rectangle Imax round = 5.4 mm2 I round
The parameters of copper conductors with rectangular and circular cross-sections are comprehensively compared, and on the basis of satisfying engineering constraints, two conductors with basically the same cross-sectional area are selected. The specific dimensions are: The rectangular cross-section copper wire is a flat wire with an insulation thickness of 3 mm, a length of 5.3 mm, and a width of 3.7 mm. The interlayer insulation thickness is 6 mm, and the cross-sectional area S 1 = 19.61 mm2 . For the round cross-section copper wire, a round wire with an insulation thickness of 3 mm and a radius of 2.5 mm is selected, the interlayer insulation thickness is 6 mm, and the cross-sectional area S 2 = 19.625 mm2 . 2.2 Copper Wire Resistance Calculation Since the driving coil is generally a solenoidal hollow cylindrical coil densely wound by copper wires, the resistance of the driving coil varies with the change of the driving coil structure parameters during the numerical solution process, and it is wound with a flat copper wire Take the driving coil of as an example, the inner diameter of the driving coil is r 1 , the outer diameter is r 2 , and the axis length is a. When the coil is actually processed, in order to improve the insulation strength of the coil, there is usually a certain gap between the turns of the coil and between the layers. Therefore, the sum of the cross-sectional area of the wire is actually smaller than the cross-sectional area of the driving coil, which defines the winding copper The ratio of the total cross-section of the wire to the cross-sectional area of the drive coil is the filling factor k, (the thickness of the interlayer insulation is 0.6 mm), the volume of the drive coil is set V, the interface street of the copper wire is S, then the volume of the copper wire is: V = kV = kπ(r22 − r12 )a
(10)
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Due to the small cross-sectional area of the copper wire, the skin effect is ignored in the calculation, and the resistance of the driving coil can be obtained: R = ρkπ(r22 − r12 )/S 2
(11)
Filling factor of rectangular cross-section wire k 1 = 0.63; Filling factor of circular cross-section wire k 2 = 0.49; Therefore, the resistance of the rectangular cross-section wire is R1 = 55.55 m, and the resistance of the round cross-section wire is R2 = 57.30 m. From the calculation results of the above two sections, it can be concluded that the cross-sectional area of the rectangular cross-section copper wire and the round crosssection copper wire are basically the same,l1 = 0.6 mm, l 2 = 1.2 mm.
3 Simulation Calculation of Copper Wire Windings with Different Cross-Sections 3.1 Calculation Model and Parameters In order to study the influence of copper wire on the coil ejector, the number of turns of the copper wire and the cross-sectional area of the single-turn copper wire are basically the same in the simulation calculation. Therefore, the cross-sectional shape and resistance value of the copper wire are the two main factors that affect the coil ejector. The resistance value R1 of the rectangular cross-section and the resistance value R2 of the round crosssection copper wire winding have been obtained through the calculation in Chapter 1. In order to study the influence of the cross-sectional shape of the wire on the ejector, assuming that the resistance value of the rectangular cross-section copper wire winding is also R2 , three groups are formed Comparing the calculation examples, in the following, the rectangular cross-section R1, the circular cross-section R2 and the rectangular crosssection R2 are used to express, and the parameters are shown in Table 1: Table 1. The parameters of simulation calculation model Parameter
Rectangular section R1
Circular cross section R2
Rectangular section R2
Discharge voltage U/V 2100
2100
2100
Capacitance value C/mF
4
4
4
Axial length of copper wire a/ mm
90
90
90
Copper wire inner diameter r 1 /mm
90
90
90
Copper wire cross-sectional shape
Rectangle
Round
Rectangle
Copper wire turns N
90
90
90 (continued)
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Table 1. (continued) Parameter
Rectangular section R1
Circular cross section R2
Rectangular section R2
Copper wire resistance 55.53 R/m
57.30
57.30 (Hypothesis)
Single-turn coil cross-sectional area S/mm
19.61
19.62
19.61
Insulation thickness between turns l1 /mm
0.6
0.6
0.6
Insulation thickness between layers l2 /mm
1.2
1.2
1.2
The Ansoft Maxwell finite element analysis software based on Maxwell’s differential equations is widely used in the field of electromagnetic fields. It transforms complex electromagnetic field calculations in engineering into huge matrix solutions through the form of finite element discretization. The structure of the induction coil catapult has axisymmetric characteristics, which can simplify the complex three-dimensional model into a two-dimensional axisymmetric model for solution. In this paper, the simulation model is solved by a two-dimensional axisymmetric model transient solver. According to the optimized design parameters of the coil ejector and the calculated calculation parameters of the copper wire, the modeling is carried out, and the mesh is divided according to the model, and the local The mesh is refined, and the simulation model of the ejector with rectangular cross-section copper wire winding and circular cross-section copper wire winding coil is shown in Fig. 1 and Fig. 2:
Fig.1. Coil catapult model of copper wire winding with rectangular section
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Fig. 2. Coil catapult model of copper conductor with circular cross section
3.2 Simulation Results The calculation model is the same except that the shape, size and resistance of the copper wire are different. The pulse power parameters are capacitance value C = 4 mF, voltage U = 2100 V, armature weight M = 8 kg, and the initial trigger position of the armature is the middle position of the coil axis. The simulation results are as follows: Table 2. Simulation results of coil catapult Parameter
Rectangular section R1
Circular cross section R2
Rectangular section R2
Discharge voltage/V
2100
2100
2100
Voltage drop time/ms
3.65
3.8
3.68
Peak current/A
3215.58
3133.58
3208.91
Time to peak current/ms
2.7
2.95
2.75
Maximum thrust/kN
44.86
44.67
41.15
Armature exit speed m/s
15.89
15.26
15.81
Emission efficiency
11.45%
10.56%
11.34%
Figure 3 shows the characteristic curve of the discharge circuit of the coil ejector. From the curve, we can see that the discharge voltage drop time and the current rise time and amplitude of the rectangular cross-section R1 and the rectangular cross-section R2 are very close, and the current peak difference ratio is only 0.2%; the circular crosssection The discharge voltage drop time and current rise time of R2 are both longer than
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the rectangular cross-section R1, but its peak discharge current is significantly lower than the rectangular cross-section R1, and the current peak difference ratio is 2.55%, indicating that the change in resistance has little effect on the coil ejector In contrast, the cross-sectional shape of the copper wire has a more significant effect on the discharge circuit of the coil ejector.
Fig. 3. Characteristic curve of discharge loop of coil catapult
Fig. 4. The change curve of the axial thrust on the armature
Figure 4 shows the change curve of the axial thrust of the armature of the coil ejector; Fig. 5 shows the change curve of the armature speed. It can be seen from Figs. 4 and 5 that the axial thrust change curve and speed value change curve of the armature of rectangular cross section R1 and rectangular cross section R2 are very close; the axial thrust of the armature of rectangular cross section R1 is very close. The value is significantly larger than the circular section R2. The armature exit velocity of the circular section R2 coil ejector is 15.26 m/s, and the ejection efficiency is 11.45%; the rectangular
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section R1 coil ejector armature exit velocity is 15.89 m/s, and the ejection efficiency is 10.56%; Compared with the circular section R2, the exit speed of the rectangular section R1 is increased by 4.13%, and the efficiency is increased by 7.78%. A comprehensive comparison found that the ejection performance of the rectangular cross-section copper wire winding coil ejector was significantly better than that of the circular cross-section coil ejector, indicating that the cross-sectional shape of the copper wire has a significant impact on the performance of the coil ejector, and the coupling degree of the rectangular cross-section copper wire and the armature is significantly better. For round cross-section copper wires.
Fig. 5. The change curve of the armature velocity
Figure 4 shows the change curve of the axial thrust of the armature of the coil ejector; Fig. 5 shows the change curve of the armature speed. It can be seen from Figs. 4 and 5 that the axial thrust change curve and speed value change curve of the armature of rectangular cross section R1 and rectangular cross section R2 are very close; the axial thrust of the armature of rectangular cross section R1 is very close. The value is significantly larger than the circular section R2. The armature exit velocity of the circular section R2 coil ejector is 15.26 m/s, and the ejection efficiency is 11.45%; the rectangular section R1 coil ejector armature exit velocity is 15.89 m/s, and the ejection efficiency is 10.56%; Compared with the circular section R2, the exit speed of the rectangular section R1 is increased by 4.13%, and the efficiency is increased by 7.78%. A comprehensive comparison found that the ejection performance of the rectangular cross-section copper wire winding coil ejector was significantly better than that of the circular cross-section coil ejector, indicating that the cross-sectional shape of the copper wire has a significant impact on the performance of the coil ejector, and the coupling degree of the rectangular cross-section copper wire and the armature is significantly better. For round cross-section copper wires. In literature [8], during the coil ejection process, the driving coil receives a radial force far exceeding the axial force. Therefore, the strength of the coil structure should
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be fully considered. In the simulation, the radial force on each turn of the copper wire is calculated. The analysis of the radial force curve and pressure cloud graph is as follows: Figure 6(a) shows the radial force on each turn of the rectangular copper wire of the driving coil during the ejection of the coil. From the figure, it can be seen that the radial force of each turn of the copper wire during the ejection process increases first and then decreases., And a small part of the curve appears negative, the inflection point basically appears at time t = 2.8 ms, combined with Fig. 6(b) when t = 2.8 ms, the radial force and pressure cloud diagram of each turn of the rectangular copper wire, comprehensive analysis shows that it is close to The radial force of the copper wire on the armature side is positive, and the maximum value appears at the upper side of the side close to the armature, with an amplitude of about 5782 N. The radial force of the copper wire on the side away from the armature is negative, with an amplitude of about 1400 N, Indicating that the closer the copper wire is to the armature, the higher the coupling degree, and the radial force is mainly concentrated on the side close to the armature. Figure 7(a) shows the radial force on the round copper wire of each turn of the driving coil during the coil ejection. The curve change trend is the same as that of the rectangular wire. The inflection point basically appears at t = 2.8 ms, Fig. 7(b) The radial force and pressure cloud diagram of each turn of the rectangular copper wire at t = 2.8 ms, comprehensive analysis shows that the radial force of the copper wire on the side close to the armature is positive, and the maximum value appears at the upper position on the side close to the armature, and the amplitude is about 5364 N, the radial force of the copper wire on the side far from the armature is negative, and the amplitude is about 1351 N, which is significantly lower than that of the rectangular wire, indicating that the axial force and radial force on the round wire winding is better than that of the rectangular wire during the ejection process. Therefore, the structural strength of the drive coil should be fully considered in actual engineering applications to ensure that the drive coil meets the requirements of use.
Fig. 6. Radial force on rectangular section copper wire of each turn in the drive coil
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Fig. 7. Radial force on the circular section copper wire of each turn in the drive coil
4 Electromagnetic Ejection Test and Finite Element Simulation Verification Based on the above analysis results, a single-stage electromagnetic coil catapult is designed and tested. Single-stage coil ejector parameters rectangular cross-section R1 simulation parameters are designed, the driving coil turns N = 90, the armature material is aluminum alloy 6063, the pulse power parameters are the same as in the simulation, and the discharge circuit characteristic value is collected by the oscilloscope during the armature test, The speed is measured by a laser speedometer with a range of 25 m/s. The test and simulation results of the single-stage coil catapult are as follows (Table 3): Table 3. Simulation results of coil catapult Parameter
Test results
Simulation and test error
Discharge voltage/V
2100
–
Voltage drop time/ms
3.92
–
Peak current/A
3126.26
2.78%
Time to peak current/ms
2.85
–
Armature exit speed m/s
15.56
1.70%
Emission efficiency
10.98%
4.10%
Figure 8 shows the comparison diagram of the characteristic curve of the testsimulation discharge circuit. Figure 9 shows the speed measurement of the laser tester, which can be obtained from Table 2, Fig. 6, and Fig. 7. The change trend of the discharge voltage and discharge current curve of the test is consistent with the simulation, and the voltage drop time It is close to the current rise time, and the peak current error is 2.78%. The speed change curve measured by the laser tachometer is consistent with the simulation speed change curve trend, and the armature decreases after reaching the maximum value. This is caused by the reverse of the induced current in the armature
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Fig. 8. Characteristic curve of discharge loop of coil catapult
Fig. 9. Laser velocimeter measures speed
and the armature being subjected to the reverse axial tension., In line with theoretical analysis. During the test, the armature exit speed is 15.56 m/s, the emission efficiency is 10.98%, the error from the simulation value is only 1.70%, and the emission efficiency error is 4.10%. Comprehensive comparison test and simulation of the basic discharge circuit characteristics, and the change of armature speed can be obtained: the test results are consistent with the simulation results, which proves the correctness of the simulation model and method, and the simulation results are credible.
5 Conclusion This paper first uses the design parameters optimized by the orthogonal experiment method to calculate and select the copper wire cross-section parameters of the coil catapult drive coil winding, and verifies that the selected copper wire meets the engineering
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constraints, and then uses the Maxwell two-dimensional transient simulation model The coil catapults are respectively rectangular section windings and circular cross-section windings are simulated and calculated, and the results are analyzed. Finally, a singlestage coil catapult with rectangular cross-section windings is fabricated and tested. The test results are consistent with the simulation results, which proves The correctness of the simulation model and method is verified. The following conclusions can be drawn from this article: (1) In a certain range, compared with the resistance value, the change of the crosssectional shape of the copper wire has a more significant impact on the coil ejector; (2) During the ejection process, the radial electromagnetic force on the copper wire winding is mainly concentrated near the armature One side; (3) For the model in this article, the ejection performance of the rectangular cross-section copper wire winding is better than the circular cross-section coil catapult, the launch speed is increased by 4.13%, and the launch efficiency is increased by 7.78%, but the circular cross-section winding copper wire is more stressed. Good; (4) In the case of fully considering the strength of the drive coil structure, the rectangular cross-section copper wire is more suitable for processing and manufacturing the drive coil winding.
References 1. Li, J., Yan, P., Yuan, W.: Electromagnetic gun technology and its development. High Voltage Eng. 40(4), 1052–1064 (2014). (in Chinese) 2. Li, Z., Ma, Y., Lu, M., et al.: Design and study of electromagnetic launch system for unmanned aerial vehicle. Adv. Technol. Electr. Eng. Energy 37(8), 68–74 (2018). (in Chinese) 3. Abdalla, M.A., Mohamed, H.M.: Asymmetric multistage synchronous inductive coilgun for length reduction, higher muzzle velocity, and launching time reduction. IEEE Trans. Plasma Sci. 27(1), 1–25 (2016) 4. Liu, K.-P., et al.: Key design parameters and optimum method of medium- and high-velocity synchronous induction coilgun based on orthogonal experimental design. Chin. Phys. B 28(2), 024102 (2019) 5. Sun, Q., Li, W., Luo, B., et al.: Design and research of a solenoid double C coil with compatibly coupling diversity coils and large offset tolerance. Adv. Technol. Electr. Eng. Energy 38(5), 33–41 (2019). (in Chinese) 6. Zhang, Y., Ruan, J., Niu, X., et al.: Optimization analysis study of a multi-stage SICG based on OED. IEEE Trans. Dielectr. Electr. Insul. 22(4), 2073–2080 (2015) 7. Fan, G., Jiang, M., Long, X., et al.: Effects of driving coil connection modes on emission efficiency of MFEL 38(4) (2017). (in Chinese) 8. Zhang, Y., Zhang, W., Yang, S., et al.: Mechanical property and manufacture technology of electromagnetic driving coil. High Voltage Eng. 40(4), 1186–1193 (2014). (in Chinese) 9. Yu, C., Lin, Z., Liang, Z.: Simulation analysis of magnetic field of three-dimensional wireless power transmission coil. Electr. Technol., 204–208 (2018). (in Chinese) 10. Zhang, Y., Xiao, G., Wang, Z., et al.: Key design parameters selection of synchronous induction coil launcher based on orthogonal experiment. High Voltage Eng. 42(9), 2843–2849 (2016). (in Chinese) 11. Xiang, H., et al.: Analysis of parameter sensitivity of induction coil launcher based on orthogonal experimental method. IEEE Trans. Plasma Sci. 43(5), 1198–1202 (2015) 12. El Refaie, A.M.: High speed operation of permanent magnet machines. The University of Wisconsin-Madsion, USA (2005)
Effect of Temperature on the Performance of Induction Coil Launcher Yadong Zhang1,2(B) , Mingzhi Zhu1,2 , Kaixiang Li1 , Xiong Lin1 , and Ao Zhou1 1 Wuhan University, Wuhan 430000, Hubei, China
[email protected] 2 Shandong University of Technology, Zibo 255000, Shandong, China
Abstract. Under the action of continuous pulse current, the Joule heat of the synchronous induction coil launcher will continue to accumulate with the increase of the number of pulses, resulting in a significant increase in the temperature of the coil. The mechanical and thermal parameters of the coil and reinforcement materials will change with the increase of the temperature. At present, most studies usually set the relevant mechanical parameters and thermal parameters as constants that do not change with temperature, ignoring the influence of temperature on the relevant parameters. In order to explore the influence of material parameters changing with temperature on the mechanical and thermal properties of induction coil launcher, the 2D transient magnetic-structure-thermal field coupling calculation model of a single-stage coil launcher is established. The temperature dependent material parameters and anisotropic material conditions are added to the model. The von mises stress on the coil during continuous pulse discharge of the single-stage coil launcher is simulated, and the heat dissipation process of the coil under natural cooling is analyzed. The results show that: after 15 pulse discharges, compared with the material parameters that change with temperature, the stable temperature is 5.5 °C lower than that of material parameters that do not change with temperature, which is a decrease of 5.63%. For mechanical properties, the stress level of the inner conductor of the material parameters that change with temperature is increased by 30 Mpa, which is an increase of 17.34%. Keywords: Electromagnetic coil · Continuous pulse discharge · Von Mises stress · Heat dissipation
1 Introduction Electromagnetic launch (EML) is a new kinetic energy launching technology [1, 2]. According to the different working principles and structures, the launcher can be divided into electromagnetic coil (EM) launcher and EM rail launcher [3, 4]. Synchronous induction coil launcher (SICL) is an important device of launch, which is mainly composed of multiple coils and an armature. Each coil can be fed by a pulse capacitor to generate an induced current and electromagnetic force in the conductor armature. Coils are triggered
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 103–110, 2022. https://doi.org/10.1007/978-981-19-1870-4_11
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step by step to accelerate the armature and drive the payload to the specified velocity [5]. After a single launch, the temperature will rise due to Joule heating. Under continuous pulse discharge, the temperature rise will gradually accumulate. If the temperature is too high, the insulation will be damaged [6]. At the same time, the mechanical and thermal parameters of the coil and reinforcement materials change with the temperature rise. The material parameters changing with temperature can not be ignored. Therefore, it is necessary to accurately analyze the temperature rise characteristics of the coil under the action of continuous pulse discharge. A temperature rise model of electromagnetic coil is established in reference [7], the simulation results show that the maximum temperature rise of armature and coil under single pulse discharge is 4.2 °C and 7.7 °C respectively. Golovashchenko mentioned that the heat load problem will seriously affect the service life of the coil, especially in the process of short-cycle continuous discharge [8, 9]. Ma fuqiang established the 3D transient coupling heat transfer model for the solenoid pulse inductor with liquid cooling mode. The simulation results show that during continuous discharge, the temperature of the inductor in the outlet zone is the highest and continues to increase, but the rising speed rapidly slows down. The temperature of the inductor in the inlet zone is the lowest and does not change much. The forced convection heat transfer between the deionized water and the coil is the main way of heat dissipation, and most of the accumulated heat during continuous discharge is stored in the coil [10].
2 Model and Parameters of Single-Stage Induction Coil Launcher The schematic diagram and external circuit of single-stage induction coil launcher are shown in Fig. 1 and Fig. 2. The structure parameters, mechanical material parameters and thermal material parameters are shown in Table 1, Table 2 and Table 3 respectively.
Fig. 1. Two dimensional axisymmetric schematic diagram of electromagnetic induction coil launcher
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Fig. 2. External coil circuit control chart of electromagnetic induction coil launcher
Table 1. Electromagnetic induction coil launcher parameter Internal diameter/mm
Thickness/mm
Length/mm
Armature 37.5
Turns
Internal diameter/mm
Length/mm
Coil 10
100
26
Capacitance/mF
Voltage /V
Power supply 60
80
2
5000
Table 2. Material parameters needed for structure field analysis Parameter
Young’s modulus Er
Poisson’s ratio Eϕ
Ez
Vrz
Vrϕ
Copper
1.396274E11 − 5077626.0T − 191131.5T2 + 290.7333T3 − 0.2058552T4 + 5.385261E−5T5
0.339846 + 2.405498E−5T
Epoxy resin
0.2376E9 + 0.03158E9T − 5.742e4T2
0.6138 − 0.00188T + 2.96E−6T2
−11.88E9 + 1.579E9T − 2.871E6T2
0.2376E9 + 0.03158E9T − 5.742E4T2
0.06138 − 0.000188T + 2.96E−7T2
Vzϕ
0.06138 − 0.000188T + 2.96E-7T2
Table 3. Material parameters needed for structure field analysis Parameter
Specific heat J/(kg * K)
Thermal conductivity W/(m * K)
Density (kg/m3 )
Copper
342.764033 + 0.133834821T + 5.5352529E−5T2 − 1.97122089E−7T3 + 1.1407471E−10T4
423.7411 − 0.3133575T + 0.001013916T2 − 1.570451E−6T3 + 1.06222E−9T4 − 2.64198E−13T5
9062.242 − 0.3913962T − 8.947644E−5T2
Epoxy resin
3.2T
0.0001576T1.3
1560
3 Comparison Between Finite Element and Circuit Model Method In order to verify the accuracy of the calculation results of the finite element simulation software, the same model is built in the finite element software and the self compiled circuit model software respectively. The time step is 10 μs, and the total calculation time
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is 3 ms. The curves of discharge voltage, discharge current, axial electromagnetic force on the armature and armature speed are compared in Fig. 3.
(a) discharge voltage waveform
(c) electromagnetic force waveform
(b) coil current waveform
(d) armature speed waveform
Fig. 3. Comparison of calculation results of different method
The calculation results of finite element simulation software and circuit model are shown in Table 4. Table 4. Comparison of single stage electromagnetic induction coil launcher results Parameter
Finite element software
Circuit model
Exit speed/(m/s−1 )
71.54
72.95
Peak current/(kA)
21.78
20.38
Peak electromagnetic force/(kN)
97.76
110.27
By comparing the curves in Fig. 3 and the results in Table 4, it can be seen that the calculation results of the two methods are not much different. The accuracy of the finite element simulation software is verified.
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4 Influence of Temperature on Launch Characteristics of Coil 4.1 Coil Heat Dissipation Analysis By setting the material parameters changing with temperature and fixed material parameters in the finite element simulation software, 15 pulse discharges are carried out continuously. Launch every 15 s. The heat dissipation curves of continuous pulse discharge of the single EM coil launcher and the cloud diagram of the 15th pulse discharge temperature are shown in Fig. 4.
(a) considering temperature
(b) without considering temperature
(c) comparison diagram of temperature rise curve of continuous pulse discharge coil
Fig. 4. Comparison of heat dissipation of continuous pulse discharge coil
It can be seen that after 15 s heat dissipation of the coil, due to the heat conduction process inside the coil, the temperature on the wire is transferred to the epoxy resin through heat conduction. But the thermal conductivity of the epoxy resin is very small, so it is difficult to quickly diffuse the heat into the air. For this reason, the coil cannot quickly carry out pulse discharges continuously. It can be seen from Fig. 4(c) that the temperature difference between the two models is gradually obvious due to the increase of the pulse discharge. Take the middle plane, the axial section of inner conductor of the coil as Fig. 1 after the 15th pulse discharge to study the overall temperature distribution of the coil which is shown in Fig. 5.
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(a) temperature rise curve along the middle plane
(b) temperature rise curve along the axial direction of inner coil
Fig. 5. Overall temperature distribution of the coil
It can be seen from Fig. 5(a) that the temperature decreases gradually from the innermost to the outermost along the middle plane. The temperature of the material parameter considering the change with temperature is lower than that without considering the change with temperature as a whole; Fig. 5(b) shows the temperature rise comparison between axial inner coil and its axial adjacent epoxy resin. it can be seen from the figure that after 15 pulse discharges, the highest temperature of material parameters that change with temperature is 5.5 °C lower than that of do not change with temperature, which is a decrease of 5.63%. 4.2 Coil Stress Comparison Analysis In order to study the influence of temperature on the mechanical properties of induction coil launcher, considering temperature and the anisotropy of epoxy resin, the electromagnetic-thermal-stress coupling is calculated by finite element simulation. The upper and lower boundaries of the coil are fixed. Firstly, the electromagnetic force is obtained through electromagnetic field analysis, and the electromagnetic force is loaded into the structural field as a load for mechanical analysis. At the same time, the electromagnetic loss obtained from the electromagnetic field analysis is loaded into the temperature field as a load, resulting in the temperature rise of the coil. Secondly, the coil temperature rise is loaded into the structural field as a load to change the mechanical material parameters related to temperature. Finally, it is compared with the calculation results of material parameters that do not change with temperature to explore the influence of temperature on the mechanical properties of induction coil launcher. The cloud diagram of von mises stress at the peak current of the 15th pulse discharge of single induction coil launcher is shown in Fig. 6. It can be seen from Fig. 6 that due to the epoxy resin reinforcement layer is an anisotropic material with high elastic modulus, the maximum stress appears in the innermost epoxy resin reinforcement layer. Because the temperature related material parameters and fixed material parameters are added to the two models respectively, the maximum von mises stress of the two models are 306 Mpa and 286 Mpa respectively.
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(b) without considering temperature
Fig. 6. Mechanical parameters distribution of single stage induction coil launcher
The middle plane of the coil and the axial direction along the inner conductor are taken to study the influence of temperature on the mechanical properties of the coil after the 15th pulse discharge. The von mises stress curve at the peak current time is shown in Fig. 7.
(a) stress comparison along the axial direction of inner coil (b) stress comparison along middle plane
Fig. 7. Curve of coil von mises stress
Figure 7(a) shows that the von mises stress of material (including inner conductor and epoxy resin) changing with temperature is slightly greater than of not change with temperature. So, the temperature has little effect on the axial stress of coil launcher. Figure 7(b) shows that compared with the material parameters that do not change with temperature, the stress level of the inner conductor with material parameters changing with temperature increases by 30 Mpa, an increase of 17.34%, and the stress level of the outer conductor increases by 11 Mpa, an increase of 9.57%. Therefore, temperature should be considered in the material parameters especially in continuous pulse discharge.
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5 Conclusion The main conclusions are as follows: In order to verify the accuracy of the finite element simulation software, a same model is built the self compiled circuit model software. Through comparative analysis, the accuracy of the finite element simulation software is verified. The analysis shows that the temperature of the material parameter considering the change with temperature is lower than that of the fixed material parameter, and the maximum temperature difference is 5.5 °C, which is reduced by 5.63%. The influence of temperature on the coil stress level is analyzed. Compared with the material parameters that do not change with temperature, the stress level of the inner conductor with material parameters changing with temperature is increased by 30 MPa, increased by 17.34%, and the stress level of the outer conductor is increased by 11 MPa, increased by 9.57%.
References 1. Haghmaram, R., Shoulaie, A.: Study of traveling wave tubular linear induction motors. In: 2004 International Conference on Power System Technology, PowerCon 2004, pp. 288–293 (2004) 2. Elliott, D.G.: Traveling-wave synchronous coil gun. IEEE Trans. Magn. 27(1), 647–649 (1991) 3. Schroeder, J.M., Gully, J.H., Driga, M.D.: Electromagnetic launchers for space applications. IEEE Trans. Magn. 25(1), 504–507 (1989) 4. Zhang, T., et al.: Design and evaluation of the driving coil on induction coilgun. IEEE Trans. Plasma Sci. 43(5), 1203–1207 (2015) 5. Kaye, R.J.: Operational requirements and issues for coilgun electromagnetic launchers. IEEE Trans. Magn. 41(1), 194–199 (2005) 6. Dai, X., Xiao, Z.: Temperature characteristics of coaxial cable under continuous fast pulse high current. J. Nav. Eng. Univ. 28(z1), 61–64 (2016). (in Chinese) 7. Min, X., Zhang, Y., Gong, Y., et al.: Study on temperature rise of single-stage electromagnetic induction coil launcher. Strong Laser Part. Beam 32(3), 114–121 (2020). (in Chinese) 8. Golovashchenko, S., Bessonov, N., Davies, R.: Design and testing of coils for pulsed electromagnetic forming. In: Proceedings of the 2nd International Conference on High Speed Forming, vol. 3, pp. 20–21 (2006) 9. Golovashchenko, S.: Material formability and coil design in electromagnetic forming. J. Mater. Eng. Perform. 16(3), 314–320 (2007) 10. Ma, F., Li, B.: Thermal analysis of the pulse inductor for electromagnetic launch under continuous discharge condition. IEEE Access 9, 88027–88036 (2021)
Research of Mechanical Sensitive Factors of a Electromagnetic Rail Gun Cradle Jun Xu(B) The 713 Research Institute of CSSC, Zhengzhou 450015, China [email protected]
Abstract. A electromagnetic rail gun cradle structure, including neck barrel, is introduced. And, mechanical sensitive factors and their variation characteristics affecting deflection of the cradle are analyzed in multi-dimension. The boundary load of the cradle under bad working conditions is calculated by analytic method, which is used as the boundary condition of simulation to carry out calculation. Based on the finite element theory, a simulation model is established to calculate the maximum deflection of the cradle in three sensitive factors, namely, the length of the gun breech guide, the thickness of the neck barrel and the thickness of the frame rib plate. Various simulation results are obtained by changing the parameters of the sensitive factors, and the deflection trend in the analysis results is compared to form the law of the influence of the sensitive factors on the cradle maximum deflection. The conclusion can be used as an important basis for lightweight and overall design of the cradle of naval gun. Keywords: Electromagnetic rail gun · Cradle · Deflection · Mechanical sensitive elements
1 Introduction The cradle is a carrier for important components such as the gun launch system, which aims the gun in a high and low direction by means of a pitching motion. During the firing process, the load is transferred to the other components through the cradle, which is an important structural component of the gun. Modern structural optimization design methods are widely used in the engineering field and they provide new ideas for the innovative design of the gun. According to finite element technology, Fu Wei, Sun Quanzhao, Qian Huizong, and Li Zhixu [1–4] carried out a multi-objective optimization design of a gun cradle. Also, rigid strength and mass were taken into account by them. According to topological optimization, Lei Li, B. Ullah, X. Huang, Zhu Jiaxuan, Zhang Xinjian, et al. carried out an innovative design of the structure [5–9]. In the existing literature on the structural design of guns, detailed indicators of the sensitivity factors affecting the stiffness of the cradle have not been mentioned. This does not facilitate the practical application of engineering. That is, the structure of the cradle is repeatedly modified to perform optimization calculations when the scheme design is in a state of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 111–118, 2022. https://doi.org/10.1007/978-981-19-1870-4_12
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unknown sensitivity to the sensitive factors. This ultimately leads to the desired result. Such a design is less efficient. In this paper, the structural dimensions of the cradle are optimized and designed based on a finite element model of the electromagnetic rail gun cradle. At the same time, the engineering reality is combined and the factors influencing the cradle deflection are extracted. In addition, the sensitivity of the factors influencing the cradle deflection is analyzed and the lightweight design is guided.
2 Mechanical Simulation Model of Electromagnetic Rail Gun Cradle The structure of the electromagnetic rail gun cradle is different from that of the conventional gun, mainly in that the size in the width direction is significantly larger than that of the conventional gun, and the upper portion of the trunnion mass is significantly higher than that of the lower portion. In response to the above characteristics, a mechanical model is established to analyze the cradle deflection sensitivity factors. The main loads on the cradle can be summarized as cradle and neck barrel gravity, tube and feeder gravity, recoil section and cradle friction, feeder gravity, balancing machine force, park and retreat reentry machine and high and low tooth arc forces[9]. The calculated values of the above loads are obtained by numerical calculations when the firing system is in horizontal position. Using the software to establish the cradle model, simplify the structure, add constraints, apply load, divide the mesh, and get the cradle mechanical calculation model as shown in Fig. 1. By analyzing the mechanical model, the factors that affect the cradle deflection are mainly the forceful action displacement and its own structure. Since the main interface of cradle is the input content remains unchanged, the analysis focuses on three influencing elements, which are the length of gun breech guide, the material thickness of neck barrel and the material thickness of cradle rib plate.
Fig. 1. The mechanical calculation of cradle.
In the model, parameters such as model properties, constraints, contact and drive speed are set. The model parameters are shown in Table 1.
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Table 1. The model parameter. Name of applied load
Size of applied load (kN)
Cradle’s Gravity
Automatic calculation
Tube and feeder gravity
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Friction of the recoil 15 section against the cradle Gravity of the ammunition delivery machine
7
Balancing machine force
100
Single stationary retractor 70 High and low tooth arc torque
4 kNm
Multiple simulation calculation models were established, and three variables, gun breech guide length, material thickness of neck barrel and material thickness of cradle rib plate, were varied to perform batch calculation on the simulation models and obtain the calculation results.
3 Simulating Calculation 3.1 Changes to the Length Calculation Analysis of the Gun Breech Guide Figure 2 shows a schematic diagram of the length of the gun breech guide, changing the length of the gun breech guide changes the distance at which the tube is fixed to the force acting on the cradle, which in turn affects the balance of the cradle force and the maximum deflection value.
Fig. 2. The sketch of length of tube guide rail.
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As Fig. 3(a–f) shows the calculated deformation cloud of cradle by varying the length of the GUIDE RAIL under the same load. From the deformation cloud, it can be seen that the deformation of the cradle is gradually increased by spreading outward with the trunnion as the center. At the same time, the distal-most neck barrel deflection value gradually decreases as the length of the guide rail increases. Therefore, when designing the gun breech guide, the length can be increased appropriately in order to reduce the maximum deflection value of the cradle when the space dimension allows.
Fig. 3. (a) The guide rail length 200 mm. (b) The guide rail length 300 mm. (c) The guide rail length 400 mm. (d) The guide rail length 500 mm. (e) The guide rail length 600 mm. (f) The guide rail length 700 mm
3.2 Changes to the Analysis of the Calculation of the Material Thickness of the Neck Barrel As shown in Fig. 4(a–f), the calculated cradle deflection clouds are calculated by varying the truss neck barrel material thickness under the same conditions. From the deflection cloud, it can be seen that when the neck barrel material thickness is 6–12 mm, the position of the maximum deflection value is located at the front of the neck barrel and the deflection cloud distribution does not change much. When the thickness of the neck barrel is 2–4 mm, the maximum deflection value is located at the lower side of the rib plate, and the deflection of the rib plate is larger and can be distinguished visually. The reason for the above phenomenon is that when the material thickness of the neck barrel is 6–12 mm, the overall mechanical structure of the neck barrel is the main factor influencing the maximum deflection value and the individual material is the secondary factor. When the material thickness of the neck barrel is 2–4 mm, the deformation of the individual material is the decisive factor for the maximum deflection value.
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Fig. 4. (a) The neck thickness 12 mm. (b) The neck thickness 10 mm. (c) The neck thickness 8 mm. (d) The neck thickness 6 mm. (e) The neck thickness 4 mm. (f) The neck thickness 2 mm
3.3 Changes to the Analysis of the Calculation of the Material Thickness of the Cradle Rib Plate As shown in Fig. 5(a–d) for the same conditions, changing the cradle welded plate material thickness, the calculated cradle deflection cloud map. It can be seen from the deflection cloud diagram that the deflection cloud distribution changes less when the rib plate material thickness is changed, and the maximum deflection value changes by a small amount, indicating that the cradle rib plate material thickness has a limited effect on its maximum deflection value.
Fig. 5. (a) The welding plate thickness 15 mm. (b) The welding plate thickness 12 mm. (c) The welding plate thickness 10 mm. (d) The welding plate thickness 8 mm
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4 Interpretation of Result The finite element analysis of the cradle was carried out by varying three factors: the length of the gun breech guide, the material thickness of the neck barrel and the material thickness of the cradle rib plate to form a cloud of cradle deformation, and the results of the changes in the cloud were analyzed. As shown in Fig. 6, the curve corresponding to the length of the gun breech guide and the maximum deflection of the cradle, it can be observed from the curve that the length of the guide rail is negatively correlated with the maximum deflection of the cradle, and the curve is a concave curve. When the length of guide rail increases to a certain value, the maximum deflection value of cradle decreases insignificantly.
Fig. 6. The corresponding curve between the length of guide rail and the maximum deflection of cradle
As shown in Fig. 7, the curve corresponding to the maximum deflection of the material thickness of the neck barrel and the cradle, it can be observed from the curve that the length of the guide rail is negatively correlated with the maximum deflection of the cradle, and the curve is concave. When the material thickness of neck barrel
Fig. 7. The curve between the thickness of the neck cylinder and the maximum deflection of the cradle
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is 2–4 mm, the maximum deflection value decreases sharply as the material thickness increases, and the stiffness of neck barrel increases significantly. When the material thickness of the neck barrel is more than 6mm, the maximum deflection value still decreases gradually, but the change is not obvious, and the stiffness of the neck barrel does not increase obviously. As shown in Fig. 8, the curve corresponding to the material thickness of the cradle rib plate and the maximum deflection, it can be concluded from the curve that the material thickness of the cradle rib plate is approximately linearly negatively correlated with the maximum deflection, and the maximum deflection value of the cradle decreases as the material thickness of the rib plate increases.
Fig. 8. The curve between the thickness of the welding plate and the maximum deflection of the cradle
5 Conclusion The maximum deflection value of the cradle changes significantly by changing three factors: the length of the gun breech on the cradle guide rail, the material thickness of the neck barrel and the material thickness of the cradle rib plate, therefore, all three are mechanically sensitive elements. The maximum deflection value of cradle can be reduced by increasing the length of gun breech guide and increasing the material thickness of neck barrel and cradle rib plate. The guide rail length, neck barrel material thickness and cradle maximum deflection showed a concave curve variation, and the maximum deflection value decreased insignificantly by continuously increasing the guide rail length and neck barrel material thickness. For neck barrel material thicknesses of 6–12 mm, the overall mechanical structure of the neck barrel is the main factor influencing the maximum deflection for neck barrel material thicknesses of 2–4 mm, the individual rib plate’s own deformation is the decisive factor influencing the maximum deflection value. Through the above study of the mechanically sensitive factors of electromagnetic rail gun cradle deflection, the data and conclusions formed provide a theoretical basis for the design of cradle lightweight, and lay the foundation for the study of mechanically sensitive factors of structural components.
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References 1. Fu, W., Wu, Q., Gong, J., Zhao, S., Zuo, Y.: Structural optimization of large caliber naval gun cradle. Appl. Sci. Technol. 47(01), 118–122 (2020). (in chinese) 2. Sun, Q., Yang, G., Ge, J.: Improved design of a gun upper frame structure. J. Mil. Eng. 33(11), 1281–1285 (2012). (in chinese) 3. Qian, H., Gu, K., Peng, D., et al.: Multi-objective optimization design of ultralight guncradle based on NSGA-II algorithm. Mach. Des. 29(6), 36–39 (2007). (in chinese) 4. Li, Z., Yang, G., Ge, J.: Multi-objective optimization of a certain gun cradle considering errors in material property parameters. J. Nanjing Univ. Technol. 41(6), 671–675 (2017). (in chinese) 5. Li, L., Khandelwal, K.: An adaptive quadratic approximation for structural and topology optimization. Comput. Struct. 151, 130–147 (2015) 6. Ullah, B., Trevelyan, J., Ivrissimtzis, I.: A three-dimensional implementation of the boundary element and level set based structural optimisation. Eng. Anal. Bound. Elem. 58, 176–194 (2015) 7. Huang, X., Li, Y., Zhou, S.W., Xie, Y.M.: Topology optimization of compliant mechanisms with desired structural stiffness. Eng. Struct. 79, 13–21 (2014) 8. Zhu, J., Pan, Y., Sun, M.: Topology optimization design of a certain type of gun cradle structure. Mil. Autom. 36(6), 17–20 (2017). (in chinese) 9. Zhang, X., Gu, K., Liu, G.: Topology optimization of the upper carriage of a gun under multiple working conditions. J. Gun Launch Control 40(03), 56–60 (2019). (in chinese)
Research on Nonlinear Servo Speed Identification Based on Two-Stage Electric Cylinder Pengfei Li(B) and Danfeng Wang 713 Research Institute of China State Shipbuilding Corporation, Henan, China [email protected]
Abstract. The movement of the gun barrel of a naval driven by the electric cylinder is a kind of non-linear movement, in order to solve the disturbance problem in the servo control of the electric cylinder and the problem of difficult position feedback. By applying the traditional control algorithm and speed identification algorithm to the electric cylinder control, the optimal control algorithm under the system is obtained through simulation verification. First, a mathematical model of AC permanent magnet synchronous motor is established, and the motor is controlled by speed identification, and on this basis, a mathematical model of the nonlinear motion of the electric cylinder is introduced. Through the speed identification and compensation, a better effect can be obtained for the nonlinear motion of the electric cylinder. Finally, through simulation experiments, the sliding mode observer can solve the problems of jitter, difficult position feedback, and low accuracy in the system. Keywords: Naval gun electric cylinder · Permanent magnet synchronous motor · Non-linear motion · Speed identification
1 Introduction 1.1 Modeling and Analysis of Vertical Erection Device With the development of technology, the multi-electricity and even full electrification of artillery, missiles and special vehicles have increasingly become the trend of future technological development. For example, the French “Leclerc”, the German “Leopard” 2A5/A6, the Israeli “Mekava” 4, the British “Challenger Series” tank artillery system and the American Martin rocket launch system use electric drive systems; The CLAWS air-to-air missile launch vehicle also uses electric drive control as shown in Fig. 1 [1]. At present, in the field of rapid vertical erection of the launcher, the fundamental purpose of multiple electrification is to use electric energy as much as possible to replace secondary energy such as hydraulics and pneumatics. Fundamentally solve the “running, emitting, dripping, and leaking” problems of the hydraulic system [2–4], and at the same time improve the control performance of the system. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 119–129, 2022. https://doi.org/10.1007/978-981-19-1870-4_13
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Fig. 1. CLAWS air-to-air missile launch vehicle
The research and application of electric cylinder servo control strategy has entered a new research field in recent years. In the tilt and erection system of artillery and small and medium missile launchers, electric drives have gradually replaced hydraulic drives; in large missiles and artillery launches. The research on the vertical erection technology of the device has just started, and it has become an important development trend in the future [5]. The electric cylinder is a linear motion actuator that integrates a servo motor and a screw. Its working principle is to convert the rotary motion of the motor through the screw into a linear reciprocating motion of the push rod, and the load is driven by the push rod. Compared with the two-stage electric cylinder Single-stage electric cylinders have a longer stroke, and are widely used in erection devices such as industrial field equipment, agricultural machinery and agricultural tools that require compact structures, and large-stroke military radars, artillery, and missile landing gears. 1.2 Kinematics Model of Vertical Erection Device The typical structure of the super-heavy electric erection device is shown in Fig. 2. The system is mainly composed of two-stage electric cylinder, servo motor and load. The rear end of the load is hinged with the base fixing device, the lower lug of the electric cylinder is hinged with the fixing device, and the upper lug of the electric cylinder is hinged with the load. When the system is working, the electric cylinder drives the super load to rotate around the fixed axis, so as to realize the erection of the load [6].
Fig. 2. Schematic diagram of erection device structure
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In the high and low system of the electric cylinder, the telescopic length of the lead screw determines the height of the high and low platform. When the telescopic amount is 0, the high and low platform is in a horizontal position, and the load is vertical from the horizontal position to a position of 70° with the horizontal plane. A is the heavy load trunnion, B is the rotation center of the upper lug of the electric cylinder, C is the rotation center of the lower lug of the electric cylinder, E is the rotation center of the upper lug of the electric cylinder when the load is 0°, P is the mass center of the heavy load, D Is the horizontal projection length of the load trunnion to the lower lug, h is the distance from the trunnion point to the lower hinge point, e is the distance from the center of mass of the body tube to the heavy load trunnion, and c is the distance from the trunnion to the upper lug of the electric cylinder, DAC = α, DCA = β, BAE = γ, BAC = ψ, so, in the oblique ABC, ψ = γ − α + 90°, the extension length s of the electric cylinder and the load rotation angle γ. The relationship is: 2 + l 2 − 2l l (1) s = lBC − lEC = lAC AB AC cos ϕ − lEC AB When the electric cylinder drives the load to move, it must first consider overcoming the torque generated by gravity, and then the excess torque is used to accelerate the torque. Since the moment of inertia of the system is constant and the acceleration of the system is constant, the acceleration torque can be analyzed separately. Since the system overcomes the real-time change of the gravitational moment, the process is more complicated. First, analyze the relationship between the load rotation angle γ and the torque F of the electric cylinder to overcome the gravity G when the electric cylinder only overcomes gravity at different angles: Moment of gravity: TG = G ∗ sin(180◦ − (β + 90◦ )) ∗ e = Ge cos β
(2)
Thrust distance: TF = F ∗ sin B ∗ c = Fc ∗ sin B
(3)
There is the law of sine in ABC to get: sin B =
b ∗ sin A a
(4)
From the mechanical analysis, it can be seen that the relationship between the output F and the load rotation angle γ at different angles is: F = G ∗ a ∗ e cos(90 − arctan(h/l)) ÷ c ∗ b ∗ sin(γ − arctan(h/l) + 90)
(5)
The relationship between the motor speed and the movement speed of the electric cylinder: W = 60 nv/d
(6)
where W is the motor speed (rpm), v is the electric cylinder speed (m/s), and d is the electric cylinder lead (m).
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1.3 Basic Theory and Mathematical Model of PMSM In this system, the permanent magnet synchronous motor adopts three-phase star winding connection, and the permanent magnet synchronous motor is modeled by the d-q method. The equation in the d-q coordinate system can be obtained as did − ωc Lq iq dt
(7)
diq − ωc Ld id + ωc ωf dt
(8)
ud = Rs id + Ld uq = Rs iq + Lq Te = J
2 pn ϕf iq − (Lq − Ld )id iq 3 d ωn − Bωn = Te − TL dt
(9) (10)
where ud and uq are stator voltage; and iq are stator current; and Lq are stator inductance; ψf is rotor flux, Rs is stator inductance; is moment of inertia; B is viscous friction coefficient; c is electromagnetic torque; L is load torque; c and Wm are electrical angular velocity and mechanical velocity.
2 Control Strategy of Electric Cylinder Servo System The two-stage electric cylinder is a non-linear, multi-variable system. When the control system is affected by external disturbances or the internal parameters of the motor change, the traditional PI cannot meet the requirements. Sliding mode control is insensitive to disturbances and parameters, and has a fast response speed. Permanent magnet synchronous motor vector control is the earliest developed and most widely applicable control strategy in the field of automatic control. It is widely used in industrial control and military fields with simple algorithms, good robustness and high reliability. In vector control, in order to achieve a high-performance permanent magnet synchronous control system, it is generally necessary to obtain accurate rotor position and speed information, sensorless control technology, this kind of method permanent magnet synchronous motor fundamental wave excitation mathematical model and speed-related quantities The position and speed of the rotor are estimated, and the overall system architecture is as follows: 2.1 PI Control Permanent magnet synchronous motors have the advantages of wide speed range and high efficiency, and are widely used in servo control systems. The classic PI control method has the advantages of simple design, good system steady-state performance, strong reliability, and easy physical realization. However, there are many linear and non-linear factors in actual working conditions. Vector control will be used to control the permanent magnet synchronous motor, as shown in Fig. 3 below:
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Fig. 3. PI vector control diagram
2.2 Model Reference Adaptive Speed Identification Control Model reference adaptation (MRAS) is mainly composed of three parts, including adjustable model [7–9], reference model and parameter adaptation law. Model reference adaptation is to treat the same motor identification parameters in the reference model and the adjustable model as known parameters and unknown parameters respectively, and the physical meaning of the two models is the same, the two models are subjected to difference processing, and then established Appropriate parameter adaptation law identifies the motor parameters. The algorithm procedure is shown in Fig. 4.
Fig. 4. Schematic diagram of model reference adaptive control
The matrix expression of the d-q axis is: Rs − Ls ωr 1 vd id id = + p . −ωr − RLss Ls vq iq iq
(11)
In the formula, ωr can be used as the adjustable model of the system, and the permanent magnet synchronous motor is used as the reference model. According to Popov’s superstability theory, when the system satisfies the following two conditions, the system has asymptotic stability: 1) The state matrix H (s) = D(sI − A)−1 is strictly a positive real number; 2) Popov’s Integral Inequality: t vT wdt ≥ −γ02
p(0, t0 ) = 0
(12)
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In the formula, −γ02 is a finite normal number related to t. Sliding mode variable structure control (SMC) is a nonlinear control method that achieves high-performance control of the system by selecting a suitable sliding mode surface. The control method is simple, the accuracy of the system model is not high, and the robustness is strong. 2.3 Definition of Sliding Mode Variable Structure Control The linear time-varying system can be defined as: .
x = f (x, u, t)(x ∈ Rn , u ∈ Rm , t ∈ R)
(13)
Among them, x is the system variable; u is the control quantity, and t is the time. Define the hypersurface in the space as shown in the following figure, where A is the usual point, B is the starting point, and C is the ending point. If the switching surface is called the “sliding mode area”, as shown in Fig. 5 below:
Fig. 5. Schematic diagram of sliding mode variable structure
The conditions for moving to the sliding mode zone are: .
lim s s ≤ 0
S −→
(14)
0
Design of Sliding Mode Controller Based on Reaching Law [10], This paper adopts the approaching law control method to design the speed loop sliding mode controller, which controls the approaching motion quality and controls the jitter together. The law of reaching formula is: .
s = −εsign(s) − ksε > 0, k > 0
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Select the sliding surface as: s = x2 + cx1 The specific vector control program is shown in Fig. 7 below (Fig. 6):
(16)
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Fig. 6. Schematic diagram of sliding mode variable structure vector control
2.4 Rotation Speed Identification by Sliding Mode Observation Method In the mathematical model of the sliding mode observer (SMO) [11, 12], the sign function is used to replace the actual value of the deviation, which has higher gain characteristics, speeds up the response speed of the sliding mode observer, and effectively eliminates the chattering phenomenon. The back EMF of PMSM is estimated online by sliding mode observer to solve the prediction of nonlinear motion torque changes. The sliding mode observer is designed as follows: ⎫ Rˆ k1 ˆ d ˆid ud ⎪ = − id + − F(id − id )⎪ ⎬ dt L L L (17) ⎪ d ˆiq uq Rˆ k1 ˆ ⎪ ⎭ = − iq + − F(iq − iq ) dt L L L In the formula, is the observed value, k1 and k2 are the sliding mode gains; F is the switching function, and the function expression is: ⎧ ⎪ ⎨1 x > 0 sgn(x) = 0 x = 0 (18) ⎪ ⎩ −1 x < 0 The sliding mode observer control diagram in vector control is shown in Fig. 8 below.
Fig. 7. Schematic diagram of vector control of synovial observer
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3 Simulation Results In order to verify the effectiveness of the above control algorithm in the non-linear motion of the electric cylinder, firstly, the characteristics of several algorithm steps and the ability to resist load disturbance are verified in the simulation. Among them, PI and SMC measure the speed feedback, and SMO and MRAS identify the speed feedback through observation.. Secondly, obtain the nonlinear velocity and torque movement characteristics of the electric cylinder during the movement of the barrel load at a constant speed. Finally, the motion characteristics are brought into the four control algorithms, and the optimal control algorithm for the nonlinear motion of the electric cylinder is verified. The simulation parameter table is shown in Table 1. Table 1. Simulation parameters Parameter
Value
Load operating speed °/s
5
Load running acceleration °/s
5
Projection length from load to trunnion mm
2276
The distance from the trunnion point to the lower hinge point mm
4370
Body tube centroid to heavy load trunnion mm
1315
Distance from trunnion to upper lug of electric cylinder mm
2000
Stator phase resistance ohm
0.05
q-axis inductor H
0.0006
d-axis inductor H
0.0006
Magnetic link v.s
0.192
Inertia kg/m2
1.05
Viscous damping N.m.s
0.001
Permanent magnet pole pair number p
4
3.1 Characteristic Simulation Under Step Speed and Load Disturbance (see Fig. 9) 3.2 Simulation of the Motion Characteristics of the Electric Cylinder The load barrel moves at a speed of 5°/s and an acceleration of 5°/s2 , and the changes in the barrel and the end displacement of the electric cylinder is required as shown in Fig. 10.
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Fig. 8. Step characteristic motor speed simulation diagram and Partial enlarged view of step characteristic motor speed
Fig. 9. Electromagnetic torque change graph and SMO measurement speed and identification speed map
Fig. 10. Body tube speed change graph and Displacement diagram of the end of electric cylinder
3.3 Motion Characteristics Under Actual Working Conditions Bring the calculated electric cylinder motion characteristics into the nonlinear speed identification algorithm control, and obtain the nonlinear theoretical motor speed and
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tracking speed motion characteristics and the nonlinear torque and tracking torque are shown in Fig. 11 below.
Fig. 11. Theoretical speed and tracking change diagram and Theoretical torque and tracking torque change diagram
4 Conclusion It can be seen from the simulation results that the servo speed identification control algorithm based on the sliding mode observer can track the theoretical speed of the motor very well, the algorithm tracking speed is fast, and the tracking accuracy is high; the identified speed is used for the vector control of the permanent magnet synchronous motor, The motor speed can track the given speed well, and the dynamic performance is good; the identification speed can replace the speed sensor, realize the speed sensorless control, and save space; the simulation results confirm that the servo speed identification algorithm of the sliding mode observer is compared with the other three With this algorithm, the electric cylinder has better tracking performance during the rotation of the barrel load.
References 1. Gyürsi, M.: New claws for Polish Kubs (2004) 2. Liu, Z., Li, P., Jiang, J., Liu, B.: Research on vibration characteristics of mill rolls based on nonlinear stiffness of the hydraulic cylinder. J. Manuf. Process. 64, 1322–1328 (2021) 3. Qin, X., Jiang, M., Liu, Y., et al.: Research of active disturbance rejection control technique in the electric cylinder servo system. J. Gun Launch Control (2019) 4. Zou, Q.: Observer based sliding mode control for hydraulic driven barrel servo system with unknown dynamics. IEEE Access 8, 131370–131379 (2020) 5. Huang, G., Huang, W., Li, Z., et al.: An improved sliding-mode observer based equivalent input disturbance approach for permanent magnet synchronous motor drives with faults in current measurement circuits. Trans. Inst. Meas. Control 43, 2589–2598 (2021) 6. Luo, Y.L., Zeng, C., Yao, Y.U., et al.: Kinematics analysis of working device of hydraulic excavator based on AutoCAD VBA. Mach. Des. Manuf. (2012) 7. Kang, J., Zeng, X., Wu, Y., et al.: Study of position sensorless control of PMSM based on MRAS. In: 2009 IEEE International Conference on Industrial Technology. IEEE (2009)
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8. Zhao, J., Liu, X., Xiao, P.: Sensorless vector control system of permanent magnet synchronous motor based on MRAS. Electromech. Inf. 638(32), 128–129 (2020). (in Chinese) 9. Lei, J.: Model reference adaptive doubly-fed motor speed sensorless control based on rotor current. Ship Electric Technol. 6, 39–42 (2020). (in Chinese) 10. Zhang, X., Xu, Y., Zou, J.: Research on sliding mode variable structure speed control algorithm of winding segmented permanent magnet linear synchronous motor. In: 2021 13th International Symposium on Linear Drives for Industry Applications (LDIA) (2021) 11. Huang, G., Huang, W., Li, Z., et al.: An improved sliding-mode observer-based equivalentinput-disturbance approach for permanent magnet synchronous motor drives with faults in current measurement circuits. Trans. Inst. Meas. Control. 43, 2589–2598 (2021) 12. Zhuo, D., Cao, H., Zhang, X.: Damage identification of semi-rigid connection in structures based on nonlinear vibration characteristics. IOP Conf. Ser. Earth Environ. Sci. 719(2), 022003 (2021)
The Continuous High Precision Measurement Technique of Bore Spacing About Rail-Gun Pengchao Pei(B) , Bin Cao, Mingtao Li, and Xia Ge Northwest Institute of Mechanical and Electrical Engineering, Xianyang 712099, Shaanxi, China [email protected]
Abstract. The change of bore spacing directly affects the sliding electrical contact state in the process of electromagnetic launch, so obtaining the data of bore spacing accurately is very important for analyzing the launch process. A continuous high precision measuring device is designed based on the internal gun structure and the characteristics of angular bisector, and the principle and machining error of the whole system are analyzed, and then checked the actual error with the help of high-precision measuring equipment and detection tooling, the results show that the real error is smaller than or equal to 0.5 mm. At the same time, using the device to measure and obtain the bore spacing of a certain caliber rail-gun, and guided the assembly process and assembly process. Practice has proved that the device has ideal engineering application value, and can provide indispensable measurement means for later numerical modeling, assembly process and performance testing. Keywords: Rail gun · Bore spacing measurement · Angular bisector characteristic · Continuous high precision measurement
1 Introduction Electromagnetic gun is a new concept weapon that relies on electromagnetic force to launch projectiles at high speed [1]. As a kind of electromagnetic gun, rail-gun uses electromagnetic force to launch projectiles [2]. It has high initial velocity, long range, simple control, and the high cost-effectiveness ratio. At present, the world’s military powers have carried out the development of electromagnetic gun weapon systems, which has extremely high potential for military applications in the future [3–5]. The launching process of the rail-gun is essentially a sliding electrical contact process between the armature and the rail under high voltage and large electricity [6, 7]. The rail is the core part of the electromagnetic rail-gun launching assembly, and its processing accuracy and assembly errors directly affect the launch. During the process, the sliding electrical contact state is changed by the fluctuation of the bore spacing. When the contact gap is too large, severe arc ablation occurs at the gap, which has a serious impact on the life of the rail and the attitude of the projectile [8]. At the same time, the random fluctuation of the rail spacing will cause asymmetric wear and collision of the contact surface and other adverse effects, which is extremely detrimental to the launch process and increases the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 130–138, 2022. https://doi.org/10.1007/978-981-19-1870-4_14
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risk of disintegration in the bore and rail damage. After consulting related literature, when domestic and foreign researchers deal with the problem of electrical contact between the armature and rail, they regard the contact as the ideal contact state, that is, maintaining sufficient and good contact between the armature and the rail [9]. There are few research reports on the influence of bore spacing changes on the launch process, the main reason is that there is no effective orbital distance high-precision measuring device for the special bore section of the rail-gun. Therefore, carrying out the high-precision measurement of the bore distance of the rail-gun, analyzing the influence of the change of the rail distance on the sliding electrical contact during the launching process, has important guiding significance for the study of rail damage, armature ablation, etc. It is an indispensable analytical method for the simulation modeling of electromagnetic gun weapon systems, life assessment and assembly testing.
2 The Principle of Bore Spacing Measurement Under ideal conditions, the two rails in the rail-gun maintain a spatial parallel relationship after the assembly is completed. However, in the actual assembly process, due to processing errors, assembly environment and process differences, various errors introduced will cause the bore distance to vary randomly within a certain range along the length. At the same time, during the electromagnetic launch process, the rail is subjected to electromagnetic repulsion. When the rail is assembled, the trail displacement will be restrained in various forms along the length, thereby limiting the range of the rail pitch [10], so the possibility of large deformation of the rail pitch is relatively small. Assuming that the rail spacing changes uniformly within a certain length range, the spatial position relationship between the two rails can be equivalent to two straight lines at a certain angle, as shown the lines C1 D1 and C2 D2 in Fig. 1. By taking any point E on its angular bisector AB to make lines EE1 and EE2 , the lines C1 D1 and C2 D2 are perpendicular to points E1 and E2 , respectively, and connecting points E1 and E2 . According to the related characteristics of the angular bisector, E1 E2 and AB perpendicularly intersect at Point E3 , then EE1 = EE2
(1-1)
Therefore, the trail pitch at point E is the length of the line E1 E2 , and the straight line distance through the measurement line E1 E2 is the rail pitch at point E.
3 System Measurement Error Analysis According to the rail spacing measurement principle shown in Fig. 1, build the test system prototype, and theoretically analyze the errors of each part of the prototype. The system error mainly includes two parts, namely the test principle error and the system processing error.
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Fig. 1. Principle of track spacing test
3.1 Error Analysis of Measurement Principle Because the test principle is based on the uniform change of the rail in a certain length range, in practice, there is often a certain degree of bending deformation after the rail assembly, which is the main reason for the principle error of the test method. Assuming that the rail bending deformation within the length range of the measured prototype is shown in Fig. 2, the error introduced by the test principle is S, so
Fig. 2. Schematic diagram of test principle error
S =R−
R2 − (L/2)2
(1-2)
In the formula, R is the radius of the curved arc of the rail, and L is the distance of the measuring prototype. It can be seen that the relationship between R and S is linear inversely proportional, that is, to say the larger the R, the smaller the S. According to the design experience of conventional artillery, the tactical index requirements can be met when the variation range of artillery caliber does not exceed 1% of the caliber. In order to ensure the measurement reliability, sufficient margin is reserved. The measurement principle is applicable to the variation range of rail spacing within 5% of the bore caliber. For a rail-gun with a caliber d and a barrel length l, assuming that the rail is deformed as shown in Fig. 3 after the initial installation, when the bending deformation of the rail is 5% of the caliber d, it can be calculated according to formula (1-3) The bending radius R of the exit rail is: (1-3) R − R2 − (l/2)2 = 0.02d
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(0.05 × d )2 + l 2 /4 2 × 0.05 × d
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(1-4)
Fig. 3. Schematic diagram of track bending
According to the above analysis, when the rail length and bore diameter are determined, the principle error introduced by this test method is only related to the length of the measuring prototype. Assuming that a rail-gun has a length of 4 m and a caliber of 50 mm, and the measured prototype length L = 130 mm, it can be known that when the bending deflection of the entire rail is 5% of the caliber, the principle error introduced by the test method is 1.8 µm. 3.2 Analysis of Errors Introduced by System Machining Precision The test principle is based on the assumption that the bore spacing changes uniformly within a certain range. The position relationship between the upper and lower rails is regarded as two straight lines forming a certain angle with each other, and the angle bisector is used as the theoretical reference. Therefore, when the processing error causes the deviation of the test standard in the test prototype, it will bring errors to the test system. As shown in Fig. 4, suppose point O is the connection point between the front support mechanism and the reference plate, the length of the reference plate is recorded as 2 times OE1 , point E is the sensor installation position, that is, the sensor is installed in the middle of the reference plate length, E1 F1 is the rail spacing theoretical measurement value, and is denoted as d, and the length OE1 is set to L1 . When the reference plate rotates around point O by angle β due to machining error, that is, when OE1 rotates to OE2 , the measurement direction E1 F1 is deflection angle β along with it, and the measured track distance is E2 F2 ,marked as d1 .It can be seen that the system test error caused by the processing error is: δ = d − d1
(1-5)
OE1 = OE2 = L1
(1-6)
E2 G = OE2 · sin β = L1 · sin β
(1-7)
As can be seen from Fig. 4:
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Fig. 4. Measurement error analysis
E2 F2 =
E1 F1 − E2 G E1 F1 − L1 · sin β = cos β cos β δ = E1 F1 − E2 F2
(1-8) (1-9)
In the formula, d is the bore diameter of a certain gun, β is the deflection angle of the reference plate, when the gap between the mounting holes at both ends of the reference plate is a, and the length of the reference plate is L. It can be seen that the rail pitch test error becomes larger as L and β increase. When the measurement plan is determined, L will remain unchanged. At this time, the error δ is mainly affected by δ and β is mainly caused by the matching gap between the support mechanism and the reference plate. In this test plan, L1 = 65 mm, d = 30 mm, L = 130 mm. When the H 7/h7 fit tolerance is adopted between the current and rear support mechanism and the reference plate, it can be seen that β = 0.05, and the size of the error introduced is 11 µm, which can be seen that the error introduced by the measurement principle is less than 1% of the caliber, so the test principle is feasible.
4 Systematic Error Measurement In order to accurately evaluate the error of the test system, take the whole measuring device as the detection object to verify the system error, the verification principle is shown in Fig. 5. Firstly, the test prototype is placed on a smooth stone measuring plane, and the height ruler is used as the debugging tooling. The slider can slide freely along the height ruler. Taking the measuring benchmark as the reference zero position, it passes through the high-precision electronic altimeter measure the height of the slider from the measurement benchmark, and record it as Hi . At the same time, use the measuring prototype to measure the height of the slider, record it as hi , and record the initial position height as 0. Compare the two groups of measured slider height data, and the results are shown in Fig. 6. It can be seen from Fig. 6 that the slider height obtained by the test device basically coincides with the slider height change curve obtained by the electronic altimeter. As the measurement height increases, the two sets of measurement data begin to differ due to the accumulation of errors. The maximum error of the two sets of data is regarded as the total error of the system, and the total error of the system is less than or equal to 0.05 mm.
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(a) Measuring principle of distance test data (b) Spacing data measurement process
Fig. 5. Inspection principle and process of track spacing measuring device system
Fig. 6. Comparison of calibration data of track spacing measuring device system
5 Prototype Adaptability Verification In order to compare the advancement of this rail spacing measuring device and the traditional “plug gauge” rail spacing measuring device, the data measured by the “plug gauge” track spacing measuring device is compared with the measurement results of this test measuring device, as shown in Fig. 7.
(a) Traditional plug gauge
(b) measuring principle
Fig. 7. Traditional plug gauge for measuring bore size and its measuring principle
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Firstly, use the traditional” plug gauge” to measure the rail spacing at a certain position of the rail, and compare the measured results with the rail spacing measuring device, measured results as shown in Table 1: Table 1. Comparison of track spacing measurement data Serial number
Distance from muzzle (m)
Plug gauge measurement result (mm)
Bore spacing measurement results (mm)
Error size (mm)
1
0.8 m
29.2
29.175
−0.025
2
1.6 m
29.8
29.789
−0.011
3
2.4 m
29.1
29.072
−0.028
4
3.5 m
28.9
28.872
−0.028
From the results in Table 1, it can be found that the measurement data using the traditional “plug gauge” method is similar to the rail spacing measurement data, and the difference is small, indicating that the rail spacing measurement device measurement data is accurate and credible. Because the traditional plug gauge is measured by changing the thickness of the adjusting washer, the thickness of the adjusting washer can only be changed by 0.1 mm each time due to the processing accuracy. Therefore, the measurement accuracy of the traditional plug gauge can only be 0.1 mm, and it can only measure partial rail pitch at the point.
6 Engineering Measurement of Bore Spacing Carry out the measurement of the rail spacing of a screw-fastened rail-gun. The rail spacing was measured along the barrel axis with the tail as a starting point. The acquired rail spacing data and measurement process are shown in Fig. 8. It can be seen from Fig. 8 that after the initial tightening, the bore spacing changes randomly along the length of the rail, and the change is large. The maximum spacing is 49.68 mm and the minimum spacing is 49.38 mm, which does not meet the rail spacing assembly requirements. Excessive changes in the orbital distance will cause the projectile to collide with the orbit during the launch process, resulting in unstable launching of the armature, and posing safety hazards to the launching process. In order to meet the assembly requirements, the rail spacing measuring device is placed in the inner bore. By adjusting the rail binding force of each part, and monitoring the change of bore spacing of each part with the preload, the trail spacing in the bore length can be changed evenly. After adjusting the preload of each part, remeasure the track spacing. The results are shown in Fig. 9.
7 Conclusion According to the special structure of the rail-gun, an innovative orbital distance measurement principle based on the angular bisector characteristics is proposed, and the
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(b) Bore spacing measurement result
Fig. 8. Measured variation curve of rail-gun bore spacing
Fig. 9. Measured variation curve of rail-gun spacing after adjusting preload
error size of the measurement system caused by the measurement principle error and the processing accuracy is analyzed. The theoretical analysis result shows that the system error is ≤0.05 mm. Then take the entire measurement system as the calibration object, and use the high-precision detection device to verify the accuracy of the entire measurement system. After measurement and testing, the system error of the entire measurement device is less than or equal to 0.05 mm, which can meet the engineering needs. Through engineering actual measurement of the bore spacing of a certain caliber electromagnetic rail-gun, it is found that the rail spacing varies randomly along the length of the barrel. In order to ensure the assembly accuracy requirements, the bore spacing measuring device is placed in the inner bore to monitor the inner bore distance in real time. By changing various parts The preload force in the borehole can achieve the consistent change requirement of the inner bore spacing, and has achieved good engineering applicability.The proposed continuous high-precision measurement method for rail-gun bore spacing provides a necessary detection method for rail-gun simulation modeling, assembly inspection and performance evaluation, and is of great significance to the development of electromagnetic rail-gun technology.
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References 1. McNab, I.R.: Westinghouse EMACK railgun. IEEE Trans. Plasma Sci. 49(5), 1714–1723 (2021) 2. Hundertmark, S.: Investigations on the energy chain for a naval railgun. IEEE Trans. Plasma Sci. 48(11), 3991–3996 (2020) 3. Laurian, G., Bogdan, C.: New design of an electromagnetic launch system for tactical UAVs. Sci. J. Silesian Univ. Technol. 108, 45–51 (2020) 4. Kondamudi, S.C., Thotakura, S., Pasumarthi, M.R., Reddy, G.R., Sathyaraj, S.M., Jiang, X.X.: A novel type coil-multipole field hybrid electromagnetic launching system. Results Phys. 15(C), 102786–102792 (2019) 5. Xu, L., Geng, Y.: Dynamics of rails for electromagnetic railguns. Int. J. Appl. Electromagn. Mech. 38(1), 47–64 (2012). (in Chinese) 6. Chen, Y., Xu, W., Yuan, W., et al.: Sliding electrical contacts between aluminum armature and different material rails in railgun. High Voltage Eng. 39(4), 937–942 (2013). (in Chinese) 7. Li, H., Li, Z., Lei, B., et al.: Analysis on rail performance of EM rail-gun with different cross sections. Fire Control Command Control 39(4), 0597–0605 (2014). (in Chinese) 8. Che, Y., Zhao, W., Wang, Z., et al.: Influence of armature-rail contact surface morphology on starting characteristics of armature. High Power Laser Part. Beams 32(5), 112–116 (2010). (in Chinese) 9. Li, M., Sun, X., Li, J., et al.: Pre-tightening mechanism analysis of barrel design in electromagnetic rail-gun. J. Gun Launch Control 35(4), 11–15 (2014). (in Chinese) 10. Pei, P., Cao, B., Li, M., et al.: An analysis of measurement method for rail spacing of rail-gun based on angular bisector characteristics. J. Gun Launch Control 41(1), 89–92 (2020). (in Chinese)
Research on Armature Loading Control Accuracy Based on Cloud Model Algorithm Xue Han1 , Dongdong Zhang2(B) , Zhiqiang Wang2 , Guofeng Li2 , and Jingshong Li2 1 Dalian Neusoft University of Information, Dalian 116023, Liaoning, China 2 Dalian University of Technology, Dalian 116023, Liaoning, China
[email protected]
Abstract. An electromagnetic launch propulsion system is developed, using the timer and interrupt function of STM32 chip, the output signals of displacement sensor and pressure sensor are collected and processed, and transmitted to the host computer through two USB channels for real-time online observation. Then, the expected displacement of the armature is set by the developed loading control system, and the command is sent to the controller through the serial port to stop the push rod. In order to reduce the sampling error of displacement and thrust, a protection circuit is added to the hardware circuit design, and the designed NFC conversion circuit is experimentally verified. The relationship between voltage and frequency in NFC circuit is determined by fitting, and the average error of acquisition system is analyzed to be 4 Hz. Finally, the control system uses the cloud model, which can accurately control the armature position and detect the displacement and pressure changes in the armature loading process. The developed electromagnetic rail gun loading control system has a propulsion range of 0– 1000 mm and a pressure range of 0–5 t. The armature displacement error is less than 5 mm. Keywords: Electromagnetic rail gun · DSP · Rail gun propulsion system · Cloud model
1 Introduction As an electromagnetic energy equipment to realize the instantaneous high-power conversion between electromagnetic energy and kinetic energy, the electromagnetic rail launch system can drive the armature to obtain extremely high speed (>2000 m/s) through great current (MA) in a very short time (ms), and the speed can be accurately controlled, It has great potential advantages and broad application prospects in both military and civil fields [1–5]. In the repeated launch experiment, when the charging voltage, armature quality and other parameters remain unchanged, different armature loading distance will lead to different launch speeds, that is, the armature loading distance will affect the consistency of speeds. Therefore, accurately controlling the loading position of the armature can maintain the consistency of multiple launch experimental speeds [6, 7]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 139–146, 2022. https://doi.org/10.1007/978-981-19-1870-4_15
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The cloud model algorithm reflects the uncertainty of the concept in the process of human cognition through the three digital features of expectation, entropy and hyperentropy [8–10]. At present, there are mainly cases that have been applied in the field of smart cars. To enhance the control accuracy and minimize the system error, cloud model algorithm is adopted in designing the loading control system. The controller improves the control accuracy and robustness, thereby improving the high-precision control and measurement of the electromagnetic rail gun propulsion system. This paper designs the propulsion system based on the cloud model. The control range of this system is 0–1000 mm, the error is controlled within ±5 mm, and the displacement and propulsive force are detected in real time. The safety and robustness of the system have been verified, and the high-precision control requirements have been met.
2 Design of the System The loading system for an electromagnetic railgun is composed of a host computer, sensors, signal processing part, hydraulic part and power unit. Figure 1 shows the block diagram of the system.
Fig. 1. Block diagram of the loading system
Figure 2 shows the structural block diagram of the signal processing. (1) Power supply module provides three-phase voltage to the hydraulic system, and has 12 V and 24 V voltage for displacement sensor and pressure sensor, +15 V voltage for V/F circuit, 5 V and 3.3 V voltage for control chip STM32. Voltage stabilizing chip 7805 is added in the application to ensure the stable operation of the system. (2) STM32 signal processing system is composed of STM32F103 chip, peripheral reset circuit and crystal oscillator circuit. (3) Signal sensing system are processing displacement data and pressure data. The control accuracy of pressure sensor can reach 0.01t, which can realize thrust measurement with a range of 0–2 T. The displacement sensor adopts the pull line incremental type, with an accuracy of 0.15 mm, and the round-trip speed can reach 1000 mm/s. (4) V/F conversion circuit realizes the conversion of analog voltage into frequency. The output frequency signal of the conversion circuit is in positive proportion to the input voltage value. It is mainly designed by using LM331 chip and peripheral resistance capacitor circuit. Compared with the current general analog-to-digital converter, the resolution of V/F conversion circuit can be very high. (5) Relay control system realizes the forward and backward stop state of the control push rod, which is controlled by the upper computer,
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and is composed of two solid-state relays and 5 V power supply. (6) TTL to USB transmission system is controlled by pl2303hx chip to convert the TTL level of TX and Rx signals from STM32 control system into USB output signal. (7) Host computer control system realizes online real-time displacement display and pressure display.
Fig. 2. Structural block diagram of signal processing
3 Design of the Control System 3.1 Theory of Cloud Model The cloud model is a conversion model that uses linguistic values to express the uncertainty between a certain qualitative concept and its quantification, so as to reflect the uncertainty of things in the natural world or human knowledge concepts [8]: Fuzziness and randomness Nature not only gives an explanation from random theory and fuzzy set theory, but also reflects the relevance between fuzziness and randomness, which constitutes a mapping between quantitative and qualitative. (1) Expectation: expectation is the central value in the universe space, representing the expected distance reached by the armature; (2) Cloud drop: the distribution of expected displacement in the universe; (3) Entropy: jointly determined by the randomness and fuzziness of qualitative concepts, it represents the measurable granularity of a qualitative concept. It is a measure of the randomness of qualitative concepts, reflecting the dispersion degree of this cloud drop, and also the dispersion degree of the expected distance; (4) Super entropy: Super entropy is a measure of the uncertainty of entropy, which reveals the cohesion of the uncertainty of all points of language values in the universe space and the correlation between fuzziness and randomness, which is the randomness of the dispersion degree of periodic expected distance. 3.2 Control Strategy of the Cloud Model For electromagnetic launch technology, armature loading position will affect the consistency of electromagnetic launch speed. The loading control system is designed to control
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the propulsive force. The STM32 core controller is mainly applied, and the upper electromechanical pivot loading control system is developed in combination with LabVIEW. It can observe the changes of pressure and displacement in the loading process in real time, and can locate the armature at the specified position, and the error can be controlled within 5 mm. Figure 3 shows the block diagram of information processing.
Fig. 3. Block diagram of information processing
3.3 The Propulsive Force Control System The propulsive force control system is a SISO control model. Figure 4 show the setting value of the armature, in which P is the distance between position 1 to position 3, L is the distance between position 1 to position 2, and S is the distance between position 2 to position 3. Normally, due to the inertia or measurement error of the system, there will be an error between the actually reached position and the set value.
Fig. 4. Setting of the propulsive force control system
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In order to improve the accuracy of armature propulsion distance, the system adopts cloud model. The basic principle of this algorithm is to use language value to represent the transformation model of uncertainty between a qualitative concept and its quantitative concept, so as to reflect the uncertainty of things in the natural world or human knowledge concepts: fuzziness and randomness, It not only gives the explanation from the random theory and fuzzy set theory, but also reflects the correlation between fuzziness and randomness, which constitutes the mapping between quantitative and qualitative. In this control system, the input displacement value is taken as the expectation, the expected 5/100 is taken as the entropy, and 1/10 is taken as the super entropy. The values of entropy and super entropy are obtained according to the empirical value. Finally, cloud droplets are generated to control the precise position of the push rod. In order to effectively reduce the amount of calculation and improve the accuracy, the number of cloud droplets n = 100 is set. First, generating a normal random number with expectation and standard deviation according to the number feature (); Second, generating a random number with expectation and standard deviation; Third, calculate the uncertainty that x belongs to qualitative concept C. At last, repeat above all until n cloud droplets are generated. The control regulations are illustrated in Table 1. Table 1. The control regulations of railgun loading system If (Displacement -D)
Positive value is too big
Positive value is too small
Then (Propulsive force-N)
Positively larger Positively smaller
Zero
Negative value is too small
Negative value is too big
Zero
Negatively smaller
Negatively larger
According to Table 1, the cloud generator parameter settings are illustrated in Table 2. Table 2. Parameter settings Parameter
Positively larger
Positively smaller
Zero
Negatively smaller
Negatively larger
D
(18, 1.1, 0.003)
(8, 0.25, 0.001)
(0.0.15, 0.002)
(−8, 0.35, 0.002)
(−18, 0.03, 0.002)
N
(40, 0.15, 0.001)
(20, 0.25, 0.002)
(0.0.15, 0.002)
(−20, 0.3, 0.002)
(−40, 0.1, 0.001)
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3.4 Software Implementation Figure 5 shows the processor program chart. The main function of the STM32 controller is to process the output frequency signal received from the V/F circuit, convert it into displacement and pressure values, and then transmit it to the upper computer through the serial port for real-time online detection. Firstly, the initialization system includes the input and output of the controller, and the communication baud rate with the upper computer is set to 9600. Then, the upper computer sends the desired displacement D to the controller through the serial port, and the lower computer saves it as the condition for the stop of the push rod. At this time, the sensor starts to collect the displacement signal and pressure signal, and convert the V/f pressure and frequency, After being accepted by STM32 controller, it is transmitted to the upper computer again by serial port protocol for real-time display of displacement signal and pressure signal.
Fig. 5. Processor program chart
4 Experimental Results Figure 6 shows the frequency error distribution versus voltage. And Fig. 7 shows the comparison of the error distributions with and without cloud model algorithm.
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Fig. 6. The frequency error distribution versus voltage
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Fig. 7. Error distribution diagram with and without cloud model algorithm
Figure 6 is the distribution of frequency errors. As can be seen from MATLAB analysis, the average error is 4.2070 Hz and the standard deviation is 5.4749. With the change of voltage, the frequency error is caused by the temperature of the device, the accuracy of the measuring tool and other factors. As shown in Fig. 7, the blue curve is the error distribution measured before the application of the algorithm, and the red curve is the error distribution measured after the application of the algorithm. It can be seen from the figure that the error value represented by the blue curve fluctuates greatly, and its range is within ±8 mm; The error value represented by the red curve fluctuates relatively small, and its range is controlled within ±5 mm. Therefore, the application of cloud model algorithm has an obvious effect on improving the accuracy of armature positioning, and the control error of the system can be further reduced to ±5 mm.
Fig. 8. Displacement cloud drop distribution chat
Figure 8 shows when the target distance is set to 280 mm, the entropy is 0.1 and the super entropy is 0.01. It can be seen from the displacement cloud drop distribution in the figure that the probability of occurrence will increase as the distance is closer to 280 mm. When the distance is equal to 280 mm, the probability value of occurrence will be 1. Because the measurement error distribution conforms to the random distribution,
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therefore, The cloud droplets generated by the cloud model algorithm can compensate the random error generated by the system, which is of great significance to improve the accuracy of electromagnetic launch loading.
5 Summary Using stm32f103 chip and LabVIEW, an armature loading control system is developed. Firstly, using the timer and interrupt function of STM32 chip, the output signals of displacement sensor and pressure sensor are collected and processed, and transmitted to the host computer through two USB channels for real-time online observation. Then, the expected displacement of the armature is set by the developed loading control system, and the command is sent to the controller through the serial port as the judgment condition for the stop of the armature push rod. In order to reduce the sampling error of displacement and thrust, a protection circuit is added to the hardware circuit design, and the designed NFC conversion circuit is experimentally verified. The relationship between voltage and frequency in NFC circuit is determined by fitting, and the average error of acquisition system is analyzed to be 4 Hz. Finally, the control system uses the cloud model control algorithm, which can accurately control the armature position and detect the displacement and pressure changes in the armature loading process. The developed electromagnetic emission loading control system has a propulsion range of 0–1000 mm and a pressure range of 0–5 t. The accuracy of controlling armature displacement can reach 5 mm. A protection program is added in the system design to improve the safety and stability of the system and ensure the normal operation of the system.
References 1. Ren, R., Ye, W., Dong, Z., Liu, J., Zhang, Y.: Research on application of bus-bar in electromagnetic launching weapon system. J. Phys. Conf. Ser. 1507, 072021 (2020) 2. Guan, S., Wang, D., Guan, X., Guo, D., Wang, S., Liu, B.: Current sharing analysis of coil for electromagnetic launching. IEEE Trans. Plasma Sci. 47(5), 2393–2398 (2019) 3. Inger, E.: Electromagnetic launching systems to geosynchronously equatorial orbit in space and cost calculations. IEEE Trans. Plasma Sci. 45(7), 1663–1666 (2017) 4. Zhou, Y., Zhang, D., Yan, P.: Modeling of electromagnetic rail launcher system based on multifactor effects. IEEE Trans. Plasma Sci. 43(5), 1516–1522 (2015) 5. Gores, P.A., Vincent, G., Schneider, M., Spray, J.G.: Appraisal of rapid-fire electromagnetic launch effects on ceramic targets. IEEE Trans. Plasma Sci. 99, 1–6 (2019) 6. Li, C., Chen, L., Xu, J., Ruan, J., Xia, S.: Influence of caliber height on armature current melt erosion in rail gun. IEEE Trans. Plasma Sci. 48(8), 1–7 (2020) 7. Wang, Z., Chen, L., Xia, S., Li, C.: Experiments and analysis of downslope low-voltage transition in c-type solid armature rail gun. IEEE Trans. Plasma Sci. 99, 1–7 (2020) 8. Li, D., Cheung, D., Shi, X., Ng, V.: Uncertainty reasoning based on cloud models in controllers. Comput. Math. Appl. 35(3), 99–123 (1998) 9. Wei, D., Wei, L., Xu, Z.: A cloud model theory based trust inference mechanism. In: 5th Annual China Grid Conference, Guangzhou, China (2010) 10. Saez, D., Cipriano, A.: Design of fuzzy model based predictive controllers and its application to an inverted pendulum. In: Proceedings of 6th International Fuzzy Systems Conference, pp. 915–919 (2002)
Model Predictive Control for Electromagnetic Launcher of UAV Guanglei Xie, Jun Wu(B) , Yunzhou Zhang, and Yu Yang School of Intelligent Science, National University of Defense Technology, Changsha 410073, Hunan, China [email protected]
Abstract. Aim to improve the power density of the electromagnetic ejection system of UAV, the finite control set model prediction is adopted as the control strategy from the perspective of improving the efficiency. The semi-active control of hybrid energy storage system and the drive control of ejection motor are considered together. According to the different requirements of commutation and non-commutation, the finite control set of the electromagnetic ejection system is designed, control optimization is carried out from the system. Simulation results show that the proposed control strategy can effectively reduce thrust fluctuation, stabilize bus voltage, reduce switching loss and improve the efficiency of electromagnetic ejection system. Keywords: UAV · Electromagnetic ejection · Power density · Model predictive control
1 Introduction With the continuous development of artificial intelligence technology, UAV is more and more widely used in military and civil fields. As a launch mode with controllable speed in the whole process, electromagnetic ejection has the advantages of high reliability, strong concealment, easy maintenance and wide application range [1]. It is a research hotspot of UAV take-off mode at present. UAVs usually carry precision instruments, which requires the electromagnetic ejection system to have small overload impact, small thrust fluctuation and good controllability in the ejection process, so as to avoid damage to airborne equipment [2]. At the same time, UAVs of different types and weights should be ejected to the target speed according to different takeoff conditions, so as to fully reflect the advantages of electromagnetic ejection controllability [3]. With the development of high-speed microprocessor, model predictive control (MPC) is gradually applied to motor drive [4–6], power electronic converter [7, 8] and power system [9–11]. MPC does not rely on the accurate model of the controlled object and has the characteristics of “rolling optimization”. At the same time, considering the state of the system in the future, it can optimize multiple control objectives. Therefore, it can achieve high-performance control effect for strong coupling, multi-objective and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 147–159, 2022. https://doi.org/10.1007/978-981-19-1870-4_16
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nonlinear motor system [12, 13]. Reference [14] proposes a finite set model predictive fault-tolerant control algorithm, which solves the problem of easy loss of excitation of permanent magnet synchronous motor under complex working conditions, and realizes the loss of excitation fault-tolerant control. Compared with the traditional PI control method, this method has stronger fault-tolerant ability and robustness; Reference [15] introduces high current constraint, switching state limit, maximum torque current ratio optimization (MTPA) and torque control into value function, which significantly improves the efficiency and robustness of permanent magnet synchronous motor control system while realizing MTPA control; Reference [16] proposed the control strategy of double vector MPC current loop, which acts two voltage vectors in one control cycle, increasing the selection range of voltage vector. The experiments show that the improved control algorithm effectively suppresses the torque fluctuation of permanent magnet synchronous motor, improves the response ability and tracking performance of current loop, and avoids the limitations of single vector MPC current loop; Document [17] analyzes the causes of commutation torque fluctuation of brushless motor in detail. By adding three states of convex, concave and constant non-commutation current in the commutation process, the stability of non-commutation current is effectively maintained and commutation torque fluctuation is reduced. To sum up, MPC for permanent magnet synchronous motor mainly focuses on reducing torque ripple, improving efficiency and response speed by optimizing value function, expanding vector selection and increasing prediction cycle, so as to improve the performance of permanent magnet synchronous motor. The research on permanent magnet brushless DC motor system mainly focuses on the commutation stage. The commutation fluctuation is suppressed by increasing the control vector during the commutation stage, but the traditional PI control is still used in the non-commutation stage. Moreover, at present, all research is mainly focused on rotating motor, and the research on permanent magnet brushless linear DC motor is still blank. Different from the rotating motor, in the ejection stage, the permanent magnet brushless linear DC motor has been in the acceleration state. It has no steady state, only transient process. Therefore, the control performance of the ejection system has a great impact on the launch process of UAV. Therefore, this paper models the UAV electromagnetic ejection system as a whole, considers the energy control of the hybrid energy storage system and the drive control of the ejection motor, controls the ejection system as a whole, reduces the system loss, and improves the system efficiency.
2 Model Predictive Control Method for Electromagnetic Launcher of UAV The electromagnetic ejection system of UAV consists of ejection motor, control system, drive system and energy storage system. The control idea of FCS-MPC is: since the switching states of power converters at the end of hybrid energy storage system and motor inverter are limited (DC/DC converter at the end of energy storage system includes 2 power converters, a total of 4 switching states; ejection motor inverter includes 6 power converters, a total of 8 switching States), the prediction model of hybrid energy storage system and ejection motor can be established, Calculate the predicted values of system
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control variables corresponding to all switch states at the next time; Then, the value function is constructed to comprehensively evaluate the predicted value of the calculated system control variables, and the switching state corresponding to the minimum value function is selected; Finally, the switching state is applied to DC/DC converter and ejection motor inverter. Firstly, the prediction model of UAV electromagnetic ejection system needs to be established; Secondly, the objective function is designed for the object to be optimized. The model predictive control scheme of UAV electromagnetic ejection system is shown in Fig. 1. The outer loop of the system is speed loop and the inner loop is FCS-MPC current loop.
Fig. 1. Model predictive control scheme of UAV electromagnetic ejection system
The main circuit structure of UAV electromagnetic ejection system is shown in Fig. 2, which is mainly composed of hybrid energy storage system, inverter and ejection motor. In this paper, the hybrid energy storage system and ejection motor are predicted respectively. Hybrid energy storage system
Inverter Ejection motor
S1
S3
T1
T3 a
L1
b
Ubat Usc
S2
T5
c T4
T6
Ra
La
ea
Rb
Lb
eb
Rc
Lc
ec
T2
Fig. 2. Schematic diagram of main circuit structure of UAV electromagnetic ejection system
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Current Prediction of Hybrid Energy Storage System. The structural block diagram of the hybrid energy storage system is shown in Fig. 3, which has four states and two working modes, as shown in Table 1. Among them, “1” is used when the power switch is on and “0” is used when it is off.
+
S1 L1
Ubat
Udc
+ S2
Usc _
_
Fig. 3. Structure block diagram of hybrid energy storage system
Table 1. Working mode of hybrid energy storage system Mode
States
S1
S2
Boost
1
0
1
Boost
2
0
0
Buck
3
1
0
Buck
4
0
0
The four working states are discretized by the first-order Euler method, and the predicted current of the hybrid energy storage system at time is obtained as follows: Ts Usc (k) + isc (k) L Ts isc_2 (k + 1) = [Usc (k) − Udc (k)] + isc (k) L Ts isc_3 (k + 1) = [Udc (k) − Usc (k)] + isc (k) L Ts isc_4 (k + 1) = − Usc (k) + isc (k) L
isc_1 (k + 1) =
(1)
Ejection Motor Current Prediction. The three-phase windings of the ejection motor are star connected, the motor is driven by square wave current, and the two-way conduction mode is adopted during operation. The simplified equivalent circuit is shown in Fig. 4, where T1–T6 is IGBT power device, U_DC is the bus voltage and N is the neutral point of the motor.
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+ T1
T3
T5
R
Udc
_
L
e N
T4
T6
T2 O
Fig. 4. Simplified equivalent circuit model of ejection motor
The voltage balance equation of the ejection motor is ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ R00 L00 ea uno uao ia ia d ⎣ ubo ⎦ = ⎣ 0 R 0 ⎦⎣ ib ⎦ + ⎣ 0 L 0 ⎦ ⎣ ib ⎦ + ⎣ eb ⎦ + ⎣ uno ⎦ dt uco ic ic ec uno 00R 00L
(2)
Where uao , ubo , uco is the voltage of the three-phase winding end of the ejection motor to the ground; ia , ib , ic is the three-phase current of the ejection motor; ea , eb , ec is the three-phase back EMF of the ejection motor; R is the equivalent resistance of each phase winding of the ejection motor; L is the equivalent inductance of each phase winding of the ejection motor; uno is the neutral point to ground voltage of the ejection motor. The ejection motor adopts the conduction control mode of three-phase and six states, which is divided into two situations. Current Prediction in Normal Two-Phase Conduction Stage. In an electrical cycle, the ejection motor corresponds to six two-phase conduction modes, and the conduction condition and optional switching state of the corresponding power switch are shown in Table 2.
Table 2. Optional switch States in non-commutation mode Non-commutation mode
Turn on the power switch tube
States 1
States 2
I
T1 T2
110000
100000
II
T3 T2
011000
001000
III
T3 T4
001100
001000
IV
T5 T4
000110
000010
V
T5 T6
000011
000010
VI
T1 T6
100001
100000
Since the processes of six two-phase conduction modes are consistent, mode I is taken as an example. As shown in Fig. 5, it is the schematic diagram of switching state 1 in the two-phase conduction stage. At this time, the power switch tube T1T2 is on.
