ELECTRIMACS 2022: Selected Papers – Volume 1 3031248368, 9783031248368
This book collects a selection of papers presented at ELECTRIMACS 2021, the 14th international conference of the IMACS T
307 18 39MB
English Pages 616 [617] Year 2023
Preface to Electrimacs 2022, Volume 1
Contents
Part I Control and Power Management of Electrical Systems
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval Propulsion System Associated with Supercapacitor Energy Storage
1 Introduction
2 System Description and Modeling
2.1 Propeller Modeling
3 Experimental Results
4 Conclusion
References
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
1 Introduction
2 Design Methodology
3 Model and Parameters
3.1 General View of the Case Study
3.2 pms
3.3 fc and DC/DC Converter
3.4 Battery and DCDC Reversible Converter
3.5 dc Bus
3.6 DC/AC Converter and Motor
3.7 Ship and Propeller
3.8 Pilot
3.9 Short Circuit
4 Results
4.1 Evaluation of the Model on 30 min Travel
4.2 Faulty Study
5 Conclusion
References
Neural Network Model for Aggregated Photovoltaic Generation Forecasting
1 Introduction
2 Data Sources for the Model
2.1 Meteorological Data
2.2 Photovoltaics Plant Information
2.3 Historical Photovoltaic Energy Generation Data
3 Performance Metrics
4 Neural Network Model Description
4.1 Data Preparation
4.2 Naïve Approach
4.3 Convolutional Neural Network Approach
5 Results
6 Conclusions
References
Electrification of River Freight: Current Status and Future Trends in Europe
1 Introduction
2 Inland Freight Boats Technical Constraints
2.1 Boats Technical Constraints
2.2 River Transport Regulations
2.3 Economic Constraints
3 Reducing River Freight Emission
3.1 Alternative Fuel Boats
3.2 Battery-Electric River Freight Vessels
3.3 Hybrid Electric River Freight Vessels
4 Discussion
4.1 Key Challenges
4.2 Current Trends
5 Conclusion
References
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost DC-DC Converters
1 Introduction
2 Modeling and Conventional PI Controllers
2.1 Modeling and Representation
2.2 Conventional PI Controllers
3 Proposed Average Model-Based Sliding Mode Control Schemes
3.1 Single-Stage Sliding Mode Control Scheme
3.2 Cascade Sliding Mode Control Scheme
3.2.1 Voltage Control (Outer Loop)
3.2.2 Currrent Control (Inner Loop)
3.2.3 Control Parameters Determination
4 Results and Discussions
5 Conclusions
References
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic Pulse Width Modulation Applied to a Flying Capacitor Leg Inverter
1 Introduction
2 N-Level Generic PWM Scheme for Flying Capacitor Topology
2.1 PWM Flying Capacitor Model
2.2 Solution Set
2.3 Boundaries Expression for the Solution Set
3 Average Model of 3-Level FC Inverter
4 Average Model of 5-Level FC Inverter
5 Margins of the Degrees of Freedom λ
5.1 Margins of λ1
5.2 Margins of λ2
5.3 Margins of λ3
5.4 Influence of the D.O.F on Dynamic Behaviour of Floating Capacitor Voltages
5.5 Simulation
6 Conclusion
References
Control Strategy for Orbital O2 Tidal System Based on EMR Model
1 Introduction
2 Orbital O2 Integrated into Orkney Grid
3 Control Strategy Based on EMR
3.1 Rotor Side Control (RSC)
3.2 Grid Side Control (GSC)
4 Marine Current Profile and EMR Model Results
5 Conclusions
References
A Hybrid Fourier and Wavelet-Based Method for the Online Detection and Characterization of Subsynchronous Oscillations
1 Introduction
2 Hybrid SSO Detection and Characterization
2.1 Outline of the Proposed Hybrid Method
2.2 Fast Fourier Transform
2.3 Wavelet Analysis
3 Numerical Results
3.1 SSO Detection and Characterization
3.2 Computation Time Performance
4 Conclusion
References
Optimal Sizing for Fuel Cell Hybrid Power Sources Under Reliability and Energy Performance Indexes
1 Introduction
2 Optimal Design Approach Based on Imbricated Architecture
3 Imbricated Optimisation Loops
3.1 External Optimisation Loop
3.2 Internal Optimisation Loop
3.2.1 Energy Consumption Module
3.2.2 Reliability Module
4 Simulation Results and Analysis
5 Conclusions
References
Compliance Evaluation of WTG and WPP Controllers for Self and Black Start Operation
1 Introduction
2 System Description
3 Operational and Stability Requirements
4 Simulation Test Cases
5 HVAC Connected WTG Control
6 Compliance Evaluation
6.1 Off-Shore AC Grid Start-Up Operation
6.2 Off-Shore HVAC Substation Energisation
6.3 HVAC Export Cable Energisation
7 Conclusions
References
Experimental Study of the Cold Start Capabilities of a Closed Cathode PEM Fuel Cell
1 Introduction
1.1 Shut Down Strategies
1.2 Cold Start Strategies
2 Experimental Methods
2.1 Experimental Setup
2.2 Testing Procedure
3 Results and Discussions
3.1 Successful Cold Start
3.2 Failed Cold Start
4 Conclusion
References
Part II Modelling and Simulation of Power Electronics Systems
Discussion on Classification Methods for Lifetime Evaluation of a Lab-Scale SiC MOSFET Power Module
1 Introduction
2 From the Module Failure Study to the Signature
2.1 SiC MOSFET Based Power Modules
2.2 Possible Failure Mechanisms
2.3 How to Constitute a Relevant Failure Signature?
3 Classification of a 10-Dimension Signature
3.1 Reduction of the Signature
3.2 Classification with SVM and kNN Using S3 and S10
3.3 With the Neural Network
4 Discussion on the Lifetime Evaluation of a New Module
4.1 Test of Cubic SVM, Fine kNN and Neural Network Approach on Data from a New Module
4.2 How to Interpret the Classification of the Neural Network Model?
5 Conclusion
References
Dielectric Material Significance on Common Mode Transient Immunity of a Shielded Pulse Planar Transformer
1 Introduction
2 Pulse Transformer Illustration
2.1 Pulse Transformers in Gate Drivers
2.2 Pulse Transformer Design
3 Pulse Transformer Model Simulation Analysis
3.1 Simulation Technique
3.2 Pulse Transformer Electronic System
3.3 Simulation of Dielectric Material Relevance
4 Experimental Verification
4.1 Experimental Arrangement
4.2 CMTI Experimental Results
5 Conclusions
References
Transient Modeling and Simulation of Power Converter Including Parasitic Elements
1 Introduction
2 Modeling Methodology
2.1 Bond Graph Modeling
2.2 Model of Power Switches
2.3 Model of Transmission Lines
3 Modeling of a Buck Converter
3.1 General Studied System
3.2 Parasitic Elements
3.3 Power Transmission Lines
3.4 Model of the Whole System
4 Simulation of the System
4.1 Time Response
4.2 Frequency Response
4.3 Time-Frequency Analysis
5 Conclusion
References
Enhanced Static and Dynamic Modeling of a Series-Series Inductive Power Transfer System with a Buck Post-Regulator
1 Introduction
2 PR-IPTS Static Modeling Based on FHA
2.1 Series-Series PR-IPTS
2.2 FHA-Based System-Level Static Modeling
3 PR-IPTS Dynamic Modeling Based on CMT
3.1 IPT Stage Dynamic Modeling
3.2 PR-IPTS System-Level Dynamic Modeling
3.3 Digital Controller Design
4 Experimental Tests
5 Conclusions
References
Design and Optimization of a Post-Regulated Inductive Power Transfer System with a Series-Series Compensation
1 Introduction
2 PR-IPTS Static Modeling Based on FHA
2.1 PR-IPTS with Series-Series Compensation
2.2 PR-IPTS Static Modeling
3 Static Model Predictions
3.1 Compensation Capacitors Selection
3.2 PR-IPTS Sensitivity Analysis
4 PR-IPTS Controllability Verification
5 Experimental Results of PR-IPTS Prototype
6 Conclusions
References
PWM-Induced Current Modelling in Stator Slots with Multiple Stacked Coils
1 Introduction
2 Stacked Coils Sharing the Same Magnetic Circuit
2.1 Generic Problem
2.2 Study Case of Two Stacked Coils
3 LF Electrical Model and Losses Assessment
3.1 LF Electrical Equivalent Circuit
3.2 Application to the Case of Study
3.3 LF Losses Assessment
4 Investigation of the Control Degrees of Freedom on the PWM-Induced Losses
4.1 PWM Harmonic Based Model
4.2 Synthesis
5 Conclusion
References
Current Sensor Fault Tolerant Control for a Synchronous Machine Based on Stator Current Estimation
1 Introduction
2 System Description
3 Fault Detection in Current Sensors
3.1 Fault Detection Algorithm
3.2 Fault Isolation
3.3 Reconfiguration
4 Current Sensorless Control
4.1 Model of the Machine
4.2 Stator Current Estimation
5 Simulation Study
6 Experimental Results
7 Conclusions
References
Investigating and Modeling the Soft Switching Losses of IGBTs Under Zero Current Switching Conditions
1 Introduction
2 Test Bench and Measurement Procedure
3 Turn Off Energy Loss Behaviour
3.1 Influence of the Maximum Collector Current
3.2 Influence of Zero Current Phase Duration
3.3 Influence of the Magnetizing Inductance
4 Stored Charge Model
5 Conclusion
References
Design and Control of a Synchronous Interleaved Boost Converter Based on GaN FETs for PEM Fuel Cell Applications
1 Introduction
2 IBC4 Prototype Overview
2.1 Synchronous IBC4 Architecture
2.2 Control Architecture
3 Digital Control Considerations
3.1 Digital PWM Signals Generation
3.2 High Resolution PWM (HRPWM) Signals
3.3 Sensors Bandwidth and Propagation Delay
3.4 Real-Time Management of Critical Tasks
3.5 Digital Compensator Selection
4 Reverse Current Protection in DCM
4.1 Conduction Mode Detection Algorithm
4.2 Gate Drive Considerations
5 Conclusions
References
Electromagnetic Transient Modeling of Power Electronics in Modelica, Accuracy and Performance Assessment
1 Introduction
2 Power Electronic Models in Modelica
2.1 Nonideal Diode Model
2.2 Ideal Diode Model
2.3 Nonideal IGBT Model
2.4 Ideal IGBT Model
2.5 Three-Phase Three-Level Converter Model
2.6 Three-Phase Two-Level Converter Model
2.7 Single-Phase Two-Level Converter Model
2.8 SPWM Generator (3-Level)
3 Model Verification and Validation
3.1 Three-Phase Three-Level Converter Model
3.2 Short-Circuit Simulation
3.3 Single-Phase Two-Level Converter
4 Conclusions
References
Fuse on PiN Silicon Diode Monolithic Integration for New Fail-Safe Power Converters Topologies
1 Introduction
2 Components Design Procedure
2.1 Fuse Characteristics and Design
2.2 Fuse-on-Diode Design Approach
3 Simulations Results
3.1 Case 1- Fuse Conductive and Diode Off-State
3.2 Case 2- Fuse Open and Diode On-State
3.3 Case 3- Fuse Open and Diode Off-State
4 Experiments and Results
4.1 Cut-off Tests
5 Conclusion
References
Part III Microgrids and Smart Grids
A Distributed Secondary Control for Autonomous AC Microgrid Based on Photovoltaic and Energy Storage Systems
1 Introduction
2 Studied System
3 SoC Balancing and Voltage/Frequency Regulation in a Fully Distributed Architecture Controller
3.1 Graph Theory and Distributed Control Based on Consensus
3.2 DESSs SoC Balancing and Voltage/Frequency Regulation
4 Proposed Fully Distributed Control for RESs and DESSs Coordinated Operation
5 Simulation Results
5.1 Test 1: Typical Day Operation
5.2 Test 2: Communication Network Failure
6 Conclusions
References
Behavioural Modelling of Multi-MW Hybrid PV/Diesel Modular Power Plant
1 Introduction
2 Methodological Approach
2.1 Data Collection and Classification
2.2 Correlation Between the PV Production and the Irradiance (W/m2)
2.3 PV Power Conditioning Performance as a Function of Irradiance
2.4 Thermoelectric Generator Behaviour Modelling
3 Behavioural Model Validation
4 Discussion and Concluding Remarks
References
Simulation and Operation Analysis of a Smart Grid Using Simulink
1 Introduction
2 Methodology
2.1 Selected Solver
2.2 Development Issues
2.3 Possible Causes
2.3.1 Solver Settings
2.3.2 The Combination of Breakers and Dynamic Loads
2.4 Possible Solutions
2.4.1 Changing the Breakers with Variable Resistors
2.4.2 Composite Block Simulation
2.4.3 Commenting Breakers in/out Using a MATLAB Script
3 Case Study and Results Discussion
3.1 Medium Voltage Distribution Network Power Flows
4 Conclusions
References
Modelling and Optimization of Power Allocation and Benefit Sharing in a Local Energy Community
1 Introduction
2 Collective Self-Consumption
2.1 Energy Allocation and Bill Computation
3 Management Method of an Energy Community
3.1 Energy Management Strategy
3.2 Energy Allocation Through Keys of Repartition
3.2.1 KoR1: Identical Repartition
3.2.2 KoR2: Prorate Consumption
3.2.3 KoR3: Limit Individual Energy Prices
4 Result Analysis
4.1 Case Study
4.2 Managing the Energy Community
4.2.1 Energy Management Strategy
4.2.2 Keys of Repartition
5 Conclusions
References
Social Data to Enhance Typical Consumer Energy Profile Estimation on a National Level
1 What Is Profile Estimation
2 Social Media Data
2.1 Twitter
2.2 Social Data Collection
2.2.1 Explore Data
3 Validation
3.1 Modeling
4 Conclusions
References
Small Signal Stability Study for Island Distributed Generation System Controlled by IDA-PBC-IA and Power Decoupled DroopControl
1 Introduction
2 Foreword on Small-Signal Stability Analysis of a Distributed Generation Microgrid
3 Local Stability Analysis in a Microgrid with Two Distributed Generation Units
3.1 Small Signal Modelling of the Studied Micro-Grid
3.2 Modelling of Power Control Laws in Small Signals
3.3 Modelling of the Internal Control
3.4 Load Modeling
3.4.1 Linear Load (RL)
3.4.2 Constant Power Load (CPL)
3.5 Sensitivity Analysis (Modal Analysis)
3.5.1 Influence of Droop Control Parameters
3.5.2 Influence of Passive System Elements on System Stability
4 Conclusion
References
MANA-Based Load-Flow Solution for Bipolar DC Microgrids
1 Introduction
2 Description of BDCMGs
3 Proposed MANA Formulation
3.1 Modelling of Bipolar DGs
4 Case Study
4.1 Effect of Line Resistances
4.2 Effect of Droop Coefficients
5 Conclusion
References
Analysis and Assessment of a Commercial Microgrid Laboratory Platform
1 Introduction
2 Microgrid Laboratory Prototype Description
3 Microgrid Test Protocols
3.1 Test Protocol for the EMS Inverters of the Prosumers
3.2 Test Protocol for Central Inverter
4 Platform Test Results and Discussion
5 Conclusions
References
A Review of Frequency Control Techniques Using Artificial Neural Network for Urban Microgrid Applications
1 Introduction
2 Urban Electrical Microgrid
3 Fundamentals About Frequency Control
3.1 Primary Control
3.2 Secondary Control
4 Artificial Intelligence in MG
5 Artificial Neural Network
5.1 Principle
5.2 Artificial Neural Networks for Control in MG
5.3 Application in System Management Supervision
5.4 Application in Local Control System
6 Conclusions
References
Stator Interturn Short-Circuits Detection in the PMSM Drive by Using Current Symmetrical Components and Selected Machine Learning Algorithms
1 Introduction
2 Theoretical Basis
3 Symmetrical Current Components Spectral Analysis
4 Experimental Stand
5 Hyperparameters Tuning of the Proposed Fault Classifiers
6 Online Verification of the Proposed Fault Classifiers
7 Conclusions
References
Part IV Energy Storage Systems
Potential Operation of Battery Systems to Provide Automatic Frequency Reserve Restoration (aFRR) Service
1 Introduction
2 The Automatic Frequency Reserve Restoration Service
2.1 Operation
2.2 Market
3 Strategy
3.1 Spanish aFRR Service Simulator
3.2 Battery Operation
4 Results
4.1 Simulation Results
4.2 Discussion
5 Conclusion
References
Incremental Capacity Analysis as a Diagnostic Method Applied to Second Life Li-ion Batteries
1 Introduction
2 Diagnostic Methods for Second Life Batteries
3 Incremental Capacity Analysis
3.1 Principle
3.2 Experimental Tests
3.3 Interpretations
3.4 C-Rate Influence on the ICA
4 HPPC Profile Characterization
5 ICA Comparison with the 'Alawa Toolbox
6 Conclusions
References
A Li-Ion Battery Charger with Embedded Signal Generator for On-Board Electrochemical Impedance Spectroscopy
1 Introduction
2 Architecture of the Current Signal Generator
2.1 Hardware Implementation
2.2 FPGA Waveform Generator
3 Experimental Results
4 Conclusions and Perspectives
References
A Survey of Energy Management Systems Considering Battery State of Health Preservation in Microgrid Applications
1 Introduction
2 Battery Degradation Models
3 EMSs Considering Battery SOH Preservation
4 Open Issues and Future Directions
5 Conclusions
References
Impedance Modeling for Multichannel EIS in Industrial Scale Vanadium Redox Flow Batteries
1 Introduction
2 Background
3 The Experimental Set Up
3.1 Industrial-Scale VRFB
3.2 Experimental Measurements
4 Results and Discussion
5 Conclusions
References
Numerical Assessment of Cooling Systems for Thermal Management of Lithium-Ion Batteries
1 Introduction
2 Methodology
2.1 Experimental SET-UP
2.2 Mathematical Model
2.2.1 Fluid Model
2.2.2 Heat Transfer Model
2.3 Model Validation
3 Results and Discussion
4 Conclusions
References
Modeling of the Thermal Runaway Phenomenon of Cylindrical 18650 Li-Ion Cells
1 Introduction
2 Material and Methods
2.1 Material
2.2 DSC
2.3 Cone Calorimeter
3 Mathematical Models
3.1 The Electrochemical Model
3.2 Thermal Model
3.3 Venting and Boiling Model
4 Modelling Procedures
4.1 Charge-Discharge Cycle
4.2 Thermal Abuse
5 Discussion
6 Conclusions
References
Part V Optimisation in Complex Electrical Systems
User Experience Inquiry to Specify COFFEE: A Collaborative Open Framework For Energy Engineering
1 Introduction
2 Collaborative Platforms for Open Energy Modelling
2.1 Interests of Open Energy Modelling
2.2 Including Human Actors in the Design Process
2.3 Characteristics of Online Collaborative Platforms in the Energy Field
3 Collaborative Open Framework For Energy Engineering (COFFEE)
3.1 COFFEE Concept
3.2 COFFEE Implementation
3.3 CAUTIC Inquiry: Method and Results
4 Discussion and Perspectives
5 Conclusions
References
Supplementary Material
Optimal Sizing of Tramway Electrical Infrastructures Using Genetic Algorithms
1 Introduction
2 Studied System
3 Formulation of the Optimization Problem
3.1 Optimization Variables
3.2 Objective Functions
3.3 Constraints
4 Optimization Method NSGA II
4.1 Problem Characteristics and Optimization Method Choice
4.2 Genetic Algorithm Elements: Chromosome and Genes
4.3 Crossover Operator
4.4 Mutation Operator
4.5 Influence of the Hyper-Parameters
5 Results
5.1 Test Case
5.2 Choice of the Hyper-parameters
5.3 Results
6 Conclusion
References
A Comparative Study of Existing Approaches for Modeling the Incident Irradiance on Bifacial Panels
1 Introduction
2 Bifacial Cell Modeling
2.1 Bifaciality Factor
2.2 Bifaciality Gain
2.3 Electrical Model
3 Tools for Modelling the Incident Irradiance
3.1 Input Parameters
3.2 Raytracing: Bifacial_radiance
3.3 Sandia View Factor Model
3.4 pvfactors
4 Comparison
5 Conclusion
References
Self-Adaptive Construction Algorithm of a Surrogate Model for an Electric Powertrain Optimization
1 Introduction
2 Surrogate Modeling
2.1 Definition
2.2 Sampling Plan
2.3 Kriging
2.4 Efficiency of Kriging
3 Enrichment
3.1 Typical Methods
3.2 Sub-Latin Hypercube
3.3 SHL Results
4 Conclusion
References
Optimization of Neural Network-Based Load Forecasting by Means of Whale Optimization Algorithm
1 Introduction
2 Echo State Network
3 Whale Optimization Algorithm
3.1 Exploration Phase
3.2 Exploitation Phase
4 WOA-ESN Combined Model
5 Simulation and Results
6 Conclusions
References
Part VI Modelling and Simulation of Electrical Machines and Electromagnetic Devices
Estimation of Steady-State Torque of Line Start Permanent Magnet Synchronous Motor Using Reluctance Network Approach
1 Introduction
2 Studied Machine
3 Reluctance Network Approach (RNA)
3.1 Nonlinear Reluctance Network
3.2 Simplified Reluctance Network
4 Steady-State Torque Characteristics
5 Finite Element Method Simulation
5.1 Flux Density in the Air-Gap and Back EMF
5.2 Steady-State Torque Calculation
6 Comparison of the Results
7 Conclusions
References
An Overview of High-Speed Axial Flux Permanent Magnets Synchronous Machines
1 Introduction
2 Possible High-Speed Topologies
3 Mechanical Constraints Analysis
3.1 Centrifugal Forces and Corresponding Stresses
3.2 Permanent Magnets
3.3 Attraction Forces
4 High-Speed Additional Losses
5 Suitable Materials for High Speed
5.1 Soft Magnetic Components
5.2 Permanent Magnets
5.3 Conductors
5.4 Retaining Sleeve
5.5 Bearings Selection
6 Application Domains of High-Speed Axial Flux Machines
7 Conclusion
References
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Lecture Notes in Electrical Engineering 993
Serge Pierfederici Jean-Philippe Martin Editors
ELECTRIMACS 2022 Selected Papers – Volume 1
Lecture Notes in Electrical Engineering Volume 993
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, Fakult¨at f¨ur Elektrotechnik und Informationstechnik, TU M¨unchen, 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 R¨udiger 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 Universit¨at M¨unchen, 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 M¨oller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering and 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, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universit¨at 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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Serge Pierfederici • Jean-Philippe Martin Editors
ELECTRIMACS 2022 Selected Papers – Volume 1
Editors Serge Pierfederici Université de Lorraine, CNRS, LEMTA Nancy, France
Jean-Philippe Martin Université de Lorraine, CNRS, LEMTA Nancy, France
ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-3-031-24836-8 ISBN 978-3-031-24837-5 (eBook) https://doi.org/10.1007/978-3-031-24837-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface to Electrimacs 2022, Volume 1
ELECTRIMACS is the short and well-known name of the international conference of the IMACS TC1 Committee. The conference is focused on the theory and application of modeling, simulation, analysis, design, optimization, identification, and diagnostics in electrical power engineering. The conference is a meeting point for researchers to share ideas and advances in the broad fields of electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, electric and hybrid vehicles, renewable energy systems, energy storage, batteries, supercapacitors, and fuel cells. ELECTRIMACS 2022 was held in Nancy, France, from 16 to 19 May 2022. Three tutorial sessions, 20 oral sessions, 4 technical tracks, 4 plenary sessions with thought leaders from academia and research centers, and 6 special sessions were included in the conference program. The conference hosted 102 oral presentations of papers, selected among 120 submissions received. The review process involved at least three reviewers per paper. The main institutional sponsor of the conference is the Université de Lorraine. The conference received also a technical co-sponsorship from the important scientific society IMACS, and a financial co-sponsorship from Region Lorraine. Private companies sponsored the event or took part in the industrial exhibit. This book collects a selection of 47 papers presented at ELECTRIMACS 2022 Nancy. These papers are particularly focused on electrical engineering simulation aspects and innovative applications. The collection is organized into six thematic parts: Control and Power Management of Electrical Systems, Modelling and Simulation of Power Electronics Systems, Microgrids and Smart Grids, Energy Storage Systems, Optimization in Complex Electrical Systems, and Modelling and Simulation of Electrical Machines and electromagnetic devices. General Chairs Jean-Philippe Martin, Université de Lorraine, France Serge Pierfederici, Université de Lorraine, France
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Preface to Electrimacs 2022, Volume 1
Local Organizing Committee Thierry Boileau, UL, France Farid Meibody-Tabar, UL, France Babak Nahid-Mobarakeh, McMaster University, Canada Ignace Rasoanarivo, UL, France Noureddine Takorabet, UL, France Matthieu Urbain, UL, France Mathieu Weber, CNRS, France Technical Program Chairs Ramon Blasco-Gimenez, Universitat Politécnica de Valéncia, Spain Eric Monmasson, Université de Cergy-Pontoise, France Benoit Robyns, HEI Lille, France Giovanni Spagnuolo, Università degli studi di Salerno, Italy Track Chairs Seiichiro Katsura, Keio University, Dept. of System Design Engineering Yokohama, Japan Nicolas Patin, UTC Compiègne, LEC, Compiègne, France Georges Barakat, Université Le Havre Normandie, GREAH, Le Havre, France Noureddine Takorabet, Université de Lorraine, GREEN, Nancy, France João Pedro Trovão, University of Sherbrooke, e-TESC Lab, Sherbrooke, Canada Bruno Francois, Ecole Centrale de Lille, L2EP, Lille, France Manuela Sechilariu, UTC Compiègne, AVENUES, Compiègne, France Bruno Sareni, Université Paul Sabatier, ENSEEIHT, Toulouse, France Maria Carmela di Piazza, CNR, Palermo, Italia Afef Bennani Ben Abdelghani, University of Carthage, INSAT, Tunis, Tunisia Frédéric Richardeau, CNRS Dir., LAPLACE, University of Toulouse, CNRS, UPS Toulouse, France Rodolfo Araneo, Dipartimento di Ing. Astronautica, Elettrica ed Energetica, Sapienza Università di Roma, Italy Giuseppe La Tona, Institute of Marine Engineering of National Research Council (CNR), Italy Giovanni Petrone, DIEM - Dipartimento di Ingegneria dell’Informazione ed Elettrica e Matematica Applicata, Università degli studi di Salerno, Italy Massimiliano Luna, Institute of Marine Engineering of National Research Council (CNR), Italy Walter Zamboni, DIEM - Dipartimento di Ingegneria dell’Informazione ed Elettrica e Matematica Applicata, Università degli studi di Salerno, Italy Salvy Bourguet, Université de Nantes, IREENA, France Benoit Delinchant, Université Grenoble Alpes, G2Elab, France Samir Jemei, Univ. Bourgogne Franche-Comté, FEMTO-ST Institute, FCLAB, CNRS, Belfort, France Mohsen Kandidayeni, University of Sherbrooke (e-TESC lab) and University of Quebec in Trois-Rivières (IRH lab), Quebec, Canada
Preface to Electrimacs 2022, Volume 1
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Franc¸ois Vallee, University of Mons, Power Systems & Markets Research Group Mons, Belgium Vincent Debusschere, Université Grenoble Alpes, G2ELAB - ENSE3 Grenoble INP, France Scientific Committee Ennio Andrea Adinolfi Giovanni Lutzemberger Ennio Andrea Adinolfi Giovanni Lutzemberger Giovanna Adinolfi Jean Mahseredjian Yacine Amara Mariusz Malinowski Julia Amici Patrizio Manganiello Giovanni Battista Appetecchi Emmanuel Marcault Seddik Bacha Fabrizio Marignetti Lotfi Baghli Jean-Philippe Martin Mahmoud Barakat Nicolas Mary Georges Barakat Hajer Marzougui Efstratios Batzelis Alessandro Massi Pavan Hector Beltran Paolo Mattavelli Afef Ben Abdelghani-Bennan Pascal Maussion Manel Ben Ghorbal Farid Meibody-Tabar Mohamed Benbouzid Alexander Micallef Mohamed Fouad Benkhoris El Hadj Miliani Michel Benne Marta Molinas Olivier Bethoux Nazih Moubayed Nicu Bizon Piercarlo Mustarelli
Italy Italy Italy Italy Italy Canada France Poland Italy Netherlands Italy France France Italy France France France Canada France Tunisia United Kingdom Italy Spain Italy Tunisia France Tunisia France France Malta France France France Norway France Lebanon Romania Italy
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Preface to Electrimacs 2022, Volume 1 Frede Blaabjerg Babak Nahidmobarakeh Silvia Bodoardo Wissem Naouar Thierry Boileau Maria Assunta Navarra Loic Boulon Radouane Ouladsine Salvy Bourguet Djaffar Ould Abdeslam Alain Bouscayrol Yoann Pascal Gianluca Brando Nicolas Patin Giovanni Brunaccini Alireza Payman Piergiacomo Cancelliere Marie-Cecile Pera Jean-Frederic Charpentier Emilio Pérez Soler Daniele Davino Giovanni Petrone Alexandre De Bernardinis Matheepot Phattanasak Bruno Dehez Maria Pietrzak-David Louis-A Dessaint Pierpaolo Polverino Luigi Di Benedetto Arturo Popoli Maria Carmela Di Piazza Miguel Pretelli Christian Dufour Ionela Prodan Benoit Durillon Mohammad Rafiei Maurice Fadel Bertrand Raison Erina Ferro Hubert Razik Bruno Francois Mattia Ricco Fei Gao
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Preface to Electrimacs 2022, Volume 1 Javier Riedemann Luis Antonio Garcia Gutierrez Delphine Riu Jean-Paul Gaubert Xavier Roboam Jean-Yves Gauthier Robin Roche Roghayeh Gavagsaz António Roque Joern Geisbuesch Paola Russo Chris Gerada Sébastien Sanchez Malek Ghanes Francisco José Sánchez Pacheco Francesco Grasso Bruno Sareni Francesco Grimaccia Christophe Saudemont Giambattista Gruosso Manuela Sechilariu Josep Guerrero Samuel Simon Araya Pierluigi Guerriero Jacopo Sini Ruben Sigifredo Pena Guinez Sondes Skander Mustapha Alonso Gutierrez Galeano Ilhem Slama-Belkhodja Mickael Hilairet Francesca Soavi Samir Hlioui Cyril Spiteri Staines Azeddine Houari Kateryna Stoyka Diego Iannuzzi Phatiphat Thounthong Nadir Idir Francesco Antonio Tiano Lahoucine Id-Khajine Abdelmounaim Tounzi Samir Jemei Joao Pedro Trovao
ix Chile France France France France France France Iran Portugal Germany Italy United Kingdom France France Spain Italy France Italy France Italy France Denmark Denmark Italy Italy Chile Tunisia France Tunisia France Italy France Malta France Italy Italy Thailand France Italy France France France Canada
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Preface to Electrimacs 2022, Volume 1 Wattana Kaewmanee Andrea Trovo’ Hadi Kanaan Christophe Turpin Seiichiro Katsura Seppo Valkealahti Youssef Kraiem Philippe Viarouge Alexander Kuznietsov Dmitri Vinnikov Patrizia Lamberti Stephane Vivier Kari Lappalainen Hanqing Wang Antonino Laudani Xin Wen Walter Lhomme Lin-Shi Xuefang Elizaveta Liivik Medhi Zadeh Marco Liserre Walter Zamboni Ramon Lopez Erauskin Majid Zandi Massimiliano Luna Rongwu Zhu Blake Lundstrom Hesan Ziar
Nancy, France Nancy, France
Thailand Italy Lebanon France Japan Finland France Canada Germany Estonia Italy France Finland France Italy France France France Estonia Norway Germany Itlay Spain Iran Italy Germany United States Netherlands
Serge Pierfederici Jean-Philippe Martin
Contents
Part I Control and Power Management of Electrical Systems Performance Analysis of a Hardware in the Loop Based Emulation of a Naval Propulsion System Associated with Supercapacitor Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nabil Benyahia, Jean-Frederic Charpentier, Franck Scuiller, and Florent Becker Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Franc¸ois Roux, Florian Dupriez-Robin, Guéna¨el Le Solliec, and Franc¸ois Auger
3
15
Neural Network Model for Aggregated Photovoltaic Generation Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Belenguer, J. Segarra-Tamarit, J. Redondo, and E. Pérez
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Electrification of River Freight: Current Status and Future Trends in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Amoros, J. F. Charpentier, W. Lhomme, J. Y. Billard, and B. Nottellet
41
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost DC-DC Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hai-Nam Nguyen, Bảo-Huy Nguyễn, Thanh Vo-Duy, Minh C. Ta, and João Pedro F. Trovão Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic Pulse Width Modulation Applied to a Flying Capacitor Leg Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mariem Jday and Paul-Etienne Vidal
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69
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Contents
Control Strategy for Orbital O2 Tidal System Based on EMR Model . . . . . Ahmed Al Ameri, Alireza Payman, Brayima Dakyo, and Mamadou Ba¨ılo Camara A Hybrid Fourier and Wavelet-Based Method for the Online Detection and Characterization of Subsynchronous Oscillations. . . . . . . . . . . Keijo Jacobs, Reza Pourramezan, Younes Seyedi, Houshang Karimi, and Jean Mahseredjian
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Optimal Sizing for Fuel Cell Hybrid Power Sources Under Reliability and Energy Performance Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Toufik Azib, Olivier Bethoux, Adriano Ceschia, and Francisco Alves Compliance Evaluation of WTG and WPP Controllers for Self and Black Start Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 J. Martínez-Turégano, S. A˜nó-Villalba, S. Bernal-Perez, and R. Blasco-Gimenez Experimental Study of the Cold Start Capabilities of a Closed Cathode PEM Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 J. Villaume, E. Pahon, A. Ravey, and S. Jeme¨ı Part II Modelling and Simulation of Power Electronics Systems Discussion on Classification Methods for Lifetime Evaluation of a Lab-Scale SiC MOSFET Power Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Malorie Hologne-Carpentier, Bruno Allard, Guy Clerc, and Hubert Razik Dielectric Material Significance on Common Mode Transient Immunity of a Shielded Pulse Planar Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Loreine Makki, Antoine Laspeyres, Anne-Sophie Descamps, Julien Weckbrodt, Marc Anthony Mannah, Christophe Batard, and Nicolas Ginot Transient Modeling and Simulation of Power Converter Including Parasitic Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Baptiste Trajin and Paul-Etienne Vidal Enhanced Static and Dynamic Modeling of a Series-Series Inductive Power Transfer System with a Buck Post-Regulator . . . . . . . . . . . . . 193 Kateryna Stoyka, Antonio Vitale, Eugenio Venere, and Paolo Visconti Design and Optimization of a Post-Regulated Inductive Power Transfer System with a Series-Series Compensation . . . . . . . . . . . . . . . . . . . . . . . . . 209 Antonio Vitale, Kateryna Stoyka, Eugenio Venere, and Paolo Visconti PWM-Induced Current Modelling in Stator Slots with Multiple Stacked Coils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Antoine Cizeron, Hugo Milan, Javier Ojeda, and Olivier Béthoux