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T3
T5
R
L
e
Udc
_
N T4
T6
T2 O
Fig. 5. Schematic diagram of switch state 1 in two-phase conduction stage
The voltage equation of the ejection motor is ⎧ uao = ia R + Ls didta + ea + uno ⎪ ⎪ ⎨ uco = ic R + Ls didtc + ec + uno ⎪ i = −ic ⎪ ⎩ a uao − uco = 2ia R + 2Ls didta + ea − ec =Udc
(3)
By discretization, the predicted current of phase a at K + 1 is ia (k+1) = ia (k) +
Ts [Udc (k) − (ea (k) − ec (k)) − 2ia (k)R] 2Ls
(4)
As shown in Fig. 6, it is the schematic diagram of switching state 2 in the two-phase conduction stage. + T1
T3
T5
R
L
e
Udc
_
N T4
T6
T2 O
Fig. 6. Schematic diagram of switch state 2 in two-phase conduction stage
By discretization, the predicted current of phase a at K + 1 is ia (k+1) = ia (k) +
Ts [−(ea (k) − ec (k)) − 2ia (k)R] 2Ls
(5)
Current Prediction Model in Commutation Stage. The optional switch states under different commutation modes are shown in Table 3. There are four circuit conduction states under each commutation mode.
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Table 3. Optional switch states in different commutation modes Non-commutation mode
States 1
States 2
States 3
States 4
I
001000
011000
101000
111000
II
000100
001100
010100
011100
III
000010
000110
001010
001110
IV
000001
000011
000101
000111
V
100000
100001
100010
100011
VI
010000
110000
010001
110001
Taking commutation mode I as an example, at this time, phase C is non-commutation phase, phase A is off phase and phase B is on phase, then dic dib − ) + (ea − eb ) dt dt dib dic ubo − uco = (ib − ic )R + Ls ( − ) + (eb − ec ) dt dt dic + (ea + eb − 2ec ) uao + ubo − 2uco = −3Ric − 3Ls dt
uao − ubo = (−2ib − ic )R + Ls (−2
(6)
By discretization, the predicted current of phase C at K + 1 is (1 +
RTs Ts )ic (k+1) − ic (k) = [(ea (k) + eb (k) − 2ec (k)) Ls 3Ls − (uao (k) + ubo (k) − 2uco (k))]
(7)
Make e(k) = ea (k) + eb (k) − 2ec (k) u(k) = uao (k) + ubo (k) − 2uco (k)
(8)
Can be reduced to (1 +
RTs Ts )ic (k+1) − ic (k) = [e(k) − u(k)] Ls 3Ls
Then at K + 1, the predicted current of phase C is
Ts 1 ic (k+1) = [e(k) − u(k)]+ic (k) s 3Ls 1 + RT Ls
(9)
(10)
Similarly, the terminal voltages corresponding to different switching states under different commutation modes can be obtained, as shown in Table 4 (UDC is represented by 1). The predicted current value of the non-commutating phase at K + 1 can be calculated.
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Commutation mode
I
II
III
IV
V
VI
1
011
001
101
100
110
010
2
010
011
001
101
100
110
3
111
000
111
000
111
000
4
110
010
011
001
101
100
Model Switching Algorithm of Ejection Motor Table 5. Ejection motor commutation time detection table Commutation mode
Non-commutation
Start time of commutation
End time of commutation
Judgment conditions
I
C
H2↑
ia = 0
H2 = 1, ia > 0
II
B
H1↓
ic = 0
H1 = 0, ic < 0
III
A
H3↑
ib = 0
H3 = 1, ib > 0
IV
C
H2↓
ia = 0
H2 = 0, ia < 0
V
B
H1↑
ic = 0
H1 = 1, ic > 0
VI
A
H3↓
ib = 0
H3 = 0, ib < 0
Fig. 7. Ejection motor prediction model switching process
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The commutation time of the ejection motor is shown in Table 5. When the rising edge and falling edge signals of the hall signal are detected, the ejection motor enters the commutation stage. The specific switching process is shown in Fig. 7. Rolling Optimization. The optimization objectives of FCS-MPC in this paper include the following points: The Thrust Fluctuation is Small. The ejection motor described in this paper is a permanent magnet brushless DC linear motor, which will produce large thrust fluctuation during commutation. It can be seen from literature [18] that the thrust fluctuation is F =
(Fmin − Favg ) Udc − 4E − 3Ri = Favg Udc + 2E + 3Ri
Therefore, the optimization objective is inon (k + 1) − inon_ref
(11)
(12)
Where inon (k + 1) is the predicted current at the time K + 1,inon_ref is the calculated reference current. Less Switching Times of Power Devices. On the premise of determining the structure of UAV electromagnetic ejection system, the system loss can be reduced by reducing the switching times of power converter, so as to improve the efficiency of electromagnetic ejection system [19], which is Sswitch (k + 1) = |Sa (k + 1) − Sa (k)| + |Sb (k + 1) − Sb (k)| + |Sc (k + 1) − Sc (k)|+|Sdcdc (k + 1) − Sdcdc (k)|
(13)
Where the first three items are the switching action times of phase a, b and c power devices of inverter respectively; |Sdcdc (k + 1) − Sdcdc (k)| is the switching action times of DC/DC converter. Super Capacitor Current Tracking Error is Small. That is, the discharge current of super capacitor is required to track the calculated reference current in time. The optimization objectives is isc (k + 1) − isc_ref (14) Where isc (k + 1) is the predicted current of supercapacitor at time k + 1; isc_ref is the supercapacitor reference current calculated by power distribution.
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Therefore, in the UAV electromagnetic ejection system, in order to improve the power density, from the perspective of improving efficiency, in order to reduce the thrust fluctuation, the switching times of power devices and the battery discharge current fluctuation, the multi-objective value function can be formulated as follows min J (k + 1) = α inon (k + 1) − inon_ref + βSswitch (k + 1) + λ isc (k + 1) − isc_ref (15) Where α, β, λ are the weight coefficients corresponding to the control target respectively. K moment
Sampling current
iinonsc
Y
N
Commutation state
i = 1~8
i= 1~4
commutation forecasting model
Non-commutation forecasting model
Cost function
Cost function
i< 8
i< 4
Y
N
Y
N
Select the corresponding switch mode of min J DC/DC converter
inverter
K+1 moment
Fig. 8. FCS-MPC control process of UAV electromagnetic ejection system
In this paper, the FCS-MPC control strategy adopts the single-step prediction method, and the prediction step and control step are 1. Therefore, in the prediction process, the “exhaustive method” can be used to solve the optimal switching sequence of the system. The FCS-MPC control process of UAV electromagnetic ejection system is shown in Fig. 8.
3 Simulation Analysis In order to verify the effectiveness of the FCS-MPC control algorithm proposed in this paper, the simulation model of UAV electromagnetic ejection system is built in
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Matlab/Simulink environment for analysis, and the MPC algorithm is compared with the traditional PI control algorithm. The working voltage of UAV electromagnetic catapult is 340 V, and the parameters used in simulation are shown in Table 6. Table 6. Simulation parameters of UAV electromagnetic ejection system Classes
Parameter
Nominal voltage of lithium battery/V
340
Nominal capacity of lithium battery/Ah
200
Nominal voltage of supercapacitor/V
288
Nominal capacity of supercapacitor/F
45
Phase inductance of ejection motor/mH
0.085
Phase resistance of ejection motor/
2.875
The simulation results are shown in Fig. 9. 341.5
550 MPC
339
MPC
341.0
PI
500
PI
338.5
340.5 338 340.0
U v
F N·m
450
400 500 350
300
250
337.5 0.35
339.5
338.0 300
0.352
0.05
0.354 0.1
0.356
0.358
0.15
0.2 Time(s)
337.5 0.25
0.3
0.35
0.4
337.00
0.05
10
8
MPC
0.15
0.2 Time (s)
0.25
0.3
0.35
0.4
4
MPC
Number of switches (n)
PI
20 30 29.52
10
0.1
0.1
(b) Terminal voltage contrast
30
Ejection Speed (m/s)
0.36
338.5
400
(a) Thrust contrast
00
0.355
339.0
0.2 Time (s)
0.3
0.4
(c) Switch frequency comparison
PI
6
4
2
0
0
0.1
0.2 Time (s)
0.3
0.4
(d) The ejection velocity contrast
Fig. 9. Comparison of FCS-MPC and PI control strategy simulation results
Figure 9(a) shows the thrust comparison between FCS-MPC control strategy and PI control strategy. It can be seen that in the early stage of ejection, the thrust fluctuation
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of FCS-MPC control strategy is 3.2%, while that of PI control strategy is 5.8%. In the later stage of ejection, with the increase of the mover speed, the back EMF of the motor is satisfied Udc − 4E < 3Ri, and PI control can not suppress the thrust fluctuation. At this time, the maximum thrust fluctuation reaches 45.3%, resulting in the decrease of effective thrust. The FCS-MPC control strategy can effectively maintain the stability of non-commutation current, suppress the thrust fluctuation within 13.7% and effectively reduce the thrust fluctuation by increasing the vector selection of ejection single machine during commutation. Figure 9(b) shows the terminal voltage comparison between FCS-MPC control strategy and PI control. It can be seen that in the early stage of ejection, the required power of the motor is less than that provided by the battery. At this time, all power is provided by the lithium battery. The current of the lithium battery increases with the increase of ejection speed, and the terminal voltage decreases with the increase of battery output current. When the required power of the ejection motor is greater than the maximum power provided by the battery, the insufficient power is supplemented by the super capacitor. At this time, the lithium battery maintains the maximum discharge current and the terminal voltage does not drop. By adopting FCS-MPC strategy, the fluctuation of terminal voltage in the later stage of ejection can be reduced from 1.5 V to 0.5 V, which effectively protects the battery. Figure 9(c) shows the comparison of switching times of power devices controlled by FCS-MPC and PI. By introducing a new switching vector in the motor commutation process, the switching times can be effectively reduced. In one ejection process, the switching times can be effectively reduced by 31%. Figure 9(d) shows the ejection speed comparison between FCS-MPC control strategy and PI control. It can be seen that in the same ejection time, the ejection end speed of FCS-MPC is greater than that controlled by PI, which shows that FCS-MPC algorithm has higher efficiency and can indirectly improve the system power density.
4 Conclusion In order to reduce the loss and improve the efficiency of UAV electromagnetic ejection system, an FCS-MPC method is proposed to manage the energy from the whole system, and optimize the motor thrust fluctuation, bus voltage fluctuation and power switching loss. Compared with traditional PI control, FCS-MPC method can optimize multiple objectives at the same time, which is embodied in: (1) The thrust fluctuation during commutation is reduced from 45.3% to 13.7%, and the thrust fluctuation during non-commutation is reduced from 5.8% to 3.2%; (2) The fluctuation of bus voltage is reduced from 1.5 V to 0.5 V, which improves the stability of lithium battery terminal voltage; (3) In one ejection process, the switching times of power devices are effectively reduced by 31% and the switching loss is reduced; (4) At the same time, FCS-MPC has higher ejection terminal velocity, indicating that FCS-MPC scheme can effectively improve system efficiency.
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References 1. Wang, H., Yang, M.: Development status and trend of U.S. UAV. Flying Missile 2, 46–50 (2020). (in Chinese) 2. Wang, X., Wu, J., Meng, Q.: Design of a continuous electromagnetic ejection system for UAV. Fire Command Control 46(4), 7 (2021). (in Chinese) 3. Du, P., Lu, J., Li, X., et al.: Interior ballistic characteristics of electromagnetic rail launcher considering the dynamic characteristics of real launcher. IEEE Trans. Ind. Electron. 68(7), 6087–6096 (2021) 4. Ahmed, A.A., Koh, B.K., Lee, Y.I.: A comparison of finite control set and continuous control set model predictive control schemes for speed control of induction motors. IEEE Trans. Ind. Inform. 14(4), 1334–1346 (2018) 5. Li, X., Wang, Y., Guo, X., Cui, X., Zhang, S., Li, Y.: An improved model-free current predictive control method for SPMSM drives. IEEE Access 9, 134672–134681 (2021) 6. Mousavi, M.S., Davari, S.A., Nekoukar, V., Garcia, C., Rodriguez, J.: Finite-set model predictive current control of induction motors by direct use of total disturbance. IEEE Access 9, 107779–107790 (2021) 7. Wang, M., Shi, Y., Shen, M., et al.: Model voltage predictive control of three-phase voltage source rectifier. J. Electrotech. Technol. 30(16), 49–55 (2015). (in Chinese) 8. Rodríguez, J., Heydari, R., Rafiee, Z., Young, H.A., Flores-Bahamonde, F., Shahparasti, M.: Model-free predictive current control of a voltage source inverter. IEEE Access 8, 211104– 211114 (2020) 9. Rodriguez, J., Garcia, C., Mora, A., et al.: Latest advances of model predictive control in electrical drives. Part I: basic concepts and advanced strategies. IEEE Trans. Power Electron. 37, 3927–3942 (2022) 10. Rodriguez, J., Garcia, C., Mora, A., et al.: Latest advances of model predictive control in electrical drives. Part ii: applications and benchmarking with classical control methods. IEEE Trans. Power Electron. 37, 5047–5061 (2021) 11. Hu, J., Shan, Y., Guerrero, J.M., et al.: Model predictive control of microgrids–an overview. Renew. Sustain. Energy Rev. 136, 110422 (2021) 12. Rodriguez, J., Cortes, P.: Predictive Control of Power Converters and Electrical Drives (2012) 13. Xi, Y.: Predictive Control. National Defense Industry Press, Beijing (2013). (in Chinese) 14. Zhao, K., Chen, Y., Zhang, C., et al.: Finite set model predictive fault-tolerant control of PMSM loss-of-excitation fault. J. Electr. Meas. Instrum. 33(7), 84–92 (2019). (in Chinese) 15. Liu, X., Liu, W.: Based on the maximum torque current ratio control of permanent magnet synchronous motor. J. Model Predictive Control Mot. Control Appl. 4 (2017). (in Chinese) 16. Lin, J., Xie, G., Wan, Q., et al.: Improved double vector MPC current control of permanent magnet synchronous linear motor. Micro-spec. Mot. 47(8), 48–53 (2019). (in Chinese) 17. Zhang, Y., Cui, W., Liao, J.: Brushless DC motor torque ripple suppression method based on model predictive control. Micro-spec. Mot. 43(2), 58–61 (2015). (in Chinese) 18. Lu, S., Zhao, H., Wu, J.: Fluctuation analysis of commutation thrust of brushless DC linear motor for ejection. Micro Mot. 38(6), 10–12 (2010). (in Chinese) 19. Luo, R., He, Y., Chen, H., et al.: SVPWM strategy of neutral point potential balance and low switching loss of three-level converter. J. Electrotech. Technol. 33(14), 3245–3254 (2018). (in Chinese)
Research on Control Strategy of the Electromagnetic Launch System for Fixed Wing UAV Yao Li(B) , Donghuai Zhang, Xinyu Zhang, Xiaoxiao Ma, Hongwei Yao, and Yanming Li Beijing Mechanical Equipment Institute, Beijing, China [email protected]
Abstract. Electric energy is used as the power source for electromagnetic launch system, and the linear motor of the system can be precisely controlled. Rapid loading can realize low-cost, high-density and rapid continuous launching of UAV, meet the requirements of diversified combat capabilities of UAV in future wars, and improve the comprehensive combat performance of UAV. At the same time, electromagnetic boost launch can control the ejection process acceleration according to the take-off requirements of UAV, and realize the safe and reliable ejection take-off of various TYPES of UAV, which has the characteristics of universality. To achieve the advantages of highly controllable and fast relaunching, this paper conducts a research on the 100 kg UAV electromagnetic launch system, specifically introduces the control strategy of the UAV electromagnetic launch system based on the field-oriented control. A 100 kg UAV electromagnetic launch prototype is built, and the proposed control strategy of the system is verified by experiments. The experiment results show that the electromagnetic launch of the UAVs is stable and reliable and it can meet the demands of fast relaunch of the UVAs. Keywords: Fixed wing UAV · Electromagnetic launch · Field-oriented control · Fast relaunch
1 Introduction In recent years, UAV and its related technologies have been rapidly developed and applied all over the world. It should also be noted that the rapid launch and reliable recovery of UAVs are the difficulties encountered in the development of UAVs [1, 2]. UAV launch refers to the process that UAV can reach a certain initial speed in a certain place and in a certain way. The launch of UAVs has a direct impact on the battlefield survivability, reusability, regional adaptability and operational flexibility of UAVs [3]. There are various launch modes of UAV, such as taxiing take-off, rocket boost, ejection take-off, hand throw launch, airborne launch, vertical take-off, etc. In the specific selection, many factors such as UAV model, quality, size, service conditions and combat tasks should also be fully considered. The most basic requirement for UAV launch system © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 160–169, 2022. https://doi.org/10.1007/978-981-19-1870-4_17
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is that UAV can take off safely and reliably, among which handcast launch is only suitable for launching micro-UAV, and vertical take-off is only suitable for taking off rotorcraft UAV. Taxiing takeoff refers to the UAV taking off on the runway through the landing gear by using the thrust of its own engine. The advantages of this method are simple and reliable, less supporting ground support equipment, small acceleration overload and low use cost; Its disadvantage is that it needs runway or better ground environmental conditions and poor mobility. Rocket assisted launch means that UAV uses the thrust of rocket booster to accelerate its launch in a short time. It has the advantages of small floor area, low initial investment and little influence by environmental conditions, and can well meet the requirements of fast and mobile battlefield; Its disadvantage is that it involves the storage, transportation and use of explosive materials, and has strong physical characteristics such as sound, light and smoke, which are easy to expose the launching position [4]. Ejection take-off is to convert different forms of energy such as liquid/pneumatic energy, elastic potential energy and electromagnetic energy into UAV kinetic energy, so as to accelerate UAV to safe take-off speed on a certain length of slide rail. The advantage of ejection take-off is that it does not need a special take-off airport and runway, has good mobility, can take-off in mountainous areas with limited space, and has good safety and concealment; Its disadvantage is that the ejection mechanism and control system are complex [5, 6]. According to the different launching power energy, ejection takeoff can be divided into elastic ejection, pneumatic ejection, electromagnetic boost launch and so on. The main characteristics are compared in Table 1. (1) Elastic ejection: the elastic force of the rubber band helps the UAV to take off. The advantages of this way are simple structure, low cost and easy operation and maintenance; The disadvantage is that the catapult thrust is small, the UAV’s exit speed is low. In plateau conditions, the air is thin, and the ejection speed is difficult to meet the requirements of UAV take-off. (2) Pneumatic ejection: the UAV is boosted to take off by air pressure. This ejection method can provide larger outlet speed for the UAV, and is flexible in use and good in concealment. However, the pressure system is susceptible to the environment, especially the low pressure brought by high altitude, which will affect the thrust force of pneumatic ejection. In addition, the overload Table 1. The comparison of different means for UAV eject launch Ejection form
Advantages
Disadvantages
Elastic ejection
Small size, light weight, simple structure, easy to carry, low cost
Small ejection ability, poor environmental adaptability, temperature sensitivity, individual differences
Pneumatic ejection
Excellent ejection capability, reuse, low cost
The high altitude adaptability is poor and the launch process is less controllable
Electromagnetic assisted launch
Excellent ejection ability, rapid reuse, excellent controllability, good environmental adaptability
The system is complex and the cost is high
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control ability of the pneumatic ejection system is weak in the process of ejection takeoff, and the ability of rapid and continuous ejection is poor. (3) Electromagnetic boost launch: It is a new UAV launch technology that uses electric energy as energy and accelerates objects through electromagnetic thrust generated by the principle of electromagnetic action, and converts electric energy into launch power efficiently to achieve catapult takeoff of UAV. The electromagnetic boost launch system can control the acceleration of the ejection process according to the requirements of UAV ejection, and realize the safe and reliable ejection take-off of UAV. At the same time, the electromagnetic boost launch system is suitable for the launch of UAVs with the maximum payload weight below, which meets the needs of the launch platform generalization. The electromagnetic launch of UAV with different weight and take-off speed can be realized quickly by parameter binding. Due to the use of electric energy as the power source, the operation process of linear motor is accurate and controllable. Through rapid loading, low-cost, high-density and rapid continuous launching of UAV can be realized, which can meet the requirements of diversified combat and anti-saturation attack capability of UAV in future wars, and improve the comprehensive combat performance of UAV. In order to realize the advantages of strong controllability of the launch process and rapid repeated launch of the electromagnetic boost launch system, this paper takes the 100 kg UAV electromagnetic boost launch system as the research object, focuses on the key control technology of the unmanned electromechanical magnetic boost launch system based on vector control, and introduces the composition of the 100 kg UAV electromagnetic boost launch system. The key control technology of the system is verified by 65 kg simulated load test, which lays a foundation for the application of UAV electromagnetic boost launch system.
2 Key Control Technology of UAV Electromagnetic Boost Launch System The electromagnetic boost launch system of 100 kg UAV is mainly composed of linear motor electromagnetic boost launcher, driving power supply system and system controller. The system composition is shown in Fig. 1.
UAV electromagnetic ejection system
Electromagnetic catapult
ServoThe control buffer mechan pulley switcher mechanism device launcher ism
Linear Winding motor
Electroma gnetic
Locking release
Portable controller
Drive power supply
Charge Energy and storage discharge combinati module module module on
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Power supply module
Fig. 1. Electromagnetic launch system composition for fixed wing UAV
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The UAV electromagnetic boost launch system uses electric energy as power energy, charges the energy storage module through the charging module in the charge-discharge combination, reaches the set bus voltage, and enters the launch readiness state. Press the transmit button, and the power module converts the electric energy of the energy storage module into the ac power required by the linear motor drive according to the preset program of the control module. The stator conduction where the actuator is located is controlled by the winding segmented controller to generate electromagnetic thrust and accelerate the actuator, pulley and UAV connected with the pulley to realize the conversion of electric energy to the kinetic energy of the launch load and push the UAV to leave the launch pad at a preset target speed. The high-speed linear electromagnetic booster actuator and pulley are braked by electromagnetic and mechanical buffering brake units. After the launch, the actuator is reset to enter the next launch process. 2.1 Mathematical Model of Linear Motor The executive mechanism of 100 kg UAV electromagnetic boost launch system is threephase permanent magnet synchronous linear motor. Since the UAV is connected with linear electric motor through pulley, we transform the control of UAV ejection process into the control of permanent magnet synchronous linear motor. The stator of permanent magnet synchronous motor is composed of permanent magnet, and the electromagnetic coupling relationship between the stator and permanent magnet is complicated. In the construction of mathematical model, it is necessary to ignore the harmonic component, windings spatial distribution and other factors that have little influence. The current, voltage and flux in the three-phase stator windings in ABC coordinate system are transformed to the rotating D-Q coordinate system by coordinate transformation, and the mathematical model of three-phase permanent magnet synchronous motor is obtained. The stator voltage equation is:
ud uq
⎡ dψ ⎤ d −ωr ψq i Rs 0 d ⎢ dt ⎥ = +⎣ ⎦+ d ψq 0 Rs iq ωr ψd dt
(1)
Flux equation is:
ψd ψq
Ld 0 = 0 Lq
ψf id + iq 0
(2)
In the formula, ud and uq respectively represent the components of the stator voltage on the d and q axes; Rs represents the equivalent resistance of each phase winding of the stator; id and iq respectively represent the components of the stator current in the d and q axes; ud and ψ q Respectively represent the components of the stator flux on axis d and q; ωr represents rotating electric angular velocity; L d and L q are components of the stator inductance in the d and q axes respectively; ψ f is mover permanent magnet flux linkage. Because the system adopts hidden pole bilateral permanent magnet synchronous
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linear motor, L d approximately equals to L q , then L d = L q . Ignoring the influence of temperature change on permanent magnet, ψ f can be considered as a constant. The voltage equation is:
ud uq
⎡ ⎤ did 0 id Rs −ωr Lq Ld 0 ⎢ dt ⎥ = + ⎣ ⎦+ diq ωr Ld Rs 0 Lq ωr ψf iq dt
(3)
The electromagnetic thrust equation of hidden pole permanent magnet synchronous linear motor is: Fe =
3π pn ψf iq 2τ
(4)
In the formula, Pn is the number of motor poles, τ is the pole distance of linear motor. Due to the long length of the linear motor, considering the efficiency of the drive power supply and the cost of the whole electromagnetic boost launch system, the linear motor needs to be segmented, and the stator segmented working time is determined by the position of the actuator. The mathematical model mentioned in Eqs. (3) and (4) is the mathematical model of single-segment permanent magnet synchronous linear motor with the actuator and stator completely overlapping, and the mathematical model of stator segment 1 at t1 in Fig. 3. At t2, the actuator is between stator segment 1 and stator segment 2, and the mathematical model of PMSM is correlated with the relative position of the stator of the actuator. For the first stator segment, with the gradual withdrawal of the mover, the coupling area decreases, the amplitude of excitation potential decreases, the armature current increases and the electromagnetic thrust decreases. When the mover enters the second stator, the amplitude of the post excitation EMF gradually increases, the armature current decreases, and the electromagnetic thrust increases in the form
Power
Power
Supply 1
Supply 2
Stator section 1 t1 Moment mover
Stator section 2
Stator section 3
t2 Moment mover
(a) Sectional power supply of linear motor
(b) Relative relationship between mover and stator during operation of linear motor Fig. 2. Section of permanent magnet linear motor
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of pulsation. When the mover is completely within the range of the second section of stator, the amplitude of excitation EMF remains unchanged and the output of the motor is relatively stable. When the mover is about to exit the second section of stator, with the decrease of excitation EMF amplitude, the armature current increases and the electromagnetic force decreases gradually. This is repeated. The rotor position in the stator section of linear motor has an influence on the stator inductance d, q-axis inductance components L d and L q and rotor permanent magnet flux ψ f in the mathematical model of permanent magnet synchronous motor. Ignoring the harmonic effect, the inductance components L d and L q and the flux linkage ψ f of the mover permanent magnet change approximately linearly. As shown in Fig. 3(b), the mover length is a, the segment length of single section stator is b, and the mover displacement is s. for long primary linear motor, b > a, so the mover coefficient k is expressed as: ⎧s ⎨a s≤a k= 1 a 2e + He+
Bolsig+
R4
e + N2 => e + N2 (C3 )
Bolsig+
R5
e + N2 => 2e + N2 +
Bolsig+
R6
e + N2 + => N2 He+ + 2He => He2 + + He He* + N2 => He + N2 + + e He* + 2 He => He2 * + He He2 * + N2 => 2He + N2 + + e
4.8 × 10–13 (Te /Tg )−0.5
R7 R8 R9 R10
1.1 × 10–43 (m6 /s) 7.6 × 10–17 (m3 /s) 2.0 × 10–46 (m6 /s) 3.0 × 10–17 (m3 /s) (continued)
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Table 1. (continued) No.
Reaction formula
Reaction coefficient
R11
He2 + + N2 => N2 + + He2 * 2He2 * => He2 + + 2He + e 2He* => He2 + + e He2 + + e => He + He* N2 + + 2N2 => N4 + + N2 N4 + + e => 2N2 N4 + + N2 => N2 + + 2N2 N2 + + N2 + He => N4 + + He N4 + + He => N2 + + N2 + He N2 (C3 ) => N2 + hv
1.4 × 10–15 (m3 /s)
R12 R13 R14 R15 R16 R17 R18 R19 R20
1.5 × 10–15 (m3 /s) 1.5 × 10–15 (m3 /s) 8.9 × 10–15 (Te /Tg )−1.5 5.0 × 10–41 (m6 /s) 2.0 × 10–12 (m3 /s) 2.5 × 10–21 (m3 /s) 1.9 × 10–41 (m6 /s) 2.5 × 10–21 (m3 /s) 2.5 × 107 (1/s)
Fig. 1. A 2D axisymmetric model is established in this study: (a) global model and the (b) local model of SMH and SOH
3 Results and Discussion 3.1 Characteristics of Neutral Gas Flow The steady-state distributions of global velocity for different substrates are the similar. Therefore, the axial and radial velocity global distributions for substrate without hole is chosen as an example, shown in Fig. 2. The axial velocity is positive in the positive Y-axis direction, and radial velocity is positive in the direction away from the axis of symmetry. It can be seen that the axial velocity was negative, which meant that the direction of axial velocity pointed to the negative Y-axis direction. The axial velocity was larger in
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the tube. However, with the increase distance, the axial velocity decreased outside the tube. Compared with the value of axial velocity, the value of radial velocity was much smaller. It can be seen that the radial velocity existed the negative value. Due to the flow convergence, the flow moved towards the axis of symmetry at the metal electrode head so that the radial velocity occurred the negative value. Near the axis of symmetry, the axial velocity is dominant. However, near the substrate, the radial velocity is dominant. The distribution of helium mole fraction is shown in Fig. 2c. It can be seen that the heliu mole fraction was almost equal to 1 in the tube. The helium flowed out the tube and mixed with the nitrogen. When the helium reached the substrate, the helium flowed in the form of emission due to the obstruction of the substrate. To investigate the effect of different substrates on the characteristics of neutral gas flow, axial velocity and radial velocity near substrate (Z = 0.01 mm) were compared and analyzed, as shown in Fig. 3. It can be seen that the axial velocity was almost zero for SOH. However, for SMH, axial velocity existed a conversion between positive and negative values near the edge of micro-hole, confirming vortex forming. which was conductive to mass transfer of fluid. In the addition, the axial velocity value of SMH was larger than that of SOH near the symmetry axis. According to the Bernoulli equation, it can reduce local high pressure near the symmetry axis, which was beneficial to the propagation of electron and ions towards the center. The radial velocity distribution is shown in Fig. 3b. The radial velocity distribution of SOH first increased and then decreased in the direction away from the axis of symmetry. However, for the substrates with micro-hole, the curves of radial velocity distribution exhibited a big fluctuation. The peak value appeared at the center of hole. Higher velocity was beneficial to propagation the particles. The fluctuation of axial and radial velocity was more intense near the SMH, which promoted the diffusion of fluid and the transportation of particles near the substrate.
Fig. 2. The (a) axial velocity distributions; (b) radial velocity distributions; and (c) the distribution of helium mole fraction for substrate without hole
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Fig. 3. The radial evolution curves of velocity: (a) axial velocity and (b) radial velocity at Z = 0.01 mm
3.2 Characteristics of Plasma Discharge The radial evolution of electron density at Z = 0.001 mm for SOH and SMH with different micro-hole depth at 100 ns is shown in Fig. 4a. As we can see, for SOH, the radial distribution of electron density was relatively uniform, and its value was stable at about 1 × 1015.5 . However, for the SMH, the radial distribution of electron density fluctuated greatly. The electron density values for the flat part of the substrates with micro-hole were similar with that for the SOH, but the electron density values near and in the micro-hole of the SMH were significantly higher than that for the SOH by almost four orders. The electron density was proportional to the electric field intensity, and the radial evolution of electric field intensity at Z = 0.001 mm for SOH and SMH with different micro-hole depth are shown in Fig. 4b. It can be seen that the electric field
Fig. 4. The radial evolution: (a) electron density; and (b) electric field intensity at z = 0.001 mm for different substrates
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intensity was higher near the edge of micro-hole, and the electric field intensity was smaller in the micro-hole. With the increased micro-hole depth, the peak electric field intensity increased near the edge of micro-hole. To explore the effect of different substrates on the various particle density, the average values of various particle number density were compared in the area near the substrate, shown in Fig. 5. For the excited particles He* , He2 * and N2 (C3 ), the number density of He* was smaller, and the number densities of He2 * and N2 (C3 ) were larger. With the increased micro-hole depth, the number densities of He* , He2 * and N2 (C3 ) were first increased and then decreased, and when the micro-hole depth was 0.05 mm, the maximum number densities of excited particles He* , He2 * and N2 (C3 ) were obtained. For charged particles e, He+ , He2 + , N2 + and N4 + , the number density of N4 + was dominant, which was consist with Ref. [10]. Similarly, with the increased micro-hole depth, the number densities of He+ , He2 + , N2 + and N4 + were first increased and then decreased, and when the micro-hole depth was 0.05 mm, the maximum number densities of excited particles He+ , He2 + , N2 + and N4 + were obtained. The generation of charged particles was closely related to the ionization reaction rate. The ionization reaction rates for different substrates near the substrate are shown in Fig. 6. It is evident that the ionization reaction rate was the maximum value when the micro-hole depth was 0.05 mm. The acceleration of the ionization reaction rate promoted the formation of various charged particles, which was related to diffusion motion of gas molecules and local high electric field intensity.
Fig. 5. The average values of various particle density for different substrates in the area near the substrate
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Fig. 6. The ionization reaction rates for different substrates near the substrate
4 Conclusions In this study, A 2D axisymmetric model was established to simulate the interaction between APPJ and SOH and SMH with different micro-hole depth. The characteristics of neutral gas diffusion and plasma discharge near the substrate were focused on. The following conclusions were obtained: 1) Compared to the SOH, vortex existed on the substrates with micro-hole, which was conductive to the neutral gas diffusion. With the increased micro-hole depth, the neutral gas diffusion was stronger. 2) The radial evolution of electron density for the SMH was locally higher than that for the SOH, which was due to the local high electric field intensity near the microhole. The local high electric field intensity accelerated the ionization reaction rate, thus increased the electron density. 3) The number densities of various excited and charged particles for the substrates with micro-hole were significantly higher than that for SOH. With the increased microhole depth, the number densities of various excited and charged particles were first increased and then decreased, and the maximum number densities for various excited and charged particles were obtained when the micro-hole depth was 0.05 mm. Acknowledgments. This work was financially supported by the National Natural Science Foundation of China (51877205, 52011530191) and the Fundamental Research Funds for the Central Universities (buctrc201906).
References 1. Reuter, S., Von Woedtke, T., Weltmann, K.D.: The kINPen-a review on physics and chemistry of the atmospheric pressure plasma jet and its applications. J. Phys. D Appl. Phys 51(23), 233001 (2018) 2. Zhang, J., Wang, Y., Wang, D., Economou, D.J.: Numerical simulation of streamer evolution in surface dielectric barrier discharge with electrode-array. J. Appl. Phys. 128, 093301 (2020)
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3. Wang, R., Xu, H., Zhao, Y., Zhu, W., Ostrikov, K., Shao, T.: Effect of dielectric and conductive targets on plasma jet behaviour and thin film properties. J. Phys. D Appl. Phys. 28, 074002 (2018) 4. Xu, M., An, Z., Wang, Y., Yin, H., Cheng, G., Zhang, X.: Effect of non-thermal plasms modification on surface characteristics of polyimide nanocomposites film. Insulating Mater. 54(5), 47–53 (2021). (in Chinses) 5. Wang, R., Li, W., Zhang, C., Ren, C., Ostrikov, K., Shao, T.: Thin insulating film deposition on copper by atmospheric-pressure plasmas. Plasma Processes Polym. 14(7), 1600248 (2017) 6. Suresh, V., Jegan, A., Kumar, S.L.: Microstructure mechanical and tribological characteristics of plasma and HVOF sprayed Cr3 C2 -PS.ZrO2 coatings. Mater. Today Proc. 33, 1137–1143 (2020) 7. Huang, Q., et al.: Super-hydrophobic film deposition by an atmospheric-pressure plasma process and its anti-icing characteristics. Plasma Sci. Technol 21(05), 144–152 (2019) 8. Babaeva, N.Y., et al.: Plasma bullet propagation and reflection from metallic and dielectric targets. Plasma Sources Sci. Technol. 28(9), 095006 (2019) 9. Hasan, M.I., Bradley, J.W.: Computational study of the afterglow in single and sequential pulsing of an atmospheric-pressure plasma jet. Plasma Sources Sci. Technol. 24, 055015 (2015) 10. Jiang, Y., Wang, Y., Cong, S., Zhang, J., Wang, D.: Effects of nitrogen impurity on the atmospheric pressure helium plasma jets exposed to a nitrogen environment. Phys. Plasmas 27, 103511 (2020)
Simulation and Experiment Analysis of Opening Characteristics for High-Current Fast Switch Based on Double-Acting Mechanism Wei Zhao, Bing Zhao, Yanjun Zhao, Zhiwen Xie, Wei Wang, and Ning Xie(B) Electric Power Research Institute of Guangdong Power Grid Co., Ltd., Guangzhou, China [email protected]
Abstract. In view of requirements of high current medium voltage DC circuit breaker for faster opening speed and greater contact pressure in closing position, a fast mechanical switch based on double spring permanent magnet operation and electromagnetic repulsion double-acting mechanism is proposed. The action process of the double acting mechanism involves multi-field coupling of electromagnetic field, temperature field, dynamic field and displacement field. In this paper, based on the finite element method, the multi-physical field coupling calculation is carried out for the fast mechanical switching based on the dual-spring permanent magnet operator and the electromagnetic repulsive double-acting mechanism, and the influence of the input of the driving coil of the permanent magnet operator and the different driving coil currents on the opening process of the switch is analyzed. The simulation results show that the springback phenomenon can be avoided when the driving coil of permanent magnet operating mechanism and the opening coil of electromagnetic repulsion mechanism are put into operation at the same time. Moreover, due to the large electromagnetic repulsion force at the initial opening stage, the input of the driving coil of the permanent magnet operating mechanism has little impact on the initial opening stage. After the electromagnetic repulsion disappears, the greater the current of the driving coil of the permanent magnet operating mechanism in a certain range, the greater the speed when reaching the rated opening distance. Compared with the coil current and stroke curves obtained in the opening process of the actual prototype, they have good consistency, which provides a certain simulation method and theoretical reference for the optimal design of this kind of high current fast mechanical switch. Keywords: High current fast switch · Double spring permanent magnet operating mechanism · Electromagnetic repulsion mechanism · Optimization design
1 Introduction Hybrid DC circuit breaker is an important development direction of DC interruption technology at present [1, 2], which fully combines the advantages of low on-state loss of mechanical switch and fast interruption speed of power electronic switch [3]. As the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 249–260, 2022. https://doi.org/10.1007/978-981-19-1870-4_27
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medium voltage DC distribution network system moves towards the direction of highcapacity power transmission, the hybrid DC circuit breaker will carry more DC current, which means that, as the main current branch, the fast mechanical switch needs to pass more rated current in the steady state of the power grid. In case of power grid fault, the fast mechanical switch needs to transfer larger fault current and bear higher instantaneous recovery voltage. The characteristics of large current fast mechanical switch require that the pressure on contacts is very large when closing and the speed is very fast when opening. Because the contact opening distance of large current vacuum interrupter used in medium voltage distribution network is small and the mass of moving parts is large, it is very difficult to overcome strong resistance to accelerate and decelerate large mass moving parts in short stroke. In order to ensure that the high-current fast mechanical switch has enough contact pressure in the closing position, permanent magnet operating mechanism [4] is widely used at present. In the holding position, the suction of permanent magnet is large and stable, and the moving parts of permanent magnet operating mechanism are simple, the opening and closing current is small, and the requirements for operating power supply are relatively simple. However, under current technical conditions, the speed of permanent magnet operating mechanism can’t be rapidly increased at the initial stage of opening and closing process. In order to ensure that the opening speed is fast enough, the electromagnetic repulsion mechanism is widely used in fast mechanical switches [5–7]. Through the electromagnetic eddy current effect, a fast reverse magnetic field is generated between the discharge coil and the repulsion plate, and the electromagnetic repulsion force pushes the repulsion plate to move rapidly. The greater the rising gradient of the discharge coil current, the faster the repulsion force on the repulsion plate increases. Therefore, most of the mechanisms in the fast mechanical switches used in large-capacity medium-voltage hybrid DC circuit breakers are designed based on the common use of electromagnetic repulsion and permanent magnet operation [8, 9]. That is, permanent magnet operating mechanism is used for closing and keeping, and electromagnetic repulsion mechanism is used for quick opening. Obviously, the high-current fast mechanical switch based on the two mechanisms has a wide application prospect. However, due to the small opening distance of the contacts and the large mass of the moving parts, there is still a problem of unstable opening process in the field of medium voltage high current switch. In this paper, the opening process of fast mechanical switch based on double spring permanent magnet operation and electromagnetic repulsion mechanism is modeled and simulated by finite element method. By changing the cooperative action mode of the two mechanisms and the current of the driving coil of the permanent magnet operating mechanism, the multi-physical field coupling simulation calculation of electromagnetic, thermal and displacement is carried out for the opening process of the mechanical switch based on the double acting mechanism. The influence of the current change of driving coil in the permanent magnet operating mechanism on the opening process of the whole switch is analyzed, which provides theoretical support for the rational design of high current fast mechanical switch.
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2 Working Principle Figure 1 is a structural diagram of a high-current fast mechanical switch in the closing position based on the simultaneous action of a double-spring monostable permanent magnet operating mechanism and an electromagnetic repulsion mechanism. It mainly includes: 1-static contact, 2-moving contact, 3-connecting rod, 4-moving guide rod with boss, 5-opening spring, 6-contact spring, 7-permanent magnet, 8-static core, 9permanent magnet mechanism operating coil, 10-moving core, 11-moving core opening limit plate, 12-repulsion disk, 13-opening coil, 14-opening buffer coil. The moving contact, connecting rod, moving guide rod with boss and repulsion plate are the main moving parts as a whole. The opening spring and contact spring transmit the force to the moving parts through the moving guide rod with boss. When the two mechanisms move, the moving iron core moves as another independent part. Because the moving iron core has small mass relative to the main moving parts, Therefore, in the following calculation and analysis, the moving iron core is only subject to its own magnetic field force and changing contact spring force.
Fig. 1. Structure diagram of fast mechanical switch based on double acting mechanism
The control and driving principle of permanent magnet operation electromagnetic repulsion mechanism is shown in Fig. 2, mainly composed of the driving circuit of the permanent magnet operation mechanism and the electromagnetic repulsion mechanism. When the switch is in the closing position, the static and dynamic iron cores of the permanent magnet operating mechanism are sucked together, and the contact spring is compressed by the moving guide rod with the boss to give a certain pressure to the contact. When the switch is opened, the controller controls the IGBT in the driving circuit of the permanent magnet operating mechanism to turn on and off, so that the
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energy storage capacitor C0 discharges to the driving coil with a certain current, and the driving coil generates a continuous magnetic field opposite to the permanent magnet to counteract the permanent magnet force. At the same time, the controller controls the thyristor D11 to discharge the energy storage capacitor C to the opening coil, thereby generating a millisecond pulse current in the opening coil. Driving circuit of permanent magnet operating mechanism
IGBT
Fast mechanical switch controller
C11
Driving coil of permanent magnet mechanism
R0
C0
R1
D11
Opening coil
D12
D21 C12
R2
Opening buffer coil
D22
Driving circuit electromagnetic repulsion mechanism
Fig. 2. Schematic diagram of control principle of double acting mechanism
The pulse current produces a changing magnetic field around the coil, and an eddy current opposite to the coil current is induced inside the repulsion disk near the driving coil due to the existence of electromagnetic induction phenomenon, thereby generating electromagnetic repulsive force in the repulsive disk to push the moving parts to accelerate. Because the moving parts are too fast, it will damage the mechanism and cause the opening rebound phenomenon when reaching the limit. Therefore, when the repulsion disk moves to a certain distance, the controller controls the thyristor D21 to turn on, and the energy storage capacitor C12 discharges to the delay coil, which generates the opposite repulsion force in the repulsion disk, reduces the speed of moving parts and plays a necessary buffer role.
3 Multi-physical Field Simulation Analysis 3.1 Geometric Model According to the design requirements of the prototype mechanism, a simulation geometric model approximating 1:1 is established for calculation and analysis. Because the actual mechanism is symmetrical along the axis, the axisymmetric model is used for equivalent calculation in this paper, and the simulation geometric model is shown in Fig. 3. In order to approach the actual structure to the maximum extent, the setting of relevant parameters in the geometric model is consistent with the prototype structure, and the geometric dimensions and material properties of its core components are as follows:
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1) Permanent magnet operating mechanism: The inner diameter of the permanent magnet is 54 mm, the outer diameter is 63 mm, the height is 40 mm, and the material is NdFeB. The inner diameter of the operating coil is 47 mm, the outer diameter is 63 mm, the height is 40 mm, the wire diameter is 4 mm2 , the coil turns are 200, and the material is copper. The static iron core is 25 mm, the outer diameter is 75 mm, the height is 80 mm, and the material is soft iron. The moving iron core is 25 mm, the outer diameter is 75 mm, the height is 24 mm, and the material is soft iron. 2) Electromagnetic repulsion mechanism: The inner diameter of the opening and slowing coil is 25 mm, the outer diameter is 107 mm, the cross-sectional area of the coil is 1 mm × 7 mm, the number of turns of the coil is 55, and the material is copper. The repulsion disk has a radius of 90 mm, a thickness of 15 mm, and the material is aluminium.
Permanent magnet Static iron core Operating coil Moving iron core Permanent magnet operating mechanism Air domain
Opening coil Repulsive disk Opening buffer coil Electromagnetic repulsion mechanism
Fig. 3. Simulation geometric model of double acting mechanism
3.2 Simulation Mathematical Model 1) Electromagnetic field equation ∇ ×H =J
(1)
B=∇ ×A
(2)
J = σE
(3)
E=−
∂A ∂t
(4)
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B = μH
(5)
D = εE
(6)
In the equation: B is the magnetic flux density, H is the magnetic field strength, A is the magnetic vector potential, D is the potential shift, E is the electric field strength, σ is conductivity, μ is the permeability, ε is the dielectric constant. 2) Heat transfer equation ρCp
∂T − ∇ · k∇T = Q ∂t
(7)
1 σ |E|2 2
(8)
Q=
In the equation: ρ is density, Cp is specific heat at constant pressure, T is temperature, k is thermal conductivity and Q is induced heat source. 3) Equation of motion Because the moving guide rod of the double spring permanent magnet operating mechanism is different from the moving core in the moving process, the moving contact, connecting rod, moving guide rod with boss and repulsive disk are taken as the main moving parts for motion analysis, while the moving core is taken as another part for motion analysis, and the friction produced in the moving process is not considered in this paper. Fem0 +Fg +Ff −Fc −Fz ∂v s≥0 ∂t = m1 (9) Fem0 +Fg +Ff −Fem1 −Fz ∂v = s 0, β q > 0. f s = [f ds f qs ]T is the sliding mode control function. Subtracting formula (14) from formula (13), the error equation of the sliding mode observer is obtained as follows e˙ 1 = e2 − f s (15) e˙ 2 = f − βf s where e1 = [ed1 eq1 ]T , ed 1 = id − ˆid , eq1 = iq − ˆiq , e2 = [ed2 eq2 ]T , ed 2 = Fd − Fˆ d , eq2 = Fq − Fˆ q . In this paper, the sliding surface s = e1 is selected. In order to suppress sliding mode chattering, the exponential reaching law is adopted and the sign function is replaced by a saturation function [15], which can be expressed as follows s˙ = −ksat(s) − γ s sgn(s), |s| > Δ sat(s) = s Δ , |s| ≤ Δ
(16)
where k = diag(k d , k q ), k d > 0, k q > 0, γ = diag(γ d , γ q ), γ d > 0, γ q > 0, Δ = [d q ]T , d > 0, q > 0. Substituting Eq. (16) into (15), it can be obtained −ksat(e1 ) − γ e1 = e2 − f s
(17)
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If e2 is regarded as disturbance, the sliding mode function can be rewritten as f s = ksat(e1 ) + γ e1
(18)
The stability of the SMO is proved by Lyapunov theorem. The positive definite function V is selected and its derivative can be expressed as follows 1 1 1 2 V = sT s = ed2 1 + eq1 2 2 2 V˙ = eT1 e˙ 1 = eT1 (e2 − f s )
= eT1 e2 − ksat(e1 ) − γ e1
(19)
(20)
In order to ensure the stability of the SMO, the above equation needs to be less than or equal to zero, then we can get the condition that k needs to be satisfied as k ≥ |e2 | − γ |e1 |
(21)
Since the norms of e1 and e2 are bounded, the conditional formula (21) holds when taking k d = k q ≥ max(|e2 |) − γ min(|e1 |). Therefore, there must be a value of k that satisfies the Laypunov stability condition to ensure the stability of the designed SMO. By discretizing the designed SMO, the following results can be obtained ⎧ ⎨ ˆi(k + 1) = ˆi(k) + Ts F(k) ˆ + αu(k) + ksat(e1 (k)) + γ e1 (k) (22)
⎩ F(k ˆ + 1) = F(k) ˆ + Ts β ksat(e1 (k)) + γ e1 (k) Therefore, the current prediction model including the observed value of F can be described as ˆ + 1) + αu(k + 1) Ts ip (k + 2) = ip (k + 1) + F(k (23)
3.3 Model Free Predictive Current Control Based on SMO In order to reduce the calculation cost of predictive control, the expected voltage vector u* can be obtained by substituting ip (k + 2) = i* into Eq. (23) according to the principle of deadbeat current control, which can be described as u∗ =
ˆ + 1) i∗ − ip (k + 1) F(k − αTs α
(24)
The optimal voltage vector uopt can be selected by simply judging the sector where the desired voltage vector u* is located, as shown in Fig. 1. For example, when u* is in sector I, the active voltage vector u1 , which is closest to u* , is selected as the optimal voltage vector uopt . Therefore, in each control cycle, only one expected voltage vector calculation and sector judgment are required instead of traversing all voltage vectors
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Fig. 1. Space voltage vector
and repeatedly calculating the cost function to select the optimal voltage vector, which greatly reduces the calculation amount of predictive control. The duty cycle modulation is adopted to calculate the optimal voltage vector action time, and go , gopt and t opt can be obtained as go = Fˆ q (k + 1)
(25)
gopt = go + αq uq (k + 1)
(26)
iq∗ − iq (k + 1) − go Ts p
topt =
gopt − go
(27)
The SM-MFPCC system block diagram of PMSM is obtained, as shown in Fig. 2. Based on the measured dc-bus voltage, stator current and rotor speed, the unknown ˆ + 1) in the ultralocal current model is estimated by the SMO. Then the ip (k + 2) is F(k calculated by the model-free predictive controller with delay compensation. Afterwards, the optimal voltage vector uopt is selected, and its action time t opt is calculated according to formula (27). Finally, the switching signals sa , sb and sc generated by the synthesized voltage vector act on the inverter.
Fig. 2. Block diagram of SM-MFPCC system
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4 Simulation and Experimental Results In this section, to demonstrate the effectiveness of the proposed MFPCC approach, simulations and experiments of the conventional DM-MPCC method, the MFPCC method in [12], and the SM-MFPCC method in one PMSM system were carried out. Simulations are established in Simulink. The experiments platform is constructed by TI TMS320F28335 processor and the sampling frequency is 10 kHz. In addition, the experimental motor is ECMAC30604PS and its parameters are listed in Table 1. Table 1. Parameters of the PMSM Parameter
Value
Parameter
Value
Rated power
PN = 0.4 kW
Rated current
I N = 2.6 A
d- and q-axis inductances
L d = L q = 6.71 mH
Number of pole pairs
np = 5
Stator phase resistance
Rs = 1.55
Rotational inertia
J = 0.277 × 10–6 kg·m2
Flux linkage of PMs
ψ f = 0.047 Wb
Viscous friction coefficient
B=0
Since the resistance deviation has little impact on the predictive control performance, refer to [6], and it is ignored here. Only the influence of inductance and flux linkage changes on the system performance will be discussed below. Considering that the decrease of motor inductance caused by magnetic field saturation and the decrease of flux linkage amplitude during long-term operation of the motor, in addition, due to the fact that the actual parameters of the motor are not easy to change, the stator inductance and PM flux linkage amplitude in the control algorithm are manually adjusted and set to 1.4 times of their nominal value respectively for parameter perturbation experiment. The simulation curves of PMSM stator current and speed response are shown in Fig. 3. Here, when the motor runs stably with full load (1.27 N·m) at 2000 r/min, the stator inductance and flux linkage parameters are suddenly changed at 0.1 s, and the given speed is mutated to 500 r/min at 0.2. After that, the motor load is mutated to noload at 0.3 s, and finally the given speed is mutated to 2000 r/min at 0.4 s. The simulation currents of different methods are listed in Table 2. In Fig. 3, in the case of no parameter perturbation, the stator current fluctuations generated by the DM-MPPC and SM-MFPCC methods are almost the same when the motor is running at high speed and full load, while the current ripples generated by the MFPCC method are slightly larger. In the case of parameter perturbation, the stator current fluctuations generated by the three methods have all increased. Meanwhile, when the motor is running at low speed, the q-axis stator current fluctuation values of the DM-MPCC and SM-MFPCC methods both decrease slightly, while that of the MFPCC method increases. Simulation results show that the control performance of the proposed method is significantly better than the other two methods.
Sliding Mode Model-Free Predictive Current Control of PMSM 8
iq
iq
iq
id
id
id
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4 0
-4
n/(r·min -1)
-8 2500 2000 1500 1000 500 0 0
0.1 0.2 0.3 0.4 0.5 0 t/s
0.1 0.2 0.3 0.4 0.5 0 t/s
(a)DM-MPCC
(b)MFPCC
0.1 0.2 0.3 0.4 0.5 t/s
(c)SM-MFPCC
Fig. 3. Simulation waveform of stator current and speed with parameter perturbation
Table 2. The simulation currents of different methods Method
Variable
DM-MPCC
q-axis stator current 0.47 A iq
0.86 A
83.0%
d-axis stator current 0.59 A id
0.95 A
61.0%
q-axis stator current 0.65 A iq
0.76 A
16.9%
d-axis stator current 0.69 A id
0.81 A
17.4%
SM-MFPCC q-axis stator current 0.45 A iq
0.53 A
17.8%
d-axis stator current 0.63 A id
0.74 A
17.5%
MFPCC
No parameter change Parameter change Increased by
The feasibility of the method is further verified on the PTS-1000 power electronics experimental platform. The test waveform can be observed and recorded by GDS-2304A oscilloscope and virtual oscilloscope in PSIM software. The experimental results of the three control strategies are shown in Fig. 4, and the experimental currents are listed in Table 3. The experimental results are consistent with the simulation results under various operating conditions. Obviously, the proposed SM-MFPCC strategy can significantly reduce the prediction error when the motor parameters are mismatched, thereby reducing the stator current fluctuations and improving the robustness of the system parameters.
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iq
iq
id
id
id
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t/(5s/grid)
t/(5s/grid)
n/(500r·min -1/grid)
i/(4A/grid)
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(a)DM-MPCC
(b)MFPCC
(c)SM-MFPCC
Fig. 4. Dynamic response curve of stator current and speed with parameter perturbation
Table 3. The experimental currents of the three control strategies Method
Variable
DM-MPCC
q-axis stator current 0.57 A iq
1.34 A
135.1%
d-axis stator current 0.67 A id
1.75 A
161.2%
q-axis stator current 0.85 A iq
1.13 A
32.9%
d-axis stator current 0.78 A id
1.09 A
39.7%
SM-MFPCC q-axis stator current 0.55 A iq
0.76 A
38.2%
d-axis stator current 0.63 A id
0.86 A
36.5%
MFPCC
No parameter change Parameter change Increased by
5 Conclusion In order to solve the problem of the control performance degradation of the MPCC strategy for PMSM when the motor parameters are mismatched, a SM-MFPCC is proposed. The unknown in the ultralocal current model of PMSM is estimated by a sliding mode observer, which is used in the MFPCC with delay compensation to enhance the robustness of the system. Then the optimal voltage vector is directly selected based on the sector judgment of the expected voltage vector, and the duration of the voltage vector is calculated by using the deadbeat control principle. Thus, the computational complexity of predictive control and stable current ripple are reduced. Simulation and experimental results verify the effectiveness and feasibility of the proposed method.
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References 1. Petkar, S.G., Eshwar, K., Thippiripati, V.K.: A modified model predictive current control of permanent magnet synchronous motor drive. IEEE Trans. Industr. Electron. 68(2), 1025–1034 (2020) 2. Qin, Y., Yan, C.W., et al.: Three-vector model predictive current control strategy for permanent magnet synchronous motor drives with parameter error compensation. Trans. Chin. Electrotech. Soci. 35(2), 255–265 (2020). (in Chinese) 3. Liu, X., Zhou, L., Wang, J., et al.: Robust predictive current control of permanent-magnet synchronous motors with newly designed cost function. IEEE Trans. Power Electron. 35(10), 10778–10788 (2020) 4. Zhang, C., et al.: Robust fault-tolerant predictive current control for permanent magnet synchronous motors considering demagnetization fault. IEEE Trans. Industr. Electron. 65(7), 5324–5334 (2018) 5. Chen, Z.Y., Qiu, J.Q., Jin, M.J.: Adaptive finite-control-set model predictive current control for IPMSM drives with inductance variation. IET Electr. Power Appl. 11(5), 874–884 (2017) 6. Zhang, X., Zhao, Z., Cheng, Y., et al.: Robust model predictive current control based on inductance and flux linkage extraction algorithm. IEEE Trans. Veh. Technol. 69(12), 14893– 14902 (2020) 7. Zhang, X.G., Zhang, L., Zhang, Y.C.: Model predictive current control for PMSM drives with parameter robustness improvement. IEEE Trans. Power Electron. 34(2), 1645–1657 (2019) 8. Zhang, X.G., Hou, B.S., Mei, Y.: Deadbeat predictive current control of permanent-magnet synchronous motors with stator current and disturbance observer. IEEE Trans. Power Electron. 32(5), 3818–3834 (2017) 9. Siami, M., Khaburi, D.A., Abbaszadeh, A., et al.: Robustness improvement of predictive current control using prediction error correction for permanent magnet synchronous machines. IEEE Trans. Industr. Electron. 63(6), 3458–3466 (2016) 10. Lin, C., Liu, T., Yu, J., et al.: Model-free predictive current control for interior permanentmagnet synchronous motor drives based on current difference detection technique. IEEE Trans. Industr. Electron. 61(2), 667–681 (2014) 11. Fliess, M., Join, C.: Model-free control. Int. J. Control 86(12), 2228–2252 (2013) 12. Zhang, Y.C., Jin, J., Huang, L., et al.: Model-free predictive current control of PMSM drives based on ultra-local model. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–5 (2019) 13. Zhang, Y.C., Jin, J., Huang, L.: Model-free predictive current control of PMSM drives based on extended state observer using ultralocal model. IEEE Trans. Industr. Electron. 68(2), 993–1003 (2021) 14. Zhang, Y., et al.: Performance improvement of model-predictive current control of permanent magnet synchronous motor drives. IEEE Trans. Industr. Appl. 53(4), 3683–3695 (2017) 15. Lu, X., Lin, H., Feng, Y., et al.: Soft switching sliding mode observer for PMSM sensorless control. Trans. Chin. Electrotech. Soc. 30(2), 106–113 (2015). (in Chinese)
Design of High-Power Converter for Hydrogen Production Wenqiang Yang, Xiaowen Xing(B) , Xun Sun, and Sihan Wang National Institute of Clean-and-Low-Carbon Energy, Changping, Beijing 102211, China [email protected]
Abstract. Low voltage, high current, low ripple, and high efficiency of 1200 Nm3 /h are the requirements of electrolyzer, a high-power DC/DC converter based on 6 groups of IGBT modules in parallel and 8 branches interleaved output is designed, with a maximum output power of 5.74 mw (700V × 8200 A), efficiency more than 98%. The conduction time interval of 8 branches is T/8 in turn. The inductance current of each branch is superimposed with each other to make the output current ripple less than 1%. In addition, according to the multimode operation requirements of electrolyzer, a controller based on DSP + FPGA is designed including voltage/power droop control and output voltage stabilizing control. The porotype test results show that the design is effective and feasible, finally is applied for the 2022 Beijing Winter Olympic Games. Keywords: High power DC/DC hydrogen production converter · Voltage power droop · Voltage stabilizing control · Interleaved operation
1 Introduction As one of clean and efficient carbon-free energy, hydrogen energy is an important part of the development of clean energy and the construction of a low-carbon and efficient energy system. With the vigorous advancement of wind/light and other renewable energy, hydrogen production from renewable energy has attracted the attention of scholars, enterprises, institutions, and research institutes [1–4]. For connecting the high-power electrolyzers to renewable energy power generation systems, interface converters based on power electronic devices are particularly important. In view of that the electrolyzer is a DC device, the renewable energy hydrogen production project based on the DC architecture has natural advantages, so it is imperative to study DC high-power hydrogen production converters. The 1200 Nm3 /h electrolytic cell has the characteristics of low voltage, large current and small withstand voltage and current ripple. For matching the characteristics of the electrolytic cell, the multi-phase interleaved Buck converter has certain advantages [5–7]. But how to apply the interleaved parallel Buck converter into the MW-level system needs further study. During the start-up process of the electrolyzer, the equivalent impedance is large, and the thermal efficiency is high. A high-voltage stabilized start-up is required to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 824–833, 2022. https://doi.org/10.1007/978-981-19-1870-4_87
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shorten the start-up time and accelerate the hydrogen production process. However, the start-up of voltage stabilization is passive control and cannot quickly track the changes of renewable energy such as wind/light. Considering the fast response speed and high energy density of the electrolytic cell, it can be regarded as an energy storage device to smooth wind/light output power [8]. However, in the current research, hydrogen production equipment cannot actively track changes in wind/light output, and specific control strategies need to be studied. In addition, how to coordinate the start-up constant pressure control demand of the electrolyzer and the tracking control of the renewable energy fluctuation has not yet been discussed by scholars. In view of the above problems, this paper takes a 1200 Nm3 /h electrolytic cell as an example, studies an 8-phase interleaved Buck converter with 6 groups of IGBT modules in parallel, analyzes the superimposed inductor current ripple, and designs the inductance, input capacitance and output capacitance parameters. In terms of control, combining electrolytic cell and renewable energy power generation characteristics, with the main purpose of tracking renewable energy power generation and considering the startup demand of the electrolytic cell, a two-stage control algorithm is proposed, including constant voltage control and power voltage droop control. Cooperated with Longyuan Electric Co., Ltd. to produce the hydrogen production converter, and the factory test showed that the hydrogen production converter was feasible and effective.
2 Topological Structure and Parameter Design of High-Power Hydrogen Production Converter Considering the characteristics of the electrolyzer and the production cost, this article chooses the multi-phase interleaved Buck converter; the maximum power required by the 1200 Nm3 /h electrolyzer is 5.74 MW, the voltage operating range is from 584 V to 700 V, the input voltage is 1100 V ± 50 V, and the current range is from 1250 A to 8200 A; The IGBT module model is Infineon FF450R17ME4. The maximum junction temperature of the module is 150 °C. The normal operating temperature is 110 °C and the switching frequency is 2 kHz. In order to meet the above requirements, a Buck converter with 8-phase staggered 6 groups of IGBT modules in parallel is used as the hydrogen production power interface circuit. The specific structure is shown in the Fig. 1. According to the interleaved control principle, the superimposed inductor current of the 8-phase converter is presented below. 8uin (4 8 − d )(d − 3 8) d = 0.375 ∼ 0.5 iLeq = Lfs 8uin (5 8 − d )(d − 4 8) d = 5 ∼ 0.625 iLeq = Lfs 8uin (6 8 − d )(d − 5 8) d = 0.625 ∼ 0.75 iLeq = (1) Lfs In the formula, iLeq is the current ripple after the inductor current is superimposed, d is the duty cycle, Uin is the input voltage, L is the inductance, and fs is the switching frequency.
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Fig. 1. 8 interleaved buck converter
Considering the DC inductor loss, chassis volume and inductor manufacturing process, the inductance is appropriately reduced when the inductor current of a single branch is critically continuous. Here, the inductance is reduced to 260 µH, which meets the requirement that the total output voltage and current ripple are less than 1%. After calculation, under this inductance, the superimposed current ripple is 28.26 A, and the superimposed current ripple ratio is 2.26%. According to the literature [9], the output capacitance is presented below. Leq C > Sa(π D) =
4Sa(π d ) + δ0 (2π fs )2 δ0
sin(π D) |D=0.2 = 0.94 πD
(2) (3)
Is the voltage ripple ratio, here is 1%, Leq is the equivalent inductance of the 8-phase interleaved converter, and the calculated capacitance should be greater than 26.63 µF. The input capacitance is presented below [10]. Cin = io
d (1 − d ) Upp(max) fs
(4)
Among them, Upp (max) is the maximum voltage ripple. According to the bus ripple of 1%, the available Cin should be greater than 5.5 mF, and the input capacitance is configured to be 25.6 mF when the device is manufactured.
3 Two-Stage Control Algorithm for Hydrogen Generation Power Supply The electrolyzer is the core equipment in the renewable energy hydrogen production system. Its performance directly affects the hydrogen production efficiency of the entire hydrogen production system and cannot be ignored. As a bridge between the electrolyzer
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and renewable energy, the hydrogen generation power supply needs to fully consider the characteristics of the equipment on both sides. The hydrogen generation power supply adopts a two-stage control algorithm, which is intended to consider the characteristics of the electrolysis cell based on making full use of renewable energy. 3.1 The Process of Start Up—Constant Voltage Control Usually, the theoretical decomposition voltage of water is 1.23 V, which has nothing to do with the acidity and alkalinity of the electrolyte. In the actual electrolysis process, the decomposition voltage of water is about 1.7 V, which is the root cause of the actual electrolysis voltage higher than the theoretical decomposition voltage of water. It is necessary to overcome the resistance and overpotential in the electrolytic cell. Therefore, during the start-up phase of the electrolysis cell, the electrolysis voltage can be increased to achieve rapid hydrogen production and reduce the cold start time. Here, according to the maximum limit of the electrolysis voltage of the 1200 Nm3 /h electrolytic cell, the constant voltage control is set as the start-up operation control strategy of the electrolysis system, as shown in the Fig. 2. In the figure, Uo_ref represents the reference value of the output voltage, Uo represents the actual value of the output voltage. After comparison, it enters the PI controller to obtain the total current setting. After being divided equally, it operates as the current reference value control device for each branch, and each branch is turned on. The time difference is T/8. Uo_ref +
PI -
Uo
Iref_8 I ref _ 8
8
Iref +
PI
PWM
PI
PWM8
-
iL1
iL8
Fig. 2. Start up control of DC/DC converter
3.2 The Process of Operation—Tracking Renewable Energy Increasing the electrolysis voltage during the start-up phase will increase the hydrogen production of the electrolyzer, but the overpotential will increase with the increase of the current density and running in the high voltage constant voltage mode will cause a lot of unnecessary power loss. Moreover, as the water temperature increases, the theoretical decomposition voltage of water will decrease when the pressure is constant, so there is no need to always maintain the constant pressure mode as an operation control strategy. In addition, in this mode, system fluctuations of renewable energy due to changes in natural conditions will affect the safe and stable operation of the electrolyzer. Considering the high energy density of the electrolyzer and the fast response speed after startup, the hydrogen production system can be considered as energy storage to smooth the output power of renewable energy.
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In the DC system, the bus voltage is an important indicator to measure power fluctuations, and the stabilized DC bus voltage can be considered as the main target. Under the conditions of considering the internal resistance of the DC bus and sampling accuracy, set an appropriate DC bus voltage as the equipment operating threshold, and integrate the maximum and minimum power (Pmax_L , Pmin_L ) of the electrolytic cell operation to obtain the output characteristic curve of the hydrogen generation power supply, as shown in the Fig. 3. In the Fig. 3, the voltage/power droop control is introduced here. Avoiding the occurrence of no hydrogen production in the electrolytic cell, the droop control is modified, see Eq. (5). Uin ref = UL1 + k(Phyd − Pmin _L )
(5)
U/V UH2 UH1 Urated UL1 UL2
Pmax_L
Pmin_L
P/W
Fig. 3. The feature of hydrogen DC/DC converter
In Eq. (5), Uinref is the bus voltage set, UL1 is the equipment operating threshold, k is the droop coefficient, and Phyd is the operating power set. According to the operating requirements of the electrolyzer and Eq. (5), the control strategy in the operating phase is shown in the Fig. 4. In the figure, Udc is the bus voltage. After droop calculation, the power and current settings are obtained. After the current settings are evenly divided, the reference value is provided to each branch. Similarly, the constant voltage control, the conduction time of each branch power device is sequentially different by T/8. Udc UL1
Uinref=UL1+k(PhydPmin) Iref_8=Phyd/Uo
I ref _ 8
Iref + 8
-
PI
PWM1
PI
PWM8
iL1 iL8
Fig. 4. Operation control of DC/DC converter
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After the electrolyzer is fully started, the PLC controller of the electrolyzer will transmit the start-up completion instruction to the hydrogen generation power controller. The hydrogen generation power control will switch the system from constant voltage control to droop control. A ramp function is introduced to slow down the instantaneous change rate of the current in order to avoid fluctuations caused by the switching moment.
4 Experimental Verification The equipment prototype was designed by Beijing Low-Carbon Clean Energy Research Institute and produced by the United Nations Electric Longyuan Electric Co., Ltd. The equipment prototype is shown in the Fig. 5, and the controller adopts DSP + FPAG. Ensuring the normal operation of the hydrogen generation power supply and meeting the factory requirements of the equipment, the prototype testing of the equipment has been completed, including the protection test of the equipment, sampling verification, operation function test, output ripple, efficiency and temperature rise test. This experiment mainly focuses on the operating function, output ripple and efficiency of the equipment.
Fig. 5. 5.74MW DC/DC converter porotype
4.1 Operation Tests 4.1.1 Constant Voltage Start Mode Figure 6 shows the constant voltage start function waveform. According to the power supply and load situation in the Longyuan Electric factory, the power supply is an uncontrolled rectifier output, the voltage is 580 V, and the load is two sets of 0.9 /100 kW resistors in parallel. Connect to the background and set a starting voltage of 150 V. It can be seen from the figure that after the controller receives the start command, the hydrogen generation power supply starts to work, the output test voltage is stabilized to 149 V, and the output current is 83.3 A. The equipment can be started according to the given voltage to meet the function of starting the electrolyzer.
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Fig. 6. Constant voltage start (yellow: the current of load; blue: input voltage; red: output voltage)
4.1.2 Voltage/Power Droop Control Tests When the voltage/sag control strategy is adopted, the input side needs to be equivalent to a DC current source, so that the electrolyzer can participate in the stable power fluctuation of renewable energy. In view of the plant power, experimental platform and load limitations, the voltage/power droop control is tested in the drag mode here. Four groups of the original 8-phase Buck converters operate in Buck mode and four groups operate in Boost mode. Buck mode uses a given power control and operates in a current source mode, and Boost mode uses voltage/power droop control to stabilize Buck output voltage. In addition, the use of the towing experiment strategy can also achieve full current operation of the equipment, and further complete the temperature rise test of the core device. Figure 7 shows the operating waveform of the hydrogen-producing power source under the control of voltage/power droop. The given Buck power command is 180 kW, the Boost threshold voltage is set to 330 V, and the anti-sag coefficient is −
Fig. 7. Operation curve of electrolyzer under volage/power droop control (purple: buck current; blue: boost current; green: input voltage; yellow: output voltage)
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10000. It can be seen from the figure that the buck output voltage is stabilized to 338 V, the Buck inductor current is equal to the Boost inductor current, and the internal power of the system is balanced. It can be seen the voltage/power droop control can stabilize the input side voltage. The periodic oscillation of the inductor current in the figure is caused by the uncontrolled rectification 6 pulse wave, which has been optimized in the subsequent measurement by introducing a compensation algorithm. 4.2 Analysis of Output Ripple and Efficiency of Hydrogen Production Power Supply Under the full-current operation of the hydrogen production power supply, the 4-phase interleaved inductor current ripple is analyzed and converted to the 8-phase inductor current ripple to further calculate whether the equipment parameters meet the requirements of the electrolytic cell for voltage/current ripple. Figure 8 and Fig. 9 show the Buck output voltage and current waveforms in 4-phase interleaved operation mode. It can be seen from the Fig. 8 that the average value of the output voltage in one cycle is 599.13 V, the output voltage fluctuates around 9 V, and the output ripple is about 1.5%. It can be seen from Fig. 9 that the peak-to-peak value of the inductor current is 420 A. According to the 4-phase interleaved inductor current superposition calculation formula, the output current ripple is about 6.9% under full current operation.
Fig. 8. Output voltage in one cycle
Fig. 9. Inductor current in one cycle
From the above analysis, it can be seen from Fig. 8 and Fig. 9 that the 4-phase staggered operation cannot meet the operating requirements of the electrolytic cell under
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the current parameter conditions. However, the device normally operates in 8-phase interleaved mode, so it is necessary to convert the same voltage and current data to 8-phase interleaved mode for recalculation. According to formula (1) and the general voltage ripple calculation formula of Buc circuit, the output current and voltage ripple of the hydrogen generation power supply at full current are 0.059% and 0.29%, respectively, which are both less than 1%, which meets the needs of the electrolytic cell. In addition, this test loss also includes hydrogen production power control power loss, water cooling system loss, and uncontrolled rectification platform loss. After actual measurement, the factory AC power supply voltage is 400 V, current is 84 A, and the total loss is 58.2 kW, and the total operating efficiency is 98.8%.
5 Conclusion Aiming at the demand for hydrogen production in a 1200 Nm3 /h electrolyzer, a Buck converter with 8-phase staggered 6 groups of IGBT modules in parallel was studied. According to the interleaved control principle, the output current ripple of the 8-phase interleaved converter is analyzed, and the inductor, output capacitor and input capacitor are designed according to the requirements of the ripple. After fully considering the start-up demand of the electrolyzer and the natural characteristics of the renewable energy power generation system, a two-stage operation control is proposed: constant voltage start & voltage/power droop operation. For shorting the start-up process of the electrolyzer, the high-voltage constant-voltage startup mode is adopted to control the process of electrolyzer start up; after the hydrogen production of the electrolyzer reaches the target value, it switches to the power droop control operation, which can be tracked based on reducing energy consumption. The output of renewable energy fluctuates to stabilize the input side voltage. The equipment prototype was assembled and tested in the Baoding factory of Longyuan Electric Co., Ltd. Based on the 8-phase staggered parallel platform and the 4-phase staggered towing test platform, the equipment operation functions and indicators are verified and analyzed. The results show that the designed hydrogen production power control strategy and system parameters meet the needs of the electrolytic cell and can be applied into 2022 Beijing Winter Olympics. Acknowledgement. This work is supported by the National key R&D plan (2018YFB1503100).
References 1. Zhang, J.: Prospect of hydrogen energy industry development hydrogen production and hydrogen storage & transportation. Chem. Eng. Des. 029(004), 3–6 (2019) 2. Teng, Y., Wang, Z., Li, Y., Ma, Q., Hui, Q., Li, S., et al.: Multi-energy storage system model based on electricity heat and hydrogen coordinated optimization for power grid flexibility. CSEE J. Power Energy Syst. 5(2), 266–274 (2019) 3. Lin, Y.: Research on Coordinated Control of Hydrogen Light Storage Combined Power Generation System. University of Electronic Science and Technology (2014)
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4. Liu, L., Li, L., Ding, M., et al.: Design and application of photovoltaic and energy storage microgrid for the park. Power Syst. Prot. Control 48(3), 171–179 (2020) 5. Khosroshahi, A., Abapour, M., Sabahi, M.: Reliability evaluation of conventional and interleaved DC–DC boost converters. IEEE Trans. Power Electron. 30(10), 5821–5828 (2015) 6. Dong, C., Lei, W., Junjun, Z.: Research of staggered parallel magnetic DC-DC converters based on improved average current control. Power Syst. Prot. Control 44(24), 58–65 (2016) 7. Chen, Y.-M., Tseng, S.-Y., Tsai, C.-T., Wu, T.-F.: Interleaved buck converters with a singlecapacitor turn-off snubber. IEEE Trans. Aerosp. Electron. Syst. 40(3), 954–967 (2004) 8. Pan, Y., Li, Q., Chen, W.: Energy management for islanded DC microgrid with hybrid electrichydrogen energy storage system based on minimum utilization cost and energy storage state balance. Power Syst. Technol. 43(03), 918–927 (2019) 9. Chong, L.W., Wong, Y.W., Rajkumar, R.K., Rajkumar, R.K., Isa, D.: Hybrid energy storage systems and control strategies for stand-alone renewable energy power systems. Renew. Sustain. Energy Rev. 66, 174–189 (2016) 10. AVENT Electronics Marketing. Input Capacitor Considerations for Buck DC Switching Power Supplies
Insights into the Fungicidal Activity of Low-Temperature Plasma Against the Pathogen of Navel Orange Fruit Mildew Ying Sun1 , Yu Xiang Wang2 , Yu Xu1 , Hai Lun Lu1 , Ya Li Sang1 , Jin Ping Li1 , Rui Xu1 , Qing Wang1 , Yuan Yuan Li2 , Xing Quan Wang2(B) , and Zhi Qiang Gao1(B) 1 College of Life Sciences, Gannan Normal University, Ganzhou 341000, China
[email protected]
2 School of Physics and Electronic Information, Gannan Normal University,
Ganzhou 341000, China [email protected]
Abstract. Citrus mildew can lead to significant economic losses for both farmers and fruit processing companies. Compared with conventional cold storage and chemical preservation techniques, little is known about using low-temperature plasma technology to preserve navel oranges. In this study, Gannan navel oranges were studied, while pathogenic mold spores were collected from moldy Newhall oranges. The pathogenic spores were treated with argon, helium, and oxygen for 10 min and 20 min. Trypan blue staining demonstrated that only the low-temperature plasma produced by oxygen ionization effectively killed the pathogenic spores, while the spore death rate after 4 min and 2 min of treatment was nearly 100% and the spore death rate after 1 min treatment was 80.5 ± 5.5%. The mildew activity of pathogenic spores was significantly inhibited across several treatment times. There was no difference in phenotype and quality between the treated fruit and the control. Our experimental results demonstrate that low-temperature plasma with oxygen can be used to preserve navel oranges, kill mildew, significantly reduce the fruit mildewing probability during storage, and avoid significant economic losses. Keywords: Newhall · Pathogenic spores · Low-temperature plasma · Green preservation
1 Introduction In recent years, the consumption of fruits and vegetables, which are rich in healthy nutrients, has increased. China currently has the largest planting area and overall production of fruits and vegetables in the world. However, the post-harvest loss of fruits and vegetables is ~30% and is only ~5% in developed countries. China’s annual post-harvest loss of fruits Y. Sun, Y. X. Wang and Y. Xu—Co-first authors. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 834–843, 2022. https://doi.org/10.1007/978-981-19-1870-4_88
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and vegetables is approximately 100 million tons, and causing ~100 billion economic losses. The loss of fruits and vegetables is primarily caused by improper harvesting, rudimentary post-harvest preservation technology, and inadequate storage conditions. Presently, low-temperature storage and chemical antibacterial agents are mainly used to preserve fruits and vegetables. Low-temperature storage modifies the atmosphere of the storage room by changing the gas composition. This method is durable, has low loss rates, and is safe, making it the primary method of storing fruits and vegetables in developed countries. As such, researching the biological effects of physical technology will aid a green preservation technology with no residue, high sterilization efficiency, and no side effects. Plasma is a mixture of ionized gas molecules that are commonly recognized as matter’s “fourth state”. The temperature of ionized heavy particles is very low, meaning this mixture is in a low-temperature state. This is known as low-temperature plasma or non-equilibrium plasma. Ionized gas contains active particles such as ions, electrons, excited atoms, molecules, and free radicals, and low-temperature plasma technology has been used in material preparation and surface modification [1–3], chemical catalysis [4], toxic chemical removal [5–8], chemical analysis and detection [9, 10], biomedicine [11–13], and seed germination and growth [14–16]. Low-temperature plasma can also be used for non-thermophysical sterilization, due to its high sterilization efficiency, short action time, environmental benefits, and lack of pollution. It has been used to research the preservation of fruits, vegetables, and meat [17–20]. Citrus planting has become the largest fruit industry in China, and citrus consumption accounts for approximately 16% of China’s total fruit production and 27.4% of the world’s total citrus production. The cultivation of Gannan navel oranges is a highquality industry located in southern Jiangxi province. It involves large-scale planting and production, giving rise to problems associated with fruit mildew and decay during the low-temperature and chemical preservation of navel oranges. This study primarily explores how low-temperature plasma technology affects the preservation of navel oranges and found that the low-temperature plasma produced by oxygen ionization can kill the pathogenic spores of fruit mildew in a few minutes. We observed significant reductions in the mildewing activity of pathogenic spores on inoculated fruit, and the low-temperature plasma did not affect the appearance or quality of the fruit. This indicates that citrus harvesting and processing enterprises can use low-temperature plasma technology to preserve citrus fruits during their cleaning, sorting, and storage processes.
2 Materials and Methods 2.1 Generation of Low-Temperature Plasma A high-frequency power supply (CTP-2000K) was used to generate low-temperature plasma. Its frequency stabilized at 8.87 kHz, and the input voltage was adjusted at 50 V. An axial flow discharge device was used, which had a total length of 20 cm. The upper end was sealed, the side end was an air inlet, and the plasma was collected at the tail end (Fig. 1). Figure 1A displays the schematic diagram and Fig. 1B displays the physical diagram. The discharge mode was set to dielectric barrier discharge (DBD). The periphery of the copper rod electrode (outer diameter 5.8 mm) was wrapped by a quartz
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tube (outer diameter 38 mm) to serve as a barrier medium, and the discharge gap was 5 mm wide. Helium, argon, and oxygen were used as gasses, and the inlet flow rate was 1 L/min. The discharge parameters were primarily measured using a digital oscilloscope (Tektronix TDS2012), which includes two channels. One channel was connected with a 1:1000 AC voltage probe (Tektronix P6015A) and was used to measure discharge voltage, while the second channel was connected to an AC current probe (Tektronix P6021) and was used to measure the real-time status of the output current.
Fig. 1. The low-temperature plasma generator
2.2 Collection of Pathogenic Spores of Fruit Mildew and Microscopic Observation Moldy Citrus sinensis Osbeck Newhall oranges, was stored under cold conditions at 4 °C. The moldy pathogen spore powder on the fruit surface was collected and transferred into a sterilized 200 mL reagent bottle. 1.0 g of spore powder was then weighed on the analytical balance, 400 mL sterile water was stirred in, and the suspension mixture was filtered into a 50 mL centrifuge tube with gauze. 10 µL of the spore suspension was drawn onto a blood cell counting plate, where the morphology and quantity of pathogenic spores were observed with a microscope (Leica DM4 B). This prepared pathogen spore suspension was used in subsequent experiments analyzing low-temperature plasma treatments. 2.3 Low-Temperature Plasma Treatment and Pathogenic Spore Staining The low-temperature plasma produced by the ionization of argon, helium, and oxygen was introduced into the pathogenic spore suspension from the tail outlet. The lowtemperature plasma produced by the different gasses were treated at 1 min, 2 min, 4 min, 10 min, and 20 min. 1mL of the treated pathogen spore suspension was added to a 1.5 mL centrifuge tube, and 2 drops of 0.4% trypan blue staining solution were added. After staining for 2 min, 10 µL was placed on the blood cell counting plate, after which the morphology and staining color of the pathogenic spores were observed using a microscope (Leica DM4 B). The dead cells were dyed blue using a trypan blue staining solution, while the living cells were not stained.
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2.4 Identification of Mildewing Activity of Pathogenic Spores The pathogen spore suspension was treated with low-temperature plasma, which was generated by oxygen ionization, for 1 min, 2 min, and 4 min. The fruit was then inoculated with this solution, on its surface, using an in vivo drilling method. The untreated pathogen spore suspension and sterile water were used as positive and negative controls, respectively. The mildewing phenotype of the treated and untreated pathogenic spores and sterile water was observed after 3 days of inoculation at room temperature (28 °C). 2.5 Determination of Fruit Quality Citrus sinensis Osbeck Newhall was treated with a low-temperature plasma produced by oxygen ionization. Six fruits were selected from the treated and untreated groups to determine their quality. The peel brightness value, L, and the color indexes, a and b, were measured using a color difference instrument (Lovibond RT500). The six fruits were then juiced, while the TSS (Total soluble solids) in the fruits was determined by ATAGO PAL-1 digital display refractometer and the TA (Titratable acids) was determined by an ATAGO PAL-Easy ACID1 citrus acidity tester. Three replicates were performed for each experiment.
3 Results 3.1 Lethal Effect of Low-Temperature Plasma Produced by Different Gases on Pathogenic Spores of Navel Orange Mildew The production of Gannan navel oranges is a high-quality industry based in the south of Jiangxi province. As the planting area of Gannan navel oranges expands, mildew and decay during the storage process becomes an issue (Fig. 2A, B), particularly when the oranges are subjected to extreme weather and there is a surplus of oranges after harvest. This makes timely harvesting and the proper storage of navel oranges particularly important. As such, we selected mildewed Newhall oranges that were stored at 4 °C (Fig. 2C), collected the mildewed pathogen spore powder from the fruit surface, suspended it in sterile water, and filtered it into a spore suspension with gauze. The morphology of the pathogen spores on the navel oranges can be observed with a blood cell counting plate and a microscope (Leica DM4 B), where its cell wall structure can be seen (Fig. 2D). The pathogen spore suspension was treated with low-temperature plasma produced by the ionization of argon (Ar), helium (He), and oxygen (O2 ) for 10 min and 20 min, after which the pathogen spore suspension was identified using a trypan blue staining solution. The low-temperature plasma produced by the ionization of argon and helium was not lethal to pathogenic spores. The cell wall of the pathogenic spores was wathet blue, but the interior of pathogenic spore cells was colorless (Fig. 3A–D). The lowtemperature plasma produced by oxygen ionization killed all pathogenic spores, while the interior of the pathogenic spore cells was dyed blue with a trypan blue staining solution (Fig. 3E, F).
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Fig. 2. Bagged storage of navel orange (A), moldy fruit (B, C), and pathogen spore morphology (D, 200x)
We further explored the fungicidal effect of low-temperature plasma produced by oxygen ionization by shortening the treatment time to 1 min, 2 min, and 4 min. During these treatments, the lethal effect of low-temperature plasma produced by oxygen ionization on pathogenic spores became apparent (Fig. 4). The spore lethal rate of 4 min (Fig. 4D, H) and 2 min (Fig. 4C, G) treatments approached 100%, while the spore lethal efficiency of the 1 min treatment was 80.5 ± 5.5% (Fig. 4B, F). Figure 4A and E display untreated controls. Our results demonstrate that the low-temperature plasma produced by oxygen ionization can be used to green preservation of navel oranges. 3.2 Low-Temperature Plasma Inhibits Activity of Pathogenic Spores of Fruit Mildew Pathogenic spores can be effectively killed by low-temperature plasma in vitro, though further research is needed to identify the in vivo effect that reduces the mildewing activity of pathogenic spores in navel oranges. The mildewing phenotype of pathogenic spores at the Newhall orange inoculation sites was less than the control 3 days after it was inoculated with a pathogenic spore suspension by low-temperature plasma treatment (Fig. 5). The first row of holes was inoculated with sterile water (negative control) and had no mildewing phenotype. The second row was inoculated with untreated pathogenic spores (positive control), and mold circles quickly grew 3 days after inoculation. The third row was inoculated with the spore suspension after 1 min, 2 min, or 4 min of lowtemperature plasma treatment. We found that the mildewing activity of pathogenic spores was inhibited after 1 min of low-temperature plasma treatment, and that longer treatments more effectively inhibited the mildewing activity of pathogenic spores (Fig. 5B).
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Fig. 3. Lethal effect of low-temperature plasma produced by argon (Ar), helium (He), and oxygen (O2 ) on pathogenic spores
Fig. 4. Lethal effect of low-temperature plasma produced by oxygen ionization on pathogenic spores with different treatment times. Figure 4 A and E were untreated controls. Figure 4B, F was 1 min treatment. Figure 4C, G was 2 min treatment. Figure 4D, H was 4 min treatment.
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Fig. 5. Fruit mildew phenotype of pathogenic spores treated by low-temperature plasma produced by oxygen ionization
3.3 Physical Characteristics of Low-Temperature Plasma Produced by Oxygen Ionization The biological effects of low-temperature plasma are due to an abundance of active particles, including ions, electrons, excited atoms and molecules, and free radicals. The preservation and sterilization effect of low-temperature plasma is primarily due to differences in superoxide ion components produced by the ionization of different gases. Optical Emission Spectra (Taiwan Ultramicro Optics Co., Ltd, SE2030-025-FUV2A) was used to identify the primary effective components of low-temperature plasma produced by oxygen ionization. The emission spectra are concentrated at 282 nm, 309 nm, and 738 nm, which represent ·OH and excited Oxygen atoms. Therefore, the superoxide ion component contributes to the fungicidal effect of low-temperature plasma.
Fig. 6. Spectrum and intensity diagram of low-temperature plasma produced by oxygen ionization
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4 Conclusion and Discussion This study explores how low-temperature plasma technology can be used to preserve navel oranges. Our results demonstrated that the low-temperature plasma produced by oxygen ionization can quickly and effectively kill the pathogenic spores of mildew on navel oranges (1 min–4 min) Our follow-up study found that after one month of lowtemperature plasma treatment, there was no significant difference in the appearance phenotype and internal quality (total soluble solids and titratable acid) of untreated and treated navel oranges (Table 1). This indicates that this technology has no side effects on either fruit appearance or quality. Table 1. Phenotype and quality of navel oranges before and after low-temperature plasma treatment Sample type
L*
a*
b*
Total soluble solids
Titratable acid
Before treatment
61.22 ± 2.00
37.43 ± 2.01
57.43 ± 3.28
11.58 ± 1.33
0.72 ± 0.05
Untreated
61.85 ± 2.09
37.27 ± 2.11
61.77 ± 3.32
11.75 ± 0.70
0.67 ± 0.07
After treatment
62.56 ± 2.57
36.37 ± 2.54
62.22 ± 4.99
11.13 ± 0.83
0.63 ± 0.09
Previous studies have also reported that low-temperature plasma technology has no side effects and can improve food quality. For example, there is no significant difference in surface color and internal anthocyanin content between grapes treated with lowtemperature plasma and the control [21]. Low-temperature plasma can improve the eating quality of brown rice [22], improve the storage quality of fresh-cut broccoli [18], maintain the vitamin C content of strawberries [20], and maintain the color of beef and fish [19–23]. As such, low-temperature plasma technology is a safe method of preserving food that maintains quality. The active components of low-temperature plasma exhibit a fungicidal effect [24], a biological effect that primarily depends on the superoxide components produced by gas ionization [21–25]. The lethal effects of low-temperature plasma produced by air ionization on Escherichia coli are due to changes in cell membrane permeability caused by the electric field of charged particles on the surface of bacteria. This results in cytoplasmic overflow and cell death. Moreover, the low-temperature plasma produced by argon and nitrogen has no fungicidal effect on Escherichia coli, which is consistent with the results of this study. The lethal effect of low-temperature plasma produced by oxygen ionization is closely related to ·OH and excited oxygen atoms (Fig. 6). Therefore, improving the yield of specific functional components is needed to advance green preservation technologies. For example, the combination of low-temperature plasma technology and catalytic technology can accelerate the reaction rate and improve the selectivity and energy utilization of the products [26]. The effects of factors associated with functional components, including the discharge electrode area, peak, and peak discharge voltage,
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gas type, and volume flow rate, also require further study [27], as does changing the ionization mode and materials to produce low-temperature plasma in mild environments [28]. Therefore, research on the biological effects and mechanism of low-temperature plasma and improvements in related physical materials and equipment will increase the future use of low-temperature plasma technology in agriculture. Acknowledgments. We would like to thank the undergraduate students enrolled in the horticulture 2002 class in Gannan Normal University, who helped with fruit cleaning, selection, and storage, but are not credited as authors. This research was funded by the Major Science and Technology R& D Program of Jiangxi Province (20194ABC28007), the Talent Introduction and Scientific Research Program of Gannan Normal University (414738), and the Science and Technology Project of Jiangxi Provincial Department of Education (GJJ201414).
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14. Volkov, A.G., Xu, K.G., Kolobov, V.I.: Cold plasma interactions with plants: morphing and movements of Venus flytrap and Mimosa pudica induced by argon plasma jet. Bioelectrochemistry 118, 100–105 (2017) 15. de Groot, G.J.J.B., Hundt, A., Murphy, A.B., Bange, M.P., Mai-Prochnow, A.: Cold plasma treatment for cotton seed germination improvement. Sci. Rep. 8(1), 14372 (2018) 16. Bafoil, M., Le Ru, A., Merbahi, N., Eichwald, O., Dunand, C., Yousfi, M.: New insights of low-temperature plasma effects on germination of three genotypes of Arabidopsis thaliana seeds under osmotic and saline stresses. Sci. Rep. 9(1), 8649 (2019) 17. Xu, H.Q., Yan, J.H., Tang, L.L., Deng, S.G., Miu, W.H.: Effect of cold atmospheric plasma on quality maintenance of Penaeus vannamei during cold storage. Mod. Food Sci. Technol. 37(4), 116–123, 138 (2021). (in Chinese) 18. Zhang, Y., Zhang, Z.W., Cheng, C.X., Zhang, X.F., Yang, S.L.: Storage quality improvement of fresh-cut Broccoli by cold plasma treatment. Mod. Food Sci. Technol. 37(2), 164–170 (2021). (in Chinese) 19. Qiao, W.W., Huang, M.M., Wang, J.M., Yan, W.J., Zhang, J.H., Yang, L.P.: Effect of cold plasma on sterilization and color of fresh beef. Food Sci. 38(23), 237–242 (2017). (in Chinese) 20. Ren, C.R., Liu, J.G., Wang, S.Q., Jiang, W.L., Peng, J.X.: Effect of strawberry preservation by atomospheric pressure low temperature plasma. J. Qingdao Agric. Univ. (Nat. Sci.) 34(3), 228–234 (2017). (in Chinese) 21. Jian, G.: Study on Sterilization Mechanism of Low Temperature Plasma and Sterilization of Active Water. Zhejiang University, Hangzhou (2016) 22. Meng, N., et al.: Effect of low-temperature plasma current intensity on the edible quality of brown rice. Food Res. Dev. 42(7), 20–27 (2021). (in Chinese) 23. Wang, J.M., Peng, F., Fu, T.F.: Effect of different cold plasma treatment conditions on quality of Trachinotus ovatus. Food Ind. 41(9), 30–34 (2020). (in Chinese) 24. Ambrico, P.F., et al.: Surface dielectric barrier discharge plasma: a suitable measure against fungal plant pathogens. Sci. Rep. 10(1), 3673 (2020) 25. Xu, Z., et al.: In vitro antimicrobial effects and mechanisms of direct current air-liquid discharge plasma on planktonic Staphylococcus aureus and Escherichia coli in liquids. Bioelectrochemistry 121, 125–134 (2018) 26. Wang, T., Chen, S., Wang, H.Q., Liu, Z., Wu, Z.B.: In-plasma catalytic degradation of toluene over different MnO2 polymorphs and study of reaction mechanism. Chin. J. Catal. 38(5), 793–804 (2017). (in Chinese) 27. Li, X.H., et al.: Comparative analysis on characteristics in non-thermal plasma reactor with oxygen and air. Trans. Chin. Soc. Agric. Eng. 32(11), 103–108 (2016). (in Chinese) 28. Gharib, M., Mendoza, S., Rosenfeld, M., Beizai, M., Alves Pereira, F.J.: Toroidal plasmoid generation via extreme hydrodynamic shear. Proc. Natl. Acad. Sci. U.S.A. 114(48), 12657– 12662 (2017)
Research on Smart Collaborative Optimal Control Technology of Distributed Safety and Stability Control System Ke Feng, Wang Wang(B) , Xiong Chen, Shiguang Xu, Weidong Xu, and Kaiyang Zhu NARI Group Corporation/State Grid Electric Power Research Institute, Nanjing 210003, China [email protected]
Abstract. With the gradual development of a high-proportion new energy power system to a new energy power supply as the main power system, the system’s security and stability characteristics and control behavior have gradually undergone substantial changes. In this paper, firstly, by incorporating smart electrical equipment such as wind power, photovoltaic, energy storage, and DC into the technical requirements of emergency control, the emergency control evaluation indicators are quantitatively analyzed, and the emergency control technical indicators of new energy stations are proposed based on the existing project implementation basis. Further, based on the existing security and stability control system architecture for upgrading and transformation, a distributed security and stability control system intelligent collaborative optimization control scheme is proposed, and the applicable conditions, overall architecture, information command flow and intelligent collaborative control strategy are elaborated in detail. Finally, based on the actual power grid, simulations verify the effectiveness of the proposed control architecture and control method. Keywords: Safety and stability control · New energy · Optimization · Smart collaboration
1 Introduction In order to achieve the grand goal of “carbon neutrality” and “carbon peak”, new energy development will continue to maintain rapid momentum. It is expected that in 2035, the proportion of non-fossil energy in primary energy consumption in China will reach 47%, and the proportion of new energy installations will reach 61%, becoming the main power source. This will make the power system security and stability characteristics and control behavior gradually substantial changes. Intelligent equipment, such as new energy and DC, has much lower voltage and frequency endurance than traditional generators. Fault disturbance forms and processes are complex and diverse. Cross-area DC transmission This work was supported by Science and Technology Project of SGCC (No. 5100-201928005A0-0-00). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 844–858, 2022. https://doi.org/10.1007/978-981-19-1870-4_89
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leads to wide-area transmission of system faults, which brings great difficulties to power system stability defense. Safety and stability control technology plays an important role in protecting the safe and stable operation of power system by formulating clear control strategies and realizing emergency control according to specific operation modes and fault patterns [5]. However, the traditional safety and stability control device mainly relies on the emergency cutting machine and load shedding after the accident, which not only has high control cost, but also is easy to cause negative control effect and the risk of cascading failure [6]. Power smart electrical equipment such as new energy, energy storage and DC (hereinafter referred to as smart electrical equipment) has strong plasticity, which provides new flexible control resources for power system stability control and brings new ideas to security and stability control. In recent years, many experts and scholars at home and abroad have carried out a lot of research work. In [8], proposed the fast power control technology of photovoltaic participating in the emergency control system. However, since the wind power needs to consider the load stability and the response speed is slower than that of photovoltaic, the emergency control of wind power is not involved. In [9, 10], analyzed the influence of wind turbine and thermal power unit removal on transient voltage and power angle stability of the system after system failure, and proposes an emergency cutting machine solving algorithm, which can improve the stability of the sending-end system and reduce the cutting amount required to maintain the power angle stability of the system. In [11, 12], compared and analyzed the emergency support power results of different types of DC power, pointed out that flexible DC could improve the transient stability of power grid and reduce the load shedding cost, and proposed the DC emergency support method. In [13–16], proposed the application of energy storage to improve the steady-state transmission capacity of UHV AC/DC lines after faults and to improve the level of new energy power generation as the backup energy of the sending end grid. Taking Xinjiang power grid as an example, the effectiveness of the proposed scheme was verified. The above studies have proved the feasibility of smart electrical equipment to participate in emergency control, which can be used as a control resource for safety and stability control system. However, the above research is basically qualitative research, lacking quantitative analysis, and lacking of coordinated control between intelligent electrical equipment. Considering the large number of smart electrical equipment such as new energy, the large difference of control response characteristics and engineering implementation environment, how to connect smart electrical equipment to safety control system is a difficult problem. Based on the quantitative analysis of emergency control of smart electrical equipment and the research of its engineering implementation status, this paper proposes an smart collaborative optimization control scheme for distributed safety and stability control system, and then verifies the correctness and reliability of the proposed scheme based on the experimental platform.
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2 Feasibility Analysis of Emergency Control for Smart Electrical Equipment 2.1 Analysis on Emergency Control Mechanism of Intelligent Electrical Equipment According to the Extended Equal Area Criterion (EEAC) theory, the purpose of power system emergency control is to increase the deceleration area of One Machine Infinite Bus (OMIB) isoline by emergency control, so that the unstable system can restore transient power angle stability after emergency control. The specific performance is shown in the following Fig. 1.
Fig. 1. OMIB equivalent machine first swing power angle-power difference curve
In Fig. 1, δ 0 , δ cl and δ cg are the rotor angles of OMIB at fault time, fault removal time and emergency control time, respectively. δ DSP and δ * DSP are the rotor angles corresponding to the dynamic saddle point of OMIB equivalent machine without emergency control and after emergency control respectively. Pe and Pm are the electromagnetic power and mechanical power of OMIB equivalent machine without emergency control, respectively. P* e and P* m are the electromagnetic power and mechanical power of OMIB equivalent machine after emergency control, respectively. Then ΔP is the variation of OMIB equivalent machine power difference after the implementation of emergency control. A1 is accelerated area for the first pendulum (the filling part of the red dotted line). A2 is maximum deceleration area for the first pendulum without emergency control (the filling part of the blue dotted line). A3 is increased deceleration area for the first pendulum after emergency control (the filling part of the yellow dotted line). DC power emergency support, wind power, photovoltaic emergency power response process requires power electronic equipment control power gradually close to the control measures, will eventually reach the target amount of time as the response time. This paper conservatively treats the time when the power electronic control measures reach the target as a part of the system delay, and then the control measures respond instantaneously. Assuming that from the emergency control time to the dynamic saddle point time of the OMIB equivalent machine after emergency control, the power difference
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of the OMIB equivalent machine remains unchanged. The power difference of OMIB equivalent machine without cutting machine operation is shown in the formulation. MA MS φ = Pe − Pm = Pei − Pej i∈S j∈A MT MT (1) MA MS − Pmi − Pmj i∈S j∈A MT MT S and A denote the critical group and the remainder group, respectively. Pei and Pej represent the electromagnetic power of synchronous motor in the critical group and the remainder group, respectively. Pmi and Pmj represent the electromagnetic power of synchronous motor in the critical group and the remainder group, respectively. MS and MA are the sum of inertia of the critical group and the remainder group, respectively. MT is the sum of inertia of all synchronous motor. Whether it is power fast control or DC power support of wind power, photovoltaic and energy storage, the critical group and the remaining group will not change after the machine is cut. Therefore, the difference between the electromagnetic power and mechanical power of OMIB equivalent machine after the machine is cut is: MA MS ∗ ∗ φ∗ = i ∈ SPei − j ∈ APej MT MT (2) MA MS i ∈ SPmi − j ∈ APmj − MT MT Therefore, the variation of the equivalent power difference of OMIB in the emergency control of smart electrical equipment is: ∗ MS MA ∗ i ∈ S Pei j ∈ A Pej − Pei − − Pej MT MT ∗ MA ∗ = k ∈ S ∪ A Pek − Pek + j ∈ A Pej − Pej MT ∗ MS ∗ k ∈ S ∪ A Pek − Pek = + i ∈ S Pei − Pei MT
φ ∗ −φ =
(3)
The sum of electromagnetic power variation of all synchronous motor in the emergency control time system can also be approximated as the sum of the emergency regulation active power of the smart electrical equipment at the emergency control time. Mathematical expression is: ∗ k ∈ S ∪ A Pek − Pek = Pe (4) M N Pe = Pji i=1
i=j
In the above, ΔPe is the emergency control moment of smart electrical equipment to regulate the active power sum. i represents the type, such as photovoltaic, energy storage, DC, etc. j represents the number of participating regulations. The variation of
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power difference at the forward available emergency control moment is: MA ∗ φ ∗ −φ = Pe + j ∈ A Pej − Pej MT ∗ MS =− Pe + i ∈ S Pei − Pei MT
(5)
The calculation formula of the increased deceleration area A3 after emergency control is: ∗
δDSP ∗ dδ A3 = (φ ∗ − φ) δDSP − δcg + ∫ Pe∗ − Pm δDSP
P*
(6)
δ cg and δ DSP are obtained by simulation, and the calculation formulas of δ * DSP and * e − P m are as follows: −b − b2 − 4a c + φ 2 − φ ∗ = δDSP (7) 2a ∗ ∗ 2 Pe − Pm = aδ + bδ + c + φ ∗ − φ
In the above two formulas, a, b, c are obtained by secondary fitting with the simulation data of dynamic saddle point time and its first two time. After the implementation of emergency control, when the A3 area meets formula (8), the system restores stability. A1 ≤ A2 + A3
(8)
The more the deceleration area increases after the implementation of emergency control, the better the control effect is. Therefore, the increment of stability margin under unit control amount can be used as the evaluation index of emergency control, as shown in Eq. (9): γ =
A3 /P A1
(9)
In summary, DC, wind power, photovoltaic and energy storage can all be used as emergency control resources, and the quantitative standard of their emergency power response depends on the emergency control amount and response time. The emergency controllable amount and response time of smart electrical equipment change dynamically according to the operation environment and state. It is urgent for the security control system to monitor the operation state of smart equipment in real time and intelligently adjust the collaborative control strategy. 2.2 Intelligent Electrical Equipment Emergency Control Engineering Foundation At present, the practice of using DC and energy storage as control resources has been completed in security control system engineering such as system protection, and mature
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industry standards have been formed. With the rapid development of new energy rapid power control technology, through the improvement of new energy control mode, the response time of wind-solar-storage power generation is within 100 ms, which meets the security control conditions. With this technology, the new energy power generation field can quickly receive and respond to the commands of the security and stability control system. Figure 2 shows the fast power control system of photovoltaic power station. The construction of special optical fiber ring network shortens the channel delay to 20 ms. The source control terminal is added to realize the communication ability of various protocols, such as CAN Bus, RJ485 interface, etc., to realize data interaction and high-speed control with new energy inverter. A fast power control device is added to the station to realize the decomposition of the remote-control command and the real-time upload of the inverter information. At present, the emergency control technology indicators of the new energy station that can be realized in the project are shown in Table 1. In the actual project implementation, the following points need to be improved: (1) Real-time monitoring of regulating capability of smart electrical equipment by unified safety and stability control system. (2) Specification for issuing instructions for unified security and stability control systems. (3) Unified security and stability control system and station control emergency control device communication interface and standard communication protocol. With the promotion of technology, the number of conditional power grid stability control stations will be extremely large, how to collaborative optimization control is a problem. Stability Control Device 2M Channel Fast Power Control Device
Panoramic Monitoring Server Ring Network Switch Central Control Room of Photovoltaic Station
Array 3
Gigabit Switch Protection room of girder booster station
Photovoltaic Station Communication Room
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Source Control Terminal 4 Array 4
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Ethernet
Source Control Terminal 5
CAN/485 Direct mining of cables
Source Control Terminal 1
Centralized Inverter Box Inverter Integrated Machine Array 1
Box Transformer 5
Centralized Controller
Transformer
... String Inverter
Fig. 2. Photovoltaic fast power control system
Array 5
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Index
Wind power
Photovoltaic
Transient voltage control Response time
≤50 ms
≤50 ms
Reactive power regulation ability
≥Station rated capacity 20%
≥Station rated capacity 20%
Active control response time
≤100 ms
≤50 ms
Active power control range Minimum allowable output of power station ± 10% rated power
Minimum allowable output of power station ± 10% rated power
Station control function
Dynamic assessment and emergency control function
Dynamic assessment and emergency control function
3 Smart Collaborative Optimal Control Scheme for Distributed Safety and Stability Control System The large number of smart electrical equipment, such as wind-solar-storage, and the need to monitor the running state of smart equipment in real-time make the whole distributed security and stability control system collect various types of information, different sources and different uses, and need to classify all kinds of information. The physical architecture, functional architecture and communication network architecture of distributed intelligent security and stability control system also have many typical characteristics of traditional security and stability control architecture. According to the requirements of intelligent collaborative optimization control, this chapter proposes an intelligent collaborative optimization control scheme for distributed security and stability control system based on the existing security and stability control system architecture, including the applicable conditions of coordinated control, the overall architecture, and the information command flow. It provides a basis for the engineering implementation of safety and stability coordinated control of smart controllable equipment. 3.1 Analysis of Applicable Conditions Aiming at the stability problems of overload, power angle and voltage, smart electrical equipment can be used to improve the safety and stability of power grid. Based on the above research results, the applicable conditions of intelligent collaborative optimization control between smart electrical equipment and traditional safety and stability control system are summarized as follows (Table 2).
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Table 2. Technical indicators for emergency control of new energy plants Problem
Traditional means
Smart electrical equipment
Overload
Machine cutting, load cutting
PV-wind-storage-DC
Power angle
Machine cutting, load cutting
PV-wind-storage-DC
Voltage
On / off electric reactor and load shedding
PV-wind-storage
Frequency
Machine cutting, load cutting
PV-wind-storage-DC
3.2 The Overall Framework and Information Flow of Intelligent Collaborative Control The existing security control system architecture has been widely used and runs well. Based on the existing security and stability control system architecture, this paper proposes the overall framework of intelligent cooperative control scheme, as shown in Fig. 3. Because there are different action scales between the smart electrical equipment and the traditional stability control method, the intelligent cooperative control master station should be configured to avoid the negative effect of the smart electrical equipment control by correcting the control strategy table online. At the same time, under the premise of ensuring the safety of the system, the advantages of fast and flexible electrical equipment should be given full play to reduce the amount of action of cutting machine and load shedding substation, so as to achieve the coordination of control cost and power grid security. The overall framework is a pyramid, hierarchical distributed architecture model, from top to bottom are control terminal station layer, control master station layer, control sub-station layer and monitoring execution station layer. Coordinated Control Station
Control Terminal Station Layer
Control Master Station Layer
Traditional Control Master Station
Control substation layer
Traditional Control Substation 1
...
Traditional Control Substation N
Monitoring execution station layer.
Execution station 1
...
Execution station 2
Smart Control Master Station
Smart Control Substation 1
Smart Control Substation N
...
Smart control ... monitoring, execution station 1
Smart control monitoring, execution station N
Fig. 3. Intelligent collaboration overall framework
(1) The control terminal station receives the control resources and fault information sent by each master station, forms an optimized coordinated control strategy (control strategy correction) and sends control instructions.
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(2) The traditional control master receives the control resources and fault information from each substation, and sends the total amount of statistical controllable resources and fault information to the master station. Receive the terminal station instructions and assign them to each sub-station according to the optimization principle. (3) The intelligent control master receives the operation information of smart controllable equipment uploaded by each intelligent substation, and sends the information to the terminal station. Receive the terminal station instructions and distribute them to each smart electrical equipment substation according to the optimization principle. (4) The control sub-station forms control instructions locally according to the strategy table and fault information lookup table and sends them to the execution station. Or receive the controllable resource information of each execution station, identify the fault type, and send it to the master station. Receives instructions from the master station. (5) Monitoring the execution station layer to collect control resource information and upload it to the corresponding sub-station/intelligent coordinated control substation. Collect operation information of key lines and key sections and send them to corresponding sub-stations/intelligent control sub-stations. Receiving Substation/Intelligent Control Master Station to issue instructions and take control measures. The information command flow of the collaborative control scheme is shown in Fig. 4. Information command flow mainly has two main lines. One is the information command flow of traditional security control system, and the other is the information command flow of smart electrical equipment. It is necessary to note that DC has been connected to the traditional security control system, without redesigning access to intelligent stations.
Control Terminal Station
DC fault information and maximum power loss can be increased \ decreased DC real-time operating power Cutting unit capacity Cutting load
Smart electrical equipment control command
Actual capacity of smart electrical equipment
Traditional Control Master Station
Smart Control Master Station
Traditional Control Substation DC fault information and maximum power loss can be increased \ decreased DC real-time operating power Cutting unit capacity Cutting load Control command decomposition of Smart controllable equipment
Actual capacity summary of smart controllable equipment
Smart Control Substation
DC Operation Information Unit Operation Information Load information
Monitoring Execution Station
Smart electrical equipment control command
Actual capacity of smart electrical equipment
Monitoring Execution Station
Command flow Information flow
Fig. 4. Intelligent collaborative information flow
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Begin
Calculation of offline strategy table control measures and control performance index of smart electrical equipment
Smart electrical equipment uploads dynamic adjustable capacity to master station in real time
Fault detected ? N
Y Find the offline strategy table to determine the emergency control strategy
According to the adjustable capacity difference of smart electrical equipment before and after fault, the modified emergency control strategy is calculated and implemented
N System stability ?
Y Additional control implemented in N rounds
End
Fig. 5. Intelligent cooperative control strategy control strategy
3.3 Intelligent Collaborative Control Strategy Due to the uncertain actual operating conditions of smart electrical equipment in the actual system operation, the dynamic adjustable capacity to deal with serious faults is in a dynamic state. Therefore, when the off-line control strategy table is formulated, there will be deviations whether the action of smart electrical equipment is taken into account, so it is necessary to adjust the online correction of control strategy. In this section, the intelligent collaborative control strategy of security and stability control strategy is proposed, so as to realize the collaborative optimization of smart electrical equipment and traditional security and stability control strategy. The process shown in Fig. 5 includes the following sections:
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(1) When the fault does not occur, the control measures of offline strategy table and the control performance index of smart electrical equipment are calculated according to the expected fault, and the dynamic adjustable capacity uploaded by smart electrical equipment in real time is received. (2) When the fault occurs, find the offline strategy table, determine the emergency control strategy, and calculate the modified emergency control strategy according to the real-time adjustable capacity of intelligent controllable equipment. According to the dynamic adjustable capacity C of smart controllable equipment before fault, the comprehensive control effect η of rapid adjustment of smart equipment is calculated as follows: ⎤ ⎡ C1 ⎥ ⎢
⎢ C2 ⎥ (10) η = γ1 γ2 ...γn ⎢ . ⎥ ⎣ .. ⎦ Cn
According to the performance index of the control measures in the strategy table, the off-line control strategy is modified from large to small, so that the stability margin of the system modified by the control variable is equivalent to that of the system modified by the smart electrical equipment. max l
l
Pk
k=1
γ Pk k=0 k
≤ η
(11)
4 Example Analysis When the hardware-in-the-loop experimental platform of the control system is established in the laboratory environment, the control system needs to be connected with the real-time simulation unit (Nova-Cor) through auxiliary real-time simulation resources such as power amplifier and sampling card. Limited by real-time simulation resources, it is difficult to access all control devices to the simulation environment according to the principle of 1:1 in the laboratory, as shown in Fig. 6. In the experiment, the self-developed communication interface device is used to retain the communication part between the actual control device and the upper control station, and the control instruction execution part is moved to the internal simulation model, so as to replace part of the control device to complete the experimental verification of intelligent collaborative control system and voltage emergency control system. The communication box between the communication interface device and the load master station and the voltage master station transmits data bidirectionally through 2M channel. The communication mode and communication content are highly consistent with the stability control device of the actual control system.
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Simulation System
Safety and Stability Control Device DC Subst at ion
Smart Subst at ion
Volt age Subst at ion
Ă Ă
Load subst at ion
Traditional Master Station SDH 2 3 4 5 1
Smart Master Station SDH 6
1
2
3
4
5
6
2
3
4
5
6
2M channel 1
2 3 4 5 Communications Interface Unit
6
1
Communications Interface Unit
Mesh Wire Switch GTDO/GI
GTAO Power Amplifying Mesh Wire
RTDS/GTNET
RTDS Simulation Device
Fig. 6. Simulation platform
After Jiuquan-Hexi N-2 fault occurs, the emergency control strategy is adopted, the voltage curve and power curve of Chaidamu 750 kV bus are shown in Fig. 7. The simulation results show that after Jiuquan-Hexi N-2 fault, the bus voltage of Chaidamu 750 kV loses stability, the active power of Chaidamu-Haixi changes greatly, the power reverses, and the system loses stability. After taking emergency control measures, the voltage of Chaidamu 750 kV bus is restored to stability after oscillation, and the active power of Chaidam-Haixi is improved and restored to stability, which proves the feasibility of the proposed structure.
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Chaidamu Bus Voltage/kV
700 600 500 Front taking emergency control measures
400 300
After taking emergency control measures
200 100 0
Active Power of Chaidamu-Haixi First Loop/MW
0
0.5
1
1.5
2
2.5
3 t/s
2000 1500 1000 500
Front taking emergency control measures
0
After taking emergency control measures
-500 -1000 0
0.5
1
1.5
2
2.5
3 t/s
Fig. 7. The voltage curve and power curve of Chaidamu 750 kV bus
The results of the traditional strategy and the collaborative optimization control strategy proposed in this paper are shown in Table 3. The intelligent collaborative method is applied to reduce the total cutting load of 70 MW, and the 200 MW photovoltaic and 380 MW wind turbine are removed as 450 MW photovoltaic regulation, 90 MW wind power regulation and 40 MW energy storage regulation. The feasibility and effectiveness of the proposed intelligent collaborative method are proved. Table 3. Result comparison Comparison
Tradition
Intelligent collaboration
Total cutting thermal power amount (MW)
1000
900
Total cutting load amount (MW)
700
630
Total DC modulation (MW)
400
400
Wind power (MW)
Cutting wind 380
Regulation 90
Photovoltaic (MW)
Cutting photovoltaic 200
Regulation 450
Energy storage (MW)
/
40
Transient stability margin after emergency control
45.67
26.31
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5 Conclusion With the gradual increase in the proportion of new energy, the number of smart electrical equipment in the system will be increasing. Based on EEAC theory, this paper analyzes the feasibility of wind power, photovoltaic, energy storage and DC emergency control, and puts forward quantitative evaluation indexes. Research shows that the evaluation indexes are related to the emergency controllable amount and response time of intelligent electrical equipment. Through detailed analysis of new energy fast power control technology scheme, the emergency control technology index of new energy station is summarized. Based on the upgrading of the existing security and stability control system architecture, an intelligent collaborative optimization control scheme for distributed security and stability control system is proposed. The scheme realizes real-time monitoring and fast command control of smart electrical equipment by building new intelligent master station, substation and monitoring execution station, and proposes intelligent collaborative control strategy to eliminate control deviation. The experimental results show that the intelligent collaborative optimization control technology of distributed security and stability control system can improve the traditional security control strategy and reduce the cutting load by adjusting means. The smart electrical equipment mentioned in this paper is only for power smart electrical equipment. In fact, the flexible power flow control equipment such as TCSC, SVC and UPFC in the system can also improve the stability of the system. In the future, it is necessary to further explore the integration of these resources into the framework of the distributed security and stability control system.
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Study on Integrated Modelling of Tower-Line System for UHV Transmission Lines and Weak Spot Distribution of Towers Huipeng Li1
, Daochun Huang1(B) , Yuangen Xu2,3 , Li Zhang1 , and Jiangjun Ruan1
1 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
{lhp2021,huangdc2009}@whu.edu.cn
2 Wuhan NARI Limited Liability Company, State Grid Electric Power Research Institute,
Wuhan 430074, China 3 Hubei Key Laboratory of Power Grid Lightning Risk Prevention, Wuhan 430074, China
Abstract. UHV transmission is an important form of long-distance and large capacity power transmission. Icing, high wind and other harsh environments are important factors leading to the damage of UHV transmission tower and line systems. Based on the finite element method, the integrated modelling of the tower and line system of the UHV transmission line were studied in conjunction with the mechanical characteristics of the tower and line system; a four-tower, three-span simulation model of the UHV AC double transmission line was established to analyze the stress distribution of the towers under different wind speeds and ice thicknesses, and to obtain the critical failure load combination of the towers. The results are close to the design wind speed and ice thicknesses. The analysis of structural weak spot distribution, tower failure and maximum node displacement of the pole tower was carried out to obtain the distribution of weak spots and node displacement of the pole tower, and the relationship with the thickness of ice cover and wind speed was studied. The results can be used in the research of pole tower monitoring and early warning. Keywords: UHV · Tower-line system · Finite element method · Stress · Weak spot
1 Introduction Ultra-high voltage (UHV) transmission is an important form of long-distance and largecapacity power transmission. UHV transmission lines are characterized by long span, high tower, complex geographical environment and changeable weather, and can be destroyed under the influence of various extreme loads such as earthquake, snow, ice and wind, causing huge economic losses and even casualties [1–5]. It is very important to study the structural stability of UHV Transmission Line Towers under external loads, especially under the severe weather conditions such as icing and gale. At present, researchers have done a lot of researches on the structural stability of transmission lines under external loads, and have made some research results. Lijuan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 859–866, 2022. https://doi.org/10.1007/978-981-19-1870-4_90
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Zhang had carried out the true collapse test and numerical simulation on 1000 kV UHV transmission line, and analyzed the ultimate bearing capacity of the tower under the condition of high wind and broken line [6]. By establishing the finite element model of a 500 kV dangerous tower under foundation settlement, Yan Gan simulated the stress distribution on the tower, and determined the weak member on the tower under foundation settlement [7]. The finite element analysis model of 500 kV EHV transmission line tower system was established by Zhiye Du and Li Zhang. The stress distribution of tower under different wind speeds and ice thickness was studied, and the modification and effect evaluation were carried out for the weak spot of the structure, which has certain guiding significance for the stability of the tower structure [8, 9]. In order to study the structural stability of transmission lines, Liu Wenfeng has established a 110 kV transmission line tower-line system. And the stress and strain of the tower under various non-uniform icing conditions were analyzed [10]. At present, the research on the force acting on transmission line tower structures mainly focuses on the mechanical analysis of high-voltage and ultra-high-voltage lines under the conditions of strong wind, icing, ground settlement, etc. There is no actual multi-span, double-circuit UHV transmission line tower-line system mechanical model construction, and there are few analyses on the weak spot of the tower under the combined load of icing and strong wind. Taking the 1000 kV Antang II transmission tower in Zhejiang Electric Power Grid as the research object, this paper established the mechanical finite element simulation model of the tensile section composed of the tower, conductor and ground wire, and simulated the influence of icing and strong wind. The mechanical numerical simulation was carried out to find out the weak spots of the steel structure of transmission line tower and locate it accurately, which could provide the foundation for the development of real-time monitoring device and early warning technology. And it also could provide guidance and suggestions for strengthening the weak member of the tower so as to facilitate the network maintenance personnel to timely warn and respond to the disaster.
2 Modeling Method of Tower-Line System The study on the distribution of the weak spots of transmission line tower structure is to calculate the mechanical stability of the tower-line structure system under certain load conditions, and then to check the strength of the steel structure to find the weak steel structure on the tower. To calculate the mechanical stability of tower-line system by finite element method, it is necessary to select the correct finite element modeling and analysis element types of tower, conductor, ground wire and insulator, and establish the tower-line system model which can satisfy the calculation precision. Then, the external loads, such as icing and strong wind, which are applied to the tower, conductor and ground wire, are precisely simulated according to the actual force characteristics. It is necessary to fully understand the mechanical characteristics of the tower-line system and establish an effective tower-line system model before the calculation of the distribution of the weak spots. This is the basis of correctly analyzing the structural strength of the tower and studying the distribution of the weak spots of the tower under various working conditions.
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2.1 Basic Theory of Finite Element Structural Analysis The mechanical analysis of transmission line towers belongs to the structural strength problem, which satisfies the basic equations of elastic mechanics. Elastic mechanics is the foundation of structural mechanics and material mechanics. It is widely used in the fields of mechanics and architecture. It mainly studies the changes of stress and strain caused by elastic objects under external forces, the governing equations of elasticity include the equilibrium differential equation and the constitutive equations of Materials [8]. Based on these two equations, the finite element method is used to establish the tower-line system model, define the material properties, apply load (initial strain and external load), get the stress of each node, and judge the stability of the system. In the process of loading, the tower will produce a large deformation. The steel yield from the linear stage into the nonlinear stage and the steel structure stress and strain relationship no longer meet Hooke’s law. It is necessary to carry out nonlinear analysis. 2.2 Tower-Line System Modeling Element In order to calculate and analyze the mechanical stability of UHV transmission line tower-line system, and to obtain the distribution of the weak spots of UHV transmission line tower-line system, it is necessary to select appropriate units to establish the tower-line system model. Taking into account the stress and structural characteristics of the steel tower structure, conductor, etc., BEAM188 (on Fig. 1) is selected to model the tower, and the steel structure type of the line tower is set as angle steel or pipe steel. LINK10 (on Fig. 2) cable element is used for the conductor and ground wire, and the conductor and ground wire are scattered into interconnected elements. The insulator adopts LINK8, and the connecting hardware is ignored.
Fig. 1. Diagram of beam element (BEAM188)
Fig. 2. Diagram of cable element
2.3 Finite Element Modeling of Tower-Line System Tower Modeling. The tension section selected in this paper is a three-span, four-tower, and double-circuit transmission line composed of 1000 kV Antang II line in Zhejiang Electric Power Grid. The specific circuit parameters are shown in Table 1. Considering that the tension towers on both sides have almost no influence on the force between the span, the tension towers are not modeled and only the 219 and 220
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Tower number
Type
Tower model
Nominal height (m)
Span (m)
Altitude (m)
218
Strain tower
SJ324
39
477
2.56
219
Straight tower
SZ323
69
581
2.56
220
Straight tower
SZ323
63
474
2.56
221
Strain tower
SJ321
39
/
2.56
Table 2. Steel material properties of tower Type
Q345
Q235
Elasticity modulus (Mpa)
206000
206000
Mass density (t/mm3 )
7.85E−09
7.85E−09
Poisson ratio
0.3
0.3
Yield strength (MPa)
345
235
linear towers are built. The main material properties of the two steels are shown in Table 2. In the process of tower modeling, the symmetrical characteristics of its structure were fully utilized to reduce the workload. The two linear towers defined 53 types of L-shaped section and round tube section, with 968 nodes and 2458 elements. The total tower height of No. 218 and No. 219 was 113 m and 107 m respectively. Tower-Line System Model. The conductor of the tower-line system is an eight-bundled conductor (LGJ 630/45). In order to simplify modeling, the conductor was modeled as a conductor according to the principle of equal cross-sectional area. According to the catenary equation, the coordinates of discrete nodes on the wire were obtained for modeling. The Tower, conductor, ground wire and insulator were combined into a tower-line system. After modeling, there are 6 equivalent conductors and 2 ground wires (Fig. 3).
Fig. 3. Model diagram of the tower-line system
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3 Study on Weak Spot Distribution of Towers 3.1 Load Application and Solution In addition to its own gravity, the load on the transmission line tower system is also affected by the external environment, such as the gravity of the conductor and the ice on the tower, and the natural wind force. The load can be divided into natural load, additional load and necessary degree of freedom constraint. The calculation formula of each load refers to “Code for design of 1000 kV overhead transmission line” (GB 506652011, China) and other related standards and regulations. After the modeling and the load is applied, the simulation is carried out, and the nonlinear static analysis, the stress rigidification effect and the large deformation analysis are activated. The automatic time step is started to solve and the post-processing analysis. In order to analyze the mechanical stability of UHV transmission line tower line system under icing and wind deviation and find the weak points on the tower structure, we simulated the stress of the tower line system model by changing the combination of horizontal wind speed and icing thickness. Combined with the actual meteorological conditions at the location of the towers, load combination as shown in Table 3 was applied for solution. Table 3. Wind and ice load combination Combination number
Ice thickness (mm)
Wind speed (m·s−1 )
1
0
0, 5, 10, …, 45
2
5
0, 5, 10, …, 45
3
10
0, 5, 10, …, 45
4
15
0, 5, 10, …, 45
In this paper, the stress of every member in the tower was extracted, and the danger degree of steel structure failure was judged by the ratio of stress and steel yield strength (stress ratio). The closer the stress ratio is to 1, the greater the failure risk is. When the stress ratio is greater than 1, the steel failure is judged. 3.2 Weak Spots and Failure Analysis of Tower The simulation results showed that when the ice thickness was 5 mm and the wind speed was 40 m/s, the ice thickness was 10 mm and the wind speed was 40 m/s, or the ice thickness was 15 mm and the wind speed was 35 m/s, the node had large displacement under the small increment of load. It was found that the result was close to the design ice thickness of 10 mm and wind speed of 30 m/s, which showed that the modeling and calculation method could approximately simulate and study the structural stability of UHV transmission line towers. According to the maximum stress ratio under different
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conditions, the critical failure load was selected with ice thickness of 10 mm and wind speed of 35 m/s. The maximum stress ratio appeared on tower 220, and the axial stress distribution nephogram and weak spots of tower 220 were shown in Fig. 4. The critical failure unit data of tower 220 are shown in Table 4.
Fig. 4. Nephogram of axial stress distribution and weakest element diagram
Fig. 5. Curve of maximum stress ratio
According to the simulation results, it can be found that the steel which was closest to the yield strength was the main material on the leeward side when approaching the design wind speed and ice thickness. The reason was that the direction of wind-ice combined load forced the steel on the leeward side. The force was greater because the wire between tower 220 and tower 219 was longer. The steel on the side near tower 219 reaches the yield strength first. Table 4. Summary table of critical failure element data Load
Weak element
Stress value (MPa)
Element strain
Stress ratio
Ice thickness: 10 mm Wind speed: 35 m/s
2440
−326
−0.00210
0.9446
2439
−326
−0.00239
0.9444
2434
−319
−0.00203
0.925
2433
−319
−0.00224
0.9249
2304
−314
−0.00226
0.9121
2303
−314
−0.00200
0.9113
2188
−313
−0.00201
0.9073
It can be found that the maximum stress ratios under different combination loads were summarized, as shown in Fig. 5. It can be seen that the maximum stress ratio is positively correlated with ice thickness and wind speed. The thicker the ice, the higher the wind speed, and the larger the stress ratio. At the same time, when the wind speed is less than 20 m/s, the maximum stress ratio changes little with the initial value. But
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when the wind speed is more than 20 m/s, the stress ratio increases rapidly, and the danger degree of tower increases rapidly. Special attention should be paid to the actual monitoring and prevention to prevent the occurrence of accidents. In order to avoid the failure of the weak steel structure, some measures can be taken to strengthen the strength of the steel structure. For example, the weak steel structure can be replaced with steel with higher strength, or other steel can be added to the weak position to reduce the force of dangerous steel. 3.3 Analysis of Influence of Ice Thickness and Wind Speed on Nodal Displacement In the case of critical failure (ice thickness is 10 mm, wind speed is 35 m/s), the node displacement of tower 220 is as shown in Fig. 6. It can be found that the maximum displacement of the ground support on the Leeward side is 1.892 m.
Fig. 6. Cloud map of tower node displacement distribution
Fig. 7. Curve of maximum node displacement
The maximum nodal displacements under different wind speeds and ice thickness were extracted. As shown in Fig. 7, the maximum nodal displacements increase with the increase of ice thickness and wind speed. At the same time, the influence of the ice thickness on the maximum node displacement is more and more obvious. Combined with the analysis results of the position of the maximum node displacement and the maximum node displacement under the critical failure condition, when the node displacement near the ground cable bracket of the tower reaches about 1.9 m, the tower is about to fail, which has a certain guiding significance for the research of state perception and early warning technology of UHV transmission line.
4 Conclusion In this paper, the tower-line system model of 1000 kV UHV AC double-circuit transmission line was established, and the distribution of stress and weak spots of the tower under various wind bias and icing loads was studied. The conclusions are as follows:
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(1) Through modeling and simulation of specific UHV transmission lines, it is found that when the ice thickness and wind speed reach the designed value, the calculation no longer converges, and the axial stress of steel at many places reaches the yield strength. It is proved that the integrated model of UHV transmission line with BEAM188 and LINK10 can reflect the distribution of stress and weakness of UHV transmission tower. (2) The critical failure ice thickness and wind speed are calculated by cyclic loading of ice thickness and wind speed. The critical failure hazard element is mainly part of the main steel, and the danger degree of the tower increases rapidly when the wind speed is over 20 m/s. (3) The maximum node displacement is about 1.9 m under the critical failure condition, and the maximum position appears near the tower ground wire support. The influence of the wind speed and ice thickness on the maximum node displacement is more and more obvious. Acknowledgments. This work was supported by Key R&D Program of Hubei Province of China (No. 2020BAB108).
References 1. Rajamani, P., Aravind, K.A., Rao, K.R., et al.: Experimental studies on radio interference of 1200 kV unipolar UHV DC transmission line. In: 2019 International Conference on High Voltage Engineering and Technology (ICHVET), pp. 1–4. IEEE, Hyderabad, India (2019) 2. Shovkoplyas, S.S., Chernomaz, D.A., Satsuk E.I.: Ensuring reliable operation of electrical network during ice formation on extra high voltage transmission lines. In: 2019 International Ural Conference on Electrical Power Engineering (UralCon), pp. 195–201. IEEE, Chelyabinsk, Russia (2019) 3. Shen, B., Koval, D., Xu, W., et al.: An analysis of extreme-weather-related transmission line outages. In: IEEE Canadian Conference on Electrical and Computer Engineering, vol. 2, pp. 697–700. IEEE, Waterloo, Ontario, Canada (1998) 4. Gao, F., Wu, Jun., Liu, D.: Differentiation economic assessment on UHV power system considering icing disaster. In: Proceedings of the CSU-EPSA 29(01), pp. 1–6 (2017). (in Chinese) 5. Moser, M.J., George, B., Zangl, H., et al.: Icing detector for overhead power transmission lines. In: 2009 IEEE Instrumentation and Measurement Technology Conference, pp. 1105–1109. IEEE, Singapore (2009) 6. Zhang, L., Liu, Z., Pan, H., et al.: Research on collapse failure test and numerical simulation of 1000-kilovolt ultra-high-voltage transmission tower. Steel Constr. (Chinese & English) 34(06), 19–24 (2019). (in Chinese) 7. Gan, Y., Zhou, W., Du, Z., et al.: Research of tower strain real-time monitoring and failure warning technology under land subsidence conditions. Electr. Measure. Instrum. 56(20), 9–16 (2019). (in Chinese) 8. Du, Z., Zhang, Y., Ruan, J., et al.: Failure analysis of 500 kV iced overhead transmission line by finite element method. High Voltage Eng. 38(09), 2430–2436 (2012). (in Chinese) 9. Zhang, L., Ruan, J., Du, Z., et al.: Short-term failure warning for transmission tower under land subsidence condition. IEEE Access 8, 10455–10465 (2020) 10. Liu, W., Yuan, X., He, B., et al.: Analysis of influence of uneven icing on stress of 110 kV tower. Guangdong Electric Power 32(11), 136–143 (2019). (in Chinese)
An Impedance Model of the High-Density Cultured Cells in a Bioreactor and the Cellular Impedance Detection Method Changzhe Wu1,2
, Guanghao Zhang1,2 , Cheng Zhang1,2 , and Xiaolin Huo1,2(B)
1 Beijing Key Laboratory of Bioelectromagnetics, Institute of Electrical Engineering,
Chinese Academy of Sciences, Beijing, China [email protected] 2 University of Chinese Academy of Sciences, Beijing, China
Abstract. The artificial liver support system (BALSS) can replace an illfunctioning liver to fulfill the functions of detoxication, metabolism, synthesis, and conversion. The BALSS is usually used to bridge transplantation or allow the liver to recover in patients with hepatic failure. The culture of sufficient liver cells with the desired functional protein expression in a bioreactor lies at the heart of the effectiveness of a BALSS to treat hepatic failure. Therefore, the real-time measurement of the number and functional status of liver cells in the bioreactor is of high importance for controlling the cell and environmental parameters in the bioreactor. Hence, this study aimed to propose an impedance model of high-density cultured cells in a bioreactor based on the general cellular impedance model by drawing from the recent development and applications of bioelectrical impedance technology. Specifically, we described a four-electrode impedance measurement method for the bioreactor and built an impedance measurement platform for cells in the bioreactor. An experiment was carried out to validate the impedance measurement method and the effectiveness of the impedance measurement platform. Our study laid the foundation for the real-time impedance measurement and detection of the number and functional status of cells in a bioreactor. Keywords: Bioartificial liver bioreactor · Cellular impedance high-density culture · Impedance measurement · Impedance model
1 Introduction The liver is a vital and complex organ in humans. It performs various physiological functions, including detoxication, metabolism, biosynthesis, and conversion. A large number of dead cells are found in a severely damaged liver, indicating that the liver has lost its ability to function, a condition known as hepatic failure [1]. At present, liver transplantation is considered the most effective treatment for hepatic failure. However, most patients die when waiting for donor livers [2, 3]. Bioartificial liver (BAL) is an
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 867–876, 2022. https://doi.org/10.1007/978-981-19-1870-4_91
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extracorporeal device through which plasma is circulated over living and functionally active hepatocytes packed in a bioreactor. BAL simulates the functional compensation of the human liver [4], with the aim to aid the diseased liver until it regenerates or until a suitable graft for transplantation is available. The number of liver cells and the expression of functional proteins in a bioreactor are among the decisive factors for the effectiveness of BAL [5]. A single treatment requires more than 109 properly functioning liver cells [6]. Therefore, obtaining a sufficient number of normally functioning liver cells is the major challenge facing the clinical applications of BAL. Monitoring during treatment using a BAL is crucial to meet the aforementioned requirements. The feedback control of the environmental parameters (e.g., temperature, pH, and CO2 concentration) should be implemented based on the response of the cell status to environmental parameters, or liver cells should be replaced timely if necessary [7–10]. Impedance analysis technology offers an important tool for the online noninvasive detection of cell status. Cellular electrical impedance measurement technology utilizes the electrical properties of cells and their variations in different statuses, extracting information on cell statuses. This technology has been studied and applied in the fields of cell proliferation, migration, and cytotoxicity. The modulus of cellular impedance can reflect the number of cells, while the phase angle characterizes the degree of functional integrity of the cells [11]. The current applied to measure the cellular electrical impedance is very small and only of a magnitude of a microampere. Such current cannot impair the functional status of the cells. Therefore, even long-term monitoring using the impedance analysis technology cannot affect the experimental and therapeutic effects. We proposed an impedance model of the high-density cultured cells in a bioreactor to detect the cell status. A cellular impedance detection platform for the bioreactor was then built. Our study laid the basis for investigating the correlation between cellular impedance and the number and functional status of cells in a bioreactor.
2 Impedance Model of the High-Density Cultured Cells in a Bioreactor 2.1 Single-Cell Impedance Model The cell is composed of a cell membrane and cellular fluid. The cell membrane is a phospholipid bilayer structure, where ion channels for molecule transport are embedded. Different substances, molecules, or ions can enter or exit the cells only via the corresponding channels. Therefore, the cell membrane usually has poor electrical conductivity. The entire cell membrane carries a certain amount of electrostatic charges. The phospholipid bilayer can be treated as two parallel plates of a capacitor. Hence, a cell membrane is equivalent to a membrane capacitor. The cellular fluid enclosed within the cell membrane is filled with ions having high electrical conductivity. Therefore, the cellular fluid is equivalent to a resistor [12]. Hence, a single-cell impedance model can be represented by one resistor element plus one capacitor element.
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2.2 Impedance Model of the Bioreactor Solution Without Cells When a voltage is applied across the bioreactor solution, an electrochemical reaction occurs between the electrodes and the solution. This process involves not only the movement of ions in the solution toward the electrodes but also the chemical reactions occurring at the electrodes. The equivalent circuit model for this process is shown in Fig. 1.
Fig. 1. Equivalent circuit model with excitation voltage directly applied to the bioreactor solution
In the aforementioned equivalent circuit model, Cdl is the capacitance of the site where the electrode comes into contact with the solution. That is, the two electrodes serve as two charged plates, between which charges exist. The value of this parameter is related to the substances near the plates. Rs is the resistance of the solution, which is related to the electrical conductivity and the electrical properties of the solution itself. Rp characterizes the resistance properties of the chemical reaction occurring at the electrodes. W is the Warburg impedance, which is related to the movement of ions in the solution. In the circuit, Rp and W are connected in series to generate Faradaic impedance, part of which is the impedance associated with the electrochemical reaction at the electrodes. The electrodes used to measure the bioelectrical impedance are mostly inert metal electrodes, which do not react with the solution. Therefore, the Faradaic impedance is equivalent to an open circuit, which can be further simplified, as shown in Fig. 2.
Fig. 2. Simplified equivalent circuit model of the electrode–solution interface
The simplified model in Fig. 2 treats the Faradaic impedance as an open circuit. The impedance at the electrode–solution interface is equivalent to a constant–phase angle element (CPE), whose impedance is given by ZCPE =
a (jω)β
(1)
where a is related to the attributes of the solution, for example, the solution volume and concentration; β is related to the attributes of the electrodes, and its value is determined by the electrode material and status.
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Thus, the impedance of the electrochemical reaction in the cell-free solution is given by ZS = ZCPE + Rs
(2)
Substituting formula (1) into formula (2) yields formula (3): ZS =
a + Rs (jω)β
(3)
As shown in formula (3), it is found through the experiment that the value of β approaches 1. Thus, this formula can be seen as an expression for the impedance of a capacitor multiplied by a constant a. That is, the electrode–solution interface is equivalent to a circuit where the capacitor (the capacitance being 1/a) is serially connected to a resistor. In other words, CFP is treated as a capacitor with a capacitance of 1/a: ZS =
1 + Rs jωCs
(4)
The following text further discusses the circuit model with cells in the solution. 2.3 Impedance Model of the Bioreactor with Cells in the Solution If cells exist in the solution, the circuit model should be constructed based on the comprehensive consideration of the equivalent electrical impedance of the solution, single-cell impedance model, and electrical impedance between the cells and the solution. To this end, it is necessary to include electrical parameters related to cellular impedance and the cell–solution interactions. The circuit model incorporating the aforementioned factors is shown in Fig. 3.
Fig. 3. Circuit model with cells in the solution
In the aforementioned model, the solution impedance is connected serially to the cellular impedance alongside the impedance between the electrode and the intercellular gaps. Since the CPE in a simplified equivalent circuit model for the electrode–solution
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Interface can be equivalent to a capacitor, it is represented by Cd. The circuit is equivalent to an intercellular gap capacitor Cgap connected to the intercellular gap resistor Rgap. These three models with composite impedances are serially connected to form a circuit model with cells in the solution. The model shows that when cells are suspended in the solution, the impedance of the entire circuit with electrodes attached to the two ends is given by Z = ZS + ZCELL + Zgap Z=
1 + Rs + jωCs
1 jωCcell 1 jωCcell
∗ Rcell + Rcell
+
1 jωCgap 1 jωCgap
∗ Rgap
(5)
+ Rgap
The cells in the bioreactor are cultured at a high density. the bioreactor is laden with cells and equipped with a suspension control. Assuming that the cells are uniformly packed, we can dismiss the capacitance and resistance in the intercellular gaps. In that case, all cells are in a uniform status. The cells have equal sizes and shapes (uniformly spherical). The cells are large in number and hence tightly packed in a horizontally upward direction. That is, toward the opening of the bioreactor tank (horizontal axis), the cells are already saturated. Thus, if the number of cells further increases, the cells packed along the vertical axis are considered to be connected in parallel (Fig. 4).
Fig. 4. Cell arrangement pattern in the bioreactor and its equivalent circuit
We assumed n rows of tightly packed cells. Let the overall composite resistance of a horizontal row of cells be Z1. Then, the expression for the composite impedance of the solution between the two electrodes can be written in the form of Eq. (6): 1 Z = ZS + ZCELL = Zs + Z1 n
(6)
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By introducing formulas (4) and (5) into Formula (6), we derive formula (7): Z=
Z= =
1 + Rs + jωCs 1 + Rs + jωCs
1 jωCcell 1 jωCcell 1 jωC1 1 jωC1
∗ Rcell + Rcell ∗ 1n R1 + 1n R1
R1 1 1 + Rs + ∗ jωCs n 1 + jωR1 C1
(7)
As shown in the aforementioned formula, with the increase in the number of cells n, the changes in the phase angle of the composite impedance is related to the phase angles R1 1 of jωC + Rs and 1n ∗ 1+jωR : if the phase angle of the latter is smaller than that of s 1 C1 the former, that is, the phase angle of the composite impedance of the cell suspension (culture medium) is larger than that of the composite impedance of the cells, the overall phase angle approaches that of the culture medium as n increases. In other words, the overall phase angle increases. Similarly, if the phase angle of the culture medium is larger than that of the cells, the overall phase angle also increases correspondingly as the number of cells in the bioreactor increases. On the contrary, if the phase angle of the cells is larger than that of the culture medium, the overall phase angle decreases as the number of cells increases to approach the phase angle of the cells. When the cells packed along the horizontal axis are saturated, the modulus of the impedance decreases as the number of cells increases.
3 Impedance Measurement Method for a Bioreactor The bioelectrical impedance can be measured by different methods depending on the number of electrodes, namely, two, four, six, and eight electrodes. The fourelectrode method is based on the three-element equivalent circuit model for bioelectrical impedance measurement. One capacitor is first serially connected to a resistor and then in parallel to a resistor to simulate the bioelectrical impedance Z. This circuit is known as the three-element equivalent circuit model for bioelectrical impedance measurement. In the four-electrode method, the power supply is applied across the composite impedance to be measured. Then, another electrical property (e.g., the electric current thus generated) is measured at another two nonoverlapping positions at the two ends. The corresponding voltage at these two positions is determined. The impedance is the measured voltage divided by the electric current. The four-electrode impedance measurement system is accurate and easy to use and can minimize measurement errors. We employ this method to construct a bioelectrical impedance measurement platform for the bioreactor, with the schematic diagram shown in Fig. 5.
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Fig. 5. Schematic diagram of the impedance measurement method for the bioreactor
4 Impedance Measurement Platform for the Bioreactor 4.1 Electrode Configuration for Impedance Measurement The electrodes were made of platinum. Platinum is an inert metal with stable properties, excellent corrosion resistance, and high electrical conductivity. Besides, it has a strong oxidative resistance and a high melting point. It does not react with the solution in a redox reaction. Platinum, though not participating in the electrode reaction, can conduct small electric currents. Because of these benefits, platinum has been widely used in cell measurement experiments. COMSOL Multiphysics software was used to analyze the relationship between the positions and shapes of the excitation and detection electrodes and the impedance measurement. The optimal impedance measurement scheme was developed along with the design and processing of the current injection electrodes, detection electrodes, and a dedicated bioreactor. Based on data analysis, we selected a pair of disk electrodes with a radius of 1.8 cm as the excitation electrodes. The arrangement of the excitation electrodes was first simulated. Next, the arrangement of the detection electrodes was incorporated into the simulation. Thus, the entire four-electrode measurement system was ready for the simulation experiment. During the simulation of the detection electrode arrangement, we found that changing the shape and size of the detection electrodes did not have a significant impact on the simulated electric field distribution. It is usually difficult to install the lead for needle electrodes for detection in the inner wall of the bioreactor. Besides, since the electrodes are in contact with the culture medium and the cells, the potential difference thus detected is usually not accurate and influences the final result. Another consideration in the choice of the electrode material was the cost. Hence, we prepared the detection electrodes with platinum wires and encircled the electrode once around the end cap at some distance from the excitation electrodes to avoid interference with the measurements (Fig. 6).
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Fig. 6. Results of electrode simulation
4.2 Impedance Measurement System A voltage-controlled current source was used. The electric current was injected into the cell suspension using a current injection electrode. The voltage difference between the two ends of the entire bioreactor was determined using the detection electrodes. This voltage difference was filtered and amplified with the voltage sensor. The impedance of the liver cells was calculated by dividing the voltage by the electric current within the liver cell suspension as measured by the current sensor (Fig. 7).
Fig. 7. Schematic diagram of the impedance measurement platform for the bioreactor
The overall schematic diagram of the impedance measurement system is shown in Fig. 8. 4.3 Results The experimental validation of the proposed measurement platform was carried out. Three circuits with different magnitudes of composite impedance were prepared by welding following the three-element model. Next, the composite impedance of these three circuits was determined through the joint use of the impedance analyzer and the proposed platform. The results showed that the measurements using the proposed platform agreed with those from the impedometer. The error was controlled below 5%,
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Fig. 8. Block diagram of the impedance measurement system
Fig. 9. Pictures of the dedicated bioreactor and the electrodes
which satisfied the experimental requirements. This result indicated that the proposed measurement platform was suitable for the subsequent cellular impedance measurement experiments (Fig. 9 and Table 1). Table 1. Results of the experimental validation of the impedance measurement system Serial no.
Equivalent membrane capacitance (μF)
Equivalent resistance of intracellular fluid ()
Equivalent resistance of extracellular fluid ()
Impedance analyzer Proposed platform Modulus of Phase impedance angle
Modulus of Phase impedance angle
1
1.0
170
170
96
10.4
96
10.4
2
0.1
170
200
88
6.7
87
7
3
1.0
51
51
26.7
7.5
26.9
7.2
5 Conclusions The real-time monitoring of the cell number and functional status in the bioreactor is increasingly required. We described a circuit model with and without cells in the bioreactor solution based on the general cellular impedance model by drawing from
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the recent development and applications of bioelectrical impedance technology. Next, we obtained the expression of composite impedance for the equivalent circuit through theoretical analysis and formula derivation. Then, the impedance model for the highdensity cultured cells in a bioreactor was developed. According to this impedance model, when the cells packed along the horizontal axis were saturated, the modulus of the impedance decreased as the number of cells increased. The changes in the overall phase angle were related to the phase angle of the culture medium itself and that of the cells. We further described a four-electrode impedance measurement method for the bioreactor and built a cellular impedance measurement platform in the bioreactor. An experiment was carried out to validate the impedance measurement method and the effectiveness of the impedance measurement platform. Our study laid the foundation for the real-time impedance measurement and detection of the number and functional status of cells in a bioreactor. Acknowledgments. This work was supported by the National Key R&D Program of China (2018YFC1106400, 2018YFA0108200), the Natural Science Foundation of China (Grant No. 61671428).
References 1. Aday, A., O’Leary, J.G.: Acute on chronic liver failure: definition and implications. Clin. Liver Dis. 24(3), 521–534 (2020) 2. Kapikiran, G., Bulbuloglu, S., Ozdemir, A., et al.: Knowledge and attitudes on organ donation from the perspective of liver transplant patients. Transplant Proc. 53(1), 25–29 (2021) 3. Trebicka, J., Sundaram, V., Moreau, R., et al.: Liver transplantation for acute-on-chronic liver failure: science or fiction? Liver Transpl. 26(7), 906–915 (2020) 4. Karvellas, C.J., Subramanian, R.M.: Current evidence for extracorporeal liver support systems in acute liver failure and acute-on-chronic liver failure. Crit. Care Clin. 32(3), 439–451 (2016) 5. Zhitao, W., Qing, P., Yi, G., Guoyu, P.: Advances in bioartificial liver system. Chin. J. Cell Biol. 41(4), 594–600 (2019). (in Chinese) 6. He, Y.T., Qi, Y.N., Zhang, B.Q., et al.: Bioartificial liver support systems for acute liver failure: a systematic review and meta-analysis of the clinical and preclinical literature. World J. Gastroenterol. 25(27), 3634–3648 (2019) 7. Simutis, R., LüBBERT, A.: Bioreactor control improves bioprocess performance. Biotechnol. J. 10(8), 1115–1130 (2015) 8. De Bournonville, S., Lambrechts, T., Vanhulst, J., et al.: Towards self-regulated bioprocessing: a compact benchtop bioreactor system for monitored and controlled 3D cell and tissue culture. Biotechnol. J. 14(7), e1800545 (2019) 9. Feidl, F., Vogg, S., Wolf, M., et al.: Process-wide control and automation of an integrated continuous manufacturing platform for antibodies. Biotechnol. Bioeng. 117(5), 1367–1380 (2020) 10. Heins, Z.J., Mancuso, C.P., Kiriakov, S., et al.: Designing automated, high-throughput, continuous cell growth experiments using evolver. J. Vis. Exp. (147) (2019) 11. Zhang, G.H., Huo, X.L., Wu, C.Z., et al.: A bioelectrical impedance phase angle measuring system for assessment of nutritional status. Bio-Med. Mater. Eng. 24(6), 3657–3664 (2014) 12. Jiao, Q., Xv, S.-Z., Yang, S.-S., et al.: Establishment and analysis of the equivalent circuit model of the electrical impedance of adherent cells. J. Mech. Electr. Eng. 31(9), 1107–1110, 1121 (2014). (in Chinese)
Matching and Selection of Drive Motor Controller IGBT Wenhui Zhang1(B) , Weifeng Kong2 , Song Zhao1 , Changhe Wei1 , Zhidong Qin1 , Jihong Liu1 , Ruzhi Qi1 , and Hailong Wang1 1 Beijing Auv Bus, BeiQi Foton Motor Co., Ltd., Beijing 100000, China
[email protected] 2 Beijing Institute of Technology, Beijing 100000, China
Abstract. As a high-power energy conversion device, IGBT has the advantages of large input impedance, small conduction voltage drop and simple driving circuit. Therefore, it is widely used in the driving motor controller of new energy vehicles. Its performance directly determines the stability and reliability of new energy vehicles. Starting from the working principle of IGBT and combined with the engineering application practice of bus electric drive system, this paper studies the selection basis of IGBT in the design and selection of drive motor controller. At the same time, aiming at the hidden trouble that may cause damage to IGBT in the actual operation of new energy bus, this paper analyzes and puts forward the corresponding IGBT protection strategy. It provides a certain theoretical reference for the matching application of drive motor controller IGBT of new energy bus. Keywords: New energy bus · Controller · IGBT · Matching
1 Introduction With the rapid development of global economy, energy shortage and environmental pollution have become the main problems faced by human beings in the 21st century. In order to deal with and solve the above problems, vigorously develop new energy vehicles to replace traditional energy vehicles has become the consensus of most countries in the world. In recent years, China has been at the forefront of the world in promoting new energy vehicles. The relevant national and local policies on the new energy vehicle industry are becoming more and more perfect, and the production and sales of new energy vehicles are increasing year by year. With the development of the industry and the decline of subsidy policy, new energy vehicles will return to market dominance driven by policy, and the performance of the product itself will become the key to competition. Among them, economy is the top priority of new energy vehicles, which is most concerned by customers. Major main engine manufacturers and parts manufacturers will try their best to reduce energy consumption. The drive system is the core component of new energy vehicles. As the main power source of new energy vehicles, the drive system is generally composed of drive motor © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 877–885, 2022. https://doi.org/10.1007/978-981-19-1870-4_92
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and drive motor controller. The drive system converts the electric energy provided by the battery into mechanical energy, drives the wheels to rotate, and provides power for new energy vehicles. Its output performance directly affects the power performance of new energy vehicles. As the main energy consumption source of new energy vehicles, the efficiency of driving system directly affects the energy consumption of new energy vehicles. Therefore, it is necessary to study the efficiency of the drive system. The efficiency of the drive system will directly affect the economy of new energy vehicles. The drive motor controller converts the direct current output from the battery into current through the inverter circuit, supplies it to the drive motor, and drives the motor to output speed and torque [1]. As the control device in the drive system, the drive motor controller directly determines the performance of the drive system. The inverter circuit of the drive motor controller is mainly composed of IGBT. The equivalent circuit diagram of IGBT is shown in Fig. 1:
Fig.1. IGBT equivalent circuit diagram
2 Analysis of IGBT Application IGBT is a composite full control voltage driven power electronic device, The utility model has the advantages of convenient maintenance, stable heat dissipation, high input impedance, reduced on voltage, small controller power, simple driving circuit, fast switching speed, high current density and reduced saturation voltage [2]. The IGBT use environment in new energy vehicles is more complex, so the IGBT has the following requirements [3]: (1) Broad temperature adaptability (2) Complex working conditions adaptability (3) Long service life As the control device of the power output of new energy vehicles, the drive motor controller directly determines the output performance of the drive system. Therefore, the driving motor controller is required to have high efficiency and good reliability.
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Meanwhile, new energy vehicles operate under complex and diverse working conditions, complex and diverse working conditions lead to a large range of voltage and current variation of the driving system, so the controller IGBT has a very high requirement on the adaptability of voltage and current, only reasonable matching can effectively play the performance of the driving system, effectively improve the power and economy of new energy vehicles. If the matched IGBT nominal voltage or current value is too high, resources will be wasted and the cost will increase. If the matched IGBT nominal voltage is too low, The actual voltage, which is provided by the vehicle battery will exceed the safe working voltage range of IGBT, resulting in the risk of breakdown. If the matching IGBT nominal current value is too low, the performance of the drive system cannot be fully played. At the same time, at high torque output, the current safety margin is relatively small, there is a risk of IGBT damage. Because in the actual operation, new energy vehicles often appear off break direct current bus voltage, low voltage and outage fault, will cause great damage to IGBT. Therefore, appropriate measures should be taken to protect IGBT.
3 IGBT Matching Selection 3.1 Selection of Nominal Voltage Currently on the market commonly used IGBT nominal voltage value is 600 V, 900 V, 1200 V, 1700 V and 3300 V. When choosing to use IGBT, be sure to make the IGBT work below the breakdown voltage rating, in order to prevent the breakdown of IGBT. When selecting the working voltage, it is necessary to consider the impulse voltage, namely the peak voltage, generated when IGBT is turned off. The following formula is used to select the IGBT voltage: VCE = Udc + Vpp
(1)
In the formula: VCE : IGBT voltage resistance value; Udc : DC bus voltage; Vpp : peak voltage; The IGBT off process is to apply a reverse voltage to the grid. At this time, the conductive channel in the device will slowly disappear, and the base current will gradually decrease. Finally, the collector emitter voltage of the IGBT is lower than the on voltage, and the IGBT is off. When the IGBT is turned off, the current flowing through the IGBT will generate an instantaneous high voltage [4] in the circuit, which is called the turn off peak voltage of the IGBT, as shown in Fig. 2. If the IGBT has overvoltage breakdown in the circuit, the voltage at the collector port of the IGBT will be higher than the voltage at the time of breakdown, and the collector current will not quickly drop to zero. As a power device, the working environment of IGBT is generally high current and high voltage. If the voltage value exceeds the nominal voltage value of IGBT at this time, there will be a risk of damaging IGBT. Therefore, in practical application, it is necessary to ensure
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Fig. 2. Controller IGBT peak voltage
that the maximum withstand voltage value of IGBT selected by motor controller does not exceed the nominal voltage value of IGBT. The generation of peak voltage is related to the IGBT dynamic converter process, and its value is related to the main circuit of the converter (mainly the stray inductor ESL and the capacitance value of the main capacitor), bus voltage, current flowing through the IGBT, etc. In particular, the design of the main circuit is different, resulting in a big difference in ESL, and the corresponding peak voltage will vary by several times [5]. Under the condition that the main circuit remains unchanged, the peak voltage is also affected by the IGBT collector current iC at the turn-off time. The larger the iC is, the higher the peak voltage is. Therefore, the peak voltage value is generally evaluated at the maximum working current. Considering the different design level of the main circuit and the different working current, in order to ensure the voltage safety, the empirical formula used in general engineering is: VCE = 1.7Udc ∼ 2Udc
(2)
Take a certain electric bus as an example, the rated voltage of the power battery of a pure electric bus (Udc ) was 576 V. The cut-off peak voltage value of the controller IGBT was about 250 V(Vpp ). At the same time, considering the safety allowance was about 170 V. According to the IGBT empirical formula mentioned above, the IGBT voltage resistance value(VCE ) was about 1015 V. The selected controller IGBT nominal voltage was 1200 V. China’s new energy bus power battery rated voltage platform is generally about 500 V-600 V, so China’s new energy bus drive motor controller generally choose the nominal voltage of 1200 V IGBT. 3.2 Selection of Nominal Current The nominal current value of IGBT directly determines the maximum working current of the drive motor controller, and the maximum working current of the drive motor controller directly determines the performance of the drive system. If the nominal current value of the matched drive motor controller is too small, the performance of the drive system cannot be brought into full play and the power performance of the whole vehicle will be affected; If the nominal current of the matching drive motor controller is too large, it will lead to a waste of resources [6]. Therefore, the selection of IGBT nominal current is very important in the matching process of drive motor and drive motor [7].
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At present, our common drive system can be divided into four platforms according to the peak torque value. In the process of daily application, due to the application of IGBT nominal current value of each drive system manufacturer and the different cost of IGBT of each specification, there will be different specifications of IGBT of drive motor controller matched by drive system of different manufacturers and the same platform. As shown in Table 1: Table 1. Corresponding relationship between existing drive system platform and IGBT Drive system platform
Effective value of peak current (Arm)
IGBT specification Manufacturer A
Manufacturer B
Platform 1
350
Single 600A
Single 600A
Platform 2
380
Single 600A
Single 600A
Platform 3
510
Single 800A
Double 600A
Platform 4
640
Single 800A
Double 600A
The actual application of the above drive system will make it difficult for the platform to be completely unified in the application process of the drive system. In order to ensure the platform of the drive system, reduce the cost of the drive system and ensure the output performance of the drive system, it is necessary to analyze the direct relationship between the IGBT specification of the drive motor controller and the maximum allowable current. The IGBT nominal current directly determines the maximum working current of the drive motor controller, and which directly determines the performance of the drive system. If the nominal current value of the matching drive motor controller is too small, it can not fully play the performance of the drive system, affecting the power performance of the vehicle; If the nominal current of the matching drive motor controller is too large, resources will be wasted. Therefore, in the process of driving system matching, the selection of IGBT nominal current is very important. In the matching process of the drive motor controller, the maximum allowable current of the controller IGBT shall not be less than the maximum current of the drive motor, and then the nominal current value of IGBT shall be judged according to the maximum allowable current of IGBT. The nominal current ICn of an IGBT with a nominal voltage of 1200V is generally divided into eight platforms: 400A, 600A, 900A, 1200A, 1600A, 1800A, 2400A and 3600A [8]. The nominal current specifications of IGBT commonly used in electric buses are generally: single 600A, single 800A and double 600A. The double 600A IGBT is two single 600A IGBTs in parallel, and the nominal current is about 1000A. IGBT maximum allowable current and nominal current generally exist the following relationships: √ (3) ICn = 2IC In the formula: ICn is the IGBT nominal current; IC is the maximum allowable current of IGBT.
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The IGBT nominal current and maximum allowable current of electric bus are shown in Table 2: Table 2. IGBT parameter table Specifications
ICn
IC
Single 600A
600A
420
Single 800A
800A
560
Double 600A
1000A
680
Based on the corresponding relationship among igbt specifications, nominal current value and maximum allowable current in Table 2, the IGBT specifications can be matched according to the peak current effective value of the existing drive system platform in Table 1. The IGBT specifications of the re planned drive system are shown in Table 3: Table 3. Reprogramming rear drive system IGBT Drive system platform
Effective value of peak current (Arm)
IGBT specification
Platform 1
350
Single 600A
Platform 2
380
Single 600A
Platform 3
510
Single 800A
Platform 4
640
Double800A
4 IGBT Protection Measures In the practical application of new energy bus, counter EMF should not exceed the maximum allowable value of IGBT. Considering that IGBT still generated peak voltage when it was turned off. Therefore, the maximum counter EMF of the driving motor in the real buses should not exceed 850V. Back EMF is due to the armature winding rotating in the magnetic field when the motor rotates, resulting in power generation effect. According to the electromagnetic law, when the magnetic field changes, the nearby conductor will produce induced electromotive force, and its direction conforms to Faraday’s law and Lenz’s law. It is just opposite to the voltage originally added at both ends of the coil. This voltage is the back electromotive force. The rotor of the motor rotates and cuts the magnetic line of force to produce an induced electromotive force, which is opposite to the applied voltage, so it is called motor back electromotive force [9]. The counter EMF of the driving motor is mainly determined by the motor speed, the magnetic field generated by the rotor magnet, the number of turns of the stator winding and the number of poles of the motor. The corresponding relationship is as follows:
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The corresponding relationship is as follows: Ea =
pNnϕ 60a
(4)
In the formula: Ea is the drive motor counter EMF. p is the drive motor polar number. N is the drive motor armature total conductors. n is the drive motor speed. ϕ is the drive motor magnetic flux at each pole. a is the drive motor branch cable number in pairs. It can be seen from the formula that the only variable after the design of the drive motor is the rotor angular velocity, motorspeed, which is determined by the speed, and the two are proportional, that is, when the speed reaches the maximum, the counter EMF of the drive motor also reaches the maximum [10]. The maximum counter EMF of different motors were not the same, but in practical application, when the speed reached the highest, the maximum counter EMF of some motors would exceed 1200V, at this time, there would be the risk of damage to IGBT of the drive motor controller. Therefore, measures should be taken to protect IGBT to prevent damage to IGBT due to the excessive counter EMF of the drive motor. For the power supply of new energy passenger cars, the whole vehicle takes different protection measures for the drive motor controller. The power supply of the whole vehicle is mainly divided into normal power supply and abnormal power supply. When the new energy bus is powered normally, the common protection measures are to suppress the motor counter EMF. The magnetic field generated by the current part of the motor is offset by the magnetic field generated by the motor’s magnetic steel. Thus, the maximum back potential of the motor can be suppressed to the range that IGBT can bear, so as to achieve the purpose of protecting IGBT [11]. When the power supply of new energy bus is in abnormal state, that is, the high and low voltage of the vehicle cannot be supplied normally, IGBT can be protected in three cases: 1) When the vehicle can normally supply power under low voltage, but cannot normally supply power under high voltage, that is, the vehicle has low voltage and no high voltage. Through IGBT three-phase short circuit, the drive motor UVW three-phase line is directly connected to consume energy, protect the drive motor controller from damage. 2) When the vehicle can be normally powered by high voltage but cannot be normally powered by low voltage, that is, when the vehicle has high voltage and no low voltage. The high voltage is converted to low voltage by means of a device that converts the high voltage into low voltage electricity added to the drive motor controller. Then through IGBT three-phase short circuit, the drive motor UVW threephase line is directly connected to consume energy, Protect the drive motor controller from damage. 3) When the high voltage and low voltage of the vehicle cannot be supplied normally, that is, the vehicle has no high voltage and low voltage. At this point, the counter
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EMF can also be regarded as high voltage. In the same way, IGBT three-phase short circuit is adopted to convert the high voltage into low voltage by adding the high voltage into the drive motor controller, so that the drive motor UVW three-phase line is directly connected to consume energy, Protect the drive motor controller from damage. To sum up, IGBT protection scheme of drive motor controller is shown in Table 4: Table.4. IGBT protection scheme of drive motor controller Vehicle power supply
IGBT protection scheme
1
High voltage and low voltage
The current creates a weak magnetic field that inhibits the back potential
2
Only high voltage
Low voltage power, IGBT three - phase short circuit
3
Only low voltage
High voltage power, IGBT three - phase short circuit
4
No voltage
Counter EMF power, IGBT three - phase short circuit
5 Conclusion Taking the driving system of new energy bus as an example, this paper introduces the working principle of driving motor controller IGBT and the requirements for working environment, and analyzes the influence of driving motor controller IGBT on new energy vehicle. Starting with the protection of IGBT, the relationship between the nominal voltage of IGBT of drive motor controller and the voltage platform of new energy vehicle battery is analyzed, which provides the basis for the selection of IGBT nominal voltage when the drive system of new energy vehicle is matched. By summarizing the drive motor controller IGBT corresponding to the existing drive system platform, the nominal current and maximum allowable current of several common specifications of IGBT for new energy buses and their corresponding relationship are analyzed. Provide certain theoretical support for the selection of IGBT current specification when the drive system is matched, and re plan the specification of IGBT of drive motor controller according to the existing drive system platform. Finally, considering the possible damage of the maximum back EMF to IGBT at the maximum speed of the real vehicle, four protection measures for IGBT are given from the four possible high and low voltage power supply conditions of the whole vehicle. It provides a certain reference for the protection of IGBT of driving motor controller of new energy bus. Acknowledgment. Thank you for the support of the capital science and technology leading talent training project.
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References 1. Tang, R.: Theory and design of modern permanent magnet synchronous motor. Machine Press, Beijing (2016). (in Chinese) 2. Choi, M., et al.: Power cycling test and failure analysis of molded Intelligent Power IGBT Module under different temperature swing durations. Microelectron. Reliabil. 64 (2016) 3. Xia, W.: Research on driving isolation and protection technology of IGBT module. Hefei University of Technology, Hefei (2019). (in Chinese) 4. Liang, S., Wang, X., Hou, K., et al.: Optimization design and test of t-type three-level IGBT driver. Power Electron. Technol. 328(03), 130–133+137 (2020). (in Chinese) 5. Wang, G., Ren, J.: Simulation research on high power class D power amplifier. Electron. Test 430(01), 5–7+25 (2020). (in Chinese) 6. Nakatsu, K., Nishihara, A., Sasaki, K., et al.: A novel direct water and double-sided cooled power module and a compact inverter for electrified vehicles. In: 2013 15th European Conference on Power Electronics and Applications, Lille, France, pp. 1–6 (2013) 7. Zhang, Z.: Research on permanent magnet synchronous motor control and IGBT driving technology of pure electric vehicle. Anhui Polytechnic University, Wuhu (2016). (in Chinese) 8. Zhao, B., Qin, H., Nie, X., et al.: Evaluation of isolated gate driver for SiC MOSFETs. In: 2013 8th IEEE Conference on Melbourne Industrial Electronics and Applications (ICIEA) VIC 19–21, IEEE 2013, pp. 1208–1212, June 2013 9. Liu, J., Cai, W.: Method for reducing EMF harmonics of interior permanent magnet synchronous motors for Vs. Micromotors 6(51), 7–10+15 (2018). (in Chinese) 10. Li, Y., Zheng, Z.: AC motor digital control system. China Machine Press, Beijing (2017). (in Chinese) 11. Zhu, B, Picci, G.: Proof of local convergence of a new algorithm for covariance matching of periodic ARMA models. IEEE Control Syst. Lett. 1(1), 206–211 (2017)
Study on Electromechanical Performance of Factory-Composited Cap and Pin Ceramic and Glass Insulators Hu Zhang(B) , Wenhua Wu, Rui Zhang, Jinxiang Liang, Yujia Gong, Lei Yang, and Sida Xu China Electric Power Research Institute, Wuhan, China {zhanghu,wuwenhua,zhangrui5,liangjinxiang,gongyujia,yanglei, xusida}@epri.sgcc.com.cn
Abstract. The large-scale use of factory-composited cap and pin insulators has effectively alleviated the threat of large-area pollution flashover to the power grid. As a new thing, there is little research on its electromechanical characteristics. To study the electromechanical characteristics of factory-composited cap and pin ceramic and glass insulators, the electric field simulation is carried out by using the finite element method. From the perspective of test, the electrical body resistance test, SF6 puncture withstand test, thermal-mechanical performance test, impulse puncture voltage test and thermal shock test are carried out. The simulation results show that the electric field distribution of factory-composited cap and pin insulator is similar to that of insulator body. The electrical body resistance test, SF6 puncture withstand test, thermal mechanical performance test, temperature test and thermal shock test are similar to those of uncoated insulators. The characteristics of impulse puncture voltage test are obviously different from that of insulator body. The amplitude voltage of impulse puncture voltage test in air suitable for cap and pin insulator is too high to effectively detect defective RTV coated products. The research can provide a reference for the design and maintenance of factorycomposited cap and pin insulators. Keywords: RTV coating · Cap and pin ceramic insulator · Cap and pin glass insulator · Factory-composited · Electromechanical performance
1 Introduction Cap and pin ceramic and glass insulators are widely used in UHV transmission lines because of their excellent aging resistance of inorganic materials. Due to the hydrophilicity of the insulation surface, when it’s seriously polluted and in the harsh environment such as fog, dew and drizzle, it’s easy to cause the flashover accident of high voltage transmission lines [1–3]. RTV has excellent hydrophobicity, hydrophobic mobility and recovery characteristics, coating it on the surface of ceramic and glass insulators can greatly improve its pollution flashover voltage. Therefore, coating RTV on the surface © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 886–896, 2022. https://doi.org/10.1007/978-981-19-1870-4_93
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of cap and pin ceramic and glass insulator has become a very effective anti-pollution flashover measure [4–6], so that the cap and pin insulator coated with RTV not only has good electromechanical characteristics, but also has good hydrophobic characteristics, which has been widely used in the construction and operation of power grid. Some researchers also points out that RTV with excellent performance can become a part of the permanent design of substation equipment [7]. At present, RTV coating methods mainly include spraying, brushing and dip coating [8, 9]. On site coating RTV construction mainly adopts spraying and brushing technology, which has the advantages of great flexibility, but also has problems such as large coating loss, environmental pollution, great influence by environmental and climatic conditions, and difficult quality assurance. In reference [10], the researchers pointed out that RTV coatings of operating insulators had a high spraying defect rate after investigated the application of RTV coatings in Jiangsu province. Therefore, the factory dip coating RTV with stable and controllable production conditions and consistent coating effect has become the best choice. This kind of insulator with RTV coating formed by factory-composited technology is called factory-composited insulator. Since the Lingzhou–Shaoxing UHV project in 2014, factory-composited insulators have been widely used in ±800 kV and ±1100 kV UHV projects. By the beginning of 2015, about 1 million factory-composited insulators have been put into operation in Italy and the United States [11, 12]. Large-scale use of factory-composited insulators in transmission lines effectively alleviates the threat of large-scale pollution flashover to the power grid. At the same time, as a new thing, there is little research on the electromechanical characteristics of factorycomposited insulators. At present, it mainly focuses on how to improve the performance of RTV coatings. The researchers in reference [13], starting from the matrix material, filler, additives and other related aspects of RTV anti-pollution flashover coatings, the ideas of improving RTV performance were studied. The other researchers studied the performance changes of RTV coatings after aging, and put forward the evaluation method of RTV aging [14–17]. Relevant studies have also pointed out that RTV coating will affect the steep wave impact performance of cap and pin insulators to a certain extent [18, 19]. However, there are few studies on the influence of RTV coating on its electromechanical characteristics, especially for the factory-composited cap and pin insulator. The existing research does not involve the research on its electromechanical characteristics such as electrical body resistance test, SF6 puncture withstand voltage and thermal mechanical performance. In order to study the related electromechanical performance of factory-composited cap and pin insulators, and to explore whether RTV coating will bring unpredictable risks to insulators, some representative test items are selected for comparative analysis and test. And then the main electromechanical parameters and performances of this type of insulator are obtained according to the national standard, power industry standard, enterprise standard and related test methods of cap and pin ceramic and glass insulators [20–24]. Including electrical body resistance test, SF6 puncture withstand test, thermal mechanical performance test, impulse puncture test in air and thermal shock test. The research can provide a reference for the design of factory-composited insulators and the research of related operation performance.
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2 Sample Information The samples are 550 kN cap and pin ceramic and glass insulators which commonly used in UHV projects, and their insulation surface is coated with 0.3 mm RTV coating. Ceramic insulators, glass insulators and RTV coatings used are the same batch of products from UHV qualified suppliers. The structure diagram of the sample is shown in Fig. 1, and the related specific parameters are shown in Table 1.
(a) Factory-composited cap and pin ceramic insulator
(b) Factory-composited cap and pin glass insulator
Fig. 1. The structure diagram of factory-composited cap and pin ceramic and glass insulators
Table 1. The parameters of factory-composited cap and pin ceramic and glass insulators Parameter
Factory-composited cap and pin Factory-composited cap and pin ceramic insulator glass insulator
Type
U550BP/240T
U550BP/240
Structure height Disc diameter Creepage distance
240 mm
240 mm
400 mm
360 mm
635 mm
635 mm
SFL
550 kN
550 kN
Impulse puncture value
145 kV
145 kV
Electrical body resistance 2.352 × 1010
4.182 × 109
SF6 puncture voltage
225 kV
240 kV
RTV coating thickness
0.3 mm
RTV coating area
20 mm wide annular uncoated area shall be reserved at the surface of insulation near the cap, the vertical surface on the inner side of insulating parts adjacent to the pin shall be uncoated, and other surfaces of insulation parts shall be covered with RTV coating
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3 Electric Field Simulation of Factory-Composited Cap and Pin Ceramic and Glass Insulators 3.1 Simulation Model Considering the influence of RTV coating on the electric field distribution of cap and pin ceramic and glass insulators, the simulation models are set into two categories: uncoated and coated. RTV coating thickness and coating area are shown in Table 1. The insulator design drawing is imported into the drawing software, the RTV coating is generated by shell extraction, and then imported into the finite element calculation software to establish a two-dimensional model of the single insulator. On the basis of improving the calculation accuracy and reducing the calculation amount, the calculation model is consistent with the original design scheme to the greatest extent. Under DC field, the displacement current can be ignored, and the electric field is distributed according to conductivity or resistivity. The interface conditions of different materials are degraded from normal full current continuity to normal conduction current continuity, and the insulator electric field shows the characteristics of constant current field. In the solution domain, the potential distribution of the DC insulator satisfies the Eq. (1) [25] ∂ϕ ∂ ∂ϕ 1 ∂ ρ + ρ =0 (1) r ∂r ∂r ∂z ∂z On the boundary between the high voltage terminal and the ground terminal, there are ϕ|l0 = f0 (p)
(2)
On the axis of symmetry, there are ∂ϕ ∂r = 0 Using finite element method to solve the following equations: ⎧ 2 1 1 2 ⎪ 2 ⎪ ⎪ F(ϕ) = ρ(∇ϕ) d+ ρ ϕ −f2 (ϕ) d ⎪ ⎪ 2 2 ⎪ =L1 ⎨ δF(ϕ) = 0 ⎪
⎪ ⎪ ϕ l = f0 (p) ⎪ 0 ⎪ ⎪ ⎩
ϕ L2 = 0
(3)
(4)
In which ϕ is potential; ρ is the conductivity of the medium; r and z are the coordinates in the cylindrical coordinate system; L 1 represents the boundary, L 2 is the symmetry axis, and l0 is the boundary of the high-voltage end or the low-voltage end. Ω indicates the field.
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3.2 Material Parameters and Boundary Conditions As the finite element calculation is carried out by the conduction current field method, only the resistivity or conductivity of the model assembly needs to be defined. The material resistivity of each component of insulators are shown in Table 2. The model ignores the influence of high voltage bus on insulator electric field and potential distribution. The maximum operating voltage of UHV DC system is 816 kV, and the voltage on single insulator is 11.657 kV based on the calculation of 70 units insulators. In the calculation domain, except the symmetry axis of the two-dimensional insulator model, all other boundaries are set to zero potential. Table 2. The parameters of simulation material Material
Resistivity/(·mm)
Ceramic/glass
1.6 × 1014 /7.6 × 1014
Cement
6
Steel
9.78 × 10–8
RTV coating
2 × 1012
Air
5 × 1013
Zinc ring and sleeve
5.19 × 10–8
Pin shim
1 × 108
Cap washer
1 × 1010
The model ignores the influence of high voltage bus on insulator electric field and potential distribution. The maximum operating voltage of UHV DC system is 816 kV, and the pressure on a single insulator is 11.657 kV based on the calculation of 70 units insulators. In the calculation domain, except the symmetry axis of the two-dimensional insulator model, all other boundaries are set to zero potential. 3.3 Simulation Results The electric field intensity calculation results of factory-composited insulators are shown in Table 3, and the electric field distribution of ceramic and glass insulators with or without RTV coating are shown in Figs. 2 and 3 respectively. The simulation results show that RTV coating has no obvious effect on the maximum electric field intensity inside the insulator. With or without RTV coating, the maximum electric field intensity in ceramic insulators is 928 kV/m, which are located at the heads of ceramic pieces respectively. RTV coating has no obvious effect on the whole electric field distribution of ceramic insulators, and the electric field distribution characteristics of factory-composited glass insulators are similar. the maximum electric field intensity inside glass insulators is 1390 kV/m with or without RTV coating.
Study on Electromechanical Performance of Factory-Composited Cap Table 3. The electric field simulation results Insulator material
Location
Electric field intensity/(kV/m) Uncoated
Coated
Ceramic
The maximum electric field intensity inside insulator
928
928
Pin edge
514
515
Glass
Cap edge
54
54
The maximum electric field intensity inside insulator
1390
1390
Pin edge
567
567
Cap edge
152
153
(a) Uncoated
(b) Coated
Fig. 2. The electric field distribution cloud diagram of ceramic insulator
(a) Uncoated
(b) Coated
Fig. 3. The electric field distribution cloud diagram of glass insulator
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4 Test and Analysis of Factory-Composited Ceramic and Glass Insulators 4.1 Electrical Body Resistance Test According to the standard procedure [22], the electrical body resistance R120 of 10 insulators were measured at (120 ± 2) °C. In order to avoid the error caused by surface current, conductive coating or shield should be used as protective electrode to bypass the surface current. The measurement shall be made at least 2 h after the iron cap reaches the specified temperature. Record the current value after the voltage is applied for at least 15 min. The electrical body resistance is the average of three readings of each insulator. The test photo is shown in Fig. 4. Relevant test data are shown in Table 4. The test results show that the electrical body resistance value of the disc insulator coated with RTV has a certain difference compared with the insulator body, but the overall difference is within the standard acceptable judgment range (0.5–2.0) R120 , so it can be considered that RTV coating has no obvious influence on the electrical body resistance value of the insulator.
(a) Factory-composited cap and pin ceramic insulator
(b) Factory-composited cap and pin glass insulator
Fig. 4. The test picture of electrical body resistance
Table 4. The electrical body resistance test results Sample
Electrical body resistance measurements R120 /
Cap and pin ceramic insulator
2.352 × 1010
Factory-composited cap and pin ceramic insulator
2.191 × 1010
Cap and pin glass insulator
4.182 × 109
Factory-composited cap and pin glass insulator
4.332 × 109
4.2 SF6 Puncture Withstand Test The test is carried out in SF6 gas medium, with pressure value of 0.25–0.28 MPa and temperature of 26–29 °C. Apply a positive DC voltage to the insulator steel foot, and
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raise it to the specified SF6 puncture withstand voltage as soon as possible, and keep it for 20 min. In this test, the factory-composited ceramic and glass insulators were tested successively. The applied voltages were ceramic insulator +225 kV and glass insulator +240 kV, and all the samples were tolerant, without any breakdown or explosion. Therefore, the SF6 puncture characteristics of factory-composited ceramic and glass insulators has no significant influence. 4.3 Thermal Mechanical Performance Test As the glass insulator is subjected to mechanical failure load test, only tensile load is applied, the influence of coating on the performance can be ignored. Therefore, in this test, only the thermal mechanical performance of ceramic insulators is carried out. Insulators shall be subjected to 4 times 24 h cold and hot cycles, and tensile load shall be applied at the same time, which shall be kept between 60% of the specified electromechanical failure load. Every 24 h, the cycle starts from room temperature, then cools to −(40 ± 5) °C and then heats to +(40 ± 5) °C. Temperature difference between cold and hot is not less than 80 K. Each temperature cycle lasts at least 4 h at the highest and lowest temperature levels. After four 24 h cold and hot cycles, the samples are applied with a power frequency voltage of 50 kV one by one, and a tensile load is applied between metal accessories at the same time until the samples are damaged. Table 5. Thermal mechanical performance test results Sample
Electromechanical failure load /kN
Failure form
Cap and pin ceramic insulator
656,654,653,662,658 667,658,660,665,654
Pin extended
Factory-composited cap and pin ceramic insulator
658,662,650,657,653 656,663,659,662,651
Pin extended
It can be seen from Table 5 that all failure forms are pin extended. There is little difference between the performance form and the failure form of the thermal-mechanical performance test of the insulator body. The mean electromechanical failure load of the cap and pin ceramic insulator without RTV coating is 659.7 kN, and the standard deviation is 4.74 kN; The average value of electromechanical failure load of factory-composited ceramic insulators is 657.1 kN, and the standard deviation is 4.63 kN, which has little difference and is close to each other. Therefore, RTV coating and coating thickness have no obvious influence on the thermo-mechanical performance and electromechanical failure load performance of cap and pin insulators. 4.4 Impulse Puncture Test in Air According to relevant insulator standards, the amplitude voltage of impulse puncture test in air is (2.8–3.08) p.u. Therefore, in this test, four different voltage gradients of 2.8 p.u., 2.5 p.u., 2.2 p.u. and 2.0 p.u. are selected for experimental analysis.
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Ten samples of ceramic insulators and glass insulators coated with RTV coatings were tested at four different voltage levels according to the test procedures specified in the standard. The test results are shown in Table 6. Table 6. The impulse puncture voltage test results Impulse voltage amplitude
Test results Ceramic insulator
Glass insulator
2.0 p.u
No puncture
No puncture
2.2 p.u
1 sample puncture
1 sample puncture
2.5 p.u
2 samples puncture
1 samples puncture
2.8 p.u
2 samples puncture
3 samples puncture
From the test results, it can be found that the probability of factory-composited insulators passing the impulse puncture voltage test in air changes obviously with the increase of impulse puncture amplitude. It is too strict to require factory-composited ceramic and glass insulators by the amplitude voltage of impulse puncture test in air. The voltage amplitude cannot guarantee that products with good insulation strength in the insulator body will not be judged as unqualified, and the purpose of effectively detecting defective products cannot be achieved. 4.5 Thermal Shock Test Samples are heated to 125 °C by oven, and then quickly and completely immersed in water at 20 °C, and the insulators are kept in water for 2 min. The results showed that no glass parts are damaged, and there’s no significant difference between the thermal shock test of factory-composited glass insulators and the glass insulators without RTV coating. During the peeling test of factory-composited insulators after the thermal shock test, it is also found that different manufacturers coatings show different differences, as shown in Fig. 5. After the thermal shock test of some samples, the adhesion of surface coating disappeared completely. It is suggested that the adhesion of coating after thermal
(a) Good adhesion performance
(b) Poor adhesion performance
Fig. 5. Photos of adhesion inspection after thermal shock test
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shock test can be regarded as one of the criteria for the acceptance of factory-composited insulators.
5 Conclusions In this paper, in order to analyze the electromechanical characteristics of factorycomposited insulators, the electric field distribution is simulated and calculated, and tests such as electrical body resistance test, SF6 puncture withstand test, thermal mechanical performance test, impulse puncture test in air and thermal shock test are carried out. The test results of main electromechanical characteristics of factory-composited ceramic and glass insulators are analyzed, and the following conclusions are obtained: (1) The overall electric field distribution of factory-composited ceramic and glass insulators is similar to that of ceramic and glass insulators without RTV coating, with no obvious change. (2) The impulse puncture characteristics of factory-composited ceramic and glass insulators are obviously different from those of insulator bodies, and the amplitude voltage applicable to impulse puncture test in air of ceramic and glass insulators bodies is too high, which cannot achieve the purpose of effectively detecting defective products. (3) The electrical body resistance test, SF6 puncture withstand test, thermal mechanical performance test and thermal shock test of insulators are not significantly affected, the main electromechanical parameters are relatively stable, and RTV coatings do not bring unpredictable risks to insulators. (4) During the test, it is found that RTV coatings provided by different suppliers have obvious differences in some tests, such as peel test after thermal shock test. Therefore, this test item can be considered as one of the indexes to judge the performance of factory-composited insulator coatings.