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Current Sensor Fault Tolerant Control for a Synchronous Machine Based on Stator Current Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Peyman Haghgooei, Ehsan Jamshidpour, Noureddine Takorabet, Davood Arab Khaburi, and Babak Nahid-Mobarakeh Investigating and Modeling the Soft Switching Losses of IGBTs Under Zero Current Switching Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Assil Bouach, Sébastien Mariéthoz, Arnaud Gaillard, and Micka¨el Hilairet Design and Control of a Synchronous Interleaved Boost Converter Based on GaN FETs for PEM Fuel Cell Applications . . . . . . . . . . . 263 Elie Togni, Fabien Harel, Frédéric Gustin, and Daniel Hissel Electromagnetic Transient Modeling of Power Electronics in Modelica, Accuracy and Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . 275 A. Masoom, J. Gholinezhad, T. Ould-Bachir, and J. Mahseredjian Fuse on PiN Silicon Diode Monolithic Integration for New Fail-Safe Power Converters Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Amirouche Oumaziz, Frédéric Richardeau, Abdelhakim Bourennane, Emmanuel Sarraute, Eric Imbernon, and Ayad Ghannam Part III Microgrids and Smart Grids A Distributed Secondary Control for Autonomous AC Microgrid Based on Photovoltaic and Energy Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . 307 Sidlawendé V. M. Ouoba, Azeddine Houari, and Mohamed Machmoum Behavioural Modelling of Multi-MW Hybrid PV/Diesel Modular Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Sani Moussa Kadri, Brayima Dakyo, Mamadou Ba¨ılo Camara, and Yrébégnan Moussa Soro Simulation and Operation Analysis of a Smart Grid Using Simulink. . . . . . 335 Alexander Van Waeyenberge, Bruno Canizes, João Soares, Sérgio Ramos, Simon Ravyts, Juliana Chavez, and Zita Vale Modelling and Optimization of Power Allocation and Benefit Sharing in a Local Energy Community. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Alyssa Diva Mustika, Rémy Rigo-Mariani, Vincent Debusschere, and Amaury Pachurka Social Data to Enhance Typical Consumer Energy Profile Estimation on a National Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Amr Alyafi, Pierre Cauchois, Benoit Delinchant, and Alain Berges
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Small Signal Stability Study for Island Distributed Generation System Controlled by IDA-PBC-IA and Power Decoupled Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Nidhal Khefifi, Azeddine Houari, Mohamed Machmoum, Malek Ghanes, and Mehdi Zadeh MANA-Based Load-Flow Solution for Bipolar DC Microgrids . . . . . . . . . . . . . 387 Nasim Rashidirad, Jean Mahseredjian, Ilhan Kocar, and Omar Saad Analysis and Assessment of a Commercial Microgrid Laboratory Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 Mariem Dellaly, Sonia Moussa, Sondes Skander-Mustapha, and Ilhem Slama-Belkhodja A Review of Frequency Control Techniques Using Artificial Neural Network for Urban Microgrid Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Louise Petit and Bruno Francois Stator Interturn Short-Circuits Detection in the PMSM Drive by Using Current Symmetrical Components and Selected Machine Learning Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Przemyslaw Pietrzak and Marcin Wolkiewicz Part IV
Energy Storage Systems
Potential Operation of Battery Systems to Provide Automatic Frequency Reserve Restoration (aFRR) Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Javier Cardo-Miota, Emilio Pérez, and Hector Beltran Incremental Capacity Analysis as a Diagnostic Method Applied to Second Life Li-ion Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Lucas Albuquerque, Fabien Lacressonnière, Xavier Roboam, and Christophe Forgez A Li-Ion Battery Charger with Embedded Signal Generator for On-Board Electrochemical Impedance Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 465 Luigi Mattia, Giovanni Petrone, and Walter Zamboni A Survey of Energy Management Systems Considering Battery State of Health Preservation in Microgrid Applications . . . . . . . . . . . . . . . . . . . . . 479 Maria Carmela Di Piazza, Massimiliano Luna, and Giuseppe La Tona Impedance Modeling for Multichannel EIS in Industrial Scale Vanadium Redox Flow Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 Andrea Trovò, Walter Zamboni, and Massimi Guarnieri Numerical Assessment of Cooling Systems for Thermal Management of Lithium-Ion Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Girolama Airò Farulla, Davide Aloisio, Valeria Palomba, Andrea Frazzica, Giovanni Brunaccini, and Francesco Sergi
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Modeling of the Thermal Runaway Phenomenon of Cylindrical 18650 Li-Ion Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Paola Russo, Sofia Ubaldi, and Maria Luisa Mele Part V
Optimisation in Complex Electrical Systems
User Experience Inquiry to Specify COFFEE: A Collaborative Open Framework For Energy Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Sacha Hodencq, Fabrice Forest, Théo Carrano, Benoit Delinchant, and Frédéric Wurtz Optimal Sizing of Tramway Electrical Infrastructures Using Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Anass Boukir, Vincent Reinbold, Florence Ossart, Jean Bigeon, and Paul-Louis Levy A Comparative Study of Existing Approaches for Modeling the Incident Irradiance on Bifacial Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Soufiane Ghafiri, Maxime Darnon, Arnaud Davigny, João Pedro F. Trovão, and Dhaker Abbes Self-Adaptive Construction Algorithm of a Surrogate Model for an Electric Powertrain Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 Marvin Chauwin, Hamid Ben Ahmed, Melaine Desvaux, and Damien Birolleau Optimization of Neural Network-Based Load Forecasting by Means of Whale Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Pooya Valinataj Bahnemiri, Francesco Grimaccia, Sonia Leva, and Marco Mussetta Part VI
Modelling and Simulation of Electrical Machines and Electromagnetic Devices
Estimation of Steady-State Torque of Line Start Permanent Magnet Synchronous Motor Using Reluctance Network Approach . . . . . . . . 603 Hamza Farooq, Nicolas Bracikowski, Patricio La Delfa, and Michel Hecquet An Overview of High-Speed Axial Flux Permanent Magnets Synchronous Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 Hoda Taha, Georges Barakat, Yacine Amara, and Mazen Ghandour
Part I
Control and Power Management of Electrical Systems
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval Propulsion System Associated with Supercapacitor Energy Storage Nabil Benyahia, Jean-Frederic Charpentier, Franck Scuiller, and Florent Becker
Abstract Electric autonomy, environment respect, compactness, lifespan and low maintenance costs, are real technological challenges to be taken up on the future ship propulsion system. In this paper, an experimental study of a Hardware In the Loop (HIL) based Emulation of a Naval Propulsion System associated with Supercapacitor Energy Storage System is proposed. For these purpose two electrical machines are associated in the same shaft (DC machine and PMS machine) to reproduce the behavior of the association of the electrical motor and the propeller of a ship at laboratory scale. The whole system is constituted by three subsystems. The first one is represented by a PM synchronous machine associated with a controled VSI which plays the role of the electrical propulsion motor following a realistic mission profile. The second one is constituted by a DC machine associated with a DC/DC converter which is controled in order to reproduce the hydrodynamic behavior of the propeller and the ship, and the third one is constituted by a buckboost DC/DC converter and an ultracapacitor bank, the ultracapacitor gives to the emulated mechanical shaft the ability to reinject kinetic power into the grid in case of transients. This experimental tool can be associated to innovative hybrid energy system to test and validate hybrid system configuration and can be exploited for many kinds of propellers. In addition, it gives the designer a feedback to optimise ship design. The effectiveness of the proposed HIL platform in terms of DC grid stability and 4 hydrodynamic operation of propeller is verified by experimental results.
N. Benyahia () · J.-F. Charpentier · F. Scuiller · F. Becker IRENAV – Ecole Navale Brest, Brest Cedex 9, France e-mail: [email protected]; [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_1
3
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N. Benyahia et al.
1 Introduction The maritime industry is currently forced to adapt on the ship technology choice in order to reach atmospheric and environmental pollution restrictions, which are increasingly restrictive in terms of carbon emissions. The development of the future electric or hybrid ship must necessarily be validated before by low-power experiments prototypes [1, 2]. These tools have recently been proposed and well-proven especially from the automotive industries [3, 4]. These prototypes aim to reproduce the behavior of a part or several parts of the propulsion system [5, 6]. Scaling study can complete these tools for real ships. These experimental tools are complementary with numerical models and will provide designers of ship an insight into expected performance of the whole system in term of ship dynamic, grid stability, motor speed regulation, propeller geometry and fuel consumption. Architectures of electric naval propulsion were brought forward by multiple researchers. In [7], a low power DC machine is used to emulate the propeller and ship dynamics in first hydrodynamic quadrant, where, a 5-leg Voltage Inverter Source (VSI) has been used to ensure power supply and speed control of the propulsion 5 phases motor. Therefore, the fault-tolerant control strategies under different operating conditions and a specific naval navigation profile have been presented, however, the study uses a common DC bus for the DC machine and the AC machine, which does not allow the upstream part of the grid to be studied correctly. In [8], a propeller emulator is proposed by using a DC machine operating as a generator to reproduce the dynamic characteristic of the ship. In this work, the DC generator is coupled to the induction machine and feed an electric load through a chopper, nevertheless, the study is focused to first-quadrant operations and the realised HIL is very low power, however scaling errors of the experimental set-up made for a real electric vessel can be occur. An evaluation of the potential of energy recovery in a low tonnage full electric ship has been presented in [9], in this paper, the propeller is working as a turbine during regenerative braking operations, therefore, the MPPT strategy is considered to increase the recovered energy, the main drawback of this study is that, the obtained results are limited to the numerical simulation. The developed HIL open water tests combine software and hardware components to reproduce real behaviour of the shipboard propulsion system in the towing tank has been proposed in [10]. The authors have demonstrated that HIL can be used to precisely emulate ship propulsion dynamics in the ship model basin. This work aims to develop a new method to realize a Hardware In the Loop based a naval propulsion platform able to reproduce hydrodynamical and electrical behavior of the propeller and the ship. The objective is to get a completed platform that can emulate a ship propulsion behaviour in various operating conditions. This platform is constituted of three sub-systems: the first one is represented by a PM synchronous machine associated with a controled VSI which plays the role of the electrical propulsion motor following a realistic mission profile, the second one is constituted by a DC machine associated with a DC/DC converter which is controled in order to reproduce the hydrodynamic behavior of the propeller and the ship, and
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval. . .
5
the third one is constituted by a buck-boost DC/DC converter and an ultracapacitor which are controlled to achieve a constant voltage source able to absorb or supply power during the 4 quadrant operations of the DC machine. The advantage of this topology enables studying the interaction between the sub-systems and insight an idea of the stability of DC grid during the ship speed transients for instance. We consider that the proposed work increments the published studies concerning the following criteria. First, the four quadrant open water diagrams are integrated in the propeller model dynamic by using the cinematic angle of attack (advanced angle) in the developed HIL. Second, the use of a supercacitor associated with a buck-boost DC/DC converter and the propeller emulator allows to operate in all the possible operation modes of the propulsion system. These modes include regenerating braking and propulsive mode in the two rotation directions. For propulsion modes, the SCs are able to store energy and the DC machine is controlled as a brake (generator). In generative mode, the SCs store energy while the DC machine is used as a motor to follow the hydrodynamic characteristics of the propeller and hull system.
2 System Description and Modeling The basic components of the developed HIL based naval propulsion platform are shown in Fig. 1. A Permanent Magnet Synchronous Machine (PMSM) is used for the ship propulsion, it is supplied by a DC/AC inverter. The DC machine is controlled through a four quadrants DC/DC converter and is controlled to reproduce the torque related to the propeller in the shaft considering the propeller behaviour in all the possible hydrodynamic operating conditions. The Supercapacitor is used to store or provide power to stabilize the DC voltage grid from DC machine via a DC/DC bidirectional converter. Supercapacitor System
Power Supply
Bidirectional DC / DC Converter
4Q DC / DC Converter
DC
PMS
Machine
Machine
Propeller Emulator
Fig. 1 Basic scheme of naval propulsion platform system
DC /AC Inverter
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N. Benyahia et al.
2.1 Propeller Modeling In order to analyse the performance of the propeller operation in the four hydrodynamic quadrants, the used propeller model is based on CT and CQ curves. Where, CT and CQ are non-dimensional numbers which characterize the propeller hydrodynamic behavior for a given propeller geometry. These numbers are determined by experimental tests in traction basin or numerical CFD simulations [11] as functions of the advance angle β (6). These numbers are directly linked to the thrust T and torque Q related to the propeller by Eqs. (1), (2), (4) and (5).
CT =
CQ =
T
1 2 2 ρVr
Q
1 2 2 ρVr
D 2 π4
D 3 π4
(1)
(2)
Where Vr is the relative advance velocity at 70% of the external radius of the propeller and is defined as: (3) Vr = (Va ) 2 + (0.7π nD) 2 Consequently, the Eqs. (1) and (2) can be written explicitly as: CT =
CQ =
T ((Va ) 2 + (0.7π nD) 2) ρD 2 π8 Q ((Va ) 2 + (0.7π nD) 2) ρD 3 π8
(4)
(5)
The advance angle beta is defined by Eq. (6). β = tan−1
Va 0.7π nD
(6)
This CT and CQ coefficient can be interpolated by Fourier series. Figure 2 shows the CT and CQ curves versus beta angle for the Wageningen B4–70 screw propeller series [11]. These curves allow to model the propeller in all the possible modes. It can be noticed that CT and CQ can reach positive and negative value depending of the angle beta. The sign of the CQ is directly linked to the direction of the mechanical power related to the propeller (propulsion or regenerative braking).
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval. . .
7
Fig. 2 Open water test results with B4–70 screw series in four quadrants [11]
The Fourier series of CT and CQ can be described as: CT =
∞ 1 [AT (k) cos (kβ) + BT (k) sin (kβ)] N
(7)
∞ 1 AQ (k) cos (kβ) + BQ (k) sin (kβ) N
(8)
k=0
CQ =
k=0
The equation of motion which represents the ship manoeuvring dynamics in one degree of freedom is defined as: dVship T − RT = dt Mship
(9)
Where, Vship is the ship speed, Mship is the ship masse and RT is the total force acting in the opposite direction of motion, it is also called the total hull resistance and can be expressed by (10) and is a function of many factors including ship speed, hull form and sea state. Total hull resistance increases as ship speed increases, the simplified function is shown in Fig. 3. In this case a basic curve with a theoretical calm sea state is considered. RT = RV + RW + RAA
(11)
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Fig. 3 Hull resistance curve nM
n Gearbox
TM
T Propeller dynamic Q Eq.(3) − Eq.(8)
Ship dynamic Eq.(9) − Eq.(10)
VShip
Fig. 4 Mechanical shaft model
Where, RV is the viscous (friction) resistance, RW is the wave making resistance and RAA is the air resistance caused by ship moving through calm air. The used ship global model synopsis is shown in Fig. 4. It can be seen that a gearbox can be inserted in the model to adapt the propeller speed to the motor one, where nM is the motor speed in (r/s) and TM is the motion torque.
3 Experimental Results The whole system control scheme showed in Fig. 5 is implemented on a dSPACE DS1202 MicroLabBox platform. The PMSM drive is controlled by FOC control. The FOC system consists of two control loops: A speed controller in an outer loop and a current controller in an inner loop. The PMS motor is driven by a three-leg voltage-source inverter. The DC machine is mechanically associated to the PMS motor and can be operate in the four quadrants. The resulting voltage and current are positive or negative according respectively to the PMSM speed direction and the torque imposed by the propeller (DC current reference).
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval. . .
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Fig. 5 Global system scheme
The propeller emulator (DC machine and drive) control is based on current control of the DC machine through four quadrants chopper, the DC machine reference current idcm can be obtained by multiplying the propeller torque Q related to hydrodynamic model (5) by gearbox factor kGearbox and DC machine torque constant kdcm . ∗ = kGearbox kdcm Q idcm
(12)
By using PI regulator, it is possible to obtain accurate current control over a wide range in clockwise as well as anticlockwise directions. The DC bus voltage Vbus2 is controlled as constant through the buck-boost DC/DC converter associated with the supercapacitors, the objective is to achieve with the buck-boost converter and the supercapacitors a constant voltage source able to absorb or supply power (power balance) during all the possible operation modes of the DC machine used as propeller emulator. In discharging mode, the maximum current delivered Iscmax to the DC bus depends on the capacitor voltage Vsc , maximum voltage, and the equivalent serial resistance ESRDC , Iscmax =
Vsc2 4ESR DC VscMax
(13)
In charging mode, the current Iscmax is negative. Maximum current that can be injected into the ultra-capacitor is limited by the capacitor terminal voltage. Iscmax =
VscMax − Vsc ESRDC
(14)
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Fig. 6 Propeller and ship speed
The ultra-capacitor control is implemented through two control loops: one outer voltage control loop that controls the DC bus voltage Vbus2 and inner current loops in order to control the current Isc flowing through the ultra-capacitor inductor Lsc . In order to prove the good behavior of the proposed propeller emulator under different ship operating conditions, the propulsion motor speed is controlled periodically in ahead and then in astern as shown in Fig. 6. It can be noticed that the measured speed tracks exactly the reference speed for different variation and the ship speed follows the motor speed but with a delay which is due to the ship inertia. When the boat starts to move in ahead or in astern, the propeller accelerates slightly about 85 rad/s, this phenomenon can be explained by the angle beta variation, but recovered quickly. Figure 7 shows the steady state of PMSM quadrature current component, DC machine current and supercapacitor current Isc. This illustrates also the comparison of the measurement and reference currents DC machine armature, it shows that the measurement current is close to the reference current. These results prove the good accuracy of the propeller emulator control with high dynamic response. Figure 7 illustrates that in discharge mode, the ultra-capacitor outputs an average current about of 2 A to stabilize DC bus voltage at 150 V although the DC bus current abrupt change. The fluctuation of the DC bus voltage Vbus2 depends on the ultracapacitor’s SOC. In charge mode, the DC machine provides energy to DC bus with 4 A current. In order to stabilize DC bus voltage at 150 V, the surplus energy is transmitted to the ultracapacitor. The dynamic response results of the conventional double closed loops control strategy are shown in Fig. 8. Figure 8 clearly shows that the voltage of the supercapacitor tends to decrease over time. To avoid the complete discharge of the supercapacitor, the reference of the DC bus voltage can be variable
Performance Analysis of a Hardware in the Loop Based Emulation of a Naval. . .
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Fig. 7 DCM armature, PMSM quadratic and ultracapacitor Currents
Fig. 8 DC bus, DC machine armature, and ultracapacitor voltages
according to the level of the state of charge. Figures 9 and 10 show the operation of the propeller in the four hydrodynamic quadrants, Figure 9 compares the forward speed and the shaft speed on the other hand, Fig. 10 illustrates the advance angle beta. Figure 11 shows the balance at steady state of thrust and total resistance. During ship acceleration and deceleration manoeuvres the thrust increases in response to the total resistance which depend on ship velocity. Otherwise, the difference between the thrust generated by the propeller and the ship’s resistance is nul when the ship’s velocity is constant.
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4
Ship speed (m/s)
3
2
1
0
-1 -10
-5
0 5 10 Propeller speed (r/s)
Fig. 9 Four hydrodynamic quadrant curve
Fig. 10 Beta angle variation
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Performance Analysis of a Hardware in the Loop Based Emulation of a Naval. . .
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Fig. 11 Thrust and total resistance curves Table 1 System parameters
Parameter Armature DC machine voltage Armature DC machine Current DC machine torque constant Gearbox factor (KGearbox ) Ship mass (M) Propeller diameter (D) Ultracapacitor’s rated voltage Ultracapacitor’s capacitor
Value 200 V 9A 1.2 4 400 Kg 0.5 m 160 V 5F
4 Conclusion This paper presents a solution to emulate the behaviour of a ship in a HIL approach. This solution allows to test electric ship propulsion chain configuration and control in a low scale laboratory experimental set-up. To be able to emulate the propeller hydrodynamic behavior in a mission profile a real time-controlled DC machine is associated with a supercapacitor bench which is used as a controled power source or a controled power load depending on the operating mode of the ship. This propeller emulator allows to represent the behaviour of the ship and propeller in all the possible modes (propulsion, regenerative braking in the two rotation direction of the propeller). Experimental results underline the relevancy of the approach. Several possible improvements are identified. As an example, a supercapcitor’s state of charge estimator can be associated with SC control and can be used to maintain the SOC of the SC bench arround an optimal state of charge during long term tests (Table 1).
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References 1. Ahmad, N., Meng, A., and Sultan, M., “Applications of Hardware-in-the-Loop Simulation in Automotive Embedded Systems,” 2009 SAE Technical Paper 2020-01-1289, 2020, pp. 574580, https://doi.org/10.4271/2020-01-1289. 2. N. Benyahia, T. Rekioua, N. Benamrouche, A. Bousbaine, “Fuel Cell Emulator for Supercapacitor Energy Storage Applications,” Electric Power Components and Systems Vol. 41, 2013, pp. 569-585, https://doi.org/10.1080/15325008.2012.755234 3. C. Galko, R. Rossi, X. Savatier, “Vehicle-Hardware-In-The-Loop system for ADAS prototyping and validation”, International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS XIV), 2014, https://doi.org/10.1109/ SAMOS.2014.6893229. 4. A. Soltani, F. Assadian, A Hardware-in-the-Loop Facility for Integrated Vehicle Dynamics Control System Design and Validation, IFAC-PapersOnLine, Volume 49, Issue 21, 2016, pp. 32-38, https://doi.org/10.1016/j.ifacol.2016.10.507. 5. J. Ma, F. Zhou, Z. Huang, R. James, S.; Chen, H., “Hardware-In-The-Loop Testing of Connected and Automated Vehicle Applications: A Use Case For Cooperative Adaptive Cruise Control”. 21st International Conference on Intelligent Transportation Systems (ITSC) 2018, 13, 1213. https://doi.org/10.1109/ITSC.2018.8569753 6. K. Nounou, J. F. Charpentier, K. Marouani, M. Benbouzid and A. Kheloui, “Emulation of an Electric Naval Propulsion System Based on a Multiphase Machine Under Healthy and Faulty Operating Conditions”, in IEEE Transactions on Vehicular Technology, vol. 67, no. 8, pp. 68956905, Aug. 2018, https://doi.org/10.1109/TVT.2018.2834342. 7. K. Nounou, J. F. Charpentier, K. Marouani, M. Benbouzid and Kheloui, “Hardware-in-theLoop Emulation of an Electric Naval Propulsion System Based on a Multiphase Permanent Magnet Synchronous Machine”, 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), 2017, pp. 1-6, https://doi.org/10.1109/VPPC.2017.8331006. 8. K. Marouani, H. Guendouz, B. Tabbache, F. Khoucha and A. Kheloui, “Experimental investigation of an emulator Hardware In the Loop” for electric naval propulsion system”, 21st Mediterranean Conference on Control and Automation, 2013, pp. 125-130, https://doi.org/ 10.1109/MED.2013.6608709. 9. N. Bennabi, J. F. Charpentier, H. Menana, J. Y. Billard and B. Nottellet, “Evaluation of Recovery Braking Capacities on Electric Vessel”, 2018 XIII International Conference on Electrical Machines (ICEM), 2018, pp. 2535-2541, doi: https://doi.org/10.1109/ ICELMACH.2018.8507266. 10. L., Huijgens, A., Vrijdag, H., Hopman “Hardware in the loop experiments with ship propulsion systems in the towing tank: Scale effects, corrections and demonstration”, Ocean Engineering Vol. 226, (2021), 108789 11. J.S. Carlton, “Marine Propellers and Propulsion” (Second Edition), Butterworth-Heinemann, 2007, ISBN 9780750681506, https://doi.org/10.1016/B978-0-7506-8150-6.X5000-1
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions Franc¸ois Roux, Florian Dupriez-Robin, Guéna¨el Le Solliec, and Franc¸ois Auger
Abstract Today’s requirement for improved electrical systems increase needs for accurate, fast and versatile models. MATLAB.TM /SIMULINK is a good candidate in terms of average simulation for accuracy, versatility and speed, but for detailed simulation (i.e. designed with the SimScape toolbox) it can be very slow, especially when multiple power converters are simulated. This issue can be solved by real time simulators based on FPGAs like OP-5607 from Opal-RT. With these real-time simulators, complex systems can be simulated with a time step of a few hundreds of nano-seconds. This article presents a new methodology in simulation fields which let researchers to interface fast response power electronics converters and slower physicals parts. This new methodology allows designers to evaluate systems at multiple time scales: minutes, seconds and milliseconds. This article emphasizes today’s possibilities of simulating a system as complex as the propulsion line of a cruise ship during an entire 30 min trip. Finally, this kind of simulation allows engineers to increase the accuracy of modeling, even to work on realistic faulty conditions.
1 Introduction Today’s concern about environmental issues is pushing public institutions to take action about maritime pollution [8, 14]. Nowadays, many harbors have stringent environmental regulations (i.e. limitation of CO2 emission, fine particules matters, noise. . . ) [9]. All Electrical Ships (AES) are commonly described as a good way to address these issues. Late trends in ship energy management are about
F. Roux () · F. Dupriez-Robin · G. Le Solliec CEA TECH de Nantes, Bouguenais, France e-mail: [email protected]; [email protected]; [email protected] F. Auger Institut de Recherche en Énergie Électrique de Nantes Atlantique (IREENA, UR 4642), CRTT, Nantes Université, Saint-Nazaire Cedex, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_2
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Medium Voltage Direct Current (MVDC) AES [10] because of their high integration possibilities of multiples energy source, capabilities of reconfiguration. . . Last decades evolution on power electronics, especially high voltage/current switches (6.5 kV, 1 kA [1]) allows designers to reuse regular/well known medium power topologies in high power converters. This drives the MVDC ship [7], which is the best fit for integration of renewable source/storage energy inherently Direct Current (DC). Finally, new high power Fuel Cells (FC), (e.g. Ballard 200 to 1000 kW marine FC), can be easily integrated as the main power supply for a cruise ship. The choice of modeling type in power electronics is essential, and is driven by the simulation goals. From our point of view, we have 3 main types of simulations: – Power simulations showing the power exchanges between all subsystems in a complex system without the complexity of control management. It is useful for testing the global behavior, – Average simulation is closer to real systems. The linear behavior of converters can be implemented, stability of regulators can be studied [2]. – Detailed simulation is about switches behavior, it is the most accurate way of studying converters and their interactions (high frequency noise, harmonics. . . ) The main issue is computation time: for a dozen of switches in a simulation, time ratio can reach .1/60 (i.e. for 1 s of simulation, computation time will take 1 min). The last evolution in field-programmable gate arrays (FPGAs), especially about simulating power electronics [15] on FPGAs, allows researchers to simulate complex systems with a lot of switches in real-time (i.e. unity time ratio) [16]. So, in this article we are going to simulate an AES with MVDC bus supplied by a FC and a battery on FPGAs. The following system is applied to a travel with a fault on DC bus. Simulation on FPGAs allows us to study the faulty period and impacts on the overall system. By means of new FPGAs resolution, this study can be done on multiple times scales: minutes, seconds and milliseconds. The following part of this paper is organized into tree sections: Sect. 2 introduces the methodology of this work and how information is exchanged between each part of the system. Section 3 presents used model and interactions between converters and control. Finally, Sect. 4 shows some results of this work.