References 1. Wu, G.Y.: Development of China’s insulator and the issue should be considered. Insulat. Surge Arresters 2, 7–10 (2010). (in Chinese) 2. Lv, Y.K., Zhao, W.P., Pang, G.L.: Simulation of contamination deposition on typical shed porcelain and composite insulators. Trans. China Electrotech. Soc. 33(01), 209–216 (2018) (in Chinese) 3. Zhang, Z.J., Zhang, D.D., Liu, X.H.: Effect of pollution compositions on the AC flashover performance of LXY4–160 suspension glass insulator string. Trans. China Electrotechn. Soc. 29(4), 298–305 (2014). (in Chinese) 4. Jia, Z.D., Fang, S., Gao, H.F.: Development of RTV silicone coatings in China: overview and bibliography. IEEE Electr. Insul. Mag. 24(2), 7–10 (2008) 5. Marzinotto, M., Mazzanti, G., Cherney, E.A.: An innovative procedure for testing RTV and composite insulators sampled from service in search of diagnostic quantities. IEEE Electr. Insul. Mag. 34(5), 27–28 (2018)
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6. Chen, Y., Cui, J.L., Yao, W.J.: Analysis on present status and technology policy of anticontamination flashover in power system. Electric Power 37(2), 97–101 (2004). (in Chinese) 7. Su, Z.Y., Li Q.F.: Historical review and summary on measures against pollution flashover occurred in power grids in China. Power Syst. Technol. 34(12), 124–130 (2010). (in Chinese) 8. He, L.L.: Simulation Analysis and Experimental Study of RTV Coatings Sprayed on Surface of Porcelain Insulators. North China Electric Power University, Beijing (2019).(in Chinese) 9. Zhang, C.X., Zhang X.Y., Li H.M.: Study on automatic dip-coating technology of RTV antifouling flash coating. Silicone Mater. 32(1), 49–53 (2018). (in Chinese) 10. Bi, X.T., Gao, S., Liu, Y.: Performance analysis of RTV coatings on insulators with different service years in Jiangsu Province. Insulat. Surge Arrest. 5, 219–224 (2020). (in Chinese) 11. Marzinotto, M., Cherney, E.A., Mazzanti, G.: RTV pre-coated cap-and-pin toughened glass insulators a wide experience in the Italian overhead transmission system. In: Proceedings of IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), pp.150–153 (2015) 12. Chen, Y., Wu, G.Y., Ye, T.L.: Development of factory-composited insulators for improving UHV grid configuration quality. Electric Power. 50(8), 1–15 (2010). (in Chinese) 13. Dou, R.T., Leng, X.T., Gu, F.: Research on the status of RTV anti-pollution flashover coating. New Chem. Mater. 46(5), 32–34 (2019). (in Chinese) 14. Jia, B.Y., Liu, J., Chen, C.: Aging phenomena and condition assessment method of RTV anti-pollution flashover coating. High Volt. Apparatus. 55(9), 126–133 (2019). (in Chinese) 15. Yoshimura, N., Kumagai, S., Nishimura, S.: Electrical and environmental aging of silicone rubber used in outdoor insulation. IEEE Trans. Dielectr. Electr. Insul. 6(5), 632–650 (1999) 16. Su, H., Jia, Z., Guan, Z.: Durability of RTV-coated insulators used in subtropical areas. IEEE Trans. Dielectr. Electr. Insul. 18(3), 767–774 (2011) 17. Gao, H., Jia, Z., Guan, Z.: Investigation on Yield-aged RTV-coated insulators used in heavily contaminated areas. IEEE Trans. Power Delivery 22(2), 1117–1124 (2007) 18. Deng, T., Yao, Y.M., Liang, X.D.: Application of pre-coated RTV insulators in UHV OHLs and steep-front impulse voltage tests. In: Proceedings of IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp.1–5 (2016) 19. Liu, J., Qi, P.S., Zhang, M.Z.: Analysis on abnormal breakdown problem of RTV composite glass insulator under steep slope test. Insulat. Surge Arresters 1, 201–206 (2019). (in Chinese) 20. DL/T 627:2018. Room Temperature Vulcanized Silicon Rubber Anti-Pollution Coating for Insulators. China Electric Power Press. Beijing (2018). (in Chinese) 21. GB/T 20642:2006. Impulse Puncture Test in Air on Insulators for Overhead Lines. Standards Press of China. Beijing (2006). (in Chinese) 22. GB/T 19443:2017. Insulators for Overhead Lines with a Nominal Voltage Above 1500V— Ceramic or Glass Insulator Units for d.c. Systems—Definitions, Test Methods and Acceptance Criteria. Standards Press of China. Beijing (2017). (in Chinese) 23. Su, Z.Y.: Impulse puncture tests in air applied in line insulator detecting test. Power Syst. Technol. 38(7), 1798–1805 (2014). (in Chinese) 24. Liu, Y.P., Li, L, Zhang, M.J.: Research status of interface detection for composite cross-arm. Trans. China Electrotech. Soc. 35(2), 408–424 (2020). (in Chinese) 25. Wu, W.H., Zhang, R, Yuan, J.C.: Distribution of electric field and optimization of antipollution flash coating parameters for factory-composited insulators. Electric Power. 52(1), 88–95 (2019). (in Chinese)
Model Simulation of Lithium-Sulfur Battery Based on Different Discharge Rates and Sulfur Content Yangyang Liu1,2 , Chenglin Liao1,2(B) , and Wenjie Zhang1,2 1 Key Laboratory of Power Electronics and Electric Drives, Institute of Electrical Engineering,
Chinese Academy of Sciences, Beijing 100190, China 2 University of Chinese Academy of Sciences, Beijing 100190, China
[email protected]
Abstract. Different discharge rates and sulfur content have a great impact on battery performance. Therefore, this paper uses the finite element software comsol to simulate the lithium-sulfur battery model. Change the battery discharge rate and sulfur content parameters for simulation. The simulation results show that there are two voltage platforms in the low discharge rate simulation, while only one voltage platform appears in the high discharge rate; choosing the appropriate discharge rate is very important to exert the battery performance; higher sulfur content will increase the battery capacity accordingly, thereby affecting Battery discharge time. Through this simulation, it has great guiding significance for the actual selection of the appropriate discharge rate and sulfur content of the lithium-sulfur battery. It laid the foundation for accelerating the commercialization of lithium-sulfur batteries. Keywords: Lithium-sulfur battery · Model simulation · Sulfur content · Discharge rate
1 Introduction With the development of electronic products and new energy vehicles, the demand for energy storage is getting higher and higher, so the research of new generation batteries with long range, good safety and reliability has become a hot spot. Lithium-sulfur batteries generally use lithium metal as the negative electrode and sulfur or sulfur compounds as the positive electrode. With high theoretical energy density (1675 mAh/g), low cost and environmental friendly features [1], it has become a hot spot for lithium secondary battery research. However, lithium-sulfur batteries have corresponding technical development problems, such as the shuttle effect mechanism due to the dissolution of polysulfides, which leads to capacity degradation, low coulombic efficiency, and high self-discharge rate [2] and seriously hinders the commercialization of lithium-sulfur batteries. Currently, most researchers have worked on suppressing the shuttle effect or increasing the sulfur loading of cathode materials, for example, Donghai Liu et al. [3] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 897–905, 2022. https://doi.org/10.1007/978-981-19-1870-4_94
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proposed that the most promising method to suppress the shuttle effect is to use catalysts to promote the conversion of soluble polysulfide intermediates to solid Li2 S2 /Li2 S to reduce their dissolution in the electrolyte; Priyanka Bhattacharya et al. [4] showed the possibility of achieving high sulfur loading and excellent electrochemical performance by using dendrimers as functional binders. Most of the studies were done to improve the performance of lithium-sulfur batteries by improving the cathode material, and there is little research literature on the simulation of changing cell parameters, for example, Mahmoudreza Ghaznavi et al. studied different discharge currents, cathode conductivity [5], and also diffusion coefficient as well as cathode thickness for simulation [6]. The cathode monomeric sulfur undergoes a complex series of compositional and structural changes during the discharge of lithium-sulfur batteries to form soluble polysulfide intermediates [7]. Meanwhile, some studies have revealed the complexity of sulfur redox, proposing different reduction mechanisms that lack direct and clear experimental proof [8]. In this paper, we investigate the effect of different discharge multipliers on the discharge voltage plateau and the effect of different sulfur contents on the battery capacity. The battery simulation model is mainly developed by finite element comsol software to vary the discharge multiplier and sulfur content, and the corresponding performance effects of lithium-sulfur batteries are analyzed based on the simulation results. To a certain extent, it contributes to the understanding of the mechanism of shuttle effect of lithium-sulfur batteries and the study of polysulfide blockage of separator.
2 Electrochemical Reaction of Lithium-Sulfur Battery Lithium-sulfur batteries are different from lithium-ion batteries in the charge-discharge process of lithium ion deintercalation reactions. The charge-discharge reaction process of lithium-sulfur batteries is mainly a multi-electron, multi-step redox reaction, which mainly includes the porous reaction of lithium metal, electrolyte, and sulfur. The general reaction formula is shown in formula (1). S8 + 16Li+ + 16e− ⇔ 8Li2 S
(1)
Elemental sulfur cathodes have received widespread attention due to their high specific energy. Theoretically, the complete reduction of elemental sulfur molecules (S8 ) to divalent sulfide ions (S2− ) can release a discharge capacity of 1675 mAh/g, which is approximately 10 times the discharge capacity of transition metal oxides in lithium ion batteries. There are two main discharge platforms in the discharge process of lithium-sulfur batteries: the high-voltage discharge platform is 2.3–2.1 V, which forms high-priced lithium polysulfide (S2− n , 5 ≤ n ≤ 8) soluble in electrolyte; the low-voltage discharge platform is 2.1–1.7 V, which is expensive Lithium polysulfide is reduced to low-priced polysulfide (S2− n , 3 ≤ n ≤ 4) which is soluble in electrolyte and Li2 S2 and Li2 S insoluble in electrolyte [9]. The direction of the arrow in Fig. 1 indicates that different polysulfides are formed at each stage, and they occupy the dominant position in the reaction products at this time.
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Fig. 1. Polysulfide generation process
At the beginning of the reaction, elemental sulfur is reduced to Li2 S8 , as shown in formula (2). S8 + 2e− + 2Li+ Li2 S8
(2)
When the battery is discharged, the initial product Li2 S8 is formed. Subsequently, lower molecular chains of Li2 S4 , Li2 S2 and Li2 S molecules are generated. It is known that Li2 S has electrochemical reversibility, so the solubility of short-chain polysulfides in the electrolyte has become the main factor limiting the utilization of elemental sulfur. Generally, lithium-sulfur batteries are discharged under low-rate conditions and can output a capacity of 1256 mAh/g (3/4 of the theoretical capacity of elemental sulfur). The oxidation reaction formula of lithium metal on the surface of the negative electrode during battery discharge is as follows: Li Li+ + e−
(3)
Assuming that during the discharge process, elemental sulfur is initially in a solid state, dissolved in the electrolyte and undergoes the following electrochemical reaction: 1 1 S8(l) + e− S2− 2 2 8
(4)
3 2− S + e− 2S2− 6 2 8
(5)
3 2− S 2 4
(6)
1 2− S + e− S2− 2 2 4
(7)
1 2− S + e− S2− 2 2
(8)
− S2− 6 +e
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3 One-Dimensional Electrochemical Model of Lithium-Sulfur Battery The existing lithium-ion battery modeling methods are mainly divided into three categories: numerical models, electrochemical models, and equivalent circuit models. Since the reaction mechanism of lithium-sulfur batteries is more complicated than that of lithium-ion batteries, it is very difficult to establish a full-order electrochemical model for lithium-sulfur batteries. Most electrochemical models based on certain assumptions or simplified links are established. In lithium-sulfur batteries, due to the complex reaction mechanism in the positive electrode, the discharge performance largely depends on many battery design parameters [10]. Therefore, the simplified geometric structure of the lithium-sulfur battery simulation model is shown in Fig. 2. The model area includes a lithium metal negative electrode, a separator, and a porous positive electrode composed of carbon and sulfur.
Fig. 2. Simplified model geometry of lithium-sulfur battery simulation
The electrochemical reaction process of a lithium-sulfur battery is simplified as the following processes: the diffusion and precipitation-dissolution of lithium ions and polysulfide ions in the electrolyte; the formation of the potential in the positive and negative electrodes and the electrolyte; the electrochemical kinetics process of the positive electrode and the kinetic process of lithium metal in the negative electrode. During the internal reaction of the lithium-sulfur battery, the elemental sulfur of the positive electrode is converted into polysulfide ions, and then the active lithium metal of the negative electrode is reacted in the electrolyte through the separator, and the negative electrode and the positive electrode have a certain thickness. 3.1 Matter Transport Equation In the lithium-sulfur battery model porous medium, the mass conservation equation 2− 2− 2− 2− − of the substance (Li+ /S8(l) /S2− 8 /S6 /S4 /S2 /S /A , the same below) is shown in Eq. (9). ∇Ji + u∇Ci = Ri
(9)
Among them, Ji represents current density, u represents the convection velocity of the electrolyte, Ci is the concentration of the substance, and Ri is based on the rate of the
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production or consumption of the substance in the reaction. The corresponding material flux expression in the dielectric is shown in Eq. (10). Ji = −Di ∇Ci − zi um,i FCi ∇φl
(10)
where Di is the diffusion coefficient of each substance in the porous medium, um,i is migration rate, φl is the liquid phase potential, zi is number of electrons in a chemical reaction (The parameters in the table and in the table are from the comsol model) (Table 1). Table 1. Diffusion coefficients and reference concentrations Substances (i)
Zi
Di /(m2 .s−1 )
Ci,ref /(mol • m−3 )
Li+
+1
0.88E−12
1001
S8(l)
0
0.88E−11
19
S2− 8 S2− 6 S2− 4 S2− 2 S2−
−2
3.5E−12
0.18
−2
3.5E−12
0.32
−2
1.75E−12
0.02
−2
0.88E−12
5.23E−7
−2
0.88E−12
8.27E−10
A−
−1
3.5E−12
1000
3.2 Proton and Electron Conservation Equation The current density of the liquid phase is obtained by multiplying the flow of each charged particle by the charged charge as shown in Eq. (11): il = F zi Ji (11) i
According to the law of conservation of mass of chemical reactions, the balance equation of the concentration of substances in the dielectric of lithium-sulfur batteries is shown in Eq. (12). zi Ci = 0 (12) i
3.3 Electrochemical Kinetic Equation The current density of the electrochemical reaction of substances in the lithium-sulfur battery at the solid/liquid interface is given by the Butler–Volmer equation as shown in
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Eq. (13). iloc
Ci νi αa Fηref αc Fηref Ci −νi − ) = i0,ref ( exp exp − Ci,ref RT Ci,ref RT i
i
(13) where Ci,ref is the reference concentration of the substance, R is the gas constant, T is the temperature, ηref is the reference overpotential, αa is electrochemical reaction anode transfer coefficient, and αc = n − αa is electrochemical reaction cathode transfer coefficient. The reaction overpotential is ηref = φs − φl − Eeq
(14)
η is the reaction overpotential, φs is the solid-phase potential, and φl is the liquid-phase potential,Eeq is the equilibrium potential.
4 Simulation Analysis of Kinetic Model of Lithium-Sulfur Battery Broadening the working range of battery discharge current is one of the important goals of battery research. For example, electric vehicles require particularly high current rates. In addition, the battery’s discharge voltage plateau and its cyclic performance strongly depend on the current rate during operation. Therefore, it is necessary to study the model’s response to a certain range of applied current. The battery voltage simulation results for different current discharge rates are shown in Fig. 3.
Fig. 3. Potential variation curves for different discharge multipliers
When the lithium-sulfur battery simulation is performed with the three lower discharge currents of 0.02 C, 0.05 C and 0.1 C, the battery simulation voltage curve shows two voltage platforms, and there is a slight potential offset at the junction of the high platform and the low platform. These three low discharge current simulation curves have similar shapes. The similarity of the simulation curves shows that the kinetic principle of the chemical reaction of the battery is almost the same at these low discharge rates. Taking into account the potential drop caused by the resistivity of the positive electrode
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and the electrolyte when the battery is discharged, compared to the total potential drop of the battery, it can be concluded that the kinetics of the chemical reaction that occurs during the battery discharge leads to the main conductive potential decline. When the discharge current rate increases to 0.1 C, the concentration of high-valent 2− sulfur compounds (S8(l) , S2− 8 and S6 ) as the intermediate product of the chemical reaction decreases more in the second stage than in the first stage as the reaction progresses, possibly because the second stage consumes more Reaction material. Therefore, when the reaction rate of the low-valent sulfur compound reaches a certain height and before 2− 2− Li2 S precipitation begins, the low-valent sulfur compound (S2− 4 /S2 /S ) may form a higher concentration. This series of reactions resulted in a sharp valley transition between the two voltage plateaus. When the solid elemental sulfur in the electrode is consumed, the concentration of sulfide ions in the electrolyte suddenly drops, and the current generated by the reaction also drops. The chemical reaction that occurred quickly reduced 2− almost all S2− 8 in the electrolyte. As the reaction proceeds, the S6 reduction reaction becomes the dominant reaction in the system, and at the same time low-valent sulfur compounds are produced. In the second stage of the reaction, when Li2 S precipitation begins, the concentration of S2− in the electrolyte decreases, resulting in a sharp increase in the rates of the latter two reactions. Once all the sulfur compounds are reduced, the electric potential drops suddenly. For discharge currents of 0.2 C and higher, the initial solid elemental sulfur dissolves too slowly in the electrolyte, and it is impossible to maintain a constant concentration of elemental sulfur in the electrolyte solution in a short period of time[5]. Model simulations are carried out according to the changes in the potential of different concentrations of sulfur in the positive electrode, that is, the concentration of elemental sulfur in the positive electrode is 15 mol/m3 , 20 mol/m3 , 30 mol/m3 , 45 mol/m3 , 90 mol/m3 , respectively. The simulation result is shown in the Fig. 4.
Fig. 4. Variation of potential corresponding to different concentrations of monomeric sulfur substances
It can be seen from Fig. 4(a) that at a certain discharge rate, with the increase of the liquid phase S8 concentration, the battery capacity becomes larger and larger, resulting in longer discharge time and strong battery life. When a lithium-sulfur battery is discharged, a series of polysulfur material reactions occur inside it. When the initial
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concentration of the solid phase S8 increases, the concentration of the liquid phase S8 dissolved in the electrolyte increases correspondingly, and the produced S2− 6 and 2− S4 increase, thereby accelerating the production of substances Li2 S6 and Li2 S4 ; the high-valent polysulfide reaction forms a high-voltage discharge platform. While Li2 S6 and Li2 S4 are produced in large quantities, the chain reaction proceeds accordingly to 2− ions; the ions react with Li+ of the negative electrode through the produce S2− 2 and S separator, so Li2 S2 and Li2 S gradually begin to precipitate near the positive electrode and form a low-voltage discharge platform. Increasing the concentration of the solid phase S8 will increase the concentration of substances produced in each link of the chain reaction, and increase the precipitation of the final product Li2 S of the reaction, thereby increasing the battery capacity. Although increasing the proportion of elemental sulfur in the volume fraction of the positive electrode can increase the battery capacity, the actual volume fraction of elemental sulfur in the positive electrode is less than 60%, which restricts the development of lithium-sulfur batteries. It can be seen from Fig. 4(b) that when the concentration of elemental sulfur is 90 mol/m3 , the potential difference is increased compared to 15 mol/m3 ; comparing 20 mol/m3 , 30 mol/m3 , and 45 mol/m3 , it is found that although the concentration of elemental sulfur gradually increases, the initial potential is different Not big; it shows that increasing the concentration of elemental sulfur substances by a certain value can increase the initial potential value.
5 Conclusion According to the different discharge rates, the electrochemical reactions related to the discharge reaction can occur at the same time or at different times. The electrochemical reaction produces a discharge voltage platform at the same time; two discharge voltage platforms do not occur at the same time. When discharging at a low discharge rate, both platforms exist. When the battery is discharged, the positive electrode will eventually produce precipitation Li2 S, and at the same time produce irreversible Li2 S, so that the sulfide ions are reduced, resulting in the loss of battery capacity; when the proportion of sulfur content increases to a certain level, the battery capacity will be increased accordingly. Choosing the appropriate sulfur concentration will make the battery Give full play to its effectiveness. Most of the factors in the battery reaction, such as the insulating properties of sulfur, are ignored in the model. In future research, the simulation model needs to continue to be modified. Acknowledgments. Authors are gratefully acknowledging the support by the Major Science and Technology Innovation Project of Shandong Province (2019TSLH0703) and the National Natural Science Foundation of China (52077208).
References 1. Yang, R., Deng, K., Liu, X., Qu, Y., Lei, J., Ren, B.: Research status of lithium-sulfur battery cathode composite materials. Prog. Chem. Ind. 34(05), 1340–1344 (2015). (in Chinese) 2. Knap, V., Stroe, D.I., Swierczynski, M., et al.: Investigation of the self-discharge behavior of lithium-sulfur batteries. J. Electrochem. Soc. 163(6), A911 (2016)
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3. Liu, D., Zhang, C., Zhou, G., et al.: Catalytic effects in lithium–sulfur batteries: promoted sulfur transformation and reduced shuttle effect. Adv. Sci. 5(1), 1700270 (2018) 4. Bhattacharya, P., Nandasiri, M.I., Lv, D., et al.: Polyamidoamine dendrimer-based binders for high-loading lithium–sulfur battery cathodes. Nano Energy 19, 176–186 (2016) 5. Ghaznavi, M., Chen, P.: Sensitivity analysis of a mathematical model of lithium–sulfur cells part I: applied discharge current and cathode conductivity. J. Power Sources 257, 394–401 (2014) 6. Ghaznavi, M., Chen, P.: Analysis of a mathematical model of lithium-sulfur cells part III: electrochemical reaction kinetics, transport properties and charging. Electrochim. Acta 137, 575–585 (2014) 7. Manthiram, A., Chung, S.H., Zu, C.: Lithium–sulfur batteries: progress and prospects. Adv. Mater. 27(12), 1980–2006 (2015) 8. Zheng, D., Zhang, X., Wang, J., et al.: Reduction mechanism of sulfur in lithium–sulfur battery: from elemental sulfur to polysulfide. J. Power Sources 301, 312–316 (2016) 9. Mikhaylik, Y.V., Akridge, J.R.: Polysulfide shuttle study in the Li/S battery system. J. Electrochem. Soc. 151(11), A1969 (2004) 10. Erisen, N., Eroglu, D.: Modeling the discharge behavior of a lithium-sulfur battery. Int. J. Energy Res. 44(13), 10599–10611 (2020)
Influence of Electromagnetic Launch Rail Structure on Current Distribution Yifan Ge1 , Shihong Qin1 , and Lixue Chen2(B) 1 Wuhan Institute of Technology, Wuhan 430200, China 2 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. In order to explore the influence law of rail Structural parameters on current distribution, a two-dimensional dynamic finite element model of railgun is established, and the electromagnetic thermal tight coupling rail current and temperature distribution under different rail shapes and corresponding size parameters are analyzed. The results show that reducing the spacing and height of the rectangular rail can improve the current density of inner surface of the rail, and changing the rail width has no effect on the current density distribution. Through the chamfering and the appropriate selection of the inner and outer half axis size of the elliptical rail, the current concentration phenomenon can be suppressed, rail current distribution characteristics can be improved, and the heat distribution of the rail can be optimized, which provides a reference for the size optimization design of the rail. Keywords: Rail structure · Temperature field · Current distribution
1 Introduction Electromagnetic launch is a new type of technology that uses Lorentz force to do work and promote the movement of the project [1]. One of the main technical bottlenecks of electromagnetic rail launch is the local overheating of the rail caused by current concentration. The shape of the railgun directly affects the current distribution characteristics of the railgun. Therefore, it is of great significance to obtain the influence law of rail structure parameters on rail current distribution in electromagnetic launch [2]. In view of the influence of railgun structure on the law of current and heat distribution, scholars have carried out relevant research. Keshtkar et al. Analyzed the relationship between rail thickness,width and inductance gradient, and concluded that the inductance gradient gradually increases with the increase of rail distance [3]. Glushkov et al. reduced the current density at the armature-rail interface through circular rail to avoid local heat concentration [4]. Rip et al. Designed the armature model in EMAP3D and proposed that the maximum current density of the armature can be reduced by changing the armature structure [5]. Gao Bo et al. Calculated and compared the temperature distribution © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 906–916, 2022. https://doi.org/10.1007/978-981-19-1870-4_95
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of armature with different structural parameters under multi field coupling [6]. Wang zhizeng et al. Calculated and analyzed the transient inductance gradient of railgun under the change of material conductivity [7]. Based on the skin depth and magnetic energy equivalence principle, Peng Zhiran et al. Proposed an analytical calculation method of inductance gradient considering the influence of rail size and current diffusion [8]. In order to solve the problem of railgun erosion, Liu Ming and others studied rectangular, concave and convex rails. The results show that the current density distribution on the surface of convex rails is the most uniform [9]. Chen Lixue and others compared and summarized the current distribution laws of four different shapes of armatures such as saddle C-shaped armature and C-shaped armature during launch [10]. The existing studies mainly focus on the influence of rail structure on inductance gradient and the improvement of armature shape on current distribution characteristics. There are relatively few studies on the influence of rail structure on current and temperature distribution characteristics in transient process. Based on COMSOL multipysics finite element analysis software, a two-dimensional dynamic model on the rail section of railgun is established. Considering the influence of velocity term, the current distribution of rectangular rail, double elliptical arc rail and single elliptical arc rail is calculated, and the influence law of rail size parameters of different shapes on current distribution under the influence of electro-magnetic thermal coupling is obtained, An optimized rail which can reduce local overheating is designed according to the law, which provides a reference for the optimization and design of the rail.
2 Electrothermal Coupling Model of Railgun 2.1 Electrothermal Coupling Equation Figure 1 is the schematic diagram of railgun model. Electromagnetic railgun is a typical magnetic quasi-static field. Ignoring ∂ D/∂ T, it can be obtained from Maxwell’s equations and Ohm’s law.
Fig. 1. Schematic diagram of railgun model
= − ∂B ∇ ×E ∂t
(1)
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∇×
B μ
= J
(2)
+ v × B J = σ E
(3)
E is the current density, magnetic induction intensity and electric field intenwhere J , B, sity respectively, and μ, v, σ is the permeability, relative motion speed and conductivity respectively. − → Vector magnetic potential A and scalar potential ϕ are introduced =∇ ×A B
(4)
= −∇ϕ − ∂ A E ∂t The electromagnetic field equations can be obtained − σ μv × ∇ × A = −σ μ∇ϕ σ μ ∂∂tA − ∇ × ∇ × A ∂A ∇ × σ (v × ∇ × A − ∇ϕ − ) = 0
(5)
(6)
∂t
The heat transfer equation can be obtained from Fourier theorem − →2 J ∂T ∂T → ρC + ρ− vC = ∇ · (κ∇T ) + (7) ∂t ∂x σ where κ, σ, C are thermal conductivity, conductivity and specific heat respectively, and T , ρ, t are temperature, density and time respectively. 2.2 Simulation Model In the simulation model, the size of the selected reference rectangular rail is 20 mm × 40 mm and the caliber is 40 mm. The Y-Z section of the model is taken for two-dimensional calculation. Figure 2 is the calculation model of the rail section. Due to the symmetry of the railgun model, the 1/4 Calculation Model is adopted. The shadow crossing part is the Y-Z section of the railgun, surrounded by a square air area, and its side length is ten times the rail thickness, It can be regarded as infinity.
Fig. 2. Two dimensional model of rail
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2.3 Relevant Material Parameters and Inputs In the simulation, rail adopts pure copper rail. Table 1 is the material parameters of rail, among which the parameters related to temperature are conductivity, constant pressure heat capacity and heat transfer coefficient. Table 1. Rail material parameters Parameter
Value
Unit
C κ ρ σ
360 + 0.1T 412–0.0787T 8900.0 1/(−0.24.596 + 0.671T)
J/(kg·K) W/(m·K) kg/m3 MS/m
The model is calculated by COMSOL multipysics finite element analysis software, and the current distribution and temperature distribution on the railgun section are obtained.
3 Rectangular Rail Current Distribution Input 5 ms three stage driving current with flat edge time of 0.15 ms, amplitude of 500 ka and rising edge time of 0.5 ms. 3.1 Influence of Rectangular Rail Parameters on Current Distribution Rectangular rail is the most commonly used rail structure for electromagnetic launch. Change the rectangular width w, height h and the distance d between the two rails respectively, and observe the influence of the changes of these three parameters on the current density distribution. The values of parameters w, h and D are shown in Table 2. Only one parameter is changed each time, and other parameters are the reference rail size parameter values.The simulation results are shown in Fig. 3. From the figure, it can be observed that there is a strong current concentration near the rail edge, the current density reaches the maximum at the corner, and the current density at the edge on the inner side of the rail is greater. This is because the eddy current changing along the rising edge of the driving current makes the current uneven in the rail, The skin effect makes the current distributed on the edges of the rail surface. The velocity skin effect makes the peak current density on the inner side of the rail greater than that on the outer side. The Joule heat generated by current concentration leads to local overheating of the rail. The temperature of the inner edge is significantly higher than that on the outer side. The heat is slowly transmitted to the inside of the rail with time, and its distribution is similar to that of the current density, and the maximum temperature is 337 k at 5 ms.
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Value
Unit
d w h
1, 1.2, 1.4, 1.6, 2 1, 1.2, 1.4, 1.6, 2 1, 1.2, 1.4, 1.6, 2
cm cm cm
Fig. 3. Current distribution and heat distribution of rectangular rail
Figure 4 shows the influence curve of various parameters on rail current distribution. In the figure, the abscissa is the circumference along the rail surface, the midpoint on the inner side of the rail is selected as the coordinate 0 point, the ordinate is the current density of the corresponding point on the surface, and the current density near the midpoint on the inner side of the rail tends to be constant α, call α as the platform current density. It can be observed from the figure that (1) when changing the rail distance d, the platform current density will increase with the decrease of rail distance d, and the current density of the two current peaks will also increase with the decrease of d, which has a greater impact on the inner current peak. (2) When changing the rail width w, the current density curves corresponding to different rail widths basically coincide when the arc length is small. The rail width has no effect on the platform current density, has little effect on the inner current peak, and the current density of the outer current peak also decreases with the increase of W. (3) when changing the rail height, the platform current density will increase with the decrease of rail height h, The current density of the two current peaks also increases with the decrease of h. This is consistent with the results of keshtkar et al. [3].
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Fig. 4. Influence of parameters on rail current distribution
3.2 Influence of Chamfer on Current Distribution The peak current density of the rectangular rail appears on the edges on both sides, which is easy to produce rail erosion. Therefore, the edges on both sides of the rectangular rail are chamfered. The chamfer radii on both sides are the same. The chamfer radii of 0.2 cm, 0.3 cm, 0.4 cm, 0.5 cm and 0.6 cm are taken for calculation. The calculation results are shown in Fig. 5. The current density near the midpoint inside the rail increases with the increase of chamfer radius, but the overall change is small. With the increase of chamfer radius, the current density near the chamfer increases slightly, and at the same time, the peak value of current density decreases. The two current peaks of the chamfered rail with a radius of 0.8cm become approximately one. The chamfered rail makes the current concentration point relatively uniform and plays an obvious role in restraining the current concentration.
Fig. 5. Current distribution of rectangular rail with different chamfer radius
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4 Arc Rail Current Distribution 4.1 Double Elliptical Arc Rail Current Distribution According to the inhibitory effect of chamfer on the current concentration at the edge of rectangular rail, the arc rail is used to improve the current distribution. The inner and outer sides of the rail are composed of elliptical arc. Change the length of the inner and outer half axes of the elliptical arc rail, and observe the influence of these two parameters on the current distribution law. Figure 6 shows the current density distribution in the rail when the length of the inner half axle of the rail is changed. At this time, the outer half axle length B of the rail is fixed as 1cm, and the inner half axle length a is taken as 1, 1.1, 1.2, 1.3, 1.4 and 1.5 cm. It can be observed from the figure that when a = 1 cm, there is a strong current concentration phenomenon on the inner side of the top of the left and right symmetrical rail. With the increase of the inner half axis length a, the current concentration phenomenon on the top is restrained to a certain extent. At the same time, the current density of the arc surface on the inner side of the rail increases, the distribution begins to become uneven, and the current concentration area gradually moves to the bottom with the increase of a, When a = 1.5 cm, new concentration points appear at the bottom.The curve in Fig. 6 shows the current density curve along the rail surface. It can also be seen from Fig. 6 that when a increases, the peak current density decreases, but the latter half of the curve has an upward trend. When a = 1.5 cm, the current density curve becomes monotonous increase, and the maximum value appears at the bottom of the rail. It can be seen that increasing the half axis length a on the inner side of the rail can significantly reduce the peak current density at the top of the rail, move the current concentration area to the bottom of the rail and improve the current density on the inner side of the rail.
Fig. 6. Current distribution under different length of inner half axle of rail
Figure 7 shows the rail current density distribution when changing the length of the outer half axis of the rail. At this time, the length a of the inner half axis of the rail is fixed as 1cm, and b is taken as 1, 1.1, 1.2, 1.3, 1.4 and 1.5 cm respectively. During the change of b, there is always a peak area of current density near the top of the rail arc,
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the current distribution characteristics do not change with the increase of b, the curve in Fig. 7 shows the current density curve along the rail surface. It can be seen that the change trend of the curve has not changed, but the peak current density at the top of the arc decreases with the increase of b. It can be seen that increasing the length b of the outer half axis of the rail is to homogenize the current distribution at the top of the rail and reduce the peak current density, but it will not affect the overall current distribution characteristics of the rail.
Fig. 7. Current distribution under different length of outer half axle of rail
4.2 Single Elliptical Arc Rail Current Distribution It can be seen from the above calculation results that the outer arc surface mainly plays a role in restraining the current concentration at the top of the arc, but has little impact on the current density distribution characteristics. Considering the limitation on the rail width and the simplicity of the external support structure in the experiment, it is proposed to use the rectangular rail with chamfer to replace the outer half axis of the double elliptical arc surface rail. At this time, the inner side of the rail is still arc surface, Whether the chamfer arc is connected with the arc surface may affect the current distribution. The rectangular width is 0.45 cm, the height is 2 cm as high as the arc rail, and the chamfer radius is 0.2, 0.25, 0.3, 0.35, 0.4 and 0.45 cm to explore its influence on current and heat distribution. The calculation results are shown in Fig. 8. It can be found from Fig. 8 that when r is less than 0.4, the increase of chamfer radius reduces the peak current density, but when the chamfer radius increases to connect with the arc surface, that is, when r = 0.45 cm, the peak current density increases instead. This is because the chamfer makes the current distribution uniform, and the arc top is at the peak current density, The chamfer makes the current density gathered outside the rectangular rail partially superimposed on the current density concentration point at the arc rail, thus increasing the maximum value. The change trend of the curve shows that the increase of the chamfer radius reduces the peak value of the current density, but the current density near the peak point increases relatively, and the point with the maximum current density
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moves slightly to the right. When the chamfer radius continues to increase, the range of the increase of the surrounding current density also expands, and when it increases to the aggregation point of the arc rail, a higher current density will be generated. It can be seen that the outer half axis current distribution of the single arc rail is not the more uniform, the better. When it is relatively uneven, it can reduce the peak current density. Its size needs to be matched with the inner arc size of the rail to achieve better current distribution effect, so as to reduce the heating of the rail.
Fig. 8. Current distribution of single elliptical rail under different chamfer radius
Based on the above analysis and considering the interaction between size parameters and current distribution, a single elliptical arc rail is designed, which is 2 cm high, rectangular chamfered rail on the outside, 0.45 cm wide, chamfered radius of 0.36 cm, elliptical rail on the inside, half axis length of 1.15 cm. The current distribution at the rising edge of 0.1 ms and the final heat distribution at 5 ms are shown in Fig. 9, The current is evenly distributed on the whole arc surface without obvious current concentration. The final heat distribution can also be seen that the temperature rise of the arc surface is relatively uniform. The maximum temperature at 5 ms is 326 k, which is 11 K lower than the maximum temperature of the reference rectangular rail (337 k), alleviating the local overheating of the ordinary rectangular rail.
Fig. 9. Single elliptical rail current and heat distribution
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5 Discussion (1) In the calculation process of this paper, the heat source is only the Joule heat generated by the rail resistance under the pulse current. In the actual launch process, the Joule heat caused by the armature-rail contact resistance and the friction heat at the armature-rail interface should be considered. At this time, the influence of the rail current distribution on the rail temperature rise will be more obvious. Selecting appropriate rail size parameters is important to improve the rail heat distribution It is more important to prolong the service life of the rail. (2) Inductance gradient is one of the important parameters of electromagnetic railgun. Increasing inductance gradient can significantly improve the electromagnetic thrust, so that the armature has greater out of bore kinetic energy and improve the launch efficiency of railgun. The inductance gradient is directly related to the current distribution. In the process of rail structure design, it is necessary to comprehensively consider the influence of current distribution on inductance gradient and rail temperature distribution.
6 Conclusion In this paper, a two-dimensional dynamic finite element model of electromagnetic launch rail is established. Under the coupling condition of transient electromagnetic field and temperature field, the relationship between rail size parameters and current distribution under different rail shapes is analyzed, so as to improve the local overheating phenomenon of rail gun and provide a basis for the design of rail structure. The main laws are as follows: 1) for the rectangular rail, the change of rail width w has no effect on the current density inside the rail, but reducing the rectangular rail width and rail height can improve the current density inside the rail, so as to improve the firing performance of the railgun. Chamfering can make the current density distribution uniform, and edges and corners should be avoided as much as possible in the process of rail design. 2) For the double elliptical arc rail, increasing the length b of the outer half axis of the rail can inhibit the current concentration at the top of the arc, but it will not affect the current distribution law. Increasing the length a of the inner half axis of the rail can significantly reduce the peak current density. At the same time, it can change the current distribution law and make the current concentration area moves to the bottom of the rail. 3) For the single elliptical arc rail, the peak current density can be reduced when the current distribution of the outer half axis of the rail is relatively uneven. Its size design needs to be matched with the inner arc surface of the rail to achieve better current distribution.
References 1. Ma, W., Xiao, F., Nie, S.: Applications and development of power electronics in electromagnetic launch system. Trans. China Electrotech. Soc. 31(19), 1–10 (2016). (in Chinese)
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2. Ma, S., Yu, X., Li, Z.: A review of the current research situation of inductive pulsed-power supplies for electromagnetic launch. Trans. China Electrotechn. Soc. 30(24), 222–228,236 (2015). (in Chinese) 3. Kerrisk, J.: Electrical and thermal modeling of railguns. IEEE Trans. Magnet. 20(2), 399–402 (1984). https://doi.org/10.1109/TMAG.1984.1063080 4. Glushkov, I.S., Kareev, Y., Kotova, L.G., Kuharenko, A.T., Halimullin, Y.: Investigation of techniques to increase armature transition velocity. IEEE Trans. Magnet. 33(1), 549–553 (1997). https://doi.org/10.1109/20.560072 5. Rip, L., Satapathy, S., Hsieh, K.-T.: Effect of geometry change on the current density distribution in C-shaped armatures. IEEE Trans. Magnet. 39(1), 72–75 (2003). https://doi.org/10. 1109/TMAG.2002.805906 6. Gao, B., Qiu, Q., Qie, W.: Multi-field coupling analysis and experimental research on armature of electromagnetic railgun. Trans. China Electrotechn. Soc. 35(S2), 341–345 (2020). (in Chinese) 7. Wang, Z., Yuan, W., Yan, P.: Inductance gradient for rail-type electromagnetic launcher under transient conditions. High Volt. Eng., 43(12), 4039–4044 (2017). (in Chinese) 8. Peng, Z., Wang, G., Zhai, X., Zhang, X.: Modeling and analysis of time-varying inductance gradient for electromagnetic rail launcher. Trans. China Electrotechn. Soc. 35(23), 4843–4851 (2020). (in Chinese) 9. Liu, M., Shu, T., Miao, H., et al.: Armature current distribution characteristics under different rail structures. High Power Laser Part. Beams, 30(05), 139–145 (2018). (in Chinese) 10. Ruan, J., Chen, L., Xia, S., Wang, Z., Li, L.: A review of current distribution in electromagnetic railguns. Trans. China Electrotech. Soc. 35(21), 4423–4431 (2020).(in Chinese)
Ride Through Strategy of Doubly-Fed Pumped Storage Generator-Motor Yu Zhang1,2,3(B) , Yutian Sun1 , Shumei Cui3 , Jinming Hu1 , and Jiahong Liu2 1 Harbin Electrical Machinery Company Limited, Harbin 150040, China
[email protected]
2 Harbin University of Science and Technology, Harbin 150080, China 3 Harbin Institute of Technology, Harbin 150001, China
Abstract. When a voltage sag fault occurs in the grid, in order to improve the low voltage ride-through capability and prevent the doubly-fed pumped storage unit from disconnecting from the grid, the 2 MW pumped storage prototype is proposed based on the transient analysis of the system. The super-capacitor branch is introduced on the DC bus side in the joint control strategy, and through the bidirectional DC/DC control, the instantaneous large current caused by the fault is absorbed, so as to maintain the voltage stability of the DC bus, protect the converter, and improve the low voltage ride-through capability. At the same time, this method is also based on the stator flux transient state compensation, cutting from the perspective of the impedance of the rotor side port, using virtual inductance technology to give full play to the potential of the converter. Keywords: Low voltage ride through · Virtual inductance · Super-capacitor
1 Introduction The system structure of the doubly-fed motor and the current control ability of the power converter restrict the low voltage ride-through capability of the doubly-fed motor. When a voltage sag fault occurs in the power grid, on the one hand, there is a strong coupling between the stator and the rotor, and the flux linkage cannot change suddenly. Free components will appear in the stator flux linkage, and a higher voltage will be generated in the rotor-side winding. This results in a transient inrush current in the rotor side windings, the amplitude of which can reach 4–10 times the rated value. On the other hand, the mechanical torque of the unit remains basically unchanged during the fault, while the electromagnetic torque is reduced due to the grid voltage drop fault. There will be unbalanced torque between the systems, which will increase the rotor speed of the doubly-fed motor and increase the slip power [1, 2]. The current research on low voltage ride-through technology can be divided into three aspects: fault ride-through schemes that improve control strategies, fault ride-through schemes that increase hardware protection circuits, and fault ride-through schemes that combine or coordinate with each other. Without increasing the hardware circuit, only © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 917–925, 2022. https://doi.org/10.1007/978-981-19-1870-4_96
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improving the control strategy can make the converter achieve a balance between voltage and current by weakening some amount of transient response, ensuring that the two values are in a limited range to cancel the electromotive force together, and The surplus energy is absorbed by the system itself [3], which can also offset the negative sequence and DC components in the stator flux linkage when the grid fails. The rotor-side hardware protection scheme protects the converter by absorbing excess energy through hardware devices [4, 5]. The hardware circuits include crowbar circuits, energy storage systems, fault current limiters, dynamic voltage restorers, power converters, etc. according to the type. The installation position includes the rotor side protection circuit, the DC side protection circuit, and the stator side protection circuit, so as to improve the low voltage ride-through capability in terms of reactive power compensation, balance energy, and consumption of excess energy [6, 7]. This paper proposes a joint control method combining the virtual inductance control strategy on the rotor side and the DC/DC branch. The DC bus side uses a bidirectional DC/DC converter to control the super-capacitor to achieve the purpose of absorbing accumulated energy and stabilizing the DC bus voltage.
2 The System Transient Analysis The stator flux linkage is selected as the directional vector, and a vector control strategy is formulated based on stator flux tracking. When the doubly-fed pumped-storage unit is operating normally, the stator windings are connected to the infinite grid to keep the stator flux linkage stable and the stator resistance voltage The drop is much smaller than the voltage drop of the reactance, so the stator resistance can be ignored, so that the phase of the stator flux and the stator voltage is always different by 90°, which simplifies the control system [8, 9]. In the synchronous rotation (d-q) coordinate system, the position of each vector is shown in Fig. 1, where αβis the stator coordinate system, and DQ is the rotor coordinate system.
Fig. 1. Stator flux tracking coordinate system vector diagram
Stator and rotor flux linkage equation: ⎧ ⎨ ψs = Ls Is + Lm Ir ⎩ ψr = Lm Is + Lr Ir
(1)
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Stator and rotor voltage equation: ⎧ d− → ⎪ ⎨ Us = Rs Is + ψs dt ⎪ → ⎩U = R I + d − ψs r r r dt
(2)
Simplified flux equation of doubly-fed motor is obtained from Fig. 1: ⎧ ⎨ ψsd = Ls isd + Lm ird = ψs ⎩ ψsq = Ls isq + Lm irq = 0
(3)
− → − → −→ −→ − → where ψs , ψr are the stator and rotor flux linkage vectors; ψsd , ψsq are the ψs dq axis components respectively; and isd , isq and ird , irq are the dq axis components of the stator current Is and rotor current Ir respectively; Ls is the stator self-inductance and Lm is the stator-rotor mutual inductance respectively; Us , Ur are the stator and rotor voltage vector; Rs and Rr are stator and rotor resistance respectively. Formula (1) is substituted into Formula (2), the rotor voltage can be derived: Ur =
d Lm d ψs + (Rr + σ Lr )Ir Ls dt dt
(4)
In the formula, σ is the leakage inductance coefficient, and σ = 1 − L2m /Ls Lr ; σ Lr is the rotor-side transient inductance. It can be seen from Formula (4) that the rotor voltage can be decomposed into the electromotive force induced by the stator flux linkage on the rotor side and the voltage drop produced by the rotor side impedance.
3 The Cooperative Control Method Aiming at the impact of the transient process of the grid voltage sag, starting from the problem to be solved, a specific solution strategy is proposed as shown in Fig. 2. Power grid
Water turbine Gear box
RSC
Super-capacitor branch
C bus +
Lsc
Res
Req
Ceq
–
Fig. 2. Control system block diagram
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3.1 IEC (Inductance Emulating Control) of Rotor-Side Converter Based on the impedance stability criterion, the system under study can be divided into power supply and load subsystems. The power supply terminal is modeled by Thevenin equivalent circuit, and the load subsystem is modeled by its input impedance. The following expression can be obtained: Er = −(Rr + σ Lr
d + ZRSC ) ∗ Ir dt
(5)
Rr is the rotor resistance, Ir is the rotor side current. It can be concluded that ignoring the smaller term including the rotor resistance Rr , when the rotor-side converter port impedance Z RSC is equivalent to pure inductance L sc , the overall vector direction is exactly opposite to Er. When the rotor side current can accurately track the given current reference signal, Ir∗ = Ir = −
Lm − → ψs Ls (LRSC + σ Lr )
(6)
where L RSC is the equivalent inductance of the rotor side port, and the output voltage of the rotor converter is: Ur =
LRSC Er LRSC + σ Lr
(7)
The overall block diagram of the rotor side is shown in Fig. 3.
Fig. 3. Rotor-side converter control block diagram
When the grid voltage drop is detected, the PQ control loop in the traditional vector control is removed, the stator flux linkage is tracked, and the current reference signal is given to let the rotor-side converter equivalent to the pre-calculated L RSC , provided that the limited conditions are met next, reasonable use of the converter margin to offset EMF.
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3.2 DC Bus Side Control Strategy In view of the defects of the rotor-side IEC control strategy and grid-side reactive power priority control, a super-capacitor module is added on the DC bus side to improve the low voltage ride-through capability of DFIG during voltage drops. The additional module aims to absorb the excess energy accumulated in the DC bus, prevent the pumping voltage from being too high, ensure the stability of the DC bus voltage, protect the backto-back converter, and enable the grid-side converter to focus on putting the margin into the direction to improve the reactive power support capability. As a whole, the system can withstand a severe drop in the grid voltage. The Super-capacitor branch topology is shown in Fig. 4.
Vbus
Cbus
L1 L2
R SQR
R ESR Csc
Fig. 4. Super-capacitor branch topology
The reactive power output range of the traditional grid-side converter mainly depends on two aspects, one is the capacity of the grid-side converter, and the other is the current slip power value. Assuming that the maximum capacity of the grid-side converter is Pgmax , then: − Pg2 max − λ2 Ps2 ≤ Qg ≤ Pg2 max − λ2 Ps2 (8) It can be seen that in the worst case, the grid-side converter output can become very limited. However, the control strategy introduced in this article can temporarily store slip power through super-capacitor absorption, so that the reactive power range of the grid-side converter can reach: −Pg max ≤ Qg ≤ Pg max
(9)
In the selected topology, the bidirectional DC/DC converter is used to coordinate the working state of energy storage, the control system structure is shown in Fig. 5. The DC bus rated voltage U bus_ref is used as the reference signal. The difference between the output voltage signal and the reference signal U bus_ref is adjusted by PI to form a negative feedback. After the DC/DC inductor current is subtracted, it is adjusted by the PI controller of the current inner loop, and the obtained signal UC enters the pulse width modulation generator PWM, and the generated pulse signal controls the power device IGBT. The overall strategy flow chart is shown in Fig. 6.
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Whether a drop failure
No
Yes
Inductance virtual control of RSC
Reactive power Super-capacitor priority control module control of GSC
DC-DC converter d(t)
d(t) iL2
PWM Uc
iL1
PWM
–
– Uc
PI
+ Vbus_ref +
PI
PI
No
Ubus=0.9pu Yes
+
Normal working mode
iref
–
Vbus
Fig. 5. Bidirectional DC/DC converter control system structure
END
Fig. 6. Overall strategy flow chart
Under fault conditions, the rotor-side converter cuts off the PQ control loop, tracks the stator flux linkage change, and gives a transient current reference signal. By controlling the rotor side converter to simulate the inductance, it can be fully utilized under the premise of meeting the voltage and current constraints, as well as, accelerates the attenuation of the stator flux linkage to the greatest extent; the feedforward control unit is introduced to improve the current loop’s ability to track AC commands.
4 Simulation Result Analysis In order to verify the effectiveness of the proposed strategy, a 2 MW doubly-fed pumped storage unit model has been established. The specific parameters are shown in Table 1. The initial condition is set as the slip rate −0.2, at this time the total output active power is 1 pu, and the power factor is 1, that is, the output reactive power is 0 pu. In terms of fault conditions, the most harmful three-phase symmetrical voltage drop is selected. The voltage drop occurs at 0.2 s, and the drop is the most serious 0.8 pu in the national standard, which lasts for 0.3 s. Two sets of comparative simulations are used to verify the effectiveness and superiority of the collaborative control method. 4.1 Comparison of Rotor Side Control Methods The rotor-side constant inductance control method proposed in this paper is compared with stator current feedback control show in Fig. 7(a) and de-excitation control in Fig. 7(b). Through the comparative analysis of performance parameters when these three methods are used on the rotor side, it can be seen from Fig. 7 that in the case of severe drops, when using the stator current feedback control, because the stator current
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Table 1. Parameters of simulation model Parameter
Value
Ps /MW
2
Stator voltage U s /V
690
Number of pole pairs p
2
Turns ratio u
1/3
Stator resistance Rs /pu
0.0115
Stator leakage inductance L s /pu
0.1208
Magnetizing inductance L m /pu
3.4699
Rotor resistance Rr /pu
0.0128
Rotor leakage inductance L r /pu
0.1208
feedback control only considers the current limit conditions, the current of the converter exceeds the amplitude; and when the de-excitation control method is used, because the de-excitation control only considers the voltage limit, there is a risk of excess current in the converter; when the constant inductance control is used, there is a certain margin for both quantities. This is because the constant inductance control comprehensively considers the limiting conditions. The superiority of the constant inductance control method for the rotor converter is verified.
Fig. 7. Comparison of rotor side control methods
4.2 Comparison of Overall Control Methods It can be observed from Fig. 8(a) that when the constant inductance control is simply used, although the output voltage and current of the converter can be guaranteed to be within the limited conditions through the control, it cannot solve the problem of the voltage increase of the DC bus due to the accumulation of energy, as shown in Fig. 8(a),
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the peak value of the DC bus voltage U bus is 1.11 pu, and there are fluctuations; when the super-capacitor module is simply added, the surplus energy is mainly transmitted to the DC through the rotor-side converter when the voltage drops severely.
Fig. 8. Comparison of overall control methods
Accumulation on the bus side, but because the super-capacitor module is attached to the DC bus side, it is only controlled, and the rotor side converter lacks protection, as shown in Fig. 8(b), the peak value of the output current I r on the rotor side exceeds I max to 2.2 pu, and the electromagnetic torque T em fluctuates greatly and damages the mechanical components. When using the joint control, the advantages of the two methods are combined to protect the entire system and improve the low voltage ride through capability.
References 1. Alsmadi, Y.M., Xu, L., Blaabjerg, F., et al.: Detailed investigation and performance improvement of the dynamic behavior of grid-connected DFIG-based wind turbines under LVRT conditions. IEEE Trans. Ind. Appl. 754(5), 4795 (2018) 2. Tohidi, S., Behnam, M.: A comprehensive review of low voltage ride through of doubly fed induction wind generators. Renew. Sustain. Energy Rev. 57, 412–419 (2016) 3. Mahela, O.P., Gupta, N., Khosravy, M., et al.: Comprehensive overview of low voltage ride through methods of grid integrated wind generator. IEEE Access 2019(7), 99299–99326 (2019) 4. Zhu, D., Zou, X., Deng, L., et al.: Inductance-emulating control for DFIG-based wind turbine to ride-through grid faults. IEEE Trans. Power Electron. 32(11), 8514–8525 (2017) 5. Sun, J.: Impedance-based stability criterion for grid-connected inverters. IEEE Trans. Power Electron. 26(11), 3075–3078 (2011) 6. Zhu, D., Zou, X., Zhou, S., et al.: Feedforward current references control for DFIG-based wind turbine to improve transient control performance during grid faults. IEEE Trans. Energy Convers. 33(2), 670–681 (2018) 7. Ahmad Hamidi, S., Ionel, D.M., Nasiri, A.: Modeling and management of batteries and ultracapacitors for renewable energy support in electric power systems-an overview. Electr. Power Compon. Syst. 43(12), 1434–1452 (2015)
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8. Dao, Z., Frede, B.: Optimized demagnetizing control of DFIG power converter for reduced thermal stress during symmetrical grid fault. IEEE Trans. Power Electron. 33(12), 10326– 10340 (2018) 9. Ahmad Hamidi, S., Ionel, D.M., Nasiri, A.: Modeling and management of batteries and ultracapacitors for renewable energy support in electric power systems–an overview. Electr. Power Compon. Syst. 43(12), 1434–1452 (2015)
Fast Neutral-Point Balance and Zero-Sequence Circulation Suppression for a T-Type Three-Level Inverter Parallel System Tianyu Yue1 , Alian Chen2(B) , Zhiyuan Chen2 , Qicai Ren2 , Nan Wang2 , and Tong Liu2 1 Institute of Novel Semiconductors, Shandong University, Jinan 250061, China 2 School of Control Science and Engineering, Shandong University, Jinan 250061, China
[email protected]
Abstract. The parallel connection of T-type three-level inverter is the key way to realize the large capacity of equipment. However, apart from the inherent neutralpoint potential imbalance of T-type three-level parallel system, causing problem of zero-sequence circulating current. Therefore, the article presents a neoteric PWM modulation method which takes into account the fast neutral-point balance and zero sequence circulation suppression function. First, in view of model T-type three-level convert inherent nonlinear and neutral-point balance problem, analysis reason of neutral-point voltage fluctuations, based on the point of finite time control potential quick balance method, and on the premise of not affect neutral-point balance control, zero sequence current in parallel system model, design circulation controller based on the “P + feedforward”. Finally, the simulation results verify the effectiveness of the viewpoint in the article. Keywords: Three-level inverter · Parallel system · Finite time control · Neutral-point potential balance control · Zero-sequence circulation suppression
1 Introduction Last few years, different types of three-level converters is widely utilized in new energy fields such as wind power photovoltaic power generation, generation, and electric vehicles [1]. Compared with NPC three-level converter, converter has been widely utilized on account of its advantages such as fewer components, low power loss, and high operating efficiency, and has received a lot of attention [2]. Since the power switch is limited by the rated current, the capacity of the single converter is limited. Therefore, parallel T-type three-level converters are mainstream equipment to realize the large-capacity system [3]. However, for this parallel system, there are inevitably two major problems, the unbalanced neutral-point potential and the zero-sequence circulating current [4]. On the one hand, the neutral-point imbalance of the parallel T-type three-level inverters affect performance of inverters, which easily leads to the current waveform distortion on the AC side and the uneven partial voltage of capacitor on the DC side, which increases voltage stress of capacitor on DC side © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 926–935, 2022. https://doi.org/10.1007/978-981-19-1870-4_97
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and switch tube, and increases the damage probability of the switch tube [5, 6]. In addition, transient changes in modulation depth and load power factor will cause rapid and severe fluctuations in the DC side capacitor voltage, resulting in an imbalance in the neutral-point potential [7]. If the imbalance is not immediately relieved, further transients may exacerbate the current imbalance, thereby imposing severe electrical stress on the converter components and causing failure [8]. Therefore, the fast control of neutralpoint balance of inverter is of great significance. On the other hand, for the circulation problems in the parallel system, in addition to affecting the quality of the grid-connected current, it will also cause unbalanced power distribution, which may increase system losses, cause damage to a single unit, and system running is affected [9]. In terms of neutral-point balance control, literature [10] realized the balance control of neutral-point potential by adding extra hardware circuit. However, this solution increases system cost and reduces system efficiency. Literature [11] proposed a zerosequence voltage injection method with feedforward and feedback compensation. By adjusting the PI parameter, voltage deviation between two capacitors was reduced and potential fluctuation of neutral-point was suppressed. However, the speed of this method needs to be improved. Literature [7] obtains the best compensation offset signal of different operating points through the particle swarm algorithm, and realizes the fast balance control of neutral-point potential. However, the calculation of unbalance compensation coefficient in this method is complicated, and the use of algorithms to find the optimal unbalance compensation coefficient greatly increases the workload. In terms of zero-sequence circulation suppression, literature [12] uses hardware blocking to reduce circulation, but the scheme improve the system’s volume and cost. Literature [13] uses PI controller to regulate small vector to fulfill circulating current suppression, but when the reference currents of the system are not same, control effect is not good, and circulating current spikes will appear in the process of suppression. Literature [4] introduces the feedforward term and adopts the PI + feedforward control strategy, which effectively eliminates the circulating current spike when reference currents of parallel system are not identical. However, literature [13] and [4] may cause integral saturation of the controller due to the existence of integral terms. Hence, this paper come up with the finite time control to resolve the neutral-point imbalance of the parallel system. Firstly, the relationship between neutral-point potential fluctuation and duty cycle is analyzed according to the model. Furthermore, a finite time controller is constructed to regulate duty ratio of small vector with strong regulating ability, and track the expected value to realize the fast control of neutral-point potential. To settle the zero-sequence circulation problem, a proportional plus feedforward control strategy is adopted in this paper to regulate the action time of redundant small vectors, and achieve zero-sequence circulation suppression without affecting the neutral-point potential balance.
2 Overview of T-type Three-Level Inverter Parallel System Parallel system topology of T-type three-level inverters has been exhibited in Fig. 1 [14]. Two inverters are connected by common AC-DC bus and neutral-point. The filter is l-type filter.
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In the figure, V dc is the DC bus voltage; O1 and O2 are the neutral points of the two inverters; P and N indicate positive bus and negative bus; L 1 and L 2 are the filter inductors of the two inverters; C 1 and C 2 are the DC side capacitors; O is the common point of the grid voltage; ia1 , ib1 , ic1 and ia2 , ib2 , ic2 are the output currents of T-type three-level inverters 1 and 2; Inverter 1
Inverter 2
Fig. 1. Topology of parallel T-type three-level inverter
Fig. 2. Space vector diagram of T-type three-level inverter
iag , ibg , and icg are the grid-connected current. The average model of T-type three-level inverter is presented as ukj = Lj
dikj + ek + 3uON k = a, b, c j = 1, 2 dt
(1)
where: ukj are the output voltages of inverters 1 and 2, and uON is the voltage from point O to the bus N on the DC side. The inverter has three switch states, [0], [−1], and [1]. Phase reference function of the inverter is further defined as −1, −1 → 0 → −1, nkj = k = a, b, c j = 1, 2 (2) 0, 0 → 1 → 0, The output voltage of T-type three-level inverter is defined as ukj =
Vdc dkj + nkj 2
k = a, b, c j = 1, 2
(3)
where: d kj represents the k phase duty cycle of the j-inverter. Figure 2 demonstrates that inverter’s space vector diagram is divided into six sectors. At the same time, sum nj of the reference functions of each phase of the j-th T-type three-level inverter is −1 sect or II, IV, VI nj = (4) −2 sect or I, III, V
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3 Modeling Analysis of Neutral-Point Potential and Zero Sequence Circulation 3.1 Neutral-Point Potential Modeling Analysis For T-type three-level inverter, in the three switching states of [1], [Modeling Analysis of Neutral-Point Potential and Zero 1], and [0], the [0] state makes the current flow through the neutral-point of DC side capacitor, if currents flowing into and out of the neutralpoint are not equal within a switching cycle, there will be a shift in the neutral-point potential [11]. According to Kirchhoff’s current law, time domain dynamic equation is obtained ⎧ dVPj 1 ⎪ ⎪ = iP ⎨ dt C1 j = 1, 2 (5) dV ⎪ 1 ⎪ ⎩ Nj = iN dt C2 Two T-type three-level inverters share the AC and DC bus and neutral point. Therefore, V P1 = V P2 = V P , V N1 = V N2 = V N . Define the tracking error reference signal u between V P and V N , define the tracking error as, and set C 1 = C 2 = C to get the u = C1 (iP − iN ). formula d dt Average output current iNP of neutral-point within a cycle of single switching period is be presented as [11, 15] iNP = iP − iN = dmax _0 imax + dmid _0 imid + dmin _0 imin
(6)
where: iNP is the average current at the neutral-point, imax , imid and imin are currents corresponding to maximum, intermediate, and the minimum reference voltages, respectively. d max_0 , d mid_0 and d min_0 are the zero-level duty cycle when the current value is at the maximum, middle, and minimum, respectively. In a carrier cycle, T s the maximum, middle, and minimum reference zero-level duty cycle of the T-type three-level output is presented as ds_0 = (1 − |ds |), s = max, mid , min. The average current at the neutral-point can be obtained iNP = (1 − |dmax |)imax + (1 − |dmid |)imid + (1 − |dmin |)imin
(7)
d max , d mid and d min are the reference duty ratios when the current value is at the us , s = max, mid , min. maximum, middle, and minimum, respectively. ds = 0.5u dc From Eq. (7), due to the zero-sequence circulating current, we have 1 d u = [iz − (|dmax |imax +|dmid |imid +|dmin |imin ) dt C
(8)
From Eq. (8), the neutral-point potential is decided by the DC side capacitance, circulating current, current, and duty cycle of each phase.
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3.2 Modeling and Analysis of Zero Sequence Circulation The circulating current exists between inverter parallel systems as shown in Fig. 1, and the magnitude is equal, the direction is opposite and it is not reflected to the gird. Define the zero-sequence circulating current ik1 = − ik2 (9) iz = iz1 = −iz2 = k=a,b,c
k=a,b,c
The zero sequence duty cycle can be defined as dzj =
dkj , j = 1, 2.
k=a,b,c
Then, Eqs. (1), (3), (4), (9) are simplified, and the zero sequence circulating current of first T-type three-level rectifier is obtained as Vdc diz1 = (10) (dz1 + n1 − dz2 − n2 ) dt 2 From the circulating current model given by Eq. (10), the circulating current of parallel system is decided by zero-sequence duty cycle, reference function and filter inductance. (L1 + L2 )
4 Neutral-Point Potential Balance Control and Zero-Sequence Current Suppression for Parallel Systems Assuming that reference vector V ref is in fifth cell in the first large sector, when the V P is different from the V N , it can be seen from formula (10) that by regulating action time of P/N redundant small vector, duty cycle is changed, and then neutral-point potential balance is realized. Add the control variable yFTC to regulate action time of the small vector to balance the neutral-point potential. Research has shown that due to the fractional power term in the finite-time controller, the finite-time closed-loop control system has better convergence performance than the non-finite-time closed-loop control system [16, 17]. On this basis, a finite-time controller for neutral-point potential balance is designed, and finite-time control is used to adjust the duty cycle of the small vector with strong adjustment ability. Based on the theory, the finite-time controller that balances neutral-point potential is designed as yFTC (t) = k1 sign(VP − VN )|VP − VN |α
(11)
where: yFTC refers to the adjustment of the inverter’s modulation wave by realizing the neutral-point potential balance of the parallel system, K 1 is the adjustment coefficient of the finite controller, α is the fractional power of the control variable. Figure 3 is the vector correction diagram of the T-type three-level inverter after fast neutral-point potential balance. At this very moment, neutral-point potential is balanced, and its corresponding phase state transition time t a1 , t b1 , t c1 becomes
tk1 = tk1 + yFTC Ts
k = a, b, c
(12)
where: t k1 and tk1 are the turn-on time of each phase before and after the neutral point balance, yFTC refers to adjustment of inverter modulation wave to neutral-point potential balance of the parallel system, and T s is thecxs switching period.
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Fig. 3. Neutral-point potential balance control state switching diagram.
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Fig. 4. Vector correction diagram of first T-type three-level inverter.
4.1 Circulation Suppression Scheme Due to the existence of a zero-sequence circulating current path, when the duty cycle or reference function of the two inverters is not zero, the system will produce circulation. Among them, when the circulating current of any inverter is suppressed, the circulating current of the other inverter will also be suppressed simultaneously [4]. Based on principle of volt-second balance, parallel system can achieve zero-sequence circulation suppression by regulating the action time of redundant the small vector. Assuming that reference voltage vector V ref is located in fifth cell in first large sector, Fig. 4 shows the vector correction diagram of the first T-type three-level inverter. Among them, the turn-on time of each phase after suppression of zero sequence circulation is corrected to
tk1 = tk1 + y1 Ts
(13)
where: y1 is the adjustment component of the P/N small vector action time of the first inverter, and T s is the switching period, tk1 and tk1 are the turn-on time of each phase before and after zero-sequence circulating current suppression. Incorporating Eq. (13) into Eq. (10), zero-sequence circulating current expression of first inverter is obtained 3Vdc Vdc diz1 =− y1 + (T21 − n21 ) dt 2L 4L
2 where: L = L 1 = L 2 , T21 = Ts (tx2 − tx1 ), n21 = n2 − n1 .
(14)
k=a,b,c
Laplace transform Eq. (14) to obtain the zero sequence circulating current expression of first inverter 1 3Vdc (Y1 (s) + n21 ) 2Ls 6 3Vdc 1 Iz1 (s) = − Y1 (s) + (n21 − T21 ) 2Ls 6 Iz1 (s) = −
(15) (16)
n21 is the difference Between the reference functions of the two inverters, and T21 is the difference between the zero-sequence duty cycle of two inverters.
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So as to eliminate interference term n21 and T21 circulation fluctuations and spikes caused by it, and to avoid the saturation of the integral term that may occur in the literature [4, 13] during the circulation suppression process, this essay uses a circulating current controller based on “proportional + feedforward”. The y1 output by the controller can be expressed as 1 y1 (t) = Kp (Iz1_ref − Iz1 ) − (n21 − T21 ) 6
(17)
where: y1 Refers to the adjustment amount of the modulation wave of first inverter to realize circulating current suppression of parallel system, K p is the scale factor of the proportional controller, iz1_ref is reference value of zero-sequence circulating current, and iz1 is actual feedback value of circulating current. In summary, neutral-point potential balance and zero-sequence circulation suppression are achieved by adjusting the P/N small vector action time twice in succession. From Eq. (12), the neutral-point potential balance is at this time. In this paper, parallel system uses a common AC-DC bus and neutral-point. Controller acts on the neutralpoint potential of the first inverter, and second inverter will have the same effect, and vice versa. From Eqs. (9) and (13), it can be seen that the controller only acts on the first inverter to achieve circulating current suppression. Obviously, this will inevitably affect the neutral-point potential balance control of Eq. (12). The three-phase modulation wave of two inverters are adjusted to mj = mkj + 3yFTC + 3lj yj j = 1, 2 (18) k=a,b,c
k=a,b,c
where: mkj and mkj represents the three-phase modulation wave before and after the adjustment of the first inverter, lj is the circulating current suppression adjustment factor of inverters. From Eq. (15) we can know that difference between the reference function and the zero-sequence duty cycle is not zero, which is the reason for the circulating current. Therefore, the difference of the control quantity for zero-sequence circulation suppression of two inverters is the total regulating quantity of the controller output. That is, l 1 − l 2 = y1 , |l1 | = |l 2 |. Therefore, applying l 1 and l 2 times the control amount to two inverters to suppress circulating current will not affect the neutral-point potential balance of parallel system.
5 Simulation Results In order to verify viability and correctness of idea come up in the article, a simulation analysis is performed based on the Matlab/Simulink environment. Table 1 demonstrates relevant simulation parameters. Among them, DC side capacitor voltage is standardized during the simulation process (the reference value is V dc /2). As shown in Fig. 5, in terms of neutral-point balance control: Fig. 5(a) adopts the “PI control strategy”, and it takes 0.29 s for the neutral-point potential to change from an unbalanced state to a balanced state, Fig. 5(b) adopts the “limited time control strategy”,
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Table 1. Simulation parameters Parameters
Value
DC voltage V dc
750 V
DC side capacitor C j1 /C j2 j = 1, 2
770 μF
AC voltage peak E m
311 V
Filter inductor L 1 /L 2
5/4 mH
Active current id1 /id2
15/10 A
operating frequency T s
10 kHz
and it takes 0.14 s for the neutral-point potential to change to the equilibrium state. Therefore, in terms of neutral-point balance control, compared to PI control, the control strategy of finite time proposed in this paper has a faster dynamic response speed.
Fig. 5. Neutral-point voltage simulation waveform (a) PI control (b) Finite time control
As demonstrate in Fig. 6, in terms of circulating current suppression: the reference currents of the two inverters are not identical, where id1_ref = 15 A, id2_ref = 10 A. 0–0.1 s zero-sequence circulating current is not controlled, and its peak-to-peak value is 13.5 A. From the 0.1–0.3 s simulation waveform based on “proportional control”, the circulating current is suppressed, but without considering the interference terms n21 and T21 , there is a circulating current spike, and its peak-to-peak value is about 11.5 A. 0.3–0.6 s is a simulation waveform based on “proportional + feedforward control”. Compared with the waveform under 0.1–0.3 s, the control strategy eliminates circulating current spikes and grid-connected current distortion rate is significantly reduced. Figure 7 shows the a-phase grid-connected current, circulating current and DC side capacitor voltage waveforms of inverters 1 and 2 when the given currents of two T-type three-level inverters are not identical. The given currents are: id1_ref = 15 A, id2_ref = 10 A. It can be seen from Fig. 7 that based on the decoupling idea described in 4.2 of this article, while the zero-sequence circulating current is suppressed, balance control of neutral-point potential is ensured.
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Fig. 6. Simulation waveform of zero sequence Fig. 7. Verification of decoupling control of circulation suppression zero sequence circulation and neutral-point potential equilibrium
6 Conclusion Aiming at the neutral-point potential unbalance and circulating current problems in parallel systems, this paper proposes a new SVPWM modulation method with neutralpoint fast balance and zero sequence circulating current suppression. First of all, this paper adopts the neutral-point balance control method of finite time control to realize the rapid balance control of neutral-point potential. Compared with PI, this method has faster dynamic response and better steady-state property. Then, this paper constructs a “P + feedforward” circulating current controller, which suppresses circulating current of parallel system, and effectively eliminates the integral term saturation problem of the traditional PI controller. At the same time, in the process of zero-sequence circulation suppression, this paper adopts a control decoupling idea, which effectively eliminates the influence of circulation suppression on neutral-point balance control. Acknowledgements. National Natural Science Foundation of China (U2006222), General project of national Natural Science Foundation of China (51877128), National Natural Science Foundation of China innovation Research Group Project (61821004), Major innovation project of Shandong Province (2019JZZY010904).
References 1. Wu, X., Tan, G.J., Yao, G.Y., Sun, C.D., Liu, G.H.: A hybrid PWM strategy for three-level inverter with unbalanced DC links. IEEE J. Emerg. Sel. Top. Power Electron. 6(1), 1–15 (2018) 2. Guo, X.Q., Wei, B.Z., Zhu, T.Y., et al.: Leakage current suppression of three-phase flying capacitor PV inverter with new carrier modulation and logic function. IEEE Trans. Power Electron. 33(3), 2127–2135 (2018) 3. Zhang, T.S., Xing, X.Y., Chen, A.L., Du, C.S., Zhang, C.H.: Zero-sequence circulating current control method for parallel three-level T-type inverters using SHEPWM. In: IEEE International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia), pp. 2382–2388 (2016)
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4. Xing, X.Y., Chen, A.L., Zhang, Z.C., et al.: An improved zero-sequence circulating current suppression based method in parallel three-level T-type grid-connected inverters. Proc. CSEE 37(14), 4165–4174 (2017). (in Chinese) 5. Zhang, J., Zhao, Y.: Research on control strategy of three level inverter neutral voltage balance. Control Eng. China 24(7), 1454–1460 (2017). (in Chinese) 6. Kundu, S., Mukherjee, S., Giri, S.K., et al.: A carrier-based fast capacitor voltage balancing PWM scheme for three-level NPC inverter. In: IEEE Calcutta Conference (CALCON), pp. 258–263 (2017) 7. Giri, S.K., Banerjee, S., Chakraborty, C., et al.: An improved modulation strategy for fast capacitor voltage balancing of three-level NPC inverters. IEEE Trans. Ind. Electron. 66(10), 7498–7509 (2019) 8. Giri, K.G., Mukherjee, S., Kundu, S., et al.: An improved PWM scheme for three-level inverter extending operation into overmodulation region with neutral-point voltage balancing for full power-factor range. IEEE J. Emerg. Sel. Top. Power Electron. 6(3), 1527–1539 (2018) 9. Yang, M., Luo, A., Xiao, H.G.: Circulating current analysis and suppression method for multi-inverter parallel system. Proc. CSU-EPSA 29(10), 6–11 (2017). (in Chinese) 10. Seo, J.H., Choi, C.H.: Compensation for the neutral-point potential variation in three-level space vector PWM. In: APEC 2001. Sixteenth Annual IEEE Applied Power Electronics Conference and Exposition, pp. 1135–1140 (2001) 11. Zhang, J.Z., Hu, L.C., Xu, S., et al.: Neutral potential balance control method of T-type threelevel inverter with zero-sequence voltage injection. Trans. China Electrotech. Soc. 35(04), 807–816 (2020). (in Chinese) 12. Ren, B.Y., Sun, X.D., Yu, M.J., Liu, J., Zhang, Q.: Circulating current analysis and the improved D- digital control strategy for multiparalleled three-level T-type grid-connected inverters. IEEE Trans. Ind. Electron. 67(4), 2810–2821 (2019) 13. Yao, X.Y., Jin, X.M., Li, J.K.: A neutral point voltage control strategy for parallel connected three-level inverters system. Trans. China Electrotech. Soc. 26(10), 167–173 (2011) 14. Qin, C., Zhang, C., Chen, A.L., Xing, X.Y., et al.: Circulating current suppression for parallel three-level inverters under unbalanced operating conditions. IEEE J. Emerg. Sel. Top. Power Electron. 7(1), 480–492 (2019) 15. Lee, J., Lee, K.: Time-offset injection method for neutral-point AC ripple voltage reduction in a three-level inverter. IEEE Trans. Power Electron. 31(3), 1931–1941 (2016) 16. Zhao, H., Yuan, D.Z., Wang, H.J., Yue, Y.J.: Finite time stability control strategy for power system. Control Decis. 33(12), 2283–2288 (2018). (in Chinese) 17. Du, H.B., Jiang, C.R., Wen, G.H., Zhu, W.W., et al.: Current sharing control for parallel DC–DC buck converters based on finite-time control technique. IEEE Trans. Industr. Inform. 15(4), 2186–2198 (2019)
Platform Software Scheme Based on SoftPLC Technology for New Generation of Autonomous and Controllable Protection and Measuring-Control Devices Bei Dong(B) , Yao Zhang, Yi Ding, Feng Yue, and Changsong Qin Nanjing SAC Power Grid Automation Co., Ltd., Nanjing 211153, China [email protected]
Abstract. In this paper, a software scheme of protection and measuring-control devices platform based on autonomous and controllable technology is proposed. The softPLC technology is applied to autonomous and controllable protection and measuring-control devices, and the compiled soft PLC is realized by PC. The platform uses the logic diagram visualization for application development, through the autonomous development of visualization programming IDE, reduces the compilation process, at the same time support application logic encapsulated reuse, reduce the code space, improve the validity of the protection logic development, reliability and flexibility of the application. Keywords: SoftPLC · Power system · Autonomous and Controllable · Code generating
1 Introduction Power system is a key infrastructure related to national economy, people’s livelihood and national energy security. China has built the most complex and installed power system in the world Smart grid with the largest capacity [1]. Smart substation is the core node of smart power grid construction. The protection and control device is the first line of defense to ensure the safe and stable operation of the power system. It is directly related to the essential safety of the power grid and is the most core equipment of smart substation [2, 3]. At present domestic intelligent substation protection control device depends on the basic of imported components and the operating system, localization rate less than 10%, the research and development of Autonomous and Controllable substation is imminent. Through the comparative analysis of the domestic embedded operating system [7] and the imported embedded operating system, the interface scheme design based on POSIX is carried out to reduce the dependence of the protection control device platform on the operating system. This paper proposes a protection and control device software platform based on RT-Thread, an autonomous and controllable embedded operating system. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 936–943, 2022. https://doi.org/10.1007/978-981-19-1870-4_98
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Early relay protection device using assembly language, then, intelligent device use C language, programs written to flash, logic cannot change. Product modification and maintenance cost is very high when the scene will need to modify the protection logic programs. With the development of computer technology, the development of graphical protection logic has gradually emerged. The development of graphical protection logic uses logic block diagram pattern to replace the programming language development of protection program, and realizes the effective separation of software professional knowledge and relay protection [8–10]. The platform software runs the whole protection program by analyzing the logic block diagram and resource configuration. The platform software program parses different elements through the logic engine and executes corresponding algorithm according to the preset elements sequence [11, 12]. The platform program needs to program a large number of logic elements. If new elements are added, the platform program is expanded and the code space of the platform program is increased. While the development efficiency of the protection logic developers is improved, the execution efficiency of the platform program is not reduced [4–6]. PLC technology has been very mature in industrial control [13–15]. SoftPLC is a kind of control system based on PC development structure, softPLC use a multi-task control kernel, provide a powerful instruction set, fast and accurate scanning cycle, reliable operation and can connect various I/O system and network of the open structure. It provides the same function as hard PLC. This paper proposes a software platform scheme of relay protection device based on softPLC, which combines PLC technology and protection logic diagram effectively, so the protection and platform development can be separated effectively, and the source code generation of protection logic can be realized by similar PLC technology, so as to reduce the development and code space on the device. The PLC sequence control and protection logic sequence control are effectively combined to form the device program, which is used for real-time control of relay protection device. When the protection logic changes or new protection block diagram needs to be added, only relevant protection logic needs to be modified in the integrated IDE or related protection block diagram needs to be added in the IDE. The device program can be generated by the IDE without modifying the device program, which greatly improves the development efficiency.
2 System Architecture The scheme is a programmable logic controller (PLC) soft kernel based on RTThread, and a development environment IED, together constitute a complete set of relay protection device embedded platform system. Software platforms can be quickly ported to more MCUS, saving a lot of development time. For protection developers, platform+IDE+RT-Thread provides a graphical way to develop protection devices, as shown in Fig. 1. The main features of the platform+IDE programmable system: 1. To achieve a standard extensible and open logic diagram programming system, improve the reuse rate of code, simplify the difficulty of protection development, and realize the separation of computer software and protection logic development;
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Fig. 1. System architecture.
2. The implementation of compiled softPLC, program can be cross-compiled into binary object code, compared with the interpretation of PLC, the execution efficiency is greatly improved, instruction density is higher, fault tolerance is stronger; 3. Develop graphical programming control logic with good system expansibility, not only support single-CPU control, but also support multi-CPU cooperative control. The core of IDE includes software and hardware resource configuration module, protection logic configuration module and platform program module. The logical resource configuration module realizes the control of device. Different task-driven modes are supported: Loop execution; External signal trigger; Trigger periodically.
3 Platform Software Architecture 3.1 Logic Diagram Software Model Logic diagram software model uses a layered pattern, as shown in Fig. 2, defining configurations, resources, tasks, program organization unit global variables, access paths, and so on. The configuration is at the top of the software model. For small control systems, such as a simple protection consisting of a CPU, it belongs to a configuration. A complex protection control system, such as multiple CPUs with distributed modules, also belongs to a configuration. Configuration includes hardware devices, processing resources, storage addresses for I/O channels, that is equivalent to a PLC application. Resources are located in the second layer of the software model and provide the support system for running the program. Resources provide an interface to the physical
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input and output channels of devices. There can be one or more resources in configuration. Resources provide support for all the features required for program. Each resource can support more than one application. Global variables defined within a resource are valid within that resource. Resources call run-time programs with input and output parameters. Tasks are at the third layer of the software model. A task is a scheduler of programs used to execute one or more programs. There are many types of tasks, such as primary tasks, periodic tasks, interrupt-triggered tasks, and so on. There can be multiple tasks in a resource. Once a task is set, it can control a series of program organization units to execute periodically, or to execute according to a specific event trigger. Tasks are classified into Cyclic, Event, Freewheeling and Status types. Periodic tasks are performed at fixed intervals; Event-triggered tasks start execution at the rising edge of the event variable. The internal program of the free-running task starts to execute when the task is started. A state-triggered task starts when its state variable changes to TRUE. Tasks have different priorities. A higher-priority task can interrupt a lower-priority task. Tasks are generated by IDE tools. Program include variable declaration area and code area two parts. The program can be divided into main program and subroutine, can be started by the task, and call function or function block. Global variables, address maps, and local variables can be defined in the IDE, and all variables and programs are generated by the IDE through compiled block diagrams. Access path provides a way to exchange data and information between different configurations. Many of the named variables in each configuration can be accessed through other remote configurations. 3.2 Logic Diagram Software Model Based on this logic diagram model, the software architecture of the device is formed, as shown in Fig. 3.
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Resource/logical configuration includes input resources, output resources, logical diagram configuration, and signal configuration resources. Input resources are classified into DI/AI, and output resources are classified into DO/AO/ indicator. Input resources and output resources are classified into real signals and virtual signals, which are associated with each other through a signal matrix. The main logic diagram is segmtioned and finally distributed to different functional modules to realize the distribution of application function algorithms. At the same time, the interactive data set among functional modules is established. All data set related attributes, such as cycle points, can be configured. Each logical diagram corresponds to one of the tasks described earlier. The introduction of backplane bus has a profound impact on software architecture design patterns. The backplane bus is physically divided into HSB, HCB, and ION. However, the differences are not considered in the software architecture design phase. The differences are solved in the driver layer and the mapping relationship between logical data links and physical data links is realized through configuration. A bus is a medium which different configurations exchange data. The sampling rate of the data set can be obtained from the configuration information during initialization. The sampling rate of different data sets is allowed to be inconsistent. The backplane bus adopts counter to realize data synchronization among multiple modules. A separate 32-bit counter is maintained inside the module. However, in order to
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simplify processing, such as receiving data of different sampling rates for wave recording, it is required that the relationship between sampling rates is multiple to facilitate data alignment.
4 Logic Diagram Compilation There is a corresponding code table for each element, and the corresponding code table is generated according to the sequence of the logical diagram. C code is formed according to the code table, and the input and output are associated. For any element, the name must be unique, because ultimately the list of variables and functions to be generated, as well as the input and output associations, need to be combined according to the element name. So the key issues need to be addressed as follows: 1. 2. 3. 4. 5. 6.
Definition of element name; Definition of output variables; Definition of internal variables; Implementation of element logic; Assignment of output variables; Assignment of output variables.
4.1 Element Name Definition For a element, the name is follows: Ele_A_B; A: element type; B: The name of the element. 4.2 The Definition of Element Output Variables For any element, the output variables needs to be used by by other elements in the generated code, so the output variable should be an address on the heap: 1. Reduce the stack space; 2. Variables are generated independently before the code is compiled; 3. Define as Static variables; The output structure is defined as follows: typedef struct OutputTag { Int type; Valunion val; void SetValue(const Output*val); void GetValue(Output*val); } Output; The output of element must be unique; Because the name of the element is unique, so the final generated C language element output pin definition: the element name + “_Output[x]”, x represents how many outputs of the element.
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4.3 The Definition of Internal Variables Some element without internal variables, such as and or simple logical element, other elements such as clamp, time and so on need to generate an internal static variable, the static variables can exist in the function, can also defined in a document, of course, If you need a variable, you can just generate a temporary variable inside the function. Because the internal variables of the element are only used in the function body, so the name is defined as the elements name + “_xxx”. Similarly, if temporary variables are required, the names are named in the same way. 4.4 Implementation of Element Logic For any element, the definition of internal variables has been determined by 4.3, and the definition of output variables of element has been determined by 4.2. At the same time, the input is the output from another element. At this time, all the inputs of logical calculation have been determined, and the output variables of element have also been determined. Just need to generate the corresponding code according to the logic of the element. 4.5 Assignment of Output Variables As described in the previous section, the assignment to the output variable is very simple, that is, the generated code is the assignment to the output variable, the details will not be described. 4.6 Association of Input Variables The association of element input variables is configured in the IED, and the specific details are not described.
5 Conclusion This paper designs and implements a new generation of autonomous controllable protection measurement and control device platform software based on softPLC technology. PLC technology and protection logic diagram are effectively combined to achieve the compiler softPLC, effectively solve the separation of protection development and platform development, the PLC program is cross-compiled into binary object code, and the compiler PLC is realized. The execution efficiency is greatly improved, the instruction density is higher, and the device program is generated by IDE. No need to modify the device program, greatly improving the efficiency of development and engineering.
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References 1. Chen, G., Wang, D., Qiu, Y., et al.: Challenges and development prospects of relay protection technology. Autom. Electr. Power Syst. 41(16), 1–11 (2017). (in Chinese) 2. Wang, Y., Qiu, H., et al.: A review of smart metering for future Chinese grids. Energy Procedia 152, 1194–1199 (2018) 3. Ye, Y., Xie, M., Wang, J., et al.: Real time reliability analysis of relay protection system in intelligent substation based on Markov model and GO method. Power Syst. Prot. Control 47(2), 47–55 (2019). (in Chinese) 4. Wang, X., Guo, X., Chen, Y., et al.: Design and implementation of a universal visual embedded application development platform. Power Syst. Prot. Control 44(13), 151–155 (2016). (in Chinese) 5. Xue, Z., Dong, B., Zhang, Y.: Resource configuration technical research for relay protection device. Power Syst. Prot. Control 46(4), 30–36 (2018). (in Chinese) 6. Zhong, W., Ding, N., Wu, S., et al.: Software architecture and design of the schematic programmable development platform for protective relay. Power Syst. Prot. Control 39(3), 100–104 (2011). (in Chinese) 7. Guo, C.: Research on reliability environment testing technology of domestic processor based on coordination of hardware and software. South China University of Technology, Guangzhou (2018). (in Chinese) 8. Qiu, Y., Zhou, Z., Yang, J., et al.: Research and application of remote operation and maintenance technology of relay protection. Power Syst. Prot. Control 46(18), 17–24 (2018). (in Chinese) 9. Miao, B., Tong, X.: Reconfiguration scheme of protection equipments based on IEC 61850. Autom. Electr. Power Syst. 36(23), 87–92 (2012). (in Chinese) 10. Wang, T., Xie, M., Sun, Y., et al.: Analysis of reliability for relay protection systems in smart substation. Power Syst. Prot. Control 43(6), 58–66 (2015). (in Chinese) 11. Zhang, L., Sun, Y., Luo, T.: Calculate semantic similarity based on large scale knowledge repository. J. Comput. Res. Dev. 21(11), 161 (2017). (in Chinese) 12. Vaccaro, A., Pisica, I., Lai, L.L., Zobaa, A.F.: A review of enabling methodologies for information processing in smart grids. Int. J. Electr. Power Energy Syst. 107, 516–522 (2019) 13. Chmiel, M.: FPGA-based implementation of bistable function blocks defined in the IEC 61131. Microprocess. Microsyst. 65, 35–40 (2019) 14. Simon, H., Kowalewski, S.: Mode-aware concolic testing for PLC software. Lect. Notes Comput. Sci. 1, 367–376 (2018) 15. Artale, G., Cataliotti, A., et al.: A new PLC-based smart metering architecture for medium/low voltage grids: feasibility and experimental characterization. Measurement 129, 479–488 (2018)
Characteristics of High-Frequency Resonance for Long-Distance Offshore Wind Farm Integration via MMC-HVDC System Considering the Distributed Parameter of Submarine Cable Qinghe Li, Hui Li(B) , Hongtao Tan, Jiayao Wang, Zhiting Zhou, and Jie Zheng State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044, China [email protected]
Abstract. Recently, long-distance offshore wind farm integration via modular multilevel converter based HVDC (MMC-HVDC) system has occurred an emerging type of high-frequency resonance. The accurate description of the distribution parameter of submarine cable as well as the harmonic coupling characteristics of MMC is critical for analyzing this issue. Therefore, the wind farm impedance model considering the distribution parameter and frequency dependent characteristics of submarine cables is firstly established. Secondly, the MMC impedance model with coupling harmonic components is obtained based on the harmonic state-space theory (HSS). Then, the correctness of wind farm and MMC impedance model are verified by impedance measurement. Finally, the impedance stability analysis of the gird-connected system shows that the high-frequency dynamic model that takes into account the long-distance distribution parameters and frequency dependent characteristics of submarine cable can accurately describe the high-frequency multi-resonance and negative damping effect of the long-distance offshore wind farm, which is prone to form a negative damping resonant circuit with MMC in high-frequency band, resulting in oscillatory instability of the system. Keywords: Long-distance deep offshore wind power · Modular multilevel converter based HVDC (MMC-HVDC) · Distributed parameter of submarine cable · Impedance analysis · High-frequency resonance
1 Introduction High voltage direct current (HVDC) technology based on modular multilevel converter (MMC) has become the preferred scheme for long-distance offshore wind power delivery [1]. Impedance stability analysis method is the effective means to investigate the resonant characteristics of this system, such as harmonic linearization method [3] and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 944–951, 2022. https://doi.org/10.1007/978-981-19-1870-4_99
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harmonic state-space (HSS) theory [4]. However, due to the fast control characteristics of power electronic equipment and wide-band dynamic interaction, easily leading to an emerging type of high-frequency oscillation problem [2], seriously challenging to the stable operation of power system. Currently, research related to the stability of grid-connected systems has mainly focused on sub/super synchronous oscillatory instability [5], and the few modeling studies on high frequency resonance problems have concentrated on the power supply side and controller side [6], which shows that factors such as delay links, voltage feed forward links and equivalent reactance of ac transmission line wound affect the high-frequency stability of the system [7]. Reference [8] analyses high-frequency resonance phenomena by using the π-type equivalent circuits in series to simulate submarine cables, but the high order of the submarine cable model at long transmission distances is not conducive to modeling analysis. Compared with the lumped parameter model of submarine cable, the distributed parameter model can simultaneously characterize the distribution characteristics and frequency dependence of the line parameters [9], and the analysis results are more accurate. As the ac submarine cable in long-distance offshore wind power integration via MMC-HVDC system presents the characteristics such as long transmission distance, obvious distributed capacitance and skin effect [10], its distributed parameter features cannot be ignored, and it is prone to form a resonant circuit with MMC and other equipment, resulting in the risk of high-frequency oscillation in the system. Therefore, it is necessary to accurately model the submarine cable based on the distributed parameter model for analyzing the influence of distributed parameter characteristics and frequency dependence of the submarine cable on the high-frequency resonance of grid-connected system. To sum up, the harmonic linearization method is firstly used to establish the sequence impedance model of wind turbine, while taking into account the distributed parameter characteristics of the submarine cable and the frequency dependence to obtain the wind farm outlet impedance. Then, based on the HSS theory, the closed-loop impedance model of wind farm side MMC (WFMMC) is established. Furthermore, the theoretical model is verified by impedance measurement. Finally, according to the impedance stability analysis criterion, the influence mechanism of different models and transmission length of submarine cable on the high-frequency stability of grid connected system are studied.
2 Impedance Modeling of the Grid-Connected System 2.1 Equivalent Topology of Grid-Connected System The equivalent topology of the offshore wind power generation MMC-HVDC gridconnected system is shown in Fig. 1. Since the focus of this paper is on the high-frequency stability of the interconnection system between offshore wind farm and WFMMC station under three-phase balanced condition considering the ac transmission submarine cables in both 35 kV and 110 kV network, the single machine aggregation method [5] was employed to equivalently model the offshore wind farm as one permanent magnet synchronous generators (PMSG). Taking into account the decoupling effect of the DC capacitance between the full-power converters, the wind farm model is simplified to the structure of controlled current source combined with grid-connected inverter. The
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DC transmission line and grid-side MMC station could be simplified as the DC voltage source by adopting the constant DC voltage control strategy. ZWF iin
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2.2 Impedance Modeling of the Offshore Wind Farm The conventional vector control strategy based on PLL in a rotating dq coordinate is used for the wind power inverter. The typical circuit of PMSG is shown in Fig. 2.
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Based on the harmonic linearization modeling method [3], the PMSG sequence impedance Z PM of the LC-type filter structure can be calculated as Rf1 + sLf + Kpwm Vdc Hi (s − jω1 ) − jKpd 1 //( ZPM = + Rf2 ) sCf 1 − 0.5Kpwm Vdc Tpll (s − jω1 ) I1 (Hi (s − jω1 ) − jKpd ) + M1 (1) where ω1 is the fundamental angular frequency. I 1 is the amplitude of fundamental frequency phase current at ac side. V dc is the DC bus capacitance voltage. M 1 is the amplitude of fundamental frequency modulation signal. T pll (s) is the transfer functions of PLL. H i (s) is the current loop transfer function. K pd is the cross decoupling term of current loop. mpabc is three-phase fundamental frequency modulation signal. θ pll is the output angle of the phase-locked loop (PLL). K pwm is the modulation ratio. L f , Rf1 are the filter inductance and its parasitic resistance respectively. C f , Rf1 are filter capacitor and its series damping resistance respectively. While considering the remarkable distribution characteristics and frequency dependence of the submarine cable line parameters, the relationship between the voltage and
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current at the head and end of the submarine cable line in the frequency domain can be expressed as a high-frequency dynamic model [9], namely cosh(γ (ω)l) Zc (ω) sinh(γ (ω)l) U˙ m U˙ k = (2) sinh(γ (ω)l) cosh(γ (ω)l) I˙k I˙m Zc (ω) where k, m represent the head and end of the line respectively. γ (ω) is the submarine cable propagation coefficient. Z c (ω) is the characteristic impedance of submarine cable. Z 0 (ω) is the unit impedance of submarine cable. Y 0 (ω) is the unit admittance of submarine cable. l is the length of submarine cable. In combination with Eq. (1) and Eq. (2), the impedance model of PMSG with submarine cable distribution parameters can be written as: Zc (ZPT + Zc ) + (ZPT − Zc )A(ω)2 ZWF = (3) (ZPT + Zc ) − (ZPT − Zc )A(ω)2 where A(ω) is denoted as e−γ (ω)l , which is the submarine cable transfer function. Z PT is the impedance of PMSG with conversion of transformer ratio. 2.3 HSS-Based Small-Signal Impedance Modeling of the MMC When the MMC station is connected to wind farm, the dq vector decoupling ac voltage control strategy is generally adopted to maintain the voltage and frequency stability at the point of common coupling (PCC), involving the double closed-loop ac voltage controller and circulating current suppression control (CCSC), as shown in Fig. 4 (Fig. 3). WFMMC
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According to the average model theory [4], the core expression of MMC linear time-periodic (LTP) model can be obtained as ⎧ d ic 2L dt + 2Ric + nbw u ⎪ cb + nb ucbw + nuw ucu + nu ucuw = 0 ⎪ ⎪ ⎪ d u is isw ⎨ cu Carm dt = nuw (ic + 2 ) + nu (icw + 2 ) d u ⎪ ⎪ Carm dt cb = nbw (ic − i2 s ) + nb (icw − isw ⎪ 2 ) ⎪ ⎩ d is s 2(Rs is + Ls d i dt ) + Ris + L dt + 2us = nbw ucb + nb ucbw − nuw ucu − nu ucuw
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module. L, R are arm inductance and resistance respectively. L s , Rs are ac side line inductance and resistance respectively. The subscript “w” represents the steady-state operating point of electrical quantity. The subscripts “u” and “b” represent the electrical quantities of the upper and lower arm respectively. Based on Eq. (4), the MMC linear state-space model can be further organized as the matrix form dX(t) =A(t)X(t) + B(t)U(t) dt ⎧ T
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2.4 Simulation Verification To verify the derived impedance models, a time-domain electromagnetic transient simulation model of 200 MW gird-connected system containing 5 MW wind turbine as
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presented in Fig. 1 is built in PSCAD/EMTDC platform, where the wind farm and WFMMC impedance characteristics are calculated by means of injecting small perturbation voltage signals at a series of frequencies. The comparison results are shown in Fig. 4. As it can be seen, the results of the wind farm and MMC impedance model without considering CCSC dynamics are satisfactorily fitted with the simulation data, indicating the high accuracy of the proposed model in the wide band.
Fig. 4. Verification of the subsystem impedance model. (a) PMSG. (b) WFMMC.
3 Stability Analysis of the Grid-Connected System The dynamic impedance stability of the offshore wind power integration via MMCHVDC system is determined by the impedance ratio Z WFMMC /Z WF , provided that the wind farm and the MMC system are respectively stable [5]. 3.1 Analysis of Submarine Cable Distributed Parameter The influences of 20 km submarine cable model on stability of the system are compared in Fig. 5.
Fig. 5. Influence of submarine cable model on impedance stability of grid-connected system
It can be seen from Fig. 5 that the dynamic characteristics of submarine cable mainly affect the high-frequency resonance, and there exists a sub-synchronous resonance point caused by the circulating resonance in the grid-connected system under different submarine cable model, which could be effectively suppressed by adopting
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CCSC, thus enhancing the system damping and tackling the sub-synchronous resonance issue. The traditional RL-type submarine cable model ignores the capacitance to ground and only captures the resonance point of the system at 530 Hz, which fails to reflect the multi-resonance characteristics and negative damping effect in the high-frequency band, thereby easily causing errors in stability analysis. Due to the consideration of the equivalent capacitance to ground, the high-frequency negative damping effect of the πtype submarine cable model is evident, and the number of resonant peaks is proportional to the number of circuit segments. When the distributed parameter model is used, it can more accurately describe the high-frequency multi-resonance and negative damping characteristics caused by the distributed capacitance effect, leading to a high-frequency resonance-prone region in the 150–750 Hz band. 3.2 Analysis of Submarine Cable Length The impact of the submarine cable transmission length in offshore wind farm on the stability of the grid-connected system is also compared in Fig. 6.
Fig. 6. Influence of submarine cable length on impedance stability of grid-connected system
It is evident from Fig. 6 that the high-frequency dynamic model of the submarine cable considering frequency dependence not only presents multiple resonance and negative damping characteristics in the high-frequency band, but significantly reduces the resonance peak. Due to the skin effect of the cable, the resonant gain gradually decreases and converges to a constant value, while the phase gradually approaches 0°. As the transmission length of the submarine cable increases from 20 km to 40 km, the high-frequency negative damping characteristics become more severe, greatly reducing the stability of the grid-connected system.
4 Conclusion In this paper, the impedance model of offshore wind farm integration via MMC-HVDC system are firstly explored and verified. Combined with the impedance stability criterion, the influence mechanism of ac submarine cable distributed parameter characteristics, frequency dependence and transmission length on high-frequency oscillation of the system are studied. The conclusions are as follows:
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(1) The main factor causing high-frequency oscillations in the long-distance offshore wind power integration via MMC-HVDC system is the interaction between ac submarine cable line and MMC equipment. (2) The submarine cable model considering distributed parameter characteristics and frequency dependence can effectively characterize the high-frequency multi resonance and negative damping characteristics of offshore wind farm caused by submarine cable distributed capacitance effect, with the combination of a high-precision MMC impedance model based on HSS theory, the high-frequency resonance of the grid-connected system could be accurately analyzed. (3) The high-frequency dynamic model of the submarine cable, which takes into account its skin effect, not only demonstrates the negative damping characteristics in the high-frequency band, but the amplitude and phase of impedance will gradually decrease to a fixed value. Meanwhile, the transmission length of the submarine cable plays a significant role in the high-frequency resonance of the system, the negative damping characteristics will intensify with the increase of transmission length, significantly affecting the high-frequency stability of the grid-connected system.
Acknowledgment. This work was supported by the China National High-tech Vessel Research Program under Grant (NO. MC-202025-S02).
References 1. Liu, W., Li, Q., Wang, X.: Application status and prospect of VSC-HVDC technology for large-scale offshore wind farms. Electr. Power 53(7), 55–71 (2020). (in Chinese) 2. Xie, X., He, J., Mao, H.: New issues and classification of power system stability with high shares of renewables and power electronics. Proc. CSEE 41(2), 461–475 (2021). (in Chinese) 3. Nian, H., Chen, L., Xu, Y.: Sequences domain impedance modeling of three-phase gridconnected converter using harmonic transfer matrices. IEEE Trans. Energy Convers. 33(2), 627–638 (2018) 4. Xu, Z., Li, B., Han, L.: A complete HSS based impedance model of MMC considering grid impedance coupling. IEEE Trans. Power Electron. 35(12), 12929–12948 (2020) 5. Lyu, J., Cai, X.: Frequency-domain analysis and design of stabilization controllers for wind farm integration through VSC-HVDC system. Proc. CSEE 38(14), 4074–4085 (2018). (in Chinese) 6. Zou, C., Rao, H., Xu, S.: Analysis of resonance between a VSC-HVDC converter and the ac grid. IEEE Trans. Power Electron. 33(12), 10157–10168 (2018) 7. Feng, J., Zou, C., Yang, S.: Accurate impedance modeling and characteristic analysis of VSC-HVDC system for mid- and high-frequency resonance problems. Proc. CSEE 40(15), 4805–4820 (2020). (in Chinese) 8. Song, Y., Blaabjerg, F., Wang, X.: Analysis and active damping of multiple high frequency resonances in DFIG system. IEEE Trans. Energy Convers. 32(1), 369–381 (2017) 9. Man, J., Xie, X., Tang, J.: Modeling of transmission lines for high-frequency resonance analysis of MMC-HVDC systems. Power Syst. Technol. 45(5), 1782–1789 (2021). (in Chinese) 10. Cui, P., Sun, X., Shen, H.: Linearization modeling of transmission cable for analysis of PV grid tied inversion system. Acta Energiae Solaris Sinica 42(1), 21–29 (2021). (in Chinese)
Interleaved High Step-Down Ratio DC-DC Converter with Coupled Inductor Liying Zhou(B) Jinling Institute of Technology, Nanjing 211169, Jiangsu, China [email protected]
Abstract. For the sake of addressing the difficulties of small depressurization ratio and large voltage stress of power devices in traditional Buck circuit, this work put forwards a new interleaved Buck converter based on coupled inductor. By selecting the appropriate coupled inductor turns ratio, this circuit could accomplish a great depressurization while extending the duty cycle. The interleaving technology and element rearrangement technology are used to diminish the electric tension pressure of the implement device. Moreover, the difference from the previous converters is that the converter has higher efficiency. This paper discusses the working principle of the converter, performance analysis, and verified by simulation experiments. Keywords: Interleaved technology · Coupled inductor · High step-down · Low stress
1 Introduction High step-down DC-DC converters are widely used in modern power electronics applications such as LED drivers, voltage regulator modules, telecommunications systems and battery chargers [1, 2]. Due to its wide application, it is very necessary to improve the productivity and property of several translators. Isolated converter topology [3] due to the existence of the transformer its weight, cost and loss will increase. Therefore, the non-isolated Buck converter topology is widely used in low-power buck occasions. The traditional step-down translator is almost most important no keep apart step-down DC-DC topologies because of the easy formation, low cost and mature design technology. But the previous DC-DC buck converter has some main defects in high step-down applications. For example, the exceedingly small duty ratio in big depressurization ratio conditions forces researchers to design output filters, which will greatly reduce the efficiency of the converter. Therefore, many researchers turn their attention to no keep apart big depressurization ratio translator. In the beginning, the two-stage converter [4, 5] is an important way to get a big transfer ratio. The electric tension level is reduced from high voltage to medium voltage by cascading two step-down converters, and then from medium voltage to low voltage. However, such a circuit topology is too complex, the number of components is © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 952–963, 2022. https://doi.org/10.1007/978-981-19-1870-4_100
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large, and the efficiency becomes low after cascading. On the other hand, many papers proposed a single-stage big depressurization ratio translator converter [6–21]. On the basis of the traditional Buck converter, various technologies were applied to diminish transfer ratio rate and lengthen the duty ratio, mainly including coupled inductors, series capacitors, switching capacitors, interleaving technology and so on. In References [6, 7], the coupled inductor was presented into the big depressurization ratio translator to get a higher step-down depressurization ratio by increasing the number of turns of the coupling inductance. However, while obtaining a big depressurization ratio, there are also many disadvantages, such as large input current ripple, large current stress on the junior winding margin of the coupling inductance, and large leakage inductance, resulting in high voltage spikes on the switch. For the sake of obtaining bigger depressurization ratio and lengthen the duty ratio, the depressurization ratio translator in the wake of tapping inductance is presented in [8]. Similar to the coupled inductor, this converter can obtain higher step-down ratio, but the leakage inductance between the two windings will cause serious voltage spikes on the switch, thereby reducing the efficiency of the converter. However, the problem of big galvanic current fluctuate is living as before. For the sake of reducing the current ripple, the third winding is introduced in References [9, 10] to realize the coupling of the three windings, which can reduce the current ripple and decrease the electric tension pressure of the diode, but it increases the complexity of the circuit structure, and the electric tension pressure of changers is tall as before. References [11, 12] proposed a big depressurization ratio converter in view of the contacted capacitor. Relatively speaking, the converter has larger duty cycle and higher efficiency, but the disadvantage is that the electric tension pressure of the changers is too large. Alternative approach to improve the depressurization ratio is the switched capacitor step-down converter [13, 14]. The structure is well-knit, the dominate strategy is simple, and the step-down ratio is high, but the disadvantage is also that the electric tension pressure of changers is too large. A similar technique is the switched inductor technique [15, 16], which has a bigger depressurization ratio than other translators, and because no coupling devices are used, there is no leakage inductance discharge, the switch tube has no high voltage spikes, and the voltage stress is lower. The disadvantage is that the nonlinear step-down ratio causes complex dynamic analysis. In Reference [17], a secondary step-down converter was introduced to achieve a big transfer ratio without a transformer. This structure of the translator is simple and has a large duty ratio, but the electric tension pressure of changers is big and it do not fit in the big galvanic current condition. In order to solve the problem of voltage stress, Reference [18] proposed a biquadratic depressurization ratio translator. In the identical electric tension transfer rate as the double quadratic depressurization ratio translator, the stress of the switch tube was reduced by half, but the number of components was increased, making the circuit topology complicated and increasing the cost. Except from the switching the electric tension pressure, the inlet and outlet current ripple is also an important problem of big depressurization ratio translator. The proposed interleaved step-down converter topology [19–21] solves the problem of large current ripple to a large extent. Of course, it also has problems: large the electric tension pressure of two-electrode valves and changers and petty transfer ratio.
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Based on the summary of the above literature and analysis ideas, this paper combines the interleaving technology with the coupling inductance, which could get a big transfer ratio and reduce the current ripple. At the same time, the voltage splitting technology is adopted at the input end of the interleaving converter, so that the electric tension pressure on the power device is less than inlet electric tension. In this paper, an ultrahigh voltage buck converter with low ripple and low stress for semiconductor components is proposed. This paper consists of five fragments. The second part discusses the working principle and modal analysis of the converter. The third part talks over the stable condition of the translator. The fourth part is the simulation results of the said translator. Finally, the fifth part gives the conclusion of this paper.
2 Analysis of Working Principle Figure 1 indicates the structure of the said translator. The main components of the converter are as follows: two switches (S 1 , S 2 ), two main diodes (D5 , D6 ), four auxiliary diodes (D1 , D2 , D3 , D4 ), two pairs of coupled inductors (n11 , n12 and n21 , n22 ) and five capacitors (C 1 , C 2 , C 3 , C 4 , C o ). The driving signals of two switches are two PWM pulse signals with the same duty cycle but 180° phase shift. Each coupling inductance is equivalent to the combination of leakage inductance, magnetization inductance and ideal transformer. The similar electrocircuit diagram is spread in Fig. 1 (b). In order to better explain the working principle of the translator, we can sump: 1) The capacitor value is big and the capacitor voltage is constant; 2) All power semiconductors are ideal; 3) The turn ratio of coupling inductance is defined as: n1 = n11 /n12 , n2 = n21 /n22
+ Vn n
Llk1 D1
n
n
11
S1
C1
12
+VC1
D5
C2
C1
D2 C0
Vin
+
R0 Vo
C3
n
n
21
22
C2
C0 C4
+VC3
-
C4
ILm2 D4
ILlk2
Lm2
n
R0
+
Vo
-
-V +
Llk2
(a)
D5
- + V
D3 C3
S2
S1
C2
D2
D6 C4
D4
12
Vin
-
D3
Lm1
ILm1
-
+ Vn n 12
11
11
D1 ILlk1
D6 S2
n
21
- Vn +
22
- Vn +
21
22
(b)
Fig. 1. The said translator: (a) Topological structure diagram; (b) similar electroncircuit diagram.
The Fig. 2 indicates the crux wave shape of the said translator in steady state. It can be seen that each changer time has 8 modalities. Because this circuit is symmetrical, we just discuss the former four of the all modalities. The tantamount circuit diagram of the modalities is presented in Fig. 3.
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Fig. 2. Key waveforms of the converter.
Llk1 D1
n
n
11
Lm 1
Llk1
12
D1
S1
n
Lm1
12
S1 D5
D5
C2
C1
C2
C1
n
11
D2
D2 Vin
C0
R0
+
Vo
Vin
C0
-
D3 C4
C3 D4
Lm2 Llk2
n
Llk1
n
C4 D4
S2
n
21
(a) D1
n
D6
n
21
22
(b) n
11
Lm1
C3
Llk1
12
D1
S1
n
11
Lm 1
C3
D5
n
12
S1 D5
C2
C2
D2
D2 Vin
C0
R0
+
Vo
Vin
-
D3 C4
C3 D4
Lm2 Llk2
n
22
R0
+
Vo
C4
D4
n
(c)
C0 D3
C3
D6 S2
21
Vo
S2
Lm2 Llk2
22
+
-
C3
D6
R0
D3
Lm 2 Llk2
n
21
D6 S2
n
22
(d)
Fig. 3. The similar circuit diagram under different modes: (a) the first stage; (b) the second stage; (c) the third stage; (d) the fourth stage.
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Mode 1 (t 0 –t 1 ): Before t 0 , the changers S 1 and S 2 are all cut off, corresponding to Mode 8. Due to the symmetry of the circuit, the equivalent circuit is the same as Mode 4, and the currents of magnetization inductors L m1 and L m2 flow through n11 and n21 , respectively. At the secondary side, the output capacitor C 0 is charged through D5 , n21 , D6 and n22 . At time t 0 , when S 1 is closed, the leakage inductance current I lk1 begins to increase, and the current flowing through n11 decreases linearly. In this mode, the voltage equation of the equivalent circuit is as follows: Vin = VC1 + VC3 − Vo Vo = −Vn22 VC1 = VC2 + Vn11 + VLk1 VC2 = Vn12 + Vo
(1)
Since n11 , n12 and n21 , n22 are two pairs of coupled inductors, there are: VLm1 = Vn11 = n1 Vn12 VLm2 = Vn21 = n2 Vn22
(2)
From the above formulas, the time domain expression of the inductive current is: n1 (VC2 − Vo ) (t − t0 ) Lm1 n2 Vo iLm2 (t) = ILm2 (t0 ) + (t − t0 ) Lm2 VC1 − VC2 − n1 (VC2 − Vo ) iLk1 (t) = (t − t0 ) Lk1 iLm1 (t) = ILm1 (t0 ) +
(3)
Mode 2 (t 1 –t 2 ): In Mode 1, the leakage inductance current I lk1 increases from zero. When it increases to I Lm1 , the diode D2 is reversely biased. Mode 2 begins. The equivalent circuit diagram will can be seen in the Fig. 3 (b). In this mode, the load is powered by energy storage in C 1 , n11 , n12 and magnetized inductance L m2 . The voltage equation at this stage is as follows: Vin = VC1 + VC3 − Vo Vo = −Vn22 VC1 = Vn11 + Vn12 + VLk1 + Vo
(4)
Combined with Formula (2), the time-domain expression of inductor current can be obtained as follows: iLm1 (t) = ILm1 (t1 ) + iLm2 (t) = ILm2 (t1 ) −
n1 1+n1 (VC1
− Vo )
Lm1 n2 Vo (t − t1 ) Lm2
(t − t1 ) (5)
Modal 3 (t 2 –t 3 ): In the time of t 2 , the changer S 1 is cut off. The source saved stored in the leakage inductance L lk1 makes the diode D1 on, and its current flows through the path
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L lk1 − n11 − C 2 − D1 . At this stage, the leakage inductance current I Llk1 decreases and the current of n11 increases. At time t 3 , the current in n11 increases to I Lm1 and the stray inductor current I Llk1 decreases to 0. The voltage equation at this stage is as follows: Vin = VC1 + VC3 − Vo Vo = −Vn22 = −Vn12 VC2 + Vn11 + VLk1 = 0
(6)
Combined with Formula (2), the time domain expression of inductor current in this mode is: n1 Vo (t − t2 ) Lm1 n2 Vo iLm2 (t) = ILm2 (t2 ) − (t − t2 ) Lm2 VC2 − n1 Vo iLk1 (t) = ILk1 (t2 ) − (t − t2 ) Lk1 iLm1 (t) = ILm1 (t2 ) −
(7)
Mode 4 (t 3 –t 4 ): At time t 3 , the stray inductor galvanic current is reduced to 0, and the two-electrode valve D1 is reversely biased. In this mode, both switches are off, and n12 and n22 charge the output capacitor C o through diodes D5 and D6 , respectively. The main voltage equations under this mode are as follows: Vin = VC1 + VC3 − Vo Vo = −Vn22 = −Vn12
(8)
Combined with Formula (2), the time domain expression of inductor current under this mode can be obtained as follows: n1 Vo (t − t3 ) Lm1 n2 Vo iLm2 (t) = ILm2 (t3 ) − (t − t3 ) Lm2 iLm1 (t) = ILm1 (t3 ) +
(9)
3 Characteristic Analysis The stray inductor is quite modest, thus it is ignored in the analysis procedure to facilitate the translator’s static performance analysis. In addition, the turn ratio of two pairs of coupled inductors is set to be equal, that is: n = n1 = n2
(10)
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3.1 Voltage Gain It can be seen from the equivalent circuit diagram that: Vin = VC1 + VC3 − Vo
(11)
The volt-second balance rule for L m1 (Within one cycle): n (1 − D)TS DTS − nVo · =0 (VC1 − Vo ) · n+1 2 2 (1 − D)TS DTS n(VC2 − Vo ) · − nVo · =0 2 2
(12)
The above formula can be simplified as: 1 + n(1 − D) Vo D nVo + VC1 = n+1
VC1 = VC2
(13)
Since the circuit is symmetrical, so: VC1 = VC3 VC2 = VC4
(14)
Bring formula (13) and formula (14) into formula (11) to: Vin =
2 − D + 2n(1 − D) Vo D
(15)
Then, the voltage gain of the converter is: G=
Vo D = Vin 2 − D + 2n(1 − D)
(16)
3.2 Voltage Stress of Switches and Diodes It can be known from the equivalent circuit of mode 3 that the most value of the electric tension pressure of the changer S 1 is: VS1 max = VC1 + VC2
(17)
Since the circuit is symmetrical, so: VS2 max = VC3 + VC4
(18)
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Bringing the formula (13) into the formula, you will know the maximum the electric tension pressure of the changers S 1 and S 2 is: VS max =
Dn + (n + 2)[1 − n(1 − D)] Vin (n + 1)[2 − D + 2n(1 − D)]
(19)
From the equivalent circuit of mode 2, the maximum voltage stress of diode D5 is: VD5 max = VC1 + Vn12
(20)
The voltage equation of the equivalent circuit of mode 2 (4) can be derived: Vn12 =
VC1 − Vo 1+n
(21)
According to the symmetry of the circuit, the maximum the electric tension pressure two main diodes D5 and D6 is: VD max =
1 Vin 2 − D + 2n(1 − D)
(22)
From the equivalent circuit of mode 1 and mode 3, we could get that the maximum the electric tension pressure of diodes D1 and D2 are V C1 . Combined with the voltage equation of equivalent circuit of mode 2, we could conclude that the most value the electric tension pressure of four auxiliary diodes: VD max = VC1 =
1 + n(1 − D) Vin 2 − D + 2n(1 − D)
(23)
3.3 Converter Performance Comparison For the sake of evaluating the performance of the converter in this work, as indicated in the Table 1, the said translator is contrasted with else commutation transfer. The translator in References [3, 10, 12, 19], and are compared with the converter in this paper. The relationship between the gain and duty ratio of those translators is also compared, as shown in Fig. 4 (set the number of turns n = 2). It can be seen from the figures and tables that the transfer ratio of the circuit, the electric tension pressure of the switches and diodes and so on have greater advantages in the case of the same number of switches, that is, the complexity of the circuit topology is roughly equal. Therefore, through appropriate design, the proposed high step-down ratio converter can use lower rated voltage switching elements, which can achieve higher efficiency.
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L. Zhou Table 1. Performance comparison of converters. [3]
[10]
[12]
[19]
The proposed converter
Voltage gain
D 2−D
D 2−D
D(1−D) n+D(1−D)
D 2
D 2−D+2n(1−D)
Voltage stress of switch
Vin 2−D
Vin 2−D
Vin − Vo
Vin
Dn+(n+2)(1+nD−n) (n+1)(2−D+2n−2nD) Vin
Voltage stress of diode
Vin 2−D
1+n(1−D) 2−D Vin
(1−D)Vin n+D(1−D)
Vin + Vring
1+n(1−D) 2−D+2n(1−D) Vin
Voltage current level
200-24 V,10 A
140-24 V,8.3 A
130-12 V,15 A
150-24 V,10 A
200-12 V,10 A
Fig. 4. Comparison diagram of converter gain and switching duty cycle.
4 Simulation Experiments For the sake of proving the correctness of the above work analysis, the simulation model of the said translator is built in saber environment, and the circuit element parameters of the said translator are given in the Table 2. The Fig. 5 is the output voltage waveform of the converter. Figure 6 shows the electric tension and galvanic current waveforms of the main semiconductor devices of the converter. From the figure we can get that the electric tension pressure of all components of the said translator is less than the input voltage while achieving high buck ratio, which is basically consistent with the voltage stress analysis described earlier.
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Table 2. Component parameters of converter prototype. Parameter
Value
V in
200 V
Vo
12 V
Po
120 W
fs
100 kHz
Co
47 uF
C1, C2, C3, C4
10 uF
L1 , L2
400 uH
n
2
Fig. 5. The simulation waveform of the output voltage V o .
Fig. 6. The simulation waveforms of the converter: (a) I S1 , V S1 ; (b) I D1 , V D1 ; (c) I D3 , V D3 ; (d) I D5 , V D5 .
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5 Conclusion The work introduces a unused kind of ultra-high buck interleaving circuit. The simulation results show that, unlike other buck converters based on coupled inductors, the switching electric tension pressure of the converter is far smaller than the V in , so the capacitor discharge and switching loss could be significantly decreased. By increasing the cylinder number of the coupling inductance, the transfer ratio of the circuit could be further reduced, and the source kept in reserve in the stray inductor is suck up and recovered due to the use of the clamping circuit. In addition, the proposed interleaving topology can diminish the electric tension pressure of the element. Therefore, the said converter has great advantages in the non-isolated applications of high input voltage buck conversion ratio and high power density.
References 1. Gong, W.: Digital DC/DC Converter Based on Buck Circuit. University of Electronic Science and Technology (2013) 2. Pogaku, V., Sensarma, P.: Super Buck Converter for High Step-Down DC-DC Conversion. In: IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, IEEE (2019) 3. Zhang, X.: Design of a Flyback Switching Power Converter. University of Electronic Science and Technology (2012) 4. Yao, Y., Zhang, D., Xu, D.: Optimal design and stability of output impedance of cascaded DC/DC converter. J. Electrotech. 03, 147–152 (2009) 5. Chonsatidjamroen, S., Areerak, K., Areerak, K.: The optimal cascade pi controller design of buck converters. In: 2012 9th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, Phetchaburi, Thailand, pp. 1–4 (2012). https://doi.org/10.1109/ECTICon.2012.6254130 6. Hwu, K.I., Jiang, W.Z., Yau, Y.T.: Ultrahigh step-down converter. Power Electron. IEEE Trans. 30(6), 3262–3274 (2015) 7. Zhao, X., Yeh, C.S., Zhang, L., et al.: A high-frequency high-step-down converter with coupled inductor for low power applications. In: 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), IEEE (2017) 8. Yao, K., Qiu, Y., Xu, M., et al.: A novel winding-coupled buck converter for high-frequency, high-step-down DC-DC conversion. IEEE Trans. Power Electron. 20(5), 1017–1024 (2002) 9. Hajiheidari, M., Farzanehfard, H., Adib, E.: High-step-down DC–DC converter with continuous output current using coupled-inductors. IEEE Trans. Power Electron. 34(11), 10936–10944 (2019). https://doi.org/10.1109/TPEL.2019.2899951 10. Khalili, S., Farzanehfard, H., Esteki, M.: High step-down DC-DC converter with low voltage stress and wide soft-switching range. IET Power Electron. 13(14), 3001–3008 (2020) 11. Cheshmdehmam, D., Adib, E., Farzanehfard, H.: Soft-switched nonisolated high step-down converter. IEEE Trans. Indus. Electron. 66(1), 183–190 (2019). https://doi.org/10.1109/TIE. 2018.2829471 12. Hajiheidari, M., Farzanehfard, H., Esteki, M.: Asymmetric ZVS buck converters with highstep-down conversion ratio. IEEE Trans. Ind. Electron. 99, 1–1 (2020) 13. Biswas, M., Majhi, S., Nemade, H.B.: Two-phase high efficiency interleaved buck converter with improved step-down conversion ratio and low voltage stress. IET Power Electron. 12(15), 3942–3952 (2019)
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14. Chen, P.-H., Cheng, H.-C., Chen, P.-H.: A fully integrated step-down switched-capacitor DC– DC converter with dual output regulation mechanisms. IEEE Trans. Circuits Syst. II: Express Briefs 67(9), 1649–1653 (2020). https://doi.org/10.1109/TCSII.2020.3008972 15. Mathai, R., Joseph, S., Paul, S., et al.: Switched Inductor Quadratic Buck Converter 16. Dynamic analysis of the switched inductor buck converter. In: IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society. IEEE (2019) 17. Ayachit, A., Kazimierczuk, M.K.: Power Losses and Efficiency Analysis of the Quadratic Buck Converter in CCM. IEEE (2014) 18. Sa, F., Eiterer, C., Ruiz-Caballero, D., et al.: Double quadratic buck converter. In: Power Electronics Conference. IEEE (2014) 19. Lee, I.O., Cho, S.Y., Moon, G.W.: Interleaved buck converter having low switching losses and improved step-down conversion ratio. IEEE Trans. Power Electron. 27(8), 3664–3675 (2012) 20. Liu Junfeng, H., Renjun, Z.J.: A non-isolated interleaved DC-DC power converter with high step-down ratio. J. Electrotechn. 33(020), 4763–4770 (2018) 21. Esteki, M., Poorali, B., Adib, E., et al.: Interleaved buck converter with continuous input current, extremely low output current ripple, low switching losses, and improved step-down conversion ratio. IEEE Trans. Industr. Electron. 62(8), 4769–4776 (2015)
Numerical Investigations of Electric Vehicle Wireless Charging Systems Under the Interference of Metallic Foreign Objects Jiawei Wang(B) , Jinghui Shao, and Xikui Ma State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China [email protected]
Abstract. Electric vehicle wireless charging systems based on wireless power transmission technology (WPT) are superior to conventional charging systems requiring cables due to their compact structure, convenience and reliability since they’re free of plugs. However, the efficiency and safety of the wireless systems highly rely on the carefully designed match among the transmitter coils, receiver coils and cores, which can be severely spoiled under the interference of metallic foreign objects, which are not rare in garages, charging stations or other public places where the wireless charging systems are deployed. In this work, the interactions of the Electric vehicle wireless charging systems and metallic foreign objects are thoroughly investigated via full-wave numerical simulations based on the finite element methods. We illuminate that metallic foreign objects can increase the equivalent resistances, inductances as well as the losses of the charging systems, leading to serious efficiency and safety issues. Keywords: Wireless power transmission · Electric vehicle wireless charging systems · Metallic foreign objects · Numerical simulations
1 Introduction An electric vehicle is an automobile that is propelled by one or more electric motors, which are powered by energy stored in batteries. Compared with conventional internal combustion engine (ICE) vehicles powered by gasoline or diesel, electric vehicles have much better NVH performance and more importantly, have no exhaust emissions and lower emissions overall. In recent years, electric vehicles are becoming increasingly popular due to technological developments and an emphasis on the reduction of transportation’s impact on climate change and other environmental issues. However, the power supplement for electrical vehicles is not as efficient and straightforward as that of ICE vehicles, and charging issues remain to be the main obstacle to the spread of electric vehicles. Most existing mass-produced electric vehicles require cables for charging, which are inconvenient to use. In addition, frequent plugging in and plugging out of the cables © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 964–977, 2022. https://doi.org/10.1007/978-981-19-1870-4_101
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make the charging systems unreliable. Electric vehicle wireless charging systems based on wireless power transmission (WPT) technology [1–3] are superior to conventional charging systems with cables due to their compact structure, convenience and reliability since they’re free of plugs. In 2017, Mercedes-Benz developed a plug-in hybrid electric (PHEV) sedan vehicle S500e equipped with WPT charging system [4]. In 2018, Bavarian Motor Works (BMW) presented 530e iPerformance PHEV sedan, which may be the first mass-produced electric vehicle with a WPT charging system, the efficiency of which is 85% [5]. Late 2017, China’s largest automobile manufacturer SAIC Motor pushed out an electric sport utility vehicle named Marvel X, which also has a WPT charging system of 85% efficiency. Though WPT charging systems for electric vehicles seem promising, efficiency and safety issues must be resolved prior to practical applications [6]. the efficiency and safety of the WPT systems rely on the carefully designed match among the transmitter coils, receiver coils and cores, which can be severely spoiled under the interference of metallic foreign objects. Unfortunately, WPT charging systems are often deployed in public places including garages and charging stations, where metallic foreign objects like coins, aluminum cans and coins are not rare. The WPT charging system of the aforementioned 530e iPerformance PHEV sedan requires that the horizontal and vertical deviations of the parking position are less than 14 cm and 7 cm to launch. A typical aluminum can of 11 cm height and 3.5 cm radius would distort the distribution of local magnetic field flux and break down the charging system. Therefore, the influence of metallic foreign objects on WPT charging systems must be evaluated via accurate numerical simulations. Y. Liu et al. [7] carried out full-wave analysis of the shielding effect of the metallic underpans on the WPT charging systems based on the method of moment. They also advocated a unified design methodology taking into account both the WPT charging systems and the electromagnetic environment. However, this work didn’t account for the influence of metallic foreign objects. Z. Ma et al. extended [7] and presented finite element analysis of the impact of metallic cubes on the WPT charging systems [8]. They also compared the efficiency of the charging system under interference under cubes made of copper and iron. This manuscript focuses on the numerical investigations of the influence of practical metallic foreign objects on WPT charging systems based on the magnetic coupling structure and the widely adopted DD coils, the geometry of which is given in Fig. 1. The numbers of turns of the primary coil and the secondary coil are set to 9 and 12, respectively. Except for metallic sheets, this research also presents analysis regarding two practical metallic foreign objects, namely an iron clip and an aluminum can.
2 The Influence of Metallic Foreign Objects on WPT Systems from a Circuit Perspective There are two types of metallic foreign objects, which are distinguished from each other by their permittivity μ. The first kind of foreign objects, which are referred to as nonmagnetic objects hereinafter, exhibit high conductivity while the relative permittivity μr ≈ 1. The other type of foreign objects, typically made of iron, cobalt, and nickel, are called ferromagnetic objects and exhibit high γ and μ simultaneously. When interacting
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with electromagnetic fields, both types of foreign objects lead to eddy current effect while only ferromagnetic objects can produce magnetic effect. When metallic foreign objects intrude the energy transfer regions of WPT systems, the resultant eddy current effect can be recognized as a short-circuit current ring, thus a current coil coupled to the transmitter coils of WPT systems are often adopted in circuit simulations to model eddy current effect, as is shown in Fig. 2.
Fig. 1. Geometry of the DD coils.
R4
R1
L4
I4
I2
I1
L2
L1
Us C1
R2
RL M
C2
Fig. 2. The equivalent circuit model indicating the coupling among coils and foreign object.
In Fig. 2, L4 and R4 denote the equivalent inductance and resistance of the metallic foreign objects, respectively. These two parameters are determined by the material and volume of foreign objects as well as the working frequency of the WPT systems. The mutual inductance between the foreign objects and the transmitter coils is represented by M, which is related to the volume and position of the foreign objects. Based on circuit theory, the equivalent resistance R1 , inductance L 1 and mutual inductance coefficient M C of the transmitter coils can be calculated as
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R1 = R1 + L1 = L1 −
2 R4 ω2 M14
R4
(1)
L4
(2)
ωM14 M24 R4 + jωL4
(3)
R24 + ω2 L24 2L ω2 M14 4
R24 + ω2 L24
MC = M12 − j
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The invasion of nonmagnetic foreign objects leads to increase in R1 and decrease in L 1 and M C . The invasion of ferromagnetic objects, on the other hand, result in more complex phenomena since there exist both eddy current effect and magnetic effect. The inductance of the transmitter coils for ferromagnetic foreign objects and rectangular coils are given by [8] L1 =
2μr μ0 li4 π(li2 + z 2 ) li2 + z 2
(4)
where μ0 is the absolute permeability of the vacuum, μr the relative permeability, l i the edge length of the i-th turn of rectangular coils, z the distance from the observation points on the axis of coils to the plane on which the coils are placed. When there’s no ferromagnetic objects in the energy transfer region, μr equals to 1. Ferromagnetic objects increase effective μr as well as L 1 . The equivalent impedance of the transmitter coils can be further calculated as Z11 = R1 +
2 R4 ω2 M14
2L ω2 M14 4 R + jω(L − L4 + L5 ) 4 1 2 2 2 2 2 R4 + ω L4 R4 + ω L24
(5)
where L 5 denotes the mutual inductance of the ferromagnetic objects and the transmitter coils. This inductance arising from the magnetic effect is related to the permeability, volume, and position of ferromagnetic foreign objects. In summary, the eddy current effect due to the invasion of nonmagnetic objects increases the equivalent resistance of the transmitter coils while the inductance is decreased. In the presence of ferromagnetic foreign objects, both eddy current effect and magnetic effect appear. The latter leads to increase in the equivalent inductance of the transmitter coils. The resultant inductance is related to the material, shape, volume, and position of the foreign objects. Accurate extraction of circuit parameters as well as the prediction of electromagnetic response of the WPT systems require full-wave finite element analysis, which is the focus of the following section.
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3 Finite Element Analysis of Metallic Sheets’ Influence on the WPT Systems In this section, we adopt the commercial software COMSOL Physics to carry out the finite element analysis of the metallic sheets’ influence on the WPT systems. 3.1 Comparison of the Influence of the Metallic Sheets of Different Materials on the WPT Systems The geometry of the finite element model built by COMSOL is depicted in Fig. 3, in which the air domain and the absorbing boundaries are hided. Aluminum plates of 5 mm and 3 mm thickness are adopted for shielding the transmitter coils and receiver coils, respectively. Metallic sheets of 50 mm × 75 mm × 1 mm, which are made of aluminum and steel, are placed at the observation point (x = 0, y = 0, z = 10 mm). The material properties for aluminum and steel are given in Table 1, where C p is the specific heat capacity, ρ the mass density, γ the conductivity and μr the relative permeability.
Fig. 3. Geometry of the wireless power transmission system interfered by a metallic sheet created with COMSOL. (Air domain and the absorbing boundaries are hided.)
Table 1. Material properties of the metallic sheets Parameter
Value Aluminum
Steel
μr
1
100
γ /(S/m)
3.77 × 107
4.03 × 106
C p /(J/(kg·K)
900
475
ρ(g/cm3 )
2.7
7.85
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Table 2. Equivalent circuit parameters of the wireless power transmission system with and without interference of foreign objects Parameter
Value No foreign object
Aluminum sheet
Steel sheet
f (kHz)
20
20
20
L 1 (µH)
278.22
278.22
278.70
L 2 (µH)
309.25
309.26
309.25
M (µH)
75.167
74.164
75.132
k
0.2563
0.2562
0.2559
Table 2 presents the equivalent circuit parameters of the WPT system with and without interference of foreign objects. It can be observed that the aluminum sheet has very little impact. The steel sheet, on the other hand, increase the self-inductance of the transmitter coils while the mutual inductance as well as k are decreased. However, the influence of steel sheet is not significant due to its small dimension compared with the coils. 3.2 Discussion Regarding the Positions of Metallic Sheets Figure 4 depicts the distribution of magnetic flux density of the WPT system without the interference of metallic sheets. The energy transfer region can be roughly divided into self-coupling (SC) domains and mutual-coupling (MC) domains. We only label the SC and MC domains for the transmitter coils for simplicity.
Fig. 4. The distribution of magnetic flux density of the wireless power transmission system without interference of foreign objects (x-z view).
Firstly, we investigate the influence of the position of the aluminum sheet on the WPT systems. The movement of the aluminum sheet is restricted to an x-y plane (z = 10 mm). The sheet moves towards negative x-direction and some snapshots of the distribution of the magnetic flux density are presented in Fig. 5, where x1 denotes the x-coordinate of
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the barycenter of the sheet. When x1 = −200 mm, the eddy current effect considerably neutralizes the magnetic coupling and decreases the mutual inductance. When x1 equals to −100 mm and −300 mm, the aluminum sheet offsets the self-coupling magnetic flux density of the transmitter coils, leading to decreased self-inductance. In addition, distortion of the distribution of magnetic flux density around the aluminum sheet can be observed. Figure 6 presents some snapshots of the distribution of the magnetic flux density when the sheet moves towards positive y-direction. It can be seen that in this case the aluminum sheet has very little influence on the field distribution, which agrees well with the conclusion in [8]. Secondly, we discuss the case for moving steel sheet. Still, we restrict the movement of the steel on the aforementioned x-y plane (z = 10 mm). Figure 7 shows a series of snapshots of the distribution of the magnetic flux density while the sheet moves towards negative x-direction. It can be observed that the steel sheet can also neutralize the magnetic flux density of the WPT system. However, the influence of the steel sheet is not as strong as that of the aluminum sheet. This is because steel objects produce eddy current and increased μr simultaneously. These two effects offset each other, thus the superposition of them is not as significant as eddy current effect alone.
(a) x1=0 mm
(b) x1=-100 mm
(c) x1=-200 mm
(d) x1=-300 mm
(e) x1=-400 mm
Fig. 5. Magnetic flux density under the interference of an aluminum slice moving along the x-axis.
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(a) y1=0 mm
(b) y1=100 mm
(c) y1=200 mm
(d) y1=400 mm
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Fig. 6. Magnetic flux density under the interference of an aluminum slice moving along the y-axis
(a) x1=0 mm
(b) x1=-100 mm
(c) x1=-200 mm
(d) x1=-300 mm
(e) x1=-400 mm
Fig. 7. Magnetic flux density under the interference of a steel slice moving along the x-axis.
When the steel sheet moves towards positive y-direction, we draw a similar conclusion to that for the aluminum case that the metallic sheet has very little influence. The snapshots of field distribution are omitted.
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3.3 Influence of the Metallic Sheets on the Equivalent Circuit Parameters on the WPT Systems The variations of the equivalent parameters of the WPT systems when metallic sheets moving on the x-y plane with z = 10 mm, where M is the mutual inductance, k the coupling coefficient, and L1 and L2 the self-inductances of the transmitter coil and receiver coil, respectively. It’s worth noting that all parameters are normalized by the values extracted without any foreign object. It’s observed from Fig. 8(a) that the invasion of the aluminum sheet moving along the x-axis leads to decreased self-inductance of the transmitter coils while for receiver coils this value is almost invariant. The mutual inductance and coupling coefficient decrease to their minimums and then increase as the aluminum sheet move along the x-axis from the inner self-coupling domain towards the outer self-coupling domain. Both minimal values are reached when x is somewhere between 100 mm and 200 mm. Figure 8(b) indicates very similar conclusions for the case involving the steel sheet. Figure 9 illuminates the variations of the equivalent parameters while the metallic objects are moving along the y-axis. For the aluminum sheet, all parameters remain almost invariant, while the steel sheet slightly increase the self-inductance of the transmitter coils. A little decrease in mutual inductance as well as the coupling coefficient both is also observed.
Fig. 8. Variations of the equivalent circuit parameters of the coils under the interference of metallic slices moving along the x-axis
The last scenarior to be investigated is that the metallic sheets have equivalent displacements in x- and y- directions. From Fig. 10 we notice that the self inductance of the transmitter coils decrease first and begin to increase when the displacement exceeds somewhere between 100 mm and 200 mm. The coupling coefficient keeps increasing as the displacement enlarges. When the displacement reaches 400 mm, the metallic sheets can hardly influence the coils since they’re out of the transfer region. The above conclusions apply to both aluminum and steel sheets.
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Fig. 9. Variations of the equivalent circuit parameters of the coils under the interference of metallic slices moving along the y-axis
Fig. 10. Variations of the equivalent circuit parameters of the coils under the interference of moving metallic slices with identical x- and y- coordinates
3.4 Loss Analysis The calculated losses of the metallic sheets as well as the WPT system are presented in Fig. 11. Here the total losses refer to the losses of the WPT system, which includes the aluminum plates for shielding. It’s observed that the steel sheet leads to much larger losses than those caused by the aluminum sheet. The total losses are almost the same regardless of the material of the metallic sheet.
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Fig. 11. Variations of the losses of the wireless power transmission system under the interference of moving metallic slices.
4 The Influence of Two Practical Metallic Foreign Objects on the WPT System 4.1 Clip The geometry of the clip is given by Fig. 12. The length, width, and diameter of the clip are 29 mm, 8 mm and 1 mm, respectively. The clip is made of iron with γ = 1.12 × 107 S/m and μr = 4000. The barycenter of the clip is placed at (−100 mm, 100 mm, 10 mm), which according to Sect. 3 is where the foreign objects produce the strongest interference. The equivalent circuit parameters extracted by COMSOL are listed in Table 3, from which we conclude that the WPT system is hardly affected due to the small dimension of the clip. In addition, the loss of clip is 0.1359 W, which is also ignorable.
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Fig. 12. Geometry of the clip
Table 3. Equivalent circuit parameters of the wireless power transmission system under interference of foreign objects. Parameters
No foreign object
Clip
Aluminum can
L 1 (µH)
278.22
278.22
276.30
L 2 (µH)
309.25
306.26
308.51
M (µH)
75.167
75.169
74.607
k
0.256258
0.255537
0.255537
Q1 (W)
0
0.1359
94.107
Q2 (W)
156.17
156.38
157.53
The distribution of the magnetic flux density in the presence of iron clip is shown by Fig. 13. From the zoom-in view we notice that the neighboring field distribution of the clip is distorted. Again, due to the small dimension the distortion can hardly affect the overall performance of the WPT system.
Fig. 13. Magnetic flux density under the interference of a clip.
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4.2 Aluminum Can The geometry of the finite element model involving the aluminum can is given in Fig. 14. The outer diameter and the height of the can are 57.7 mm and 102.1 mm, respectively. The thicknesses of the bottom, the side wall and the lid are 0.21 mm, 0.11 mm and 0.28 mm, respectively. The conductivity and relative permeability of aluminum are 3.77 × 107 S/m and 1, respectively. The barycenter of the clip is still placed at (−100 mm, 100 mm, 10 mm). The equivalent circuit parameters extracted by COMSOL are listed in Table 3.
Fig. 14. Geometry involving an aluminum can as the foreign object to the wireless power transmission system
Fig. 15. Magnetic flux density under the interference of an aluminum can.
It can be observed from Table 3 that in the presence of the aluminum can, the selfinductance of the transmitter coils and the receiver coils, the mutual inductance and the coupling coefficient decrease considerably. More importantly, the loss due to the can reaches 94.107 W, which is comparable to that of the WPT system and leads to serious temperature raise of the can. This is a severe risk to the WPT system. The distribution of the magnetic flux density in the presence of iron clip is shown by Fig. 15. In this case the distortion of the field distribution is no longer ignorable due to the large dimension of the foreign object.
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5 Conclusions In this manuscript, the influence of metallic foreign objects on the WPT system using the magnetic coupling structure is investigated based on the finite element simulations. The following conclusions are drawn. (1) The invasion of nonmagnetic metallic objects causes eddy current effect, while the invasion of ferromagnetic objects leads to eddy current effect and increased permeability simultaneously. The eddy current effect has more obvious impact on the WPT charging systems. (2) The efficiency of the WPT systems is related to the material, volume, and position of the foreign objects. The clip has little influence due to its small dimension. For comparison, the aluminum can weaken the coupling of the coils and produces considerable loss, because its dimensions are comparative to those of the WPT systems. Therefore, the aluminum cans can cause serious safety issues, making them unignorable foreign objects to WPT charging systems. (3) Metallic foreign objects result in decreased inductance and increased resistance. These equivalent circuit parameters can be exploited as the characteristic indexes for the recognition of metallic foreign objects. Furthermore, Eq. (5) illuminates that the real and imaginary components of the coils’ impedance can be used to differ ferromagnetic objects and nonmagnetic objects.
Acknowledgements. This research is sponsored by the state key laboratory of electrical insulation and power equipment, Xi’an Jiaotong University under grants EIPE21302 and EIPE21311.
References 1. Tesla, N.: High frequency oscillators for electrotherapeutic and other purposes. Proc. IEEE 87(7), 1282–1292 (1999) 2. Kurs, A., Karalis, A., Moffatt, R., et al.: Wireless power transfer via strongly coupled magnetic resonances. Science 317(5834), 99–110 (2007) 3. Zhang, B., Shu, X., Huang, R.: The development of inductive and resonant wireless power transfer technology. Trans. China Electrotech. Soc. 32(18), 1–17 (2017). (in Chinese) 4. Miller, J., Onar, O., White, C., et al.: Demonstrating dynamic wireless charging of an electric vehicle: the benefit of electrochemical capacitor smoothing. IEEE Power Electron. Mag. 1(1), 12–24 (2014) 5. Shin, J., Shin, S., Kim, Y., et al.: Design and implementation of shaped magnetic-resonancebased wireless power transfer system for roadway-powered moving electric vehicles. IEEE Trans. Ind. Electron. 61(3), 1179–1192 (2013) 6. Guo, W.: Study on the Electromagnetic Environment and Shielding Technology for the Electric Vehicle Wireless Charging System. Beijing Jiaotong University, Beijing (2016).(in Chinese) 7. Liu, Y., Ren, Y., Hao, H., et al.: Full-wave simulation method of resonant wireless power transmission system (Natural Science Edition) 25(4), 518–522 (2013). (in Chinese) 8. Ma, Z., Liao, C., Wang, L.: Analysis of metal foreign object setting on electric vehicle wireless power transfer system. Adv. Technol. Electrical Eng. Energy 36(2), 14–20 (2017). (in Chinese)
Development of Experimental Platform for Low-Power Photovoltaic Energy Storage Inverter System Yiwang Wang1,2(B) , Bo Zhang1 , Yao Zhang3 , Xiaogao Chen4 , Jie Wang2 , and Jin Zhang5 1 Jiangsu Engineering Research Center for Photovoltaic Power Generation, Suzhou Vocational
University, Suzhou 215104, China [email protected] 2 CQC Intime Testing Technology Co., Ltd., Suzhou 215104, China 3 RENAC Power Technology Co., Ltd., Suzhou 215151, Jiangsu, China 4 Wuxi Solartale PV Technology Co., Ltd., Wuxi 214174, China 5 Suzhou Xuanyida Optoelectronics Technology Co., Ltd., Suzhou 215104, China
Abstract. Due to the uncertainty, intermittentness and instability of photovoltaic power generation, with the continuous promotion and application of energy storage system, the demand for energy storage inverter power supplies is also increasing. Compared with the single-function photovoltaic grid-connected inverter power generation system, the energy storage inverter system has more complicated circuit topologies, operating mode, energy control and system management due to the addition of energy storage links. In order to realize the faster and more efficient development of the energy storage inverter system, the universal modular storage inverter experimental development platform system can reduce the design difficulty of entire system, shorten the development cycle and reduce the research cost. A low-power photovoltaic energy storage system experimental development platform was designed in this paper, the architecture, circuit and composition of the experimental development platform were introduced in detail, adopting modular technical ideas and using digital control technology, which provides a platform and experimental support for the development of a new generation of energy storage system devices. Keywords: Energy storage inverter · Photovoltaic system · Experimental development platform · Low power
1 Introduction With the technological advancement and cost reduction of photovoltaic power generation systems, the photovoltaic power generation systems are more and more widely used and will become one of the main clean energy sources in the future [1–5]. The traditional photovoltaic energy utilization is mainly grid-connected power generation, that is, the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 978–985, 2022. https://doi.org/10.1007/978-981-19-1870-4_102
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electric energy generated by photovoltaic is fed into the grid after being inverted through a grid-connected inverter. That is, the electric energy generated by photovoltaic is connected to the grid after being inverted. The photovoltaic utilization method is simple, which is also the most commonly used photovoltaic power generation method at present [5–10]. However, due to the volatility of photovoltaic power generation and the absorption capacity of the existing grid, if the pure grid-connected power generation mode is adopted, it will bring new challenges to the stability of the grid and the reliability of users’ electricity consumption. Energy storage systems can improve the stability of photovoltaic power generation and realize the power peak-shift absorption. In the future, with the advancement of energy storage technologies and the reduction of costs, photovoltaic power generation systems with energy storage functions will become the main form of distributed clean energy utilization. In the energy storage system application engineering, the energy storage inverter is the core conversion and energy distribution component, and it is also the main equipment of the entire photovoltaic energy storage system. Differences from single-function grid-connected inverters, energy storage inverters not only need to contact the grid side, but also need to connect the energy storage terminal battery and the local loads, energy storage management and the ability to supply power to the local load. In summary, it is necessary to design a general-purpose energy storage inverter research platform to provide support and experimental test verification, guarantee for the development of energy storage inverter systems for photovoltaic applications.
2 System Architecture and Composition The photovoltaic energy storage inverter system platform mainly includes simulated photovoltaic power supply, inverter system, energy storage power supply, simulated load and monitoring system [6–13], the system block diagram is shown in Fig. 1.
Fig. 1. Composition of photovoltaic energy storage system
As shown in Fig. 1, the photovoltaic power generation (simulated photovoltaic power supply) is the conversion of solar energy into direct current (DC) electricity output. The energy storage inverter is a device that converts DC power generated by photovoltaic
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into alternating current (AC) power output and realizes various power conversion management, which is also the core component of the entire photovoltaic energy storage system. The energy storage system composed of various energy storage devices, and is connected to the DC bus through a DC conversion circuit; the inverter output can be connected to the grid-connected AC grid (on-grid mode) or local load (off-grid mode). The most common operating modes of the photovoltaic energy storage system include as shown in Fig. 2.
Fig. 2. The main operating modes of photovoltaic energy storage system
3 Experimental Platform Design and Development The structure of the platform’s core energy storage inverter is shown in Fig. 3.
Fig. 3. Experimental platform inverter circuit composition
In the experimental system platform, the photovoltaic array input can be realized by using a dedicated photovoltaic power generation programmable simulated power supply. The grid-connected output of the inverter is directly connected to the AC grid, and the off-grid output load can be connected with a simulated load. The key design of the energy storage inverter system is to develop the energy storage inverter equipment, and the development of the energy storage inverter is divided into the main conversion circuit and the control circuit design. The main circuit includes two
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parts: DC/DC1 for DC conversion and DC/DC2 for energy storage DC conversion. The DC/AC circuit is composed of an inverter circuit and a grid-connected/off-grid switching circuit.
Fig. 4. Schematic diagram of energy storage inverter
The main circuit of the photovoltaic energy storage inverter [6–15] is shown in Fig. 4. The front-stage DC/DC1 adopts BOOST circuit to realize the conversion of photovoltaic input voltage and the maximum power point tracking (MPPT), then provide the required voltage for the DC bus; DC/DC2 in the charging side adopts bidirectional BUCK/BOOST circuit (high-voltage energy storage) or dual active full bridge (Dual Active Bridge, DAB) + BUCK/BOOST combined circuits (low-voltage energy storage) to achieve BUCK charging and BOOST discharge The electric energy conversion; the inverter part is composed of H6 circuit. The output load realizes the on-grid and local load switching of the inverter output through the grid-connected/off-grid switching circuit composed of K11/K12–K31/K32. 3.1 Photovoltaic Input Side Converter Similar to the grid-connected photovoltaic power generation system, the BOOST boost circuit is used to increase the photovoltaic input voltage and achieve the maximum power point tracking control MPPT function on the photovoltaic input side [8–13], so that the intermediate stage DC bus voltage meets the voltage level required for the subsequent grid-connected inverter. The input and output relationship of the DC/DC1 converter is as follows: UDC_ BUS =
UPV 1 − DS1
(1)
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Where UPV and UDC_ BUS are the photovoltaic input and the DC bus voltage respectively, DS1 is the duty cycle adjustment control signal of the BOOST converter. According to Eq. (1), when the photovoltaic input voltage is lower than the bus DC voltage requirement, the voltage conversion and MPPT control functions are realized through algorithm control adjustment DS1 . If multiple photovoltaic inputs are required, multiple BOOST converters can be used in parallel. 3.2 AC Side Inverter The AC-side inverter circuit converts the electrical energy from the DC side into alternating current, which is input to the grid or supplied to the local loads. The classic H6 circuit structure is used for non-isolated low-power applications [9–15]. For the different operation modes of the energy storage system, it is necessary to realize the application scene transform when the grid is connected to the grid and the local load (the system has the function of independent power supply). 3.3 Energy Storage Side Electric Energy Conversion The energy storage side mainly completes the charge and discharge management of the energy storage batteries, and converts the bus voltage to the energy storage battery required DC voltage. For the high voltage energy storage batteries, a single bidirectional BUCK/BOOST circuit can be used [12–14]. UBAT = UDC_ BUS DS2 Ch arg e (2) UBAT Disch arg e UDC_ BUS = 1−D S3 where UBAT is the bus voltage of the energy storage battery, DS2 and DS3 is the duty ratio of the control signal of the switch S2 and S3. For energy storage applications such as low-voltage 48 V, a two-stage bidirectional DAB+BUCK/BOOST cascade circuit composition is utilized. UBAT = UDC_ BUS NDAB_ C DS2 Ch arg e (3) U NDAB_ D UDC_ BUS = BAT Disch arg e 1−DS3 where NDAB_ C and NDAB_ D is the input-to-output conversion ratio in the equivalent charging and discharging state of the DAB circuit.
4 Experimental Platform Design and Development Using the modular design, various conversion and control circuits have been designed to build an 5 kW photovoltaic energy storage system development platform prototype as shown in Fig. 5.
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Fig. 5. Low-power photovoltaic energy storage system research and development platform
5 Experimental Test Analysis The typical test experiments on the low-power photovoltaic energy storage system experimental platform were carried out, the test experimental results under different operating conditions are analyzed, and provide experimental data support for the research and development of photovoltaic energy storage inverter system. 5.1 Photovoltaic MPPT Control Experiment The photovoltaic input MPPT control experimental test were carried out in the platform prototype. The control signal DS1 of the DC/DC conversion circuit is adjusted to realize the MPPT. It can be seen that the MPPT control is accurate and efficient. The experimental results show that MPPT tracking control efficiency can be as high as 99.9%. 5.2 Experimental Research on Start-Up of Energy Storage Inverter Energy storage inverter start-up experimental tests of the photovoltaic storage inverter system under different conditions were studied. The start-up control experiment under the photovoltaic input condition, by controlling DC/DC1 to realize the DC-bus voltage stable startup and realize the inverter current output. When under the storage battery as energy input condition, by controlling DC/DC2 to achieve the start-up stability of the DC-bus voltage. It can be concluded that both photovoltaic and storage batteries startup can quickly reach stable operation of the bus voltage and meet the operating requirements of inverter output.
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5.3 Grid-Connected/off Grid Control Experiment Experiments on the transition between grid-connected and off-grid modes to realize the switching control of on-grid operation and off-grid power supply to achieve the engineering requirements of different application scenarios. Experimental results show that the platform prototype can meet the needs of grid-connected/off grid testing and development. According to the setting or the AC output side parameter changes, it can realize automatic grid-connected and off-grid switching control. 5.4 Efficiency Test Experiment The system efficiency of the experimental platform and the energy storage charging and discharging efficiency was tested. The test data shows that the working efficiency of the whole machine can reach 97.6%, and the efficiency of battery charging and discharging can reach 94.0%, which can meet the application requirements of engineering energy storage inverter development.
6 Conclusion Aiming at the engineering development and application requirements of photovoltaic energy storage systems. The design scheme of a low-power photovoltaic energy storage inverter system design and development test platform based on the modular design idea was introduced in detail. The photovoltaic energy storage system platform prototype was built to meet the test and experimental requirements of photovoltaic energy storage system engineering development, and the main experimental test of the test system was carried out and the related experimental results were given. The working performance of the designed photovoltaic energy storage inverter and system are verified. The photovoltaic energy storage inverter system designed and developed in this paper. In order to research and develop key power conversion devices for future new energy storage applications, which provides an experimental system solution and test platform support. The designed platform has good engineering application value, makes up for the lack of existing experimental platforms, and can comprehensively meet the experimental test requirements of energy storage systems with different voltages. Acknowledgments. This work was supported in part by the project of the Jiangsu Overseas Research and Training Program for the University, the Qinlan Project of Jiangsu Province, the Science and Technology Planning Project of Suzhou City, and the Collaborative Innovation Center and Industry-University-Research Base Construction Project of Suzhou Vocational University.
References 1. Yang, D., Zhang, H., Liu, C., Pei, Z., Lin, L., Song, X.: Novel high-frequency isolated cascade pv inverter topology based on multibus DC collection. IEEE J. Emerg. Select. Top. Power Electr. 9(2), 2122–2135 (2021)
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2. Lo, K., Chen, Y., Chang, Y.: Bidirectional single-stage grid-connected inverter for a battery energy storage system. IEEE Trans. Industr. Electron. 64(6), 4581–4590 (2017) 3. Kim, N., Parkhideh, B.: PV-battery series inverter architecture: a solar inverter for seamless battery integration with partial-power DC–DC optimizer. IEEE Trans. Energy Convers. 34(1), 478–485 (2019) 4. Haddadi, A.M., Farhangi, S., Blaabjerg, F.: An Isolated bidirectional single-stage inverter without electrolytic capacitor for energy storage systems. IEEE J. Emerg. Select. Top. Power Electr. 7(3), 2070–2080 (2019) 5. Sangwongwanich, A., Yang, Y., Sera, D., Blaabjerg, F.: Lifetime evaluation of grid-connected PV inverters considering panel degradation rates and installation sites. IEEE Trans. Power Electron. 33(2), 1225–1236 (2018) 6. Chen, L., et al.: SMES-battery energy storage system for the stabilization of a photovoltaicbased microgrid. IEEE Trans. Appl. Supercond. 28(4), 1–7 (2018) 7. Custer, S.G.: Inverter protection and ride-through: today’s photovoltaic and energy storage inverters. IEEE Electr. Magaz. 9(2), 43–49 (2021) 8. Yao, Q., Dong, L., Li, W., Li, G.: Research on power oscillation suppression strategy of twostage photovoltaic with energy storage. Electr. Measur. Instrumen. 56(13), 86–90 (2019). (in Chinese) 9. Hashemi, S., Østergaard, J.: Efficient control of energy storage for increasing the PV hosting capacity of LV grids. IEEE Trans. Smart Grid 9(3), 2295–2303 (2018) 10. Zhou, X-C., Fang, Y., Gu, Y-K., Cao, S-Y.: Study of operating principle and control method of h6-bridge based on single phase photovoltaic energy storage inverter. Power Electron. 54(03), 71–74 (2020). (in Chinese) 11. Wang, C., Yang, Y., Li, X., Liao, H.: Improvement of grid-connected current of H6 topology single-hase photovoltaic grid-connected inverter. Electr. Measur. Instrument. 56(16), 116– 122(2019). (in Chinese) 12. Li, X., Zhu, H., Zhang, W., Qiu, Y., Shao, J.: Modeling and control of buck/boost-dab cascaded converters with wide range inputs. Acta Energiae Solaris Sinica 42(05), 67–73(2021). (in Chinese) 13. Xiangyun, F., Guosheng, T., Hongfen, C., Ting, Y., Chen, W., Fuchang, Y.: Study on power regulation and control based on DAB for a hybrid system with photovoltaic and storage. J. Electr. Power Sci. Technol. 35(06), 138–143 (2020). (in Chinese) 14. Qinfei, S., Rengang, Y., Xianfei, Z., et al.: Control method of grid-connected power for battery storage inverters based on digital phase-locked loop. Trans. Chinese Soc. Agricult. Eng. 29(Supp. 1), 138–142 (2013). (in Chinese) 15. Sun, Y., Long, Y.: Research and application of deadbeat control based on the calculation of balanced power point for single-phase grid tied inverter. Electr. Energy Manag. Technol. 02, 51–55+72 (2018). (in Chinese)
Research on Short Circuit Failure Mechanism of Press Pack IGBT Device Based on Al-Si Diffusion Molecular Dynamics Simulation Li Hui, Yu Yue(B) , and Yao Ran State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Shapingba District, Chongqing 400044, China [email protected]
Abstract. Press pack insulated gate bipolar transistor (PP-IGBT) is widely used in HVDC converter valves for the advantages of high power density and short circuit failure mode (SCFM). In view of macroscopic measurement research on SCFM of PP-IGBT, which is difficult to reveal the failure mechanism caused by microscopic material failure, the SCFM mechanism of PP-IGBT based on Al-Si diffusion molecular dynamics (MD) simulation was proposed. Firstly, a MD model for the Al-Si diffusion of the IGBT chip was established, and the validity of the model was verified. Then, the law of Al-Si diffusion under different temperatures and stress were studied, and the occurred conditions of short circuit failure were got. Finally, a multi-physical coupling model of the PP-IGBT was established to study the transient thermal-mechanical distribution under short current. Based on the conditions of Al-Si diffusion, the mechanism and location of SCFM were analyzed. The results show that the Al-Si diffusion is more likely to occur at the boundary between the chip and the emitter molybdenum plate, which is the site of SCFM in the device. Keywords: Press pack IGBT · Short circuit failure · Al-Si diffusion · Molecular dynamics simulation
1 Introduction The press pack IGBT (PP-IGBT) device has the advantages of high power density, double-sided heat dissipation, short circuit failure mode (SCFM), widely used in HVDC systems [1, 2]. However, the SCFM analysis is mainly based on experimental results. It is difficult to monitor the change of performance parameters during failure and analyze the mechanism and location of failure, resulting in that MMC converter valves are still equipped with bypass switches and protection diodes, difficult to take advantage of SCFM of the device. Therefore, in order to optimize engineering cost of HVDC, it is urgent to research on the SCFM mechanism and location of PP-IGBT device, which is of great significance for condition monitoring and reliability improvement. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 986–994, 2022. https://doi.org/10.1007/978-981-19-1870-4_103
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Satish used EDS to verify that after a long-term power cycle, the Al and Si materials on the chip surface undergo a electrochemical reaction to form a conductive alloy and cause SCFM [3]. Based on the phase diagram of Al and Si, when the eutectic temperature is higher than 577 °C, Al and Si will form eutectic alloy, which is common in solar cell failure [4]. Balucani shows that the reaction temperature will be lowered under high stress, and Al-Si diffusion occur at about 330 °C [5]. Present research only considers macroscopic process, and lacks analysis of SCFM mechanism and location of the device caused by the microscopic material changes, resulting in limited failure analysis. The difficulty is that the internal composite stress changes in the device are complex and difficult to measure, and SCFM occurs quickly and difficult to monitor. Molecular dynamics (MD) simulation gives a microscopic evolution process of the system from atomic level, and intuitively reveals the mechanism and law of experimental phenomena. Compared with experimental observations, it has the advantage of qualitatively and quantitatively studying diffusion characteristics of different materials [6]. Qin used MD to obtain the structure and thermodynamic properties of liquid Al-Si alloy [7]. Choi verified the Al-Si diffusion at high temperatures through MD [8]. Present research provides a theoretical basis for the use of MD to study the characteristics of Al-Si materials. In order to analyze the conditions and processes of Al-Si diffusion of IGBT chips, it is necessary to research on MD-device multilevel coupling simulation of SCFM for PP-IGBT device. This paper proposes a method based on Al-Si MD to study the SCFM mechanism of PP-IGBT device. Firstly, based on the interface structure of the IGBT chip, a MD model of Al-Si diffusion was established and the validity of the MD method was verified. Then, the influence of interface temperature and stress on the Al-Si diffusion under different working conditions was studied, and the Al-Si diffusion critical temperature change curve was obtained; Finally, a multi-physics coupling model of PP-IGBT was established to study the transient thermal distribution under the impact of overcurrent, and the probability of SCFM in each area of the IGBT chip was analyzed (Figs. 1 and 2).
2 Al-Si Interface MD Simulation of IGBT Chip 2.1 Structure of IGBT Chip
Fig. 1. Structure of PP-IGBT
Fig. 2. Interface structure of chip
PP-IGBT device uses external force to rigidly press the components of each layer together. The internal structure of a 3.3 kV/50 A single-chip device is shown in Fig. 1. From top to bottom, each layer is the collector copper plate (CCP), collector molybdenum plate (CMP), IGBT chip, emitter molybdenum plate (EMP), silver shim plate
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(SSP), and emitter copper plate (ECP), and the surface of IGBT chip is covered with a very thin layer of Al with thickness about 10 um.The interface structure of the IGBT chip is shown in Fig. 2. The CMP and EMP jointly apply force to the chip and Al coating, so that the Al-Si interface generates stress. 2.2 MD Model of Al-Si Interface The geometry of the Al-Si interface was established shown in Fig. 3. The contact surface is an ideal plane. The left part is a crystal super cell of 432 Al atoms with a size of 4 × 4 × 8(Al)3 .The right part is a crystal super cell of 576 Si atoms with a size of 3 × 3 × 6(Si)3 . Periodic boundary conditions are applied in x and y directions. In the z direction, three layers of atoms are fixed on the both sides to prevent the atoms from moving out of bounds. The initial velocity of the atoms are given by the Maxwell velocity distribution at room temperature. The model ground coordinate z = 0 is specified.
Fig. 3. Al-Si interface geometry
2.3 Validity of MD Model In order to verify the validity of the MD model, set the axial stress of the interface to 10 MPa and the interface temperature range to 600–640 K. The morphology of the Al-Si interface at different temperatures for 1000 ps is shown in Fig. 4.
Fig. 4. Morphology of Al-Si interface at different temperatures
Figure 4 shows that only a few of atoms diffuse at 600 K and obvious diffusion occurs at 620 K and above, where a lot of atoms diffuse together. In order to verify the critical temperature of Al-Si diffusion, the atom relative content (At %) of interface after diffusion at 620 K for 1000 ps as shown in Fig. 5. The area where the At % exceeds 5% is specified as diffusion layer with a thickness about 6.8 Å. For further study of the influence of temperature on diffusion, the change in the thickness of the diffusion layer after 1000 ps at different temperatures is shown in Fig. 6. Figure 6 shows that little diffusion occurs when temperature less than or equal to 610 K and the thickness of the diffusion layer changes little, about 5.2 Å. Therefore, atoms only undergo a slight diffusion at this temperature. When temperature greater than
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or equal to 620 K the diffusion layer has an obvious inflection point, which increases rapidly with the increase of temperature. Combining with the diffusion morphology, the interface has a violent diffusion. It is believed that when the axial stress is 10 MPa, the critical temperature for Al-Si diffusion is 620 K, which is about 2.7% error from 603 K in the literature. Therefore, the validity of the MD model and method is verified. 1.0 Al Si
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3 Influence of Different Conditions on Al-Si Diffusion 3.1 Influence of Interface Temperature The diffusion layer changes not significantly with a low temperature, and it is difficult to quantitatively study the influence of the stress on Al-Si diffusion. The mean square displacement (MSD) of the atoms increases with time, indicating the diffusion motion, and the speed of the upward trend reflects the intensity of the diffusion at this moment. Figure 7 shows the MSD of Si atoms at 600 K–640 K when the axial stress is 10 MPa. When the temperature is less than or equal to 610 K, the MSD changes very little, and the slope is close to zero. When the temperature is greater than or equal to 620 K, the MSD increases linearly with the temperature within the same diffusion time. The result indicates that the interface temperature will promote the Al-Si diffusion, and when the temperature is greater than the diffusion condition 620 K, the promoting effect is more obvious.
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Considering that the melting points of Al and Si are 933 K and 1683 K respectively, the interface diffusion temperature must meet the melting point of 0.6–0.8. In order to study the influence of a larger temperature range, the interface temperature is set to 500
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K, 700 K, and 800 K. The axial stress is 10 MPa for 1000 ps diffusion, and the interface morphology is shown in Fig. 8(a)–(c). Figure 8 shows that there is no diffusion layer at 500 K, and a thicker stable diffusion layer can be formed at 700 K, and all Al atoms except for the fixed layer atoms at 800 K diffused into Si atoms. The thickness of the diffusion layer is positively correlated with the temperature. Since a higher melting point of Si, the Si-Si covalent bond is stronger than the Al-Al metal bond. The Al structure is first destroyed under high temperature and stress. The vacancies and defects formed after Al-Al bonds break facilitate the diffusion of Si atoms into the Al matrix, so the diffusion layer is mainly on the side close to Al. 3.2 Influence of Interface Stress When the PP-IGBT device is impacted by overcurrent, the internal material thermal expansion cause the stress in some areas of the chip surface to reach hundreds of megapascals. The axis stress between the Al-Si interface is set to 0–500 MPa, and the influence of stress is analyzed. The results in Sect. 3.1 show that when temperature set to 800 K, the Al-Si diffusion will occur before the system temperature rises to 800 K, difficult to analyze the MSD change, so 500–700 K is selected for analysis. The MSD of Si atoms versus the stress at different temperatures are shown in Figs. 9, 10 and 11. 1.2 0.16
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Figure 9 shows that the MSD at 500 K fluctuates with time, indicating that diffusion does not happen and the atoms vibrate near the equilibrium position. Figure 12 shows the change of the diffusion layer under different stress at 700 K for 1000 ps. Therefore, increasing the axis stress will promote the development of Al-Si diffusion to a certain extent. This is because the stress causes serious distortion of the crystal lattice at the interface, leading to structural defects such as dislocations and vacancies, and promote the formation of channels for rapid diffusion of atoms in the matrix. 3.3 Influence of Combined Stress Figure 13 shows the MSD with time under the combined conditions of different temperatures and stress.When the stress increases to 280 MPa, the MSD at 610 K for 1000 ps is 1.11 A.When the stress increases to 500 MPa, the MSD at 600 K for 1000 ps is 1.10 A. Therefore, the Al-Si diffusion degree under different temperatures and stress conditions can be equivalent. The increase of the stress will reduce the critical temperature of Al-Si diffusion to a certain extent. The relationship between critical temperature and stress is fitted as following formula: TC = −0.041σ + 620.711
(1)
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4 SCFM Analysis of PP-IGBT Device 4.1 FEM Model of PP-IGBT Device Based on the 3.3 kV/50 A single-chip PP-IGBT device structure given in Fig. 1, COMSOL is used to build the multi-physics coupling FEM model. The material parameters of each layer are shown in Table 1.
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In order to reduce the simulation time, structures such as PEEK, gate pin, PCB board, and housing that have very little effect on power loss and temperature are ignored. Set a heat dissipation coefficient of 5000 W/(m2 ·K) on the surface of the CCP and ECP to simulate the double-sided heat dissipation of the device. A uniform clamping force of 1200 N is applied to the collector, and the emitter is set as a fixed support. The FEM model and boundary conditions are shown in Fig. 14.
Fig. 14. FEM model of PP-IGBT device
4.2 Weak Point of PP-IGBT Device Short circuit experiment was carried out on the PP-IGBT device, and the SCFM occurred after about 800 us [9]. According to the experiment parameters, the transient simulation parameters are set as shown in Fig. 15. The change of the temperature with time is shown in Fig. 16. Based on the temperature condition of SCFM, the maximum temperature reaches 620 K when the simulation is performed at 480 us, which has reached the critical value obtained in Sect. 3.3. At this time, the temperature and stress distribution on the chip surface are shown in Fig. 17. Figure 17(a) shows that the maximum temperature area of the IGBT chip is located near the gate, about 620 K, where the peak value is 645.1 K. The area with high temperature about 500–620 K is the active area of chip that is not in direct contact with EMP. This area cannot effectively dissipate heat in a short period of time. The active area in contact with EMP can be dissipated, and has a temperature of 490 K. The temperature of the terminal area is the lowest, about 280–480 K, and the minimum is 284.1 K. Figure 17(b) shows that the stress in the edge area in contact with EMP is more concentrated, about 350–450 MPa. The maximum stress is located near the gate, about
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491.1 MPa. The rest of the chip in direct contact with EMP has a stress about 270 MPa, and the terminal area around the chip not in contact with the EMP has the smallest stress, and the minimum is 5.9 MPa. On the basis of Fig. 17 and Fig. 13, the relative probability distribution of SCFM of the chip is shown in Fig. 18, where the darker the color area indicates the greater the probability. The active area near the gate and the corner area in contact with EMP have the highest probability of SCFM, which is the weakest area of chip, where the SCFM is usually the first to occur. The increase in stress reduce the critical temperature of the Al-Si diffusion, and promote the further diffusion, so that the edge area in contact with EMP meets the conditions with high probability of SCFM. The probability in other areas of the chip surface is almost zero.
Fig. 17. Simulation result at 480 us
Fig. 18. Probability distribution of SCFM
5 Conclusion • MD simulation shows that the critical temperature of Al-Si diffusion is 620 K under the axis stress of 10 MPa. Both increasing the temperature and stress promote Al-Si diffusion. In particular, increasing stress reduces the critical temperature to a certain extent. When the stress increases to 500 MPa, the critical temperature is reduced to 600 K. This explains why SCFM occurs at lower temperatures. • For the IGBT chip, the active area near the gate and the corner area in contact with EMP have the largest probability of SCFM. The probability in the edge area in contact with EMP is relatively large, and the probability in other areas of the chip surface is almost zero.
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References 1. Jin, R., Yu, K., Zhang, P., et al.: Development of IGBT devices and the typical application in the smart grid. Smart Grid 1(2), 11–16 (2013). (in Chinese) 2. Zhang, W., Tang, G., Zha, K., et al.: Application of advanced power electronics in smart grid. Proc. CSEE 30(4), 1–7 (2010) 3. Gunturi, S., Schneider, D.: On the operation of a press pack IGBT module under short circuit conditions. IEEE Trans. Adv. Packag. 29(3), 433–440 (2006) 4. Murray, J.L, McAlister, A.J: The Al-Si (aluminum-silicon) system. Bull. Alloy Phase Diag. 5(1), 74 (1984) 5. Balucani, M., Serenelli, L., et al.: Aluminum-silicon interdiffusion in screen printed metal contacts for silicon based solar cells applications. Energy Procedia 43, 100–110 (2013) 6. Rapaport, D.C.: The Art of Molecular Dynamics Simulation. Cambridge University Press (2004). https://doi.org/10.1017/CBO9780511816581 7. Qin, J., Pan, S., et al.: The structure and thermodynamic properties of liquid Al–Si alloys by ab initio molecular dynamics simulation. J. Non-Crystal. Solids 433, 31–37 (2016) 8. Ih Choi, W., Kim, K., Narumanchi, S.: Thermal conductance at atomically clean and disordered silicon/aluminum interfaces: a molecular dynamics simulation study. J. Appl. Phys. 112(5), 054305 (2012) 9. Li, H., Yao, R., et al.: Modeling and analysis on overall fatigue failure evolution of press-pack IGBT device. IEEE Trans. Electron Dev. 66(3), 1435–1443 (2019)
Maintenance Optimization Strategy of Modular Multilevel Converter Li Liu1,2 , Meng Huang3 , Liangjun Bai3(B) , and Min Qiao4 1 Key Laboratory of Control of Power Transmission and Conversion, Ministry of Education,
Shanghai Jiao Tong University, Shanghai 200240, China 2 State Grid Zhoushan Power Supply Company, Zhoushan 316000, China 3 Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
[email protected] 4 State Grid Zhejiang Electric Power Co. Ltd., Hangzhou 310007, China
Abstract. Flexible DC transmission technology is an important trend of future transmission development, in which modular multilevel converter (MMC) is the core equipment of flexible DC transmission. The paper proposes a reliability-based maintenance optimization strategy for MMC in hot standby mode to improve the reliability of Flexible HVDC and reduce maintenance costs. Firstly, the reliability model of MMC in hot standby mode is established. On this basis, a maintenance scheme with reliability as the center and minimum maintenance cost is proposed. The relationship among reliability of MMC, redundancy of submodule, maintenance and cost is further discussed through an example. The proposed reliability model and reliability centered maintenance scheme provide guidance for MMC maintenance decision-making. Keywords: MMC · Maintenance cycle · Reliability model · Maintenance optimization strategy
1 Introduction As a new generation of power transmission technology, flexible DC transmission has great advantages compared with traditional DC transmission or AC transmission. Flexible direct current transmission technology has a wide range of applications such as island power supply, urban distribution network expansion and transformation, largescale renewable energy grid connection. The cost of installation, operation and maintenance of flexible DC transmission equipment is much higher than that of the traditional transmission equipment department. Among them, the flexible DC converter valve accounts for 25% to 30% of the total project cost. Therefore, exploring the reliability of flexible DC converters and establishing a reliability-centered maintenance plan is of great significance to the further development of flexible DC transmission.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 995–1003, 2022. https://doi.org/10.1007/978-981-19-1870-4_104
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The performance of MMC reliability research is as follows: 1) Analyze the reliability of MMC based on the operation strategy of MMC [1]. 2) Establish a reliability evaluation model around the topological structure research of the sub-modules to provide services for the optimal circuit design of MMC [2]. However, in addition to IGBT devices in MMC, other devices such as capacitors, power drivers, control and protection systems also have an important impact on the reliability of MMC, which are rarely involved in the existing literature. The maintenance strategy of the flexible DC transmission converter is also an issue that needs people’s attention as it is put into operation. Some researchers have put forward their opinions on the operation and maintenance strategy of converters [3]. The Weibull distribution is used to simulate the aging failure process of power devices in MMC and then preventive maintenance is analyzed based on the MMC topology in [4]. In engineering, the MMC maintenance model mainly includes regular maintenance and conditional maintenance. Regardless of regular maintenance or conditional maintenance, the impact of reliability on the operation of MMC is not considered. Reliability-centered maintenance (RCM) has become a systematic engineering method for preventive maintenance and optimizing the maintenance system. The related research of RCM mainly focuses on the traditional power system and a certain device in the power system. It is rarely seen in the RCM research on flexible DC transmission converters. Therefore, this paper starts from the operation of the flexible DC converter, with reliability as the center, and seeks suitable maintenance strategies and maintenance cycles. Reliability-centered MMC maintenance and repair program is proposed in this article. 1) Based on the consideration of sub-modules, capacitors, power drivers, control and protection systems, etc., a detailed reliability model of MMC is established; 2) A maintenance plan with minimal maintenance costs is established; 3) Analyze the MMC reliability, SM redundancy, maintenance cycle, and the interaction between cost and aging based on the case studies.
2 Reliability Model of MMC The reliability of MMC actually refers to the statistical law of converter failure under specified conditions and specified time. The reliability model of MMC is analyzed through the topological structure of MMC in this section. 2.1 Reliability Model of MMC SM The reliability block diagram of the MMC sub-module (SM) is shown in Fig. 1. Each SM is a series system and its reliability is jointly determined by the IGBT module, capacitor, SM control system, and power drive. According to the reliability block diagram of the half-bridge SM shown in Fig. 1, the reliability of the SM is RSM (t) = R2T (t)R2D (t)RC (t)RSC (t)RPS (t)
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where RT (t), RD (t), RC (t), RSC (t), RPS (t) is the reliability function of IGBT module, reverse freewheeling diode, capacitor, SM control system, and power drive respectively.
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Assuming that each component in the MMC system SM is in a stable operating cycle in the life curve, that is, the life of each component obeys the exponential distribution, then the reliability of the component at time t obeys the exponential distribution, namely
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Fig. 1. Reliability block diagram of half-bridge SM
R(t) = P{T > t} = e−λ(t)
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where λT (t), λD (t), λC (t), λSC (t), λPS (t) respectively represent the failure rate of IGBT module, reverse freewheeling diode, capacitor, SM control system, power drive and sub-module. The reliability function of the SM can be established according to a similar method if the MMC SM adopts a full-bridge topology.
3 Reliability Model of MMC Each bridge arm of the MMC is composed of N SMs with exactly the same topology and devices. Redundant SMs are used in each bridge arm of the converter to improve the reliability of the MMC system. MMC can still work normally when some number of SMs fail and these failed SMs will be replaced in the next maintenance. It should be shut down immediately for maintenance when MMC fails and the number of faulty SMs is greater than the allowable value. Suppose there are N SMs in each bridge arm of MMC. k are redundant SMs in these N SMs. Combined with the binomial distribution model and the reliability described by the k-out-of-n system, the reliability function in the steady state operation of MMC can be expressed as Rk/N (t) =
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(3) where FSM (t) is the life distribution of SM. Each bridge arm of MMC is composed of N SMs and a bridge arm reactor in series, so the reliability of each bridge arm is the product of the reliability of the series valve and the bridge arm reactor Rarm (t) = Rk/N (t)Rrac (t), Rrac (t) is the reliability function of the bridge arm reactor. The reliability block diagram of MMC is constructed according to the topological structure and operating principle of MMC, as shown in Fig. 2. In addition to the A, B, and C three-phase upper and lower bridge arms, MMC also includes converter station control and protection systems and valve cooling systems. The establishment of the
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reliability function of MMC considers the basic equipment and secondary equipment as follows: RMMC (t) = [Rarm (t)Rvb (t)]3 Rcp (t)Rcl (t)
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Fig. 2. Reliability block diagram of MMC
4 Reliability Model of MMC 4.1 Maintenance Strategy There are two types of periodic maintenance strategies for converters. A converter can work normally to the moment of preventive maintenance. Replace the faulty submodule and perform preventive maintenance on the remaining submodules. It is also assumed that MMC is restored to a brand state after preventive maintenance. This kind of fault that occurs in MMC from normal operation to preventive maintenance is called the first type of fault. Another type of fault occurs when MMC fails before the scheduled maintenance time. When MMC fails, replace the faulty sub-module and perform preventive maintenance on the remaining sub-modules. The age of MMC starts from 0 again after the replacement. This kind of MMC failure before the scheduled maintenance time is called the second type of failure. 4.2 Maintenance Cycle Optimization Model The Average Maintenance Cycle of MMC. Assume MMC is in a brand state that at t = 0. Let Y1 ,Y2 , · · · … obey independent random variables with life as. Without considering preventive maintenance, {Y1 , Y2 , · · · } is the time sequence of the second type of fault in MMC. Let Yi∗ = min{Yi , T }, then denote the length of the i-th maintenance cycle
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of MMC. If considering MMC fault maintenance time T1 and preventive maintenance time t2, MMC update cycle is E(Y1∗ ) + tf , Y1 > T (5) TMMC = E(Y1∗ ) + tp , Y1 < T where T is the age of MMC. Therefore, the average maintenance cycle of MMC is E(TMMC ) = E E(Y1∗ ) + tf RMMC (T ) + E E(Y1∗ ) + tp [1 − RMMC (T )] T (6) = RMMC (t)dt + FMMC (T ) tf − tp + tp 0
Loss of MMC During a Maintenance Cycle. MMC works normally to the preventive maintenance time T and the number of faulty SMs in the bridge arm does not exceed k when the first type of fault occurs in MMC. Therefore, the maintenance cost for the first type of failure of MMC is Cp = {cp + 6
k−1 i · cSMf + (N − i) · cSMp } · CNi [1 − RSM (T )]i [RSM (T )]N −i
(7)
i=0
where cp is preventive maintenance makes the loss caused by the planned shutdown of MMC, cSMf is replacement cost for each failed SM, cSMp Preventive maintenance costs for each non-faulty SM. The second type of fault occurred in MMC. Assume that k-1 SMs in the bridge arm have failed before time and the kth SM has failed at time t. At this time, corrective maintenance should be carried out on MMC. Cost of faulty maintenance of MMC is
Cf = cf + 6 k · cSMf + (N − k) · cSMp ·
T 0
N −k+1
[RSM (t)]
Cnk−1 [1 − RSM (t)]k−1 ·
(8)
(N − k + 1)λSM dt
Therefore, the total cost of converter repair is Cp + Cf . Maintenance Cycle of MMC. The unit maintenance cost in maintenance cycle T is C(T ) =
Cp + Cf E(TMMC )
(9)
The maintenance cycle under the minimum cost of MMC is to solve the minimum value of the above formula. Let dC(T ) dT = 0. There is a unique T* that minimizes C(T ) according to the theorem. Formula (14) is a transcendental equation and a numerical method is used to find the maintenance cycle T of the optimal section.
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5 Case Study In order to verify the effectiveness of the method proposed in this paper, a three-phase MMC whose sub-module is a half-bridge topology is taken as the research object. The total number of SMs in each bridge arm is 216, of which 16 are redundant SMs. The various parameters can be found in [5–8]. It can be seen from Fig. 3 that the maintenance cost has a similar performance in the two failure rates. The maintenance cost per unit time is very high when the value of the maintenance cycle T is small. This is because the number of SM failures was small when MMC first started operation. The main performance is the cost loss caused by preventive maintenance shutdown. The maintenance cost per unit time gradually decreases and the rate of decline gradually slows down with the extension of the maintenance cycle. There is a maintenance cycle with the smallest unit maintenance cost as shown in Fig. 3. After that, the maintenance cost began to rise with the increase of the maintenance cycle T. The rate of increase in maintenance costs has accelerated with the extension of the maintenance cycle. This is because the reliability of MMC gradually decreases with the increase of the running time of MMC and the cost loss caused by the downtime of MMC is dominant.
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λ = 0.0399 λ = 0.043
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Fig. 3. Maintenance cost per unit time
The two curves in Fig. 3 respectively show the maintenance cost curves of MMC under two different sub module failure rates. When the failure rate of the SM is 0.0399, the maintenance cost of MMC is the least when the maintenance cycle is t = 0.96 year and the minimum value is 2261.90 k$. When the failure rate of the sub module is 0.043, the maintenance cycle of the converter is t = 0.9 years and the maintenance cost is the least. At this time, the maintenance cost is 2417.89 k$. At the same time, combined with the reliability analysis, when the redundancy is 8%, the reliability of MMC is greater than 0.99 in the maintenance cycle under the two failure rates. This means that the proposed maintenance strategy ensures the minimum maintenance cost per unit time on the premise of ensuring reliability.
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It can be seen from Fig. 4(a) that the maintenance cycle changes with the change of the failure rate. The maintenance cycle is reduced by about 0.7% for every 1% increase in the failure rate in the same SM redundancy. Figure 4(b) shows that the minimum maintenance cost increases as the failure rate of the SM increases. Maintenance costs increased by 0.9% for the failure rate of the sub-module increases by 1% every time. The effect of sub-module redundancy on maintenance time and maintenance costs as shown in Table 1. It can be seen from Table 1 that the minimum maintenance cycle gradually increases as the number of redundant sub-modules increases. Therefore, the reduction in the number of redundant sub-modules can be compensated by more frequent maintenance in which case the maintenance cycle is shorter, and vice versa. There is a linear correlation between the redundancy number of each bridge arm submodule and the maintenance period as shown in Table 1. This means that the increased redundancy of sub-modules can extend the maintenance cycle of the MMC. When the sub-module redundancy increases by 1%, the maintenance interval increases by 29.5%. At the same time, it is also shown from Table 1 that the minimum cost decreases as the redundancy of each bridge arm sub-module increases. In the range 0 ≤ k ≤ 5 of the number of redundant SMs in the bridge arm, the maintenance cost decreases rapidly with the increase of the redundant number. When the number of redundant SMs is k ≥ 5, the rate of decrease in maintenance costs slows down until it is almost a smooth straight line as k increases. This is because the reliability of the variable transformer is greatly affected by the redundancy of the sub-modules when the SMs in the bridge arm are not redundant or the number of redundancy is small. At this time, the maintenance cost of the converter is mainly manifested as the downtime loss caused by the faulty shutdown. The maintenance cost of the variable transformer is mainly manifested as the downtime loss caused by preventive maintenance. When the redundancy of the bridge arm sub-modules increases to a certain number.