2 Design Methodology Models are implemented under MATLAB.TM SIMULINK environment. The first step is about validation of topologies with the specialized SimScape electronics toolbox, the main objective been simplifying Hardware In the Loop simulation (HILs) and then future Power HILs integration (e.g. decoupling control from physical systems). Once all models are running together under the SIMULINK environment, electronic part is implemented under OPAL -RT Shematic editor and compiled on FPGAs. Control is intentionally based on very common/well known strategies in order to evaluate the impact of faulty conditions on power electronics without advanced
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
17
regulation strategies. In order to be closer to the physical behavior, most of the exchanged information between control and physical simulation is done by wired signals. Finally in this paper, we perform a simulation of the propulsion line of an AES, from production to propeller. The overall system was applied to a cruise ship 30 min long travel (from Fromentine to ˆıle d’Yeu. e.i. from a continental french harbor to a near french island). Eventually FPGAs programming allows us to explore faulty configurations like creating short circuits on the DC bus.
3 Model and Parameters In this section, we will present as exhaustively as possible the model and the parameters of this work. We will start by the Power Management System (PMS), which manages elements in this simulation, then the electrical model of power converters and their close control. Finally, we will show how the mechanical response of a ship impacts the electrical part. Models and control are always managed by a close safety supervisor. Its first purpose is to manage starting/faulty conditions, high level implementation is presented in Fig. 1. It is in these close supervisors that safety and respect of standards
Start
Mode Starting mode = 0 Safety check Initialisation (e.g. loading capacitor)
Normal operation mode = 1
Faulty
mode = -1
Reset & Safety
Safety check
Safety mode mode = -1
Start OK Normal operation Mode = 1 (e.g. power limitation) Mode = 1
Fig. 1 General view of a supervisor algorithm
mode = 0
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are managed. The main practice that we are following is IEEE Std 1709.TM 2010 about faulty tolerance in MVDC, which mainly consists of 10% tolerance on DC bus and 10 ms to clear faulty condition [7]. The second purpose is the application at converters level of PMS control signals and limitations.
3.1 General View of the Case Study In ship, symmetry/redundancy is a key for safety, in case of failure of a part of propulsion line the ship can return to the nearest harbor with the remaining power. Because of the that, we are only studying a half ship, the global architecture is presented in Fig. 2.
3.2 PMS The PMS is the supervisor of the entire ship. Its goal is to give orders to every converters supervisors: – – – –
start and stop, power limitation, high level control (i.g. DC bus level, battery charge, etc), dispatching between power sources etc.
The PMS is based on information provided by converter supervisors, state (starting, steady and fault) and few other information (power, Stat Of Charge (SOC). . . ). The PMS algorithm is based on the algorithm of supervisors.
3.3 FC and DC/DC Converter The FC used in this work is based on [11] (MATLAB.TM SimScape Model). The associated converter is an Interleaved Boost Converter (IBC) (Fig. 2), because of inherent operation of FC, this converter is not reversible. This converter is current controlled by a single Proportional Integral (PI) controller. Design of IBC is based on boost equations [6]. Because of the unavailability of data sheet of 800 kW FC we use data sheet of a 50 kW FC. In this purpose, in order to preserve dynamics and behavior, current provided to the FC model is divided by 16. D =1−
.
Vinmin . Voutmax
(1)
19
Fig. 2 General view of the studied electrical architecture
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
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LBoost ≥ Rch ∗
D ∗ (1 − D)2 . 2 ∗ FScw
CBoost ≥ VDC ∗
(2)
Vout ∗ D FSw ∗ ΔVout ∗ Rch
(3)
3.4 Battery and DCDC Reversible Converter The battery used in this work is based on [13] (MATLAB.TM SimScape Model). In this topology, the only converter which can act as an Active Front End (AFE) is the battery DCDC converter. Its main goal is to control the bus voltage. As an AFE, it must be reversible in order exchange energy with the bus. We choose a well known boost medium power topology presented in Fig. 2. This boost is controlled by two cascaded PI controllers, the outer loop controls bus voltage and inner loop controls current [2]. The design of the boost converter is based on Eqs. (1)–(3) (Table 1).
Table 1 Simulation parameters Fuel cell (SimScape) Type: PEMFC Power: 50 kW Voltage: 625 Vdc
Battery (SimScape) Type: Lithium-ion Rated capacity: 1000 Ah Voltage: 800 Vdc DC bus C: 1 mF .RC : 50 k. .RP reload : 10 . Engine (PMSM)[12] .Ld = .Lq : 0.476 mH .Rs : 1.502 .m p: 8 Flux linkage: 3.55 Rated speed: 200 rpm
IBC Frequency: 20 kHz Number of legs: 3 L = 0.115 H .RL : 50 .µ C: 0.1 mF .RC : 50 k. Boost Frequency: 20 kHz Ron: 0.1 .m C: 3.11 mF .RC : 50 k. L: 50 .µH .RL : 50 .µ .RP reload : 10 . Inverter Frequency: 20 kHz .Ron : 0.1 .m C: 3.11 mF
Controller Current regulator −4 s−1 .A−1 .Ki : 2.64 10 −5 .Kp : 3.70 10 A−1 Saturation: [0 0.95]
Controller Voltage regulator .Ki : 1158 A/(V.s) .Kp : 3.62 A/V Current regulator −1 −1 .Ki : 0.018825 s .A −1 .Kp : 0 A Controller Regulator .Ki : 200 V/(A.s) .Kp : 0.1 V/A Saturation: .± Vdc
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
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3.5 DC Bus A capacitor has been introduced between DCDC converters and the DCAC converter, to ensure a better stability, for starting stage a preload resistor and its switch were added (Fig. 2).
3.6 DC/AC Converter and Motor Finally, a two level DCAC converter (Fig. 2) converts from DC bus to the Alternative Current (AC) Permanent-Magnets Synchronous Motor (PMSM). The control is based on Direct Torque Control (DTC) [4]. Pulse Width Modulation (PWM) generation is managed by specialized OPAL -RT digital outputs.
3.7 Ship and Propeller The ship model is based on [12] and experimental data. Table 2 shows power over velocity of the studied ship, total resistance to ship advance is computed by .Rship[N] = P[W ] /v[m/s] . Equation (4) shows the result of a second order linear regression between resistance and velocity, which is used as model for the ship resistance. Rship = 371 Va2 + 24 Va
.
(4)
The estimation of external characteristics of the propeller is based on OpenProp [5]. Multiple analysis were performed in order to meet ship linear velocity, required thrust and rotational motor speed. Propeller characteristics are presented in Table 3. Torque and thrust of propellers are usually computed from an adimensional advance (5), thrust (6) and torque (7) coefficients [3]. Js =
.
Table 2 (Half) ship power and velocity
Va . ωD
Engine power [kW] 485 340.5 280.5 243.5 83 26.5 0
(5)
Ship velocity [kn] 21.2 18.8 17.6 14.1 11.8 8.2 0
Resistance [kN] 44 35 31 20 13 8 0
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Table 3 Ship power (half ship) and velocity
Js KQ . KT ρ D
Ship Maximum thrust: 44 kN Speed: 20 kn Ship mass: 107 t Inertia: 1440 kgm.2
Propeller Diameter: 2.3 m Number of blades: 3 Hub diameter: 0.23 m Rotor speed: 200 rpm Propeller type: NACA 65A010
TP rop = KT (Js ).ρ ω2 D 4.
(6)
QP rop = KQ (Js ).ρ ω2 D 5
(7)
: advance coefficient QP rop : torque [Nm] : torque coefficient TP rop : thrust [N] : thrust coefficient Va : ship speed [m/s] : water density [kg/m3 ] ω : rotor speed [rad/s] : propeller diameter [m]
OpenProp computes thrust and torque coefficients from external characteristic propeller. Table 3 summarizes parameters which feed OpenProp. These .KT , KQ versus .Js coefficient are feeding the propeller model ((5)–(7)). At last, because of the unsymmetrical behavior of propeller for positive and negative advance coefficients, negative thrust is decreased by .50%. Finally fundamental dynamics relations are applied to compute the ship and rotor speed (8) and (9). mV˙a =
.
J ω˙ rotor =
.
f orce = TP rop − RShip.
(8)
torque = Γrotor − QP rop
(9)
m : ship mass [kg] Γrotor : rotor torque [Nm] J : inertia (rotor + Propeller) [kg.m2 ]
3.8 Pilot Pilot determines the level of power applied to the propulsion engine. Basic rules are presented in Fig. 3, in order to achieve the ship travel (speed over time) defined in Fig. 4 (Speed envelope) 5 kn into harbor and channel, 20 kn at sea.
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
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Speed [kn]
Fig. 3 Pilot logigram
20 10
Pilot consign [%]
Rotor speed [rad/s]
0
Ship Speed Speed envelope
0
5
10
15
20
25
30
0
5
10
15
20
25
30
15
20
25
30
50 0 -50
100
1.5% (5kn)
0 -100 0
5
10
Time [min]
Fig. 4 Full travel
3.9 Short Circuit As an illustration of advanced simulation possibilities on FPGAs, we implement a short circuit between DC bus and DCAC converter. To this aim, line impedance has been added at relevant locations (see Fig. 2). To ensure compliance with IEEE standard, a short circuit of a duration .< 0.01 s was performed. In theses conditions, the system should stay in steady state.
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4 Results 4.1 Evaluation of the Model on 30 min Travel
Power [kW]
Battery 1000
85
0
80
-1000
75
-2000 0
10
20
70 30
Power [kW]
FC 1000
Battery charge end 20 to 5 kn
500 0
5 to 20 kn
0
10
20
30
Power [kW]
Engine 3000 2000
Faulty event
1000 0 0
10
20
Time [min] Fig. 5 Power through converters
30
SOC [%]
Figure 4 shows the modeled speed of the ship during the 30 min case study. On this figure, we can see the evolution of speed (rotor and linear) over speed shape. The simulated ship is within specifications. The third part emphasizes implemented pilot commands (Fig. 3). Figure 5 shows power exchange between source (FC), storage (Battery) and engine. We can see that the battery is charging for the first 20 minutes until its reaches 80% of SOC (limit which has been chosen in the PMS as the end of the force battery recharge). So on FC curve a drop occurs when battery is fully charged. As expected, we can see that the FC supplies an average power to the system (engine power and charging the battery), battery is continuously working as an AFE (i.e. keeps DC voltage bus constant) whether its charging or discharging. On the engine section Fig. 5, the pilot commands are displayed.
Real-Time Simulation of an Electric Ship in Normal and Faulty Conditions
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Voltage [V]
DC bus 1500 1000
Zoom
500
default
0 -500
0
0
Default time counter
default
0.5
5
1
10
15 ms
1.5
2
Fault time detection 0.01 0.005 0
5
10
15 ms
0 0
0.5
1
2
1.5
rotor speed [rad/s]
Engine 45 40 0
35
5
10
15 ms
30 0
0.5
0
0.5
1
1.5
2
1
1.5
2
Current [A]
2000
0
-2000
Time [s]
Fig. 6 Faulty and recovery
4.2 Faulty Study Figure 6 shows the impact of the short circuit on the DC bus. As we can see, the time counter of the boost (used as a watchdog) is counting until its end. If it reaches 10 ms the system switches in safety mode (all switches are forced open) and is waiting for a reset. But in this case, we want to cause a fault that does not prevent the system from continuing to work. On the engine session we can see the reaction of the engine : on magnified views, the engine speed decreases during short circuit, as expected, then the speed increases because of the PI controller response during fault, but everything is back to normal within a second. At time .t = 0.2 s, a second fault occurs, because the motor restarts, and thus starts to draw energy from the DC bus again, whereas during the first fault it was supplying energy. This phenomenon is amplified by the saturation state of the controller. Finally we can see one limitation of this set up, engine currents are limited at 1600 A because of acquisition line saturation.
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5 Conclusion As described in this paper, a new bit-stream approach dedicated to power electronics in FPGAs brings electronics simulation to the next level in terms of accuracy, simulation time and versatility. Engineers with the same model can explore multiple aspects of a system with a high level of fidelity with an improved in simulation time. This article reveals a lack about control strategy: PI control is enough for quasi steady state but not relevant when faulty conditions occur, but it was not the objective. From our point of view, this article is a good baseline, future development could explore different control strategies. The objective was to develop a method which allows engineers to simulate a system with different dynamics (power electronics [.µs], engine [ms], hydrodynamic and inertia [s]) with high accuracy and long term impacts assessment. Moreover, with this kind of simulation, research on power, even energy management system can be pursued with detailed model rather than less accurate average models. These kind of results can only be obtained using FPGAs, CPU simulation would be very time consuming. Finally, this method is a step forward of HIL toward Power HIL and rapid control prototyping. Acknowledgments This work was supported by the project “Monitoring and management of marine renewable energies” granted by the French “Pays de la Loire” region.
References 1. ABB. HiPak IGBT module. 2. Seddik Bacha, Iulian Munteanu, and Antoneta Iuliana Bratcu. Power Electronic Converters Modeling and Control. Advanced Textbooks in Control and Signal Processing. Springer London. 3. Michael Bernitsas, Ray Debashis, and P Kinley. Kt, kq and efficiency curves for the wageningen b-series propellers. Technical report, Department or Naval Architecture and Marine Engineering, The University of Michigan, Michigan, Ann Arbor, 1981. 4. Bimal K Bose. Modern power electronics and ac drives. Prentice Hall, 2001. 5. B P Epps, M J Stanway, and R W Kimball. OpenProp: An Open-source Design Tool for Propellers and Turbines. In SNAME Propellers and Shafting conference, page 12, Williamsburg, VA, 2009. 6. B. M. Hasaneen and Adel A. Elbaset Mohammed. Design and simulation of DC/DC boost converter. In 2008 12th International Middle-East Power System Conference, pages 335–340. IEEE. 7. IEEE. IEEE recommended practice for 1 kV to 35 kV medium-voltage DC power systems on ships. 8. Bin Lin and Cherng-Yuan Lin. Compliance with international emission regulations: Reducing the air pollution from merchant vessels. 30(3):220–225. 9. Susana López-Aparicio, Dag Tønnesen, The Nguyen Thanh, and Heidi Neilson. Shipping emissions in a nordic port: Assessment of mitigation strategies. 10. T.J. McCoy. Trends in ship electric propulsion. In IEEE Power Engineering Society Summer Meeting,, volume 1, pages 343–346. IEEE.
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11. S.M. Njoya, O. Tremblay, and L.-A. Dessaint. A generic fuel cell model for the simulation of fuel cell vehicles. In 2009 IEEE Vehicle Power and Propulsion Conference, pages 1722–1729. IEEE. 12. Huachao Peng, Xiaoyuan Zhu, Liu Yang, and Guichen Zhang. Robust controller design for marine electric propulsion system over controller area network. 13. Olivier Tremblay and Louis-A. Dessaint. Experimental validation of a battery dynamic model for EV applications. pages 289–298. World Electric Vehicle Journal. 14. L. van Biert, M. Godjevac, K. Visser, and P.V. Aravind. A review of fuel cell systems for maritime applications. 15. Amine Yamane, TejKiran Rangineed, Luc-Andre Gregoire, Syed Qaseem Ali, Jean-Nicolas Paquin, and Jean Belanger. Multi-FPGA solution for large power systems and microgrids real time simulation. In 2019 IEEE Conference on Power Electronics and Renewable Energy (CPERE), pages 367–370. IEEE. 16. Adrien Genic, Petar Gartner, Murilo Almeida, and Dragan Zuber. Hardware in the loop testing of shipboard power system’s management, control and protection. In 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), pages 1–6. https://doi.org/10.1109/VPPC.2017.8331026.
Neural Network Model for Aggregated Photovoltaic Generation Forecasting E. Belenguer, J. Segarra-Tamarit, J. Redondo, and E. Pérez
Abstract This paper presents a forecasting model from 1 to 10 days for the aggregated photovoltaic energy production in Spain. The model uses a convolutional neural network which inputs are meteorological forecasts, historical generation data and the location and installed power of existing plants. The model output is the hourly production of the photovoltaic energy production for the whole system for the following ten days. The results of the model can be used for generation scheduling and system operation on one side and for energy trading in the day-ahead market or in derivative markets on the other side.
1 Introduction In the context of a rapid growth of renewable energies in the whole world, photovoltaic generation is currently facing in Spain a spectacular growth like in many other countries. From 2019 to 2020, photovoltaic generation went up from the 3.6% to the 6.3% of the total electricity generation. Installed power grew from 8913 MW in 2019 to 11,714 MW in 2020 [1] and an objective of 39,000 MW has been planned by year 2030 [2]. Like other renewable energy sources, photovoltaic production depends on weather conditions and, consequently, is intermittent by nature. This characteristic has a strong influence in the operation of the whole electric power system as other generation units must be prepared for a sudden change in solar power. The short-term forecasting of solar power plants is therefore an essential tool for generation scheduling which in Spain is carried out the previous day. Moreover,
E. Belenguer () · J. Segarra-Tamarit · E. Pérez Department of Industrial Systems Engineering and Design, Universitat Jaume I, Castelló de la Plana, Spain e-mail: [email protected] J. Redondo feníe Energía, Las Rozas, Madrid, Spain © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_3
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solar forecasting from one to several days can also be used by electricity trading companies to optimize their bids in the day-ahead or in derivative markets. Artificial Neural Networks (ANNs), like other computational intelligence models, are able to model complex non-linear systems proving to be a valuable tool for short-term forecasting. For example, the forecasting tool used by the Spanish TSO [3] uses weather forecasts (irradiance and cloud cover) together with detailed information about the characteristics and location of all the photovoltaic plants in the country and real-time measures of the largest plants energy generation. The ANN forecast is first carried out individually for a set of power plants geographically close and later aggregated to find the whole system predicted generation. In [4] a convolutional neural network is used taking as inputs three weather forecasts (irradiance, cloud cover, temperature) and two standard models (clear sky irradiance and persisntent power generation) spatially distributed with a grid of .0.25◦ × 0.25◦ for longitude and latitude. The model generates 5-channel images with each channel corresponding to a weather variable. The objective of the work is the development of an ANN forecasting model able to predict the aggregated photovoltaic generation of the Spanish electric system from 1 to 10 days without using real-time measurements. The paper is organized as follows. Section 2 describes the different data sources while Sect. 3 presents the performance metrics used to evaluate the model. A detailed description of the model is developed in Sect. 4 together with the description of a basic approach or na¨ıve model for the sake of comparison. In Sect. 5, the results for each model are presented and, finally, some conclusions are drawn in Sect. 6.
2 Data Sources for the Model 2.1 Meteorological Data Meteorological forecasting data is served by the European Centre for MediumRange Weather Forecast (ECMWF), a research organization composed of 34 member states that can provide weather forecasts to private companies. The data set used for the model is the Set I: Atmospheric Model high resolution 10-day forecast. This set is served twice a day, at 00:00 and at 12:00 h, the weather forecasts for the next 10 days with a granularity of one hour for the first 90 hours, three hours up to hour 144 (6 days) and six hours up to hour 240 (10 days). The meteorological forecasts served by ECMWF and used by the model are: – Temperature (K) – Global Horizontal Irradiance, GHI (W/m.2 ) The spatial resolution of the forecasts is 0.5º.×0.5º (approximately 56 .×56 km) for an area including the Iberian Peninsula and the Balearic Islands as shown in Fig. 1. The resulting matrix has 21 rows and 31 columns and covers a region
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Weather forecasts Municipalities -10
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Fig. 1 Spatial distribution of the weather forecasts
from (45ºN,10ºW) to (35ºN, 5ºE). Files are served in General Regularly-distributed Information in Binary form (GRIB).
2.2 Photovoltaics Plant Information The information about the characteristics of all the photovoltaic plants in Spain is extracted automatically from two databases generated by the Spanish administration, PRETOR [5] and ELECTRA [6]. This information is combined with another database with the geographical location of all the municipalities in Spain so each plant can be geographically located and approached to the closest weather forecast point.
2.3 Historical Photovoltaic Energy Generation Data The data about historical photovoltaic generation is provided by ESIOS [7], the information system of the Spain’s TSO. All the information related to the Spanish electricity system including historical data about demand and generation can be publicly accessed using a Python API [8]. Data about energy demand and generation is aggregated hourly to match the hourly time granularity of the electricity market.
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3 Performance Metrics Several performance metrics can be used in order to evaluate the forecasting models. They can be used for the evaluation of different aspects of the model [9, 10]. The forecasts obtained in this work are evaluated using the most frequent metrics, which are the Bias, the mean absolute error (MAE) and the root mean square error (RMSE). All of these metrics have the same units as the studied variable. The Bias quantifies the mean value of the error and can be calculated as N 1 yˆk − yk , .Bias = N
(1)
k=1
where .yk is the measured value, .yˆk is the forecast and N is the number of samples. This metric shows if the forecasts have a tendency to overestimate (positive Bias) or underestimate (negative Bias). The main drawback of the Bias is that the positive errors can compensate the negative ones, obtaining low Bias values even for models with bad performances. The MAE solves this problem by taking the absolute value of the errors: N 1 yˆk − yk .MAE = N
(2)
k=1
This metric represents the absolute difference between the two variables, however, as it does not show if the deviations are upwards or downwards, the MAE should be used along with the Bias. Finally, the RMSE is used to evaluate the average spread of the forecasting errors. N 1 2 yˆk − yk .RMSE = N
(3)
k=1
As the RMSE uses the squared value of the errors, it has a high sensitivity to outliers. This makes this metric suitable for training short term forecasting. However, as this work aims at forecasting 10 day horizons, the MAE is used to train the neural networks. Finally, the relative value of these performance metrics (rBias, rMAE and rRMSE) can be obtained by dividing each one of them by the average value of the measured variable over the calculation period (.y). ¯ These relative metrics facilitate the interpretation of the final results.
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4 Neural Network Model Description 4.1 Data Preparation Before data can be fed into the neural network, they need to be properly prepared. Ideally, it would be convenient to have as an input, for the location of every PV power plant, the GHI forecast as well as its peak power, as the product of these variables is a rough approximation of its power production. However, as shown in Fig. 1, the spatial resolution of the forecasts is too limited to allow this. Therefore, a methodology to link the municipalities where the installations are located with the forecast points is needed. In this work, it is proposed to use a bilinear interpolation which proportionally distributes the peak power of each installation to the four nearest points of the forecasts grid. The result of this distribution is then multiplied by the irradiance forecast giving a sequence of .21 × 31 values which can already be used as inputs. Furthermore, as previously discussed, the .21 × 31 temperature values of the forecast points are also fed to the neural network. Data preparation also includes a 0–1 normalization (taking 0–1000 W/m.2 and 253–319 K, respectively, as irradiance and temperature ranges) and a Data Cleaning process for the elimination of outliers (with a total of .0.5% of the points discarded).
4.2 Na¨ıve Approach The product of irradiance and peak power of each PV power plant can be used as a na¨ıve prediction of the aggregated production by simply adding up all its terms. Figure 2 shows a dispersion graph for this model. It can be seen that the model underestimates the generation in winter while it works more accurately in summer. Two hypotheses are considered to explain this phenomenon: the effect of temperature and the variation of the Sun’s position. Temperature is already one of the inputs for the neural network model but, in order to take into account the second effect, a new variable is defined as an input: a solstice variable which linearly changes from 0 for the winter solstice to 1 for the summer solstice.
4.3 Convolutional Neural Network Approach The forecasting model should take advantage of the geospatial information contained in the irradiance, temperature and installed power matrices. This is done by processing these data with convolutional layers. These layers can process all the matrices at the same time as each of the color channels in an image. The objective of the proposed architecture is to extract several features from the input matrices and
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Abril - Octubre Noviembre - Marzo
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Fig. 2 Na¨ıve approach dispersion graph
generate the forecasts using fully connected layers and additional inputs. This ANN with different kinds of data, such as geospatial information and numerical variables is also known as Mixed Data [11]. In order to select the best ANN architecture several model configurations have been analyzed using data from 2016 to 2018 as the training set and data corresponding to 2019 as the test set. With these tests both the best architecture and the best way to encode the inputs (either each matrix separately or the irradiances matrix scaled by the power at each location) have been selected. Furthermore, each ANN architecture has been evaluated three times and the mean performances are shown in Table 1. The names of the models represent the number of channels in the images for the convolutional part of the model and the size of the arrays in the feedforward part. For example, the model CH2 - CH5 - CH1 - 651 - 40(+1) - 3 - 1, which is shown in Fig. 3, has as its main input a two channel image, the temperature and the irradiance scaled by the installed power. Then, a first convolutional layer expands the input to 5 channels and a second layer reduces it back to 1 channel. The result is then flattened to become a 651 values array (21.×31) and goes through a dense layer with 40 neurons. After this layer, the (+1) indicates that the solstice variable is added to the result of the previous layer and the resulting array is processed in two final layers with 3 and 1 neurons in order to produce the forecasted PV generation. As shown in Table 1, the architectures using two input channels (temperature and irradiance scaled by the installed power) have a better performance than the ones
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Table 1 Evaluation of different ANN architectures Model CH2 - CH1 - 651(+1) - 40 - 1 CH2 - CH5 - CH1 - 651 - 40(+1) - 3 - 1 CH2 - CH5 - CH1 - 651(+1) - 3 - 1 CH2 - CH5 - CH1 - 651 - 100(+1) - 40 - 1 CH2 - CH7 - CH1 - 651 - 40(+1) - 5 - 1 CH2 - CH5 - CH5 - CH1 - 651 - 40(+1) - 5 - 1 CH2 - CH3 - CH3 - CH1 - 651(+1) - 40 - 5 - 1 CH3 - CH4 - CH4 - 651(+1) - 40 - 1 CH3 - CH2 - CH1 - 651(+1) - 40 - 1
rMAE (%) 13.71 10.39 11.53 11.44 11.33 12.85 10.53 19.44 17.47
rRMSE (%) 26.95 19.70 21.17 21.35 20.77 24.66 19.78 36.07 29.68
rBias (%) .−7.54 .−0.90 .−0.31 .−4.18
0.06 .−5.14
1.14 14.52 .−8.57
Fig. 3 Proposed ANN architecture with convolutional and dense layers
with three channels. Some of these architectures with two input channels can achieve values of rMAE close to 10.5% and rRMSE lower than 20%. The best architecture is the one shown in Fig. 3 and highlighted in Table 1, which has been previously described. This ANN has a lineal activation at the output layer and rectified linear units (ReLu) at each of the other layers. Moreover, all the convolutional layers have zero padding such that output matrices have the same height and width dimensions as the input ones. Using ANNs the results obtained by the na¨ıve model described in the previous subsection (18.15% rMAE) can be significantly improved, as the proposed model can achieve a rMAE of 10.39%. Once the best ANN architecture has been selected, the period of data used to train the model can be fine-tuned to further improve the model. This study is shown in Table 2, where different amounts of data previous to the forecasting time are considered. The results show that the ANN has a higher performance when it’s trained using all the historical data previous to the forecasting time. Conversely, training the model with a few previous days produces the worst results. A more detailed analysis of the results shows that the ANN has its best performance between May and July. During this period the rMAE reaches values close to the 5%. However, between November and February, the rMAE increases to values around 15%.
36 Table 2 Evaluation of the model trained with different periods of data
E. Belenguer et al. Training data 15 previous days 30 previous days 60 previous days 10 previous days from each year 30 previous days from each year 60 previous days from each year 1 previous year 2 previous years 3 previous years All previous data since 2016
rMAE (%) 14.93 12.31 12.47 10.02 13.71 12.98 9.95 10.19 9.20 9.02
5 Results To analyse the performance of the model (D+10 model) and evaluate its progression from 1 to 10 days, the results are compared with the na¨ıve model and with the same model but applied every day, for the 10-day period, with a forecasting horizon of 24 h (D+1 model). As an example of the model output, Fig. 4 represents a 10-day forecasting initiated on 2020/02/15. Table 3 shows the rMAE for the three cases. The model is also evaluated in a period of 5 months, from 2020/01/16 to 2020/05/09, including a total of 115 10-day forecasts. Performance metrics are shown in Table 4 and Fig. 5. Unsurprisingly, the error (rMAE and rRMSE) increases with the time horizon. The value of rMAE for the D+10 model goes from 11.5% for the first day to 29.2% for the tenth day while the value of rRMSE increases from 19.8 to 47.2%. It can be concluded that from the sixth day on, the model losses effectiveness following the weather forecasts lower accuracy and that similar results are obtained with the na¨ıve Model. The value of rBias is close to 0% for the first prediction days but, as the forecast horizon increases, a clear overestimation occurs due to an overestimation on the irradiance forecasts. From a more detailed analysis of rMAE (Table 5 and Fig. 6), it can be said that the median value for the first day is about 10% so the error for half of the forecasts is lower than 10%. It is also observed that, from the sixth day on, the error can increase to values higher than 100% in some cases. It is interesting to compare the results of the model with the corresponding results of the Spanish TSO tool (SIPRESOLAR). Table 6 shows the comparison for a 2-day forecast as no longer forecast times are available from SIPRESOLAR. It can be seen that our model behaves slightly worse than SIPRESOLAR but needs much less data. In particular, SIPRESOLAR uses more meteorological data, a higher spatial resolution and, more importantly, real-time energy production measurements of the largest photovoltaic plants that are not publicly available.
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Fig. 4 10-day forecasting initiated on 2020/02/15 Table 3 rMAE for a 10-day forecasting initiated on 2020/02/15
rMAE(%) D+1 D+2 D+3 D+4 D+5 D+6 D+7 D+8 D+9 D+10
D+10 model 2.8 4.1 6.1 7.8 14.1 10.2 9.1 9.8 8.3 7.4
Na¨ıve model 24.3 23.8 17.9 24.6 31.4 27.3 28.6 29.3 28.9 26.7
D+1 model 3.1 3.6 7.6 10.5 7.1 8.5 7.9 8.2 8.2 9.6
D+7 23.1 37.6 6 23 12.2
D+9 26.2 42.4 8 24.8 12.5
Table 4 Model performance metrics D+1 D+10 model rMAE (%) 11.5 D+10 model rRMSE (%) 19.8 D+10 model rBias (%) .−1.4 Na¨ıve model rMAE (%) 16.7 D+1 model rMAE (%) 11.4
D+2 12.1 20.7 .−0.6 16.8 11.2
D+3 14.1 23.8 .−0.2 17.5 11.1
D+4 15.9 26.9 2.2 18.4 11.8
D+5 17.4 29.3 3.7 18.6 12.4
D+6 21.4 35.5 6.3 20.8 12.6
D+8 23.8 38.8 9.2 23.3 12.5
D+10 29.2 47.2 9.4 27.7 12.7
6 Conclusions This paper introduces a forecasting model for predicting the aggregated PV energy generation in the Spanish electrical system with a ten days horizon, which can be used for energy trading in derivative markets or for generation scheduling. Several network architectures and input combinations have been tested, giving the best results for models with two convolutional and three dense layers and inputs defined as Mixed Data of two matrices (temperature and the product of installed
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Fig. 5 Model performance metrics Table 5 rMAE statistical key figures Mean (%) Standard deviation (%) Minimum (%) Q1 (%) Q2 (%) Q3 (%) Maximum (%)
Fig. 6 rMAE boxplot for different forecast horizons
D+1 11.5 6.5 2.8 6.5 10 14.8 36.3
D+2 12.1 7.1 3 7.3 10.4 15.3 41.6
D+3 14.1 9.1 2.7 8.4 12 17.1 55.5
D+4 15.9 13.2 3.6 7.7 12.4 18 95.9
D+5 D+6 17.4 21.4 14.4 18.6 4.8 3.6 9.4 10.3 12.7 15.9 19.5 28.2 84.9 153
D+7 D+8 D+9 D+10 23.1 23.8 26.2 29.2 17.1 21.4 21.6 26.9 4.3 5 3 4.4 10.3 9.6 11.6 11.2 15.8 15.7 18.1 19.8 32.1 27.8 33.5 34.5 90.4 114 113 143
Neural Network Model for Aggregated Photovoltaic Generation Forecasting Table 6 Comparison of D+10 model and SIPRESOLAR
D+1 rMAE D+1 rRMSE D+1 rBias D+2 rMAE D+2 rRMSE D+2 rBias
D+10 Model 10.6% 17.2% .−0.7% 11.3% 18.11% .−0.4%
39 SIPRESOLAR 8% 13.5% .−1.8% 9.4% 16% .−2.3%
power and irradiance forecast) and a solstice variable (representing the distance in time to the winter solstice). Different data ranges for the training of the model have also been considered, and experiments show that the best results are achieved when the full historical data series is used. The performance of the model is then evaluated, by means of widely used metrics, showing a good behaviour, clearly outperforming a na¨ıve approach for the first five days. Further on, results are very similar. Furthermore, the model is also compared with the Spanish TSO forecasting tool and results are only slightly worse, although less information is used for the prediction (most importantly, real-time energy measurements not publicly available). Further work on this topic will focus on integrating this model with other forecasting tools in order to develop ANN models for the prediction of the energy prices in the Spanish market. Acknowledgments The authors would like to thank the financial support provided by the Universitat Jaume I from Castelló (Spain), the Generalitat Valenciana (GV), the European Social Fund (ESF) and the Spanish Ministry of Science and Innovation. This work was developed within the context of the projects with codes UJI-B2021-35 and grants ACIF/2019/106 and PID2020112943RB-I00.