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Fig. 4. Maintenance strategies under different sub module failure rates (a) Influence of SM failure rate on maintenance cycle (b) Influence of SM failure rate on optimal maintenance cost
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Maintenance cycle/year
Minimum cost/k$
0
0.03
33627.31
2
0.10
9782.61
4
0.20
5218.03
6
0.32
3743.57
8
0.44
3072.82
10
0.57
2709.52
12
0.70
2491.49
14
0.83
2352.79
16
0.96
2261.90
18
1.10
2201.65
20
1.23
2162.27
22
1.36
2137.72
6 Conclusion This paper establishes a maintenance optimization model of modular multilevel converter based on half-bridge structure. The reliability function of MMC is established by analyzing the failure of MMC auxiliary components. The optimization model based on the minimum maintenance cycle of the cost is proposed. The following conclusions can be drawn through numerical calculation: 1) The maintenance cost in MMC varies with the maintenance cycle under a certain degree of redundancy. There is an optimal maintenance cycle and the maintenance cost is the smallest at this time. 2) The maintenance cycle of MMC is positively correlated with the redundant number of sub-modules in the bridge arm. The maintenance cycle increases accordingly as the redundancy increases.
References 1. Guo, J., Wang, X., Liang, J., Pang, H., Gonçalves, J.: Reliability modeling and evaluation of mmcs under different redundancy schemes. IEEE Trans. Power Deliv. 30(5), 2087–2096 (2018) 2. Xu, J., Jing, H., Zhao, C.Y.: Reliability modeling of MMCs considering correlations of the requisite and redundant submodules. IEEE Trans. Power Deliv. 33(3), 1213–1222 (2018)
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3. Yuan, C., Dai, D., Qiu, J., et al.: An optimal preventive maintenance method for MMC based VSC-HVDC. In: 2020 2nd International Conference on Smart Power & Internet Energy Systems (SPIES), Bangkok, Thailand, pp. 13–16 (2020) 4. Wylie, J., Merlin, M C., Green, T.C.: Analysis of the effects from constant random and wearout failures of sub-modules within a modular multi-level converter with varying maintenance periods. In: 19th European Conference on Power Electronics and Applications, pp 1–10, IEEE, Warsaw (2017) 5. Shoudao, H., Haining, W., Fei, R., Hon, R., Baorong, Z.: Redundant configuration strategy of MMC converter valve considering system loss. Power Syst. Protect. Contr. 46(06), 1–8 (2018). (in Chinese) 6. Grinberg, R., Riedel, G., Korn, A., et al.: On reliability of medium voltage multilevel converters. In: Proceedings of 5th IEEE Energy Conversion Congress and Exposition pp. 4047–4052, IEEE, Denver (2013) 7. Tnei Services Ltd.: Offshore Electrical Equipment Reliability Figures. Manchester, UK: TNEI Services Ltd (2012) 8. Kim, C., Lee, S.: Redundancy determination of HVDC MMC modules. Electronics 4, 526–537 (2015)
Transient and Steady-State Parameters of the Synchronous Condenser Based on Field-Circuit-Network Finite Element Method Hui Li, Yunzhu Zeng(B) , Jianfu Li, Xiao Wang, Bin Yuan, Renkuan Liu, and Yue Yu State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Shapingba District, Chongqing 400044, China [email protected]
Abstract. In order to accurately characterize the influence of the magnetic field variation of Synchronous Condenser (SC) on the transient and steady-state parameters in the transient process, a model of the SC connected to UHVDC transmission system based on field-circuit-network Finite Element Method (FEM) was proposed. Firstly, the field-circuit coupled finite element model of the SC is established. The SC was connected to a typical HVDC system through double closed loop excitation control, and the combination of two-dimensional transient electromagnetic field, external circuit and power grid was realized. Then, the commutation failure of HVDC transmission system was simulated and compared with the results of traditional finite element model. Finally, based on the frozen permeability method, the transient and steady-state parameters of the SC under the failure of commutation were calculated in real time, and the variation rules of the transient and steady-state parameters under different operating conditions were studied. The results show that the saturation degree and distribution of the magnetic field are changed by the strong current, which leads to the decrease of the transient and steady-state parameters in the transient process. The larger the voltage change is, the smaller the initial lagging reactive power is, which leads to the higher the saturation degree of the magnetic field and the smaller the parameters of the transient state. Keyword: Synchronous condenser · HVDC · Field-circuit-network coupling · Frozen permeability · Transient steady state parameters
1 Introduction SC can significantly improve the ability of the converter station to resist the risk of commutation failure [1–3]. The steady-state reactive capacity of the SC depends mainly on the synchronous reactance, and its transient reactive capacity depends on its transient parameters. In existing studies, it is generally believed that the transient steady state © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1004–1011, 2022. https://doi.org/10.1007/978-981-19-1870-4_105
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parameters of the motor remain unchanged [4], but the magnetic field distribution and saturation degree of the motor will change during operating, resulting in the change of the transient characteristics of the motor. Therefore, how to establish the model influenced by HVDC system and nonlinear factors such as motor magnetic field saturation is worth paying attention to. The field-circuit coupled time-step FEM can realize the simulation calculation of the dynamic process of the motor itself [5], to be able to accurately considering magnetic field distortion and saturation, skin effect, such as nonlinear factors. This method is mainly used to study the operation of the generator itself ability and dynamic characteristics. In literature [6], the established field-circuit coupling model of generator and transformer is connected to the infinite system through interface variables, and the field-circuitnetwork coupling time-step finite element model oriented to the analysis of machinenetwork system is finally obtained. The algorithm can analyze the interaction between the generator and the grid when the system is disturbed or fails. Literature [7] established a field-circuit-network coupling time-step finite element model with excitation control system, and considers the influence of excitation dynamics and transmission system parameters. The above research uses a simple infinite power grid, without considering that the control system of the HVDC system and the excitation control of the SC lead to the change of the internal magnetic field and transient steady-state parameters of the motor in the transient process of fault. In this paper, a model of the SC connected to HVDC system based on field-circuitnetwork FEM is established. First of all, a field-circuit coupling finite element model considering specific structures such as slot wedges and damping strips is established, which can fully consider the effects of magnetic field distortion, saturation and eddy current skin effect at different times. The SC is connected to the typical HVDC system through reactive power-voltage double closed-loop excitation control to realize the combination of two-dimensional transient electromagnetic field, external circuit and power grid. Then, the commutation failure at the receiving end of HVDC system is simulated, and the results are compared with those of the traditional finite element model. Finally, the transient steady state parameters of the SC under commutation failure are calculated based on the frozen permeability method, and the transient steady state parameters under different voltage changes and initial reactive power are studied.
2 Time-Step Finite Element Model of Field-Circuit-Network Coupling for Machine-Network System 2.1 The Field-Circuit Time-Step Finite Element Model of the SC 2.1.1 Field-Circuit Coupling Model of the SC The two-dimensional transient finite element model of the SC is established, and the coupling calculation model of electromagnetic field and circuit is used to calculate the two-dimensional electromagnetic field finite element of the SC. The model was modeled according to the actual shape of stator and rotor slots of 300 Mvar SC, taking into account the different wedges of stator slots. Figure 1 shows the 2D finite element model of the SC. Local fining is used to ensure the solution accuracy.
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Fig. 1. 2D finite element model
CoilA
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Ra
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The field-circuit coupling method is adopted, and the circuit model is shown in Fig. 2. Where, CoilA-C are stator windings; La−c and Ra−c are the end leakage reactance and stator resistance respectively; CoilF is the excitation winding; Rf is the excitation resistance; Vab and Vbc are the stator voltage; Vf is the excitation voltage. 2.2 Excitation Control Model of the SC As shown in Fig. 3, in the steady state, reactive power is used to control the steady state, and in the transient state, the voltage is closed loop for fast strong excitation or strong reduction.
Fig. 3. Excitation control system of the SC
Where, Uref is the reference value of the terminal voltage; Ug is the actual value of terminal voltage; Qref is the reactive power reference value of the system; Q is the actual reactive power value of the system; Ifd is the excitation current; Efd is the excitation electromotive force. 2.3 Field-Circuit-Network Coupling Time-Step Finite Element Model Using MATLAB\Simulink 12 pulse HVDC transmission simulation model. The main circuit structure of HVDC transmission system model is shown in the right block diagram of Fig. 4. The typical DC transmission control strategy is adopted. The rectifier consists of two parts: constant current control and minimum trigger angle control. Inverter control
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consists of two parts: constant voltage control and constant extinction angle control. After passing through the boost transformer, the SC is connected to the HVDC transmission system. The block diagram of the system is shown in Fig. 4. It includes excitation control system, the SC and HVDC transmission system. Establish a co-simulation model based on Simulink and Flux platform, and take the machine end current, excitation current and speed of Simulink model as input through the Simulink-Flux interface; The terminal voltage, excitation voltage and torque in the Flux finite element model are taken as outputs to realize the simulation of the converter accessing the HVDC transmission system.
Fig. 4. Structure diagram of time-step finite element model of field-circuit-network coupling
3 Transient Characteristics of HVDC Transmission System Under Fault 3.1 Simulation Analysis of Commutation Failure of Receiving AC System Set the commutation failure of the AC system at the receiving end of HVDC at t = 5 s, and the fault duration is 0.04 s. The initial reactive power of the SC is 0 Mvar. Figure 5 obtained the transient characteristics of the SC based on the field-circuit-network coupling model, and compared with the results of the traditional finite element model using a simple infinite grid voltage sag. The field-circuit-network coupling model is affected by the HVDC control system after the fault of the power grid, and the terminal current of the SC fluctuates greatly and the recovery time is prolonged. After the fault occurs, the current at the end of the machine is stable at 0.6 s. Moreover, the SC is involved in the transient process of HVDC system recovery after failure. Affected by the excitation control of the SC, the excitation current increases to 2.33 pu, and the recovery time extends to 5.7 s. The reactive power fluctuation becomes larger, and the maximum reactive power is 1.9 pu, while the maximum reactive power of the traditional finite element model is 1.5 pu.
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Fig. 5. Comparison of the characteristics of traditional finite element model and field-circuitnetwork finite element model
4 Transient Steady State Parameters of the SC in Case of HVDC System Failure 4.1 Frozen Permeability Calculation Method Based on the frozen permeability method [8–10], the transient steady-state parameters of the SC changed in the transient process were obtained, the relative permeability distribution of the motor was locked in a certain working state, and the nonlinear problem was linearized, as shown in Fig. 6 for specific steps.
S1
2D geometric model
S2
Nonlinear finite element analysis
The core permeability distribution of stator and rotor is derived
linear finite element analysis
S3
Stator flux analysis
Transient steady state parameter calculation
Fig. 6. Frozen permeability calculation method
4.2 Transient Steady State Parameters of the SC The synchronous reactance, transient reactance and subtransient reactance of the SC at multiple time points in the transient process of commutation failure in the AC system at the receiving end of the HVDC transmission system are calculated, and the results are shown in Fig. 7. As can be seen from Fig. 7, the values of synchronous reactance and transient reactance obtained by the traditional finite element model increase instantly when the fault occurs, while the values of synchronous reactance and transient reactance obtained by
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the field-circuit-network coupling model decrease instantly when the fault occurs, and the subtransient reactance of both models decreases. The reason for the difference is that the input terminal current and excitation current in the field-circuit-network coupling model have a strong impact at the moment of failure, which causes distortion of the internal magnetic field of the motor and serious local saturation, so that the reactance decreases. At 5.05 s, the SC in the field-circuit-network coupling model is excited strongly under excitation control, and the synchronous reactance and transient reactance increase due to the saturation of the magnetic field. The leakage reactance occupies a large proportion in the subtransient reactance, and the leakage reactance is difficult to saturate, so the subtransient reactance is basically unchanged. 1.4
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Fig. 7. Transient steady state reactance of the SC at different time points
5 The Variation Law of Transient Steady State Parameters of the SC The design, operation regulation and control of reactance should consider the most serious working conditions. Therefore, the minimum value in the process of reactance parameter change under transient conditions is more valuable. At the rated initial voltage, the transient parameters of the SC under different reactive power conditions from 300 Mvar lagging phase to 200 Mvar advanced phase are calculated. Set different voltage changes from −1 to 0.3 p.u., calculate the magnetic field distribution and reactance changes in the transient transition process, extract the most saturated state of each condition, and calculate the corresponding minimum reactance.
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Fig. 8. Transient steady state reactance of the SC with different voltage rate and initial reactive power
According to the calculation results in Fig. 8, • The minimum reactance of each reactance decreases with the increase of the degree of voltage change. When the initial reactive power is 0 Mvar, the minimum value decreases from 1.165 to 0.816 with the increase of the stator voltage drop (0 to 1 p.u.), decreasing by 29.9%. This makes sense because the higher the voltage drop, the greater the transient current and the deeper the saturation. • The larger the initial reactive power of lagging phase is, the smaller the minimum reactance is. When the voltage sag degree is −0.2 p.u., the initial reactive power changes from lagging phase 300 Mvar to advanced phase 200 Mvar, and the minimum value increases from 1.017 to 1.273, which is about 25.17%. This also means that the SC should work in the low lagging phase reactive power or even advanced phase state if it is necessary to reduce the magnetic saturation during the voltage mutation process. • Synchronous reactance is more likely to saturate and is more sensitive to changes in initial reactive power. In contrast, subtransient reactance is more difficult to saturate. This is because leakage reactance accounts for a large proportion of subtransient reactance and leakage reactance is difficult to saturate.
6 Conclusion • A field-circuit-network coupling time-step finite element model is established, which includes excitation control and HVDC system and can be used to analyze the dynamic machine-network relationship. Compared with the traditional finite element model, under the influence of HVDC transmission control system, the deeper the fault degree, the greater the current fluctuation at the machine end and the longer the recovery time, the larger the excitation current and the longer the recovery time, and the more active and reactive power output.
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• The change law of reactance during the transient transition is studied. The results show that the transient strong current in the transient process will cause the distortion of magnetic field, aggravate the local magnetic saturation, and make the reactance less than the steady state value. The effects of voltage change rate and initial reactive power on minimum reactance in different transient processes are studied. The higher the voltage change rate, the higher the saturation degree, the smaller the initial lagging reactive power, the lower the saturation degree. Based on the work in this paper, a time-varying parameter motor model based on two-dimensional look-up table can be established, which lays a foundation for more accurate simulation of the SC and dynamic behavior of the power system in the future.
References 1. Wang, P., Mou, Q., Liu, X., et al.: Start-up control of a synchronous condenser integrated HVDC system with power electronics based static frequency converter. IEEE Access 7, 146914–146921 (2019) 2. Sha, J., Yang, S., Guo, C., et al.: Study on suppression effect of synchronous condenser on commutation failure of UHVDC system under hierarchical connection mode. Power Syst. Technol. 43(10), 3552–3561 (2019). (in Chinese) 3. Wang, Y., Zhang, Y., Zhou, Q., et al.: Study on application of new generation large capacity synchronous condenser in power grid. Power Syst. Technol. 41(1), 22–28 (2017). (in Chinese) 4. Wang, Q., Wang, G., Zhao, N., et al.: An impedance model-based multiparameter identification method of PMSM for both offline and online conditions. IEEE Trans. Power Electron. 36(1), 727–738 (2021) 5. Xiao, S., Ge, B., Tao, D., et al.: Calculation of rotor dynamic electromagnetic force of synchronous generator under the stator winding interturn short circuit fault. Trans. China Electrotech. Soc. 33(13), 2956–2962 (2018). (in Chinese) 6. Luo, Y., Hu, Q., Liu, X., et al.: Field-circuit-network coupled time-step finite element model for power system dynamic analysis. Proc. CSEE 29(33), 102–110 (2009). (in Chinese) 7. Ge, B., Yin, J., Tao, D., et al.: Modeling of field-circuit-network coupled time-stepping finite element for one machine infinite bus system based on excitation and speed control. Trans. China Electrotech. Soc. 32(03), 139–148 (2017). (in Chinese) 8. Xiao, Y., Chen, B., Li, X., et al.: Analysis of inductance parameters for PM-assisted synchronous reluctance motors. Electr. Mach. Control Appl. 48(06), 89–94 (2021). (in Chinese) 9. Chen, J., Li, J., Qu, R., et al.: Magnet-frozen-permeability FEA and DC-biased measurement for machine inductance: application on a variable-flux PM machine. IEEE Trans. Industr. Electron. 65(6), 4599–4607 (2018) 10. Li, J., Li, H., Zhou, Y., et al.: An improved end-winding leakage inductance calculation method based on frozen permeability for large synchronous condenser. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–5. IEEE (2019)
Research on the Voltage Balance Ability of Platinum Electrode in Valve Water Cooling System Based on Leakage Current Ripple Factor Zhenyu Li1 , Bing Gao2(B) , Biyue Cao3 , Yongchao Song4 , Zhiwei Yu4 , and Yongxing Zhu4 1 Electric Power Research Institute of China Southern Power Grid, Guangzhou 510663, China 2 School of Electrical and Engineering, Chongqing University, Chongqing 400000, China
[email protected]
3 Guangzhou Power Supply Bureau of Guangdong Power Grid Co., Ltd.,
Guangzhou 343009, China 4 China Southern Power Grid Co., Ltd., Guangzhou 510663, China
Abstract. The corrosion and sediment deposition in converter valve water cooling system is one of main causes of converter valve faults, especially the sediment deposition occurred on platinum electrode, which would worsen electrode voltage balance ability and accelerate the metal components corrosion, threatening the safety of transmission system seriously. The previous work seldom investigates the dynamic sediment deposition behavior and its influence, besides, the periodic change/clear schematic is adopted, leading to blindness and human resources wasting. Therefore, this paper addressed a secondary-velocity-mass transfer coupling model, which considers the bilateral impact between electrochemical behaviors and porous sediment deposition process. Lump circuit simulations and experiments were conducted to demonstrate the method. Results show that the proposed method can do well with the dynamic sediment deposition and radiator corrosion problem together. Then, influence of deposited sediment on the radiator corrosion and electrode electrochemical characteristic were investigated, and the leakage current ripple factor of radiators was chosen as the assessment parameter to indicate the voltage balance ability of platinum electrode. Finally, the ripple factor is determined to decide whether change/clear electrodes or not under different water conditions. The obtained results are expected to guide the design and maintenance of valve cooling system. Keywords: Converter valve cooling system · Power emergency plan · Fault line location · APTS · Genetic algorithm · Pareto optimal
1 Introduction The converter station plays important role in the high voltage direct voltage (HVDC) converter system for the energy conversion [1]. To dissipate the generated heat and avoid overheat of metal components, the cycling deionized water cooling system is © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1012–1026, 2022. https://doi.org/10.1007/978-981-19-1870-4_106
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widely used to remove heat and ensure the safety of HVDC system [2]. However, the large voltage difference among metal components would induce leakage current among metallic components, as well as electrolytic corrosion. To reduce the corrosion caused by leakage current, a certain number of platinum grading electrodes are installed at the terminals of thyristor stack to fix the water voltage level distribution of valve stack [3]. However, it is reported that the water cooling system is one of the weakest parts in HVDC system, more than 66% breakdowns of converter valve water cooling system is contributed by sediment deposition and radiator corrosion [4]. Therefore, it is essential to study the corrosion and deposition characteristic of converter valve. Some works have been done to investigate the corrosion and deposition behavior of HVDC water cooling system by means of experiments [5, 6]. More scholars pay attention to the corrosion and scaling characteristics of the valve cooling system and the unbalanced pressure sharing capacity of the electrode after scaling. Against corrosion and fouling characteristics, research mainly from the perspective of circuit method and electrochemical analysis method to carry out the work, the former is mainly based on Faraday’s law for equalizing electrode average scale layer thickness, the latter mainly by building valve cooling system in the current field and mass transfer field distribution for valve cooling system corrosion and scaling law [7, 8]; And to avoid system failure caused by electrode fouling, converter station maintenance mainly take down converter valve to clean or replace the equalizing electrode on a regular basis to eliminate the influence of fouling, and the valve cooling system manufacturers through the valve cooling system installed on the flow velocity, conductivity, oxygen sensor, monitoring and control of water quality, avoid aluminum radiator rapid corrosion cause severe fouling [9]. However, there are differences in scaling of all platinum electrodes in the cooling water branches, and the strategy of regularly cleaning or replacing electrodes to deal with electrode scaling is quite blinded, and the operation process of removing and cleaning is complicated. It is essential to study the variation rule of voltage balance capacity of electrode. Numerical simulation is one of the effective means to study the corrosion and scaling behavior of valve cooling system and its influence, and electrochemical field analysis method can be used to comprehensively understand the change law of various substances in valve cooling system and the scaling behavior of pressure equalizing electrode. As found in literature [12], the deposition of aluminum corrosion products will have blocking effect on the electrode reaction, and the electrode deposition thickness in the converter valve can be up to 0.8 mm, accounting for 40% of the electrode diameter. The influence of scale dynamic deposition cannot be ignored. In order to evaluate the impact of scale layer deposition, literature [10] proposed from the perspective of electrochemistry that the scaling trend was calculated by detecting the pH value, conductivity, reaction potential, ion concentration and leakage current of cooling water at the installation position of pressure equalizing electrode, and it was believed that maintenance was needed when the scaling trend was 0.7. Therefore, this paper analyzes the dynamic corrosion and scaling behavior of the valve cooling system, and then proposes an evaluation method for the voltage balance sharing capacity of the scaling pressure sharing electrode.
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Based on the previous work, in this paper, the secondary current-flow-mass transfer coupling model is built at first, which considers the bidirectional bewteen dynamic parameters and the porous scale layer deposition, and can indicate the valve cooling system corrosion and fouling dynamic behavior well; Secondly, the influence of scale deposition on the corrosion and scaling of the valve cooling system is analyzed. Finally, a voltage balance capability evaluation method and electrode replacement/cleaning strategy based on the ripple factor of radiator leakage current are proposed.
2 Corrosion and Scaling Electrode Reaction Analysis 2.1 Converter Valve Cooling System Structure Converter valve cooling system is divided into inside outside cold system and cooling system, the cooling system of closed cycle of deionized water, in the main circulation pump driven through the converter valve tower, to take away the heat generated by the thyristor, and then in the cooling tower cold water cooling control in cold water temperature is less than 50 °C, in water flow valve tower structure as shown in Fig. 1, figure in blue for the main inlet pipe, the temperature is low, Red indicates the main outlet pipe with high temperature. The valve tower consists of four valve layers, each consisting of two valve segments, with the main inlet/outlet pipe flowing in through the top of the valve tower and out through the bottom. To adopt the way of parallel water valve cooling system, each valve section is composed of multiple radiator and brake pipe series, shut off when the common system AC/DC voltage, large amounts of heat generated by the thyristor cooling through the cooling system, the radiator inlet/outlet pipe are connected to the water flow, and then through the aluminum radiator, reactor and other metal components for its cooling [13]. In order to reduce the corrosion of metal components by leakage current, platinum-material pressure sharing electrodes are installed at both ends of the manifold pipe, which are connected with the radiators at both ends of the valve section cooling system. Ideally there is no leakage current in the radiator tributary waterway. However, due to the distortion of the electric field on the surface of the pressure equalizing electrode, the potential difference in the waterway of the radiator tributary can be as high as 1.4 kV, and there is still leakage current in the valve cooling system. The ions generated by the corrosion of the aluminum radiator move to the pressure equalizing electrode and produce electrodeposition reaction. When the scale layer thickness reaches a certain extent, it may fall off, causing water pipe blockage, overheating of equipment and failure of the converter valve. Therefore, it is of great significance to study the corrosion and scaling behavior of valve cooling system. 2.2 Electrochemical Reaction Mechanism In order to further obtain the chemical reactions between different potential radiators and platinum electrodes in the valve cooling system, literature [6] established a valve cooling water channel simulation platform and an aluminum-platinum electrode electrochemical reaction simulation platform, and experimentally analyzed the chemical mechanism of aluminum radiator corrosion and electrodeposition on the surface of electrode at different
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potentials. Literature [14] treated the valve section cooling system as a multi-capacitor system, and analyzed the chemical reactions on the surface of electrode and aluminum radiator from the electrical and chemical perspectives. During the previous experiment, the weight loss, the SEM and the XRD test method are conducted, a pitting morphology is found on anodic aluminum sheet, which indicates the leakage current causes different reactions on aluminum sheet: Al - 3e− → Al3+
(1)
The deposition of scale layer, which is the charged negative ion generated after the corrosion of aluminum radiator, will occur at high potential voltage equalizing electrode migrates to the pressure equalizing electrode [22]: + Al(OH )− 4 +H3 O → Al(OH )3 ↓ +6H2 O
(2)
There is almost no pitting morphology on the surface of the low-potential aluminum sheet. According to literature [6, 14], it can be inferred that the chemical reaction of the low-potential aluminum sheet is as follows: 2Al + 2OH − + 6H2 O → 3H2 ↑ +2Al(OH )− 4
(3)
It is also found that bubbles will form on the surface of metal components, and electron reaction (4)–(5) will be obtained from the construction of low-potential metals, and electron loss reaction (6) will occur from high-potential metal components, namely: 2H2 O + 2e− → H2 ↑ +2OH −
(4)
2H2 O + O2 + 4e− → 4OH −
(5)
2H2 O − 4e− → 4H + + O2 ↑
(6)
Since these electrode reactions degree are contributed by the current density in water cooling system, and hence it can be regarded as an electrochemical problem. Additionally, the diffusion and migration of reaction species under influence of velocity field and concentration difference can be investigated in terms of mass transfer filed. As the growth of deposits is considerable and it would significantly affect the mass transport around electrode. Therefore, this paper proposed an electro-mass transfer-velocity coupling model to indicate the sediment deposition characteristic.
3 Secondary Current-Flow-Mass Transfer Coupling Model 3.1 Governing Equations for Current Distribution The sediment is regarded as insulation resistance, and the blended current density distribution and voltage caused is solved by current field, which satisfies the following equations [14, 15]: ∇ ·J=0 J = −σ ∇φ
(7)
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where σ is the conductivity, S/m; ε is the permittivity; J is the current density, A/m2 , φ is the potential, V. Based on the Archie’s law, the equivalent conductivity of porous sediment can be expressed as [16, 17]: σe = σ θ m sLn
(8)
where θ is the porosity of sediment, m is the cementation index, which is 2; sL is fluid saturation, which is 1; n is the saturation coefficient, n = 2 [15]. In addition, it is pointed out that the DC component take dominant in the sediment deposition under AC-DC compound case [13], the DC case is investigated in the simulation model. Since the connected radiators burden the voltage drop in series, hence, the voltage of radiators is set as the linearly decreased voltage level. On the other hand, to describe these electrodes reactions given in above section, the interface electrode reaction current distribution due to electrochemical reaction is calculated by Bulter–Volmer equation, which is given by Eq. (9). In the model, the double capacity is also considered, which is set as 0.081 F/m2 [14]. −αb Fη αa Fη ) − exp( )) RT RT η = φs − φl − Eeq
iloc = ioj (exp(
(9)
where iloc is the local current density, A/m2 ; ioj is the exchange current density; αa and αb are the transfer coefficients; R is gas constant, 8.314 J/(mol·K); T is the deionized temperature, which is 323 K; η is the over potential; φ s is applied potential, V; φ l is the electrolyte potential, V; E eq is the equilibrium potential, V. In addition, the Tafel law is adopted for describing the irreversible anodic electrode reaction, which can be presented by [18]: η
iloc = ioj 10 b
(10)
where b is the Tafel slope and has units 1/V. The detailed parameters for electric reaction field are listed in Table 1. Table 1. Electrochemical reactions parameters Parameters
io j (A/m2 )
σ (uS/cm)
T (K)
E eq (V)
b 1/V)
Reaction Eq. (1)
1.41e-4
0.5
323
−0.114
/
Reaction Eq. (2)
2e-7
0.5
323
0.401
0.145
Reaction Eq. (3)
1e-10
0.5
323
1.229
/
Reaction Eq. (5)
3e-5
0.5
323
−1.662
/
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As the species migration is also affected by the velocity field of water cooling system, the water flow distribution should be studied at first. The fluid flow in valve section can be regarded as turbulent filed. The continuous water flow is governed by the unsteady compressible flow equations [23]. ∂ρ + ∇ · (ρu) = 0 ∂t ∂ui uj ∂ui 1 ∂P ∂ ∂ui + =− + (μ ) ∂t ∂xi ρ ∂xi ∂xi ∂xi
(11)
The fluid flow is described by k-ε turbulence model, as shown in following. ∂ρkui ∂ μt ∂k ∂ρk + = [(μ + ) ] + Gk − ρεε ∂t ∂xi ∂xj σk ∂xj ∂ρεε ∂ μt ∂k C1ε ε ε2 ∂ρεε ui = [(μ + ) ]+ + Gk − C2ε ρ ε ∂t ∂xi ∂xj σk ∂xj k k
(12)
μt = ρCμ εε ∂uj ∂ui ∂ui Gk = μt ( + ) ∂xj ∂xi ∂xj where Gk is the turbulence energy contributed by average viscous gradient; C 1ε and C 2ε are the coefficient, respectively, in the paper, C 1ε = 1.44, C 2ε = 1.92, C μ = 0.09. And σ k = 1.0, σ ε = 1.03 are the parameters correspond to turbulence energy k and dissipation rate ε. The flow flux of distributary pipes is about 7 * 4.5 = 30 L/min, the boundary of tributary pipes of radiator is set as open boundary, while the other wall of pipes is set as nonslip wall boundary. The corrosive ions migrate to electrode through distributed water pipes with the effect of electric and turbulence flow field. With the occurrence of the deposition reaction, electrode position reactions take place on electrode surface. The followed equations to describe the transport and distribution of ion in the distributary pipes [19]: ∂ci +∇ · (−Di ∇ci − zi um,i Fci ∇φl +u · ∇ci )=Ri ∂t
(13)
where c is concentration of specie i, mol/m3 ; Ri is the local generation rate. zi is the charges; Di is the diffusion coefficient; F is F is the Faraday constant, 96485.3383 C/mol; um,i is the mobility (mol·m2 /(J·s)). Additionally, the diffusion coefficient Di for species in porous media should be modified as Di,e , which can be expressed as [15, 21–22]: Di,e = Di (1 − θ ) +
Di NM ,PE
θ
(14)
where R is the gas coefficient, T is the fluid temperature, N M,PE is MacMullin value, which is equal with N M,PE = 1/θ. Here, the mobility in porous sediment layer should be replacing by the equivalent diffusion coefficient in Eq. (14).
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The electrochemical reaction that occurs on the surface of electrodes, and then the fluxes of tetrahydroxy aluminates ions can be given by: N · n| e =
νd ,m iloc nd F
(15)
where nd is number of electrons in reaction; νd,m is the stoichiometric coefficient for the species in reaction m. The no flux condition is applied for the other boundaries of water pipes. 3.2 Finite Element Model and Boundary Conditions Taking the valve section cooling system as the research object, its two-dimensional model was shown in Fig. 2, which the radiator branch water path was equivalent to the inlet. The single platinum electrode was used in the valve section cooling system, and which the depth of the electrode inserted into the water pipe was 28.5 mm, the diameter of the manifold 57.5 mm, and the radius of the pressure equalizing electrode 1 mm. In this model, the confluence pipe material was PVDF and the conductivity was set to 1 × 10−6 s/m, platinum as a voltage equalizing electrode material, the conductivity was 4 × 106 s/m, the cooling medium was deionized water, which was selected 0.5 us/cm in this paper.
S1
Porous calcareous ddeposits
S2
2
3
Linearly decreased Voltage 4
5
Fig. 1. Calculation model of sediment dynamic deposition
The potential of each radiator was set to decrease in equal proportion from the anode voltage equalizing electrode potential to the cathode electrode potential in the model. The boundary of the secondary current-turbulence field-mass transfer field calculation model constructed in the thesis was shown in Table 2.
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Table 2. The boundaries of cooling system Type
Boundaries
S1
Large potential; Electrode reaction; Deposited sediment; Wall
S2
Small potential; Electrode reaction; Wall
G2
Insulation; No Flux; Open Boundary (pressure 0.15 MPa)
G3
Insulation; No Flux; Wall
G4
Linearly decreased voltage; Electrode reaction; Outlet
G5
Linearly decreased voltage; Electrode reaction; Outlet
4 Validation of Proposed Method Cation Firstly, the lump circuit model is commonly used to predict the sediment deposition characteristic [9], the cooling water between electrode and connected joint and distributary pipes are treated as resistance, which can be calculated by: R=
L L 1 × = σ S σS
(16)
where R is equivalent resistance, ; σ is the conductivity, S/m; L is the length, m; S is size of pipes, m2 . Firstly, the voltage difference value for the connect joint between simulation model and circuit model is investigated, just as shown in Fig. 2. It is obvious that the simulation coupling model result accords well with the circuit model result, with calculation error about 3.5%, and the voltage calculation difference is about 47 V.
Fig. 2. Results from proposed method and lump circuit
Meanwhile, the comparison of deposited sediment case is also investigated. Figure 3 gives the voltage and error at different distributary pipe joints. The sediment resistance
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Fig. 3. Results from proposed method and lump circuit
is about 27262 . One can see that the simulated model also accords well with the lump circuit model, with error only about 3.7%. It means that the model presents the electrochemical behavior of deposited sediment situation. Consequently, the proposed simulation model has great accuracy and deal with the dynamic corrosion and deposition behavior efficiency.
5 Voltage Balance Ability Based on Ripple Property 5.1 Analysis of Influence Law of Scale Deposition on Pressure Equalizing Electrode The variation of sediment thickness of anode with time is presented in Fig. 4. It can be seen that the long-time growth of corrosion product deposits has a remarkable feature that increases with the time in quadratic function, when the (D*t)1/2 increases about 2 cm, the increased sediment thickness is about 0.153 mm. Hence, this equation can indicate the dynamic deposition process well, and can be used for predicting the sediment thickness. Figure 5 gives the changed leakage current in distributary pipes with considering the feedback effect of sediment. One can see that the leakage current in distributary pipe with low potential decreases with sediment deposition, the maximum decreased value is about 1.4 μA. On the contrary, the leakage current in distributary pipe with large potential increases with sediment deposition, the corresponding maximum value is about 3.2 μA, the main reason is that the electric field distortion along tributary pipes would result in larger decreased potential around grading electrode. In conclusion, the sediment deposition on grading electrode would accelerate radiator corrosion.
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Fig. 4. Changes of the thickness of deposited sediment
Fig. 5. Variation of leakage current in tributary pipes
5.2 Characterization Parameters of Voltage Balance Capacity For the valve cooling system, the scaling of the pressure equalizing electrode will mainly change the leakage current of the tributary waterway of the radiator and accelerate the corrosion of the radiator, further deteriorate the deposition of the scale layer of the pressure equalizing electrode, and even cause the shedding and blockage of the water pipe in serious cases, and even cause system accidents. Therefore, the paper analyzes the leakage current variation law of each radiator tributary waterway under different scaling degree, and the scaling degree of electrode is defined as the percentage of the maximum thickness of scaling layer and electrode diameter (Table 3).
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Branches I(uA)
Sediment degree (%) 0
7.35
16.2%
21.4%
34.9%
I1
94.23
94.14
94.03
93.99
93.84
I2
56.87
56.51
56.07
55.90
55.34
I3
26.72
26.05
25.239
24.90
23.87
I4
0.002
−0.75
−2.40
−2.93
−4.57
I5
−26.73
−28.41
−30.05
−31.13
−33.60
I6
−56.88
−59.31
−61.15
−63.29
−66.89
I7
−94.24
−97.75
−100.3
−103.5
−108.7
The I 1 –I 7 value for non-sediment condition is chosen as reference basis, and the change current I for different branches after sidiment deposition, as shown in Eq. (17), and the corresponding value is adopted to indicate the variation of leakage current in all branches.
I = |Ii−se − Ii−init | × 100%
(17)
where I i-init is the leakage current for initial state, and I i-se is the leakage current after sediment deposition. Figure 6 shows the changed current I of different radiator branches under different sediment degree. It can be seen that the changed leakage current for different radiator branches decreases with the decreasing of tributary pipe voltage. Take the sediment degree 34.9% for example, the changed leakage current is about 15.46 μA for radiator branches numbered 7 with larger voltage, while the corresponding value is only 0.4 μA for radiator branches numbered 1 with lower voltage, it means that the when the voltage balance ability of platinum electrode decreases, the corrosion effect of leakage current on high potential radiator is greater than that of low potential radiator, thereby, some corrosion protection measures should be taken for radiators with large voltage. In addition, the changed leakage current is proportional to sediment degree for the same radiator tributary pipe; the leakage current increases with the sediment degree. Therefore, the changed leakage current I for radiator tributary pipe can be used to judge the variation of voltage balance ability of platinum electrode. As shown in Fig. 7, the maximum change value of leakage current of each radiator branch under different water quality conditions and scaling degree was analyzed. It can be obviously found that the maximum change value of leakage current follows the same rule under different scaling degrees: it increases exponentially with the deterioration of water quality conditions. For example, when the scaling degree is 34.9%, the water quality condition increases from 0.07 us/cm to 0.4 us/cm, the maximum change value of the leakage current of the radiator branch increases from 0.23 μA to 9.29 μA.
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Fig. 6. Current increase rate of tributary pipe under different deposition degrees
Fig. 7. The maximum current increase rate of tributary pipe under different deposition degrees and water conditions
Scaling of the voltage equalizing electrode will affect the distribution of leakage current in all branches of the radiator. Therefore, it is necessary to comprehensively consider the change of leakage current in all branches to accurately evaluate the voltage equalizing capacity of the electrode. Therefore, the ripple factor of leakage current in water pipes of all branches is selected n ( Ii − Iave )2 (18) α= i=0
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The change rule of the leakage current ripple factor α under different fouling degrees is shown in Fig. 8. It can be found that as the degree of scaling of the voltage equalizing electrode increases, the leakage current in the valve section water circuit shows an increasing trend, which is manifested as a gradual increase in the ripple factor α, that is, the worse the electrode voltage equalization ability, the larger the ripple factor α, And the law is also applicable to different water quality conditions.
Fig. 8. Variation of ripple factor under different sediments
5.3 Replacement/Cleaning Strategy of Platinum Electrode To investigate the voltage balance ability of platinum electrode in converter station at different regions, the variation of ripple factor under different water conductivity conditions is given in Fig. 9. It can be seen that the ripple factor increases in exponential function with the worsen of water conductivity. Hence, it is necessary to get the critical value of unbalanced voltage ability. In reality, the converter station is maintained each year, the statistical data indicates that the deposited sediment situation would be regarded as serious case once the thickness of sediment is over 0.8 mm, and Ref. [11] uses the 0.7 to judge whether the sediment deposition tendency increases or not. Consequently, the value of 0.8 mm is chosen as the critical value, it is that the ripple factor corresponds to sediment degree dg = 40%. For the case water conductivity σ = 0.2 uS/cm case, the voltage balance ability would be destroyed seriously once the ripple factor α > 4.88. Therefore, the safety of water cooling system is threaten greatly, some measures should be taken, such as change or clean these platinum electrodes. For other cases, the corresponding ripple factor can be obtained by figure-table methods listed in Fig. 9.
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Fig. 9. Variation of ripple factor under different water conditions
6 Conclusion A coupling model of secondary current-flow-mass transfer field in valve cooling system was established to solve the unbalanced pressure sharing capacity caused by scaling of the pressure sharing electrode. The model can effectively account for the porous characteristics of scale layer and the geometric changes of the electrode-deionized water interface caused by scaling layer deposition. In addition, the ripple factor of the leakage current in each radiator tributary waterway was proposed as the characteristic quantity of the voltage equalizing capability of the electrode, and the replacement/cleaning strategy of the voltage equalizing electrode under different water quality conditions was obtained based on ripple factor to guide the design and inspection. Acknowledgment. This work was supported in part by the China National Science and Technology Support Program under Grant (52007013).
References 1. Kunpeng, Z., Yuan, L., Gaoyong, W., et al.: Study on the test method of ±1100 kV UHVDC Valve. Trans. China Electro-Tech. Soc. 28(1), 87–93 (2013) 2. Jackson, P.O., Abrahamsson, B., Gustavsson, D., et al.: Corrosion in HVDC valve cooling systems. IEEE Trans. Power Deliv. 2(12), 1049–1052 (1997) 3. Wei, H., Wei, F., Haifeng, W., et al.: Simulation and experimental study on the evaporative cooling system of HVDC valve unit. Trans. China Electrotech. Soc. 32(2), 264–270 (2017) 4. Guangliang, Y., Nengling, T., Xiaodong, Z.: Analysis of potential dangers leading to HVDC outage in valve cooling system. Power Syst. Protect. Control 18(38), 199–203 (2010) 5. Yuanyou, W., Zhijie, H., Rui, L.: Primary analysis on corrosion and deposit in valve cooling system of Tian-Guang HVDC project. High Voltage Eng. 32(9), 80–83 (2006)
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6. Liu, X., Wang, C., Liu, N., Jiao, X.: Current-induced corrosion of aluminium heat sinks in water-cooling systems for high-voltage direct-current converters. Corros. Eng. Sci. Technol. 54(2), 131–142 (2018). https://doi.org/10.1080/1478422X.2018.1544742 7. Guangtai, Z., Yang, L., Jiping, W., et al.: The numerical calculation study on radiator corrosion of HVDC converter valve. Chin. Technol. Forum 18, 2016 (2016) 8. Binxian, L., Jianhui, G.D.Z., et al.: Equivalent electric circuit modeling for electrode reaction in valve cooling water system. High Voltage Eng. 42(7), 2199–2206 (2016) 9. Wenliang, Z., Aijun, N., Jihua, F., et al.: Study on quality control index of inner cooling water of HVDC converter valve. Shanxi Elect. Power 42(8), 76–81 (2014) 10. Cui, P., Guo, J., Wang, H., et al.: A Electrode Sediment Experiment Detection System and Method Used in HVDC Converter Valve, China, 201410552999.0, 2014-10-17 11. Wu, Q.: Research on Electrochemical Corrosion of Cooling System of Converter Valve. North China Electric Power University, Beijing (2018) 12. Yin, L., Jin, Y., Leygraf, C., et al.: A FEM model for investigation of micro-galvanic corrosion of Al alloys and effects of deposition of corrosion products. Electrochim. Acta 192, 310–318 (2016) 13. Yong, C.: Research on the water cooling circuit of sicheng HVDC converter valve. Southeast Elect. Power 04, 50–52 (2003) 14. Xu, H., Li, D., Qiu, Z., et al.: Analysis of the deposition mechanism on grading electrode in high voltage direct-current water cooling system. In: Seminar on Smart Grid Informatization Construction, Beijing, China, pp. 1–4 (2017) 15. Jiang, Y.: Deposition Behavior of Corrosion Products In Inner Cooling Water System of HVDC Converter Valve. North China Electric Power University, Beijing (2018) 16. Dongliang, Z., Shuiqing, L., Xing, J., et al.: Experiments and numerical simulations of the removal of fine particles in the coupling field of electrostatic precipitators. Proc. CSEE 36(02), 453–458 (2016) 17. Liangyong, C., Dduan Yufeng, P., Wenhao, et al.: Numerical simulation of coal-water slurry flow in horizontal pipelines. Proc. CSEE 29(05), 54–60 (2009) 18. Yanpan, Q.F.T.: Microstructural modeling of pitting corrosion in steels using an arbitrary Lagrangian-Eulerian method. Metall. and Mater. Trans. A. 48(5), 2618–2632 (2017) 19. Zhengbo, C., Chao, G., Yuekui, H.: Hidden danger analysis and maintenance of grading electrode in valve water cooling system. Low Carbon World 23, 63–65 (2016)
Transmission Line Galloping Test System Based on Adaptive Excitation Li Zhang1(B)
, Jiangjun Ruan1 , Daochun Huang1 , Wei Cai2,3 , Jian Li2,3 , and Zhihui Feng2,3
1 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
[email protected]
2 Wuhan NARI Limited Company, State Grid Electric Power Research Institute,
Wuhan 430074, China 3 Hubei Key Laboratory of Power Grid Lightning Risk Prevention, Wuhan 430074, China
Abstract. Long time transmission line galloping has brought great damage to towers, insulator strings and fittings. Due to the randomness of natural conditions, it is difficult to establish a controllable full-scale galloping test system at present. This paper designed a galloping excitation system for real overhead transmission lines by adaptive excitation. The electromagnetic force and action time required for adaptive excitation were studied based on dynamic finite element simulations. The correlation between vibration amplitude and excitation force is also studied. Results show that the transmission time of excitation wave corresponds to the inherent frequency of the overhead line system. The proposed adaptive test system can be used to simulate the actual galloping with two loops mode, and make galloping state controllable. And the vibration amplitude can be controlled by changing the exciting force. Thus, some studies related to the transmission galloping damage assessment can be carried out. Keywords: Transmission line · Galloping · Adaptive · Vibration characteristics
1 Introduction Generally speaking, transmission line galloping is a self-excited vibration caused by the wind and ice on the conductor surface. The vibration may last a long time, and the vibration amplitude may be large, thus causing damage to transmission towers, insulator strings, connecting fittings, etc. However, there is still a lack of experimental research on galloping damage and anti-galloping technology. It is needed to establish the controllable galloping test system to study the damage brought by the transmission line galloping. It can also help to further enrich the knowledge and understanding of transmission line galloping problems [1, 2]. The transmission line system will produce complex coupled vibration in vertical direction, horizontal direction and torsional direction when galloping occurs, and the main form of vibration is single or multiple half-wave vertical vibration. Therefore, for © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1027–1035, 2022. https://doi.org/10.1007/978-981-19-1870-4_107
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the study of numerical simulation about the transmission line galloping, cable elements with two or three degrees of freedom are generally used to simulate the transmission line. And influence of splitter conductor spacing, initial wind attack angle, wind speed and ice thickness on vibration amplitude and dynamic tension are analyzed by nonlinear numerical simulation method [3, 4]. For the study about galloping test, it can be divided into two different types. Wind tunnel tests can used to analyze the aerodynamic characteristics under cross sections of wires of different shapes, and the influence of different wind speed and direction on transmission line galloping [5]. But the experimental platforms are often limited by size, so it is difficult to simulate the complex aerodynamic load on the ice-coated transmission lines. For the prototype test, there are some full-scale test lines built in Japan [6], Canada, China, etc. These test lines containing a variety of different voltage levels, span lengths, transmission tower types, etc. Scholars have made a lot of achievements through carrying out the corresponding experiments about the transmission line galloping. But the test is restricted by the weather, which results in low efficiency of the test. At present, China has not established the transmission line test system with controllable vibration state. This paper designed a galloping test system for real overhead line conductors based on adaptive excitation. By the controllable periodic electromagnetic force, the vibration amplitude of the overhead wire can be controlled, and the vibration can last a long time. The adaptive action time required were studied based on dynamic finite element simulations. Considering the geometric nonlinearity, the finite element model of the system including the wire and insulators was built. Through controllable excitation force, the conductor vibration state can be controlled, and the motion characteristics during galloping can be reproduced. It can be used to analyze the bearing force of tower structure, bolt, insulator string and other subassembly of the whole transmission line system during galloping, evaluate the anti-galloping effect of interphase spacer, and provide a basis for the research of technology for fast suppression of transmission line galloping.
2 Introduction of the Galloping Test System 2.1 Mechanism According to the current research status of transmission line galloping, the recognized model that can fully describe the transmission line galloping rules is the so-called “vertical, horizontal and torsion” 3-Dof model. The governing equation in the vertical direction of this 3-Dof model is as follows [7]: L y + ky y m¨y + [2mζy ωy + 21 ρU 2 D( ∂C ∂θ + CD )]˙ ∂C 1 1 1 dz 2 ¨ = −mi r cos θ0 θ − 2 ρu DCy U dt + 2 ρU 2 DCy ∂θy
(1)
where θ is the torsion angle, θ 0 is the initial freezing angle, J is the inertia moment; m is the mass of the line and mi is the mass of the covered ice, ζ y is the damping ratio of in the vertical direction, C L is the aerodynamic coefficient, k y represents the vertical stiffness; C y is the coefficient of the wind load, ωy is the frequency, and r is the transmission line radius.
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According to the vibration equation, the vibration response of the wire is determined by mass matrix, stiffness matrix, damping matrix and aerodynamic load. If the damping matrix becomes negative: 1 ∂CL + CD ) < 0 2mζy ωy + ρU 2 D( 2 ∂θ
(2)
Due to the appearance of the “negative damping”, vertical self-excited vibration appears and then gradually developed into the stable transmission line galloping. It is caused by vertical instability, known as Den Hartog oscillation theory [8]. It is a torsionfree model. Similarly, if the damping matrix becomes negative in vibration equation of the torsional direction, self-excited torsional vibration appears. Then the system becomes unstable and the vibration amplitude may be larger and larger, which known as the Nigol’s torsional oscillation theory [9]. Long-term observation shows that actual transmission line galloping has some common characteristics [10]. The actual observation results show that the vibration amplitude of the conductor in the vertical direction increases over time and finally stabilizes near a fixed value, while the amplitude in the horizontal direction is small, and the trajectory is usually elliptical. Therefore, according to the excitation mechanism of Den.Hartog’s theory, pulse mechanical excitation can be carried out on the conductor in the vertical plane, and the positive mechanical energy will increase in the transmission line system to simulate the vertical instability in actual and the energy accumulation process of the system absorbed from the wind. The designed test system according to above principle is shown in Fig. 1. Tension insulator string
Conductor Signal line
Acceleration sensor
DAQ device
Computer
Switch group electromagnetic output device Trasmission Tower
Fig. 1. Schematic diagram of the designed galloping test system.
From Fig. 1, the galloping test system proposed consists of towers and overhead line conductors, acceleration sensors, signal line, high-power electromagnetic output mechanism, controller, switch module, traction line and other modules. Through controllable pulse electromagnetic force, the mechanical energy of the whole system will increase, which makes the static conductor vibrate. With the continuous increase of injected mechanical energy, the amplitude of the wire vibration will become larger and larger, and eventually a stable vibration mode will be formed due to damping. Because
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of exist of the energy accumulation, the excitation and maintenance process of actual transmission line galloping can be well simulated. The line system will not be subjected to large tension instantly. The wire vibration amplitude and time can be controlled by the designed high-power electromagnetic output mechanism. 2.2 Establishment of Finite Element Model At present, many articles have introduced the numerical simulation method of transmission line galloping, and these models have also been well validated. This paper takes the Euler beam element in ABAQUS software to simulate the transmission line by releasing its bending degrees of freedom. Insulator string hang points are considered fixed points. The span of the actual transmission line is 300 m, the Young’s modulus of the conductor is 65000 MPa, the area of a sub-conductor section is 696.22 mm2 , and the density of the conductor is 3168.5 kg/m3 . The length of the insulator string is 6 m. In modeling, the multi-split wire was equivalent to a single wire, and the wire was divided into 200 elements. The coordinate relation equation of conductors when modeling is as follows [11]: ⎧ γl h ⎪ y = γ σL0h=0 (sinh 2σ + sinh γ (2x−l) )− ⎪ 0 ⎨ 2σ0 γ x γ (l−x) h 2 (3) ( 2σγ 0 sinh 2σ0 sinh 2σ0 ) 1 + ( Lh=0 ) ⎪ ⎪ γl 2σ0 ⎩L = sinh h=0
γ
2σ0
where h is the altitude difference between the two insulator string hang points, l is the span, here is 300 m, γ is the ratio of the gravity to its section; σ 0 is the horizontal stress. After static analyse by applying gravity load to the transmission line system, perform modal analysis on the model and the results is shown in Table 1. Table 1. In-plane modal analysis results. Loop number
Mode shape
Frequency
1
0.1979 Hz
2
0.3954 Hz
3
0.5926 Hz
4
0.7891 Hz
Since horizontal vibration is usually forced vibration, only the in-plane vibration is considered in this paper. A concentrated force of 5 kN was applied to the transmission line end node. The force is acting in a straight downward direction and the acting time was 0.1 s. The adaptive step size was used for simulation. The calculation results were shown in Fig. 2
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(a) Excitation point and 1/4 point.
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(b) Mid-point and 3/4 point.
Fig. 2. In-plane displacement-time curves under single excitation.
After the excitation force is loaded, the excitation wave appeared and then transmitted to the other side of the wire system. The maximum amplitude of each point is 0.2 m and the vibration characteristics of each point are very similar. After 1.25 s, the oscillation starts at the mid-span of the line. The time for the excitation wave to travel back and forth is about 2.5 s, which is consistent with the second natural period. Due to damping, the amplitude of the overhead line conductor vibration decreases with time.
3 Study on Excitation Method 3.1 Excitation with Fixed Intervals As mentioned above, the time for the excitation wave to travel back and forth is consistent with the second natural period. Thus, the superposition of excited waves can be used to simulate the double-half wave vibration mode. According to the spectrum analysis results of the system, the conductor was loaded with concentrated force at a time interval of 2.5 s. In this way, there are always two waves with opposite directions in the wire system, and they will meet at the mid part of the wire to simulate the galloping phenomenon. The concentrated force per cycle is still 5 kN, and the acting time is set as 0.1 s. Analysis results of the displacement-time curves are shown in Fig. 3. The vibration amplitude increases continuously at 1/4 and 3/4 point of the wire in the first 50 s by using the fixed interval excitation method. The vibration amplitude is stable at about 1.4 m during 50 s to 140 s. The vibration amplitude is the largest at the position of 1/4 and 3/4 point, and the smallest at the midpoint of the line, which is only 0.2 m. After 140 s, the amplitude of vibration at all points decrease continuously.
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(a) Displacement of the excitation point.
(c) Displacement of the mid-point.
(b) Displacement of the 1/4 point.
(d) Displacement of the 3/4 point.
Fig. 3. Displacement response under excitation at fixed intervals.
Results of the vertical displacement spectral analysis are shown in Fig. 4 below:
Fig. 4. Vertical displacement spectrum analysis results.
It can be seen from Fig. 4 that the main peak value of the spectrum at all points are about 0.4 Hz, and it is consistent with the second inherent frequency of the conductor system, and the spectral components of other orders are smaller. In general, the in-plane vibration presents a stable double wave pattern in 50–140 s, which is consistent with the characteristics of Den. Hartog’s two loops mode galloping.
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3.2 Excitation with Adaptive Intervals But the conductor system is a nonlinear geometrical construction. As a result, the inherent frequency of the system will change with the vibration amplitude changes. Because the loads are applied at fixed time intervals, the motion state of the excitation point is uncertain when the excitation force is applied in each period. Therefore, the system cannot maintain a stable vibration state, and the vibration amplitude of the transmission line decreases continuously after 140 s.Thus, the time intervals of the excitation force should be adjusted adaptively according to the wire vibration state. The key is to find change of wire vibration characteristics caused by excitation wave. From Fig. 2, transmission of the excitation wave will cause nodes on the wire to drop first and then rise obviously. After the excitation wave leaves, the displacement vibration amplitude of the wire node is small. Thus, three parameters α, β and γ are used to judge the time intervals of the excitation force: t > α & β1 1000 °C) is required for its high densification, which is adverse to energy storage and environmental protection. In this work, the effects of the transient liquid phase LiOH·H2 O, sintering time, and applied pressure on the electrical properties and microstructure of the cold sintered LLZTO electrolyte are investigated. The results show that the ionic conductivity of the cold-sintered LLZTO specimenis proportional to its relative density. The LLZTO specimen prepared with 5 wt% of LiOH·H2 O transient liquid phase and cold sintered at 300 °C under the applied pressure of 300 MPa for 3 h shows a relatively high density of 85.51%, and an improved ionic conductivity of 1.16 × 10–8 S/cm at room temperature. Keywords: Solid electrolyte · Cold sintering process · LLZTO · Ionic conductivity
1 Introduction Recently, lithium-ion batteries has been widely applied with the vigorous development of extensive energy storage/power systems such as electric vehicles, grid energy storage, and small/micro-energy storage requirements in micro-electromechanical equipment. Traditional lithium-ion batteries contain combustible organic electrolytes and require a special container, which hinders the miniaturization of lithium-ion batteries and prevents them from achieving a good match with silicon-based semiconductor devices. At the same time, organic electrolytes are highly corrodible and flammable, which makes © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1059–1066, 2022. https://doi.org/10.1007/978-981-19-1870-4_111
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traditional lithium-ion batteries an unavoidable safety hazard. In comparison, solid state lithium batteries are safe and leak-free. Moreover, metal lithium as the cathode can significantly improve the voltage output and energy storage density. Therefore, solid state lithium batteries are potential as energy storing devices and are experiencing a rapid development in the new energy market. For the past few years, the garnet-type ceramic electrolytes were widely studied because of their good chemical and electrochemical stability. Especially, the cubicphase Li7 La3 Zr2 O12 , (Abbr. LLZO) presents a stable electrochemistry performance. Another garnet-type ceramic electrolyte, Li6.4 La3 Zr1.4 Ta0.6 O12 (Abbr. LLZTO) can be fabricated via doping an appropriate amount of Ta element into LLZO, and its lithiumion conductivity can be improved to around 10−3 S/cm at room temperature [1–4]. It is noteworthy that the lithium-ion conductivity of the garnet-type ceramic electrolyte is also related to its crystal phase, grain boundary resistance, and relative density. The grain boundary resistance of LLZTO can be greatly influenced by grain size. Generally, LLZTO with large grain size, low porosity, and high relative density shows a high lithium-ion conductivity [5]. The high-temperature sintering is widely used to increase the relative density and reduce the grain boundary resistance, thereby increasing the ceramic electrolyte ionic conductivity. However, high temperature sintering of lithiumion solid electrolytes will result in lithium loss and a new secondary phase at the interface between anode material and the solid electrolyte after co-firing at a high temperature, blocking the conduction of lithium ions during the electrochemical cycle [6]. Lithium ions can be rapidly conducted in the crystal grains because of the highly ordered spatial structure inside the crystal grains. However, the conduction process can be hindered by the disordered structure such as the pores and grain boundaries in solid electrolytes. Therefore, ceramic electrolytes with larger grain sizes, fewer pores, and higher relative density generally have higher lithium-ion conductivity. In order to prepare the high ionic conductivity oxide ceramic electrolyte, a high sintering temperature up to 50 ~ 75% of the material’s melting point is required [7]. The temperature of the conventional sintering is generally higher than 1000 °C, and the sintering time is as long as several hours to several days. It leads to a high energy costs and a limitation for the synthesis of organic-inorganic composite materials [8–11]. Recently, the research group of Pennsylvania State University developed the cold sintering process (CSP), which can achieve the densification of ceramics (relative density reaches 80 ~ 99%) in a very low-temperature range (25 ~ 300 °C) and a short time (1 min ~ 3 h) [12, 13]. However, a suitable transient liquid phase such as water, acetic acid solution or some specific additives is required, which can introduce a “dissolution − precipitation” process for a successful CSP [12–14]. In this work, LiOH·H2 O is selected as the transition liquid phase to synthesize Li6.4 La3 Zr1.4 Ta0.6 O12 (Abbr. LLZTO) ceramic solid electrolyte, which can accomplish cold sintering of LLZTO without introducing impurity elements. As the temperature rises, H2 O can be dehydrated from the LiOH·H2 O and temporarily exists in the form of a liquid phase, which helps to accomplish the densification of LLZTO electrolyte at a low temperature (≤ 300 °C). The influence of LiOH·H2 O on electrical properties and the microstructure of cold-sintered LLZTO specimens were discussed.
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2 Experimental Preparation LiOH·H2 O (Sigma-Aldrich Company) particles (≥99.0%) and LLZTO cubic phase powder (Hefei Kejing Company, particle size < 500 nm) (99.99%) were used as raw materials. The LLZTO specimens added with 0, 1, 3, 5, 7, and 10 wt% LiOH·H2 O were prepared by CSP. Experimental procedures for CSP are shown in Fig. 1. Before the experiment, the LLZTO was put in a vacuum drying oven for 24 h at 100 °C to remove residual moisture in powder.
Fig. 1. Experimental procedures for cold sintering of LLZTO.
The mixture of LiOH·H2 O and LLZTO were grinded evenly using a mortar and pestle. Afterwards, the mixed powder is put into a die with a diameter of 12.7 mm and pressed under 100–300 MPa using a hand press (firstly pre-pressed at room temperature for 10 min, and then further heat to 300 °C with a ramp rate of 10 °C/min and held for 3 h). Ultimately, LLZTO specimens prepared by CSP were taken out from the die and put in a vacuum drying oven for 24 h at 100 °C. The density, phase composition, microstructure, and electrochemical properties of the LLZTO samples were charactered using the electronic analytical balance (EX224ZH), scanning electron microscopy (SEM, Quattro S), X-ray diffraction (XRD, Empyrean), and broadband dielectric spectroscopy (Novocontrol Concept 80), respectively.
3 Results and Discussion 3.1 Density Relative density is an essential indicator for assessing the quality of ceramic materials, which is closely related to electrical properties. Generally, the excellent lithium-ion conductivity depends on the high relative density and low porosity of the solid electrolyte. In this work, the density of specimens was measured by Archimedes method, as shown in Fig. 2.
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Fig. 2. The density of LLZTO ceramic electrolyte specimens with different amount of LiOH·H2 O.
Fig. 3. Relative density of LLZTO specimens with different pressure.
It can be seen that when the transient liquid LiOH·H2 O gradually increases from 0 wt% (pure LLZTO specimen) to 5 wt%, the cold-sintered LLZTO specimens relatively density increases from 74.77% to 85.51%, and then the relative density of the specimen decreases slightly as more LiOH·H2 O further is added. The results show that 5 wt% LiOH·H2 O is the optimal ratio for the densification of LLZTO specimens during CSP. The effect of applied pressure on the densities of the specimens with 5 wt% LiOH·H2 O was further investigated in Fig. 3. It is found that the specimens relative density is enhanced from 72.9% to 85.5% with the applied pressure increases from 100 to 300 MPa, and then keep nearly a constant when a higher pressure is applied. 3.2 XRD and SEM The XRD patterns of the LLZTO powder with 5 wt% LiOH·H2 O and the cold-sintered LLZTO ceramic electrolytes with 1, 3, 5, 7, and 10 wt% LiOH·H2 O are shown in Fig. 4. It can be seen that all solid electrolyte specimens exhibit a good crystallinity, and the diffraction peaks of each main crystalline phase of the specimens can match the standard
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PDF card (JCPDS 45–0109), showing that the cold-sintered LLZTO specimens have a cubic phase structure. In addition, a small amount of LiOH phase in the cold-sintered specimen can be observed. It means that LiOH·H2 O lost its crystalline water during the cold sintering process. SEM graphs of the cross-section of the cold-sintered LLZTO specimen with 0, 1, 3, 5, 7, 10 wt% LiOH·H2 O are shown in Fig. 5, and the grain size distribution is in the insets. Microstructure is observed from the cross-section of the as-sintered LLZTO ceramic electrolyte specimen. The average grain size (Xc) of the LLZTO ceramic electrolyte specimens is determined by linear intercepts method, as shown in the insets of Fig. 5(a)–(f). We can see that the grain size of the LLZTO ceramic specimens increases with the addition of LiOH·H2 O, and the grain grows from 3.56 µm to 7,67 µm. The grain size of the cold-sintered LLZTO specimens with 5 wt% LiOH·H2 O looks relatively uniform.
Fig. 4. XRD spectra of LLZTO specimens with 1, 3, 5, 7, and 10 wt% LiOH·H2 O.
Fig. 5. SEM graphs and particle size statistics of cold sintered LLZTO specimens with (a) 0 wt%, (b) 1 wt%, (c) 3 wt%, (d) 5 wt%, (e) 7 wt% and (f) 10 wt% LiOH·H2 O.
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3.3 Lithium-Ion Conductivity The LLZTO electrolyte grain boundary resistance was tested(Fig. 6). The grain boundary resistance of the LLZTO ceramic electrolyte specimens decreases firstly and then increases with the addition of LiOH·H2 O. The specimen with 5 wt% LiOH·H2 O presents the smallest resistance.
Fig. 6. Impedance comparison of LLZTO specimens with different LiOH·H2 O.
Fig. 7. Ionic conductivity and relative density (25 °C) of LLZTO ceramic electrolyte specimens with different LiOH·H2 O.
The lithium-ion conductivity at room temperature and relatively density of the LLZTO electrolyte specimens prepared with different LiOH·H2 O (Fig. 7). From the graph we can see that the lithium-ion conductivity at room temperature of the specimens increases from 3.65 × 10–11 S/cm (0 wt%) to 1.16 × 10–8 S/cm (5 wt%), which is increased for several orders of magnitude. When more LiOH·H2 O (> 5 wt%) was added, the lithium-ion conductivity showed a significant decrease at room temperature. It was believed that excessive LiOH will increase the grain boundary resistance and aggregate at the grain boundary, leading to a low lithium-ion conductivity [15]. Therefore, the
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optimal LiOH·H2 O was 5 wt% in the cold sintering process. As presented in Fig. 7, the result demonstrates that the lithium-ion conductivity of the specimens is positively correlated with their relative densities.
4 Conclusion and Prospect In the work, LiOH·H2 O liquid phase is used to improve the performance of LLZTO electrolyte by CSP. A low temperature of 300 °C, 5 wt% LiOH·H2 O and a pressure of 300 MPa were used to obtain a dense LLZTO bulk, and its lithium-ion conductivity reach 1.16 × 10–8 S/cm at room temperature. In addition, CSP can significantly reduce the sintering temperature, which is helpful to energy saving and environmental protection in the specimen preparation process. However, the lithium-ion conductivity of the coldsintered LLZTO specimen is still not high. We believe that a new auxiliary sintering liquid phase or high-temperature annealing is needed to increase the lithium-ion conductivity before it can be commercially applied in the future. Acknowledgment. This work was financially supported by Fund of the National Natural Science Foundation of China (No. 51877016), Fund of the Natural Science Foundation of Chongqing (No. cstc2019jcyj-xfkxX0008), and Fok Yingdong Education Fund Project of Ministry of Education (No. 171050).
References 1. Liu, K., Wang, C.A.: Garnet-type Li6.4 La3 Zr1.4 Ta0.6 O12 thin sheet: fabrication and application in lithium-hydrogen peroxide semi-fuel cell. Electrochemistry Communications 48, 147–150 (2014) 2. Li, Y., Han, J.T., Wang, C.A., Xie, H., Goodenough, J.B.: Optimizing Li+ conductivity in a garnet framework. J. Mater. Chem. 22(30), 15357–15361 (2012) 3. Buschmann, H., Berendts, S., Mogwitz, B., Janek, J.: Lithium metal electrode kinetics and ionic conductivity of the solid lithium-ion conductors Li7 La3 Zr2 O12 and Li7-x La3 Zr2-x Tax O12 with garnet-type structure. J. Power Sources 206, 236–244 (2012) 4. Ren, Y., Deng, H., Chen, R., Shen, Y., Lin, Y., Nan, C.W.: Effects of Li source on microstructure and ionic conductivity of Al-contained Li6.75 La3 Zr1.75 Ta0.25 O12 ceramics. J. European Ceramic Soc. 35(2), 561–572 (2015) 5. Kumazaki, S., et al.: High lithium ion conductive Li7 La3 Zr2 O12 by inclusion of both Al and Si. Electrochem. Commun. 13(5), 509–512 (2011) 6. Liu, Y., Sun, Q., Wang, D., Adair, K., Liang, J., Sun, X.: Development of the cold sintering process and its application in solid-state lithium batteries. J. Power Sources 393(March), 193–203 (2018) 7. Guo, H., et al.: Hydrothermal-assisted cold sintering process: a new guidance for lowtemperature ceramic sintering. ACS Appl. Mater. Interfaces. 8(32), 20909–20915 (2016) 8. Smith, B.L., et al.: Molecular mechanistic origin of the toughness of natural adhesives, fibers and composites. Nature 399(6738), 761–763 (1999) 9. Kruzhanov, V., Arnhold, V.: Energy consumption in powder metallurgical manufacturing. Powder Metall. 55(1), 14–21 (2013)
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10. Miloserdov, F.M., McKay, D., Muñoz, B.K., Samouei, H., MacGregor, S.A., Grushin, V.V.: Exceedingly Facile Ph-X Activation (X=Cl, Br, I) with Ruthenium(II): Arresting Kinetics, Autocatalysis, and Mechanisms. Angew. Chem. Int. Ed. 54(29), 8466–8470 (2015) 11. Renard, F., Bernard, D., Thibault, X., Boller, E.: Synchrotron 3D microtomography of halite aggregates during experimental pressure solution creep and evolution of the permeability. Geophys. Res. Lett. 31(7), 1–4 (2004) 12. Guo, H., Baker, A., Guo, J., Randall, C.A.: Cold sintering process: a novel technique for lowtemperature ceramic processing of ferroelectrics. J. Am. Ceram. Soc. 99(11), 3489–3507 (2016) 13. Guo, J., et al.: Cold sintering: a paradigm shift for processing and integration of ceramics. Angew. Chem. Int. Ed. 55(38), 11457–11461 (2016) 14. Bhagat, S., et al.: LiOH·H2 O as a novel dual activation catalyst for highly efficient and easy synthesis of 1, 3-diaryl-2-propenones by claisen-schmidt condensation under mild conditions. J. Mol. Catal. A: Chem. 244(1–2), 20–24 (2006) 15. Li, Y., et al.: Hybrid polymer/garnet electrolyte with a small interfacial resistance for lithiumion batteries. Angew. Chem. Int. Ed. 56(3), 753–756 (2017)
Early Stage of Bubble Dynamics via Electrical Explosion in Water Yuchen Cao1 , Ruoyu Han1(B) , Chen Li1 , Wei Yuan1 , and Rui Liu2 1 School of Physics, Beijing Institute of Technology, Beijing 100081, China
[email protected] 2 State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology,
Beijing 100081, China
Abstract. Underwater discharge is an indispensable method to simulate underwater explosions, and it has received more and more attention in recent years. In this paper, the electrical explosion (a kind of pulsed discharge) of copper/aluminum wires connected in parallel in water was used as the research object. Electrical parameter diagnostics in combination with high-speed shadow photography were adopted to study the spatiotemporal evolution behavior of explosion products (plasma) bubbles. Experiment results indicated that after the electric explosion (phase explosion) occurred, the shock wave and ionization process proceed successively. Then the high-impedance warm dense matter promotes the energy deposition and expansion of the explosion products. After the discharge finished, the ionized metallic gas continued glowing for a period of time. time. It was also observed that clusters of protrusions on the explosion product-water interface, which might be related to local explosions/discharges. The copper wire explosion product interface was smooth and explicit, while the aluminum wire had a flocculent boundary layer. In addition, the Richmyer-Meshkov instability caused by the shock wave between the metal double wires was not obvious. Keywords: High-voltage pulsed discharge · Underwater discharge · Electrical explosion of wire · Explosion and shock · Underwater explosion simulation
1 Introduction Electrical explosion of wires (electrical explosion of wires, referred to as wire explosion) is an important application of pulsed power technology. It refers to injecting a pulse current of a certain parameter range into a metal wire. Under the action of Joule heating, the metal wire undergoes a sharp phase change. The solid, liquid, gaseous and plasma states eventually develop into plasma channels, accompanied by physical phenomena such as optical radiation and shock waves. Electric explosions can occur in vacuum, gas, and liquid, with obvious differences in phenomena [1, 2]. As a special type of pulse discharge, conductor electric explosion can produce shock waves or sound waves in terms of mechanical effect. The energy conversion efficiency and controllability of discharge channel of electrical explosion are much higher than © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1067–1074, 2022. https://doi.org/10.1007/978-981-19-1870-4_112
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that of water-gap breakdown [3, 4]. Therefore, electric explosion using thin conductors (wire/foil) in water can effectively simulate the complex dynamic behavior of shock waves and explosion products under different charge layouts, which has high scientific research and application value and has received more and more attention in recent years [5]. Two problems need to be considered in the physical simulation of underwater explosion effect, one is the simulation of shock wave effect, the other is the simulation of bubble dynamic process. Domestic and foreign scholars have carried out a lot of research work on the shock wave of the wire explosion in the water, and initially established a self-consistent description of the magnetohydrodynamic (MHD) model [6]. There are also rich and detailed experimental data and empirical formulas [7, 8], and we already have a comprehensive understanding of the shock wave behavior of electric explosion as a whole. But little attention has been paid to the research of the electric explosion process after the arc-like plasma is established, and there are few special reports on the properties of explosion product (plasma bubble). Theocharous and Bland et al. used Xray radiography to clearly observe the details of the wire structure during current-driven explosions and shock waves [9]. It is clear that, similar to a water-gap discharge, plasma bubbles generated by wire electric explosion also have pulsation process, which can be verified by shock wave experiment in the anechoic pool [10]. For longer time scales (ms level or slower), the explosion product bubbles have fully evolved into a spherical shape, which can simulate the behavior of bubbles on different boundaries (free surfaces, rigid walls, etc.) [11, 12]. However, for electric explosions, the generation of shock waves depends on the acceleration process of the discharge channel-aqueous medium interface (piston). As the channel expands → plasma conductivity increases → energy deposition rate (electrical power) decreases → channel expansion slows down. The separation of the discharge channel and the shock wave is inevitable, and the sound velocity of the water medium is about 1500 m/s. Therefore, on the time and space scale, the shock wave process is faster than the bubble process: the shock wave enters the medium shortly after the electric explosion begins, and the bubble process gradually enters the pulsation process after the end of the discharge and plasma recombination. Therefore, the existing research on the bubble process in the early stage of electric explosion from the plasma stage to the bubble pulsation process is insufficient. The physical picture of the behavioral evolution from columnar plasma to spherical bubble is also unclear, so it is urgent to carry out research. Based on the literature [5] experimental platform and diagnostic methods, this pa-per uses parallel copper/aluminum wires in water as a load to carry out electrical explosion experiments. Using discharge parameter diagnosis combined with shadow method high-speed photography, the spatiotemporal evolution behavior of explosion products (plasma) bubbles after the start of discharge was studied. Focus on: 1) The spatiotemporal evolution process of explosive products within a few milliseconds from the start of the discharge to the end of the discharge; 2) The role of plasma in the dynamic behavior of the bubble; 3) The interaction between the discharge channels; The influence of wire size and material on the bubble process.
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2 Experimental Setup The experiment uses a DC high-voltage power supply to charge a 6 µF (rated voltage of 50 kV) pulse capacitor. The capacitor was connected to the electric explosion chamber by a coaxial high-voltage cable through a three-electrode spark switch. When the capacitor is charged to the required voltage, the spark switch is activated. The pulsed current is transmitted to the wire load through the coaxial high-voltage cable to drive an electric explosion. The schematic diagram of the experimental de-vice and the schematic diagram of the load device are shown in Fig. 1.
Fig. 1. Experimental Setup
In the experiment, the voltage and current signals were measured by PVM-5 Probe high voltage probe (bandwidth 80 MHz) and Pearson101 coil (bandwidth 4 MHz). The optical radiation signal is measured by the ET-2030 photoelectric probe, and the Phantom VEO high-speed camera (fps 260,000) is used to synchronize with the oscilloscope to record the spatial-temporal evolution image of the electric explosion process. The observation window opposite the camera is equipped with a 200 W LED light for taking back-lit images. The signal measured in the experiment is stored by a Tektronix DPO4104B oscilloscope. Among them, the load resistance voltage, electric power, and deposition energy are calculated by the following formula: UR = U − LW
dI dI − Ls dt dt
P = UR I
(1) (2)
W =
T Pdt
(3)
where U represents the voltage measured by the probe; L W represents the inductance of the wire; L S represents the intrinsic inductance of the equipment structure between the measuring point and the metal wire, and T represents the duration of each stage of the electric explosion.
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3 Experimental Results and Discussion The experiment studied the underwater electric explosion and initial stage of bubble dynamics process by using two-paralleled double copper wires through the space-time resolved images taken by the high-speed camera. The influence of different wire diameters (50, 100, 200 µm) on bubble dynamics was explored. In addition, using aluminum wire as an comparison, the differences in electric explosion process and bubble dynamics of metal wires of different materials are studied. The length of the fixed wire in the experiment is 4 cm, and the energy storage is 250 J. The camera frame rate is 260,000 fps, the exposure time is 0.84 µs, and the interval between each frame in the image is about 3.83 µs.
Fig. 2. Image of double copper wire electric explosion in water
The first frame in Fig. 2 shows the initial position of two copper wires with a diameter of 50 µm, about 6 mm apart. The camera’s field of vision basically covers the whole copper wire area. At the initial stage of explosion, both filaments underwent relatively uniform phase transformation process, and after breakdown, two relatively bright plasma columns were formed, as shown in #1. After that, the discharge channel gradually expands. During this process, many tiny bubbles can be seen, as shown in #3-#13. These tiny bubbles may come from the desorption of impurity gas in the tap water. As the discharge channel continues to expand, the plasma radiation is absorbed by the interface of high-density plasma channel and water. With the expansion of the two discharge channels, the two channels gradually overlapped about 0.39 ms after the electric explosion. It is worth noting that the density distribution changes during the interaction of the two discharge channels. Since this image is a backlit shadow map, the
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Fig. 3. Double-wire electric explosion images in water when the diameter of copper wire is 100 µm (a) and 200 µm (b)
density changes appear as changes in the light-transmitting area. In #103, we can see that there is a narrow strip of bright area in the center. After that, in #202, two symmetrical bright areas appear at a position about 3.7 mm away from the center, and a very fine bright area remains in the center. But in #251, the center bright area disappears. About 1.8 ms after the electric explosion, the two discharge channels have basically overlapped.
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When the discharge channel develops to about 2.4 ms, as in #629, columnar high-density areas only exist in a small area, and their boundaries are no longer smooth. However, in the later stage, large-scale bubbles can be observed in #814. After analyzing the evolution process of the double copper wire electric explosion discharge channel in water with a diameter of 50 µm„ the double copper wires with diameters of 100 µm and 200 µm were also selected to carry out underwater electric explosions. The effects of increased mass (diameter) on electric explosions and bub-ble dynamics were compared. At the initial stage of electric explosion, the first and second frames in Fig. 3(a) and (b) still formed bright columnar plasma channels accompanied by a small number of tiny bubbles. However, with the increase of wire diameter, a large number of tiny bubbles appear on the surface of the early discharge channel, which makes the discharge channel no longer appear as a sharp boundary. In #21 of Fig. 3(a), it can be observed that the bubbles attached to the surfaces of the two discharge channels have been connected to each other before the discharge channels overlap. In addition, the density distribution under the condition of small diameter does not appear in the underwater electric explosion of double copper wire with increasing diameter. After the two discharge channels expand and overlap, they appear as dim columnar channels, and large-scale bubbles can be observed after a period of time. However, it is noteworthy that the emergence time of large-scale bubbles seems to be delayed with the increase of wire diameter. According to the results of the high-speed camera, when the diameter of the copper wire is 50, 100, and 200 µm, the time to observe the large-scale bubbles for the first time is about 3.1, 3.9, and 6.8 ms, respectively. In the process of increasing the diameter of the metal wire, especially when the diameter of the copper wire is 300 µm, it can be observed that the expansion of the discharge channel is obviously uneven, as shown in #12-#30 in Fig. 3(b). At this time, the middle part of the discharge channel obviously has a faster expansion speed, which may have a certain impact on the development of bubble dynamics in the later stage. The experiment also investigates the underwater electric explosion and bubble dynamics of metal twin wires of different materials. Figure 4 shows an underwater electric explosion image of a double aluminum wire with a diameter of 200 µm. Since aluminum has a lower melting point than copper, its early phase transition process is faster. For the first frame of the copper wire image, the aluminum wire has formed a bright and wide plasma channel when the camera is triggered for about 3.84 µs. In #2, there are many tiny bubbles between the two discharge channels, and the brightness of the bubbles indicates that the internal breakdown and discharge have occurred. The phenomenon is similar to the above-mentioned electrical explosion of copper wires with a diameter of 50 µm, but is different from the electrical explosion of copper wires with large diameters (100, 200 µm). After that, the two discharge channels gradually expanded and interacted. It can be observed from #21 that the boundary of the aluminum wire discharge channel is not flat, but has many pointed spurs. In the 34th frame, it can be seen that the discharge channels have overlapped, and bubbles have begun to be generated inside. By the 48th frame, the bubbles have diffused into the entire camera field of view. In the 82nd frame, a density distribution phenomenon similar to the abovementioned electrical explosion of a copper wire with a diameter of 50 µm was observed. A low-density area appeared in the central part, and many periodic horizontal stripes
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Fig. 4. Image of double aluminum wire electric explosion in water
could be observed. As the discharge channel develops, the optical radiation is absorbed by the high-density plasma and water interface, and the channel brightness drops sharply. Compared with the electrical explosion of copper wires with different diameters mentioned above, the large-scale bubbles of aluminum wires appear later after the electrical explosion, and the time recorded by the camera is about 7.8 ms.
4 Conclusion This paper takes the electric explosion of copper wires and aluminum wires connected in parallel in water as the research object, using discharge parameter diagnosis combined with high-speed photography using shadow method. Experiments have found that as an electrical explosion occurs, the ionization process of the shock wave will proceed one after another. The generated plasma matter will promote the energy deposition and expansion in the explosion products. This paper compares the high-speed photography shadows of parallel copper wires and finds that as the diameter of the metal wire increases, the discharge channel will have a faster expansion speed. The appearance of large-scale bubbles will be delayed. The experiment also investigates the bubble dynamics of the parallel aluminum wire electric explosion. It is observed that the copper wire explosion product interface is smooth and clear, while the aluminum wire has a flocculent boundary layer.
References 1. Chace, W.G., Moore, H.K.: Exploding wires. Plenum Press, New York (1959) 2. Rososhek, A., et al.: Evolution of a shock wave generated by underwater electrical explosion of a single wire. Physics of Plasmas 26(4), 042302 (2019)
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3. Efimov, S., et al.: Addressing the efficiency of the energy transfer to the water flow by underwater electrical wire explosion. Journal of Applied Physics 106(7), 073308 (2009) 4. Han, R., et al.: Experiments on the characteristics of underwater electrical wire explosions for reservoir stimulation. Matter and Radiation at Extremes 5(4), 047201 (2020) 5. Han, R., et al.: Electrical explosion across gas–liquid interface: aerosol breakdown, shock waves, and cavity dynamics. Physics of Fluids 33(7), 077115 (2021) 6. Grinenko, A., et al.: Nanosecond time scale, high power electrical wire explosion in water. Physics of Plasmas 13(4), 042701 (2006) 7. Gurovich, V.Ts., et al.: Simplified model of underwater electrical discharge. Physical Review E 69(3), 036402 (2004) 8. Sarkisov, G.S., Rosenthal, S.E., Struve, K.W.: Thermodynamical calculation of metal heating in nanosecond exploding wire and foil experiments. Review of Scientific Instruments 78(4), 043505 (2007) 9. Theocharous, S.P., et al.: Use of synchrotron-based radiography to diagnose pulsed power driven wire explosion experiments. Review of Scientific Instruments 90(1), 013504 (2019) 10. Zhou, H.: Study on shock wave generation mechanism and energy conversion characteristics of underwater cu-wire micro-second explosion. Xi’an: Xi’an Jiaotong University (2017). (in Chinese) 11. Phan, T.H., Nguyen, V.T., Park, W.G.: Numerical study on strong nonlinear interactions between spark-generated underwater explosion bubbles and a free surface. International Journal of Heat and Mass Transfer 163, 120506 (2020) 12. Liang, W., et al.: Interaction of two approximately equal-size bubbles produced by sparks in a free field. Physics of Fluids 33, 067107 (2021)
The Evaluation of Electric Power Emergency Plan Exercise Based on EMD Method Yongchao Song1 , Zhenyu Li2(B) , Zhiwei Yu1 , Biyue Cao3 , and Yongxing Zhu1 1 China Southern Power Grid Co. Ltd., Guangzhou 510663, China 2 Electric Power Research Institute of China Southern Power Grid, Guangzhou 510663, China
[email protected] 3 Guangzhou Power Supply Bureau of Guangdong Power Grid Co. Ltd.,
Guangzhou 343009, China
Abstract. The existing power emergency deductions are all based on static scripts, and the deduction evaluation is also the assessment of the standardization of the deduction disposal process by emergency experts. Good or bad results of the evaluation cannot fundamentally improve and perfect the power emergency plan. Based on dynamic and irregular power emergency online deduction, this paper gives three key emergency deduction evaluation indicators under different time scales. The short-time-scale evaluation index based on the elasticity index can constantly reflect the power grid’s resilient handling ability to emergencies in the deduction. The medium and long-term scale evaluation index based on the dispatch coefficient reflects the rationality of emergency deduction dispatching. Finally, important static evaluation indexes are extracted for fitting and used as the long-term scale evaluation index for power emergency deduction. For the evaluation indicators of different time scales, this paper uses the empirical mode decomposition method to reduce the frequency and stabilize the dynamic data of the indicators. Through the power emergency deduction dynamic evaluation model in this paper, it can effectively improve the power emergency online deduction based on the dynamic irregular mechanism, so that the corresponding emergency plan has a higher execution efficiency in the event of an emergency. Finally, this paper uses a power emergency deduction evaluation example simulation in Guangzhou to verify the effectiveness of the method. Keywords: Electric power emergency plan · Drill evaluation · Empirical mode decomposition · Evaluation scale · Discreteness weight
1 Introduction Electric power emergency exercise, namely, electric power anti-accident exercise, is an important part of electric power emergency, and also is an important activity in the prevention stage [1–4]. Power emergency deduction plays an irreplaceable role in evaluation, on one hand, it evaluates the power grid’s ability of dealing with accidents [5–7], and shows the advanced technologies and ways for power grid to deal with power © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1075–1088, 2022. https://doi.org/10.1007/978-981-19-1870-4_113
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accidents, on the other hand, it also assesses the power grid employees’ ability to deal with accidents. Most of the existing emergency deduction is carried out under static script, and the cost of actual practice deduction is high, so the normalization of emergency deduction cannot be realized. Therefore, the deduction evaluation model designed for this kind of electric power emergency deduction cannot really put forward instructive improvement suggestions for the deduction itself. Online deduction has the advantages of low comprehensive cost, little influence on the actual operation of power grid and easy to realize normalization, so it has been widely used in power grid. In addition, the electric power emergency exercise evaluation is the most effective way to improve and optimize the dection, and reasonable deduction evaluation model can find shortcomings existing in the process of emergency response, at the same time, it also can test the effectiveness of the contingency execution plans, hence, the emergency exercise evaluation model attracts more attention in the field of electric power emergency. In this paper, from the global perspective, the multi-time scale electric power emergency line deducting dynamic evaluation model is built, through the analysis of the evaluation results, we can find and timely improve the shortcomings of the corresponding electric power emergency plan, so that the electric power emergency deals with actual emergencies with higher execution efficiency.
2 Power Emergency Assessment Index System Based on Different Time Scales System 2.1 Electric Power Emergency Demonstration At present, there are many evaluation items for electric power emergency deduction [8, 9], but most of them make the evaluation results redundant, and cann’t draw a summary conclusion. In addition, the existing evaluation indexes for electric power emergency deduction are only considered from the normative perspective of the implementation of the deduction plan, which makes the emergency deduction divorced from reality. The existing electric power emergency online deduction model mainly hve the following problems: (1) Static deduction script. Most of the existing electric power emergency deduction is based on static script implementation, the result of this practice will make the deduction divorced from the objective reality, while the occurrence and development of emergencies have dynamic characteristics, so the electric power emergency deduction model should be built on basis of dynamic scenario construction, to achieve irregular emergency deduction. (2) Whether the deduction scale can be normalized. The scale of the electric power emergency practical deduction is relatively large, and the simulation of the mass emergency deduction under emergencies will inevitably affect the stable operation of the power grid, so power emergency deduction is done every a several years, this condition inevitably reduces the proficiency personnel dealing with emergencies, affect the efficiency of emergency response.
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(3) The comprehensive cost of deduction is high. No matter the operation cost or organization cost, the existed electric power emergency deduction has no obvious economic advantage. The high cost of electric power emergency deduction causes decreasing of the proficiency personnel in actual response to electric power emergencies, hence, the value of deduction can not be truly reflected. (4) Coordination and linkage of deduction. In the electric power emergency deduction, the internal and external emergency departments of electric power enterprises should coordinate and coordinate. In electric power enterprise, the enterprise headquarters, the provincial company and all functional departments within the unit where the accident occurred carry out internal linkage, or linkage between the upper and lower departments. For external power enterprises, the emergency leading group should be responsible for coordinating with the management department, while other external units shall be coordinated by functional departments at various levels according to the nature of division of labor. In conclusion, the electric power emergency deduction should realize the random dynamic response, and the power emergency line deduction is the best way. However, undisciplined deduction is not mature enough, it is essential to continuous improve and develop the emergency exercise evaluation. Besides, the emergency assessment is suit to improve and develop the non-emergency inference rules, through the reasonable evaluation model, we can find the deficiency in power emergency deduction, and making the actual performance of irregular power emergency deduction can be really improved quickly. In this paper, three evaluation indexes of emergency inference with different time scales are constructed to evaluate the rule-based dynamic online emergency inference. 2.2 Short Time Scale Evaluation Indicators When the power system is faced to an emergency, it will be accompanied by changes in system performance [10, 11]. In the electric power emergency deduction, the supplydemand balance of the power network is often used as a short-time scale evaluation index to measure the deduction quality, mainly beause the system performance changes rapidly and the change cycle is short. Therefore, this paper selects the elasticity index of the power system as the evaluation index of short time scale. The definition and analysis of the elasticity index are shown in Fig. 1. In Fig. 1,PR (t) is the degree of supply-demand imbalance of the system at time t, as shown in Eq. (1). PR (t)= Pg (t) + (Pedch (t) − Pech (t))− Pl (t) P˜ w (t)+ P˜ p (t) + w∈W
p∈P
g∈G
e∈E
l∈D
(1) where
w∈W
P˜ w (t),
p∈P
P˜ p (t),
g∈G
Pg (t),
e∈E
(Pedch (t) − Pech (t)) are the total power genera-
tion of wind power, photovoltaic power, thermal power and battery of the system at time Pl (t) is the total system load at time t. The system is in equilibrium at t,respectively; l∈D
time t 0 , so PR (t) = 0, when the system is disturbed by an emergency, the imbalance
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Δ PR(t)
uncertain perturbation Initial state
Δ PR(t0)
Steady state destabilization Perturbation state
t0
t1
td
tr
Δ PR(tf) Recovery state
tf
t
Fig. 1. Change chart of supply and demand balance of power grid
degree of supply and demand decreases and reaches the lowest at time t d . If effective emergency measures are taken, the imbalance degree of supply and demand of the system gradually increases and reaches stability at time t f . Therefore, the elasticity index of the system is defined in this paper as follows: K(t) =
PR (t) − PR (td ) t ≥ t0 PR (t0 ) − PR (td )
(2)
2.3 Medium and Long Time Scale Evaluation Indicators Since the load of the power system changes in real time, but the scheduling capacity of the system can be considered unchanged in a short time [12–14]. Therefore, this paper selects the scheduling coefficient as the evaluation index of the medium and long time scale of emergency deduction. The dispatching resources of power grid include transmission lines between upper and lower layers, controllable loads, energy storage devices in micro grid, etc. The scheduling coefficient index A(t) is established to consider the rationality of emergency dispatching of power grid to deal with load changes caused by emergencies. From the perspective of the dispatcher, the micro-grid resources and load resources in the dispatching distribution network should be given priority to meet the power matching in response to load changes, and then the power on the transmission line between the upper and lower layers should be increased or decreased. Scheduling coefficient is a virtual coefficient which can be given by dispatchers according to the actual operation of the power grid. Taking the scheduling coefficient of energy storage devices in the power grid as an example, its calculation formula is listed as follows: ⎧ ⎪ ESi (t) = ESi max ⎨ 1, 1−λMGi,min (3) λMGi (t) = ES −ES , ESi min < ESi (t) < ESi max ⎪ ⎩ 0, i min i min ES = ES (t) i i min
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where ES i (t) is the power reserves at time t for energy storing device in microgrid i; ES imax and ES imin are the maximum and minimun reserves for for energy storing device in microgrid i; λMGi,min is the minimum scheduling coefficient allocated to microgrid i. The energy storage in the microgrid is preferentially used to deal with shock load when the energy storage capacity of the microgrid is sufficient. Controllable load scheduling coefficient λCL and scheduling coefficient of transmission line resources λtrans are often constant. In terms of a couple of coefficients, usually λMGi,min > λL > λtrans and it indicates that when dealing with shock load, the energy storage capacity in local power grid should be prioritized, followed by flexible load response, and finally the transmission power on the upper and lower power grid connection line is adjusted. Scheduling coefficient indexe of power emergency deduction are as follows: A(t)=
λMGi (t)PMGi (t)+λCL (t)PCL (t)+λtrans μtrans (t)Ptrans (t) Pcj (t)
(4)
where PMGi (t) is the scheduling efforts at time t, λMGi (t) is the correpondant scheduling coefficient; PCL (t) is the controllable scheduling efforts, λCL (t) is the controllable scheduling coefficient. In addition, the scheduling coefficient in load side is regrarded as constant value since the signed load scheduling protocol between grid company and customer; Ptrans (t) is the exchanged scheduling efforts between distribution network and the upper grid, λtrans is the echanged coefficient, μtrans (t) is uded to indicate the on-off state for call wire, the selected value 0 and 1 represent the open and close states, respectivitly; Pcj (t)is the changed shock load value at time t. 2.4 Long Time Scale Evaluation Indicators Power emergency exercise help the electric power enterprise, and emergency workers effectively reduce incidents influence to power grid, hence, the electric power enterprise need frequent emergency deduction, which requires emergency exercise comprehensive cost cannot be too high [15], and electric power emergency deduction of comprehensive cost including the cost deduction running cost and deduction. Meanwhile, the response loss in power emergency plans includes equipment loss of the system [16], consumption of emergency supplies and the number of personnel involved. Finally, contingency plans also hope the electric system can recover to the state before the emergencies once the emergency response is taken. Therefore, this paper gives the long time scale evaluation index of electric power emergency demonstration: the running costs deduction, deduction of the organization cost, personnel, equipment loss, emergency supplies consumption quantity and system recovery condition. In this paper, DEA method is used to synthesize these long time scale evaluation indexes of power emergency deduction into a static calculation index, as shown in the following equation: ρ=
1+
1 3
c1 +c2 csum loss + mmtotal
1− eloss etotal
+
puse ptotal
η
(5)
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Where ρ is the calculation index of static fitting in a long time scale; c1 , c2 are thee deductive operating cost and organizational cost, respectively; csum is the total budgeted cost; eloss is the amount of equipment loss; etotal is the total number of electrical equipment; mloss is the consumption of emergency supplies; mtotal is the total amount of emergency supplies; puse is the actual number of personnel mobilized for deduction; ptotal is the total number of participants; η is the recovery percentage of the system. In summary, the evaluation index system of electric power emergency plan is shown in Fig. 2. Power emergency assessment index
System Recovery Number of staff involved Consumption of emergency supplies Equipment loss quantity Drill organization cost Drill operation cost
Scheduling coefficient index
Elastic index
Medium Short and long time time scale scales
Long time scale
Fig. 2. Evaluation index system of electric power emergency drill
3 Standardization of Index Data Based on EMD 3.1 Introduction to EMD Methods Modal decomposition method (EMD) is a new adaptive signal time-frequency processing method creatively proposed by N.E. Huang and others [17, 18], which is considered as a major breakthrough in linear and steady-state spectrum analysis based on Fourier transform. It decomposes the signal according to the time scale characteristic of the data itself without setting any basis function in advance. This point is fundamentally different from Fourier decomposition and wavelet decomposition which are based on harmonic basis function and wavelet basis function. Because of such characteristics, EMD method can be applied to any type of signal decomposition in theory, so it has a very obvious advantage in processing non-stationary and nonlinear data. It is suitable for analyzing nonlinear and non-stationary signal sequences and has a high signal-to-noise ratio. In practical operation, the essence of signal decomposition by EMD method is to decompose signals or fluctuations of different scales step by step to generate a series of signal data sequences with different scales, and each data sequence is regarded as an intrinsic modal function component (IMF).
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3.2 Application of EMD Method In the plan of assessment of deduction, for short time scale evaluation index and evaluation index of long time scale, the index values can be considered as nonstationary discrete data of different time node, the EMD method can be used to deal with the two evaluation datas, and them can treated as the final deduction evaluation index data. As shown in Fig. 3, the dynamic data is processed by EMD, the obtained stable integration index value can be used as the input index value of the final electric power emergency drill evaluation.
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Evaluation value
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2
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5
6
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8
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Comprehensive expert evaluation
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Final integrated evaluation
Fig. 3. Comprehensive evaluation and integrated evaluation of experts
It is obvious that the dynamic index value floates up and down around the final integration guideline values, which can be treated as a kind of high frequency signal dynamic indexes; for short time scale index, it has the highest signal frequency, while the signal frequency is minimum for static indicators. The EMD method reduce the frequency for both short time scale and long time scale dynamic index, making they keep in the same frequency as the static index, without losing the itself index characteristics, by this way, it can standardize the evaluation index of different time scales. The specific steps are as follows: (1) Set the dynamic index evaluation value into signal sequence X(t), it is interpolated into the upper and lower envelope of the original sequence by spline interpolation function and the average envelope sequence is calculated m1 (t), the new signal sequence is obtained by subtracting the average envelope from the original sequence h1 (t): h1 (t) = X (t) − m1 (t)
(6)
(2) Repeat the above steps several times until the average envelope approaches 0 and the first IMF component is obtained c(t), this component is the highest frequency
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component in the dynamic index evaluation value, and the new sequence is obtained by removing this component: r1 (t) = X (t) − c1 (t)
(7)
(3) Repeat the above two steps for several times until the last sequence cannot be divided again. In this case, the remaining sequence is the dynamic indicator evaluation value after frequency reduction, as shown in the following formula: n R(t) = X (t) − c1 (t) (8) i=1
(4) Obtain the mean value of the R(t) series of each dynamic index R , which is the integrated value of dynamic index in the plan deduction. From the above analysis, it can be known that the above model can be used to reduce frequency of short time scale evaluation indexes and medium and long time scale evaluation indexes, while the above operation is not required for static long time scale evaluation indexes.
4 Evaluation Model of Electric Power Emergency Deduction 4.1 The Weight of Evaluation Index is Determined It is an important part to determine the index weight of electric power emergency plan deduction evaluation. The commonly used index weight method is entropy weight method and analytic hierarchy process. The entropy weight method has very strict requirements on the deductive evaluation data. However, in this paper, the entropy weight method is not applicable to the deductive evaluation method of electric power emergency plan because the evaluation indexes are all language evaluation scales and there are uncertain evaluation scales. However, AHP method requires evaluation experts to score the weights, and different experts may have different perceptions of the importance ranking of indicators, which would result in inevitable differences in the weight of indicators, so it is not suitable for the evaluation method in this paper [19]. Based on the above considerations, this paper adopts the adaptive weight model to assign weights to three evaluation indexes at different time scales, the detailed information can be seen in reference [20], and the weight of evaluation indexes at different time scales can be obtained as follows: (9) It should be noted that the power emergency deduction evaluation in this paper is different from the emergency plan decision-making in the literature, hence, there is no comparison between the same indicators, and the index similarity in this paper is defined as:
(10) d1 = 1 − Ri × 100%
Where d i is the similarity of different indicators, Ri is the integrated evaluation values of different indicators after EMD processing, the static fitting indicators for long time scales Ri is equal to ρ.
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4.2 Variable Weight Correction Coefficient In practical application, it is easy to find that some indicators are not invariable to the final evaluation results in the process of evaluation. Once the “quantitative change” of the index value exceeds a certain standard, it will have a “qualitative change” effect on the final evaluation results. If the index fell to a certain degree, even if the other parameter values are large in emergency exercise evaluation index, the final evaluation result should be a sharp variation, using weights fixed model is difficult to reflect the “quantitative change causes the qualitative change” phenomenon, this article introduced variable weight correction coefficient, to fix on the weight of evaluation index. In this paper, the state variable weight factor is introduced to adjust the constant weight. The specific calculation method is as follows: ai −max(ai ) t max(a i )−min(ai ) ai > max(ai ) (11) Si = e 1 others where S(ai ) is thevariable weight factor of each indicator; max(ai ), min(ai ) are the maximum and minimum values of reasonable indicators, respectively; t is punishment level, if t > 0, the larger t means the larger of punishment level. After introducing the state variable weight factor, the weight of each evaluation index is: (12)
4.3 Comprehensive Evaluation Model This paper adopts Topsis model to conduct comprehensive evaluation of electric power emergency deduction, and the specific methods are as follows: Firstly, the Euclidean distance between the power emergency inference evaluation index and the positive and negative ideal solution is calculated at different time scales. The Euclidean distance between the evaluation index of three different time scales and the positive ideal solution is: 3
+ dbest = Ri − Ri = ωi (Ri − 1)2 (13) i=1
Euclidean distance between each evaluation index and negative ideal solution is: 3
− dworst = Ri − Ri = ωi (Ri )2 (14) i=1
As the three evaluation indexes at different time scales in this paper are all high quality indexes, the positive ideal solution is 1.0 and the negative ideal solution is 0 in the above equations. Then the dynamic evaluation closeness degree of electric power
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emergency deduction is calculated C. The larger C means the better effect of electric power emergency deduction, otherwise, the worse of electric power emergency deduction effect. C=
dworst dbest + dworst
(15)
5 The Example Analysis One online emergency deduction held by the Southern Power Grid company is chosen to blackout the validation of our proposed evaluation method, this deduction is based on the dynamic non-rules electric power emergency deduction, the main reason of the incident is that a 220 kV substation fault cause chain transmission line fault, the inference time is 2 h, and all the time scales of evaluation index is shown below. Firstly, for the short-time scale evaluation index on basis of elasticity index, which is done with a time step of 2 min. The power grid elasticity index under emergencies can be obtained, as shown in Table 1. Table 1. Dynamic change value of short-time scale index based on elasticity index under emergencies Time
K(t)
Time
K(t)
Time
K(t)
Time
K(t)
Time
K(t)
Time
K(t)
2
1.000
22
0.831
42
0.331
62
0.008
82
0.166
102
0.640
4
1.000
24
0.778
44
0.268
64
0.004
84
0.220
104
0.683
6
1.000
26
0.727
46
0.217
66
0.009
86
0.256
106
0.729
8
1.000
28
0.675
48
0.168
68
0.011
88
0.301
108
0.773
10
0.998
30
0.643
50
0.133
70
0.013
90
0.366
110
0.808
12
0.998
32
0.552
52
0.083
72
0.001
92
0.410
112
0.851
14
0.989
34
0.510
54
0.031
74
0.013
94
0.461
114
0.896
16
0.989
36
0.461
56
0.000
76
0.020
96
0.506
116
0.945
18
0.936
38
0.403
58
0.000
78
0.065
98
0.551
118
1.000
20
0.884
40
0.361
60
0.000
80
0.130
100
0.596
120
0.999
By using Eq. (6) to (8), the frequency reduction is done for elastic index value, and the curve as shown in Fig. 4. Finally, the short-time scale evaluation index value derived from the elasticity index is R1 = 0.489.
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Integrated index value
Elastic index value
IMF1
IMF2
Fig. 4. Numerical EMD model frequency reduction of elasticity index
Then, for the medium and long time scale index derived from the scheduling coefficient, the time step is selected as 5 min, the scheduling coefficient index values under emergencies can be obtained, as shown in Table 2. Table 2. EMD decomposition of expert evaluation information Time
A(t)
Value
IMF1
IMF2
15
0.131
0.606
−0.333
−0.143
30
0.193
0.636
−0.31
−0.133
45
0.361
0.586
−0.158
−0.068
60
0.586
0.601
−0.0311
−0.017
75
0.731
0.588
0.1001
0.043
90
0.886
0.603
0.198
0.085
105
0.961
0.586
0.263
0.113
120
1
0.603
0.278
0.119
Similarly, Eq. (6) to (8) are used to reduce the frequency of scheduling coefficient value, and the corresponding curve is shown in Fig. 5. Finally, the evaluation index of medium and long time scale derived from scheduling coefficient can be obtained, which is R2 = 0.408.
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IMF1
IMF2
Fig. 5. IMF component comparison
Then, the static index values of this electric power emergency deduction are shown in the table below. In addition, Eq. (5) is used to calculate the size of static fitting index in a long time scale, as shown in Table 3. Table 3. EMD decomposition of expert evaluation information Index
Value
Standard
Value
c1
11
csum
30
c2
6
eloss
3
etotal
13
mloss
3
mtotal
16
puse
30
ptotal
60
η
95%
ρ
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By using the weight division model in Sects. 4.1 and 4.2, the index weight size in different time scales can be obtained as follows: ω = (ω1 , ω1 , ω3 ) = (0.4011, 0.3316, 0.2673) Finally, topsis model is used to calculate the Euclidean distance between each evaluation index and the positive ideal solution of this electric power emergency deduction: 120 120 dbest = ω1 ( R1 (t) − 1)2 + ω2 ( R2 (t) − 1)2 + ω2 (ρ − 1)2 t=2
= 0.5885
t=15
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The Euclidean distance between each evaluation index and the negative ideal solution is: dworst
120 120 2 = ω1 ( R1 (t)) + ω2 ( R2 (t))2 + ω2 (ρ)2 t=2
t=15
= 0.4215 Finally, the dynamic evaluation closeness degree of electric power emergency deduction is calculated. C=
dworst = 0.4173 dbest + dworst
lt can be seen that C < 0.5 means the distance between the evaluation index and the positive ideal solution is far away, and the electric power emergency deduction still needs to be improved. The evaluation index values of the three different time scales are all lower than 0.5, which indicate that the current irregular dynamic electric power emergency deduction model still needed to improved greatly. Traditional drill evaluation is based on static index system to construct the evaluation model, ignoring the dynamic uncertainty characteristics of plan itself. Comparing with general emergency plan drill evaluation, this paper constructs short time scale and long time scale indicators to fully demonstrate the change of plan implementation effect under different time scales. Meanwhile, the long time scale index in static mode makes the evaluation of emergency plan more reasonable.
6 Conclusion This paper puts forward an evaluation model of electric power emergency deduction based on different time scales, which can well reflect the actual effect of dynamic irregular emergency deduction by dividing the evaluation indexes under different time scales. Again by the empirical mode decomposition method has reduced the assessment indexes of different time scale frequency processing, so that they can be applied to a unified assessment model, the simulation example shows that the model well the actual application value, and also by an example at this stage of random dynamic power emergency exercise mode has much room to improve, By comparing the evaluation results, the irregular inference model is improved and perfected, so that the responding electric power emergency plan can give full play to its maximum response effect when dealing with actual emergencies.
References 1. Fu, Q., He, J., Lv, L., et al.: Optimal dispatch of multi microgrid emergency integrated resources considering DG operation characteristics and load importance. Electr. Measur. Instrum. 56 (2), 33–40 (2019)
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2. Wang, H., Xu, C., Zou, L., et al.: Comprehensive evaluation method of distribution network emergency reliability based on Improved Grey Clustering. Electr. Measur. Instrument. 54 (18), 22–28 (2017) 3. Xing, W., Tianyu, L., Xiuchen, J., et al.: Reactive power optimization of offshore wind farm based on improved genetic algorithm. Electr. Measur. Instrument. 57(4), 108–113 (2020) 4. Hui, H., Jianzhong, Z., Yongchuan, Z., et al.: Current situation analysis of electric power emergency drilling at home and abroad and Its Enlightenment to China. Power Syst. Protect. Control 38(24), 236–241 (2010) 5. Cheng, Z., Fang, X., Yu, G., et al.: Vulnerability evaluation of power emergency system. Power Syst. Protect. Control 38 (19), 51–54 (2010) 6. Chao, W., Shengchuan, Z., Yuanlong, L.: Construction and application of urban power grid emergency system based on auxiliary decision making of power grid accident handling. Power Syst. Protect. Control 39(8), 135–138 (2011) 7. Di, W., Dongjun, C., Xinyan, F., et al.: Application of dynamic comprehensive evaluation method in power grid emergency capability evaluation. Power Syst. Protect. Control 47(16), 101–106 (2019) 8. Xianghui, C., Junyong, L., Han, F.: Auxiliary decision analysis of power emergency command center startup based on accident situation level evaluation. Power Syst. Protect. Control 39(16), 46–52 (2011) 9. Shuting, Y., Ning, X., Saiyi, W.: Optimal configuration of mobile emergency power supply based on different user requirements. Power Syst. Protect. Control 45(5), 116–119 (2017) 10. Zhigang, L., He, L., Zhang, D., Zhao, B., Zhang, J., Zhao, H.: A Security level classification method for power systems under N-1 contingency. Energies 10(12), 2055 (2017). https://doi. org/10.3390/en10122055 11. El-Saadawi, M., Hatata, A.: A novel protection scheme for synchronous generator stator windings based on SVM. Protect. Contr. Modern Power Syst. 2(2), 257–268 (2017). https:// doi.org/10.1186/s41601-017-0057-x 12. Xiaoming, G., Junyong, L.: Research on power grid emergency resource dispatching scheme. Power Syst. Protect. Control 39(20), 11–16 (2011) 13. Hui, H., Hao, G., Xiang, X.: Research on power emergency material dispatching model based on node comprehensive weights. Power Syst. Protect. Control 47(8), 165–171 (2019) 14. Ming, G., Wenyun, L., Dejun, Y.: Quantitative analysis of the completeness of emergency plans for power grid dispatching automation system using fault tree theory. Power Syst. Protect. Control 38(17), 58–63 (2010) 15. Gao Zhaoli, X., Mingkai, D.S.: Optimal dispatch of multi-point fault emergency repair based on improved artificial bee colony algorithm. Power Syst. Protect. Control 47(13), 108–113 (2019) 16. Wang, Y., Hu, Y.: Hidden Markov based forced outage rate model considering human factors. Power Syst. Protect. Control 46(18), 108–113 (2018) 17. Zhaoyan, X., Gongxun, Y.: Application of empirical mode decomposition method in prediction of atmospheric time series. J. Autom. 34(1), 97–101 (2008) 18. Renjun, Z., Ruixian, C.: Group decision making method based on EMD to extract rating information of Zhangjia language. Syst. Eng. Theory Pract. 36(3), 744–749 (2016) 19. Xiaoyong, Z., Jianbing, C., Xianqiang, W.: Research on power grid emergency support capability index based on adaptive weight. Power Syst. Protect. Control 39(8), 108–111 (2011) 20. Li, L., Ding, P., Fang, X.: Index evaluation method of power emergency plan based on weight adaptive. Power Syst. Protect. Control 47(16), 28–33 (2019)
Stability Enhancement Strategy for Low-Voltage Multi-terminal DC System Using MPC Based Additional Control Ying Zhuang1 , Wei Pei1,2(B) , and Wei Deng1,2 1 Institute of Electrical Engineering of Chinese Academy of Sciences, Beijing 100190, China
{zhuangying,peiwei,dengwei}@mail.iee.ac.com 2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract. Aiming at the voltage stability problems such as DC voltage fluctuation, over-limit or even voltage drop, oscillation instability caused by uncertain fluctuation of distributed generation and DC loads connected to the low-voltage multi-terminal DC system, a model predictive control (MPC) based additional control strategy is proposed to improve the DC voltage stability of the system under master-slave control. Firstly, the typical topology and control strategy of low-voltage multi-terminal DC system under master-slave control are introduced. Then, a discrete predictive model of multi-terminal DC system based on small signal analysis is established. Furthermore, aiming at the minimizing DC voltage fluctuation as well as the additional regulation instructions, the proposed control strategy is capable of stabilizing the DC voltage fluctuation under multiple uncertain disturbances using minimum power output, improving the power quality of the system and ensuring the stable operation of the system. Finally, the accuracy and effectiveness of the proposed additional control strategy are verified through the example analysis and simulation of a three-terminal low-voltage DC system. Keywords: Low-voltage multi-terminal system · Model predictive control · Distributed generation · Additional control
1 Introduction Because of the rapid development of distributed renewable energy (DER) and the increasing demand for DC loads such as electric vehicles (EVs) and LEDs, the AC distribution network is now facing challenges such as diversified load demand and complex network structure [1, 2]. Compared with the AC distribution network, the low-voltage multiterminal (MTDC) DC system has advantages such as reducing energy conversion links for DC loads and DER access, diversified structures, flexible and controllable power flow, so it has been widely concerned and applied [3].
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1089–1099, 2022. https://doi.org/10.1007/978-981-19-1870-4_114
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The low-voltage MTDC system has the characteristics of high power electronic, weak damping and low inertia, its stability problem is therefore more prominent. In particular, it is more sensitive to the uncertain disturbance caused by DERs and DC loads connected to the system, which easily leads to voltage stability problems such as DC voltage fluctuation, flicker, even voltage drop and oscillation and further reduces the system power quality and seriously affects its safe operation [4]. Experts and scholars have done lots of research on how to improve the voltage stability of MTDC system under multiple uncertain disturbances [5, 6] designs the system feedback control strategy by using Lyapunov theory, and applies additional current control to each system converter station in order to stabilize voltage fluctuation. The above methods are mainly applicable to linear systems. For nonlinear systems, [7] proposes a control strategy based on nonlinear robust optimization for MTDC systems operating in island mode, which generates additional power regulation commands to solve voltage over-limit problem. However, the proposed algorithm depends highly on the communication system. In order to overcome the shortcomings of the above methods, a model predictive control (MPC) based additional control strategy under master-slave control is proposed in this paper. MPC, also known as rolling time-domain optimization control, is an intelligent optimization algorithm with excellent dynamic performance, which can perform optimized control on multiple variables and is applicable for complex nonlinear systems [8]. The MPC based additional control strategy takes the minimum system voltage fluctuation and minimum power output as optimization objectives. Based on a complete system discrete-time predictive model, using rolling optimization and feedback correction, it can stabilize the system voltage fluctuation and ensure the safe operation of the system. Finally, the case study simulated using MATLAB/Simulink platform verifies the effectiveness of the control strategy.
2 Low-Voltage Multi-terminal System 2.1 System Structure The structure diagram of a typical low-voltage MTDC system is shown in Fig. 1. Generally, the system includes multiple converter stations, DERs, energy storage system, DC bus and DC loads. The central controller collects the key parameters information such as voltage, current, power, etc. from local controllers. The MPC based optimization algorithm takes this information as input variables and calculates the optimal additional instruction. Then the central controller sends back the control signal and the additional instructions to the corresponding local controller in order to maintain the DC bus voltage stability and power balance in real-time.
Stability Enhancement Strategy for Low-Voltage ......... AC system n
AC system 3
Local controller
AC system 1
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......... VSCn
VSC3
VSC1
AC system 2
VSC2 DC bus
Local controller
DC/DC Converter
DC DC
Local controller
Photovoltaic
DC DC
Local controller
Energy storage system
DC DC
Local controller
Local controller
Load
Central controller
Fig. 1. Schematic diagram of low-voltage MTDC system
2.2 Typical Structure for VSC In this paper, the power grid at VSC AC-side is considered as a stiff grid, so the influence of PLL is ignored in the following analysis [9]. Taking the nth VSC in the system as an example, its classical equivalent circuit diagram is shown in Fig. 2:
usan usbn uscn
VSCn Rsn isan Lsn isbn iscn
uoan
+ uobn
uocn
udcn -
Fig. 2. VSC equivalent circuit
In Fig. 2, usan , usbn , uscn and isan , isbn , iscn respectively represent voltages and currents of phases A, B and C at the AC-side of VSCn ; L sn and Rsn respectively represent the filter inductance and equivalent resistance at the AC-side of VSCn ; uoan , uobn and uocn respectively represent voltages of phases A, B and C at the bridge-arm side of VSC, and, udcn represents the DC-side voltage of VSCn . 2.3 Control Strategy of Low Voltage MTDC System The low-voltage MTDC system studied in this paper adopts master-slave control mode. There is only one master station in the system, adopting constant DC voltage control, which is mainly responsible for maintaining the DC voltage stability and power balance
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of the system. Other VSCs, as the slave stations of the system, adopt constant power control. The principles of the constant voltage control and the constant power control are shown in Fig. 3 (a) and (b) respectively.
(a)
(b)
Fig. 3. Master-slave control (a) Constant voltage control (b) Constant power control
In Fig. 3, Prefn * , Qrefn * are the control commands for active power and reactive power, Pn , Qn are the actual values for active power and reactive power, Pn * and Qn * are the optimal additional instructions for active power and reactive power control calculated by the MPC based additional control algorithm in real-time.
3 Small-Signal Model for Low Voltage MTDC System 3.1 Small-Signal Modeling for VSCs Under Master-Slave Control According to Fig. 2, the AC-side small-signal model in dq coordinate frame for slave station VSCn is obtained, where represents the small change of variable near the steady-state operating point P0 (1): ⎧ d i sdn ⎪ = −uodn + ωLs isqn − Rs isdn ⎨ Ls dt ⎪ ⎩ L d isqn = −u − ωL i − R i s oqn s sdn s sqn dt
(1)
Under dq coordinate frame, the active power, reactive power and power transmitted to VSCn DC-side satisfy (2): ⎧ ⎨ Pn = 1.5usdn isdn (2) Q = −1.5u sdn isqn ⎩ n Pdcn = 1.5 uodn isdn + uoqn isqn The small-signal model of the external and internal control loop for VSCn can be obtained based on Fig. 3. The subscript “0” represents the steady-state value: ∗ isdn,ref = Kpp (Prefn − 1.5usdn,0 isdn ) + WPn (3) ∗ isqn,ref = KpQ (Qrefn + 1.5usdn,0 isqn ) + WQn
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⎧ Kip ∗ ⎪ − 1.5usdn,0 isdn ) (Prefn ⎨ WPn = s ⎪ ⎩ W = KiQ (Q∗ + 1.5u Qn sdn,0 isqn ) refn s uodn = Kpd (isdn − isdn,ref ) + Wdn + ωLs isqn uoqn = Kpq (isqn − isqn,ref ) + Wqn − ωLs isdn ⎧ ⎨ W = Kid (i − i dn sdn sdn,ref ) s ⎩ Wqn = KiQ (isqn − isqn,ref )
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(4)
(5)
(6)
The complete small-signal model for a slave station VSCn is obtained by integrating (1)–(6): d xns = Ans xns + Bns uns . (7) dt
T where the state variables are xns = udcn isdn isqn WPn WQn Wdn Wqn , control variables ∗ ∗ T are uns = Pn Qn , and Ans and Bns are the state matrix and input matrix respectively
The small-signal modeling process of the master station is similar to that of the slave station. The only difference is that for master station, it needs to maintain the stability of the bus voltage, so the voltage reference value is always constant. Thus, there is no control variables. 3.2 Small Signal Modeling for DC Network In this paper, the model of DC network is considered asπ-type. The energy storage system and photovoltaic unit that connected to the DC bus through the DC/DC converter will exhibit constant power load characteristics during the closed-loop control [12]. Therefore, they are modelled as constant power loads. The small-signal model of the DC network is (8): d xg = Ag xg + Bg ug + Bd ud dt
(8)
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where the state variables are xg = [udc i1 i2 · · · in ]T , the DC network control
variables are ug = [udc1 udc2 · · · udcn ]T , the disturbance variable is ud = Peq , where Peq is the equivalent aggregate load power consisted of DER and DC loads, which is the main disturbance variable in the system. 3.3 Completed Small Signal Model of Low-Voltage MTDC System Combining the above small-signal models, the complete predictive model of a lowvoltage n-terminal DC system under master-slave mode can be further obtained: ⎧ ⎨ d x = A x + B 1u + B 2u s s s ds (9) dt ⎩ y = Cs x
T where, the state variables are x = x1 x2 · · · xn xg , the con
T trol variables are u = 01×2 u2 · · · un 01×(n+1) , the disturbance vari
T ables are uds = 01×n ud 01×n and the output variables are y =
T udc1 udc2 · · · udcn udc 01×n .
4 MPC Based Additional Control Strategy MPC is a discrete predictive model based finite-time domain closed-loop optimal control algorithm. It is mainly divided into three steps: predictive model, rolling optimization and feedback correction. The MPC control principle is shown in Fig. 4.
now Past
Future
Reference Prediction Horizon
Control Horizon
Nc
Np
Fig. 4. Control principle of MPC optimization algorithm
4.1 The Design of MPC Based Additional Control Strategy Predictive Model. Based on the continuous small-signal model (9), the system predictive model is established in (10): x(k + 1) = Ad x(k) + Bd1 u(k) + Bd2 uds(k) (10) y(k) = Cd x(k) + y(k − 1)
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T
T where Ad = eAsTs , Bd1 = 0 s eAsτ d τ · Bs1 , Bd2 = 0 s eAsτ d τ · Bs2 . In this paper, the Euler equation is used to discretize the complete small-signal model, and the sampling time step for model (11) is set to T s . represents increment of discrete variables within the adjacent times, namely, x(k) = x(k)−x(k−1), u(k) = u(k)−u(k−1), uds (k) = uds (k)−uds (k−1). Objective Function and Constraints. The objective function of MPC optimization algorithm mainly considers two factors: firstly, to ensure the stability of DC voltage and avoid DC voltage oscillation divergence under uncertain disturbance; secondly, ensuring the minimum additional control instruction at each time, which means to stabilize the system DC voltage with the minimum output power to improve the economy of control strategy. Thus, the objective function of the system is established: min J (x(k), u(k)) = Y(k + 1|k) − R(k + 1)2 + wu u(k)2
u(k)
(11)
where, Y(k + 1|k) = [y(k + 1|k) y(k + 2|k) · · · y(k + Np|k) ] represents the output matrix for next Np time calculated at time k. R(k + 1|k) = [R(k + 1|k) R(k + 2|k) · · · R(k + Np|k) ] is the output reference matrix, and u(k + 1|k) = [u(k + 1|k) u(k + 2|k) · · · u(k + Nc|k) ] is the optimal control increment matrix for next Nc time calculated at time k. Wu is the weight matrix, which is used to evaluate the performance and control effect of the MPC optimization algorithm. Reasonable constraints can guarantee the additional control effect. For the output matrix Y (k), the output matrix fluctuation shall be within 90%–110% of the rated voltage, and the fluctuation range of optimal control and control increment matrix shall be within ± 20% and ± 5% of the rated power respectively. The corresponding constraints is as follows: ⎧ ⎪ ⎨ umin (k) ≤ u(k) ≤ umax (k) umin (k) ≤ u(k) ≤ umax (k) (12) ⎪ ⎩ ymin (k) ≤ y(k) ≤ ymax (k) MPC Optimization Algorithm. The objective function and constraints mentioned above are complex and its optimal solution cannot be obtained directly. Therefore, the objective optimization function (11) needs to be rewritten into a quadratic programming problem. The specific expression is as follows: ⎧ ⎪ min J = min 0.5uT Hu + f T u ⎪ ⎪ u u ⎨ T (13) S + w H = 2 · S u u u ⎪ ⎪ ⎪ ⎩ f = 2 · STu · −R(k + 1) + Sx x(k) + Sy y(k) + Sd uds(k) where, Su , Sx , Sy and Sd represent the coefficient matrices of input variables, state variables, output variables and disturbance variables in a complete prediction cycle, including the prediction results of NP times.
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When the disturbance is detected, the MPC optimization algorithm in the central controller starts to work, calculates the optimal additional power instruction matrix. In order to reduce the prediction error, only the first value in the sequence is sent to the local controller. Then the additional control instructions are superimposed with the previous power control command. With the continuous measurement and update of state and input variables, the rolling optimization and feedback correction is achieved in order to minimize the control error and better suppress the voltage fluctuation.
5 Simulation Verification The MPC based additional control strategy is simulated and verified by Matlab/Simulink. The quadratic programming problem of MPC optimization algorithm can be quickly solved using the quadprog function in MATLAB optimization tool library. An example of a three-terminal low-voltage MTDC system is analyzed. VSC 1 is the master station, with a rated voltage of 800 V. VSC 2 and VSC 3 are slave stations with rated power of 50 KW and 30 kW respectively. The rated power of the equivalent aggregate load at the DC bus is 30 kW. Detailed parameters are shown in Table 1. Table 1. The parameters of three-terminal low-voltage DC system Parameter
Value
Parameter
Value
Parameter
Value
Rs
1.5 m
Rdc2
0.2
K ip
500
Ls
2 mH
C2
0.5 mF
K pq
1
C
0.6 mF
L dc3
0.75 mH
K iq
100
L dc1
0.5 mH
Rdc3
0.15
K pd
10
Rdc1
0.1
C3
0.5 mF
K id
500
C1
1 mF
K iQ
100
Ts
0.02 s
L dc2
1 mH
K pp
10
1. Short time random power disturbance A short time random power disturbance which lasts 28 s is applied to the DC bus as shown in Fig. 5. The voltage changes at VSC DC-side under the same disturbance for the system with traditional master-slave control strategy and the system with MPC based additional control strategy are shown in Fig. 6 (a) and (b).
Figure 6 shows that the DC voltage at each terminal of system using the traditional master-slave control strategy fluctuates severely, resulting in the voltage over-limit problem, which badly affects the system stable operation. After adopting the optimal control strategy proposed in this paper, the DC voltage fluctuation at each terminal is significantly suppressed, the voltage over-limit problem is effectively solved, and the voltage fluctuation is well maintained within the range of 90%–110%.
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Fig. 5. Load power at DC bus
Fig. 6. Output voltage at VSC DC-side (a) Under traditional master-slave control strategy (b) Under MPC based additional control
2. Load power jump The system is now works under rated conditions (Pdc1 = 50 kW, Pdc2 = 30 kW, Pload = 30 kW). At t = 2 s, the load power at the DC bus suddenly increases to 100 kW (Pdc1 = 50 kW, Pdc2 = 30 kW, Pload = 100 kW). The DC bus voltage changes for the systems adopting the traditional master-slave control and the MPC based additional control strategy are shown in Fig. 7 (a) and (b).
Fig. 7. DC bus voltage (a) Under traditional master-slave control strategy (b) Under MPC based additional control
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Figure 7 shows that when the load power at DC bus changes sharply, the DC bus voltage using the traditional master-slave control system will fluctuate greatly and oscillate lose its stability after about 0.1 s. However, when the system adopts the MPC based additional control strategy, the DC bus voltage first endures a short fluctuation due to power jump at 2 s. At this time, the additional control strategy starts to work. Therefore, by adjusting the power output according to the additional control instruction, the DC bus voltage quickly reach the steady state value again after about 0.1 s which proves that the MPC based additional control strategy is capable of quickly suppress the voltage fluctuation during sudden load power jump which improves the stability of DC voltage and ensure the system safe operation.
6 Conclusion Aiming at how to improve the operation stability of low-voltage MTDC systems under multiple uncertain disturbances due to DERs access and DC load, an additional control strategy based on MPC is proposed for low-voltage MTDC systems under masterslave control. The proposed optimal control strategy can suppress the voltage fluctuation caused by the uncertain disturbances, solve the DC bus voltage oscillation instability due to the sudden change of DC bus load power, and effectively improve the system voltage stability performance and power quality. The optimal control strategy proposed in this paper has good control performance and fast dynamic response, which can meet the requirements of engineering application. Acknowledgment. This work was supported in part by the China National Science and Technology Support Program under Grant (XDA21050000) and the National Natural Science Foundation of China under Grant (U1134204) and the Key Research and Development Program of Jiangsu Province under Grant (BE2020081-3).
References 1. Li, X.L., et al.: Research review on operation and control of DC distribution networks. High Volt. Eng. 45(10), 3039–3049 (2019). (in Chinese) 2. Yu, X.W., et al.: Power management for DC microgrid enabled by solid-state transformer. IEEE Trans. Smart Grid 5(2), 954–965 (2014) 3. Liang, Y.L., et al.: Application and development prospect of new generation of LVDC supply and utilization system in “new infrastructure”. Proc. CSEE 41(1), 13–24+394 (2021) (in Chinese) 4. Wang, C.S., et al.: DC bus voltage fluctuation classification and restraint methods review for DC microgrid. Proc. CSEE 37(1), 84–98 (2017). (in Chinese) 5. Wei, D., Wei, P., Luyang, L.: Active stabilization control of multi-terminal AC/DC hybrid system based on flexible low-voltage DC power distribution. Energies 27(3), 1–20 (2018) 6. Pierre, M., Babak, N., Serge, P.A.: Stabilizer for a multi-loads DC-power network. IEEE Trans. Smart Grid 2(5), 1–8 (2011) 7. Hosseinzadeh, M., Salmasi, F.R.: Robust optimal power management system for a hybrid AC/DC micro-grid. IEEE Trans. Sust. Energy 6(3), 675–687 (2015)
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8. Xiao, H., Pei, W., Kong, L.: Multi-time scale coordinated optimal dispatch of microgrid based on model predictive control. Autom. Elect. Power Syst. 40(18), 7–14+55 (2016) (in Chinese) 9. Li, L.Y., et al.: Active damping strategy for improving VSC and line interaction instability in DC distribution network. High Volt. Eng. 45(09), 2884–2894 (2019). (in Chinese)
Research on Fast Location Method of Fault Line Based on Intelligent Power Emergency Plan Mode Zhenyu Li1(B) , Biyue Cao2 , Jianping Gong3 , Yongchao Song3 , Zhiwei Yu3 , and Yongxing Zhu3 1 Electric Power Research Institute of China Southern Power Grid, Guangzhou 510663, China
[email protected]
2 Guangzhou Power Supply Bureau of Guangdong Power Grid Co. Ltd.,
Guangzhou 343009, China 3 China Southern Power Grid Co. Ltd., Guangzhou 510663, China
Abstract. In response to the transmission line fault caused by the emergency accident, the existing electric power emergency plan reflects the obvious shortage of accuracy and timeliness. The reason is that the location of the fault line can not be accurately and timely located at the initial stage of response, which makes the emergency response lag. The intelligent power emergency plan is based on the reasoning mechanism of the accident, and realizes the dynamic emergency response without script under the condition of considering the state operation of the system. Therefore, under the intelligent emergency plan, the key of dynamic emergency response is to accurately and timely locate the fault transmission line location. In this paper, by combining the simplified APTS model of power network with the improved genetic algorithm, a fast fault line location method under the intelligent emergency plan is constructed. This method has the advantages of fast location speed and high location accuracy, and has very good performance Strong practicability. Finally, this paper takes a small distribution network in Guangzhou as an example to verify its rationality and feasibility. Keywords: Intelligent · Power emergency plan · Fault line location · APTS · Genetic algorithm · Pareto optimal
1 Introduction Looking back at the emergence and development of new crown pneumonia in 2020, in the face of emergencies, the timeliness of emergency response by the government and enterprises related to national economic safety has become an important content of public safety construction in modern society. Electricity, as the basic industry of the national economy, plays an important role in supporting and guaranteeing economic and social development and people’s lives. No matter what emergencies occur, electric power
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1100–1114, 2022. https://doi.org/10.1007/978-981-19-1870-4_115
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safety is the primary concern in public safety. This makes electric power emergency plan is particularly important in power safety [1–6]. However, with the continuous expansion of the scale of the power grid, higher requirements are put forward for the practicability, simplicity, and operability of the plan. The existing emergency plans for electric power companies continue to expose their bloated and complicated shortcomings. In addition, most of the existing power emergency plans are based on static scripts, ignoring the objective fact that the occurrence and development of power accidents are random, which makes the accuracy and timeliness of the response of the plan not well guaranteed. In the power system, the transmission line is extremely vulnerable to emergencies. The complexity of the structure of the distribution network and the addition of distributed power sources make it more susceptible to emergencies, while ensuring the reliability and safety of power supply is also the normal operation of power transmission lines. Therefore, in view of the insufficient accuracy and timeliness of the existing power emergency plans in responding to this type of power disaster accidents, this article proposes a rapid fault line location model under the smart power emergency plan, which has solved the problem of the lack of accuracy and timeliness of the existing emergency plan in dealing with the line failure type emergency. With the continuous development of modern power grid big data technology and the gradual popularization and application of FTU (Feeder Terminal Unit), it is possible to collect switch information in real time. The power emergency plan can be dynamically adjusted according to the development trend of the situation, thereby construct an intelligent electric emergency plan with dynamic perception capabilities. Based on the above analysis, this paper constructs a faulty line rapid location model under the smart emergency plan. The model can quickly and accurately find the faulty line location due to emergencies, Thereby, improving the timeliness and accuracy of the intelligent power emergency plan to locate the respond objects. The method in this article can quickly locate the location of the faulty line without removing the DG when an emergency event causes a line failure, so that it can get a fast power emergency response and restore the normal operation of the line.
2 APTS Simplified Model 2.1 Basic Principles of the Model It can be known from experience that the distribution network in the power system has structural characteristics such as closed-loop design, open-loop operation, and radial network structure. When considering how the power emergency plan accurately locates the faulty line in the case of a distributed power network, regarding the distribution network containing distributed power sources as a directed graph, the network connectivity graph with degree 1 and power points (including distributed power sources) as vertices in the directed graph is defined as an active tree. The remaining network path after removing the active tree is called a passive tree. Using the active and passive tree simplification (APTS) model, the entire power distribution system containing distributed power. The network is divided into a directed network consisting of an active tree and multiple passive branches. The active tree in the power system contains all power sources (including
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distributed power sources). When the distribution network causes a line failure due to an emergency, each power source will generate a fault current. Therefore, there must be fault current in the active tree network. However, the passive tree itself has no power source. Even if there is a fault current flowing through it, it is provided by the active tree. When a passive tree is fault-free, no fault current flows through all nodes of the entire passive tree chain. Therefore, it can be removed during the positioning process, so that it is not considered. This can shorten the dimension of the solution in the algorithm to a certain extent and improve the calculation efficiency. 2.2 APTS Simplify the Implementation Process The IEEE33 node diagram is used to explain the APTS simplified model theory. As shown in Fig. 1, assuming that the line L30 fails due to an emergency, the smart power emergency plan needs to find the location of the faulty line at the fastest speed. Under normal circumstances, it is necessary to judge the operating status of 33 lines in the system one by one to find out the actual faulty line location. If the system is divided into active tree and passive tree, the fault current flows through the passive trees L6 to L17. Therefore, it can be directly eliminated and ignored, thereby reducing the calculation dimension of the algorithm from 33 to 21, which greatly reduces the amount of calculation of the model. S18
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Based on the above analysis, combined with the knowledge of network graph theory, this paper presents the simplified model flow chart of APTS for fault line location under the smart plan, as shown in Fig. 2.
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Start Parameters initial: the number of DG is n, ENdnode is m, Power Tree And Passive branch is cleared, making i=j=a=b=1 DG (I) stored in Power tree, deep search from DG (I) to main transformer Whether node j is main transformer power supply node?
Yes No Whether node j exists in Power tree?
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If i 0 and λs < 0, then θ = 90◦ , and the pressure deflects the spontaneous magnetization to a direction perpendicular to it, as shown in Fig. 2(c); when σ < 0 and λs > 0, then θ = 90◦ , and the pressure deflects the spontaneous magnetization to a direction perpendicular to it, as shown in Fig. 2(d).
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The phenomenological theory of the magnetomechanical effect is described as above. In the process of the technical magnetization, the change of the ferromagnetic material magnetization after applying stress depends not only on the material properties and the stress, but also on the shape of the ferromagnetic material, external magnetic fields and so on. At present, due to no perfect theoretical model, the magnetomechanical effect of the ferromagnetic materials is usually studied by experiments.
3 Experiment of the Steel Specimen The plate-shaped material with a thickness of 20 mm was derusted and made a steel specimen, the length, width and height of which were 70 mm, 40 mm and 18 mm respectively. The stress application equipment adopts CMT5105 microcomputer controlled electronic stress system. The magnetic field measurement equipment adopts 7100-MMS magnetic field automatic measurement system with range of 0–50000 nT, resolution of 1 nT and sampling frequency of 5 Hz. The geomagnetic environment of the test is 34500 nT horizontal component and 35500 nT vertical component. During the test, the magnetic sensor is 15 mm away from the steel specimen.
stress loading device terminal 15mm
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One of the difficulties in the whole test is to minimize the interference magnetic field of the test environment, which mainly includes the geomagnetic daily variation, the stray field when the electronic stress system works, and the field variation caused by specimen deformation, etc. In order to accurately assess the test results, the environmental interference magnetic field in the test is analyzed, the amplitude of which is about 100 nT. In the test, the change of z-axis magnetic induction intensity is recorded to describe the magnetomechanical effect. Assuming that the diving depth is 200 m, the corresponding pressure is about 2 Mpa, and the actual stress area of the specimen in the test is 2800 mm2 , so the corresponding applied force in the test shall not exceed 6 kN. The applied force amplitude of the test starts from 1 kN to 6 kN, and then the force is unloaded step by step. When the force increases to 6 kN, the deformation of the steel specimen is only 0.18 mm, and the measurement error of the ambient magnetic field is acceptable.
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The test results are shown in Fig. 4 and Fig. 5. It can be seen that the force loading and unloading curves almost coincide, which indicates that the magnetomechanical effect is reversible. When the pressure is less than 2 kN, the magnetic field changes linearly with the applied force. With the increase of the force, the magnetic field decreases gradually.
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When the force is 2 kN, it is about 1000 nT different from the original magnetic field. When the force is greater than 2 kN, the variation range of the magnetic field changes within environmental magnetic field, and it can be considered that the force does not change the magnetization of the steel specimen. According to the pressure theory, the diving depth corresponding to 2 kN is about 70 m. The magnetic field variation caused by the pressure changes linearly with the increase of the water depth within 70 m. When the depth exceeds 70 m, the magnetic field will not change with the increase of the pressure, and the magnetic field value at 70 m depth will be maintained. It is worth pointing out that due to the variety of steel types of submarines and limited by the test condition, the above conclusion maybe needs more experimental verification.
4 Experiment of the Simple Submarine Model The oxygen tank (diameter 21.5 cm, total length 140.0 cm, ferromagnetic material HP295) is regarded as the simple submarine model for the test. In the experiment, the magnetic field of nine typical measurement points at 1.6 times the depth below the model is measured during the simple submarine model pressure releasing. As shown in Fig. 6, the same magnetic field measurement system as the previous experiment is adopted, which is composed of ten fluxgate sensors, and one sensor is used for environmental magnetic field monitoring and nine are used to measure the magnetic field of the simple submarine model varying with the pressure. S
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As shown in Fig. 7, firstly, pressurize the submarine simple model to 8.5 Mpa in the test, place it on the non-magnetic track in the north-south direction, and keep it perpendicular to the track. The head of the submarine simple model points to the geomagnetic
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Fig. 7. The submarine simple model experiment picture
west (i.e. transverse magnetization); secondly, depressurize the submarine simple model step by step, and measure a group of the magnetic field values with an interval of 0.5 Mpa until it is completely unloaded. In order to compare and analyze the variation rule of the measured magnetic field with the stress of the submarine simple model under different magnetization states, the submarine simple model is also placed on the EastWest non-magnetic track and kept perpendicular to the track. The head of the submarine simple model points to geomagnetic north (i.e. longitudinal magnetization state), and the above pressurization, depressurization and magnetic field measurement processes are carried out. Figure 8, 9 and 10 shows the variation curves of the three components of the magnetic field with pressure under transverse magnetization. #1
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Fig. 10. The variation curves of Bz magnetic field with the pressure at the typical measurement points
The test results show that the magnetic field of the submarine simple model changes obviously with the pressure. Taking 8.5 Mpa as the reference point, the maximum variation amplitude of the magnetic field is about 1800 nT. From the change trend, the curves also have an obvious inflection point and show the characteristics of the piecewise linear change. From the variation value, when the pressure decreases from 8.5 Mpa to 0.1 Mpa, the X component magnetic field near the bow under the submarine keel decreases by 175 nT, the Y component magnetic field decreases by 662 nT and the Z component magnetic field increases by 1389 nT. At the center of the simple submarine model, the X component decreases by 524 nT, the Y component increases by 1800 nT and the Z component increases by 651 nT. Near the tail of the simple submarine model, the X
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component decreases by 297 nT, the Y component increases by 200 nT and the Z component decreases by 1307 nT. It can be seen that the variation trend and amplitude of the magnetic field at different positions are both different. The magnetic field variation caused by the change of the stress in longitudinal magnetization state is significantly greater than that in transverse magnetization state.
5 Conclusion In order to obtain the variation rule of the magnetic field around the submarine with the stress of the hull steel in the process of floating and diving, the measurement tests of the magnetomechanical effect of the typical steel specimen and the simple submarine model are designed, and the corresponding experimental platform is built. Through the actual measurement, the preliminary rules of the variation of the magnetic field of the steel specimen and the simple submarine model with the stress are obtained. Firstly, the stress can cause the significant variation of the magnetic field of the steel specimen and the simple submarine model, and the amplitude at the typical measurement points can reach thousands of nates; secondly, the magnetic field has an obvious inflection point, and generally presents piecewise linear change. The test methods and relevant research conclusions in this paper can lay a certain foundation for the further study of the variation rule of the magnetic field around the submarine with the stress of the hull steel in the process of floating and diving, so as to realize the real-time control of the magnetic silencing state of submarines.
References 1. Schulze, P.C., Chan, P.D., Funasaki, P.E., et al.: Case study of a navy magnetic silencing facility. In: Tri International Conference on Ports (2010) 2. Zhou, J., Chen, J., Shan, Z.: Analysis of submarine magnetic signature using 2D Fourier transform. In: 2017 IEEE International Magnetics Conference (INTERMAG). IEEE (2017) 3. Wang, M., Liang, X., Wang, H., et al.: The magnetic array study of effective detection and location for submarine pipeline. In: The 29th International Ocean and Polar Engineering Conference, ISOPE 2019 4. Keller, J.: Industry to develop magnetic anomaly detector (MAD)-equipped UAV for antisubmarine warfare (ASW). Military Aerosp. Electron. 30(8), 30 (2019) 5. Wang, F., Song, Y., Dong, L., et al.: Magnetic anomalies of submarine pipeline based on theoretical calculation and actual measurement. IEEE Trans. Magn. 55(4), 1–10 (2019) 6. Yang, R., Xiong, X., Guo, X., et al.: research on model and simulation of airborne magnetic anomaly detection sweep width based on magnetic dipole model. Acta Armamentarii 35(09), 1458–1465 (2014). (in Chinese) 7. Zhang Y, Mao S. modeling analysis and application of submarine space magnetic field. Ship Electron. Eng. 38(283), 141–144 (2018). (in Chinese) 8. Zhou, J., Chen, J., Shan, Z., et al.: Submarine magnetic field modeling using boundary elements method for aeromagnetic anomaly detection. Electron. Opt. Control 15(2), 82–84 (2018). (in Chinese) 9. Wu, F., Wu, M., Lin, Y.: Frequency domain analysis of the submarine magnetic field signal based on welch method. J. Naval Aeronaut. Astronaut. Univ. 35(03), 29–33 (2020). (in Chinese)
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10. Liu, S., He, B., Zhao, W., et al.: Least squares support vector machine for solving reflection model of submarine s internal and external magnetic field. J. Nat. Univ. Defense Technol. 42(06), 80–84 (2020). (in Chinese) 11. Huang, Y.: Study on force magnetic effect of ferromagnetic specimen based on metal magnetic memory. Nanchang Hangkong University, Nanchang (2016).(in Chinese) 12. Ma, S.: Study on magnetomechanical effect in weak magnetic field. Harbin Institute of Technology, Haerbin (2012). (in Chinese) 13. Liu, Y.: Study on weak magnetic field detection of austenitic stainless steel based on magnetomechanical effect. Nanchang Hangkong University, Nanchang (2019).(in Chinese) 14. Ren, J., Chen, C., Liu, C., et al.: Experimental research on microcosmic mechanism of stressmagnetic effect for magnetic memory testing. J. Aeronaut. Mater. 05, 41–44 (2008). (in Chinese) 15. Xi, X.: Numerical simulation and experimental study on stress magnetization and reversal effect of ferromagnetic components. Nanchang Hangkong University, Nanchang (2016).(in Chinese) 16. Li, Y., Wang, B., Zhang, B.: Study on Piezomagnetic effect of Galfenol alloy and force sensor. Trans. China Electrotechn. Soc. 34(17), 87–93 (2019). (in Chinese) 17. Lin, L.: Study on evolution law of residual magnetic field of steel under tensile action. Zhejiang University, Zhejiang (2015).(in Chinese) 18. Chen, H., Zhao, W., Liu, S., et al.: The effect of external stresses on magnetic field of a submarine and magnetic detection in the air. Marine Electric Electron. Eng. 37(266), 85–89 (2017). (in Chinese) 19. Gao, J., Zhang, S., Zhou, G.: Effect of external stresses on magnetic field of a submarine. Marine Electric Electron. Eng. 36(09), 77–80 (2016). (in Chinese) 20. Liu, Y., Zhou, G., Wu, K.: Effect of a certain type of low magnetic steel on the magnetic field of surrounding space before and after welding. Technol. Innovat. Appl. 035, 17–21 (2018). (in Chinese) 21. Yin, S., Xiao, C., Zhou, G.: Experimental study on relationship between tension stress and magnetic field for a type of ship steel. J. Naval Univ. Eng. 23(03), 104–107 (2011). (in Chinese) 22. Dai, D., Qian, K.: Ferromagnetism, 2nd edn. Science Press, Beijing (2021).(in Chinese)
Structural Optimization Design of Rotor Magnet of Large High Temperature Superconducting Condenser Zhengjun Shi1,2 , Song Meng1,2 , and Wenxu Liu3(B) 1 Guangdong Power Grid Co., Ltd., Guangzhou 510699, China 2 Power Superconducting Joint Laboratory of China Southern Power Grid Corporation,
Dongguan 100124, China 3 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China
[email protected]
Abstract. High temperature superconducting (HTS) condenser has the advantages of small volume, light weight, and high efficiency, and is widely used to adjust the reactive power balance in the power grid. To meet the requirements of the air gap magnetic field, the rotor in a large Rotor-Type HTS condenser usually needs to be stacked with multiple Racetrack-Type magnets. To reduce the influence of magnetic field on magnets operation and improve the critical current of magnets, four stacked methods of racetrack magnets with different structures are proposed and simulated through finite element software. Through the comparison of simulation results, the optimal stacked structure is obtained, and the structural parameters are optimized. The results show that the maximum vertical component of the magnetic field generated by the magnets in structure (c) is the smallest, which has a greater critical current and safety margin of the magnets and can also increase the air gap magnetic field above the magnets. Keywords: High temperature superconducting condenser · Rotor magnet · Structural optimization · Electromagnetic analysis
1 Introduction With the development of DC transmission technology, UHV DC transmission lines are widely used in the construction of power grids. At the same time, new energy power generation technologies such as wind power generation and photovoltaic power generation are also in a stage of vigorous development, and more and more new energy power is connected to the power grid [1]. However, the connection of Large-Scale DC power and new energy power will lead to a serious shortage of dynamic reactive power in the receiving power grid, resulting in voltage fluctuation and affecting power quality [2–4]. High temperature superconducting (HTS) condenser has the advantages of small size, light weight, high efficiency, etc., which can effectively adjust the reactive power imbalance in the power grid and enhance the power quality [5]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1302–1310, 2022. https://doi.org/10.1007/978-981-19-1870-4_137
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To meet the requirements of the air gap magnetic field for Large-Scale HTS condensers, the rotor is usually stacked by multiple Racetrack-Type superconducting magnets. Concurrently, the magnets will operate in a larger magnetic field environment, causing the reduction of the critical current of magnets. By optimizing the design of the stacked magnets, the critical current can be increased, which is vital to improve the safety margin and reduce the manufacturing cost [6, 7]. In this paper, four types of stacked magnets of the large HTS condenser are proposed. By establishing the finite element simulation models, the magnetic fields generated by these four types of stacked magnets are simulated and calculated respectively, and the magnetic induction intensity distribution on the magnet and the air gap magnetic field distribution at 10 mm above the magnets are obtained. After comparing the results, the optimal stacked structure is obtained, and the structural parameters are optimized.
2 Design of Magnets Structure 2.1 Introduction of Basic Principles According to the Biot-Savart law, the magnetic induction micro-element generated by − → the current micro-element Id l at point O at any point P in space is: − → → Id l × − r − → d B = μ0 4π r 3
(1)
where μ0 is the permeability in vacuum and r is the distance between point O and point P. The magnetic induction intensity generated by the magnet with volume V at any point in the space is: ¨ B = μ0
− → → Id l × − r 3 4π r V
(2)
The above formula shows that the magnetic field generated by the magnet is closely related to the geometric structure of the magnets. The 2-G HTS tapes have obvious anisotropy, which critical current is related to the magnetic field environment. The critical current of the tapes is related not only to the magnitude of the magnetic field but also to the angle θ between them. The dependence of the critical current of tapes on the magnetic field is [8–10]: 2 Jc = Jc0 (1 + k 2 B// + |B⊥ |2 /B0 )−α (3) where Jc0 is the critical current of the tapes without an external magnetic field, B// is the magnetic field component parallel to the tapes, B⊥ is the magnetic field component perpendicular to the tapes. B0 , k and α are material-dependent constants, and k < 1. That is, the critical current of HTS tapes is mainly affected by the magnetic field perpendicular to the tapes.
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2.2 Model of Magnets Structure In this paper, four types of stacked magnets of the HTS condenser rotor are proposed. The rotor magnets of each type are stacked by five Racetrack-Type HTS Double-Pancake coils. The specific stractures of stacked magnets are shown in Fig. 1.
Fig. 1. Structure diagram of magnets with different stacked methods. (1) 3D schematic diagram of magnets of stacked magnets (a). (2) Section diagram of stacked magnets (a), (b), (c), and (d).
R0 , R1 are the minimum inner radius and the maximum outer radius of the semicircle part of the stacked magnets respectively. d is the thickness difference between two adjacent Double-Pancake coils, expressed as d. And the thickness difference d of any two adjacent Double-Pancake coils in the same structure is equal.
3 Finite Element Model of Electromagnetic Simulation 3.1 Establishment of Finite Element Model of Electromagnetic Simulation Using the finite element simulation software, the 3D finite element models of the above four types of stacked magnets with different structures are established respectively. The superconducting tapes used in the magnets in this paper are YBCO tape produced by the Shanghai Superconducting Company. The specific parameters of YBCO superconducting tape are shown in Table 1. Using finite element simulation software, 3D finite element models of stacked magnets proposed were established respectively. In this paper, the superconducting tapes used in the magnets are YBCO tape produced by the Shanghai Superconducting Company. The specific parameters of the YBCO superconducting tape are shown in Table 1.
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Table 1. Paramters of YBCO superconducting tape Parameters
Value
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6
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0.2
Critical current without external field Ic (A)
267
In the magnets design process, the amount of superconducting tapes used by superconducting magnets with different structures is equal to ensure the economy of optimization results. To facilitate the comparison of the simulation results, the thickness difference Δd in magnets with different stacked magnets is equal. At the same time, the thickness difference Δd of two adjacent Double-Pancake coils in the same structure magnets are also equal. The specific model parameters of the stacked magnets are shown in Table 2. Table 2. Model parameters of stacked magnets with different structures Structure (a)
Stracture (b)
Minimum inner radius R0 (mm)
100
100
80
90
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160
140
150
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10
Operation current I op (A)
Stracture (c)
Stracture (d)
160
To ensure the safe operation of the magnets and prevent the magnets from quenching during operation, a degree of the safety margin should be reserved in the design of the magnets. Safety margin α: α=
Iop Ic
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where Iop is the operation current of the magnets and Ic is the critical current of the superconducting tapes without an external magnetic field. In this paper, the safety margin is 0.6. 3.2 Post-processing of Finite Element Simulation Results Because the critical current of the 2-G HTS tapes is mainly affected by the vertical magnetic field component acting on the tapes, while the parallel magnetic field component has little effect on the superconducting tapes. Therefore, in the Post-Processing of simulation results, the magnetic induction intensity vector should be decomposed into two components, which are parallel and perpendicular to the superconducting tapes respectively. To simplify the models, in the subsequent processing, we only consider the
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influence of the magnetic field component perpendicular to the tapes, while ignoring the influence of the parallel magnetic field component. For Racetrack-Type magnets, the magnetic induction intensity component modulus B⊥ which is perpendicular to the magnet tapes can be divided into two parts: the magnetic induction intensity component modules Bl⊥ in the straight area and the magnetic induction intensity component modules BS⊥ in the semicircular area. Figure 2 shows the finite element model of the stacked magnets (a). In the coordinate system shown in Fig. 2, the Bl⊥ is: (5) Bl⊥ = By and the Bs⊥ is: Bs⊥
(x − a) (y − b) = Bx + By (x − a)2 + (y − b)2 (x − a)2 + (y − b)2
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where, Bx is the component of magnetic induction intensity in the X-direction, By is the component of magnetic induction intensity in the Y-direction. x is the distance from the center of the semicircular area to the X-axis, and y is the distance from the center of the semicircular area to the Y-axis. Bx and By can be obtained directly by finite element software. Through the above formula, the vertical component modulus of the magnetic induction intensity at any point of the Racetrack-Type stacked magnets can be obtained, and obtain the maximum vertical component modulus of the magnetic induction intensity B⊥max of the magnets.
Fig. 2. Schematic diagram of finite element model of stacked magnets (a)
4 Simulation Results and Analysis Combined with the Post-Processing method to calculate and analyze the simulation results, the distribution of the vertical component modulus of the magnetic induction intensity of the stacked magnets can be obtained respectively, and B⊥max of magnets can be calculated. The critical current of the superconducting tapes with the maximum B⊥max is the critical current of the whole magnets.
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Fig. 3. Modulus of the vertical component of magnetic induction intensity of stacked structure (a)
Figure 3 shows the distribution of the vertical component modulus B⊥ of the magnetic induction intensity of the stacked magnets (a). It indicates that the maximum value of the vertical component modules of magnetic induction intensity in magnets (a) is located in the middle of the upper and lower surfaces of the magnets semicircle area. The maximum value B⊥max can reach 2.24 T, the minimum value B⊥min is 3.18e-8 T, and the minimum value is close to 0 T. The value of B⊥max of the stacked magnets (a), (b), (c), and (d) is shown in Table 3.
Fig. 4. Modulus of the vertical component of magnetic induction intensity on section
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To better observe the B⊥ inside the stacked magnets, Fig. 4 shows the B⊥ on the sections of stacked magnets (a), (b), (c), and (d). Since the stacked magnets are designed for the HTS condenser rotor, to ensure the normal operation of the condenser, the air gap magnetic field above the stacked magnets should be large enough to meet operating requirements. In this paper, the maximum value of magnetic induction intensity modules and magnetic flux in the rectangular region (320 mm × 700 mm) which is located directly above the Z-axis of the magnets are calculated. The calculation results are shown in Table 3. Table 3. Comparison of calculation results of magnets with different structures Magnets
Maximum vertical component modulus of the magnetic induction intensity B⊥max (T)
Air gap magnetic induction Bδ (T)
Magnetic flux F(Wb)
a
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1.87
0.290
b
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1.95
0.313
c
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2.04
0.308
d
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2.01
0.313
Comparing these four types of stacked magnets, it can be seen that the B⊥max of stacked magnets (c) is the smallest, that is, the stacked magnets (c) have the largest critical current. When the same operating current is connected, the stacked magnets (c) have a greater safety margin. At the same time, the air gap magnetic induction intensity Bδ above the stacked magnets (c) is also the largest of these four types of magnets, which can better meet the requirements of the air gap magnetic field of the condenser. The modulus of the magnetic field generated by the stacked magnets (c) is related to the thickness difference Δd. By scanning the thickness difference Δd, the optimal
Fig. 5. Relationship between maximum vertical component modulus of magnetic induction intensity of magnets B⊥max and thickness difference Δd
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structure parameters of the stacked magnets (c) can be obtained. Figure 5 shows the relationship curve between the B⊥max of the stacked magnets (c) and the thickness difference d. It can be seen that the larger the thickness difference d, the smaller the B⊥max .
5 Conclusion The rotor magnet of the large HTS condenser is usually composed of multiple RacetrackType Double-Pancake coil stacks. In this paper, four types of stacked magnets with different structures are proposed, and the corresponding finite element simulation models are established. The maximum vertical component modules of the magnetic induction intensity B⊥max and the maximum magnetic induction intensity modules Bδ above the magnet are obtained respectively. Through comparison, it is found that the B⊥max in the stacked magnets (c) is the smallest, that is, the critical current of the stacked magnets (c) is the largest, and the magnets have a greater safety margin. It also indicates that the stacked magnets (c) have a larger air gap magnetic field, which is easier to meet the needs of the air gap magnetic field of the condenser. By analyzing the thickness difference d of parameters in the stacked magnets (c), it is found that the B⊥max of the magnet is relevant to the different thickness d. The value of the B⊥max of the stacked magnets decreases with the increase of the different thickness d. The research results of this paper provide a certain theoretical basis and data support for the design of the rotor magnets of the large HTS condenser. Acknowledgement. Thanks for the support of China Southern Power Grid science and technology project (GDKJXM20172779).
References 1. Kalsi, S.S., Weeber, K., Takesue, H., Lewis, C., Neumueller, H., Blaugher, R. D.: Development status of rotating machines employing superconducting field windings. Proc. IEEE 92(10), 1688–1704 (2004) 2. Li, Y., Hou, Y., Ma, M.: Analysis of electromagnetic torque under dynamic response of large-scale condenser. Large Electr. Mach. Hydraul. Turb. 04, 1–5 (2021). (in Chinese) 3. Chu, L.: Multiple measures to promote the high-quality development of offshore wind power in China. Electromech. Bus. Daily, 2021-07-19(A07). (in Chinese) 4. Xu, C.: Research on the Influence of Synchronous Condenser on Voltage Stability of HVDC Transmission System. Harbin University of Science and Technology (2020). (in Chinese) 5. Yang, Y.: Analysis of Influence of Large-capacity Condensers on Reactive Power Voltage of Provincial Power Grid. Zhengzhou University (2020). (in Chinese) 6. Yao, G.: Optimal Design of High Temperature Superconducting Magnetic Energy Storage Magnet. Southeast University (2019). (in Chinese) 7. Liu, J.: Geometric Structure Design and Optimization of Hing Temperature Superconducting Magnetic. Nanjing University of Posts and Telecommunications (2018). (in Chinese) 8. Kim, Y.B., Hempstead, C.F., Strnad, A.R.: Magnetizationand critical supercurrents. Phys. Rev. 129(2), 528–535 (1963)
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9. Irie, F., Yamafuji, K.: Theory of flux motion in non-ideal type-II superconductors. J. Phys. Soc. Japan 23(2), 255–268 (1967) 10. Song, W.: AC Loss Investigation of High Temperature Superconducting Assembled Conductor and Superconducting Coil. Beijing Jiantong University (2019). (in Chinese)
Electromagnetic Performance of the Nickel-Iron Alloy in High Frequency Shengming Zhou1 , Jian Zhao1 , Hua Zhou1 , Boping Su2 , and Jianqiang Wei2(B) 1 State Key Laboratory of Nickel and Cobalt Resources Comprehensive Utilization,
Jinchuan Group Co., Ltd., Jinchang 737100, China 2 Lanzhou University, Lanzhou 730000, China [email protected]
Abstract. This study proposes ball-milled nickel-iron alloy powder for highfrequency electromagnetic compatibility. It indicates that the complex permeability of the flake nickel-iron alloy powder/epoxy resin composite is enhanced efficiently. The magnetic resonance is attributed to the nature resonance. The electromagnetic parameters of the flake metal micro-powder/epoxy composite material with a volume concentration of 10% are simulated with HFSS. It indicates strong electromagnetic noise suppression performance with a lighter surface density. The simulation results show that when the thickness is 1.2 mm for 10 GHz, the electromagnetic noise suppression reached 99% nickel-iron alloy powder/epoxy resin composite can be attractive candidates for thinner microwave coating in high frequency. Keywords: Ni-Fe alloy · High frequency electromagnetic property · Electromagnetic performance
1 Introduction With the development of modern electronic communication and the electronics industry, a large number of electronic devices were introduced to improve quality of life, but at the same time it also made the electromagnetic environment of space become more complex, and the impact of electromagnetic wave radiation on the environment is also increasing. Due to breakthroughs in key material [1–3], the large-scale use of highfrequency switching power supplies and other devices [4–7] results in the electronic components highly integrated, and the electromagnetic interference is becoming more and more serious; with the use electromagnetic wave communication equipment, the problem of electromagnetic information leakage has also attracted a lot of attention. At present, the requirements for electromagnetic materials in the application field are thin, light, wide and strong. The so-called thin refers to the thickness to be thin; light refers to light weight; wide refers to the electromagnetic wave absorption frequency bandwidth; strong refers to the mechanical strength of material. The magnetic filler is granular, the mechanical properties of the electromagnetic material are mainly determined by the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1311–1316, 2022. https://doi.org/10.1007/978-981-19-1870-4_138
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adhesive of the composite. The density of iron-based metal magnetic powder is about 7.8 g/cm3 , which is much greater than the density of adhesives such as paraffin wax and epoxy resin (about 1 g/cm3 ), so the volume ratio and density of the magnetic filler are the key factors of areal density of electromagnetic materials. The thickness of the electromagnetic coating shows a greater impact on the absorbing performance, and also determines the areal density of the electromagnetic coating. For a single-layer absorbing coating, if the emitted wave and reflected wave of the absorbing coating have the same amplitude and opposite phase, the two waves will be perfectly cancelled out. This situation is called perfect matching. If only the phase is opposite, the amplitudes of the outgoing wave and the reflected wave are not equal, and there will be cancellation, which is called imperfect matching. To make the phase of the emitted wave and the reflected wave opposite, the thickness of the electromagnetic coating should follow the formula [1]: t=
nλ0 nλ = √ 4 4 |μr εr |
(1)
where λ0 and λ are the wavelength in vacuum and material, μr and εr are the complex permeability and permittivity of the material relative to vacuum, respectively. absorbing materials with higher μr and εr can be beneficial to reducing the thickness of the coating. The permittivity can be tuned conveniently by using the conductive polymer, however, an unlimited increase in the dielectric constant will cause impedance mismatch and increase the reflectivity of electromagnetic waves. Therefore, larger permeability in high-frequency and moderate permittivity are needed at the same time for a thin and good electromagnetic coating. Traditional magnetic materials are limited by the Snoek limit [8], and the permeability in high-frequency is difficult to improve. The flake-like magnetic powder can greatly enahnce the high-frequency electromagnetic properties of the material for introducing planar anisotropy. Nickel-iron alloy is an excellent soft magnetic material, and there have been a lot of research on its high-frequency electromagnetic characteristics, however, there is little research on its anti-electromagnetic interference characteristics [9–11]. In this paper, plane anisotropy was introduced into the atomized nickel-iron alloy material by the method of ball milling, and high-frequency electromagnetic characteristics were studied. With mixing the micro-powder particles and resin thin film materials can be prepared by blade casting. At present, this method is widely used in anti-electromagnetic interference and wave-absorbing materials, however its thickness and volume ratio may affect the high-frequency characteristics. In order to further study its high-frequency anti-electromagnetic interference performance, simulation was carried out with HFSS according to the requirements of IEC 62333-2-2015 [12–17], and its high-frequency anti-electromagnetic interference characteristics were obtained.
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2 Experimental In this study, the raw material is 350 mesh water atomization Fe50 Ni50 alloy prepared, and the miller is Lianrui 01-HD grinder. The balls are 3 mm stainless steel, and the ball/powder ratio is 30:1. The process control agent is alcohol, and the speed is 300 r/min for 4 h. The sample and epoxy resin are mixed uniformly at a certain volume concentration, and then the sample is pressed to form a cylindrical toroidal specimen in the mold with an inner diameter of 3.04 mm, outer diameter of 7.00 mm, and thickness of 1.5–3 mm. The measurement of high-frequency electromagnetic characteristics adopts the Sparameter method, using an Agilent E8363B vector network analyzer (VNA) with an APC7 coaxial line. Then, complex permeability and permittivity in the range of 0.1–18 GHz were determined with the S parameter, according to Nicolson’s transmission/reflection model.
3 Results and Discussion 3.1 Morphology and Crystal Structure of Milled Nickel-Iron Powder Figures 1a and b show the SEM images of Fe50 Ni50 alloy powder before and after grinding, respectively. The original powder is of irregularly shape, with the particle size distribution of about 20 µm. After ball milling, the size of the micro-powder is about 60 µm, the thickness is reduced to less than 1 µm, and formed a good flake structure. Figure 2 is the X-ray diffraction pattern of the alloy powder before and after grinding. The results show both are the structure of fcc FeNi alloy phase, which reveal the grinding did not change the crystal structure of the powder.
Fig. 1. SEM images of the raw powder (a) and the ball-milled powder (b)
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Fig. 2. XRD patterns of the raw powder (a) and the milled powder (b)
Fig. 3. Frequency dependence of complex permeability spectra of the raw powder/resin composite (a) and the ball-milled powder/resin composite (b)
3.2 Electromagnetic Characteristics of Milled Nickel-Iron Powder Figure 3 shows the microwave permeability spectrum of Fe50 Ni50 alloy powder/epoxy composite before and after grinding with a volume fraction of 10%. The spectrum of the raw material powder presents a relaxation type magnetic spectrum without obvious resonance. The initial permeability is 1.7. The real part of the permeability gradually decreases to about 1.1 with the increase of frequency, and the imaginary part of the permeability is almost a constant, about 0.2. After grinding, the initial permeability of the Fe50 Ni50 alloy powder/epoxy composite is 2.7. The real part of the permeability gradually decreases to around 1.0 with the increase of frequency. The resonance frequency is around 7 GHz. At high frequency, the main magnetic loss mechanism is domain wall resonance, eddy current loss and natural resonance. The frequency of domain wall resonance is relatively low, usually not considered in the microwave frequency band. After
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grinding, the thickness of the micro-powder is less than 1 µm, which is lower than the skin depth, the resonance is attributed to natural resonance [1, 11]. 3.3 Anti-electromagnetic Interference Characteristics of Milled Nickel-Iron Powder/Epoxy Composite In order to further study the anti-electromagnetic interference characteristics of the flake nickel-iron powder/epoxy composite, the electromagnetic noise suppression performance in the 0.1–10 GHz frequency band was simulated in HFSS according to the IEC 62333-2-2015.The permittivity and permeability of the milled micro-powder/epoxy composite with a volume ratio of 10% are imported into HFSS for simulation [12, 13]. According to IEC 62333-2-2015, the electromagnetic noise suppression performance is calculated in accordance with the following Eq. (2): Ploss = −10lg(
P1 ) P2
(2)
The calculated electromagnetic noise suppression performance results are shown in Fig. 4. The attenuation is enhanced with the increase of the thickness. Most of the electromagnetic waves are lost at 10 GHz at 1.2 mm.
Fig. 4. Noise suppression Ploss with varying thickness
4 Conclusions In this study, the electromagnetic parameters of the flake metal micro-powder/epoxy composite material with a volume concentration of 10% are simulated with HFSS. It indicates strong electromagnetic noise suppression performance with a lighter surface density. The simulation results show that when the thickness is 1.2 mm for 10 GHz, the electromagnetic noise suppression reached 99%.
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References 1. Wei, J., Zhang, Z., Wang, B., Wang, T., Li, F.: Microwave reflection characteristics of surfacemodified Fe50Ni50 fine particle composites. J. Appl. Phys. 108(12), 123908 (2010). https:// doi.org/10.1063/1.3524546 2. Li, Z.W., Yang, Z.H., Kong, L.B.: Ultrabroad bandwidth of single-layer electromagnetic attenuation composites with flaky fillers. Appl. Phys. Lett. 96(9), 092507 (2010). https://doi. org/10.1063/1.3340460 3. Li, Z.W., Lin, G.Q., Wu, Y.P., Kong, L.B.: High-Frequency Properties and Attenuation Characteristics of WBa Hexaferrite Composites with Doping of Various Oxides. IEEE Trans. Magnet. 45(2), 670–677 (2009). https://doi.org/10.1109/TMAG.2008.2007757 4. Yan, F., Xiaofeng, Z., Guo’an, D., et al.: Research on coordination strategy for an offshore wind power DC chopper device and protection. Power Syst. Protect. Control, 49(15), 178 (2021) 5. Liang, S., Xiaofei, Y., Liguo, S., Yichen, L., Chuang, L.: Frequent deviation-free control for microgrid multi-inverters based on improving a virtual synchronous generator. Power Syst. Protect. Control 49(11), 18–27 (2021) 6. Wu, X., Li, Z., Liu, F., et al.: Analysis of the emergency control strategy of system frequency considering system frequency distribution characteristics under large power disturbance. Power Syst. Protect. Control 49(3):104–114 (2021) 7. Yuan, C., Chu, H., Chen, Y., et al.: Single phase ground fault location method for high voltage cables considering the metal sheath coupling. Power Syst. Protect. Control 49(2), 115–120 (2021) 8. Xue, D.S., Li, F.S., et al.: Bianisotropy picture of higher permeability at higher frequencies. Chin. Phys. Lett. 25, 4120–4123 (2008) 9. Wei, J.Q., et al.: Effect of shape of Fe3Al particles on their microwave permeability and absorption properties. J. Magn. Magn. Mater. 323, 2608–2612 (2011) 10. Zhou, J., et al.: 2D materials: large-area and high-quality 2D transition metal telluride (Adv. Mater. 3/2017). Adv. Mater. 29, 3 (2017). https://doi.org/10.1002/adma.201770015 11. Wei, J.Q., Zhang, Z.Q., Han, R., Wang, T., Li, F.S. Microwave reflection properties of planar anisotropy Fe50Ni50 powder/paraffin composites. Chinese Phys. B 21 (3), 037601 (2012) 12. IEC 62333-2-2015 Noise suppression sheet for digital devices and equipment: measuring method 13. Nam, B., Lee, J., Choa, Y.H., Oh, S.T., Lee, S.K., Kim, K.H.: Evaluation of tailored magnetic composite films for near-field electromagnetic noise suppression. Res. Chem. Intermed. 36, 827–834 (2010) 14. Marrocco, G.: The art of UHF RFID antenna design: impedance-matching and size-reduction techniques. Anten. Propag. Magaz. IEEE 50(1), 66–79 (2008) 15. Li, H., Haibo, Y., Di, Z., Yujuan, N., Feng, X., Hong, W.: Improved dielectric and magnetic properties of 1–3-type Ni0.5Zn0.5Fe2O4/epoxy composites for high-frequency applications. J. Phys. D: Appl. Phys. 46 (12), 125003 (2013) 16. Li, J., et al.: Flexible organic tribotronic transistor memory for a visible and wearable touch monitoring system. Adv. Mater. 47(2), 479–492 (2015) 17. Zhou, Y., Zhou, W., Li, R., Mu, Y., Qing, Y.: Enhanced antioxidation and electromagnetic properties of Co-coated flaky carbonyl iron particles prepared by electroless plating. J. Alloys Compd. 637, 10–15 (2015)
Study on the Influence of Skin Effect on AC Loss of YBCO Tape Ying Xu1(B) , Hong Xie2 , Zhining Lv2 , Zhenzi Wang2 , Zhe Wang2 , Bangzhu Wang1 , and Shaotao Dai1 1 Beijing Jiaotong University, Beijing 100044, China
[email protected] 2 Shenzhen Power Supply Co., Ltd., Shenzhen 518048, China
Abstract. Since the discovery of high-temperature superconductivity, superconducting technology has gradually been widely used in electric power. Hightemperature superconductors have losses under an alternating magnetic field, which affects the economy and safety, and stability of superconducting equipment, and limits the development of high-temperature superconducting (HTS) devices to a certain extent. Therefore, it is of great importance to do research on the AC loss of HTS tapes. The YBCO tape is a multi-layer composite structure with a skin effect. The copper layer is located on both sides of the tape as a reinforcing layer and is affected by the skin effect. Utilizing the H model, this study conducts finite element analysis on the second-generation HTS tapes. Through the refined model, the frequency influence of the AC loss of YBCO tapes and the influence of the copper reinforcement layer on the AC loss are studied. The results show that as the frequency increases, the influence of the copper stabilizing layer on the AC loss increases, and the thicker the stabilizing layer, the greater the proportion of the AC loss. The study of the skin effect on the AC loss of YBCO tape has reference value for the design and development of HTS equipment. Keywords: YBCO tape · AC loss · Skin effect · Frequency · Copper stabilizing layer
1 Introduction Since the discovery of superconductors, especially the discovery of the second generation of high-temperature superconductors, with its high current-carrying density, low loss, and other characteristics, superconductivity technology has been extensively researched and developed worldwide [1]. The application range of superconducting tape is also gradually expanding, such as superconducting cables, superconducting motors, superconducting current limiters, superconducting transformers, superconducting energy storage, superconducting transformers, etc. [2]. High-temperature superconducting (HTS) tapes produce AC loss under alternating current, which is an important issue that needs to be considered in the design and application of power equipment [3]. Due to the existence © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1317–1325, 2022. https://doi.org/10.1007/978-981-19-1870-4_139
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of AC loss, it affects the economy and safety, and stability of HTS equipment, which is a restrictive factor for the development of superconductivity. In the application of electric power technology, according to the different application scenarios and application requirements, the HTS tape as a composite structure has different structural parameters and different working conditions. In addition, because of the skin effect, different working conditions or different structural tapes will cause differences in the size of the AC loss. The study of the effect of the skin effect on AC loss is of great significance to the design and research of superconducting power equipment. At present, the calculation methods of AC loss at home and abroad are relatively mature, but the research on the influence of skin effect on AC loss needs to be in-depth [4–9]. In this paper, the AC loss of YBCO tape is calculated and studied. Based on the method of finite element analysis, a refined model of YBCO tape is established. By studying the influence of the current frequency and the thickness of the superconducting tape reinforcement layer on the AC loss, it is obtained The relationship between the AC loss of superconducting tape and the skin effect.
2 YBCO Tape Structure Analysis Based on the structure of YBCO superconducting tape, this paper carried out refined modeling and studied the correlation of the AC loss and the skin effect through finite element analysis. The structure of YBCO tape is shown in Fig. 1, which mainly includes a superconducting layer, a silver layer, a substrate layer, a stabilizing layer, and a buffer layer. The main source of superconductor AC loss is hysteresis loss, which comes from the superconducting layer, and a small part of the loss is eddy current loss and coupling loss.
Fig. 1. Structure of YBCO tape.
To model the superconducting tape, consider the main structure superconducting layer, silver layer, substrate layer, and stabilizing layer, as shown in Fig. 2, and its parameters are shown in Table 1.
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Cu-up Ag HTS Substrate Cu-down Fig. 2. The structure of the simulation model. Table 1. The parameters of the HTS tape Parameter
Value
Tape width
4 mm
HTS layer thickness
4 µm
Ag layer thickness
2 µm
Cu layer thickness
150 µm
Substrate layer thickness
50 µm
Critical current density Jc
1.25 × 1010 A/m2
The resistivity of Ag layer
2.70 n · m
The resistivity of the Cu layer
1.97 n · m
The resistivity of substrate layer
1.5 µ · m
n
38
3 AC Loss Calculation 3.1 Critical State Model For the reason that the resistivity of the superconductor is nonlinear, which is influenced by current, temperature, and magnetic field, a critical state model is needed to describe it. Considering that during normal operation, the current and temperature are both lower than the critical value, many scholars have proposed models that how magnetic field impacts the critical current of superconductors [10]. In the early years, some scholars believed that the magnetic field have no influence on the critical current. The tape critical current density is zero in the non-permeable magnetic flux region. In the magnetic flux penetration zone, the current density J in the superconductor is equal to the critical current density Jc . It is 0, E = 0 |J | = (1) Jc , otherwise In Kim’s model, he believes that the critical current is influenced by the magnetic field [11], that is Jc (B) = Jc0
B0 |B| + B0
(2)
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where Jc0 means the critical current density when there is only self-field, B0 is a fitted constant related to its characteristics. Kim Anderson modified the Kim model because the vertical magnetic field and the parallel magnetic field have different effects on the critical current, and his modified model can better reflect their relationship and it is more detailed [7]. It is described by the equation Jc (Bx , By ) =
(1 +
Jc0 k 2 |Bx |2 +|By | B0
2
(3) )α
where Bx means the parallel magnetic field, at the same time, By means the vertical magnetic field. 3.2 H-formulation Regarding the AC loss calculation methods of superconducting tapes, currently commonly used T-A formulation, A-∅ formulation, T- formulation H- formulation, etc., they obtain the final results by solving different physical quantities. At present, the calculation speed of the T-A method is relatively fast, but it is inconvenient to calculate the current distribution on the surface of the tape including the stability layer, the substrate layer, and the silver layer. So the H equation is chosen to analyze the influence of the skin effect on the AC loss. Assuming that the current of each tape is I(t): I(t) = J(t)dxdy (4) where J is the current density. According to the law of total current of Maxwell’s equations, when power frequency alternating current is applied, the current frequency is 50 Hz, the electric field change can be ignored and can be calculated as a quasi-static field: ∇ ×H =J
(5)
In which, H means the magnetic field. Faraday law describes the relationship between electric field and magnetic field: ∇ ×E =−
∂B ∂t
(6)
where E represents the electrical field, B represents the magnetic flux density, and the magnetic flux density can be calculated by B = μo μr H, with the uniform medium. In which, μ0 is vacuum magnetic permeability, μr is relative magnetic permeability. The above formula can be written as ∇ × E = −μ0 μr
∂H ∂t
(7)
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A control equation is obtained to describe the model. Besides, E-J power law as follows is adopted to represent the resistivity of the superconducting layer [8]: Ec J n−1 (8) ρHTS = Jc Jc Ec means the criterion when the critical current density Jc is attained, it equals 1 µV/m. Superconducting cable AC loss is calculated by: Q = E · Jdxdy (9) The average loss of a cycle is Q=
1 T
2T
E · Jdxdy
dt T
(10)
4 Results and Analysis In this study, adopting the H method, the finite element analysis of the superconducting tape is carried out, the AC loss calculation results are obtained, and the relationship between the skin effect and the AC loss of the YBCO superconducting tape is analyzed. 4.1 The Influence of Transmission Current Frequency on AC Loss At 50 Hz, the AC loss of each layer of the YBCO tape with 50 μm copper is shown in Fig. 3. It shows that the AC loss mainly comes from the superconducting layer, and the copper layer, silver layer, and substrate layer account for less than 1%. The relationship between the overall AC loss and frequency of the YBCO tape is shown in Fig. 4. As the
Fig. 3. Correlation between each layer AC loss and current when f = 50 Hz
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Fig. 4. Correlation between total AC loss and current under different current frequencies.
frequency increases, the overall AC loss increases. When the frequency reaches 5 kHz, the loss is two orders of magnitude different from that at 50 Hz. Figure 5 shows the AC loss of each functional layer at different frequencies and currents. The AC loss of the superconducting layer is the largest. The AC loss of the copper layer on the side of the substrate layer is greater than that of the copper layer on the side of the silver layer, and the current density of the copper layer on the side of the substrate layer is greater. Because of its high resistivity, the substrate layer has the smallest current density and the lowest loss.
Fig. 5. Correlation between AC loss of each layer and frequency under different current amplitude.
Figure 6 shows the percentage of AC loss between the superconducting layer and the copper layer at different currents. As the current amplitude increases, the overall AC loss ratio of the copper layer becomes larger, and the AC loss of the copper layer on the base layer side and the side of the silver layer tends to be equal. As the frequency increases, affected by the skin effect, the current density of the copper layers on both sides increases, and the proportion of losses generated by it also increases. At 0.8Ic and 5000 Hz, the proportions of the copper layer losses on the upper and lower sides are 8.98% and 10.85% respectively.
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Fig. 6. The ratio of the total AC loss to the copper layer and the HTS layer at different currents and frequencies.
4.2 The Influence of Superconducting Tape Reinforcement Layer on AC Loss The AC loss of YBCO tapes with different thickness reinforced layers at power frequency is calculated. As shown in Fig. 7, when the thickness of the copper layer increases from 25 µm to 125 µm, the overall AC loss does not differ by more than 1%. The copper layer has little effect on the AC loss.
Fig. 7. Correlation between AC loss and copper thickness
Figure 8 shows the proportion of the AC loss of the two copper layers of YBCO tapes. As the thickness of the copper reinforcement increases, the proportion of the AC loss increases. As the thickness of the copper reinforced layer increases, the proportion of the AC loss increases. The greater the thickness, the greater the difference in the proportion of the AC loss of the copper layers on both sides, and the AC loss of the bottom copper layer is still greater than that of the upper copper layer.
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Fig. 8. The ratio of the total AC loss to copper layer with different thickness
5 Conclusion In this paper, the H method is used to perform finite element analysis on YBCO tapes, the influence of current frequency on the AC loss of each layer is calculated, and the influence of the thickness of the copper reinforced layer on the AC loss is calculated. The results show that affected by the skin effect, the skin effect becomes more obvious when the frequency is higher, and the proportion of the AC loss of the copper layer gradually increases. When the thickness of the copper layer increases, the overall AC loss is basically unchanged, but the proportion of the AC loss of the copper layer increases. The calculation results in this paper provide a certain reference for the application of YBCO tape in different scenarios and provide a basis for the design and research of superconducting power equipment. Acknowledgments. This work was supported by Southern Power Grid Major Science and Technology Program (SZKJXM20170410).
References 1. Chen, Z., Geng, G., Fang, J., et al.: Design and characteristics analysis of a new hightemperature superconducting composite conductor. IEEE Trans. Appl. Supercond. 29(2), 1–5 (2018) 2. Zhang, J.Y., Tang, W.B., Xiao, L.Y.: Application of superconducting technology in the future power grid. Physics 50(02), 92–97 (2021) 3. Ogawa, J., Fukui, S., Oka, T., et al.: AC loss distribution in two-layer HTS cable. IEEE Trans. Appl. Supercond. 28(3), 1–4 (2018) 4. Lee, S.J., Yang, H.S.: Recent progress and design of three-phase coaxial hts power cable in Korea. IEEE Trans. Appl. Supercond. 29(5), 1–5 (2019) 5. Li, Z.Y., Gu, F., Ma, Y.H., et al.: Influence of transport modes on AC loss characteristics of cylindrical single-layer conductors consisting of various HTS tapes. Phys. C: Superconduct. Appl. 569, 1353589 (2020) 6. Altov, V.A., Balashov, N.N., Degtyarenko, P.N., et al.: Design versions of HTS three-phase cables with the minimized value of AC losses. J. Phys. Conf. Ser. 969(1), 012049 (2018) 7. Song, W., Jiang, Z., Zhang, X., et al.: AC loss simulation in a HTS 3-Phase 1 MVA transformer using H formulation. Cryogenics 94, 14–21 (2018)
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8. Prigozhin, L., Sokolovsky, V.: 3d simulation of superconducting magnetic shields and lenses using the fast fourier transform. J. Appl. Phys. 123(23), 233901 (2018) 9. Zhang, Y., et al.: Dependence of AC transport loss of HTS-coated conductor on current parameters in the frequency range under 1MHz. J. Superconduct. Novel Magnet. 34(9), 2271– 2280 (2021). https://doi.org/10.1007/s10948-021-05946-3 10. Yazdani-Asrami, M., Gholamian, S.A., Mirimani, S.M., Adabi, J.: Investigation on effect of magnetic field dependency coefficient of critical current density on the AC magnetizing loss in HTS tapes exposed to external field. J. Supercond. Novel Magn. 31(12), 3899–3910 (2018). https://doi.org/10.1007/s10948-018-4664-1 11. Kim, Y.B., Hempstead, C.F., Strnad, A.R.: Magnetization and critical supercurrents. Phys. Rev. 129(2), 528–535 (1963)
Simulation and Comparative Analysis of Permanent Magnet Motor with Rectangular-Wire and Circular-Wire Guanglong Jia1(B) , Ming Jing2 , Yeliu Xu2 , and Fengge Zhang2 1 National Engineering Research Center for Rare-Earth Permanent Magnet Machines, Shenyang
University of Technology, Shenyang 110870, China [email protected] 2 School of Electrical Engineering, Shenyang University of Technology, Shenyang 110870, China
Abstract. Because of its high efficiency, high slot fill factor, short end-winding and good heat dissipation, rectangular-wire motor has become the development trend of new energy vehicle drive motor. With the increasing requirements of high-speed drive motor, the eddy current loss of rectangle-wire motor windings is particularly remarkable, which affects the efficiency. Firstly, AC loss caused by skin effect and proximity effect are analyzed and simulated at different speeds. Then, a rectangular-wire motor and a circular-wire motor with same rotor and same core length are designed and simulated. Finally, the testing platform is built and the two kinds of prototype motor are experimented and compared. And the BEMF and continuous output capability of the prototypes were compared and analyzed. It turns out to be that continuous output capability of the rectangular-wire motor was about 20% higher than that of the circular-wire winding motor. Keywords: Rectangular-wire winding · Permanent magnet motor · AC copper loss · High efficiency
1 Introduction In the last years, with the rapid development of the new energy vehicle industry, the demand of power performance and economy are continually improved. Especially after the concept of carbon neutral is proposed, the performance and environmental protection requirement of the new energy vehicle drive motor are further improved [1]. As the consequence, the requirement of the machine applying on the new energy vehicle drive motor is more and more strict in terms of the torque density, efficiency and other electromagnetic performances. The rectangular wire winding machine has aroused more and more attention due to characteristics of high efficiency, high slot fill factor, short end-winding and good heat dissipation which can become the proper candidate [2]. At present, the design and manufacturing technology of rectangular wire winding are constantly improved. The rectangular wire winding technology of GM and Denso © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1326–1333, 2022. https://doi.org/10.1007/978-981-19-1870-4_140
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is more representative. The rectangular wire winding permanent magnet synchronous motor was first released in the United States [3, 4]. With the speed increasing, the AC copper loss is increased rapidly which is caused by skin effect and proximity effect. In order to decreasing the AC winding loss, the number conductor per slot is increased [5]. The existing problems of rectangular wire winding motor have been researched by many scholars and institutions. The different winding arrangement modes are introduced and the design principles of winding connection are proposed. On this basis, the AC loss of motor with different connection modes was compared and analyzed [6]. The 3D simulated model of motor is established and the magnetic field is simulated. It turns out to be that the eddy current losses of conductor in the stator slot are much larger than endwinding. On this basis, the method of splitting the conductor are proposed for reducing AC loss of winding. The simulation results show that when the rectangular conductor is divided into two parts along the circumferential direction, the eddy current loss is most obviously decreased [7]. An asymmetric winding structure with unequal height of the conductor is proposed for reducing AC copper loss. And the distribution of AC copper loss in conductor is more uniform [8]. The influence factors such as current harmonics, slot opening heigh, conductor size and position are analyzed. It turns out to be that AC loss will be significantly reduced by optimizing the parameters such as notch height, rectangular conductor size and so on [9]. The AC losses of motor with 4-layer winding and 8-layer winding at different operating speed are analyzed. Compared with 4-layer winding, the high-efficiency area of 8-layer winding motor is larger and the average efficiency is improved by about 2% [10]. In this paper, AC loss caused by skin effect and proximity effect are analyzed and simulated. And a circular wire motor and a rectangular conductor winding motor with the same rotor, core length and slot-pole combination are designed. At the last, the prototype testing platform is built and the performances of two prototype motor are experimented under the same conditions.