References 1. Red Eléctrica de Espa˜na, Avance del informe sobre el sistema eléctrico espa˜nol en 2020 (2021). 2. Gobierno de Espa˜na, PLAN NACIONAL INTEGRADO DE ENERGÍA Y CLIMA 2021–2030 (2020). 3. S. Fresnillo-Velasco, J. Diaz-Garcia, J. R. Dorronsoro, SIPRESOLAR. Solar power forecasting system (2012). 4. J. Mathe, N. Miolane, N. Sebastien, J. Lequeux, PVNet: A LRCN Architecture for Spatio-Temporal Photovoltaic PowerForecasting from Numerical Weather Prediction arXiv: 1902.01453. 5. Minetur, Sede Eléctrónica PRETOR. 6. Minetur, Electra: Registro de productores de energía eléctrica. 7. Red Eléctrica de Espa˜na, Esios. Sistema de información del Operador del Sistema. URL https://www.esios.ree.es/es/analisis 8. S. Penate Vera, Comprehensive library to access the Spanish electricity market entity (ESIOS), in python 3 (2016). URL https://github.com/SanPen/ESIOS
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9. J. S. Armstrong, Principles of forecasting: a handbook for researchers and practitioners, Vol. 30, Springer, 2001. 10. R. J. Hyndman, G. Athanasopoulos, Forecasting: principles and practice, OTexts, 2018. 11. A. Rosebrock, Keras: Multiple Inputs and Mixed Data (2019).
Electrification of River Freight: Current Status and Future Trends in Europe F. Amoros, J. F. Charpentier, W. Lhomme, J. Y. Billard, and B. Nottellet
Abstract As the needs for sustainable freight transport solutions grow, river freight cargo is considered to be a very promising track. Large carriage boats allow up to three times less fuel consumption than trucks per ton.km. However, the use of traditional river freight ships leads to a high level of NOx and PM (particulate matter) emissions. Late evolution in regulation, large lifetime, 60 years for hull and 20 years for engine, as well as economical tightness have slowed down technological improvements. European solutions, such as the use of alternative fuels, electric or hybrid propulsions are studied. Projects with zero emissions are favoured as well as projects with easy potential adaptation into zero emission boat: full-electric vessels and hydrogen powered hybrid ships are the main solutions to be considered. Some new generations of vessels are already launched or planned. This paper aims to expose the challenge and to present the current status and trends for improving the impact of river freight.
F. Amoros () French Naval Academy Research Institute, Brest, France University of Lille1, Lille, France SEGULA Technologies, Le Havre, France e-mail: [email protected] J. F. Charpentier · J. Y. Billard French Naval Academy Research Institute, Brest, France e-mail: [email protected]; [email protected] W. Lhomme University of Lille1, Lille, France e-mail: [email protected] B. Nottellet SEGULA Technologies, Le Havre, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_4
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1 Introduction Freight transportation takes an important role in the global economy, and is responsible for 7% of global CO2 emissions [1]. With around 80% of the volume of international trade in goods carried by sea, naval architects are facing many challenges for developing sustainable transportation [2]. Even if maritime transportation is highly developed, inland waterways are still rarely used. In Europe, 6.1% of inland freight transportation are made via waterways versus 76.3% for trucks and 17.6% for trains [3]. The European Commission NAIADES III program has defined the objective to transfer 75% of inland freight from road to train and waterways transportation [4]. Inland Waterways Transportation (IWT) is one of the most efficient modes: it appears to be safer, less noisy, ecologically efficient and cheaper. IWT also allows a mass transport offer for any goods with highly predictive delivery time. A lot of trucks can be replaced efficiently, thus improving road traffic in urban area. All these advantages lead to intensive development of IWT projects. As examples, various canals buildings and infrastructure projects are scheduled such as Canal Nord Seine Europe to link Paris with Northern Europe waterway network. Wharves electrification projects and logistics studies linked with the development of new solutions for the “last kilometre delivery” are also emerging. With 20,000 km of wide-gauge waterways in the USA and Europe, more than 100,000 km in Russia and China and also a large underused network in South America, inland navigation is a global opportunity [5]. In a general way, existing waterways networks are underemployed while railway infrastructure and truck roads are already reaching their limits. This allows a significant growth potential for IWT. According to [6], an average inland vessel emits 3 times more CO2/t.km than an average European train and over 25 times less than an average heavy duty truck. Nevertheless, very few on board measurements have been done to evaluate river freight ecological performances. The PROMOVAN program [7] is one of these. Three boats have been instrumented: a self-propelled barge, a pusher boat and a passenger boat. This program shows that the big carriage capacity of the vessels leads to very low fuel consumption and CO2 emission by t.km (5 times less than Euro II 25 t payload truck). Recent heavy goods vehicles show better performances for main pollutants (NOx, PM, HC and CO). Euro V trucks emit 2 times less NOx and CO than the pusher studied while using or emitting 3 times more fuel or CO2 by ton.km. The study concludes that IWT has better efficiency if the cargo is above an around 1000 t threshold. Passenger transport, closely linked to the tourism sector, represents another aspect of the river economy. The electrification of passenger river vessels has already been studied in [8–10] for example. Furthermore, many passenger vessels are already launched using innovative propulsion chains. This paper deals with rivers freight only. In this context, electrification projects for freight boats in inland waterways are slowly emerging with prototypes vessels already launched. To match different types
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of mission covered by river freight ships, future needs and access to energy, the choice of multiple energy supplies seems to be a very promising solution. Transition to a new generation of river ships using non-conventional propulsion choices leads to political, economic and environmental concerns. River freight vessels durability, 60 years for the hull and around 20 years for engines, is an obstacle to a fast and pertinent transition. The choice of energy propulsion solutions is directly linked to constraints on costs, routing, storage, production, infrastructure and logistics [11]. This paper aims to expose the challenge and to present the current status and trends for improving the impact of river freight. This paper is divided in three sections. In the first section, constraints applied to IWT are described, considering the current state of the European fleet, the regulations and the economic features. In the second section, solutions to perform a greener inland navigation sector are discussed presenting examples of innovative boats already in use or planned to be built. The third part is an overview of current trends and obstacle for the development of innovative propulsion systems.
2 Inland Freight Boats Technical Constraints Inland vessels are fundamentally different from seagoing ones. River currents tend to lower the efficiency of IWT compared with sea-shipping [12]. Moreover, the navigation in calm water results in boats with long and flat hulls or pushers with barges.
2.1 Boats Technical Constraints IWT is more efficient as boats payload grows: trends since the 2000s show a size transformation, large units are favoured. However, it is impossible to build and use only pushers carrying many barges. Waterways characteristics: size, depth eventual lock and currents are constraints for both river freight boat construction and usage. Table 1 shows the classification of inland vessels by size with their average payload and propulsion power. For example, the future Canal Seine-Nord Europe will be built for European classes V(b) or below (Table 1). The European IWT fleet is old; a significant part of the fleet was built between 1960 and 1990 [13]. The durability of river hulls, despite being beneficial for economic and ecological purpose, is also a slowdown for the greening of the fleet. Some units are not well designed for their current missions. For example, container shipping is relatively new in river freight. Originally designed for break bulk, many vessels lose a lot of payload while carrying this kind of cargo.
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Table 1 Different kinds of vessels characteristics [13] Kind of vessels Length × Beam × Draught Freycinet – CEMT I 38.5 × 5.05 × (1.8–2.5) m Campinois – CEMT II (50–65) × (6.05–7) × (2.5–2.6) m CEMT III (67–85) × 8.2 × (2.5–2.9) m CEMT IV (80–105) × 9.5 × (2.5–2.8) m Rhénan – CEMT V(a) (95–110) × 11.4 × (2.5–3.4) m Grand Rhénan – CEMT V(b) 135 × 11.4 × (2.5–3.4) m EUROPA II – 1 to 4 barges CEMT VI a,b,c (100–185) × 11.4 × (2.5–4.5) m CEMT VII – 3 × 3 barges (195–285) × 34.2 × (2.5–4.5) m
Payload (t) 250–400 t
Power (kW) 184 kW
650–750 t
405 kW
950–1250 t
590 kW
1350–2000 t
515–735 kW
2000–3000 t
880 kW
2500–3500 t
1400 kW
2000–2750 t/barges 1470 (2b.)4200 (4b.) kW
14,500–27,000 t
N/A
2.2 River Transport Regulations For years, a huge gap between river and road regulations has been observed. River regulations tend to move towards road ones. The regulation of air pollutant emissions has drastically strengthened since January 1, 2020, with the implementation of NRMM’s phase V regulations (Non-Road Mobile Machinery) (Fig. 1) [14]. It concerns main propulsive engines and bow thruster engines as well as generators. Those regulations are applied to new boats and retrofit; motorists have to sell engine corresponding to current regulation. As boat engines can operate around 20 years before a change, the current fleet has not seen its pollutant emission decrease a lot with the evolution of regulation. According to the NRMM regulations, usable engines for inland navigation are categorized as Inland Waterway Propulsion, Inland Waterway Auxiliaries, NonRoad Engine (originally for agricultural or buildings machinery) and truck engines with EU-EURO-VI certification. Among those engines Inland Waterway Propulsion are the classical ones developed for marine propulsive applications. Use of NonRoad Engines is an interesting solution but the emission constraints for this category are stricter. Non-Road Engines and truck engines need an expensive process for adaptation to maritime environment. Most of the time, this marinization process cannot fit the budget allowed to ITW ship projects. Truck engine also are not designed to be used at high continuous power like Inland Waterway Propulsion ones. Their lifetime is then significantly limited in ITW. Most of the available engines need particulate filters to fit PM emission regulation.
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Evolution of regulation for IWT and Road 0,7 0,6 USA 2011 >600kW
0,5 PM (g/kWh)
CCNR I 2002
NRMM IIIA 2009
0,4 0,3 NRMM V 2019 300kW Euro IV
CCNR II 2007 600kW
USA 2011 >600kW
4
6
8
10
12
14
NOx (g/kWh)
Fig. 1 River and road evolution for pollutant emission regulation [15]. CCNR Central Commission for Navigation on the Rhine C) Table 2 Average cost (A per t.km of inland freight in Netherland for different modes and different load type [18]
Dry bulk Break bulk Liquid bulk Container
IWT 0.023 0.028 0.032 0.023
Truck 0.297 0.198 0.111 0.1035
Train 0.59 2 0.76 0.85
More detailed regulations for European inland navigation are available in [16, 17], including performance and safety requirements. European shipping industry associations [4] have defined the objectives to reduce by 50–70% emissions from inland navigation without specifying the date of reference for 2050.
2.3 Economic Constraints IWT is the cheapest inland freight mode. Table 2 shows the cost of freight transportation in euro per ton.km for different kinds of carriages and for the three main inland modes. IWT is more than 4 times cheaper than truck and 20 times cheaper than train. However, with the development of just-in-time economy, IWT suffered the concurrency of road transportation that, despite being more expensive, have the advantage of being more flexible and faster. As ecological interest rises, IWT becomes more popular. Moreover, goods transported on rivers are agricultural and food products for 15%, building materials for 26% or energy products for 25%, according to [3]. The use of waterways to transport mostly bulk materials with low-added value results in significant economic pressure on river ship-owners. Cash flows are low and so is the potential investment in greener vessels.
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3 Reducing River Freight Emission The greening of passenger ship fleet is already an ongoing research topic. Some electrified ships are launched, mostly ferries in northern Europe. However, for freight vessels, things are moving slowly. Freight transportation seems late on the topic. In the 2000s, the Cleanest Ship project [19] aimed to reduce emissions of a classic internal combustion engine motorized boat with pilots advising, particles filter and low-sulphur fuel. It was one the first demo ship for IWT.
3.1 Alternative Fuel Boats Alternative fuels can play a significant role to reduce the environmental impact of IWT. Gas fuels (Liquefied Natural Gas LNG – Compressed Natural Gas CNG) and hydrogen are the subject of much study. Low sulphur Diesel lead to significant emission reductions (−17% PM; −99.5% SOx according to [19]), Methanol and Bioethanol can also be mentioned. “Compagnie Fluviale de Transport” (CFT) company has already tried to substitute diesel with Oleo100, a fuel from colza oil with a 6-month experimentation on their barge “Sandre” [20]. Results are promising with 60% fewer greenhouse gases emitted. The company is currently trying to use other fuels such as Alten’s PUR-XTL, a synthetic diesel produced from waste oils. Figures 2 and 3 from [6, 21] shows costs and emission related to different fuels. According to the data and [22] BioCNG and methanol are the best fit for river freight vessels. Hydrogen appears as the worst fuel with its high cost and low Net Calorific Value (NCV). Moreover, it is the fuel which needs to face the greatest technological challenge with the needs of mature solutions in terms of fuel cells and storage technologies. Most of the other alternative fuel solutions can be integrated into conventional propulsion without significant modification. However, cost prediction and its great ecological performance make hydrogen a viable solution for future exploitation in the next decade. Further investigations are needed to estimate the feasibility of those solutions for ITW with bunkering and distribution chain potential analysis.
3.2 Battery-Electric River Freight Vessels Consequently, to a competitive and niche market and despite the European objective to achieve carbon neutrality in 2050, very few full-electric inland vessels are launched. The needs for long autonomy and large payloads are the main obstacles to the development of this full electric technology. However, some electric barges project exists in Europe. For example, PortLiner proposes two kinds of full electric inland shipping vessels for containers transport already navigating in Germany and Netherlands. Zero Emission Service has inau-
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Cost 2020 (€/kWh) 0,25 0,2
0,15 0,1 0,05
Di
es
el
H
yd
ro
El
ge
n
ec
G N C
G Bi
oC
N
G LN
G TL
0
Fig. 2 Alternative fuel cost [21]
Emission (Kg CO2e/kWh) 0,35 0,3 0,25 0,2 0,15 0,1 0,05 0 L GT
LN
G Bi
oC
NG
CN
G
El
ec H
r yd
og
en
Di
es
el
Fig. 3 Alternatives fuel emissions [6]
gurated the Alphenaar (Fig. 4): a 100% electric barge, 90 metres long, carrying 4 MWh of batteries allowing 4–8 hours (60–120 km) autonomy [23]. The particularity of this boat is its recharging mode: batteries are stored in containers that can be exchanged at a station with charged battery containers. Norway has also taken a big step towards greening inland navigation freight transport with the Yara Birkeland: the first autonomous electric cargo boat (80 m – 7MWh of batteries) [24]. Some research already investigates the design of new electrical drive for inland navigation applications [25]. For example, [26] studies the potential 2% gain by using a direct drive high torque low speed permanent magnet motor for driving the propeller.
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Fig. 4 The Alphenaar [23]
Fig. 5 Parallel hybrid (left) and series hybrid architectures (right)
3.3 Hybrid Electric River Freight Vessels Hybrid powered boats seem more relevant to reach river freight ship specifications in terms of autonomy, significant payload and upstream navigation. In the following part, it is assumed that hybrid boats have at least two energy sources to propel vessels. This definition specifically excludes the so-called Diesel-Electric architecture (without storage systems). Three hybrid propulsion solutions are considered (Fig. 5): – Parallel hybrid; internal combustion engines and electric motors are both mechanically coupled (by clutch/gearbox system) to the propeller shafts. Energy Storage systems can be used in the electrical power chain. – Series hybrid; a combination of batteries (or other energy storage Systems, ESS) and electrical power sources (diesel generators, fuel cells or other sources) provide electric power a variable speed electric motor and drive coupled to the propeller shaft
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– Series parallel hybridization; both electrical and mechanical couplings are used in a complex architecture not yet studied for inland vessels. For light-duty vehicles, it is well-known that the most interesting configuration is the series-parallel HEV [27]. However, series-hybrid propulsion is a favoured solution due to its simplicity, redundancy and also because it can be easily retrofitted to future electric sources and ESS technologies such as fuel cells, gas generators or super capacitor. A comparison between these two architecture for small vessels is available on [28]. Parallel hybrid vessels are studied in literature [29, 30] without many data available on real boats launched. Transfluid company already markets the component allowing the mechanical coupling of the various energy sources. Partnerships with engine manufacturers (Caterpillar, Yanmar) allows Transfluid to offer complete propulsion solutions, mostly for small pleasure boats with below 1 MW powertrain. The MTU branch of Rolls-Royce also proposes parallel-hybrid solution for ship propulsion (1–4 MW). This propulsion system is installed on ferries, patrol boats, etc. Series hybrid is a suitable solution for hydrogen fuel cells and gas-fuelled vessels; diesel-electric hybridization is also a possibility [31]. Even if LNG solutions are already available for trucks, safety issues make it harder to fit for inland navigation needs [32]. Every LNG boat needs to be classified by a classification society. Green Deliriver’s project intends to build a series hybrid gas pusher with a smart floating warehouse as an innovative urban logistic solution [33]. Hydrogen freight vessels with fuel cells are promising solutions. Sogestran plans to inaugurate the first hydrogen powered barges by the end of 2021. Dutch companies have ordered two more vessels: the Antonie van Lenten (Concordia Damen) that is expected to be launched by 2023 and will be able to carry 3700 t; and the Maas (Future Proof Shipping) will be retrofitted. The Maas design includes 300 kWh batteries for bow thruster, 200 kWh batteries for propulsion, 3 fuel cells of 275 kW rated power each, and 1 ton of Hydrogen in swappable containers. Series parallel hybrid vessels for river freight are, for now, only an academic prospective topic [34, 35].
4 Discussion 4.1 Key Challenges ITW ecological transition is late compared to road and train. This is mainly due to weak regulation evolution over the past decades, but also to engines and ships structures durability: engine lifetime is around 20 years. The constraints respected by those engines correspond to their installation time regulations. Therefore, regulations study are not sufficient to show the emission for river freight. Very few measurements have been carried out on board inland vessels. However, large-
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scale studies are available to evaluate the sector overall pollutant emissions such as ADEME [15] and Central Commission for Navigation on the Rhine (CCNR) [36] ones. The lack of studies on ITW ecological performance makes it harder to identify improvement possibilities and to find budget for electrification projects. Increasing electrical storage autonomy with limited volume and cost is a key point for the development of full electric river freight ships. Classical operational cycle for inland vessels are long cruises relative to current batteries autonomy (more than 10 hours) at around 12 km/h. The cost and the loss of payload due to the installation of large batteries limits the possibility to use ESS for long cruise mission profiles. With current electrical storage systems, autonomy is limited at best to 2– 4 hours range for full-electric ship systems. For alternative fuels, issues are economic. For now, ship-owners have no interest in increasing their operational cost with more environmentally friendly fuel. Gas technologies are not mature enough. Available LNG engines are either too powerful ones for maritime applications, old engine that cannot fit current regulations or truck engine which need costly marinization. Finding a gas engine is complex and for now, only generators can match the cost and emission criteria. One of the main challenges is to decrease the ecological impact without increasing significantly the cost of freight transportation. Many of the obstacles for the development of innovative propulsion systems are then linked with economic constraints.
4.2 Current Trends Analysis of the existing projects shows an important interest for potential zeroemission systems. Trends in regulations predict future definitions of Zero Emission Zones. Battery or Hydrogen powered electric vessels can reach this objective. To deal with economical tightness, retrofit can be a relevant solution: old hull in needs of new engines are retrofitted to include fuel cells, battery and electric motors in their propulsion chain. Those projects are, for now at the demonstrator phase. To fit the recent regulation and cost criteria, most of ship-owners choose to setup exhaust after treatment with particulate filters. Selective Catalytic Reduction might also become a possibility as it integration is easier for inland boats than sea-going vessels [37]. The equipment of ducted propeller is a known way to improve boats efficiency and is encouraged by the Central Commission for Navigation on the Rhine.
5 Conclusion In this paper, the constraints applied to river freight has been examined, as well as the variety of solutions proposed by academic searchers and ship-owners. A trend
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for potential zero-emission vessels is identified alongside strong issues that slow down the greening of the European inland fleet. As regulation becomes more stringent and public interest for cleaner shipping industry increases, projects on new propulsion chain emerge. European train emissions level can be defined as an objective for IWT, which is already the cheapest transport mode. Development of innovative propulsion projects will increase with the already-going development of river freight.
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Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost DC-DC Converters Hai-Nam Nguyen, Bảo-Huy Nguyễn, Thanh Vo-Duy, Minh C. Ta, and João Pedro F. Trovão
Abstract The nonlinearity of boost DC/DC converters is well-known in the field of power electronics control. Traditionally, the converter model can be linearized at an operating point which is the small-signal linearization. On the other hand, the converter can be regulated by using nonlinear controllers in which sliding mode control (SMC) method is commonly applied. The previous works of SMC were often based on the switching model of converter which suffer from nonuniform switching frequency and/or chattering. This paper proposes two novel average model-based SMC schemes for bidirectional boost DC/DC converters; one is a single-stage controller and the other one is a cascade control loop. The new controllers outperform the traditional ones in terms of response time and accuracy that is validated by critical simulation scenarios. The proposed approach can be extended to other complex power electronics converters.
1 Introduction Bidirectional boost DC/DC converter has a nonlinear structure [1], to deal with it several methods have been developed in literature using linear and nonlinear approaches. The linear approach is commonly small-signal linearization for to be
H.-N. Nguyen · B.-H. Nguyễn () · T. Vo-Duy CTI Lab. for EVs, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam e-mail: [email protected] M. C. Ta CTI Lab. for EVs, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam e-TESC Lab., Université de Sherbrooke, Sherbrooke, QC, Canada J. P. F. Trovão e-TESC Lab, Université de Sherbrooke, Sherbrooke, QC, Canada Polytechnic of Coimbra, IPC-ISEC and INESC Coimbra, Coimbra, Portugal © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_5
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applied with PID controllers [2]. The previous nonlinear controllers consist of model predictive control (MPC) [3], fuzzy logic control [4], and sliding mode control (SMC) [5, 6]. MPC is of high performance but complicated that makes it difficult to be utilized in practical applications, while fuzzy logic controller is depended on the users’ understanding of the system. Meanwhile, SMC is often used thanks to its design simplicity, stability, and robustness under a wide range of operating conditions. Applying SMC for bidirectional boost converters in previous studies has presented promising results [6, 7]. DC/DC converters have a variable structure [8]; hence, the method widely used in these studies is often the bang-bang type control, developed from the switching model of the converter. This direct switching control law causes the issue of nonuniform switching frequency. To overcome this drawback, pulse-width modulation (PWM) with fixed frequency can be applied by using the so-called equivalent control signal .ueq which has been deduced in several previous works, such as [5]. The .ueq is often obtained from the derivative of the sliding surface, then “translated” to duty cycle for PWM implementation. This paper proposes an alternative approach by which the SMC law can be directly conducted based on the average model of the converter. Using this approach, two novel SMC schemes are developed. The first one is a single-stage sliding mode controller with both errors of capacitor voltage and inductor current taken into account in the sliding surface. The second scheme is a cascade sliding mode control loop with an inner current controller and an outer voltage loop. Both are applied on the average model of a bidirectional boost converter, which is organized by using energetic macroscopic representation (EMR) [9]. This formalism is a graphical method to tackle complex energetic systems. The paper is organized as follows. Section 2 presents the model configuration of the converter and conventional PI controllers. The two proposed sliding mode controllers and their parameters selection are introduced in Sect. 3. In Sect. 4, simulation results and discussions are addressed. Finally, conclusions and perspectives are drawn in Sect. 5.
2 Modeling and Conventional PI Controllers 2.1 Modeling and Representation The configuration of the boost converter is shown in Fig. 1. The converter consists of a DC voltage source, an inductor, a chopper, and a load, which are directly connected in series. EMR elements are used to represent the converter’s components as subsystems linked by the action and reaction principle and the physical-integral causality principle [9], as shown in Fig. 2. The studied converter average model included five parts are therefore expressed below.
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
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Fig. 1 A bidirectional boost converter configuration
Fig. 2 EMR and inversion-based control of DC/DC converter (first control scheme)
The input voltage .uS is represented by a source element (oval pictogram). The inductor with its parasitic resistance and the capacitor are accumulation elements (crossed rectangle pictogram) and addressed by: L
.
diL = uS − riL − uch dt
(1)
duC = ich − iload dt
(2)
C
.
where .uC , .iL are the capacitor voltage and the inductor current, respectively. The chopper is a mono conversion element (square pictogram) which is expressed by the following: .
uch = mch uC ich = mch iL
, with 0 ≤ mch ≤ 1
(3)
where .mch is the average modulation function to modulate the switches of the chopper. The load is presented as a DC source (oval pictogram).
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2.2 Conventional PI Controllers The control scheme can be traditionally organized by the inversion-base principle [9]. Firstly, the capacitor is an accumulation element; hence, with the input voltage reference .uC ref and the measured voltage .uC meas , the PI voltage controller can be deduced as an indirect inversion (crossed parallelogram) of the capacitor model:
.
ich ref = iload meas + kP C (uC ref − uC meas ) t (uC ref − uC meas )dt + kI C
(4)
0
in which .ich ref is the chopper current reference, .iload meas the measured load current, .kP C and .kI C the PI coefficients. The chopper reference .ich ref then enters the direct inversion (parallelogram pictogram) of the chopper which has an output as the inductor current reference given by: iL ref =
.
ich ref mch
(5)
The chopper voltage reference .uch ref is achieved by a similar indirect inversion PI controller as (4) with the input .iL ref as follows: uch ref = uS meas − kP L (iL ref − iL meas ) t . (iL ref − iL meas )dt − kI L
(6)
0
where .uch ref is the chopper current reference, .iL meas the measured inductor current, and .uS meas the measured DC source voltage. Finally, the average modulation function .mch is obtained by dividing .uch ref to .uC meas as follows: mch =
.
uch ref uC meas
(7)
which is the control variable of the studied boost DC/DC converter.
3 Proposed Average Model-Based Sliding Mode Control Schemes In this paper, we propose two SMC schemes which are directly deduced based on the average model of the boost converter. The obtained control law of the chopper
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
59
Fig. 3 Single-stage sliding mode control of the studied system (second control scheme)
modulation function is then modulated by the PWM to operate the converter in the fixed switching frequency.
3.1 Single-Stage Sliding Mode Control Scheme The control scheme is shown in Fig. 3. The most important part of designing a sliding mode controller is to determine the sliding surface. The surface must contain the error of the state variable. In this approach, the surface is chosen to be a linear combination of the capacitor voltage and the inductor current errors as follows: S = k1 (uC − uC ref ) + k2 (iL − iL ref )
.
(8)
where .k1 , .k2 denotes the positive sliding coefficients for the voltage and current errors, respectively. According to [10], the reference inductor current .iL ref can be determined as: iL ref =
.
iload uC uS
(9)
The method of nonlinear controller design is based on Lyapunov stability shown by the reaching law: S
.
dS ρ S/ρ if |S| ≤ ρ
(13)
where the saturation gain .ρ is a slope coefficient. Expanding (11) with combination of (1) (2) and (3), the average control signal .mch has the following form:
mch =
(k1 − k2
.
uS − riL iload iload − k2 − ksat (S/ρ) ) uS C L iload iL uC ) − k2 (k1 − k2 uS C L
(14)
the control law can be decomposed into two parts as: mch = mch re + mch sl
.
(15)
where .mch re is the reaching component and .mch sl is the sliding component, with: mch re =
.
mch sl =
−ksat (S/ρ) . iload iL uC ) − k2 (k1 − k2 uS C L iload iload uS − riL − k2 ) uS C L . iload iL uC ) − k2 (k1 − k2 uS C L
(16)
(k1 − k2
(17)
The component .mch re is used when the system is in the reaching mode. At this mode, the errors are forced to reach the sliding surface .S = 0. Meanwhile .mch sl is applied when the system is in sliding mode with the following equation:
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
.
dS = 0. dt
61
(18)
The problem is arose in determining the coefficients .k, .k1 , and .k2 . When the system is in the sliding phase: S = k1 e1 + k2 e2 = 0
.
(19)
where the tracking errors are denoted as: .
e1 = uC − uref e2 = iL − iref
(20)
and the voltage error can be computed by: |e1 | =
.
k2 |e2 |. k1
(21)
k2 and the desired reaching time .tr , the static voltage error .e1 k1 can be obtained to meet the control requirements. By tuning the ratio .
3.2 Cascade Sliding Mode Control Scheme In this section, a cascade SMC scheme is proposed (see Fig. 4) with the aim of reducing the steady-stage error by separately controlling the capacitor voltage and the inductor current. The outer voltage loop and the inner current loop are designed using the same approach addressed in Sect. 3.1.
Fig. 4 Cascade sliding mode control of the bidirectional boost converter (third control scheme)
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Voltage Control (Outer Loop)
The sliding surface of the voltage controller is defined by: Su = k1 (uC − uC ref )
.
(22)
where .k1 is a positive coefficient. Similar to the previous SMC design process, the derivative of the sliding surface is: .
dSu = −ku sat (Su /ρ) dt
(23)
where .ku is a positive constant parameter, the output of the voltage controller is the current reference to be imposed on the inner loop. Carried out from (2), (3) and (23), the current reference has the following form:
iL ref =
.
k1
iload − ku sat (Su /ρ) C mch k1 C
(24)
that is the control law of the outer voltage SMC loop.
3.2.2
Currrent Control (Inner Loop)
The aim of the inner control loop is to control the inductor current .iL to follow the reference .iL ref obtained from (24). The sliding surface is chosen as : Si = k2 (iL − iL ref )
.