2 Analysis and Calculation of AC Loss 2.1 Theoretical Analysis When circular wire winding motor is supplied by AC source, the AC copper loss caused by skin effect and proximity effect can be ignored due to the small area of each wire. Therefore, the total copper loss can be expressed by DC copper loss which calculated according to PCu = 3I 2 R
(1)
where PCu is the total copper loss, I is the phase current and R is the phase resistance.
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When rectangular wire winding is supplied by AC source, the current is concentrated on the surface of the conductor rather than uniformly distributed in the cross section of the conductor, especially at high speed. The skin depth can be expressed as ρ δ= (2) π μ0 μr f where δ is skin depth, ρ is conductor resistivity, μ0 is the vacuum permeability, μr is the relative permeability of conductor and f denotes the electric frequency. It can be seen from Eq. 2 that δ will be decreased with the increase of f . And the current distribution will be closer to the conductor surface. When the conductors in the stator slot are supplied by the same direction current, the current will be concentrated in the farthest side of the conductors. Conversely, the current in the conductor will be concentrated in the closest side. Both of the two cases, the effective cross-sectional area of the conductor will be decreased and the resistance of conductor will be increased. It turns out to be that the skin effect and the proximity effect for rectangular wire winding motor will not be neglected. The total copper loss can be expressed as Ptotal = PDC + Ps + Pp
(3)
Where Ptotal is the total copper loss, PDC is the DC copper loss, Ps is the AC copper loss caused by skin effect and Pp is the AC copper loss caused by skin effect. 2.2 Simulation Analysis of AC Copper Loss In order to accurately calculating the AC copper loss of motor with rectangular wire winding, a simulation model of motor is established. And there are 8 conductors in each slot as it is shown in Fig. 1. The AC copper loss of motor is simulated at different speeds and the result is shown in Fig. 2. It can be seen from Fig. 2 that the AC copper loss of stator winding is increased with the increase of speed. The AC copper loss is increased rapidly, especially when the motor speed is greater than 4000 r/min. The AC copper loss is 1.95 times greater than DC copper loss when the motor operating speed is 14000 r/min.
Fig. 1. Simulation model of motor with rectangular-wire winding
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Speed (r/min)
Fig. 2. AC loss of motor with different speed
3 Characteristic Simulation The motor with peak power of 150 kW and maximum speed of 14000 r/min is designed and the performances are simulated. The parameters of the motor are shown in Table 1. When the armature winding is opened and the permanent magnet temperature is 20 °C, the speed of motor is dragged to 14000 r/min. At this moment, the waveform of BEMF is shown in Fig. 3. It can be seen from Fig. 3 that the amplitude value of BEMF is 591 V which meets the controller’s requirement. In order to improving the performance of cogging torque and torque ripple, skewed pole is used. And the simulated waveform of cogging torque is shown in Fig. 4. Table 1. The parameters of rectangle-wire motor Parameter
Value
Slot number Poles number Rated voltage Core length Outer stator diameter Air-gap length Peak power Rated power Peak torque Rated torque
48 8 235 V 128 mm 230 mm 0.8 mm 150 kW 70 kW 310 Nm 140 Nm
It can be seen from Fig. 4 that the peak-to-peak value of cogging torque is 0.5 Nm which meets the design requirement. When the value of armature winding’s current is 500 A, the simulation waveform of peak torque is shown in Fig. 5. And the torque ripple of motor peak torque is 4.2%.
BEMF (V)
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Cogging torque (Nm)
Fig. 3. Curve of BEMF
Time (us)
Fig. 4. Curve of cogging torque
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Fig. 5. Curve of peak torque
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4 Comparative Study and Analysis The two prototype motors with rectangular wire winding and circular-wire winding are respectively developed which adopts the same rotor, pole number, stator slot number and core length. And the testing platform is built as shown in Fig. 6.
Prototype motor
Dynamometer Controller
Fig. 6. Testing platform
The speed of prototype motor is dragged from 1000 r/min to 10000 r/min and the values of BEMF are measured which are shown in Fig. 7. It can be seen from Fig. 7 that the error between the simulated value and the measured value of motor with the circularwire winding is 3.05%, while the error between the measured value and the simulated value of the motor with rectangular-wire winding is 2.96%. The reason for the error is the performance deviation of permanent magnet and manufacture. In addition, the BEMF of motor with rectangular-wire winding is 1.047 times than that of the motor with circular wire winding, which is caused by the fact that the pitch of motor with rectangular wire winding is full pitch while the pitch of motor with circular wire winding is short pitch.
BEMF (V)
Measured value of motor with circular wire Simulation value of motor with circular wire Measured value of motor with rectangular-wire Simulation value of motor with rectangular-wire
speed (r/min)
Fig. 7. BEMF of motor
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When the terminal voltage limit of prototype motor is 235 V and the inlet temperature of the motor is less than 65 °C, the test starts from the cold state and the continuous operating time is 30 min while the maximum temperature of winding is not more than 150 °C. And the continuous operated ability of the motor at different speeds is measured, and the test results are shown in Fig. 8. It can be seen from Fig. 8 that the continuous output capacity of the motor with rectangular wire winding is increased by about 20% which verifies the dissipation capacity is better. And with the increase of speed, the gap of the two prototype motors decreases continuously which is caused by skin effect and proximity effect that leads to the increase of the winding temperature AC copper loss. The output capacity is also decreased.
Motor with circular wire Motor with rectangular wire
Power (kW)
Torque (Nm)
Motor with circular wire Motor with rectangular wire
Speed (r/min)
(a) Continuous output torque
Speed (r/min)
(b) Continuous output power
Fig. 8. Continuous operating condition
5 Conclusion The AC loss caused by skin effect and proximity effect are analyzed and simulated at different speed in this paper. The simulation model of motor is established and the operation characteristics of motor with rectangular wire winding motor are simulated. On this basis, the prototype motors with rectangular wire winding and circular wire winding are designed and developed. And the testing platform is built. Then the two kinds of prototype motors are experimented and compared. It turns out to be that the heat dissipation capacity and continuous operating output capacity of motor with rectangular wire winding are better than that of motor with circular wire winding. And the continuous performance of motor with rectangular wire winding is improved by about 20%. Through the above research work, it lays a foundation for the further research of motor with rectangular wire winding. Acknowledgment. This work is supported by the National Natural Science Foundation of China (grant no. 51920105011).
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References 1. Jianlin, L., Yaxin, L., Xichao, Z., Li, W.: Analysis of energy storage policy in commercial application. Power Syst. Protect. Control 48(19), 168–178 (2020). (in Chinese) 2. Preci, E., Valente, G., Bardalai, A., et al.: Rectangular and random conductors: AC losses evaluations and manufacturing considerations. In: IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society. IEEE, pp. 1076–1081 (2020) 3. Rahman, K., Jurkovic, S., Savagian, P.J., et al.: Retrospective of electric machines for EV and HEV traction applications at general motors. In: 2016 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, pp. 1–8 (2016) 4. Momen, F., Rahman, K.M., Son, Y., et al.: Electric motor design of general motors’ Chevrolet Bolt electric vehicle. SAE Inter. J. Altern. Powertrains 5(2), 286–293 (2016) 5. Jurkovic, S., Rahman, K., Bae, B., et al.: Next generation chevy volt electric machines; design, optimization and control for performance and rare-earth mitigation. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE), IEEE, pp. 5219–5226 (2015) 6. Berardi, G., Bianchi, N.: Design guideline of an AC hairpin winding. In: 2018 XIII International Conference on Electrical Machines (ICEM), IEEE, pp. 2444–2450 (2018) 7. Aoyama, M., Deng, J.: Visualization and quantitative evaluation of eddy current loss in barwound type permanent magnet synchronous motor for mild-hybrid vehicles. CES Trans. Electr. Mach. Syst. 3(3), 269–278 (2019) 8. Islam, M.S., Husain, I., Ahmed, A., et al.: Asymmetric bar winding for high-speed traction electric machines. IEEE Trans. Transport. Electrif. 6(1), 3–15 (2019) 9. Jibin, Z., Shanlin, J., Weiyan, L.: AC loss in a high speed BLPM motor considering proximity effect. Electric Mach. Control 14(5), 49–55 (2010). (in Chinese) 10. Yongzhi, M., Lianghui, Y.: Simulation analysis of rectangle-wire motor with different conductor layers and its vehicle performance. J. Power Sources 22(7), 26–31 (2021). (in Chinese)
A Power Distribution Control Strategy for the Cascaded H-Bridge Energy Storage System Tong Yu1,2 , Fanqiang Gao1,2(B) , and Zhixuan Gao1 1 Laboratory of Power Electronics and Electric Drives, Institute of Electrical Engineering,
Chinese Academy of Sciences, Beijing 100190, China [email protected] 2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract. The cascaded H-bridge (CHB) converter can integrate the split lowvoltage small-capacity supercapacitor modules into the high-voltage high-power applications. However, the discrepancy of the supercapacitors’ parameters can lead to overcharge, and underutilization of some supercapacitors’ capacity. In this paper, the steady-state power balance in the sub-modules of a CHB with an integrated DC-DC converter scheme is studied. In this way, a power distribution control strategy for the CHB energy storage system (ESS) is proposed. MATLAB/Simulink simulation results shows the accuracy and effectiveness of the proposed power distribution control strategy. Keywords: Cascaded multilevel · Energy storage converter · Energy storage system · Energy balancing
1 Introduction In recent years, the energy storage technology has been increasingly applied in quite a few fields, such as power systems [1–3], rail transit systems [4], and electromagnetic emission systems [5]. With the large-scale application of energy storage technology, the demand for power storage with large capacity and high voltage is expected to increase in future. The cascaded H-bridge energy storage system have been presented as a good solution for high-power applications [6, 7]. There are three main ways that energy storage devices can be integrated into the CHB sub-modules: direct parallel, paralleled through non-isolated DC-DC converters and paralleled through isolated DC-DC converters. This paper focuses on the topology of the non-isolated DC-DC cascaded multilevel energy storage converters.There is a problem that the discrepancy of the super-capacitors’ parameters can lead to overcharge, and underutilization of some super-capacitors’ capacity, which need to be solved for its development prospect. To handle the energy imbalance of cascaded multilevel energy storage converters, scholars around the world have been conducting a wealth of research. In the direct parallel cascaded multilevel energy storage converter field, the dominant power distribution © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1334–1344, 2022. https://doi.org/10.1007/978-981-19-1870-4_141
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strategies are as follows: references [8–12] proposed a power balance strategy by sorting the super-capacitor voltage in one arm with step waveform modulation. The reference [13] put forward a power balance control method based on zero-sequence voltage injection with carrier phase-shift modulation, which can realize the independent adjustment of the active power of each sub-module and power balance control among phases. The reference [14] demonstrated a power distribution control strategy for the cascaded multilevel hybrid energy storage system based on the selection of the initial operating point. The selection method of the initial operating point can realize the reactive power distribution among sub-modules, and thus improve the reliability and redundancy of the system. The reference [15] offered a hierarchical control architecture. The upper-level control aims to determine power distribution and provide power reference for the lowerlevel control, and the lower-level control is responsible for the active and reactive power control of the system and the power distribution among sub-modules. By analyzing the system principle of the non-isolated DC-DC cascaded multilevel energy storage converters, this paper based on the analysis of the system’s multilevel power transmission, proposes a power distribution control strategy for sub-modules of non-isolated DC-DC cascaded multilevel energy storage converters to flexibly and independently regulate and control the voltage of the super-capacitor. In this paper, simulation experiments are conducted with Matlab/Simulink simulation software, and the accuracy and effectiveness of the proposed power balance control strategy are verified in one arm.
2 Working Principle of Cascaded H-bridge Converter Topology The topology of the three-phase non-isolated DC-DC cascaded multilevel energy storage converters discussed in this paper is shown in Fig. 1(a). Each arm circuit is composed of N sub-modules and arm inductance L m in series. The topological structure of the power sub-modules is shown in Fig. 1(b). C m is defined as the capacitance of sub-module capacitor, C sc is defined as the capacitance of super-capacitor. Table 1 demonstrates the working modes of the bidirectional DC-DC link. The super capacitor is being charged in the Buck mode and discharged in the Boost mode. Table 1. DC-DC operation modes Modes
Super capacitors
T1/T3
T2/T4
Boost
Discharge
0
PWM
Buck
Charge
PWM
0
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Lm
Lm
Lm
(a) Three-phase topology of the dual-stage cascaded multilevel energy storage converter a
T1 T3
Io Idc S1
S3
Icm
Csc
L1
IL1
L2
IL2
Cm T2 T4
Iac S2
S4
Isc
(b)Inner topology of the power sub-module
b
Fig. 1. The topology of non-isolated DC-DC cascaded multilevel energy storage converters
3 Simulation Model Each sub-module in the energy storage converters is composed of a DC-DC link and a DC/AC link in series, and the AC/DC link and DC/DC link are coupled with each other, which makes the dynamic power regulation process complicated. Since the power distribution issue discussed in this paper does not involve coupling among three phases, it can be analyzed separately in single phases. Since the cascaded topological, we can consider and simulate to each sub-module circuit separately.The power transmission of each sub-module energy storage converter is shown in Fig. 2: Based on Table 2, the power expression of each link is shown as follows: Pacik = iaci uik cos φ = iaci sik usmik cos φ
(1)
Pdcik = usmik ismik cos φ
(2)
Pscik = uscik iscik cos φ = usmik ioik cos φ
(3)
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Fig. 2. Diagram of power flow
Table 2. Working condition Working condition
(Psc, Pac, Pdc)
SC state
Power flow
1
(1,1,1)
Charge
Pac → Pdc + Psc
2
(1,1,0)
Charge
Pac → Psc
3
(−1, − 1, − 1)
Discharge
Psc → Pdc + Pac
4
(1, 1, 0)
Discharge
Psc → Pac
Pacik = Pscik + Psmik
(4)
Substituting Eqs. (1, 2 and 3) into Eq. (4) yields the following expression: iaci sik usmik cos φ = usmik ismik cos φ + Pscik
(5)
Where Pacik is the active power on the AC side; Pdcik is the active power; Pscik is the active power; sik is switch function of AC/DC; cosϕ is the total power factor of the system. when the sub-module capacitor voltage remains unchanged, the following equation is obtained: Cm
dusmk = ismik = 0 dt
(6)
And thus, the sub-module capacitor voltage and the power transmission can be decoupled: Pacik = Pscik
(7)
In addition, as the power sub-modules of the converters are cascaded, the AC side current iac of each power sub-module is equal, and substituting this condition into Eq. (5) yields: si1 si2 siN = =···= Psci1 Psci2 PsciN
(8)
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Thus, for independently controlling the charge and discharge power of each power sub-module, we might as well set the ratio according to the energy difference: ksci1 ksci2 = 2 2 Csci1 usci1MAX − usci1initial Csci2 usci2MAX 2 − usci2initial 2 ksciN =···= CsciN usciNMAX 2 − usciNinitial 2
(9)
Psci1 Psci2 PsciN = =···= ksci1 ksci2 ksciN
(10)
Where k ik is the distribution factor of the super capacitor charging and discharging power; uscikMAX is the voltage value of the fully charged super capacitor; and uscikinitial is the initial voltage of the charging and discharging super capacitor. Combining Eqs. (8, 9 and 10), and setting the ratio of the switching function of each power sub-module as: si2 siN si1 = =···= ksci1 ksci2 ksciN
(11)
By controlling the wave amplitude modulation of each power sub-module in carrier phase-shift PWM modulation, Eq. (21) is set as: mi1 mi2 miN = =···= ksci1 ksci2 ksciN
(12)
mik is the adjustment coefficient of the PWM modulation ratio in the DC/AC link. Applying mik to the PWM process of the DC/AC link of each power sub-module through multiplication yields: mik M = Mik
(13)
Where M is the design value of the modulation ratio of the total output voltage on the AC side of the system. M ik is the PWM modulation ratio of the DC/AC link. According to the double Fourier decomposition expression of the total AC output voltage using carrier phase-shift modulation: f (t) =
N
Mk Um sin ωs t +
k=1 N −1 L=0
Jn ( mM2 π ) m
4 Um π
∞
±∞
m=2,4,··· n=±1,±3,···
(14)
πL sin[m(ωc t − ) + nωs t] N
For the carrier frequency ratio range that satisfies the Shannon sampling theorem, and whose fundamental wave frequency is carrier phase-shift PWM modulation under the operation condition, the component of the sideband harmonics mapped to the fundamental wave is almost negligible. So the fundamental wave component in the first term, as long as the following equation is satisfied. N k=1
mik M = NM
(15)
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Mik = mik M ≤ 1
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(16)
Therefore, a suitable limiter should be added in the calculation of the distribution coefficient k ik of the charging and discharging active power of the super capacitor in the design. Finally, it can be concluded that when the modulation ratio of each power sub-module at the DC/AC link satisfies the mathematical relationship of Eqs. (12), (15), and (16), and under the premise of not affecting the output voltage quality of the total AC side of the single-phase, independent distribution control to charge or discharge active power of each super capacitor in arm can be realized by distributing the PWM modulation values which is equal to the ratio at the DC/AC link of each power sub-module in arm. However, the above is just an ideal condition. In actual engineering applications, due to problems like inconsistent switching device losses or even gradually diverge when the capacitor voltage sum of sub-modules remains unchanged. Therefore,this paper sets the sub-module voltage equalization closed-loop control link, that is, to construct the sub-module capacitor voltage equalization coefficient nik : nik = Ksm (usmiaverage − usmik ) ∗ sign(iac )
(17)
Where nik is the equalization coefficient of the sub-module capacitance voltage; K sm is the voltage equalization ratio coefficient; usmiaverage is the average voltage.The calculated equalization coefficients can be distributed to the modulation ratio of each power sub-module through addition and subtraction operations: mi1 mi2 miN = =···= ki1 + ni1 ki2 + ni2 kiN + niN N
nik = 0
(18)
(19)
k=1
Since after substituting Eq. (19) into Eq. (18), the modulation ratio of the DC/AC link of each power sub-module still satisfies the relationship in (15), and thus the sub-module capacitor voltage equalization control link does not affect the voltage quality on the AC side. But for the relationship in (12), a slight deviation emerges after the sub-module capacitance voltage equalization control is conducted. The equalization coefficient n is a disturbance term for the consistency of energy transmission, and thus it is possible to design a relatively small voltage equalization proportional coefficient K sm at the cost of the rapidity of sub-module voltage equalization control to some extent as the voltage difference of the sub-module capacitor is relatively small in the system operation. The equalization coefficient n is limited to sharply reduce its impact on the consistency of the energy transmission.
4 Control Strategy The energy storage converter in this paper is designed for the grid-connected charging and discharging process. For the charging process, in the blocking of the DC-DC link,
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the sub-module capacitor is uncontrollably charged to 650 V, and then is charged under the dual closed-loop control of the grid-connected U sm and Q. When the sub-module capacitor is fully charged and stably controlled, the DC-DC link is unlocked, and the super capacitor is charged with constant power. Figure 3 shows the control block diagram of the DC/AC link of the super capacitor energy storage system. The overall control process has three sub-control links: 1) Power and voltage control under grid-connected operation 2) Capacitor voltage balancing control of sub-modules in each phase 3) Super capacitor charging and discharging control of DC-DC link in each phase
3N
usma1,usma2,
3N
Paca1*,Paca2*,
,usmaN ,PacaN* Σ
usmik*
Q*
ua ub uc ia ib ic
uao* ubo*
Power voltage control
uco*
Average value calculating
Pacak* Pacbk* Pacck*
Σ
Σ ÷
Paca
*
÷
Pacb
Σ *
÷
Pacc
*
×
Equation(17)
nak* + nbk* +
×
nck* +
ubn*
+ ×
uan* +
ucn*
+
Fig. 3. DC/AC control strategy
4.1 Power Voltage Control The active power control of the energy storage converter adopts the classic strategy of a four-quadrant converter [16]. Through double closed-loop control, the outer loop controls the sum of the sub-module capacitor voltage and reactive power Q, and the inner loop controls the active current and reactive power current. 4.2 Sub-module Capacitor Voltage Equalization Control It is necessary to conduct voltage equalization control on the capacitor voltage of the sub-modules. Calculate the average voltage of the a-phase sub-module capacitors, and then substituting it into Eq. (17) to calculate the sub-module capacitance equalization coefficient nik . As shown in Fig. 4, the addition operation is conducted on the modulated voltage generated by the active power control. 4.3 Super Capacitor Charging and Discharging Control in the DC-DC Link As mentioned above, the single current loop control over the DC-DC link can be used to independently set the super capacitor charging and discharging power of each power
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sub-module. The specific distribution steps are as follows: check if there is an energy difference between the super capacitors of the sub-modules, and regarding the energy differences between the super-capacitors, select a standard sub-module for reference, which is the first sub-module in this case, and the charging power of the standard sub-module is set based on the required charging starting time, and then set different charging power of the super capacitors of other power sub-modules according to Eq. (7). According to: 1 (20) WCik = Ci uscikMAX 2 − uscikinitial 2 2 2 Ci uscMAX 2 −usci Pscik (t1 − t0 ) (21) = 2 Psci1 (t1 − t0 ) C1 uscMAX 2 −u sc1
where t 0 is the starting time and t 1 is the ending time of the charging and discharging processes; C i is the capacitance value of the super capacitor. Thus, the mutual ratio k ik of the super capacitor charging and discharging power of each power sub-module can be expressed as: 2 Ci uscMAX 2 −usci Pscik (22) = kik = 2 Psci1 C1 uscMAX 2 −usc1 Finally, as shown in Fig. 4, substituting the set ratio k ik of the super capacitor charging or discharging power of each power sub-module into the super-capacitor charging or discharging power of the standard sub-module to acquire the reference value Psc * to achieve the constant power DC-DC control. Pscik * uscik
+
Kp + -
Ki s
iscik
Pscik * uscik
+
iscik
+
uscikinitial usmkMAX
Kp + -
+
Ki s
+ +
u 1 − scikinitial usmkMAX
Fig. 4. Bidirectional DC-DC control
5 Simulation Verification In order to verify the above theory, a simulation model of a three-phase two-stage cascaded energy storage converter is constructed in the MATLAB/Simulink environment.
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The circuit topology of the converter is shown in Fig. 1, and the simulation parameters are shown in Table 3. Figures 5 and 6 demonstrate the voltage and current waveforms of the energy storage converter in the simulation experiments. Figure 6 shows that at 47 s, the voltage difference percentage of the super capacitor reduces from 50% to 0%, and all power sub-modules are charged fully to 600 V. The results prove that the power distribution control strategy of sub-modules proposed in this paper can achieve excellent energy balance control even with capacitance value differences. Table 3. Design parameters Parameters
Value
Number of sub-modules in bridge arms N
15
Rated capacity of transformers S /MVA
10
Effective value of line voltage on the AC side uac /kV
8
Sub-module capacitance value C m /mF
60
Super capacitor capacitance C sc /F
25 (sub-module 2 is set as 22.5 separately)
Internal resistance of super capacitor Rsc/
47.25
Inductance value of energy storage inductor L 1 , 200 L 2 /µH Internal resistance of energy storage inductor R1, R2 /m
5
Initial voltage of super capacitor U sc /V
300(sub-module 2 is set as 150 Separately)
Initial voltage of sub-module capacitor U sm /V
650
Equivalent inductance of power grid incoming line L m inductance value/H
0.05
Equivalent resistance of power grid incoming line Rm resistance value/
0.002
Fig. 5. Simulation results of super capacitor voltage
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a
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Simulation results of sub-module capacitor voltage
b Simulation results of output voltage of the converter’s AC side
c Simulation results of super capacitor current
d Simulation results of three-phase current all process Fig. 6. Simulation results of cascaded multilevel energy storage converter
6 Conclusion Based on the topology of non-isolated DC-DC cascaded multi-level energy storage converters, analysis of working conditions and charging and discharging characteristics of super capacitors, a power distribution control strategy for non-isolated DC-DC cascaded multi-level energy storage converters is proposed. With the strategy, the DC-DC link in the sub-modules can actively control the charging and discharging dynamic characteristics of the energy storage units, and realize the balancing of sub-module capacitor
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voltage in arm and the active power distribution of the super capacitors. This paper verifies the effectiveness and accuracy of the power distribution control strategy in arm with the simulation results of MATLAB/Simulink, and confirms the remarkable effects of steady-state power balance in the sub-modules of a CHB.
References 1. Chengmin, W., Weiqing, S., Tao, Y., et al.: Overview of application planning and benefit evaluation methods of energy storage technology in smart grids. Proc. CSEE 033(007), 33–41 (2013) 2. Li, X., Yao, L., Hui, D.: Optimal control and management of a large-scale battery energy storage system to mitigate fluctuation and intermittence of renewable generations. J. Modern Power Syst. Clean Energy 4(4), 593–603 (2016) 3. Ying, Z., Yunbo, G., Haixiang, Z., et al.: Overview of smoothing technology for output power of wind turbines. Autom. Electric Power Syst. 1, 182–191 (2018) 4. Kun, Z., Yanrong, W., Dewei, W., et al.: Indirect current control strategy for vehicle-mounted super capacitor energy storage system. Trans. China Electrotech. Soc. 09, 124–129 (2011) 5. Weiming, M., Fei, X., Shixiong, N.: Application and development of power electronic technology in electromagnetic emission system. Trans. China Electrotech. Soc. 31(019), 1–10 (2016) 6. Ai Hongke, W., Junyong, H.L., et al.: Research on the battery self-balancing control strategy in the cascaded energy storage system. Trans. China Electrotech. Soc. 30(014), 442–449 (2015) 7. Jinghua, Z., Ya’ai, C.: Principle and Application of High-Performance Cascaded Multilevel Converters. China Machine Press (2013) 8. Jinghua, Z., Fan, W., Xiang, J., et al.: Overview of key control strategies for the cascaded H-bridge energy storage power conversion system. Electr. Energy Manag. Technol. 000(001), 8–17 (2018) 9. Tolbert, L.M., Peng, F.Z., Habetler, T.G.: Multilevel converters for large electric drives. IEEE Trans. Ind. Appl. 35(1), 36–44 (2002) 10. Chatzinikolaou, E., Rogers, D.J.: Hierarchical distributed balancing control for large-scale reconfigurable ac battery packs. IEEE Trans. Power Electron. 33(99), 5592–5602 (2018) 11. Yi, W., Hu, C., Ding, R., et al.: A nearest level PWM method for the MMC in DC distribution Grids. IEEE Trans. Power Electron. 11, 1 (2018) 12. Hongke, A., Junyong, W., Liangliang, H., et al.: Research on the battery self-balancing control strategy in the cascaded energy storage system. Trans. China Electrotech. Soc. 30(014), 442– 449 (2015) 13. Maharjan, L., Yamagishi, T., Akagi, H.: Active-power control of individual converter cells for a battery energy storage system based on a multilevel cascade PWM converter. IEEE Trans. Power Electron. 27(3), 1099–1107 (2012) 14. Weifeng, H., Hongbing, S., Guanjun, L., et al.: Power distribution control of the cascaded multilevel hybrid energy storage system based on the selection of initial operating points. Power System Technol. 44(438(05)), 47–59 (2020) 15. Zhang, Q.: Control of PV battery hybrid system using cascaded H bridge converter. In: IEEE International Future Energy Electronics Conference & Ecce Asia, IEEE, pp. 2008–2012 (2017) 16. Qu, X., Han, H., Wong, S.C., et al.: Hybrid IPT topologies with constant current or constant voltage output for battery charging applications. IEEE Trans. Power Electron. 30(11), 6329– 6337 (2015)
Research on a New Intelligent Transformer Integrating SVG and DVR Xi Wan1 , Wenqin Lu1 , Bo Xue1 , Han Yan2(B) , and Jianhua Wang2 1 State Grid Jiangsu Electric Power Co., Ltd. Changzhou Power Supply Branch,
Changzhou 213002, China 2 School of Electrical Engineering, Southeast University, Nanjing 210096, China
{yh124,wangjianhua}@seu.edu.cn
Abstract. In order to overcome the disadvantages of the existing power electronics transformers such as low energy conversion efficiency, small transmission capacity and high cost, a new intelligent hybrid distribution transformer with SVG and DVR functions is proposed, combining the advantages of the power frequency multi-winding transformer and the back-to-back converter, and its basic working principle is analyzed. On this basis, according to the characteristics of the two-stage structure of the back-to-back converter, the corresponding controller and control strategy are designed respectively for the rectification stage and the inverter stage, which can realize the function of reactive power compensation and the recovery of dynamic voltage sag of important loads respectively. Finally, the simulation model of the proposed hybrid transformer is built based on PSIM simulation software, and the correctness and effectiveness of the proposed topology and the designed control method are verified. Keywords: Hybrid distribution transformer · Back-to-back converter · Grid reactive compensation · Voltage sag support
1 Introduction As the core equipment of power transmission and voltage level conversion, transformer plays an important role in power grid. Although the traditional transformer has the advantages of low cost, high reliability and high efficiency, its function is too single and cannot fully meet the requirements of modern power system [1]. With the continuous progress of high-power power electronic devices and power electronics technology, Power Electronic Transformer (PET), which can realize voltage conversion and energy transmission in power system through all-power electronic devices, has been developed and received widespread attention. However, the current shortcomings of PET itself, such as complex structure, many switching devices and high cost, limit the research and development and application of PET. In this regard, in recent years, some foreign scholars have proposed the concept of Hybrid Distribute Transformer (HDT), which can effectively combine the advantages of both power electronic © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1345–1352, 2022. https://doi.org/10.1007/978-981-19-1870-4_142
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equipment and traditional transformers, and has good research value and application prospects [2]. Up to now, scholars at home and abroad have carried out some studies on HDT: Literature [3] proposed the concept of hybrid transformer combining AC/AC converter with traditional transformer. In literature [4, 5], a hybrid transformer based on a single-stage matrix converter is proposed, which solves the shortcoming of the traditional hybrid transformer failing to control the output voltage phase. At present, some literatures introduce the structure of Modular Multi-level Converter (MMC) into the hybrid transformer [6–9]. The direct AC/AC Converter has no DC link and the conversion rate of electric energy is high. However, MMC has many bridge arms, complex structure, and additional inter-module voltage balance control and circulation suppression methods, which are also not conducive to application. Aiming at the above problems, this paper combines the advantages of stable and reliable power frequency multi-winding transformer and the characteristics of strong controllability of two-stage back-to-back converter, proposes a new type of intelligent transformer with simple structure and integrated functions of Static Var Generator (SVG) and dynamic voltage regulator (DVR). On this basis, according to the characteristics of the two-stage structure of the back-to-back converter, the corresponding controller and control strategy are designed for the rectifier stage and the inverter stage respectively. Finally, a simulation model of the proposed hybrid transformer is built based on PSIM simulation software, which verifies the correctness and effectiveness of the proposed topology and designed control method.
2 The Topology and Working Principles of HDT
R1
R2
Y1
Ua D1
R3
Sensitive load
Ub Uc L1
D2
S1
S2
L2
S3
S7
S8
S9
S10
C
L4
Ta
L5
Tb
L6
Tc
L3 C4 S4
Threewinding transformer
C1
C2
S5
S6
S11
S12
S13
C5
S14 Ln
C3
C6
By-pass switch
Cn
Back to back converter
Fig. 1. The topology of HDT.
The HDT topology in this paper is shown in Fig. 1. In addition to the filtering circuit, the system mainly contains a set of three-phase three-winding transformers, a set of back-to-back converters and a set of bypass switches. The three windings in the threephase three-winding transformer are primary side winding D1, secondary loop winding D2 and main loop winding Y1. Among them, the output of the auxiliary circuit winding D2 serves as the AC input of the rectifier stage of the back-to-back converter, and each
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phase of the main circuit winding Y1 is connected to the load through series connection with the inverter level output of the back-to-back converter. The rectifier stage of the back-to-back converter is realized by a three-phase two-level rectifier, and the inverter stage consists of a three-phase four-arm inverter. The bypass switch is used to switch on or off the inverter output. In the HDT of this paper, the main loop is used for AC power transmission, which has the same function as traditional transformers. However, by controlling the back-toback converter in the auxiliary circuit, it can realize the power quality compensation and support functions that the traditional transformer does not have. According to the structure and functional characteristics, the back-to-back converter can be divided into two stages: rectifier stage and inverter stage. The functions and characteristics of the two stages can be analyzed separately as follows. In this paper, the rectifier stage is connected to the secondary loop winding D2 through filter inductor and connected to the load loop in parallel through transformer coupling, which can provide the function of SVG and provide reactive power compensation for the power grid when necessary. In this paper, the output of the inverter stage is directly connected in series to the power supply circuit of the sensitive load, and it works as a three-phase DVR to adjust the voltage in the main circuit, provide voltage support for the sensitive load, and maintain the stability of the load voltage. The output of inverter DVR can be controlled by controlling the opening and closing of the three-phase bypass switch composed of thyristors.
3 The Control Strategy of HDT Rectifier Stage The main control objectives of the rectifier stage converter are as follows: one is to control the capacitor voltage at the dc side to maintain the reference value; the other is to absorb or send reactive power through controlling the output reactive current to complete the reactive power compensation to the grid. In order to achieve these two control objectives, this paper adopts a double closed-loop PI control structure of voltage outer loop and current inner loop, as follows. 3.1 Control Strategy of Outer Voltage Loop According to the low-frequency model of three-phase two-level rectifier and the imagination that the controlled grid currents are sinusoidal, when PI controller is applied to control dc bus voltage, the control structure of dc bus voltage outer loop is shown in Fig. 2 [10]:
Udc*+ -
GV(s)
GI(s)
Im
0.75
idc +
iL
-
1 sC
Udc
Fig. 2. Control block diagram of outer voltage loop.
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In Fig. 2, GV (s) represents the DC side voltage controller, and GV (s) represents the current loop equivalent transfer function. I m represents the peak current at the grid side. The current loop transfer function can be approximated as a small inertia link, then ⎧ 1 + Tv s ⎪ ⎪ ⎨ GV (s) = Kv Tv s (1) 1 ⎪ ⎪ ⎩ GI (s) = 3TS s + 1 where, K v and T v are the parameters of the voltage controller, T s represents the sampling period. Figure 2 shows that the open-loop transfer function of voltage outer loop is Wov (s) =
0.75Kv (1 + Tv s) CTv s2 (3TS s + 1)
(2)
According to Eq. (2), the parameters of the voltage outer loop controller can be designed. 3.2 Control Strategy of Inner Current Loop Based on the dq model of the three-phase two-level rectifier and the dq feedforward decoupling PI control strategy, with considering the sampling delay and the inertia characteristics of PWM, the id current inner loop structure of feedforward decoupling can be drawn as shown in Fig. 3.
id*
ed 1 Ts s + 1
KiP +
KiI s
K PWM 0.5Ts s + 1
1 sL + R
id
Fig. 3. d axis current inner loop control block diagram.
In Fig. 3, K iP and K iI are the proportion gain and integral gain of PI of the current inner loop respectively. id * and iq * are the reference values of the grid current on dq axis respectively. K PWM is the PWM equivalent gain of three-phase two-level rectifier. After zero-pole correction according to type I system, the open-loop transfer function of current inner loop is [10]. Woi (s) =
KiP KPWM Ls(1.5TS s + 1)
(3)
According to Eq. (3), parameters of the current inner loop controller can be designed. To sum up, the control block diagram of double closed loop decoupling control strategy is shown in Fig. 4.
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ud +
u rd
-
PI
+ idref -
ωL
id
-
ωL +
u rq
-
PI
∗ udc
usdc
iq -
PI
+
+
i + qref
uq
Fig. 4. Control block diagram of double closed loop decoupling control strategy.
4 The Control Strategy of HDT Inverter Stage In this paper, the inverter stage of the back-to-back converter mainly works as DVR, which provides voltage support when the load voltage falls and ensures the voltage stability of the sensitive load. Therefore, the control strategy of inverter level is mainly divided into two parts, one is the voltage detection algorithm of parallel dot, the other is the output control strategy of inverter level. In this paper, voltage and current double closed-loop control is selected as the control method of inverter output. u*compd *
u
compd
+
PI
-
ucompd
PLL
Upccabc
abc
dq
vd vq
LPF
Vd
vrms
Vq
θ
Volt age sag?
Y
DVR ON
N
-
iLd iLq
ωC f
+
No compensation
Fig. 5. Flow chart of voltage sag detection.
+ ωC f
ucompq u*compq
+
i*Ld +
PI
+
i*Lq-
P
+
+ -
uloadd
ω Lf
iLd
ω Lf
P
+
+
uloadq
u*compq
Fig. 6. Inverter stage output control diagram.
4.1 Detection Process of Grid Connection Point Voltage Park transformation is performed on the three-phase voltage at the collected junction point to obtain the three-phase voltage at the junction point in the dq coordinate system, which is filtered by a low-pass filter to judge whether voltage sag occurs at the junction point. If no voltage sag occurs, no compensation is performed. If voltage sag occurs, the DVR compensation is started, the compensation voltage reference value in the dq coordinate system is calculated, and the voltage sag on the DVR compensation load is controlled through the voltage and current double closed-loop control. The voltage sag detection process of connection point is shown in Fig. 5. 4.2 Compensation Control Strategy of Inverter Stage The inverter output control structure is shown in Fig. 6. This paper adopts the control structure of voltage outer loop and current inner loop [11, 12]. The voltage outer loop
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adopts PI controller and the current inner loop adopts proportional control. After obtaining the output control compensation voltage of the inverter level converter in the dq coordinate system, reverse Park transformation is carried out to obtain the control compensation voltage of the inverter level converter in the abc three-phase static coordinate system, and SVPWM modulation is carried out to obtain the switching control signal of the inverter level converter.
5 Simulation Results and Analysis In order to verify the effectiveness of the HDT topology and the corresponding back-toback converter control strategy in this paper, a simulation model based on PSIM is built for simulation analysis. The parameters of the simulation model are shown in Table 1: Table 1. Parameters of HDT simulation model. Parameters
Values
Ratio of voltage levels between windings (D1:Y1: D2)
10kV:400V:23V
Dc bus voltage /V
60
Dc bus capacitance/µF
4700
Ac side inductance /µH
50
Ac side resistance /
0.005
Ac side filter capacitance /µF
60
Controller parameters of rectifier stage (K vP , K vI , K iP , K iI )
1, 100, 0.6, 0.001
Controller parameters of inverter stage (K vP1 , K vI1 , K iP1 )
0.4, 0.008, 0.5
5.1 Simulation Results of Rectifier Stage Converter In order to verify the reactive current control effect of the rectifier level converter, the reference value of the q-axis reactive current was set as 0–0.4 s and 5 from 0.4 s to 0.8 s. During the whole simulation period, the bypass switch was closed and the output of the inverter level converter was bypassed. The simulation results of dc side voltage, q axis reactive current and ac side three-phase current of rectifier stage are shown in Fig. 7. Figure 7 (a) shows the simulation results of DC side voltage. It can be seen from the figure that the control strategy designed in this paper can keep dc side voltage stable at the reference value of 60 V. Figure 7 (b) shows the q-axis reactive current iq simulation results. It can be seen that the rectifier level converter adjusts the output reactive current following reference value under control after the 0.4 s reactive current is given a change, indicating that the rectifier level converter designed in this paper has the ability to control reactive current and compensate the reactive power of the system. Figure 7 (c) shows the simulation results of iabc on the ac side. It can be seen that the variation trend of iabc is consistent with that of reactive current, which further verifies the effectiveness of rectifier stage converter as SVG function in this paper.
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65 60 55
30
10
AC currents iabc(A)
Reactive current iq (A)
DC bus voltage（V）
70
8 6 4 2
0.2
0
0.6
0.4 Time (s)
0
10 0
-20 -30
0
0.8
20
-10
-2
50
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(a)
0.4 Time(s)
0.6
0.8
0
0.2
(b)
0.4 Time (s)
0.6
0.8
(c)
Fig. 7. Simulation results of rectifier stage converter.
5.2 Simulation Results of Inverter Stage Converter In order to verify the reactive current control effect of the inverter level converter, the voltage compensation function of the inverter level converter is simulated and verified. Set at 0.4 s, the sudden increase of impedance causes 10% voltage sag of the grid voltage, the bypass switch is disconnected, and the output of the inverter level converter is connected to the main circuit to compensate the load voltage. Figure 8 shows the simulation results of inverter node voltage, three-phase compensation voltage and threephase load voltage.
200 0
-200 -400 0
0.2
0.4 Time (s)
0.6
(a)
0.8
60
400
40
Load voltage(V)
CompensationVoltage (V)
PCC Voltage (V)
400
20 0 -20 -40
0 -200 -400
-60 0
200
0.2
0.4 Time (s)
0.6
0.8
0
0.2
(b)
0.4 Time(s)
0.6
0.8
(c)
Fig. 8. Simulation results of inverter stage converter.
Figure 8 (a) is the simulation result of voltage of three-phase connection point. It can be seen from the figure that, consistent with the conditions set, 10% voltage sag of connection point voltage occurs due to sudden impedance at 0.4 s. Figure 8 (b) shows the simulation results of three-phase compensation voltage. It can be seen that when the voltage of 0.4 s connection point falls, the inverter level converter outputs compensation voltage rapidly according to the voltage compensation control strategy, and stably outputs compensation voltage in the following simulation time under the support of dc voltage provided by the rectifier stage. The simulation results of inverter-level three-phase load voltage in Fig. 8 (c) show that the three-phase load voltage is fully compensated and remains stable, which proves the effectiveness and strong compensation ability of the inverter-level converter of HDT presented in this paper as DVR.
6 Conclusions This paper proposes a new intelligent transformer topology that integrates SVG and DVR functions, and designs the corresponding control strategy. HDT of this paper USES the combination of three winding transformer with back-to-back converter, while keeping
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stable power frequency transformer, on the basis of the advantages of low cost and compatible with the characteristics of the power electronic converter is easy to control, and through the design appropriate control strategies to achieve the reactive power compensation and active power of power grid voltage support, and other functions, Finally, the effectiveness of the proposed topology structure and control strategy is verified by simulation analysis. The in-loop simulation and prototype experiment of relevant hardware in this paper are in progress, and the follow-up work will be further carried out on the basis of this paper. Acknowledgements. This work was supported by State Grid Jiangsu Electric Power Co., LTD Science and Technology Program (J2021077).
References 1. Ji, Z.: Research on Key Techniques of Cascaded Power Electronic Transformer. Southeast University, Nanjing (2015).(in Chinese) 2. Yang, B., Zhao, J., Ji, Z., Wang, J., Liu, K.: Overview of hybrid transformer technologies. Electr. Power Autom. Equip. 40(02), 205–213+1–3 (2020). (in Chinese) 3. Szczesniak, P., Kaniewski, J.: A voltage regulator/conditioner based on hybrid transformer with matrix converter. In: IECON 2014–40th Annual Conference of the IEEE Industrial Electronics Society, pp. 3292–3297, Dallas, TX, USA (2014) 4. Szczesniak, P., Kaniewski, J.: Hybrid transformer with matrix converter. IEEE Trans. Power Delivery 31(3), 1388–1396 (2016) 5. Szczesniak, P.: A modelling of AC voltage stabilizer based on a hybrid transformer with matrix converter. Arch. Electr. Eng. 66(2), 337–346 (2017) 6. Chen, P., Liu, J., Zeng, H., Zeng, P., Yang, B., Wang, J.: Simulation research of a novel hybrid power electronic transformer. Transformer 54(11), 35–39 (2017). (in Chinese) 7. Liu, M., Fan, D., Jin, C.: Research on hybrid power electronic transformer based on modular multi-level converter and its control strategy. Electr. Energy Manag. Technol. 01, 64–70 (2020). (in Chinese) 8. Liu, J., Zeng, H., Chen, P., Zeng, P., Yang, B.: Research on the control strategy of the hybrid transformer based on the modular multilevel converter. Transformer 54(10), 28–32 (2017). (in Chinese) 9. Yang, B., Liu, K., Zhang, S., Zhao, J.: Design and implementation of novel multi-converterbased unified power quality conditioner for low-voltage high-current distribution system. Energies 11(11), 3150 (2018) 10. Zhang, X., Zhang, C.: PWM Rectifier and Its Control Theory. China Machine Press, Beijing (2012).(in Chinese) 11. Hagiwara, M., Akagi, H.: Control and experiment of pulse width modulated modular multilevel converters. IEEE Trans. Power Electron. 24(7), 1737–1746 (2009) 12. Rivera, S., Wu, B., Lizana, R., et al.: Modular multilevel converter for large-scale multistring photovoltaic energy conversion system. In: Energy Conversion Congress and Exposition, pp.1941–1946, Denver, CO, USA (2013)
Open-Circuit Fault Diagnosis of Quasi-Z-Source Inverter Based on Cloud Model Jifang Li1 , Huishan Guo1(B) , Mengbo Guo2 , and Genxu Li1 1 School of Electrical Engineering, North China University of Water Resources
and Electric Power, Zhengzhou, China [email protected] 2 State Grid Henan Electric Power Company Luoyang Power Supply Company, Luoyang, China
Abstract. Quasi-Z-source inverter is an important part of photovoltaic system, when a fault occurs, it will seriously reduce the power quality and even cause secondary damage to the equipment. Therefore, this paper proposes an opencircuit fault diagnosis method of Quasi-Z-source inverter based on cloud model to improve its reliability. First of all, by analyzing the working principle and fault current characteristics of Quasi-Z-source inverter, the fault types of Z-source inverter are summarized, and the diagnostic variables of single IGBT open circuit and two IGBT open circuit of the same bridge arm are derived. Secondly, using the cloud theory to combine the fuzziness and randomness in the uncertain concept, the membership cloud model is generated, and the membership relationship between the fault diagnosis variables and the IGBT state is obtained. According to the membership degree, the occurrence and location of the IGBT open circuit fault are judged. Finally, the feasibility and correctness of the method are verified by simulation, which provides a new idea for fault diagnosis of Quasi-Z-source inverter. Keywords: Quasi-Z source inverter · Open-circuit fault · Average current · Park transform · Cloud model
1 Introduction At present, the grid-connected photovoltaic power generation system [1–3] can be divided into single-stage and two-stage photovoltaic power generation systems. QuasiZ-source inverter [4] can realize the function of two-stage system by unipolar power transformation, which is especially suitable for photovoltaic power generation system. Therefore, it gradually replaces the traditional inverter and becomes a hot topic of concern and research. According to the study in Reference [5], at least 80% of the faults in the inverter are caused by power device faults. Power device faults are mainly divided into open circuit faults and short circuit faults [6, 7]. When the open circuit fault occurs in the system, the current in the fault phase and the normal phase is unbalanced, and such fault may cause secondary damage to other components. When the short-circuit fault is very dangerous, it will lead to abnormal overcurrent, which may damage the inverter. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1353–1361, 2022. https://doi.org/10.1007/978-981-19-1870-4_143
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Therefore, in order to achieve fast fault detection, the inverter is usually equipped with fast fuses to turn short-circuit fault into open-circuit fault. Therefore, the open-circuit fault diagnosis of Quasi-Z-source inverter [8] is crucial to improve the reliability and stability of the power generation system. So far, there is little research on the fault diagnosis of Quasi-Z-source inverter. In reference [9], an open-circuit fault diagnosis method of Quasi-Z-source inverter based on voltage is proposed. The fault phase can be quickly diagnosed by using the discontinuous characteristics of the terminal voltage waveform. However, it cannot be specifically located whether the upper arm opens or the lower arm opens. The fault phase is cut off and the redundant bridge arm is connected to fault tolerant operation. In Reference [10], a fuzzy logic fault diagnosis method based on inverter output current was proposed. The fault was detected and located by using the average current vector trajectory error and phase interval, but this method was highly dependent on the load. Based on the existing research, the open-circuit fault diagnosis method based on current is applied to the Quasi-Z-source inverter in this paper. The fault diagnosis variables are obtained by using the average current, the average value of the absolute value of the current and the modulus of Park vector. The cloud model is used to combine the fuzziness and randomness in the uncertain concept, and the membership relationship between the obtained fault diagnosis variable value and the corresponding IGBT state is obtained. It can judge whether the IGBT has open-circuit fault and realize fault location, so as to avoid the failure to diagnose the fault in time due to excessive dependence on the threshold. And for a variety of faults occur simultaneously can also quickly and timely determine the fault phase and fault bridge arm.
2 Principle of Fault Diagnosis of Quasi-Z Source Inverter 2.1 Fault Classification According to the different characteristics of the output current waveform when the opencircuit fault occurs, the open-circuit fault can be divided into four categories and 21 types. The specific fault types are shown in Table 1. Table 1. Fault classification Fault type
Fault characteristics
Fault location
I
Single IGBT open circuit fault
S1 , S2 , S3 , S4 , S5 , S6
II
Two IGBT open circuit faults in the same bridge arm
S1 & S4 , S3 & S6 , S5 & S2
III
Two IGBT open circuit faults on different sides of different bridge arms
S1 & S6 , S1 & S2 , S3 & S4 S3 & S2 , S5 & S4 , S5 & S6
IV
Two IGBT open circuit faults on the same side of different bridge arms
S1 & S3 , S1 & S5 , S3 & S5 S4 & S6 , S4 & S2 , S6 & S2
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When the third and fourth types of faults occur, for each bridge arm, it belongs to a single IGBT open-circuit fault. Therefore, this article only studies the first and second types of faults, and no longer analyzes the third and fourth types of faults. 2.2 Single IGBT Open Circuit Fault Diagnosis
-
VC2
+
+
C2 + Vin -
L1
D
+ L2
C1
VC1 -
S1
+ Vdc
-
S1
S3
S5
S4
S6
S2
Vdc i1 -
Fig. 1. A-phase upper side IGBT open circuit
S4
Fig. 2. Current path after open circuit of upper IGBT of A-phase
As shown in Fig. 1, S1 has an open-circuit fault: A-phase current will only pass through the freewheeling diode on S4 , and eventually decay to zero, then the positive half of A-phase current is approximately zero. The current path is shown by the arrow in Fig. 2. The following relationship can be used to classify each phase current sample as whether it is close to zero, which is defined as a near zero judgment signal [11] ωl (n): 1, |il (n)| ≤ K0 ωl (n) = (1) 0, |il (n)| > K0 Average near zero judgment signal: Wl (n): Wl (n) =
N 1 ωl (n) N
(2)
n=1
In the formula: l represents the three phases of A, B, and C; n represents the sampling point; K0 represents the threshold. According to the experiment;N represents the total number of samples in each cycle. According to the average current value, a fault diagnosis strategy can be formulated when a single IGBT fails. Average phase current ilav : ilav =
N 1 il(n) N
(3)
n=1
Average value of absolute value of phase current ilabs : ilabs =
N 1 il(n) N n=1
(4)
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The ratio fls between the average value ilav of the phase current amplitude and the average value ilabs of the absolute value can be obtained: fls =
ilav
(5)
ilabs
In the formula: s means a single IGBT has failed. In order to avoid the misdiagnosis caused by the sudden change of the current when the fault occurs, the fault diagnosis variable Pls is obtained by multiplying the two variables Wl (n) and fls . Pls = Wl (n)fls = Wl (n)
ilav
(6)
ilabs
The IGBT state is divided into three states: the upper IGBT is open, no single IGBT is open, and the lower IGBT is open, which are represented by H , Z and L respectively. The theoretical value of Pls is shown in Table 2. Table 2. Quasi-Z source inverter single IGBT state IGBT state
Pls Theoretical value
Open IGBT on the upper side H
−0.5
No single IGBT open circuit occurred N
0
Open IGBT on the lower side L
0.5
2.3 Fault Diagnosis of Open Circuit of Two IGBTs in the Same Bridge Arm -
VC2
+
+
C2 + Vin -
L1
D
+ L2
C1
VC1 -
S1
+ Vdc
-
S1
S4
S3
S6
S5
S2
Fig. 3. A phase two IGBT open circuit
Vdc -
S3 i1=0
S4
S6
S5 i2 S2
i3
Fig. 4. Current path after A-phase two IGBT open circuit
As shown in Fig. 3, there is only one situation after S1 and S4 open-circuit faults. Neither S1 nor S4 can work normally. The current path is shown by the arrow in Fig. 4. When two IGBTs in the same bridge arm fail, the average value of the absolute value of the phase current can be used Develop a fault diagnosis strategy.
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Let the initial phase be 0◦ , then Park transformation: ⎧ 2 1 1 ⎪ ⎪ id = ia − ib − ic ⎨ 3 3 3 1 1 ⎪ ⎪ ⎩ iq = √ ib − √ ic 3 3
(7)
The modulus of the ideal current Park vector I : I = id2 + iq2
(8)
The average value ilabs of the absolute value of the phase current is normalized, and the ratio with the Park [12] vector modulus is used as the fault diagnosis variable Pld . −
i
Pld =
labs
(9)
I
In the formula: d represents the failure of two IGBTs. The IGBT states are divided into two states: two IGBT open circuits in the same bridge arm and two IGBT open circuits in the same bridge arm did not occur, denoted by Y and N respectively. The theoretical value of Pld is shown in Table 3. Table 3. Quasi-Z source inverter with IGBT status of the same bridge arm IGBT state
Pld Theoretical value
Two IGBTs in the same bridge arm are open Y
0
There is no open circuit of two IGBTs in the same bridge arm N
[0.5, 0.7]
2.4 Fault Diagnosis and Location Based on Cloud Model In this paper, the cloud model is used to determine the membership relationship between the fault diagnosis variables Pls and Pld and the IGBT state and the occurrence of the fault can be judged when the fault diagnosis variables just deviate from the normal value, so as to avoid excessive reliance on the threshold and the inability to diagnose in time (Figs. 5 and 6).
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1
0.8
0.8
0.6 0.4 0.2
No single IGBT open circuit occurred Z
Upper bridge arm failure H
0 -0.5
-0.25
0
Lower bridge arm failure N
0.23
Membership
Membership
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0.4 Two IGBTs in the same bridge arm open circuit Y
0.2 0
0.5
Fault diagnosis variables
Fig. 5. Single IGBT open circuit Pls membership degree
0.6
0
Two IGBTs in the same bridge arm are not open N
0.2 0.3 0.4
0.6
Fault diagnosis variables
Fig. 6. Two IGBTs in the same bridge arm open circuit Pld membership degree
3 Simulation 3.1 Simulation Environment An SVPWM modulated quasi-Z-source inverter model is built in the Matlab/Simulink environment, and the four open-circuit faults are simulated using the fault diagnosis method proposed in this paper. The parameter settings of the Quasi-Z source inverter in the photovoltaic power generation system are shown in Table 4. Table 4. Quasi-Z source inverter parameters Parameter
Numerical value
Input voltage Vin /V
120
DC bus voltage Vdc /V
200
Inductance L1 /mH
1.5
Inductance L2 /mH
1.5
Capacitance C1 /µF
3.2
Capacitance C2 /µF
3.2
Operating frequency fs /kHz
10
3.2 Single IGBT Open Circuit Fault Simulation After an open-circuit fault occurs on the upper IGBT of A-phase within 0.1 s, the waveform is shown in Fig. 7, and the positive half of the A-phase current is missing. The fault diagnosis result is shown in Fig. 8.
a
Currents(A)
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3.3 Simulation of Two IGBT Open Circuit Faults in the Same Bridge Arm
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3.4 Simulation of Open-Circuit Faults of IGBTs on Different Sides of Two Bridge Arms After an open-circuit fault occurs on the upper side of the A-phase and the lower side of the B-phase IGBT in 0.1 s, the waveform diagram is shown in Fig. 11. The fault diagnosis result is shown in Fig. 12. 3.5 Simulation of Open-Circuit Faults of IGBTs on the Same Side of Two Bridge Arms The A-phase upper IGBT and the B-phase upper IGBT have an open-circuit fault within 0.1 s. In this case, the C-phase lower-side IGBT cannot be turned on either, that is, the three IGBTs have open-circuit faults at the same time. The waveform diagram is shown in Fig. 13. The fault diagnosis result is shown in Fig. 14.
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4 Conclusion This paper proposes a fault diagnosis method for the open-circuit fault of the Quasi-Zsource inverter in the photovoltaic power generation system. The fault diagnosis method can diagnose and locate a variety of fault conditions, and meet the reliability and stability requirements of the photovoltaic power generation system. The feasibility of the method is verified by simulations of four failure situations. Acknowledgement. This work was supported by the National Natural Science Foundation of China under Grant (U1804149).
References 1. Xu, J., Xie, S., Zhang, B.: Overview of current control techniques for grid-connected inverters with LCL filters in distributed power generation systems. Chin. Soc. Electr. Eng. 35(16), 4153–4166 (2015). (in Chinese) 2. Shi, M., Yin, R., Jiang, W., Wang, Y., et al.: Overview of distributed photovoltaic flexible grid-connected cluster control technology. Electr. Measur. Instrum. (2021). (in Chinese)
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3. Ren, M., Wu, H., Liu, X.: Research on new switched inductance quasi-z source inverter for photovoltaic grid-connected. Power Electron. Technol. 54(02), 80–84+119 (2020). (in Chinese) 4. Peng, F.Z.: Z-source inverter. IEEE Trans. Ind. Appl. 32(02), 504–510 (2003) 5. Cecati, C., Oscar Di Tommaso, A., Genduso, F., et al.: Comprehensive modeling and experimental testing of fault detection and management of a nonredundant fault-tolerant VSI. IEEE Trans. Indus. Electron. 62(06), 3945–3954 (2015) 6. Yang, S., Xiang, D., Bryant, A., et al.: Condition Monitoring for Device Reliability in Power Electronic Converters: A Review (2010) 7. Choi, U.-M., Blaabjerg, F., Lee, K.-B.: Study and handling methods of power IGBT module failures in power electronic converter systems. IEEE Trans. Power Electr. 30(5), 2517–2533 (2015). https://doi.org/10.1109/TPEL.2014.2373390 8. Peng, F., Fang, X., Gu, B., et al.: Z source converter. J. Electrotech. Technol. 02, 47–51 (2004). (in Chinese) 9. Yaghoubi, M., Moghani, J.S., Noroozi, N., et al.: IGBT open-circuit fault diagnosis in a Quasi-Z-Source inverter, 66(04), 2847–2856 (2018) 10. Song, B., Nie, S., Li, X., et al.: Open-circuit fault diagnosis of Z-source inverter via deep neural network. In: Chinese Automation Congress (CAC) (2020) 11. Zidani, F., Diallo, D., Benbouzid, M.E.H., et al.: A fuzzy-based approach for the diagnosis of fault modes in a voltage-fed PWM inverter induction motor drive. IEEE Trans. Indus. Elect. 55(02), 586–593 (2008) 12. Peuget, R., Courtine, S., Rognon, J.P.: Two knowledge-based approaches to fault detection and isolation on a PWM inverter. In: Proceedings of the 1997 IEEE International Conference on Control Applications (1997) 13. Sleszynski, W., Nieznanski, J.: Open-transistor fault diagnostics in voltage-source inverters by analyzing the load currents. IEEE Trans. Industr. Electron. 56(11), 4681–4688 (2009) 14. Ren, X., Wan, H., Yu, X., et al.: Fault diagnosis of open circuit of three-level inverter based on park transformation. Ind. Min. Autom. 46(05), 82–86+93 (2020). (in Chinese)
Real-Time Demand Response Interactive Behavior Model of Electric Vehicle Cluster Ye Yong(B) , Yin Zhou, and Xiaobo Mao State Grid Jiangsu Electric Power Co., Ltd., Wuxi Power Supply Branch, Wuxi 214062, China [email protected]
Abstract. The interactive behavior model of electric vehicle cluster participating in real-time demand response is established by the combination of model and data driven method. The real-time demand response interactive behavior model is based on the physical model of electric vehicle battery charge and discharge. Firstly, the interaction dispatching capacity and dispatching cost are calculated based on the physical model. Secondly, considering the subjective willingness of the owner to participate in the response, and based on the historical data of the owner’s interactive behavior, the probability model of response is established by using the statistical machine learning method. Then the real-time demand response interactive behavior model of electric vehicle cluster is obtained by aggregating multiple electric vehicles. The effectiveness of the proposed method is verified by simulation examples with 100 electric vehicles in a certain region. Keywords: Electric vehicle cluster · Demand response · Statistical machine learning · Interactive behavior model
1 Introduction In recent years, electric vehicle demand response technology has become the focus of research at home and abroad. Compared with the general load, electric vehicles have many advantages such as rechargeable, storable, rechargeable, flexible in time and space, and are important flexible resources involved in demand response [1]. At the same time, electric vehicles have the characteristics of a large number but small individual energy storage capacity. Therefore, the participation of electric vehicles in demand response in clusters has become an important form of electric vehicles participating in grid interaction [2]. Electric vehicle clusters will become an important subject in the future power system and will play an important role in the dispatch and operation of new power systems [10]. The real-time demand response interactive behavior model of electric vehicle clusters studied in this paper is the key for electric vehicle clusters to participate in future new power system dispatch operations [3, 4]. For the power control center, mastering the interactive behavior model of electric vehicle clusters participating in demand response is a prerequisite, including interactive dispatching capabilities and dispatching costs, as well as actual response behaviors in the process of participating in demand response. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1362–1371, 2022. https://doi.org/10.1007/978-981-19-1870-4_144
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At present, there have been related researches in the interactive model of electric vehicle charging load participating in grid dispatching operation [3–13]. Liu et al. [3] established the time response capability model of the battery swap station based on the state parameters of the battery pack in the electric vehicle swap station, aiming to guide the power swap station operator to formulate the corresponding charging plan according to the operation target of the grid enterprise; Yang et al. [4] established an analysis model of electric vehicle dispatchability based on the degree of battery loss, user credit and reverse power supply capability of electric vehicles; Zhu et al. [5] proposed the uncertainty response model of electric vehicle charging and discharging, and analyzed the change law of charging and discharging potential and response fluctuation degree with economic incentives; Gan et al. [6] set up a real-time interactive scheduling model for electric vehicle clusters with the goal of minimizing daily load fluctuations and dispatch penalties; Zhang et al. [7] considered the state of charge and charge and discharge of electric vehicles, and proposed the day-ahead and intraday response capability evaluation model of electric vehicle virtual power plants; In [8], a globally optimal scheduling scheme and a locally optimal scheduling scheme for EV charging and discharging are proposed; Xu et al. [9] constructed the polyhedral uncertainty of electric vehicle clusters with the three dimensions of time, space and power interval, as well as the user’s preference being taken into account; Zhang et al. [10] established an evaluation method for vehicle-to-grid capacity of large-scale plug-in electric vehicles, which makes evaluating vehicle-to-grid capacity convenient; Yao et al. [11] designed a real-time charging scheme to coordinate charging and accommodate demand response of electric vehicles; Li et al. [12] developed a charging and discharging scheduling method based on deep reinforcement learning for a single EV user to minimize charging costs while ensuring that the EV is fully charged; Zhou et al. [13] considered that traditional electric vehicle optimization scheduling methods based on optimization models face the problems of difficulty in obtaining accurate model parameters and high calculation pressure in practical applications, and proposed a real-time automatic optimization scheduling model for electric vehicle clusters based on K-means clustering algorithm and long short-term memory neural network. Based on the above researches, this paper focuses on the interactive behavior modeling needs of electric vehicle clusters by the power control center, and uses a combination of model and data-driven methods to establish an interactive behavior model for electric vehicle clusters to participate in real-time demand response. The first is to calculate the interactive dispatching ability and dispatching cost based on the charging and discharging physical model of the electric vehicle battery. Secondly, considering the subjective willingness of the owner to participate in the response, and using statistical machine learning based on historical data to establish a probability model of whether to participate in the response. Then the real-time demand response interactive behavior model of electric vehicle cluster is obtained by aggregating multiple electric vehicles. Finally, the simulation results verify the effectiveness of the proposed method in this paper.
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2 Real-Time Demand Response Interactive Behavior Model of Electric Vehicles This paper adopts the method of combining model and data-driven methods to establish an interactive model of electric vehicle cluster participating in demand response. The first is to establish the interactive dispatching ability and dispatching cost based on the charging and discharging physical model of the electric vehicle battery. Secondly, considering the subjective willingness of the owner to participate in the response, and using statistical machine learning based on historical data to establish a probability model of whether to participate in the response. Finally, the real-time demand response interactive behavior model of electric vehicle cluster is obtained by aggregating multiple electric vehicles. The overall steps are shown in Fig. 1. Interactive behavior model of electric vehicle cluster
Interactive behavior model of electric vehicles History data of interactive behavior
Statistical machine learning Battery charging and discharging physical model
Response probability model Interactive dispatching cost Interactive dispatching ability
Fig. 1. Modeling process of demand response interactive model of electric vehicle cluster.
2.1 Physical Model of Charging and Discharging of Electric Vehicle Battery At time t, the charging and discharging physical model of the i-th electric vehicle battery can be expressed as: SOCi (t + t) = SOCi (t) + Pi (t)t
(1)
where SOCi (t) represents the remaining capacity of the battery; Pi (t) represents the charge and discharge power of the battery, which a positive value represents charging, and a negative value represents discharge; t represents the duration of the charge and discharge power Pi (t). The remaining battery capacity satisfies the following constraints: Simin ≤ SOCi (t) ≤ Simax
(2)
where Simin represents the minimum allowable capacity of the battery; Simax represents the maximum allowable capacity of the battery.
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The charge and discharge power Pi (t) satisfies the following constraints: −si (t)Pid max ≤ Pi (t) ≤ si (t)Pic max
(3)
where Pid max represents the maximum allowable discharge power of the battery; Pic max represents the maximum allowable charging power of the battery; si (t) represents the adjustable state of the electric vehicle battery, which can be expressed as follows: 1, Status of parking and charging (4) si (t) = 0, Parking not charging or driving The state of parking and charging means that the vehicle is parked in a charging parking space and connected to a charging pile, so that it can accept charging and discharging control commands. 2.2 Demand Response Interactive Model of Electric Vehicle The dispatching power of electric vehicles participating in demand response satisfies the following constraints: ⎧ ⎨ Pi (t) ≤ si (t) Pic max − Pi (t) (5) ⎩ Pi (t) ≥ −si (t) Pid max + Pi (t) where Pi (t) represents the dispatching power of the electric vehicle, which a positive value represents an increase in the charging power, and a negative value represents a decrease in the charging power. The dispatching cost of electric vehicles participating in demand response can be expressed as:
λi (t) = fi (t) − fi (t)
(6)
where λi (t) denotes the dispatching cost of electric vehicles participating in demand response; fi (t) represents the total charge and discharge cost of electric vehicles participating in demand response; fi (t) represents the total charge and discharge cost of electric vehicles not participating in demand response. The fi (t) includes two parts: charge and discharge costs fi1 (t) and demand response compensation benefits fi2 (t) during the demand response period, which are calculated as follows:
fi (t) = fi1 (t) − fi2 (t) The specific calculation formula of each part is as follows:
t+td fi1 (t) = [(Pi (t) + Pi (t))λ0 (t)d τ ] τ =t
fi2 (t) =
t+td τ =t
[Pi (t)λdr (t)d τ ]
(7)
(8) (9)
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where td represents the duration of the demand response; λ0 (t) represents the electricity price of charging and discharging; λdr (t) represents the demand response compensation price. The calculation formula for the total charge and discharge cost fi (t) of electric vehicles running at the original charge and discharge predicted power without participating in demand response is as follows: fi (t) =
te
[Pi (t)λ0 (t)]
(10)
τ =t
Whether electric vehicles participate in demand response is still affected by the subjective willingness of the owner, and the subjective willingness of the owner is uncertain. Based on the historical data of the owner’s interactive behavior, this paper uses statistical machine learning to establish its probability model, which is expressed as follows:
y Ni 1, Pil (t), SOCim (t) dr (11) pi (t) = si (t)
Ni 1, Pil (t), SOCim (t) where pidr (t) represents the probability of participating in demand response; Pil (t) represents the charging and discharging power Pi (t) of the electric vehicle is in the l-th interval; SOCim (t) represents the remaining capacity SOCi (t) of the electric vehicle is
in the m-th interval; Ni 1, Pil (t), SOCim (t) represents the historical statistical times of receiving demand response invitation that the electric vehicle is in the adjustable state (si (t) = 1), and the charging and discharging power Pi (t) is in the l-th interval and y SOCi (t) is in the m-th interval; Ni 1, Pil (t), SOCim (t) represents the historical statistical times of participation in demand response when the electric vehicle is in the adjustable state (si (t) = 1), and the charge and discharge power Pi (t) is in the l-th interval and SOCi (t) is in the m-th interval. Among them, the calculation formulas of Pil (t) and SOCim (t) are as follows:
Pi (t) + Pid max L l Pi (t) = round (12) Pic max + Pid max
Pi (t) + Pid max L l Pi (t) = round (13) Pic max + Pid max where round(*) represents the function of rounding down; L represents the number of intervals into which charge and discharge power are divided; M represents the number of intervals into which the battery capacity is divided.
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3 Real-Time Demand Response Interactive Behavior Model of Electric Vehicle Clusters Based on the demand response interaction model of the above single electric vehicle, the demand response interaction model of the electric vehicle cluster can be obtained through aggregation and superposition, where the dispatching power of the electric vehicle cluster participating in the demand response satisfies the following constraints: ⎧ N ⎪ c max
⎪ dr ⎪ P(t) s ≤ − P P (t)p (t) (t) ⎪ i i i i ⎪ ⎨ i=1 (14) N ⎪ ⎪ ⎪ ⎪ si (t)pidr (t) Pid max + Pi (t) ⎪ ⎩ P(t) ≥ − i=1
where P(t) represents the dispatching power of the electric vehicle cluster, which a positive value represents an increase in the charging power, and a negative value represents a decrease in the charging power. The dispatching cost of electric vehicle cluster participation in demand response can be expressed as: ˆ
λ(t) =
j
λj (t)
(15)
j=1
where λ(t) represents the dispatching cost of the electric vehicle cluster participating in the demand response; j denotes the number of each electric vehicle in the electric vehicle cluster in ascending order of its unit dispatching cost; ˆj should meet the following cluster dispatching power constraints: ˆ
j pjdr (t)Pj (t) ≥ P(t)
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j=1
4 Simulation Example Analysis This paper takes 100 electric vehicles as an example for analysis. The charging and discharging prices of electric vehicles in this area are shown in Table 1, and the demand response compensation price is 4 RMB/kWh. The charging and discharging power limits and remaining capacity constraints of electric vehicle batteries are shown in Table 2, where the reference value of the remaining capacity is 48 kWh of electric vehicle battery capacity.
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Serial number
Starting time
End Time
Electricity price/[RMB/kWh]
1
00:00
08:00
0.30
2
08:00
12:00
1.10
3
12:00
17:00
0.75
4
17:00
21:00
1.10
5
21:00
24:00
0.75
Table 2. The power limits and SOC limits of electric vehicles Simin
Simax
Pid max
Pic max
0.1 p.u
1.0 p.u
60 kW
60 kW
4.1 Example Analysis of Electric Vehicle The controllable state of 100 electric vehicles in the area at a certain moment is shown in Fig. 2, in which the controllable state is 1 means that the electric vehicle is in a charging parking spot and connected to a charging pile, and can participate in demand response control. The real-time charge and discharge power is shown in Fig. 3, and the remaining battery capacity is shown in Fig. 4.
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Fig. 2. The dispatchable states of the 100 electric vehicles at a certain time.
Dispatching Capacity Model. According to the dispatching power model of electric vehicles participating in demand response described in this paper, the upper and lower limits of the dispatching power of each electric vehicle are calculated as shown in Fig. 3. Dispatching Cost Model. According to the dispatching cost model of electric vehicles participating in demand response described in this paper, the dispatching cost of each electric vehicle is calculated. The dispatching cost curve of electric vehicles is shown in
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Fig. 3. The charge/discharge powers and dispatching capacity of the 100 electric vehicles at a certain time. 1 0.8 0.6 0.4 0.2 0
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Fig. 4. The battery SOCs of the 100 electric vehicles at a certain time.
Dispatching price/(RMB/kWh)
Fig. 5, in which the current moment is the peak period of charging and discharging prices, and the price is 1.1 RMB/kWh. It can be seen from Fig. 5 that the unit dispatching cost of all electric vehicles is −2.9 RMB/kWh, and a negative value indicates that electric vehicles can obtain benefits.
-1.5 -2 -2.5 -3 -3.5 -4
0
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Fig. 5. The dispatching cost curve of the electric vehicles.
Demand Response Probability Model. According to the probability model of electric vehicles participating in demand response described in this paper, and based on the
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historical data of 100 electric vehicles in the area, the probability of each electric vehicle participating in demand response is calculated, as shown in Fig. 6.
1 0.8 0.6 0.4 0.2 0
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Fig. 6. The demand response probabilities of the 100 electric vehicles at a certain time.
4.2 Example Analysis of Electric Vehicle Clusters
Dispat chin g cost/RMB
Finally, according to the calculation formula of the dispatching capacity of the electric vehicle cluster described in this paper, the upper and lower limits of the dispatching capacity of the 100 electric vehicle clusters in the region are 1092.6 kW and −2822.3 kW respectively. According to the calculation formula of the dispatching cost of the electric vehicle cluster participating in the demand response, the dispatching cost curve of the 100 electric vehicle cluster in the region is shown in Fig. 7. 10000
5000
0
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-2000
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Fig. 7. The dispatching cost curve of the 100 electric vehicle cluster.
5 Conclusion This paper focuses on the real-time interactive behavior modeling needs of electric vehicle clusters by the electric power control center, and establishes the interactive behavior model of electric vehicle clusters participating in real-time demand response by using
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a combination of model and data-driven methods. The analysis results of simulation examples verify the effectiveness of the method in this paper. Based on the charging and discharging physics model of electric vehicle batteries, interactive dispatching capabilities and dispatching costs can be calculated; A probability model of whether to response can be established using a statistical machine learning method based on historical data of vehicle owners’ interactive behaviors; The demand response interaction model of the electric vehicle cluster can be obtained by aggregating the demand response interaction model of multiple electric vehicles.
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Author Index
B Bai, Liangjun, 995 Bao, Yuqing, 657 Bo, Kai, 50 C Cai, Liangliang, 747 Cai, Wei, 1027 Cai, Xiang, 309, 347 Cai, Yumeng, 416 Cao, Bin, 130 Cao, Biyue, 1012, 1075, 1100 Cao, Xiaojun, 713 Cao, Yuchen, 1067 Cao, Zhuolin, 668 Che, Chuanqiang, 527 Chen, Alian, 926 Chen, Congcong, 224 Chen, Daopin, 511 Chen, Jia Wang, 628 Chen, Jiaming, 694 Chen, Jian, 503, 1208, 1216 Chen, Jianning, 390 Chen, Junquan, 50 Chen, Kang, 686 Chen, Liang, 1224 Chen, Lixing, 657 Chen, Lixue, 1, 906 Chen, Mengru, 503, 1208, 1216 Chen, Shaohui, 12 Chen, Xiaogao, 978 Chen, Xinyi, 668 Chen, Xiong, 844 Chen, Yanwei, 79
Chen, Yongtao, 445 Chen, Zhexing, 464 Chen, Zhilei, 454 Chen, Zhiyuan, 926 Cheng, Wei, 686 Cheng, Wenping, 59 Cheng, Yuanyang, 1051 Chi, Dianyu, 179 Chi, Yuan, 1233 Chong, Jiali, 527 Cong, Bingyu, 755 Cong, Songlin, 1254 Cui, Huifeng, 1051 Cui, Shumei, 917 Cui, Zhiming, 69 Cui, Zongze, 1036 D Dai, Shaotao, 1317 Dai, Weiju, 765 Deng, Jun, 813 Deng, Wei, 1089 Ding, Guojun, 731 Ding, Haohui, 648 Ding, Xue, 1185 Ding, Yi, 936 Dong, Bei, 321, 519, 936 Dong, Shuai, 261, 270, 495 Dong, Tianyu, 606 Dou, Wei, 291 Dou, Xun, 713 Du, Yu, 179 Du, Zhiye, 34 Duan, Dapeng, 1233
© Beijing Paike Culture Commu. Co., Ltd. 2022 X. Liang et al. (Eds.): The proceedings of the 16th Annual Conference of China Electrotechnical Society, LNEE 890, pp. 1373–1379, 2022. https://doi.org/10.1007/978-981-19-1870-4
1374 F Fang, Hui, 445, 1122 Feng, Fan, 1142 Feng, Ke, 678, 844 Feng, Ruming, 527 Feng, Yingchun, 713 Feng, Zhihui, 1027 Fu, Yijia, 785 G Gao, Bing, 1012 Gao, Chao, 309, 347 Gao, Chunjia, 224 Gao, Fanqiang, 1334 Gao, Feng, 1115 Gao, Song, 1270 Gao, Wei, 1157 Gao, Yifan, 270 Gao, Zhi Qiang, 834 Gao, Zhixuan, 1334 Ge, Jiamin, 390 Ge, Xia, 130 Ge, Yifan, 1, 906 Geng, Fei, 408 Geng, Yingsan, 179 Gong, Jianping, 1100 Gong, Shimin, 747 Gong, Yujia, 886 Guan, Feng, 1224 Guan, Honglu, 731 Guo, Huishan, 1353 Guo, Jin, 628 Guo, Lei, 731 Guo, Mengbo, 1353 H Han, Lu, 813 Han, Mengting, 616 Han, Minxiao, 399 Han, Ruoyu, 1067 Han, Rushuai, 648, 694 Han, Tian, 1193 Han, Xue, 139 Hao, Wenbin, 188, 299 He, Lingyun, 188 He, Zilan, 511 Hong, Ying, 747 Hou, Lei, 1185 Hou, Wenjun, 765 Hu, Jin, 765 Hu, Jinming, 917 Hu, Qinran, 648, 668, 694 Hu, Wei, 803 Huang, Daochun, 859, 1027 Huang, Haihong, 773
Author Index Huang, Jinkui, 1200 Huang, Liang, 570 Huang, Meng, 995 Huang, Qingdan, 552 Huang, Zheng, 503 Huang, Zhiqiang, 279 Hui, Hui, 360 Hui, Li, 986 Huo, Xiaolin, 867 J Ji, Kunpeng, 429 Ji, Xiu, 1043 Ji, Zhenya, 657 Jia, Guanglong, 1326 Jiang, Lin, 813 Jiang, Songfang, 503, 1208, 1216 Jiang, Wang, 232 Jin, Hailu, 408 Jin, Shi, 170, 232 Jin, Wuhen, 170, 232 Jing, Ming, 1326 K Kang, Shenglin, 1059 Kong, Weifeng, 877 Kong, Xianghao, 241 L Li, Chen, 1067 Li, Chengrong, 224 Li, Cong, 1043 Li, Dexin, 1270 Li, Gen, 34 Li, Genxu, 1353 Li, Guofeng, 139 Li, Hao, 657 Li, Hao Nan, 628 Li, Hongyu, 1177 Li, Houxu, 584 Li, Hui, 944, 1004 Li, Huipeng, 859 Li, Jian, 1027 Li, Jianfu, 1004 Li, Jiangtao, 560 Li, Jianlin, 480 Li, Jifang, 1353 Li, Jin, 471 Li, Jin Ping, 834 Li, Jingshong, 139 Li, Kaixiang, 103 Li, Kun, 552 Li, Mengyao, 739 Li, Mengzan, 678 Li, Mingtao, 130
Author Index Li, Peishuai, 678 Li, Pengfei, 119 Li, Pinghui, 79 Li, Pingyuan, 813 Li, Qi, 79, 90 Li, Qinghe, 944 Li, Shuai, 747 Li, Sisi, 1278 Li, Wendong, 785 Li, Yanming, 24, 160 Li, Yao, 160 Li, Yaxin, 480 Li, Yiqi, 739 Li, Yuan Yuan, 834 Li, Yuping, 471 Li, Zan, 803 Li, Zhenyu, 1012, 1075, 1100 Li, Zhi, 705 Li, Zhiyuan, 42 Li, Zhun, 1150 Li, Zongsheng, 291 Liang, Jie, 1059 Liang, Jinxiang, 886 Liang, Jun, 1208, 1216 Liang, Tao, 628 Liang, Zhizhuo, 299 Liao, Chenglin, 897 Liao, Ruijin, 1059 Lin, Chen, 495 Lin, Cheng, 208 Lin, Xiong, 103 Lin, Xuehong, 429 Liu, Dong, 511 Liu, Dongqing, 578 Liu, Guangwei, 216 Liu, Jiahong, 917 Liu, Jihong, 877 Liu, Jinjun, 200 Liu, Kun, 1242 Liu, Li, 995 Liu, Qingzhao, 90 Liu, Renkuan, 1004 Liu, Rui, 1067 Liu, Shipeng, 1200 Liu, Shuai, 170 Liu, Tao, 1131 Liu, Tianyu, 527 Liu, Tong, 926 Liu, Wanyu, 1242 Liu, Wei, 360 Liu, Wenxu, 1302 Liu, Xinyuan, 678 Liu, Yang, 731 Liu, Yangyang, 897
1375 Liu, Yaozong, 1278 Liu, Yong, 464 Liu, Yuelin, 1292 Liu, Zehui, 309 Liu, Zhendong, 1224 Liu, Zhiqi, 1278 Liu, Zhiyuan, 179 Liu, Ziqi, 1115 Lu, Guanghui, 1200 Lu, Hai Lun, 834 Lu, Haifeng, 636 Lu, Ming, 309, 347 Lu, Rengui, 261 Lu, Wenqin, 1345 Luan, Xiaoming, 535 Luo, Chunfeng, 511 Luo, Haiyun, 383 Luo, Zhiyao, 606 Lv, Fengming, 1233 Lv, Zhining, 1317 Lv, Zhipeng, 1168 M Ma, Bendong, 69 Ma, Chi, 560 Ma, Chuntian, 803 Ma, Guoming, 429 Ma, Hui, 179 Ma, Limin, 399 Ma, Ning, 360 Ma, Siyuan, 606 Ma, Xiaoxiao, 160 Ma, Xikui, 964 Maladen, Romain, 636 Man, Jinhui, 552 Mao, Xiaobo, 1362 Meng, Song, 1302 Meng, Xiangkun, 399 Meng, Xiaoqian, 803 Meng, Zhigao, 188, 299 Mu, Haibao, 606 N Na, Tuopu, 495 Ni, Yuhui, 755 Nie, Xiaofei, 616 Ning, Zhongkai, 1122 Niu, Huanna, 291 P Pan, Shuguo, 90 Pan, Wenwu, 309, 347 Pei, Lei, 437 Pei, Pengchao, 130 Pei, Wei, 1089
1376
Author Index
Peng, He, 445 Peng, Jiaoyang, 416 Peng, Junzhe, 309, 347 Peng, Pan, 299 Peng, Shuai, 279 Perrone, Michel, 636 Preve, Christophe, 636 Pu, Haitao, 1254, 1262
Sun, Hongyan, 12, 1242 Sun, Meimei, 336 Sun, Peng, 416 Sun, Xun, 824 Sun, Ying, 834 Sun, Yujiang, 232 Sun, Yutian, 917 Sun, Zihan, 560
Q Qi, Bo, 224 Qi, Ruzhi, 877 Qian, Guochao, 765 Qian, Li, 291 Qiao, Min, 995 Qiao, Zhi, 544 Qin, Changsong, 936 Qin, Shihong, 1, 906 Qin, Weiqi, 429 Qin, Zhidong, 877
T Tan, Hongtao, 944 Tan, Xiaojun, 578 Tang, Bin, 747 Tang, Fen, 1177 Teng, Xianliang, 686 Tian, Maojie, 803 Tian, Ye, 372
R Ran, Yao, 986 Ren, Qicai, 926 Ren, Xue Yu, 628 Ruan, Jiangjun, 859, 1027 S Sang, Linwei, 694 Sang, Ya Li, 834 Shan, Yang, 1168 Shao, Jinghui, 964 Shao, Linjing, 755 Shao, Ping, 713 Shao, Yunting, 372 Shen, Jingyu, 179 Shi, Jingpo, 1051 Shi, Rongbin, 429 Shi, Wei, 1193 Shi, Zhengjun, 1302 Shu, Wenxuan, 694 Si, Yunqiang, 686 Song, Haoyong, 552 Song, Kai, 270 Song, Liwei, 1036 Song, Weiqiong, 1233 Song, Yixuan, 1157 Song, Yongchao, 1012, 1075, 1100 Song, Yuyang, 329 Su, Boping, 1311 Su, Erhao, 1168 Su, Xiaoping, 188, 299 Su, Yue, 208 Summer, Raimund, 636 Sun, Haiwen, 570
W Wan, Xi, 1345 Wan, Zhiyu, 309, 347 Wang, Bangzhu, 1317 Wang, Boyu, 1036 Wang, Changbo, 90 Wang, Changquan, 383 Wang, Chao, 785 Wang, Cheng, 445, 1122 Wang, Danfeng, 119 Wang, Daocan, 739 Wang, Deshun, 437 Wang, Dong, 50, 731 Wang, Guo, 544 Wang, Hailong, 877 Wang, Heping, 1131 Wang, Housheng, 69 Wang, Jack, 636 Wang, Jianchao, 69 Wang, Jianhua, 1345 Wang, Jianqiao, 170, 216 Wang, Jiaren, 794 Wang, Jiarui, 1270 Wang, Jiawei, 964 Wang, Jiayao, 944 Wang, Jie, 978 Wang, Jingchao, 42 Wang, Kaisong, 592, 1292 Wang, Kewen, 503, 1208, 1216 Wang, Liang, 464 Wang, Nan, 926 Wang, Qing, 834 Wang, Qinglong, 336 Wang, Qiong, 527 Wang, Qisu, 1043 Wang, Rongpei, 480 Wang, Ruixue, 241
Author Index Wang, Shan, 765 Wang, Shasha, 24 Wang, Shuhong, 552 Wang, Sihan, 429, 824 Wang, Wang, 844 Wang, Wei, 249, 1177 Wang, Xiao, 1004 Wang, Xing Quan, 834 Wang, Yan, 1043 Wang, Yang, 813 Wang, Yawei, 79 Wang, Yi, 592 Wang, Yifan, 372 Wang, Yilin, 464 Wang, Yiwang, 978 Wang, Yu, 50 Wang, Yu Xiang, 834 Wang, Yufen, 1292 Wang, Yuqing, 216 Wang, Zhe, 1317 Wang, Zhenzi, 1317 Wang, Zhiqiang, 139 Wang, Zhizeng, 59 Wang, Zunxian, 535 Wei, Changhe, 877 Wei, Haikun, 437 Wei, Hao, 1036 Wei, Jianqiang, 1311 Wei, Liangliang, 578 Wen, Jun, 399 Wu, Changzhe, 867 Wu, Huijian, 584 Wu, Jun, 147 Wu, Juzhen, 224 Wu, Kena, 1292 Wu, Lihui, 511 Wu, Qian, 1150 Wu, Shouyuan, 535 Wu, Tingting, 739 Wu, Wenhua, 886 Wu, Xuezhi, 1177 Wu, Xusheng, 1157 Wu, Yi, 803 Wu, Yinan, 606 Wu, Yiping, 372 Wu, YiWen, 480 Wu, Zaijun, 648 X Xia, Lie, 454 Xiao, Renxin, 279 Xiao, Xi, 329 Xie, Beimin, 1043 Xie, Bo, 188, 299 Xie, Guanglei, 147
1377 Xie, Guangyong, 408 Xie, Hong, 1317 Xie, Jinjun, 1233 Xie, Ning, 249 Xie, Zhiwen, 249 Xing, Xiaowen, 824 Xiong, Deming, 216 Xu, Haizhen, 336 Xu, Jiansheng, 1142 Xu, Jun, 111 Xu, Junjun, 686 Xu, Lianghui, 454 Xu, Rui, 834 Xu, Shiguang, 844 Xu, Sida, 886 Xu, Tao, 1115 Xu, Weidong, 59, 844 Xu, Xiaorui, 408 Xu, Yeliu, 1326 Xu, Ying, 1317 Xu, Yiwei, 694 Xu, Yu, 834 Xu, Yuangen, 859 Xue, Bo, 1345 Xue, Jing, 188 Xue, Jinhua, 437 Xue, Mingjun, 471 Xue, Shuang, 241 Xue, Zhong, 321, 511, 519 Y Yan, Han, 1345 Yan, Jing, 179 Yan, Ping, 59 Yan, Zexin, 560 Yang, Danni, 200 Yang, Lei, 886, 1150 Yang, Lijun, 1059 Yang, Lin, 24 Yang, Qingbin, 454 Yang, Shaohua, 773 Yang, Wei, 79 Yang, Wenqiang, 824 Yang, Yang, 1059 Yang, Yu, 147 Yang, Yufeng, 686 Yao, Fuqiang, 1254, 1262 Yao, Hongwei, 160 Yao, Wei, 731 Ye, Qizheng, 616 Yong, Ye, 1362 You, Hongsen, 1233 Yu, Boyang, 200 Yu, Changzhou, 336 Yu, Jiatong, 503, 1208, 1216
1378 Yu, Peichang, 1278 Yu, Peng, 1224 Yu, Tong, 1334 Yu, Xiao, 208 Yu, Xiwen, 50 Yu, Xuan, 1200 Yu, Yue, 1004 Yu, Zhiwei, 1012, 1075, 1100 Yuan, Bin, 1004 Yuan, Dian, 648 Yuan, Jiansheng, 1200, 1233 Yuan, Jiaxin, 578 Yuan, Qing, 224 Yuan, Wei, 1067 Yuan, Yubo, 1177 Yuan, Zhe, 616 Yue, Feng, 936 Yue, Tianyu, 926 Yue, Yu, 986 Z Zang, Binbin, 705 Zeng, Peng, 188, 299 Zeng, Yunzhu, 1004 Zhang, Baichuan, 261 Zhang, Bin, 584 Zhang, Bing, 584 Zhang, Bo, 978 Zhang, Boyu, 560 Zhang, Cheng, 867 Zhang, Dandan, 309, 347 Zhang, Dongdong, 139 Zhang, Donghuai, 160 Zhang, Fengge, 216, 1326 Zhang, Guanghao, 867 Zhang, Guanjun, 785 Zhang, Hao, 471 Zhang, Haoran, 416 Zhang, Hu, 886 Zhang, Jiahui, 552 Zhang, Jiajun, 1270 Zhang, Jiexin, 1059 Zhang, Jin, 978 Zhang, Junqi, 372 Zhang, Li, 859, 1027 Zhang, Liying, 1036 Zhang, Lu, 606 Zhang, Qian, 678 Zhang, Qianfan, 261, 270, 495 Zhang, Rui, 886, 1036 Zhang, Shuqin, 408 Zhang, Tao, 471 Zhang, Weichun, 668 Zhang, Wenhui, 877 Zhang, Wenjie, 897
Author Index Zhang, Xiaojuan, 42 Zhang, Xing, 336 Zhang, Xinyu, 160 Zhang, Xinyun, 570 Zhang, Xuenan, 1193 Zhang, Yadong, 34, 103 Zhang, Yan, 200 Zhang, Yao, 321, 519, 936, 978 Zhang, Yazhou, 24 Zhang, Yisheng, 464 Zhang, Youqiang, 1122 Zhang, Youqin, 552 Zhang, Yu, 917 Zhang, Yujiao, 584 Zhang, Yunzhou, 147 Zhang, Yupeng, 347 Zhang, Zedong, 480 Zhao, Bing, 249 Zhao, Cheng, 1233 Zhao, Jian, 584, 1311 Zhao, Jianli, 464 Zhao, Jun, 527 Zhao, Ke, 1122 Zhao, Lei, 527 Zhao, Pengfei, 34 Zhao, Qingyuan, 1224 Zhao, Song, 877 Zhao, Wei, 249 Zhao, Xuetong, 1059 Zhao, Yanfang, 1262 Zhao, Yangmei, 1193 Zhao, Yanjun, 249 Zhao, Zhibin, 416 Zheng, Chengfei, 24 Zheng, Huiping, 678 Zheng, Jie, 944 Zhou, Ao, 103 Zhou, Guohua, 592, 1292 Zhou, Hua, 1311 Zhou, Jingsen, 445 Zhou, Liying, 952 Zhou, Peng, 628 Zhou, Qu, 765 Zhou, Shengming, 1311 Zhou, Yin, 1362 Zhou, Yuanxiang, 390 Zhou, Yuan-zi, 1150 Zhou, Zhiting, 944 Zhu, Bin, 705 Zhu, Chunbo, 261, 270, 495 Zhu, Hai, 628 Zhu, Kaiyang, 844 Zhu, Mingzhi, 103 Zhu, Shengyi, 1122
Author Index Zhu, Te, 445 Zhu, Xuelian, 592 Zhu, Yongxing, 1012, 1075, 1100
1379 Zhu, Zhiying, 755 Zhuang, Guanqun, 1270 Zhuang, Ying, 1089