(25)
with the positive constant .k2 . Following Lyapunov stability, the reaching law is expressed: .
dSi = −ki sat (Si /ρ) dt
(26)
with .ki is a positive coefficient. Extracted from (1), (3) and (26), the average modulation function .mch is obtained as below:
mch =
.
k2
uS − riL + ki sat (Si /ρ) L uC k2 L
that is the control law of the inner current SMC loop.
(27)
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
3.2.3
63
Control Parameters Determination
The advantages of using saturation function .sat (S/ρ) are to reduce the chattering phenomenon and to keep a fast response of the system and to gain the high robustness following Lyapunov stability. The reaching time when applying this function can approximately be calculated by (12). The response time .tr i of the inner current loop should be at least ten times faster than .tr u of the outer voltage loop [13] as follows: ⎧ |Si (0)| ⎪ tr i = ⎪ ⎪ ⎪ ki ⎨ |Su (0)| . tr u = ⎪ ku ⎪ ⎪ ⎪ tr u ⎩ tr i = 10
(28)
k2 k1 and . can be chosen following (28) with the ku ki desired response times .tr u and .tr i , respectively. The control coefficients ratios .
4 Results and Discussions The simulations are performed on Matlab/Simulink and the results are shown to validate the fast convergence, better voltage reference tracking, and the robustness of the proposed methods. The two SMC schemes of single-stage and cascade methods are sequentially compared to the conventional PI controller to verify the ability to achieve the control objectives under load and reference variations. The converter and control parameters are given in Table 1. Table 1 Bidirectional boost converter parameters
Parameter DC source .uS Inductor .L Capacitor .C Parasitic resistance .rL Single-stage SMC .k1 Single-stage SMC .k2 Single-stage SMC .tr Cascade SMC .k1 Cascade SMC .k2 Cascade SMC .tr u Cascade SMC .tr i Saturation gain .ρ
Value 24 V 0.5 mH 2200 uF 0.1 . 0.015 0.01 0.015 s 0.02 0.0087 0.01 s 0.001 s 0.01
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55
uC
u Cref
50 45 40 35 30 25
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0.8
Fig. 5 Voltage tracking with PI controller (first control scheme) Current Tracking
10
iL
i Lref
5
0
-5
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0.8
Fig. 6 Current tracking with PI controller (first control scheme)
Figures 5 and 6 show the voltage response and current response of the converter with the PI controller. While Figs. 7 and 8 address the ones of the converter using the single-stage SMC. The performance of the system using cascade SMC is plotted in Figs. 9 and 10. Finally, Fig. 11 gives the values of average modulation function signals .mP I , .mSMC 1 and .mSMC 2 of conventional cascade PI controller, singlestage SMC, and cascade SMC, respectively. The simulation time is set to be 0.8 s. First, the system works without load for the first 0.2 s. At this period, the voltage reference is 36 V and the initial capacitor voltage is 26.4 V. Then, the resistance load of .20 is connected to the system since .t = 0.2 s. The voltage reference is increased from 36 to 48 V at 0.4 s. The variation in resistance load occurs again at .t = 0.6 s when its value raises to infinity (open circuit) leading to the zero load current. The simulation scenarios are identical for the conventional cascade PI control structure and the two proposed control schemes to ensure a fair comparison. The output voltage of the converter using cascade PI controller responds in 0.1 s and it causes no steady-stage error. Meanwhile the response time of the system using the two proposed control schemes is identified following (12) and the results are
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
65
Fig. 7 Voltage tracking with single-stage SMC (second control scheme) Current Tracking
10
i Lref
iL
5
0
-5
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0.8
Fig. 8 Current tracking with Single-stage SMC (second control scheme)
shown in Figs. 7 and 9. The single-stage SMC and cascade SMC controllers allow the output voltage to quickly converge to its reference value. The response time is 0.015 and 0.01 s, respectively. Although with this type of sliding surface, the SMC can not absolutely remove steady-stage errors but the errors are practically negligible. That is demonstrated from .0.75 s to the end, the steady-state error of
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Fig. 9 Voltage tracking with Cascade SMC (third control scheme) Current Tracking
10
i Lref
iL
5
0
-5
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0.8
Fig. 10 Current tracking with Cascade SMC (third control scheme)
the single-stage SMC is 4.1 mV and the one of the cascade SMC is 0.6 mV (Figs. 7 and 9). These average modulation signals in Fig. 11 are limited within [0, 1] that satisfies the condition (3). From .0.75 s to the end, the average modulation signal of cascade PI controller changes within [0.49, 0.51]. That control signal fluctuates with a deviation of 0.03 from the desired signal. Otherwise, the single-stage SMC control
Average Model-Based Sliding Mode Control Schemes of Bidirectional Boost. . .
67
Fig. 11 Average modulation function of PI controller, single-stage SMC and cascade SMC
signal is modulated with higher fluctuation, meanwhile the cascade SMC signal’s oscillation is .0.02 in the same scenario. In the whole process, the last proposed method modulates the control signal with almost the least oscillation. Therefore, the cascade SMC controller performs the least fluctuation compared to the other counterparts.
5 Conclusions Two proposed average model-based sliding mode control schemes for nonlinear bidirectional boost DC/DC converters have been developed following a simple-buteffective design approach. A comparison between the traditional PI controller and the novel controllers have demonstrated the advantages of proposed methods. The system has tracked the voltage reference in a desired short period. The chattering phenomenon has been reduced and the robustness of the controllers has been proved through simulations under reference and load changes. With the novel cascade SMC controller, the DC/DC converter has a faster voltage response and a better robustness over various operating conditions than the first proposed single-stage SMC controller and the conventional PI controller. The novel average model-based approach can also be applied to more complex power electronics converters that would be investigated in future study.
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Acknowledgments This work was supported in part by Grant 950-230672 from Canada Research Chairs Program, in part by Grant RGPIN-2017-05924 from the Natural Sciences and Engineering Research Council of Canada, in part by FCT-Portuguese Foundation for Science and Technology project UIDB/00308/2020, and by the European Regional Development Fund through the COMPETE 2020 Program within project MAnAGER (POCI-01-0145-FEDER-028040).
References 1. H. Al-Baidhani, M. K. Kazimierczuk, and A. Reatti, “Nonlinear Modeling and Voltage-Mode Control of DC-DC Boost Converter for CCM,” in 2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018, pp. 1–5. 2. T. Vo-Duy, B.-H. Nguyen, M. C. Ta, J. P. Trovao, and N. Nguyen, “Different voltage and current control schemes for multi-pack battery of electric scooters,” in 2020 IEEE Vehicle Power and Propulsion Conference (VPPC), 2020, pp. 1–5. 3. R. Errouissi, A. Al-Durra, and S. Muyeen, “A robust continuous-time MPC of a DC–DC boost converter interfaced with a grid-connected photovoltaic system,” IEEE Journal of Photovoltaics, vol. 6, no. 6, pp. 1619–1629, 2016. 4. N. F. N. Ismail, I. Musirin, R. Baharom, and D. Johari, “Fuzzy logic controller on dc/dc boost converter,” in 2010 IEEE International Conference on Power and Energy, 2010, pp. 661–666. 5. S.-C. Tan, Y. Lai, and C. Tse, “A unified approach to the design of PWM-based slidingmode voltage controllers for basic DC-DC converters in continuous conduction mode,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 8, pp. 1816–1827, 2006. 6. S.-C. Tan, Y.-M. Lai, and K. T. Chi, “General design issues of sliding-mode controllers in dc– dc converters,” IEEE Transactions on Industrial Electronics, vol. 55, no. 3, pp. 1160–1174, 2008. 7. C. S. Sachin and S. G. Nayak, “Design and simulation for sliding mode control in dc-dc boost converter,” in 2017 2nd International Conference on Communication and Electronics Systems (ICCES), 2017, pp. 440–445. 8. R. A. DeCarlo, S. H. Zak, and G. P. Matthews, “Variable structure control of nonlinear multivariable systems: a tutorial,” Proceedings of the IEEE, vol. 76, no. 3, pp. 212–232, 1988. 9. A. Bouscayrol, J.-P. Hautier, and B. Lemaire-Semail, “Graphic formalisms for the control of multi-physical energetic systems: COG and EMR,” Systemic design methodologies for electrical energy systems: analysis, synthesis and management, pp. 89–124, 2012. 10. H. Lin, S. Ebrahimi, M. Mahdavyfakhr, and J. Jatskevich, “Analysis of sliding-mode-controlled boost converters with mixed loads,” in 2020 IEEE 21st Workshop on Control and Modeling for Power Electronics (COMPEL), 2020, pp. 1–8. 11. J.-J. E. Slotine, W. Li et al., Applied nonlinear control. Prentice Hall, 1991. 12. C. J. Fallaha, M. Saad, H. Y. Kanaan, and K. Al-Haddad, “Sliding-mode robot control with exponential reaching law,” IEEE Transactions on Industrial Electronics, vol. 58, no. 2, pp. 600–610, 2011. 13. Mathworks, “Tuning Multiloop Control Systems,” 2021. [Online]. Available: https://www. mathworks.com/help/slcontrol/ug/tuning-multi-loop-control-systems.html
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic Pulse Width Modulation Applied to a Flying Capacitor Leg Inverter Mariem Jday and Paul-Etienne Vidal
Abstract This paper introduces a dynamic Pulse Width Modulation scheme, apply to N-level Flying Capacitor inverter. A mathematical approach is detailed to solve the expression of a linear system that model the inverter leg considered. Some degrees of freedom, that have to be set, are exhibited. The proposed technique relies on the relationship made between the degrees of freedom and the voltage unbalance of the floating capacitors. Simulation results are provided to illustrate the performance of such a modulation scheme.
1 Introduction Static power converters controlled by Pulse Width Modulation (PWM) are frequently used in various industrial applications such as power generation systems [1], energy transportation systems, etc. In order to improve the overall performance of these applications, multilevel converters, a particular class of converters, are now used in a wide range of industry applications [2]. Effectively, the use of two-level power converters in high-voltage applications causes an increase of the blocking voltage of semiconductors. The use of multilevel converter structure can mitigate this problem. Several multilevel architectures have emerged in the last three decades [3]. Among them, the Flying Capacitor inverter (FC inverter) is defined [4]. This converter has intermediate voltage sources formed by floating capacitors. This converter requires balanced voltages for every floating capacitors. This functioning constraint generates a great interest to ensure the floating capacitor voltage balanced, thanks to the control applied to the converter [5]. It has been demonstrated that, in the absence of any fault, the usual carrier based PWM control ensures the natural balance of the capacitor voltages. Several studies have been made on the control of multicell series converters in order to
M. Jday () · P.-E. Vidal Laboratoire Génie de Production, LGP, Université de Toulouse, INP-ENIT, Tarbes CEDEX, France e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_6
69
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M. Jday and P.-E. Vidal
increase the performance of the converter. A particular technique, the Space Vector Pulse Width Modulation scheme (SVPWM), was presented to achieve the best performance. SVPWM consists of monitoring the output voltage as a rotating vector, and representing it on a diagram, following the states of switches. Nevertheless, for large system, SVPWM is difficult to design. In recent years, a generic model of PWM Voltage Source Inverter (VSI) was proposed [6, 7]. It is based on a generic and average model of the three-phase converter. This generic model allows to describe the inner topology of every leg and, by the use of several mathematical tools, to generate the relationships between duty cycles to apply, and the desired average output voltages. As a matter of facts, the method finally helps generating the PWM scheme to apply, whatever the topology or the number of level desired. During the process to express the duty cycles, some degrees of freedom, that have to be set, are generally exhibited. In this work, the aim is to use the generic framework described previously to ensure floating capacitor voltage balance, thanks to the PWM scheme. A PWM scheme that allows to exploit the measured or estimated capacitor voltages will be used. The floating capacitor voltage measurement will be finally related to the degrees of freedom. Indeed, every duty cycle generated will ensure voltage balance and low harmonic output current. This paper is made of five parts. In the second section, an average model of N-level FC inverter is described. A PWM control strategy is deduced. In third and fourth sections, the previous model is applied to a 3 level and 5 level FC inverter, respectively. In the fifth section, and for the latter topology, the number of degrees of freedom, their ranges of use and their expressions, are determined. This section ends with simulations performed on Matlab/Simulink. Simulations show the performance and robustness of the proposed control strategy, compared to the usual PWM control. More precisely, the robustness is assessed when a fault produces a floating capacitor unbalance.
2 N-Level Generic PWM Scheme for Flying Capacitor Topology 2.1 PWM Flying Capacitor Model N is the number of level that can be reached by the output voltage .vao . The N-level FC is composed of nested elementary switching cells, with per level capacitor as illustrated by Fig. 1. .p = N − i, stands for the ratio value of the voltage source E applied to the capacitor .Ci of the switching cell i. The elementary switching cell numbered i, is made of .Ti and its complementary switch .Ti , and the floating capacitor .Ci . When .Ti = 1, the switch is ON, OFF elsewhere. Within the inner FC structure, the difference between the two capacitors’
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
71
Switching Cell 1
Load
Fig. 1 Isolated leg of a N-level FC inverter
Fig. 2 Voltage waveform .vi of an isolated switch .Ti
voltage is .
E . For the leg connected to a load at point a, the line voltage .vao is N −1 vao =
N −1
.
vi −
i=1
E , 2
(1)
where .vi , is the lower switch .Ti voltage as illustrated in Fig. 2. The switching frequency .fs is at least ten times greater than the load steady state frequency .f0 . In this functioning, the switch voltage .vi is assimilated to its average value during .Ts . The average voltage is denoted .Vi and is expressed as .
< vi >Ts = Vi =
1 Ts
0
Ts
vi dt =
E αi , N −1
(2)
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where .αi is the duty cycle applied to the switching cell i. More precisely .αi is the time ratio when .Ti is turned on over the switching time .Ts . For every switching cell of the leg, the duty cycle column vector .α is defined such as T α = α1 . . . αi . . . α(N −1) .
.
(3)
Then, using (2), a .(1 × (N − 1)) matrix .SF C is defined such as Eqs. (1) and 1 1 .SF C = N −1 . . . N −1 . Obviously, this relationship can be extended to every ∗ supplementary phase. Indeed, the average output voltage applied to the load .Vao is ∗ Vao =< vao >Ts +
.
E = E SF C α . 2
(4)
2.2 Solution Set The duty cycles are expressed such as [6], α=
.
1 † † ∗ SF C Vao z, + I − S S F C (N −1)×(N −1) FC ref E
(5)
where .SF† C is the pseudo-inverse of .SF C . z is an arbitrary column vector that allows to explore the solution set according to the physical constraints for .α. Equation (5) can be defined as the sum of fixed part .αf and a variable part .αv : α = αf + αv , such as
.
⎧ ⎨ αf = 1 S † V ∗ E F C aoref ⎩α = I v
(N −1)×(N −1)
− SF† C SF C z
(6)
The Sylvester theorem states that the number of degrees of freedom (d.o.f), is linked to the size of the kernel of .SF C such as, nd.o.f. = dim (ker (SF C )) .
.
(7)
In the following, the variable part will be linked to d.o.f expression. The linear system described in Eq. (4) is consistent, and admits an infinity of solution. Indeed,
.
∗ ) rank(SF C ) = rank( SF C Vao ∗ . rank(SF C ) < Number of row of Vao
(8)
Effectively, as .rank(SF C ) = 1, .SF C is singular and its pseudo inverse is obtained easily. If applied to a N-level inverter, the Eq. (7) is expressed as
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
nd.o.f. = Number of row of (SF C ) − rank(SF C ) = N − 2
.
73
(9)
The d.o.f are expressed as a column vector denoted .λ, by the mean of the maximal rank factorization. Firstly, the several d.o.f. are grouped into .λ such as T λ = λ1 , . . . , λnd.o.f. .
.
(10)
Secondly, two matrices, .F((N −1)×(N −2)) and .G((N −2)×(N −1)) , are chosen such as .
I(N −1) − SF† C SF C = F G .
(11)
Then, assuming .Gz = λ, the solution is α=
.
1 † (S )V ∗ + F λ. E F C aoref
(12)
As a matter of facts, the fixed solution .αf is : αf =
.
1 † S V∗ ; E F C aoref
(13)
and the variable part .αv : αv = F λ.
.
(14)
2.3 Boundaries Expression for the Solution Set One advantage of the generic model expressed previously, is to establish the d.o.f boundaries to get admissible solutions. More precisely, as the modeling process is based on intersective modulation assumption, it implies that every duty cycle .αi is such as: 0 ≤ αi ≤ 1 .
.
(15)
As a matter of fact, it leads to express every variable part .αvi separately. Obviously F has to be known: .
−αf ≤ αv ≤ 1 − αf ⇔ −αf ≤ F λ ≤ 1 − αf ,
(16)
assuming that the fixed part .αfi is known. Indeed, the final choice for .λi is done following Eq. (16) and some additional criteria such as switching losses or Total Harmonic Distortion (THD), that will be discussed in the following sections. In the
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M. Jday and P.-E. Vidal
following, the application of the generic model to 3-level and 5-level FC converters will be done.
3 Average Model of 3-Level FC Inverter Figure 3 presents the structure of a 3-level FC inverter, where .v1 and .v2 are the elementary voltages. The average voltages’ values are expressed as: V1 =
.
E α1 , 2
V2 =
and
E α2 . 2
(17)
Moreover, the output voltage .vao is: vao = v1 + v2 −
.
E . 2
(18)
∗ is Using expression (4), the average output voltage applied to the load .Vao ∗ Vao =< vao >Ts +
.
such as .SF C =
1
1 2 2
α=
1 2
(19)
T and .α = α1 α2 . Consequently, .α is given as:
.
where .SF C = 12 deduced such as:
E = E SF C α , 2
1 † ∗ SF C Vao + I2×2 − SF† C SF C z , ref E
(20)
T and .SF† C = 1 1 . The fixed and variable parts of .α are
Load
Fig. 3 Isolated leg of a 3-level FC inverter
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
T ∗ 1 1 1 Vao ref E † .αv = I2×2 − S F C SF C z . αf =
75
(21)
.
(22)
As the number of row of .(SF C ) − rank(SF C ) = 1 , it exists 1 degree of freedom. Indeed, the .αv is expressed as .αv = F λ, where F is a matrix obtained by the full rank factorisation of . I2×2 − SF† C SF C z. −1 √1 T . Indeed, the solution .α is expressed: Finally, F is computed as .F = √ 2 2 1 .α = E
−1 √ 1 ∗ Vaoref + 12 λ. √ 1
(23)
2
In order to find out the full expression of .α, the degree of freedom .λ must be fixed. However, the boundaries for .λ must be first defined, to ensure that the duty cycles evolves in the interval .[0, 1]. Using expression (23), and (16), the margin of .λ are such as √ √ √ ∗ ∗ max( E2 Vaoref − 2), ( −E 2 Vaoref )) ≤ λ √ √ . (24) . √ ∗ ∗ λ ≤ min( E2 Vaoref , 2 − E2 Vaoref ) More details will be presented in the next section to illustrate the relationship of the capacitor voltage and the degree of freedom .λ.
4 Average Model of 5-Level FC Inverter Figure 4 presents a 5-level FC inverter. .v1 , .v2 , .v3 and .v4 are the elementary voltages ∗ is of each cell of the inverter. The average output voltage .Vao
Load
Fig. 4 Isolated leg of a 5-level FC inverter
76
M. Jday and P.-E. Vidal ∗ ∗ Vao = V1 + V2 + V3 + V4 = E SF C Vao , ref
.
(25)
T where .SF C = 14 14 14 14 . Then, every . α1 α2 α3 α4 is split in a fixed solution .αfi and a variable one .αvi , that are expressed using expression (6). As .number of row of (SF C ) − rank(SF C ) = 3, there is 3 degrees of freedom, .nd.o.f. = 3. The use of the maximal rank factorisation allows to establish .αv as follows: ⎤ ⎡ 3 − √ 0 0 ⎥⎡ λ ⎤ ⎢ 21 3 ⎢ √ − √2 1 0 ⎥ ⎢ 2 3 6 √ ⎥⎣ (26) .αv = ⎢ ⎥ λ2 ⎦ . 1 2 1 √ ⎢ √ − 2 ⎥ 6 ⎣ 2 3 √ ⎦ λ3 , 1 √ 2 3
√1 6
2 2
The final expression of .α is deduced as ⎤ ⎡ 3 ⎡ ⎤ − √ 0 0 1 α1 ⎥⎡ λ ⎤ ⎢ 21 3 ⎥ ⎢ √ − √2 1 0 ⎢1⎥ ∗ ⎢ α2 ⎥ 1 ⎢ 2 3 6 √ ⎥⎣ ⎥ = ⎢ ⎥V ⎦. .⎢ + λ ⎥ ⎢ 2 1 ⎣ α3 ⎦ E ⎣ 1 ⎦ aoref ⎢ √ √1 − 2 ⎥ 6 ⎣ 2 3 √ 2 ⎦ λ3 , α4 1 2 1 √1 √ ⎡
⎤
2 3
6
(27)
2
5 Margins of the Degrees of Freedom λ Based on the expression given in expression (24), the margins of each .λ are detailed in the following.
5.1 Margins of λ1 Note that all .αi depends on .λ1 . Therefore, it is possible to use first a single equations of .αi to define the margins of .λ1 . α1 =
.
∗ Vao ref
E
3 − √ λ1 . 2 3
(28)
The first margins of .λ1 is defined using the condition .0 ≤ α1 ≤ 1 which leads to set: √ ∗ √ ∗ 2 3Vao 2 3 Vaoref ref ( − 1) ≤ λ1 ≤ (29) . 3 E 3E
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
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Secondly, in order to find a suitable correlation between .α4 , .α3 , .α2 and .λ1 , the following equality is used: α2 + α3 + α4 =
.
∗ 3Vao ref
3 + √ λ1 . 2 3
E
(30)
Hence, there exists a second margin for .λ1 : .
∗ ∗ Vao √ Vao √ ref ref ≤ λ1 ≤ 2 3(1 − ) −2 3 E E
(31)
Finally, the overall boundaries of .λ1 are expressed as follows: ⎧ √ Vao∗ ref √ Vao∗ ref ⎪ ⎪ − 1 ≤ λ1 ≤ ⎨ max −2 3 E , 2 3 3 E √ ∗ . ∗ √ 2 3Vao Vao ⎪ ref ⎪ ⎩ min 2 3 1 − Eref , 3E
(32)
5.2 Margins of λ2 Based on the duty cycle equations, it is noticed that .α2 , .α3 and .α4 depends on .λ2 . Since .0 ≤ α2 ≤ 1 and .0 ≤ α3 + α4 ≤ 2, the overall boundary of .λ2 is expressed such as .λ2min ≤ λ2 ≤ λ2max : ⎧ λ2min= ⎪ ⎪ ⎪ √ V∗ ⎪ ao ⎪ ⎪ ⎨ max 26 ( Eref + .
⎪ λ2max= ⎪ ⎪ √ V∗ ⎪ ⎪ ao ⎪ ⎩ min 26 ( Eref +
λ√1 2 3
− 1),
λ√1 ), 2 3
√
√
6(−
6(1 −
∗ Vao
ref
E
∗ Vao
ref
E
−
λ√1 2 3
−
− 1) (33)
λ√1 ) 2 3
5.3 Margins of λ3 Similarly, given that .0 ≤ α3 ≤ 1 and .0 ≤ α4 ≤ 1, the overall margin for .λ3 are defined such as, .λ3min ≤ λ3 ≤ λ3max :
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⎧ λ3min= ⎪ ⎪ ⎪ ∗ ⎪ Vao ⎪ λ λ ref 2 2 1 ⎪ √ √ max √ ⎪ ⎪ E + 2 3 + 6 −1 , ⎪ ⎪ 2∗ ⎪ ⎪ Vao ⎪ λ2 ⎪ ⎨ √2 − Eref − λ√1 − √ .
2 3
2
6
⎪ λ3max= ⎪ ⎪ ∗ ⎪ Vao ⎪ λ2 λ√1 ref 2 ⎪ √ √ ⎪ , + + min ⎪ E 6 2 3 2 ⎪ ⎪ ⎪ ∗ ⎪ Vao ⎪ λ2 ⎪ ⎩ √2 − Eref − λ√1 − √ +1 2 3
2
(34)
6
5.4 Influence of the D.O.F on Dynamic Behaviour of Floating Capacitor Voltages The current .iCi of the capacitor .Ci is expressed as: iCi = Ci
.
dvCi , dt
(35)
where .vCi is the voltage across the capacitor .Ci . One the one hand, the expression (35), integrated onto the switching period .Ts is equivalent to: Ts Ich (αi+1 − αi ) = Ci ΔvCi
.
(36)
On the other hand, expression (27) leads to the following equations: √ ⎧ ⎪ ⎨ α4 − α3 = 2λ3 α3 − α2 = √3 λ2 − . 6 ⎪ ⎩ α − α = √2 λ − 1 2 1 3
√1 λ3 2 √2 λ2 6
(37)
Finally base on expression (36), the 3 .λi allows to be compute dynamically before the carrier based comparison stage: ⎧ λ3 = ⎪ ⎪ ⎨ λ2 = . ⎪ ⎪ ⎩λ = 1
C √3 ΔvC3 2Ts IL √ √ C3 ΔvC3 6 C2 6ΔvC2 + 6Ts IL 3Ts IL √ C√3 ΔvC3 C1 + C√2 ΔvC2 + C1 2T3Δv s IL 3Ts IL 2 3Ts IL
(38)
One notes that .ΔvCi is the sweeping of the voltage .vCi during a period .Ts such as: ∀t, ΔvCj (t) = vCjref − vCjmes ,
.
(39)
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
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where .vCiref is the reference voltage value of .vCi , .vCimes and .IL are the .Ci voltages and load current measurements, respectively.
5.5 Simulation A simulation on Matlab/Simulink is performed. The simulation is based on the 5level inverter described in Sect. 4 and Fig. 4. The parameters used are depicted in Table 1. Firstly, the duty cycles are generated using the method presented in the previous sections. Secondly, a carrier based scheme is applied, with two . π2 shifted triangular carriers, varying from 0 to 1 .@fs . ∗ As highlighted in Eq. (27), the reference voltage .Vao is an input to generate .α. ref In the following, the reference voltage applied is: ∗ Vao = Vao,max sin ω0 t + ref
.
E , 2
(40)
E and .ω0 = 2πf0 . 2 To simulate the floating capacitance fault, a voltage unbalance is applied at .t = 0.5 s across the capacitor .C1 . To do so, a leakage current .Ileak of .15% of the nominal load current is produced. .Ileak flows through the resistance denoted .R1 , V placed in parallel to .C1 . .R1 is sized such as .R1 = IC1,ref = 100 Ω. Consequently, leak a large imbalance of the .vC1 voltage is caused by the injected disturbance. In usual PWM strategies, the voltage unbalance is not taken into account thanks to the PWM scheme. It is not the case with the proposed PWM strategy, where the d.o.f is dynamically adjusted, thanks to the .vCi expressions. The simulation results are given in Figs. 5, 6 and 7, which present the 3 d.o.f. before and after the default. It is illustrated that before the fault, the d.o.f are included within their boundaries and equal 0. The spikes are due to the current value injected into Eq. (38), when its value is close to 0. After the default, the d.o.f is varying dynamically (except if the d.o.f reaches one of its boundary). In such a case, it is set at the boundary value, as illustrated. where .Vao,max is .70 % of .
Table 1 Simulation parameters
Parameter DC source E Load steady state frequency .f0 Switching frequency .fs Capacity .Ci Resistance .R1 Load resistance R Load inductance L
Value 230 V 50 Hz 10 kHz 40 .µF .100 .10 1 mH
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Degree of freedom
0.5
0
-0.5
-1 0.45
0.5
0.55
0.6
0.55
0.6
Time (s)
Fig. 5 Degree of freedom .λ1
Degree of freedom
1
0.5
0
-0.5
-1 0.45
0.5
Time (s)
Fig. 6 Degree of freedom .λ2 0.8
Degree of freedom
0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0.45
0.5
0.55
0.6
Time (s)
Fig. 7 Degree of freedom .λ3
Figure 8 depicts the 4 duty cycles and Fig. 9 presents the load current .IL and the load voltage .vao . It is illustrated that, in any case, the proposed strategy keeps the duty cycles within the boundaries .0 ≤ α ≤ 1. The voltage unbalance compensation allows to get a correct and expected multilevel functioning, for the current and voltages. More precisely, the dynamic PWM leads to maintain the reference values for the intermediate voltage levels, whereas the load current is still a sinus. Moreover, to prove the performance of the dynamic PWM strategy, a Fast
Voltage Unbalance Compensation of Flying Capacitor Based on a Dynamic. . .
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1
Duty cycles
0.8 0.6 0.4 0.2 0 0.48
0.49
0.5
0.51
0.52
0.53
0.54
0.55
0.56
0.57
Time (s)
Fig. 8 Duty cycles .αi 150 Voltage (V) Current (A)
Load voltage and current
100
50
0 10
-50
5
-100
-5
0
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-150 0.48
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0.51
0.52
0.53
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0.525
0.53
0.55
0.535
0.54
0.56
0.57
Time (s)
Fig. 9 Load voltage and current FFT analysis
Fundamental (50Hz) = 8.039 , THD= 3.33% 0.6
Mag (% of Fundamental)
0.5
0.4
0.3
0.2
0.1
0 0
1
2
3
4
5
6
7
8
9
10
Harmonic order
Fig. 10 FFT analysis of the load current for dynamic PWM
Fourier Transform (FFT) analysis is performed in both usual and proposed PWM schemes. For both PWM, the .IL FFT analyses are presented in Figs. 10 and 11, respectively. On the one hand, with the use of the dynamic PWM, the .IL spectrum analysis shows a low harmonic distortion rate (THD), equal to .3.33%. On the other hand, the .IL THD of the current increase to .5.07% in the case of the usual PWM.
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Fundamental (50Hz) = 9.152 , THD= 5.07% 0.6
Mag (% of Fundamental)
0.5
0.4
0.3
0.2
0.1
0 0
1
2
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5
6
7
8
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Harmonic order
Fig. 11 FFT analysis of the load current for the conventional PWM
6 Conclusion A dynamic Pulse Width Modulation strategy is developed in this paper. A generic N-level Flying capacitor inverter mode is first introduced. Then, the dynamic PWM scheme is exhibited and applied to a 5-level single leg. It is demonstrated that the PWM scheme can embed the expressions of 3 degrees of freedom that are related to the floating capacitor voltages. More precisely, the capacitor voltage unbalance is dynamically set as a variable part of the duty cycle expressions. Simulation results demonstrate the performance of the proposed algorithm in the case of capacitor voltage unbalance. Also, this results have shown the performance and robustness of the proposed control strategy compared to the usual PWM.
References 1. B. Gemmell, J. Dorn, D. Retzmann, D. Soerangr, “Prospects of Multilevel VSC Technologies for Power Transmission”, Transmission and Distribution Conference and Exposition, 2008. IEEE/PES, 21–24 April 2008, https://doi.org/10.1109/TDC.2008.4517192. 2. S. Kouro, M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B. Wu, J. Rodriguez, Ma. A. Pérez, and J. I. Leon, “Recent Advances and Industrial Applications of Multilevel Converters”, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 8, AUGUST 2010. https://doi.org/10.1109/TIE.2010.2049719. 3. Sadigh, A. K., Hosseini, S. H., Sabahi, M., and Gharehpetian, G. B. (2009),“Double flying capacitor multicell converter based on modified phase-shifted pulsewidth modulation”,IEEE Transactions on Power Electronics, vol. 25, no 6, p. 1517–1526. https://doi.org/10.1109/TPEL. 2009.2039147. 4. T. A. Meynard, H. Foch, P. Thomas, J. Courault, R. Jakob, and M. Nahrstaedt, “Multicell Converters: Basic Concepts and Industry Applications”, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, vol.49, no.5, Oct 2002. https://doi.org/10.1109/TIE.2002.803174. 5. G.P. Adam, O. Anaya-Lara, G.M. Burt, D. Telford, B.W. Williams, J.R. McDonald, “Modular multilevel inverter: pulse width modulation and capacitor balancing technique”, IET Power Electronics, November 2009, https://doi.org/10.1049/iet-pel.2009.0184.
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6. P.-E.Vidal, S. Cailhol, F. Rotella and M. Fadel, “Generic pulse width modulation model, based on generalized inverses and applied to voltage source inverters”, The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 2, 2019 pp. 845–861, https://doi.org/10.1108/COMPEL-07-2018-0291. 7. P.-E. Vidal, S. Cailhol, F. Rotella, “Generic Modeling of N-Level Pulse Width Modulation Voltage Source Inverters and their Control”, 20th World Congress of the International Federation of Automatic Control, IFAC 2017 World Congress, Toulouse, France, 9–14 jul. 2017. 8. W. Teulings, J.L. Schanen, J. Roudet, “Analysis of the Current Distribution Between Paralleled Capacitors in a Chopper on Printed Circuit Board”,IEEE Industry Applications Society Annual Meeting New Orleans,pp. 1066–72, 1997. https://doi.org/10.1109/IAS.1997.628993. 9. S. Maniktala, Switching Power Supplies A to Z – Second Edition,Waltham, 2012. 10. R. Cousseau and N. Patin and C. Forgez and E. Monmasson and L. Idkhajine,“Improved electrical model of aluminum electrolytic capacitor with anomalous diffusion for health monitoring”,Mathematics and Computers in Simulation, Vol. 131, pp. 268–282, 2017.
Control Strategy for Orbital O2 Tidal System Based on EMR Model Ahmed Al Ameri, Alireza Payman, Brayima Dakyo, and Mamadou Ba¨ılo Camara
Abstract Recently, electric power production using the tidal turbine system has increased in many countries. Changes in the speed of the marine current pose one of the main challenges in the planning and operation of the electrical network. This paper focuses on the analysis and simulation of Orbital O2 Tidal energy conversion (TEC) system based on Energetic Macroscopic Representation (EMR). The profile of 10 years marine current from the Pentland Firth – Orkney has been used in the EMR model system and the proposed control strategy. The simulation results show the ability of EMR model to adopt the proposed control strategy to maintain the voltage at grid side and to follow the maximum power point tracking (MPPT) at the rotor side of the O2 tidal system.
1 Introduction Humans learned how to harness the power of water to do some work long before the discovery of fossil fuels. Later, the following generations discovered the mechanism of operating electric turbines using mobile water. According to many governmental and academic reports, marine renewable energy can provide a large share of the electricity that is supplied in coastal areas, where tidal energy can be expected and the products of this energy are characterized by providing in-place and reliable electricity [1]. In addition, tidal turbines have a higher efficiency (80%) than other renewable energies such as wind and solar. The process of producing electrical energy by converting the kinetic energy of water flow is called marine current power generation systems. The movement of
A. Al Ameri () GREAH – Université du Havre, Le Havre, France Electrical Department, University of Kufa, Al Najaf, Iraq A. Payman () · B. Dakyo · M. B. Camara GREAH – Université du Havre, Le Havre, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_7
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A/ Daily profile 1.5 Flood tidal Tidal speed (m/s)
1 0.5 0
-0.5 -1 Ebb tidal -1.5 0
5
10
15
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Fig. 1 Ebb and flood tidal
water in different directions results from the influence of the forces of rotation and gravity between the moon, the sun and the earth on a daily and seasonal basis, and it reaches its highest value in the spring [2]. The tidal energy is often produced in two stages, the first stage is when the sea water level drops (ebb phase), and the second is when the seawater rises (flood phase) as shown in Fig. 1. The speed of the sea current often changes at different levels near the islands, which can be used to continuously produce energy daily. The oceans have the world’s largest renewable energy resource of about 2 × 103 TWh. Many countries have invested this energy such as France, which built the oldest tidal power plant in La Rance that produces an annual capacity of 540 GWh. In 2011, the Daewoo Engineering & Construction Company has constructed tidal power plant with a total power capacity 254 MW, which consider as the world’s largest station [3]. In 2013, the world’s third biggest plant has been constructed at Swansea Bay in the UK with the 400 GWh annual power capacity. Recently, many countries starting to invest in a two-way tidal power generation, such us Canada, Brazil, Russia, India, South Korea, China, etc. Tidal energy research centers are spread in many countries such as Canada, the United States and the United Kingdom, but Scotland is generally considered one of the world leaders in this field [4]. Studies show that the waterway between the northeastern tip of Scotland and the Orkney Islands could generate 8% of the total electricity consumed in the UK. Therefore, this region has been chosen to be host centers for many researchers with the support of the Government of Scotland as the most important centers of tidal energy in the world [5]. Recently, the graphical formalism tool has been used to represent complex and multi-physics systems as it is one of the most efficient and simple ways to describe transformation systems. In addition, the energetic aspect manages the possibility to link different domains of energy, and the causal structure gives the potential to create an inversion based control. Since 2000, Energetic Macroscopic
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Representation (EMR) has been found as a new modality to be used to analyze several conversion systems. Koita et al. [6] used an EMR tool to represent a wind energy conversion system by proposing a control strategy on parts of the system such as a permanent magnet synchronous generator (PMSG), rectifier, DC link, etc. Also, many interested papers have used EMR elements to represent Proton Exchange Membrane (PEM) electrolyser [7], fuel cell super capacitor system [8], and fuel cell battery for electrical vehicle [9]. The main objective of this paper is to be modelled the Orbital O2 tidal system integrated into Orkney network based EMR tools. The system has been controlled by both sides, rotor side control (RSC) to find the maximum power point tracking (MPPT) and grid side control (GSC) to maintain the voltage and frequency. This research is a case study focus on performing the 10 years of real data collected by European Centre for Marine Energy (EMEC). The Orbital O2 is already launched on 23 April 2021 at Birth 5 in Pentland Firth, where the data between 1996 and 2005 at this location has examined to be used in this model. This work has organized by describing the main components the Orbital O2 tidal system and Orkney grid. Next, the representation of the tidal system based on EMR has been figuring out. In the third section, the simulation results have been shown that the proposed control strategy based on EMR model was efficient and conclusion has demonstrated in section four.
2 Orbital O2 Integrated into Orkney Grid The Orbital O2 tidal system consist of 2 arms. Each one has 1 MW turbines and has been designed to provide the electricity for 2000 homes to offset around 2200 tonnes of CO2 production per year. The O2 turbine has a 20 m rotor diameter, 74 m long hull and 680 tonnes as shown in Fig. 2. The real data of marine current velocity
Fig. 2 Lay-out of orbital O2 tidal system
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Generator Side Converter
DC link Capacitor
Grid Side Converter Power Grid
Generator Side Control system
Grid Side Control system
Fig. 3 Single line diagram of Orkney system
at birth 5, where Orbital O2 has already launched, is used in this paper to show the efficiency of the proposed control strategy and the EMR model for the whole conversion system. This control strategy has been represented by RSC and GSC to inject the reactive power and to extract the maximum power output of tidal energy. The single line diagram of the main components of Orbital O2 tidal systems integrated into Orkney grid is shown in Fig. 3. The EMR tool can be an accurate approach to represent these main parts such as an Orital O2 tidal system, several conversion systems and grid. The O2 turbine has been set to 11 kV, 50 Hz, 20 m rotor diameter, and 16 rpm. The rated marine current speed is 3 m/s while the cut out and cut in velocity rated are 4.5 m/s and 1 m/s, respectively.
3 Control Strategy Based on EMR The Orkney system consists of tidal energy conversion (TEC) that represent the Orbital O2 integrated into Orkney grid. The main parts of this system are blades, shaft, PMSG conversion, rectifier, DC bus, line impedance, and transformer. It is mentioned that the main elements of EMR are: the source elements, conversion elements, accumulation and coupling elements as shown in Table 1. The EMR model of the studied system consists of the source elements (Marine current profile and Orkney grid), conversion elements (blade, PMSG, rectifier, inverter and transformer) and accumulation elements (shaft, DC Bus and line impedance). These main elements are easily figured out at EMR model shown in Fig. 4. The proposed control strategy in this work consists of two sided: rotor side control to extract the maximum power output of tidal energy and grid side control to control the DC bus voltage and to inject the required reactive power through measured references.
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Table 1 EMR elements
Fig. 4 Main elements of EMR represent TEC
3.1 Rotor Side Control (RSC) On this side of control, the proposed strategy has been developed based on the inversion of shaft and PMSG accumulation. These inversions produce references play main role in tracking the MPPT for tidal energy in operating mode. At the MPPT mode, the Orbital O2 tidal turbine can achieve the maximum efficiency. In additional, the control can overcome the fluctuation problem causes by the variation of water current speed. The power coefficient (Cp) for constant water is considered to be 0.53 which can vary according to the water speed to track the maximum power. To deduce the chain of EMR elements of control structure for Orbital O2 tidal conversion system (Fig. 5 Rotor side control, the following equation has been considered: shaf t _ref = Cont shaf t . shaf t _ref − shaf t _mes
(1)
where Γ shaft _ ref , shaft torque reference, Ω shaft _ mes , speed measured for shaft equation inversion, Contshaft shaft speed controller and Ω shaft _ ref , the reference for shaft speed. shaf t _ref =
Vtidal λopt Rturbine
Rturbine is turbine radial, λopt represents tip-speed-ratio and Vtidal is water speed.
(2)
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Fig. 5 Rotor side control topology
3.2 Grid Side Control (GSC) In this section, the main components of the grid side system have been described, then the proposed control has been modeled based EMR. The main role of this control is concerned with control of the DC bus voltage and injecting the suitable reactive power for maintaining voltage at the grid side. This control strategy is based on deduce the active and reactive current references from the active and reactive power. The reference current has to be in phase with the voltage grid to comply with grid codes and maintain the grid conditions. The chain of grid side control elements has been deduced by using the following equations: I d line_ref = .Cont dc Udcref − Udcmes
(3)
I q line_ref = .Cont q Qref − Qmes
(4)
Qmes = Uq .Id − Ud .Iq
(5)
Udcref , .Udcmes , voltage reference and measured for DC bus, Qref , Qmes , reference and measured values for reactive power, Contdc , Contq , DC bus and reactive power controllers.
.
V d inv _ref = Cont line . I d line_ref _I d line_mes
(6)
V q inv _ref = Cont line . I q line_ref − I q line_mes
(7)
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Fig. 6 Grid side control topology
Contline , controller for Iq, Idline _ ref , Idline _ mes , Iqline _ ref , Iqline _ mes reference and measured rectifier line currents. The chain elements of the EMR model for line impedance inversion and control strategy in dq current references are shown in Fig. 6.
4 Marine Current Profile and EMR Model Results During 10 years from 1996 to 2005, EMEC is measured and collect real data for marine current velocity in eight locations in the Pentland Firth in Orkney Island. The water speed profile for the birth 5 has been chosen in this paper to verify the performance of EMR model and the efficiency of the proposed control strategy to extract the maximum production of tidal energy. Figure 7 shows the profile of marine current speed in birth 5 that applied to the simulation of EMR model. The minimum Ebb tidal is 0.9 × 10−6 m/s, the maximum flood tide is 1.9887 m/s, and the yearly rate value of the current speed is 0.8414. The behavior of water speed has been analysed as time series and bi-directional as shown clearly in Fig. 8. The mode of current water profile was 0.953367, while the value of its median and percentile were 0.0532844 and 46.96, respectively. The EMR approach adopted the parameters of the Orbital O2 turbine system. The turbine radial is 10 m and the maximum power coefficient (Cp) is considered to be 0.5439. The main parameters for the PMSG smooth pole machine was set as ϕ = 11.1464 Wb and inductance with L = 4.229 mH. In the grid side, the value of capacitance in DC bus was 60mF and impedance of the line was 0.5 mH and 0 .
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1.5 1 0.5 0 -0.5 -1 -1.5 -2
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Fig. 7 Velocity of marine current in birth 5 10 Years water speed measurement
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Fig. 8 Sample of birth 5 water profile
The 10 year water profile has used to test the simulation of Orbital O2 turbine based on EMR model. The speed of PMSG machine follows the water profile as shown in Figs. 9 and 10. The rotor side control has well followed the MPPT to extract maximum tidal energy. The torque of tidal turbine was varying between 1 and 2.4 Nm as shown in Figs. 11 and 12. The range of water speeds in this simulation is adopted for the same setting of Orbital O2 which was 3.5 m/s at cut in speed and 4 m/s for cut out.
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Fig. 9 PMSG speed
Fig. 10 Zoom on PMSG speed
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Fig. 11 Torque of tidal turbine
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Fig. 12 Zoom on turbine torque 5600 5400
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Fig. 13 DC bus voltage
On the side of the grid, the proposed control strategy is well tracking the required reference. Indeed, at transient state or high step power variation, the control system is well. The proposed control was efficient to maintain the DC bus voltage and reduces disturbances caused by active and reactive power changes as results of Fig. 13. Figures 14 and 15 show that the average power output of Orbital O2 was 0.8 MW during 10 years. The chain of EMR elements has well performed through the variation of marine current velocity and the proposed control strategy for both sides was efficient according to the results obtained by Simulink/MATLAB.
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Fig. 14 Extracting power from Orbital O2
Fig. 15 Zoom on tidal power output
5 Conclusions The Islands are often fed from power sources separate from grids on the mainland. The use of renewable energy such as tidal energy in the supply of electricity to the islands can improve the efficiency of the electrical grid system and diversify the energy supply in addition to reducing the cost of energy production. The conversion system such as tidal energy is a complex energetic system (multiphysics) with several parameters that may be changed because of interactions between its subsystems. In this paper, a Simulink-based simulation was carried out to represent the Orbital O2 integrated into Orkney system using the Energy Macroscopic Representation (EMR) model. The 10 years collected data by EMEC at birth 5 in the Pentland Firth – Orkney has been used to observe the efficiency EMR tools. The chain of EMR elements has been used to represent the main subsystem of Orbital O2 turbine and proposed control strategy for rotor and grid sides. The results figure out the effectiveness of the EMR model to perform the variable marine current speed and adopted the proposed control strategy. The control parameters have been set to a suitable speed of the PMSG, to maintain the DC bus voltage and to extract maximum power generated from tidal current variation. It can conclude
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that the EMR tools which was efficient to model the Orbital O2 tidal-based system can be used for analysis and to develop control strategies under several operating system modes. In addition, this approach can be used to choose the optimal location to install the tidal turbine if we have the marine current profiles. Acknowledgements This research was funded by the European Regional Development Fund and highly supported by Integrating Tidal energy into the European Grid. The work handles green energy concerning carbon emissions in Orkney Island, located in North West Europe and adopt renewable technologies of low carbon such as electrolyzer, tidal turbine, and Energy Management System. The project of ITEG includes the partners from different countries such as the France, UK, the Netherlands and Belgium.
References 1. M. Rafiei, F. Salvatore, and F. Giulii Capponi, “Generator Topologies for Horizontal Axis Tidal Turbine,” 2020, pp. 447–459. 2. M. R. Barakat, B. Tala-Ighil, H. Gualous, and D. Hissel, “JADE-Based Multi-agent Decentralized Energy Management System of a Hybrid Marine-Hydrogen Power Generation System,” 2020, pp. 245–257. 3. N. Khan, A. Kalair, N. Abas, and A. Haider, “Review of ocean tidal, wave and thermal energy technologies,” Renewable and Sustainable Energy Reviews, vol. 72. pp. 590–604, 2017. 4. A. Fernández-Jiménez, D. F. la Cruz, J. Ruiz-Torres, J. L. Perrino-Blanco, and R. JimenoAlmeida, “Harnessing the Energy of Tidal Currents: State-of-the-Art and Proposal of Use in EV Charging Points,” Proceedings, vol. 2, no. 23, p. 1504, 2018. 5. M. A. Almoghayer, D. K. Woolf, S. Kerr, and G. Davies, “Integration of tidal energy into an Island energy system – A case study of Orkney islands,” Energy, p. 122547, Nov. 2021. 6. A. Koita, A. Payman, B. Dakyo, and D. Hissel, “Control of a Wind Energy Conversion System using the Energetic Macroscopic Representation,” in 7th International IEEE Conference on Renewable Energy Research and Applications, ICRERA 2018, 2018, pp. 1460–1465. 7. K. S. Agbli, M. C. Péra, D. Hissel, O. Rallires, C. Turpin, and I. Doumbia, “Multiphysics simulation of a PEM electrolyser: Energetic Macroscopic Representation approach,” Int. J. Hydrogen Energy, vol. 36, no. 2, pp. 1382–1398, 2011. 8. L. Boulon, M. C. Péra, D. Hissel, A. Bouscayro, and P. Delarue, “Energetic macroscopic representation of a fuel cell-supercapacitor system,” in VPPC 2007 – Proceedings of the 2007 IEEE Vehicle Power and Propulsion Conference, 2007, pp. 290–297. 9. L. Gauchia, A. Bouscayrol, J. Sanz, R. Trigui, and P. Barrade, “Fuel cell, battery and supercapacitor hybrid system for electric vehicle: Modeling and control via energetic macroscopic representation,” in 2011 IEEE Vehicle Power and Propulsion Conference, VPPC 2011, 2011.
A Hybrid Fourier and Wavelet-Based Method for the Online Detection and Characterization of Subsynchronous Oscillations Keijo Jacobs, Reza Pourramezan, Younes Seyedi, Houshang Karimi, and Jean Mahseredjian
Abstract Modern electric power systems are becoming more complex due to the proliferation of distributed energy resources (DERs) and power electronic converters. The increased penetration of power electronic-based DERs gives rise to new instability issues, particularly subsynchronous oscillations (SSO) caused by control system interactions, the induction generator effect, or resonance with torsional modes of wind turbines. If poorly damped, such oscillations can compromise the stability of the power grid, resulting in damage or disconnection of equipment and grid sections. Therefore, detecting such frequency components during both planning and operation phases is of paramount importance. This paper proposes a straightforward hybrid method combining Fourier and wavelet analysis (WA) for the online detection of the subsynchronous frequency components in power system measurements. The method leverages the speed of the fast Fourier transform (FFT) and the accuracy of the WA to determine the frequency, amplitude, and damping of SSO events.
1 Introduction Subsynchronous oscillation (SSO) events can cause severe small-signal stability issues that power system planners and operators should address. In general, SSO refers to oscillations with frequencies from 5 Hz to up to the system’s fundamental frequency (e.g., 60 Hz), and differs from low-frequency oscillation (LFO) that occurs in the range of 0.2 to 5 Hz [1]. Historically, the SSO events are caused by interactions between the synchronous generators and other components of the electrical grid, such as series capacitors. However, with the increased penetration of voltage source converter (VSC) based technologies in recent years, the interactions
K. Jacobs () · R. Pourramezan · Y. Seyedi · H. Karimi · J. Mahseredjian Polytechnique Montréal, Montréal, QC, Canada e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_8
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between their power electronics control system and other grid components give rise to new types of phenomena such as subsynchronous control interaction (SSCI) and sub/super-synchronous oscillations [2]. With the increased penetration of wind farms and high-voltage direct current (HVDC) systems and more frequent SSO events involving these technologies [3–5], the research interest in analyzing such phenomena has piqued significantly. Traditionally, model-based identification methods were used to detect and quantify the SSO events. A detailed state-space representation model is proposed in [6], and pertinent eigenvalue analysis is used to quantify the subsynchronous resonance (SSR) components in series compensated HVDC systems. Although model-based methods can be used to analytically determine the characteristics of the SSO events, they are limited due to the uncertainty of power system components and their parameters. A data-driven stochastic subspace identification method is used in [7] to obtain the state-space model of the power grid, which is then used to estimate the dominant modes and characterize inter-area oscillations. In [8], a linear harmonic model of the grid-connected VSC is presented and used to analyze the frequency and damping of harmonic oscillations caused by the parameter setting of the VSC control system. The synchrophasor data reported by the phasor measurement unit (PMU) are calculated based on the assumption of a pure sinusoidal at the fundamental frequency [9]. PMU data contain SSO components up to a specific frequency given a high enough reporting rate. Several methods for oscillation detection using PMU data have been proposed in the literature [10–12]. The existing data-driven methods mainly rely on the availability of historical data and work in an offline manner. These methods focus on estimating the frequency of SSO and do not account for the damping characteristics of the events. However, power system operators require online methods to identify and characterize the SSO events. This enables performing mitigation actions to reduce the risks of instability and ensure the secure and stable operation of power systems. This paper proposes an online hybrid SSO detection and characterization method using both FFT and WA methods. FFT is employed to detect any SSO and approximate the SSO frequencies with low but sufficient resolution. Then, WA is performed on a selected range of frequencies to improve the accuracy and determine the damping characteristics of the SSOs. The contributions of this paper are: 1. The proposed method leverages the speed of the FFT and selective wavelet analysis (WA) to enable the detection of SSO events in real-time signals. 2. The proposed WA significantly enhances the estimation of the frequency, amplitude, and damping. 3. The proposed method can detect and accurately characterize multiple simultaneous SSO events. A performance analysis conducted using MATLAB simulations confirms the accuracy and real-time capability of the proposed method. Furthermore, the method is verified on data generated via a realistic power system EMT model subjected to SSO.
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2 Hybrid SSO Detection and Characterization Let .x(t) denote a typical instantaneous signal containing both the nominal and subsynchronous components: x(t) = xdc + an cos(2πfn t + φn ) + aO e−λt cos(2πfO t + φO )
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2.1 Outline of the Proposed Hybrid Method The proposed hybrid method uses FFT and WA to detect subsynchronous frequency components, and confidently determine their frequency and damping. The accuracy of the characterization is increased progressively, as more data becomes available. The flowchart of the proposed method is shown in Fig. 1. It consists of three main steps which are applied to sampled signal data stored in a first-in, first-out (FIFO) buffer: Step 1: fast Fourier transform (FFT) Perform analysis on the sampled data to obtain the approximate frequencies. Step 2: WA frequency sweep (WAfs) Execute WAs on a selected range of frequencies encompassing the approximate from the previous step to increase the accuracy and determine the damping. Step 3: targeted WA (WA1) Execute targeted WAs on continuously updated data and monitor amplitude and damping of already detected frequencies, to increase the confidence in the obtained results. The hybrid method is described in more detail in the following. The variables f , .fˆ, and .f¯ denote the actual frequency, the frequency approximate obtained by the FFT, and the more accurate estimates obtained by the WA, respectively. The sampled data is given by .Xs = [x(t), x(t − Δts ), · · · , x(t − (l − 1)Δts )], where .Δts is the sampling time and l the buffer length. In step 1, an FFT is performed to approximate the range of any SSO oscillations. The maximum detectable frequency can be adjusted by .Δts , but is limited by the PMU device data rate, usually one or two times the fundamental frequency. Amplitude peaks above a certain threshold (here 0.02 p.u.) are extracted from the frequency spectrum obtained via the FFT, yielding .fˆO , as shown in Fig. 2a. If an SSO is detected, the algorithm continues with step 2, illustrated in Fig. 2b. A WAfs is performed on the sampled data in small frequency
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Fig. 1 Simplified flowchart of proposed hybrid method
Fig. 2 Serial implementation of the proposed hybrid method in three steps: FFT (a); WAfs (b); repeated WA1 until next FFT (c)
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steps encompassing .fˆO to determine .f¯O and .λ¯ . During step 3, shown in Fig. 2c, further WAs are executed and the obtained estimates for instant k are compared with those obtained in the previous instant .k − 1 (or several previous instants). The detected SSOs and their damping is considered accurate when the absolute difference between the results stays below predefined thresholds for .nc consecutive instants: .
k k−1 ΔfO = |f¯O − f¯O | Δλ = |λ¯ k − λ¯ k−1 |
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where .fOk and .λk are the estimated parameters at instant k, and .f and .λ are the respective accuracy thresholds. Note that step 3 is executed on continuously updated data. If and when frequencies are detected, adequate warnings, alarm signals, and protection triggers are sent. The procedure consisting of an FFT, a WAfs, and several subsequent WA1, shown in Fig. 2, represents one analysis interval. The hybrid method benefits from the reduced computation time of the FFT (as compared to a WA on the entire frequency range), and from the increased accuracy of the WA. By only executing WAs for selected frequencies, the computation time of step 2 and 3 are reduced to a minimum. Note that, besides SSOs, the hybrid method is also capable of detecting other frequency components, such as supersynchronous oscillations and harmonics. However, since the data rate of PMUs is not sufficiently high, these might not be detectable from the signal. Furthermore, if SSOs should be detectable simultaneously, a large amount of samples would be needed. This would lead to an increased computational burden and, depending on the parameters, might compromise online capability.
2.2 Fast Fourier Transform The fast Fourier transform (FFT) is a widespread method to extract frequency components from a time domain signal. The maximum detectable frequency .fmax is determined by the sample frequency .fs according to the Nyquist criterion, whereas the minimum frequency .fmin and the frequency resolution is determined by the analysis window length .Ta,FFT . The drawbacks of the FFT can be summarized as: • Limited frequency resolution: SSO frequencies may be represented as “soft peaks” with erroneous amplitudes in the frequency spectrum. • Poor characterization of SSO events: the time of SSO occurrence and its damping cannot be determined from a single FFT. • A constant time step is required and resampling might be necessary, if, for instance, variable time step simulation data is used. • Trimming or extending of time-series data to .l = 2N samples with .N ∈ N+ might be necessary, since the FFT algorithm works recursively by dividing the samples into two subsets.
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Fig. 3 FFT frequency and time resolution: STFFT (a); overlapping or sliding window FFT (b); increased frequency resolution (c)
• Analyzing signals with non-integer amount of periods causes spectral leakage. To reduce spectral leakage, windowing can be applied. However, this may affect computation time and accuracy negatively. Figure 3 illustrates the resolution issues of the FFT method. Repeating the FFT in successive analysis intervals, also known as short time (ST) FFT, provides at least some information about the location of frequency components on the time axis, as shown in Fig. 3a. Performing successive FFTs on overlapping or sliding analysis windows can enhance the time resolution at the expense of additional computation time, as shown in Fig. 3b. Figure 3c illustrates how increasing the analysis window length enhances the frequency resolution. However, it requires more samples to be stored and processed, increasing the computational burden. In principle, the frequency and amplitude accuracy can be improved by iterative adjustments of the window size and the sampling frequency and repeated FFTs after each adjustment. However, this method falls short of practicality and accuracy when multiple frequency components and noise are present.
2.3 Wavelet Analysis Contrary to FFT, WA can precisely determine the amplitude of a given frequency. A variety of techniques has been developed [13–16]. A commonly used wavelet for frequency analysis is the Morlet-type, shown in Fig. 4. It consists of a cosine function weighted by a Gauss function. In this paper the wavelet function .w(t), depicted in Fig. 4, is used with the following definitions. w(t) = g(t)
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Synthetic signal #1 #2 22.781 11.550 0.1 .−0.025 .< 0 20
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1 2π σ
e
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The wavelet is scaled to a total energy of unity. This ideally requires that the borders of the wavelet are at .±∞. However, a sufficient approximation can be achieved with truncation at a finite distance from .t = 0, allowing for a trade-off between accuracy and computational burden. For this implementation a time window of .− 3.25 f 140 kHz yields the increase of the system high-frequency losses. The intermediate bus voltage has been varied in the range V2dc = [14, 17] V by adjusting the inverter phaseshift: the conditions V2dc < 14 V are not feasible due to the Buck duty-cycle saturation, while the conditions V2dc > 17 V are not feasible over the analyzed frequency range due to the phase-shift saturation (see Fig. 5d). Figure 10 depicts the experimental efficiencies measured for four analyzed loads over the considered
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Fig. 9 Experimental set-up for PR-IPTS prototype testing fs = 105kHz
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fs and V2dc operating ranges. It can be observed that for loads RL = {7, 14, 24} , the efficiency is maximized at V2dc = 14 V, while the maximum efficiency ηmax = 91.7% is achieved for RL = 5 (Po = 28.8 W) at fs = 120 kHz and V2dc = 15 V. Finally, Fig. 11 shows the mean values of the experimental efficiency vs Po , obtained by averaging the data of Fig. 10, together with the error bars indicating the minimum and the maximum efficiency points. The plot shows that the average efficiency changes from about 71% at Po = 6 W to about 91% at Po = 28.8 W. To assess the output voltage regulation capabilities, the proposed PR-IPTS has been tested by varying the inverter switching frequency to explore both stable and unstable operating region of Fig. 5d. Figure 12a shows steady-state experimental waveforms of vo (t) and v2dc (t) measured at RL = 5 in a stable condition {fs = 120 kHz, V2dc = 15 V}. The plots highlight that the average output voltage is correctly regulated at 12 V with the amplitude of the peak-to-peak voltage ripple of 108 mV (0.9% Vo ). Lastly, Fig. 12b shows the behavior of vo (t) and v2dc (t) at RL = 7 in an unstable operating point fs = 100 kHz, together with the instantaneous value of the Buck duty-cycle estimated as D(t) = vo (t)/v2dc (t). The test starts with v2dc (t) of about 13.6 V obtained at the inverter phase-shift of d = 0.667, resulting in the Buck dutycycle saturated at D = 0.9 and vo (t) slightly lower than 12 V. Subsequently, the phase-shift is incremented to d = 0.668 leading to the increase of vo (t) beyond 12 V, and the controller decreases the duty-cycle to achieve the output voltage regulation. However, vo (t) further increases due to the non-monotonicity of the Vo vs D curve (see Fig. 6b), thus leading the controller to ever decrease the duty-cycle, resulting in a huge increase of v2dc (t). As soon as v2dc (t) exceeds a safety threshold of 19 V, the Buck duty-cycle is fixed to D = 0.9 to avoid component failures, thus leading to the decrease of both vo (t) and v2dc (t). These findings confirm that the
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Fig. 12 Experimental waveforms of vo (t) (yellow), v2dc (t) (green) and D(t) (blue) for (a) RL = 5 , fs = 120 kHz and (b) RL = 7 , fs = 100 kHz
PR-IPTS operation cannot be accomplished for the operating frequencies located in the unstable region predicted by the FHA-based static model.
6 Conclusions This paper has discussed an enhanced design procedure of an Inductive Power Transfer System (IPTS) followed by a Buck converter used as a post-regulator. A static model of the system has been developed based on a first harmonic approximation method, allowing to properly select the compensation capacitor values, as well as to determine optimal operating points ensuring the maximum efficiency and the system controllability. Experimental tests carried out on a laboratory prototype confirm the static model prediction in both stable and unstable operating conditions. The developed IPTS is able to deliver up to 29 W output power ensuring the 12 V output voltage regulation and yielding a 91.7% maximum efficiency.
References 1. V. Cirimele, M. Diana, F. Freschi and M. Mitolo, “Inductive Power Transfer for Automotive Applications: State-of-the-Art and Future Trends”, IEEE Trans. on Industry Applications, vol. 54, no. 5, pp. 4069-4079, Sept.-Oct. 2018. 2. A. Al-Attar et al., “Wireless Power Transfer for Toys and Portable Devices”, 2019 IEEE Conference on Power Electronics and Renewable Energy (CPERE), Aswan, Egypt, pp. 479-484, 2019. 3. M. Haerinia and R. Shadid, “Wireless Power Transfer Approaches for Medical Implants: A Review”, Signals, vol. 1, no. 2, pp. 209–229, Dec. 2020.
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4. Robert W. Erickson and Dragan Maksimovi´c. Fundamentals of Power Electronics. Norwell, Mass: Kluwer Academic, 2001. 5. Chwei-Sen Wang, O. H. Stielau and G. A. Covic, “Design Considerations for a Contactless Electric Vehicle Battery Charger”, IEEE Trans. on Industrial Electronics, vol. 52, no. 5, pp. 1308-1314, Oct. 2005. 6. P. Hurtuk, R. Radvan and M. Frivaldský, “Full Bridge Converter with Synchronous Rectifiers for Low Output Voltage Application”, 2011 International Conference on Applied Electronics, Pilsen, Czech Republic, pp. 1-4, 2011. 7. R. Ruffo, V. Cirimele, M. Diana, M. Khalilian, A. L. Ganga and P. Guglielmi, “Sensorless Control of the Charging Process of a Dynamic Inductive Power Transfer System with an Interleaved Nine-Phase Boost Converter”, IEEE Trans. on Industrial Electronics, vol. 65, no. 10, pp. 7630-7639, Oct. 2018. 8. H. Li, Y. Tang, K. Wang and X. Yang, “Analysis and Control of Post Regulation of Wireless Power Transfer Systems”, 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), Auckland, New Zealand, pp. 1-5, 2016. 9. Ferroxcube, P36/22 P cores and accessories, 2008, online.
PWM-Induced Current Modelling in Stator Slots with Multiple Stacked Coils Antoine Cizeron, Hugo Milan, Javier Ojeda, and Olivier Béthoux
Abstract This paper deals with the PWM-induced current and losses in a specific segmented winding structure. The proposed segmentation process enables to split a winding into several coils. These latter are supplied independently by H-bridge converters and are wound around the same magnetic circuit. This process leads to a deeper segmentation of electric drives for enhanced modularity and reduced voltage rating. The strong magnetic coupling between each coil is described, and the control degrees of freedom are presented. This study provides a model based on an analytical method and on an equivalent electrical circuit calibrated through experimental results. A trade-off is found between the losses related either to the distribution of the fundamental component of currents or to the switching power converter supply.
1 Introduction Electric drive generally involves a power electronics converter associating a DC-link voltage to an electrical machine. In standard EV drive solutions, the voltage rating is between 400 and 800 V. These voltage values meet the requirements of fast charging and are enabled by the new generation of WBG semi-conductors power components. The implementation of these solutions relies on one high power converter to feed
A. Cizeron () · O. Béthoux GeePs – Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire de Génie Electrique et Electronique de Paris, Gif-sur-Yvette, France e-mail: [email protected] Sorbonne Université, CNRS, Group of Electrical Engineering - Paris, Paris, France H. Milan · J. Ojeda Satie – ENS Paris-Saclay, Laboratory of Systems and Applications of Information and Energy Technologies, Gif-sur-Yvette, France © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_17
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the whole drive. However, the resiliency of this conventional structure is limited, and its power rate implies a separate thermal management for the converter and the electrical machine. Integrated solutions are proposed to bring the power electronics closer to the electrical machine. In these Integrated Modular Motor Drives (IMMD), the power electronics components are spatially distributed around the motor [1]. This is facilitated by the use of multiple elementary converters to supply each portion of the motor winding. Furthermore, such segmented structure enables the use of low voltage semiconductor devices, that generally present reduced losses compared to their high voltage counterparts. The various control degrees of freedom available in those segmented structure offer promising opportunities in terms of energy management and resiliency. The patent proposed in [2] extends the segmentation limit of the motor winding to the turn limit and enables the use of several stacked coils inside the same slots. [3] details the scientific and technical obstacles related to this innovative structure. Recent works like [4] expose the use of a similar structure for an integrated battery charger. In [5], authors combine this kind of segmentation with external coupled inductors to reduce mechanical vibrations. These references only consider balanced current distribution between the different winding sets during the motoring mode. The present paper addresses this issue in a representative geometry. It provides the modelling tools enabling to minimize the losses thanks to uneven current distribution between the different coils. Each elementary coil being independently supplied, the whole structure presents new control degrees of freedom, these latter were investigated in the particular case of two coils with strong magnetic coupling [6]. A PWM-induced current ripple modelling method is detailed in [7] for conventional synchronous motor. It provides accurate estimation of the current waveforms but is based on an inductance model. Other models are used to understand the PWM-induced losses [8, 9] but are not suited for taking into account the new degrees of freedom. Moreover, the influence of the air-gap on the current ripple induced by the Pulse Width Modulation (PWM) in the aforementioned stacked coils has not been yet studied. This paper emphasizes the link between the control parameters, namely the differential voltages, and the current ripple by modelling two stacked coils within the same magnetic circuit. Measurements are performed to validate the fundamental electrical model and the high frequency model, which estimates the PWM-induced losses over a wide range of operating points. The rest of this paper is structured as follows. Section 2 introduces the concept of the segmentation of ordinary winding into several stacked coils and the case of study. Then, Sect. 3 describes the analytical model applied to the fundamental frequency. Finally, Sect. 4 evaluates the aforementioned trade-off between PWM-induced losses and the losses related to the fundamental distribution of currents in the stacked coils. The last section provides conclusions and perspectives.
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2 Stacked Coils Sharing the Same Magnetic Circuit 2.1 Generic Problem Figure 1 shows a generic geometry symbolizing one phase within a concentrated winding arrangement. The conventional winding presents a number of electroconductive turns written as .Nt . These turns are wound around one stator tooth in a concentrated way as shown in Fig. 1a. This winding is then split into n electrically independent coils that are stacked around the same stator tooth. In the considered structure, each elementary coil is supplied by a low voltage full-bridge converter. This topology can be seen as an extension of the single tooth inverter integration proposed in [10]. Whereas the conventional winding Fig. 1a requires a H-bridge supply with a DC-link voltage .VDC , each elementary coil Fig. 1b only requires a H-bridge supply with a reduced DC-link voltage of .VDC /n in order to meet the same power rating of the whole structure (Fig. 2). The magnetic circuit was initially designed for the conventional winding. Therefore, the ampere-turns are kept constant to guaranty the proper use of the ferromagnetic material. Thus, the current rating remains the same in both structures since the number of turns per coils is equivalent. Compared to the conventional supply, the proposed structure presents additional control degrees of freedom since each H-Bridge inverter can be controlled independently. The PWM is used to generate the low frequency voltages applied to each coil. Thus, two frequency bands can be distinguished in this problem Fig. 1 Cross section of the proposed winding segmentation within a generic magnetic circuit. (a) Conventional concentrated winding. (b) Concentrated winding with n stacked coils
Fig. 2 Segmented supply of the stacked coils
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Fig. 3 (a) Geometry of the practical model with two stacked coils and (b) the corresponding practical model
– The Low Frequency band (LF: 0 to 1) kHz is related to the fundamental frequency of the electrical machine. It corresponds to the back electromotive force (emf) and the fundamental of current in the winding. – The High Frequency band (HF: .> 10 kHz) is related to the PWM signals applied to the winding. The behaviour of the magnetic circuit and the conductors is different in those two bands. Even if the current magnitude is usually higher in the LF band than in the HF band, [6] has shown that the HF current ripple increase in stacked coils should also be taken into account. Thus two separate models are described, the LF model, based on an analytical method assesses the losses induced by a given current distribution between the stacked coils. Then, it defines the required voltages and so the PWM signals that are injected in the HF model in order to estimate the PWM-induced current ripple.
2.2 Study Case of Two Stacked Coils A practical model was built. It is composed of two stacked coils made of 20 turns each wound around a laminated steel magnetic circuit including an air-gap. Its geometry is detailed in Fig. 3 and used for the analytical model in the LF band. The two coils are supplied either by SI MOSFET H-Bridge converters or linear amplifiers, thus enabling to investigate separately the LF and HF phenomena.
3 LF Electrical Model and Losses Assessment 3.1 LF Electrical Equivalent Circuit Generally, each coil k could be represented as a serial resistance .rk and leakage inductance .lk . One mutual inductance .Lm is used for all the stacked coils as they
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Fig. 4 (a) Analytical model of a generic conductor among a slot and (b) comparison of analytical and FEA based inductance value
are wound around the same stator tooth. The air-gap ag influences the leakage inductance .lk of each coils. The coil 1 located close to the air-gap barely has no leakage inductance value whereas coil n embraces all the flux lines that are crossing the slot and thus presents the highest leakage inductance value. The serial DC resistance is the same in all coils as they present the same number of turns and thus the same conductor length. This model rely on the fact that it exists two kinds of flux lines. The first contour .Cag corresponds to the flux lines crossing the airgap vertically (following the y-axis), the other contour .Cslot is assumed to cross the slot horizontally (following x-axis). These two paths are represented in Fig. 4a. The induction value in the air-gap and in the slot (between the conductor and the air-gap) can be approximated by: Bag =
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3.2 Application to the Case of Study The analytical model is used to identify the terms of the LF electrical modelling in the case of two stacked coils (Fig. 3). Considering the computed inductance values of one conductor within the slot (Fig. 4b), the worst case in terms of imbalance
230 Table 1 Geometric parameters of the magnetic core and conductors
A. Cizeron et al. Parameter Air-gap thickness Laminated steel thickness Number of laminated steel sheet Magnetic section Average magnetic lenght Slot depth Slot width Vaccum permeability Copper conductivity Conductor section Conductor length
Symbol .tag (mm) .et (mm) .nt 2 .Sm (mm. ) .lm (mm) .dslot (mm) .wslot (mm) .μ0 (.μH/m) .σ (S/m) 2 .Sc (mm. ) .lc (m)
Value 0.5 0.5 35 350 130 30 10 .4π/10 6 .59.6 · 10 .1.3 2.5
Fig. 5 LF electrical equivalent circuit
corresponds to take the extreme values for the self inductances of stacked coils 1 (.Y = 30 mm) and 2 (.Y = 0 mm). Since the stacked coils are practically made of 20 turns, the analytical model provides self inductance values .L1 = l1 + Lm = 180 .µH and .L2 = l2 + Lm = 220 .µH (Fig. 5). The two flux paths taken into account leads to consider that all the flux lines embraced by a conductor close to the air-gap are also embraced by any other conductor. In the case of two stacked coils, this leads to set .l1 to zero (.L1 ≈ Lm ) and to admit that the leakage inductance of the coil 2 is the difference between the self inductances : .l2 = L2 − L1 = 40 μH while .Lm = 180 .µH. By supplying successively each stacked coil with a linear amplifier ensuring sinusoidal current, it is possible to identify the inductance and resistance values of the electrical equivalent circuit (Fig. 5). The measured voltages and currents are represented in Fig. 6 and the electrical parameters are reported in Table 2. The resistance analytical value is computed taking into account the conductor length and section of the practical model. The results are in close agreement, experimental values of inductance are slightly higher than analytical values since the model neglects the inductive part of conductors outside the 2D slot geometry. The resistance measurement used here is not accurate since it is based on the temporal delay observed between .u1 and .u2 in the experimental results (Fig. 6), however, the results are in the same order of magnitude. The analytical model provide the parameters of the LF equivalent electrical circuit with an appropriate accuracy and enables to estimate the voltages that are ought to be applied to the stacked coils for any current distribution (.i1 , .i2 ). These voltages are then applied to the model that computes the PWM-induced current ripple and losses.
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Fig. 6 Voltages and currents measured when only (a) coil 1 or (b) coil 2 is supplied. 6 A peak current at .fe = 200 Hz Table 2 Parameters of the electrical equivalent circuit
Parameter = r2 .L1 ≈ Lm .l2 = L2 − Lm .r1
Analytical value 30 m. 180 .µH 40 .µH
Experimental value 40 m. 200 .µH 50 .µH
3.3 LF Losses Assessment The expression of the induction field values in the slot and air-gap can be used to assess the losses in the two materials, namely the copper conductors and the laminated iron core. Even when multiple conductors are considered, the same flux line paths (Fig. 4a) can be taken into account to compute the induction values between each conductors as in (1). Then, within the coils, the magnetic field is ruled by the following equation: ΔH = σ μ0 ·
.
∂ H ∂t
(2)
where .σ is the copper conductivity. The problem is supposed to have its only dependence following the y-axis. The influence of the position of the conductor within the slot width (following x-axis) is neglected. Equation (2) can then be projected into a 1D problem: .
∂ 2H x = σ μ0 (j ω)H x . ∂y 2
(3)
By computing the magnetic field values within each conductors, the current density induced by the flux linkage can be obtained. The losses in the copper are then computed by integrating the square of the current density on the copper volume.
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Having the induction values in any position within the slot, the induction in the iron core can be obtained through the conservation of the induction flux. A Steinmetz model is then used to assess the core losses .PCore in the geometry for any current distribution. The LF losses are then decomposed into three terms: PLF = PCopper,DC + PCopper,supp + PCore
.
(4)
by the leakage flux where .PCopper,supp corresponds to the additional losses causes in the slot through the conductors, and .PCopper,DC = R · (i1,RMS )2 + (i2,RMS )2 corresponds to the losses related to the DC resistance terms of the stacked coils. This latter is not related to the analytical model and strongly depends on the experimental setup serial resistance. In the LF band, both copper conductors and iron core have frequency dependent behaviour, respectively through the terms .PCopper,supp and .PCore . These two terms also depend on the current distribution among the several stacked coils. The 20turns coils are supposed to be arranged in two rows within the slot as Fig. 3a shows. Then, for each stacked coils, 10 conductors having twice the section of a practical conductor are used to represent the 20 turns. Among the LF losses, the terms .PCopper,supp and .PCore are computed with the analytical model represented in Fig. 4a. The term .PCopper,DC is adjusted, taking the estimated value of resistance (30 m.) into account. The two coils are each powered by a dedicated linear amplifier. In this configuration, it is possible to impose the current magnitude in each coil and measure the overall losses related to the fundamental electrical frequency .fe . For several values of fundamental frequency .fe , the total peak current in the slot is fixed at 6 A and several operating points are tested in terms of current distribution between the two stacked coils. The current imbalance varies from .−100% (.i1 = 0 A) to .+100% (.i2 = 0 A). The losses computed from (4) are compared to measured results in Fig. 7.
Fig. 7 (a) Measured and estimated LF losses versus current imbalance for several fundamental frequency values .fe and (b) Current imbalance minimizing LF losses
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The measured and estimated results are consistent, showing that a positive current imbalance (.i1 > i2 ) could lead to minimize the LF losses in the magnetic circuit and its stacked coils. At low fundamental frequency, Fig. 7b shows that the experimental optimal current imbalance is mostly due to an eventual resistance disparity and could set to a non zero value. However, when the fundamental frequency increases, the optimal current imbalance clearly shifts toward positive values (.i1 > i2 ) since the current in coil 1, because of its proximity to the air-gap, induces no induction field in the slot around the conductors of coil 2. However, this result is obtained under a linear power supply and has to be confirmed under PWM excitation.
4 Investigation of the Control Degrees of Freedom on the PWM-Induced Losses 4.1 PWM Harmonic Based Model In order to reproduce the PWM-induced current ripple in stacked coils, the LF model is not sufficient. In the HF band, the copper conductors and the iron core present non negligible skin effect. Thus the inductive term is degraded and an additional impedance may be added in parallel to each inductive term to reflect the HF losses in those materials. This is visible on Fig. 8. The impedance .zk represents the additional losses in the copper, which is directly related to the HF leakage inductance .lk . Impedance .Zm symbolizes the core losses related to the HF mutual inductive term .Lm . Considering the geometry and the frequency of the PWM excitation, an FEA method would require a refined mesh leading to high computation time. Admittance analysis can be used to observe the frequency dependent behaviour of the coils but is not accurate to estimate the current ripple and PWM-induced losses [6]. Therefore, experimental results are used here for the identification of the HF model parameters. Practically, each of these terms depend on the LF operating point where the switching period occurs. However, in order to simplify this aspect and make rapid conclusions, this dependency is neglected. It is then assumed that this HF model
Fig. 8 PWM-induced current modelling of the two stacked coils
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Fig. 9 Measured (colored) and estimated (black) PWM-induced current ripple for .Δα = 4%
Fig. 10 PWM-induced current modelling of the two stacked coils. The values are calibrated through experimental measurements at fixed duty-cycle
is valid for any switching period based on the hypothesis of magnetic material linearity. Voltages and HF currents are measured on the practical model with its two Hbridge supply (Fig. 9). The model described in Fig. 10 is calibrated on experimental waveforms of PWM-induced current ripples due to duty-cycle differences (.Δα = α1 − α2 = 0). The obtained model precisely reproduces the current ripples and provides an estimation of losses (Fig. 9). Using this modelling, it is possible to compute the HF losses due to any duty-cycle configuration (.α1 , .α2 ). In this way, the voltages provided by the LF model are applied to the stacked coils in order to meet a given current distribution. The duty-cycles used in each H-bridge are determined for any switching period. At each switching period, the voltages signals are generated from a centred PWM method. The harmonic component of these signals are then treated by the HF model in order to reproduce the PWMinduced current ripple. For each LF current distribution, the required duty-cycle values are used to assess the average HF losses over a fundamental period .1/fe . The combination of these two models thus enables to estimate the PWM-induced losses required to reach a given current distribution. The total losses are computed with Ptot = PCopper,DC + PCopper,supp + PCore + PH F
.
(5)
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Fig. 11 Measured currents in the stacked coils with LF peak total current: 6 A while maintaining (a) equal duty-cycles or (b) equal fundamental currents (.Δα < 2.5%)
Fig. 12 (a) Measured and estimated total losses .Ptot versus current imbalance for several fundamental frequency values .fe and (b) Current imbalance minimizing the overall losses
where .PH F is the PWM-induced term averaged over one LF fundamental period. The terms .PCopper,supp and .PCore are the same than in the LF model (Fig. 7). The losses in inverters are included in .PCopper,DC . This latter is computed with an equivalent resistance of 220 m.. It enables the comparison with the losses measured on the DC-link of the two inverters in the experimental setup.
4.2 Synthesis For a given Ampere-turn level in the slots, the degrees of freedom offered by the stacked coils enable to consider several current distribution. The measured current waveforms are reported in Fig. 11 showing that the control of the current distribution requires small duty-cycle differences inducing negligible current ripple modifications. The corresponding total losses seen form the DC source are presented in Fig. 12. Similarly to the LF losses (Fig. 7), the minimum of total losses including the PWM-induced losses in the coils and the inverter losses shifts toward positive values when the fundamental frequency .fe increases. It exists a non zero differential
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currents that minimizes the total losses in the two stacked coils. These minima are reported in Fig. 12b. Thanks to the high coupling between the two stacked coils, small duty-cycle differences (.< 5%) are required to ensure any LF current imbalance. Therefore, the term .PH F presents a negligible variation over the different values of current imbalance. The shift of the optimal current imbalance toward positive values is mainly due to LF phenomena represented by .PCopper,supp and .PCore .
5 Conclusion The stator winding segmentation studied in this article enables to increase the modularity of the segmented drive and to reduce the voltage rating of the elementary converter. However, the winding configuration obtained presents several coils stacked in the same slots, having then different relative position to the air-gap and strong magnetic couplings. The present papers describes the phenomena involved in these segmented supply and proposes an estimation of the losses depending on the current distribution enforced in the stacked coils. The example of two stacked coils wound around the same magnetic circuit is used to describe the modelling process and an experimental setup provides the necessary information to build the PWM-induced losses model. Finally, non zero differential currents references are investigated in order to mitigate the total losses in the magnetic circuit and conductors. This study is reinforced by taking into account the losses in the several H-bridge converters of the experimental setup. It fully justifies the use of differential currents to properly supply the stacked coils segmented structure at high fundamental frequencies.
References 1. Abdalla Hussein Mohamed, Hendrik Vansompel, and Peter Sergeant. Design of an Integrated DC-Link Structure for Reconfigurable Integrated Modular Motor Drives. IEEE Transactions on Industrial Electronics, 0046(c), 2021. 2. E Hoang and E Labouré. Electric machine supplied at low voltage and associated multicellular power train, November 28 2019. US20190363599A1. 3. H Ben Ahmed, L Béthoux, A Cizeron, E Hoang, A Juton, E Labouré, A Mercier, E Monmasson, J Ojeda, L Queval, and G Remy. Electric Traction Chain with Segmented Power Supply. 23rd European Conference on Power Electronics and Applications (EPE21 ECCE Europe), September 2021. 4. Qianfan Zhang, Henri Josephson Raherimihaja, Guoqiang Xu, and Xi Zhang. Design and Performance Analysis of Segmented Three-Phase IPMSM for EVs Integrated Battery Charger. IEEE Transactions on Industrial Electronics, 68(10):9114–9124, 2021. 5. Wentao Zhang, Yongxiang Xu, Huidong Huang, and Jibin Zou. Vibration reduction for dualbranch three-phase permanent magnet synchronous motor with carrier phase-shift technique. IEEE Transactions on Power Electronics, 35(1):607–618, 2020.
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6. A Cizeron, J Ojeda, E Labouré, and O Béthoux. Prediction of PWM-Induced Current Ripple in Admittance Analysis. Energies 2019,12 4418, 2019. 7. Le Chang and Thomas M. Jahns. Prediction and Evaluation of PWM-Induced Current Ripple in IPM Machines Incorporating Slotting, Saturation, and Cross-Coupling Effects. IEEE Transactions on Industry Applications, 54(6):6015–6026, 2018. 8. Le Chang, Woongkul Lee, Thomas M. Jahns, and Jihyun Kim. Comparative analysis of pwm power losses in ipm machines with different modulation schemes using wide-bandgap-based inverters. In 2020 IEEE Energy Conversion Congress and Exposition (ECCE), pages 3629– 3636, 2020. 9. Davide Cittanti, Vincenzo Mallemaci, Fabio Mandrile, Sandro Rubino, Radu Bojoi, and Aldo Boglietti. Pwm-induced losses in electrical machines: An impedance-based estimation method. In 2021 24th International Conference on Electrical Machines and Systems (ICEMS), pages 548–553, 2021. 10. Gerhard Reber, Martin Rittner, Michael Guyenot, Ulrich Kessler, Alexander Klemm, Rainer Holz, and Manfred Reinold. Low-inductive sic h-bridge for direct-inverter-single-toothintegration (german bmbf public funded research project ‘verse’). In CIPS 2020; 11th International Conference on Integrated Power Electronics Systems, pages 1–5, 2020.
Current Sensor Fault Tolerant Control for a Synchronous Machine Based on Stator Current Estimation Peyman Haghgooei, Ehsan Jamshidpour, Noureddine Takorabet, Davood Arab Khaburi, and Babak Nahid-Mobarakeh
Abstract In this study, a current sensor faults tolerant control method is proposed for synchronous machines. The proposed method is based on the estimation of the stator currents. A comparison algorithm between the estimated and measured currents allows detecting a possible fault in the current sensors. Once a fault is detected in the current sensors, the control system is switched to the current sensorless control. This transition to sensorless control mode is achieved quickly without stopping or slowing down the rotor speed. To validate the proposed method, simulations and experimental tests are carried out on a wound rotor synchronous machine.
1 Introduction Synchronous machines are among the most important and widely used machines in the industry. Numerous studies have been conducted on the different control methods for this type of machine. Such as nonlinear control methods [1], adaptive methods [2, 3], direct torque control based methods [4] or flatness based control methods [5].
P. Haghgooei · E. Jamshidpour () · N. Takorabet GREEN – Université de Lorraine, Vandœuvre-lès-Nancy cedex, France e-mail: [email protected]; [email protected]; [email protected] D. Arab Khaburi Iran University of Science and Technology, Tehran, Iran e-mail: [email protected] B. Nahid-Mobarakeh McMaster University, Hamilton, ON, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_18
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Typically, in most control methods, two current sensors in the stator phases and one position sensor in the rotor shaft are employed. However, many sensorless control methods have been proposed in the scientific literature to reduce the number of sensors as well as the manufacturing cost. Position-sensorless control is one of the most studied methods for synchronous machines because of the relatively high cost and time-consuming calibration of the position sensor. However, current-sensorless control is also an effective method to minimize the system size and cost, particularly for high current motors, as it eliminates two expensive sensors. In some applications, due to their high sensitivity, current sensors cannot be eliminated. Therefore, in these applications, the current sensor fault-tolerant strategies (FTS) become mandatory [6, 7]. The first steps of fault diagnosis and FTS is fault detection and localization. The current estimation techniques are very helpful for detecting current sensor faults. Indeed, by estimating the stator currents and comparing them to the measured currents, a failure in the current sensors can be reported. This study presents a current sensor fault-tolerant control for Synchronous Machines. The proposed method is based on the estimation of stator currents. The rest of this paper is structured as follows. In the second section, the studied system is presented. In the third section, the fault detection algorithm is described. Section 4 is devoted to the explanation of the current estimation method. Then, some selected simulation results are reported and discussed in Sect. 5. The experimental test results and validation are presented in Sect. 6. Finally, the last section concludes the study presented in this paper.
2 System Description The studied machine in this work is a Wound Rotor Synchronous Machine (WRSM). The used WRSM is a low voltage (12 V) machine with a rated power of 1.5 kW, which is designed by the Valeo company for a mild hybrid vehicle application. The stator of the machine is supplied by a 12 V battery through a three-phase inverter, and the rotor excitation coil is fed by a constant current power supply. The drive system is integrated with a stator current sensor fault diagnosis algorithm that detects, isolates and reconfigures the system. For the normal condition, without any fault, the motor is controlled by a classic field oriented control method. As soon as a current sensor fault is detected, the control system switches to the current-sensorless control mode. This sensorless control is described in detail in [8] and will be described briefly in Sect. 4. Figure 1 illustrates the control scheme with the current sensor fault detection system. With this system, the fault is detected and isolated in real time without the interruption of drive operation. After isolation, the control is reconfigured to a current sensorless control to guarantee the service continuity of the system. The proposed fault diagnosis is detailed in the next sections.
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Fig. 1 Motor control diagram with current sensor fault detection system
3 Fault Detection in Current Sensors 3.1 Fault Detection Algorithm To detect a current sensor fault, it is necessary to first examine the types of sensor failures. Possible current sensor failures may include disconnection of the sensor to the control board, disconnection of the power supply of the sensor, an error in the internal sensor board, and creation of an unbalanced gain at the output. In the first and second cases, the signal received at the control system is zero or may also contain some noise still in the zero range. In the case of an error in the internal sensor board, the signal received at the control can be affected by a variation of the output gain or can be a zero signal with some noises close to zero. In general, given the possible failures, some solutions can be proposed to detect the presence of an error. For example, continuous comparison of the measured current (by sensors) of phases a and b can give a solution to detect the sensor failures. In the case of imbalance between the outputs of these two sensors (considerable difference in amplitude, a significant phase difference between the two currents, etc.), conclude that at least one of the two sensors is not working properly. Another solution can be a continuous estimation of the stator currents and, by comparison with the measured currents, detect the faults. The advantage of the first method is that the system is not constantly occupied with estimating the currents. Thus, it requires less CPU computation and consumes less power. But the main disadvantage is that when an error is detected and the controller wants to switch to sensorless control, since the motor currents are non-zero, the estimated currents will be accompanied by some spikes before convergence. On the other hand, when the stator currents are constantly estimated, the system is ready to switch to sensorless mode at any time, and the initial spikes will no longer be seen. The algorithm applied in this study is based on continuous estimation of stator currents and comparison with measured currents. The fault detection algorithm is shown in Fig. 2. In this algorithm, the measured currents of each phase as well as the estimated currents for each phase are first compared with each other, and when the
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Return
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Fig. 2 Proposed algorithm for current sensor fault detection
value of the difference (given as .Δ) exceeds a limit such as .Lm , this may indicate a failure. The definition .Δ is given in (1). Δ = |imeas − iEst |
.
(1)
Where .imeas and .iEast represent the measured and estimated currents, respectively. The choice of the value of .Lm depends on several parameters such as the accuracy of the current sensors, the perfection of the current estimation method, the accuracy of the machine model, the sampling frequency, etc. This value can be selected through experiments. In this study, this value is set to 4A, which corresponds to about .3% of the machine’s rated current. Another condition to consider for detecting the fault is the percentage of error at the operating point. The difference of 4A does not have the same significance in small currents as in larger ones. To calculate the percentage error value, consider the following: ζ =
.
Δ |Imeas | + ε
(2)
This percentage is represented by .ζ . As can be seen, a constant variable such as .ε is also used in the denominator of the fraction, which prevents the
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fraction expression from diverging and imposing a heavy computational load on the microprocessor when the currents are zero. This constant can be chosen as small as about .0.01% of the machine’s rated current. In the next step, a limit (given as .Km ) needs to be defined for the minimum value of .ζ . The choice of this limit, like the selection of .Lm , depends on some factors such as the accuracy of the system model, etc., which can be tuned according to the case study. In this work, due to the potential uncertainty of the model, this limit is considered equal to .8%. In this way, an error can be detected when the value of .Δ exceeds the value of .Lm and also the value of .ζ exceeds .Km . This error can be considered as a fault in the system if it continues for a period of time like .TL . In this case, a variable (named as “Mode” in the algorithm) becomes null, which indicates the existence of a fault. The time .TL is chosen according to the sensitivity of the application and the accuracy of the estimation method. In this study, this time is selected as .TL = 4 ms. According to the proposed algorithm, when a sensor fault is detected (.Mode = 0), the estimated currents and the current received from the sensor (.imeas ) are kept compared. If during a certain time (like .TL ), their difference is again lower than the limit, the variable Mode becomes 1, indicating that there is no more fault. This algorithm is used to detect a fault in one of the current sensors. If the algorithm reports an error on one of the sensors, a fault signal is sent to the controller and the controller switch to the current-sensorless control. In case more than one sensor reports errors, the fault signal is sent, but the controller does not go into current-sensorless control, and it stops the machine. Because failures of two or three sensors simultaneously are not normal and must be investigated.
3.2 Fault Isolation The second step of a fault diagnosis is fault isolation. Unlike the inverter faults, a non-isolated current sensor fault does not risk the whole of the system, and it is not necessary to isolate it physically. But the measured currents will not be available or not accurate after a fault declaration. Therefore, a reconfiguration is mandatory to guarantee the system operation.
3.3 Reconfiguration To have a continuity of service for a post-fault period, as mentioned before, currentsensorless control is proposed in this study that is detailed in the next section. When the fault signals are activated, the conventional control method will be replaced by the proposed current-sensorless control. This reconfiguration realizes in real-time, thus the system can continue to work without any interruption.
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4 Current Sensorless Control The proposed control is a model-based method. By using the flux model and a Luenberger observer, the stator currents are estimated that allows the control of the machine.
4.1 Model of the Machine The electric model of the WRSM in the dq reference frame, can be written as (3). .
vd = Rs id − ωe ψq + vq = Rs iq + ωe ψd +
dψd dt dψq dt
(3)
where: – – – –
Rs is the stator resistance vd , .id , .ψd are the voltage, current, and the stator flux respectively in the d axis, .vq , .iq , .ψq are the voltage, current, and the stator flux respectively in the q axis, .ωe is the synchronous angular frequency. . .
In the linear case, the stator flux can be expressed as a function of the stator inductances (.Ld and .Lq ) and the mutual inductance between rotor and stator (M). However, in the case of magnetic saturation and cross-coupling between the axes, each stator flux .ψd and .ψq can be expressed by a nonlinear function of the currents as follows: ψd = g1 (id , iq , ie ) . (4) ψq = g2 (id , iq , ie ) This model can also be expressed by the currents as a function of the fluxes as (5). To obtain such a model of the machine for this study, the method presented in a previous work was used: [9]. .
id = z1 (ψd , ψq , ie ) iq = z2 (ψd , ψq , ie )
(5)
4.2 Stator Current Estimation To have the stator current values, first, the stator fluxes need to be estimated and then, the .id and .iq can be estimated by using (5). By combining (3) and (5), the state
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space equations of the system can be presented as follows: ⎧ dψd ⎪ ⎪ ⎨ dt = −Rs z1 + Np ωr ψq + vd dψq . dt = −Rs z2 − Np ωr ψd + vq ⎪ ⎪ ⎩ dωr = 1 N ψ z − ψ z − T dt
J
p
d 2
q 1
(6)
L
where, – – – –
z1 and .z2 are the functions as introduced in (5) for .id and .iq , Np is the number of pole pairs, .TL is the load torque which includes the friction also, J is the mechanical inertia of the rotor. . .
A Luenberger observer is employed to estimate the stator fluxes (.ψd and .ψq ) using the presented system model. A detailed description of this estimator, as well as the system observability, have been presented in the previous work [8].
5 Simulation Study A simulation study is performed under Matlab/Simulink to investigate the effectiveness of the proposed algorithm. The sampling frequency as well as the switching frequency are chosen 10 kHz. In the first simulation test, the current sensor of phase “a” fails and its output becomes zero, and in the second test, its output containing an erroneous gain becomes double the actual value. In these tests, the stator currents are continuously estimated and compared to the measured currents according to the proposed algorithm. As soon as a mismatch is observed, the sensor fault is detected and the control is transferred to the current-sensorless control mode. Figure 3 shows the signal received from the current sensor of phase “a” for the first and second simulations. In these simulations, the sensor fault occurs at .t = 1 s and then, at .t = 3 s, the fault disappears, and the sensor works again. Figure 4 shows the measured and estimated stator currents. This figure demonstrates the moment of detection of an error in the current sensor. Since the time .TL in these simulations is set to four milliseconds, the fault is declared four milliseconds after the beginning of the difference between the estimated and measured currents. The stator currents in dq frame are also shown in Fig. 5. This figure illustrates the measured and estimated currents. At .t = 1 s, when a fault occurs, the motor control switches to the sensorless control mode. It is seen that the control system continues to operate in a stable and error-free way. In addition, when changing the control mode, no sudden spikes in the stator currents are seen, and this change is quite fast and with good dynamics. At .t = 3 s, after correcting the fault, the algorithm detects that and switches to control mode with the sensors.
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Fig. 3 Signal received from the current sensor. (a) First simulation when the output becomes zero, (b) Second simulation when the output becomes double the actual current
Fig. 4 Measured and estimated currents of the three stator phases. (a): First simulation when the output becomes zero, (b): Second simulation when the output becomes double the actual current
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Fig. 5 Measured and the estimated currents in dq frame
Fig. 6 Rotor speed in case of a stator current sensor failure in phase a
Figure 6 also shows the rotor speed when a fault occurs. In this figure, it can be seen that when changing the type of control from the sensor-based to the sensorless control, the speed is still stable and does not change.
6 Experimental Results In this section, the proposed fault-tolerant control method is applied to the WRSM in experimental tests. The experimental test bench is illustrated in Fig. 7. This system is controlled by a dSPACE MicroLabBox. The practical results of these tests are stored in the Control Desk software linked to dSPACE and plotted in the MATLAB software. In the experimental test, first the current sensor of phase “a” is faulty, and its output gain becomes .0.1 times, then the fault is fixed, and the gain is corrected. After a few seconds the current sensor of phase “b” is at fault and finally this sensor will be repaired also in a few seconds. The purpose of this test is to observe the detection of faults in the current sensors as well as the passage in sensorless control mode. When a fault is detected, the controller must be able to switch quickly to sensorless control without significant current overshoot. Figure 8 shows the measured stator currents. As it is explained, first the current sensor of the phase “a” fails and after a few seconds it is repaired, then the current sensor of the phase “b” fails and after a few seconds it is also repaired. On this
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Fig. 7 Experimental test bench
Fig. 8 Experimental result: Measured stator currents during the faults
figure, we can also see the “Fault” signal sent by the algorithm. It is shown that this algorithm detects the fault created in the current sensors of the phases “a” and “b”. (When there is a fault, the “F ault” signal is zero). Figure 9 shows the measured and estimated stator currents with higher magnification when creating a fault and clearing the fault in the current sensor of the phase “a”. Figure 10 shows the actual and estimated stator currents in dq frame. In this figure, the actual currents are measured by current sensors that have no connection to the control system and are placed only for comparison. As can be seen, at times (.T1 , .T3 , .T5 ) when there is no error in the sensors, the control is performed with the sensors, and when a fault occurs in one of the sensors (times .T2 and .T4 ), the controller is transferred to the sensorless control mode. As can be seen, the main characteristic of this method is the fast transfer to the sensorless mode without any spike or sudden current increase.
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Fig. 9 Experimental result: Measured stator currents; during (a): fault occurrence and (b): fault removal
Fig. 10 Experimental result: Actual and the estimated stator currents in dq frame
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Fig. 11 Experimental result: Rotor speed in case of a stator current sensor failure
Figure 11 also shows the measured and estimated rotor speed. As can be seen, when moving from sensor based control mode to sensorless control mode, the rotor speed decreases a little, which is due to the lack of accurate current estimation. The amount of this decrease is .1.1%.
7 Conclusions A current sensor fault tolerant control method based on stator current estimation for a synchronous machine has been presented in this study. The proposed method was based on the estimation of the stator currents and the comparison with the measured currents through a proposed algorithm. The simulation results showed that this algorithm can detect and locate current sensor faults and can switch to a current sensorless control without stopping the rotor. Also, experimental tests were conducted to evaluate the performance of the proposed method for a wound rotor synchronous machine. The results showed that the proposed algorithm can detect and switch to sensorless control without current overshoot.
References 1. A. El Magri, F. Giri, A. Abouloifa, M. Haloua, “Nonlinear control of wound-rotor synchronousmotor”, 2006 IEEE Conference on Computer Aided Control System Design,pp. 3110–3115, 2006. 2. A. El Magri, F. Giri, A. EL Fadili, F. Z. Chaoui, “An adaptive control strategy for wound rotor synchronous machines”, International Journal of Adaptive Control and Signal Processing, pp. 821–847, 2012 3. S. A. Hashjin, S. Pang, E. H. Miliani, K. Ait-Abderrahim, B. Nahid-Mobarakeh, “Data-driven model-free adaptive current control of a wound rotor synchronous machine drive system”,IEEE Transactions on Transportation Electrification,pp. 1146–1156, 2020 4. W. Chai, H. M. Yang, F. Xing, B. I. Kwon,“Analysis and design of a PM-assisted wound rotor synchronous machine with reluctance torque enhancement”,IEEE Transactions on Industrial Electronics,2020 5. F. Veeser, T. Braun, L. Kiltz, J. Reuter,“Nonlinear Modelling, Flatness-Based Current Control, and Torque Ripple Compensation for Interior Permanent Magnet Synchronous Machines”,Energies, pp. 1590, 2021
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6. S. Karimi, A. Gaillard, P. Poure, S. Saadate, “Current sensor fault-tolerant control for WECS with DFIG”,IEEE Transactions on Industrial Electronics, pp. 4660–4670, 2009 7. Z. Li, P. Wheeler, A. Watson, ... H. Ma,“A fast diagnosis method for both IGBT faults and current sensor faults in grid-tied three-phase inverters with two current sensors”,IEEE Transactions on Power Electronics, pp. 5267–5278, 2019 8. P. Haghgooei, A. Corne, E. Jamshidpour, N. Takorabet, D. A. Khaburi, B. N. Mobarakeh, “Current Sensorless Control for a Wound Rotor Synchronous Machine Based on Flux Linkage Model”,IEEE Journal of Emerging and Selected Topics in Power Electronics,2021 9. P. Haghgooei, E. Jamshidpour, A. Corne, N. Takorabet, D. A. Khaburi, B. N. Mobarakeh, “Magnetic Model Identification of Wound Rotor Synchronous Machine Using a Novel Flux Estimator”,IEEE Transactions on Industry Applications,pp. 5389–5399, 2021
Investigating and Modeling the Soft Switching Losses of IGBTs Under Zero Current Switching Conditions Assil Bouach, Sébastien Mariéthoz, Arnaud Gaillard, and Micka¨el Hilairet
Abstract The paper presents an investigation of IGBT’s zero current switching (ZCS) losses in a quasi-sinusoidal current mode series resonant converter. Theoretically, losses does not occur when the IGBT is switched at zero current. However, experiments show the opposite and switching losses are not negligible. Manufacturer’s datasheet do not indicate IGBT’s performance under ZCS condition which results in a lack of information to reduce the impact of the converter losses in order to reach high power density. A parametric model for the stored charge evacuated from the IGBT during turn off process is proposed based on experimental results. The impact of the ZCS modulation scheme and the magnetizing inductance of the transformer on zero current switching losses is discussed.
1 Introduction Soft switching conversion techniques are very attractive in high and medium power DC/DC conversion applications. Many academic and industrial works [1–4] dealt with the evaluation and optimization of classical soft switching converter while others proposed new topologies [5, 6] to overcome some issues like the trade-off of covering a wide current operating range and a high efficiency such as in fast DC charging station of electric vehicles. IGBT modules are widely used for medium and high voltages applications [10] where very high power density is mandatory. By optimizing losses in a converter, the volume and the technology (air or water) of the cooling system can be significantly reduced. For IGBT modules, zero current switching is more effective to reduce A. Bouach () · S. Mariéthoz Power Electronics Laboratory, Institute for Energy and Mobility Research, Bern University of Applied Sciences, Biel, Switzerland e-mail: [email protected] A. Gaillard · M. Hilairet FEMTO-ST Institute, UTBM, CNRS, Université Bourgogne Franche-Comté, Belfort, France © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_19
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Fig. 1 Test bench
the switching losses due to the large tail current occurring during the turn off process [7]. The conduction losses can be deduced easily from the datasheet of the semiconductor. However, data for dissipated energy during turn off/on process are usually missing for low and zero current. In [8, 9], the physics, internal structure and different types of IGBT are reported. In [10, 11], different analytical and SPICE IGBT’s models were proposed to describe, simulate and predict the performance of the semiconductor. However, these models are based on internal physical parameters which are generally missing or inaccessible from manufacturer’s datasheet. In [12], the IGBT stored charge is studied and measured only during the conduction phase. A simplified analytical model is established using a triangular current mode and does not take into account some factors that can enhance the ZCS performance of the IGBT. In this paper, an experimental investigation in a wide range of switching current is conducted in order to study ZCS losses in an IGBT module and the different factors affecting these losses. The test bench used for this study is based on a series resonant converter topology operating in a quasi-resonant current mode and which has been widely investigated [13–15]. A parametric model for the charge evacuated from the IGBT after the turn off process under ZCS conditions is proposed in order to be used in the optimization of the ZCS modulation scheme (Fig. 1).
2 Test Bench and Measurement Procedure The series resonant converter topology, as illustrated in Fig. 2, is used as a test circuit to investigate IGBT’s ZCS losses operating in the quasi-resonant mode. The complete experimental test bench is shown in the Fig. 1. The quasi-resonant mode takes place when the following conditions are fulfilled: – The switching frequency .fsw is lower than the resonance frequency .fr . dc1 is equal to the transformer ratio m. – The voltage ratio . VVdc2
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Fig. 2 Series Resonant Converter used to study the ZCS Performance of the IGBT under test .T2
The resonance frequency .fr is given as a function of the resonant tank components by the following Eq. (1): fr =
.
1 √ 2π Lr Cr
(1)
A boost converter has been connected to the output to adjust the voltage of the DC2 bus .Vdc2 through the boost duty cycle. The same test bench has been reported in [15]. By fulfilling the quasi-resonant mode conditions, the current makes a half sine and in the second half of the resonant period, .Tr , will remains zero until the beginning of the second half of the switching period, .Tsw , where the complementary IGBTs are turned on as shown in Fig. 3. The evaluation of the turn off dissipated energy .Eoff of the IGBT under test .T2 was carried out under both hard and soft switching conditions. For a given current profile, a switched current trajectory, along which the IGBT under test, .T2 , was turned off several times for the same voltage conditions, and .Eoff is determined for each point. An example of this trajectory is represented by the black curve in Fig. 3 when .Vdc1 = 600 V. The starting point is at full duty cycle (see blue curve in Fig. 3). Then the switch off moment of IGBT .T2 (also .T4 ) is modified along the switched current trajectory until the blue PWM curve of .T2 converges to the red curve (see Fig. 3). The final measuring point corresponds to the case of a hard switching at maximum current. As a result, the turn off dissipated energy can be studied in a wide range including switching the device at zero, low and high current. In order to change the current profile, two parameters are crucial: – The input voltage .Vdc1 allows to modify the value of the wave peak current. – The switching frequency .fsw allows to modify the duration of the zero current phase .δt. The turn off dissipated energy .Eoff is calculated by integrating the product of the measured collector-emitter voltage .Vce and the measured collector current .Ic . The
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Fig. 3 Example of studied switched current trajectory for turn off dissipated energy evaluation in the device under test .T2 when .Vdc1 = 600 V
beginning and the end of the switching process is given according to the standard given by SEMIKRON in [16].
3 Turn Off Energy Loss Behaviour 3.1 Influence of the Maximum Collector Current Measurements were performed for different input voltages .Vdc1 from 300 V to 600 V with a step of 100 V. By modifying the input voltage .Vdc1 , the maximum collector current .(Ic )max through the IGBT .T2 varies and different current profiles are applied. The results of the turn off energy loss .Eoff are given in Fig. 4. When ZCS occurs, the charge has not yet been evacuated and the charge remains in the IGBT under test .T2 . When the complementary IGBT .T1 turns on, this charge is evacuated through .T1 and causes an overshoot which is visible as a peak in the collector current of .T2 as shown in Fig. 4. Current spikes of up to 90% of .(Ic )max are observed when .Vdc1 = 600 V. For the same voltage and under ZCS conditions, this peak is the highest when the IGBT under test .T2 is turned off at the beginning of the zero current phase. The minimum turn off dissipated energy .Eoff that can be reached is about 21% of .Eoff at maximum collector current as shown in Fig. 4 when .Vdc1 = 600 V.
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Fig. 4 Turn off energy loss for different maximum collector current in .T2 when .fsw = 17 kHz
.Eoff can be slightly reduced even more by giving up the soft switching techniques and turning off the IGBT at a low current as shown for .Vdc1 = 600 V. This method is more efficient for higher resonant current. Indeed, for a maximum resonant current of 24.07 A (cf. Fig. 4 when .Vdc1 = 600 V), the turn off dissipated energy is reduced by about 67% by switching the device under test at .toff = −1.6 µs instead of .toff = 0 µs, while for a maximum resonant current of 13 A, as illustrated in Fig. 4 when .Vdc1 = 300 V, .Eoff is reduced by about 30%. From .−1.7 µs onwards, the reduction of .toff no longer leads to an improvement of losses. The losses increase and the resonant current switches to diode .D1 and thus a complete hard switching process occurs.
3.2 Influence of Zero Current Phase Duration The input voltage .Vdc1 was fixed at 600 V. A series of measurements was performed for a switching frequency 15 kHz. The results of the turn off energy loss .Eoff are given in Fig. 5. If the switching frequency decreases, the energy lost at the opening of the IGBT .T2 is reduced. In fact, the switching period increases by decreasing .fsw and the phase of the zero current becomes longer in the discontinuous conduction mode.
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Fig. 5 Turn off energy loss in .T2 when .Vdc1 = 600 V, .(Ic )max = 24.3 A and .fsw = 15 kHz
This provides additional time for the stored charge in the IGBT under test to be evacuated in a lossless manner. At the end of this zero current phase, the remaining charge in the IGBT .T2 is removed when the complementary IGBT .T1 of the same leg is turned on and losses occur. The lower the switching frequency is, the lower the losses are but the limited the transferred power becomes. Figure 5 shows that the collector current .ic alternates. When .ic becomes negative, the IGBT .T2 starts to discharge and the resonant inductance stores energy, which explains the decrease of .Eoff between .0 µs and .2.4 µs. When the current .ic changes sign and becomes positive, the IGBT .T2 is charged and the energy restored in the resonant inductance is transferred to IGBT .T2 which explains the increase of .Eoff between .2.4 µs and .4.2 µs. Similarly, the energy continues to alternate between the resonant inductor and the IGBT T2 until the end of this operation mode. To conclude, in order to minimize the losses in the IGBT, it is advisable to switch it at the moment when the current passes through zero at the end of the latest discharge phase.
3.3 Influence of the Magnetizing Inductance It should be noted that the transformer used for the different measurements presented above has 30 mH as magnetizing inductance. A new transformer has
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Fig. 6 Turn off energy loss in .T2 for different magnetizing transformer’s inductance
been designed with a low magnetizing inductance of about 3 mH. Reducing the magnetizing inductance allows to increase the magnetizing current at the primary of the transformer. This current will flows through the IGBT .T2 when it is turned on. Two series of measurements were carried out using the transformer with low magnetizing inductance at .Vdc1 = 400 V/500 V and .fsw = 17 kHz. Figure 6 shows the results obtained from the experiments. It is observed that the peak on .Eoff reached in soft switching in the case of a very low current (.Lm = 30 mH) has been drastically reduced by decreasing the magnetizing inductance. During the soft switching phase, the magnetizing current flows through the IGBT .T2 . This will remove part of the stored charge and trigger IGBT .T2 in a hard way. In the case where the magnetizing current is sufficient to evacuate all the stored charge from IGBT .T2 , the voltage .Vce across its terminals changes to .Vdc1 . Consequently, the voltage across the complementary IGBT of the same leg .T1 goes to zero, which allows to perform zero voltage switching for .T1 when it is turned on.
4 Stored Charge Model In this section, a reduced parametric model is proposed to the stored charge in the IGBT when it is turned off under ZCS condition. Neglecting the effect of oscillation during the zero current phase, It was previously shown that in soft switching operation, it is better to switch the IGBT at full modulation in order to provide more time to the stored charge in the IGBT
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Fig. 7 Comparison between the analytical model and the experimental measurements of .Qoff
to be evacuated without occurring losses in the IGBT. Switching the device at full modulation is considered for the model. If no current flows through the IGBT and it is subject to a . dV dt , the charge carriers in the IGBT are triggered and a current spike appears through the device. This charge, noted by .Qmin can be identified whether by interpolating the different experimental curves in Fig. 7 until .(Ic )max = 0 A or it can be measured during the first turn on of the IGBT at the start-up of the converter. In order to overcome the problem of overlapping of the IGBTs of the same leg, a dead time, or so called interlock time .δt0 , is imposed. If the duration of the zero current phase .δt is less than this dead time, the IGBT is turned off at low current and the losses decreases. The analytical equation proposed to model the stored charge in the IGBT used in this test bench is as follows:
.
Qoff ((Ic )max , δt) =
a + Qmin (δt exp(− δtb ) − δt0 )2 c + (δt − δt0 )2
(2)
(Ic )max exp(−d.(Ic )max ) + Qmin where: δt: the duration of the zero current phase. δt0 : the duration of the interlock time. .(Ic )max : the maximum collector current flowing through the IGBT. .Qmin : charge at zero maximum collector current. a, b, c and d: parameters that depend on the semiconductor physics and the circuit parameters and are determined from experimental measurements. . .
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By fitting the experimental measurements, all model’s parameters are determined. Figure 7 shows a comparison between the analytical model established and the experimental measurements performed. Thus, the soft switching losses of the IGBT can be estimated based on this model in the case where the semiconductor switches at full modulation having the shape and profile of the applied current as an input, more precisely, the maximum current and the duration of the zero current phase in the quasi-resonant current mode.
5 Conclusion The behaviour of the stored charge in an IGBT has been investigated in a wide range of switching current through experimental analyses. In a quasi resonant current mode, it has been demonstrated that zero current switching losses can be minimized by improving the ZCS modulation scheme and/or improving the design of the transformer by reducing the magnetizing inductance. Improving the ZCS modulation scheme can be performed by increasing the duration of the zero current phase in discontinuous mode or switching at very low current and the design of the transformer can be improved by reducing the magnetizing current. These enhancements will allow to extract the IGBT stored charge in a lossless manner. A new parametric model of the IGBT charge evacuated during the soft turn off process has been proposed where parameters can be identified through curve fitting of experimental data measured with the test bench proposed in this paper.
References 1. R. L. Steigerwald, R. W. De Doncker and M. H. Kheraluwala, “A comparison of high power DC-to-DC soft-switched converter topologies,” Proceedings of 1994 IEEE Industry Applications Society Annual Meeting, Denver, CO, USA, 1994, pp. 1090–1096 vol.2. 2. I. Barbi, F. P¨ottker, “Soft Commutation Isolated DC-DC Converters”, Springer, 2018. 3. L. Lindenm¨uller, R. Alvarez and S. Bernet, “Optimization of a series resonant DCIDC converter for traction applications,” 2012 IEEE Energy Conversion Congress and Exposition (ECCE), 2012, pp. 2201–2208, doi: 10.1109/ECCE.2012.6342442. 4. L. Jia, S. Lakshmikanthan, X. Li and Y. Liu, “New Modeling Method and Design Optimization for a Soft-Switched DC–DC Converter,” in IEEE Transactions on Power Electronics, vol. 33, no. 7, pp. 5754–5772, July 2018, doi: 10.1109/TPEL.2017.2751064. 5. S. Mariethoz and T. Delaforge, “A New Hybrid Isolated DC-DC Converter Topology for Realizing Very High Efficiency Isolated AC-DC Chargers,” 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), 2017, pp. 1–5, doi: 10.1109/VPPC.2017.8330953. 6. T. Delaforge and S. Mariéthoz, “Optimal design of a low cost 20 kW 99.1% efficiency active ZCS isolated dc-dc converter,” 2018 International Power Electronics Conference (IPECNiigata 2018 -ECCE Asia), 2018, pp. 3820–3824, doi: 10.23919/IPEC.2018.8507410.
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7. P. Ranstad and H. Nee, “On Dynamic Effects Influencing IGBT Losses in Soft-Switching Converters,” in IEEE Transactions on Power Electronics, vol. 26, no. 1, pp. 260–271, Jan. 2011, doi: 10.1109/TPEL.2010.2055581. 8. B. Jayant Baliga, “Fundamentals of Power Semiconductor Devices”, Springer, 2008. 9. A. Volke, M. Hornkamp, “IGBT Modules: Technologies, Driver And Application”, Infineon Technologies AG, 2012. 10. B. J. Baliga, “Analytical Modeling of IGBTs: Challenges and Solutions,” in IEEE Transactions on Electron Devices, vol. 60, no. 2, pp. 535–543, Feb. 2013, doi: 10.1109/TED.2012.2222415. 11. R. Azar et al., “Advanced SPICE modeling of large power IGBT modules,” Conference Record of the 2002 IEEE Industry Applications Conference. 37th IAS Annual Meeting (Cat. No.02CH37344), 2002, pp. 2433–2436 vol.4, doi: 10.1109/IAS.2002.1042786. 12. G. Ortiz, H. Uemura, D. Bortis, J. W. Kolar and O. Apeldoorn, “Modeling of Soft-Switching Losses of IGBTs in High-Power High-Efficiency Dual-Active-Bridge DC/DC Converters,” in IEEE Transactions on Electron Devices, vol. 60, no. 2, pp. 587–597, Feb. 2013, doi: 10.1109/TED.2012.2223215. 13. C. Dincan, P. Kjaer, Y. Chen, S. Nielsen and C. L. Bak, ”Analysis and design of a series resonant converter with wide operating range and minimized transformer ratings,” 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe), Warsaw, 2017, pp. P.1–P.10. 14. J. J. Sandoval, S. Essakiappan and P. Enjeti, ”A bidirectional series resonant matrix converter topology for electric vehicle DC fast charging,” 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), Charlotte, NC, 2015, pp. 3109–3116. 15. A. Bouach, S. Mariéthoz and T. Delaforge, “Series Resonant Converter for DC fastcharging electric vehicles with wide output voltage range,” 2019 21st European Conference on Power Electronics and Applications (EPE ’19 ECCE Europe), 2019, pp. P.1–P.8, doi: 10.23919/EPE.2019.8914828. 16. U. Nicolai, A. Wintrich, “Determining switching losses of SEMIKRON IGBT modules,” SEMIKRON, Application Note, AN 1403, 2014-08-19.
Design and Control of a Synchronous Interleaved Boost Converter Based on GaN FETs for PEM Fuel Cell Applications Elie Togni, Fabien Harel, Frédéric Gustin, and Daniel Hissel
Abstract This paper shares some solutions in order to implement a state-of-theart synchronous Interleaved Boost Converter (IBC), based on gallium nitride (GaN) power transistors. The solutions discussed have been implemented and validated on a synchronous 4-phase IBC (IBC4) prototype operating at a switching frequency of 250 kHz, specially designed to control the electric power delivered by a Proton Exchange Membrane (PEM) fuel cell module to a lithium battery pack. This paper focuses on digital control, such as PWM signal generation and the MCU requirements to reach high switching frequencies. It also discusses the issues related to the propagation delay of the sensors used and how to address them. The high switching frequency enabled by GaN transistors, combined with this DC/DC converter architecture and its phase-shifted control strategy, might heavily strain the load of the single MCU embedded. The real-time management of the different control loops is therefore exposed.
1 Introduction Silicon, which has been adopted as the mainstream technology in power electronics over the last five decades, is now getting closer to its theoretical bounds [1]. Today, this material is widespread all around the world, especially inside integrated circuits and switch-mode power converters through MOSFETs, IGBTs and diodes components. Even if some improvements continue to be performed on existing products, manufacturers and researchers are leaning on better materials, such as wide bandgap (WBG) semiconductors for new power devices development.
E. Togni () · F. Gustin · D. Hissel FEMTO-ST, FCLAB, Université Bourgogne Franche-Comté, CNRS, Belfort, France e-mail: [email protected]; [email protected]; [email protected] F. Harel Université Lyon, Université Eiffel, ENTPE, LICIT-ECO7, Belfort, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_20
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These materials are allowing smaller size devices to operate at higher switching frequencies, withstanding higher voltages and temperatures while having a lower on-resistance compared to silicon [2]. These outstanding intrinsic capabilities are leading to more efficient power conversion semiconductors, pushing further the enhancement in power electronics. Two promising technologies have emerged during the last decade and are already competing with previous ones: gallium nitride (GaN) and silicon carbide (SiC). Many electrical applications, such as power converters, variable-speed motor drives, LiDAR (Light Detection And Ranging), envelope tracking, audio amplifiers, or wireless power supplies arouse the interest of GaN semiconductors manufacturers [3]. However, literature and manufacturers rarely raise the opportunities to use GaN power semiconductors in fuel cell applications, while several of today’s commercial products are showing wellsuited characteristics for these applications. In the current context of search for more efficient energy solutions, fuel cells associated with new technology power electronics converters, such as GaN-based DC/DC converters, seems an interesting option to consider. The remainder of the paper is structured as follows: Section 2 brings a quick overview of the IBC4 prototype developed with GaN transistors, Sect. 3 provides most of the technical solutions that have been implemented to control such a DC/DC converter, Sect. 4 is dedicated to a reverse current protection and the paper ends with conclusions in the Sect. 5.
2 IBC4 Prototype Overview The objective of this work was to develop a prototype of a high-efficiency and highly compact DC/DC converter, suitable for a series hybrid PEM fuel cell system. The main function of this power converter was to ensure the transfer of electrical energy between a fuel cell module (composed of a stack of 80 cells and a nominal power of 3.3 kW) and a lithium battery pack of 120 V. The various theoretical, technical, and economic considerations have directed this research towards the development of a digitally controlled synchronous interleaved Boost converter (IBC), comprising four parallel elementary Boost power stages, whose switching cells have been made with latest-generation GaN transistors (ref. EPC2034C) from the American manufacturer EPC. Figure 1 shows the developed prototype in the front of the PEM fuel cell stack. With heatsinks and fans, the converter occupies a volume of approximately 1.5 l for a mass of 650 g (i.e. a power density of approximately 2 kW/l and 5 kW/kg). The motherboard, which includes all the components measures 21 cm long and 16 cm wide, and the half-bridge boards are 3 cm high. The digital control of the prototype was carried out using a dual-core microcontroller (ref. TMS320F28379D) clocked at 200 MHz. This microcontroller made possible the control of GaN transistors at a switching frequency of 250 kHz while performing various communication tasks through different protocols (I2C, SPI and CAN). In addition, a 90◦ phase shift of the control of each of the phases relative
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Fig. 1 IBC4 prototype in front of an air-cooled 80-cell/ 3.3 kW open-cathode PEM fuel cell
to each other has been implemented. This control strategy reduces the current ripple delivered by the fuel cell in addition to drastically reducing the size and the number of filter capacitors. The apparent frequency at the input and the output of the converter reached 1 Mhz. This converter has been experimentally validated within an hybrid fuel cell system, composed of an air-cooled fuel cell module based on the previous stack of Fig. 1 and a lithium battery pack, as shown in Fig. 2:
2.1 Synchronous IBC4 Architecture A simplified diagram of the synchronous IBC4 is depicted in Fig. 3:
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Fig. 2 Experimental setup used to validate the IBC4
Fig. 3 Synchronous IBC4 simplified architecture
2.2 Control Architecture The closed-loop control architecture of the IBC4 is depicted in Fig. 4. A first voltage loop is used to control the output voltage of the converter and set a limit equivalent to the maximum battery pack voltage. Four inner current loops are used to control the average current through each phase. Therefore, the current delivered by the fuel cell can be adjusted using the upper limit of the saturation block within the voltage loop.
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Fig. 4 Simplified cascade control loops
3 Digital Control Considerations 3.1 Digital PWM Signals Generation The eight PWM (dedicated to the control of the synchronous switching cells of the four phases of the IBC4 converter) were generated from four symmetrical triangular counters (Timer 1 . . . 4), synchronized and phase-shifted from one another by 90◦ , as depicted in Fig. 5. These counters have the advantage of enabling to center each of the PWM digital signals (PWM1A . . . 4A) on the top of their respective counter, and to easily generate their complementary signals (PWM1B . . . 4B).
3.2 High Resolution PWM (HRPWM) Signals The control of a power converter at a switching frequency above 100 kHz may result in technical difficulties and the microcontroller in charge of controlling the power switches has to embed advanced PWM peripherals. Indeed, these signals must have a sufficient quantization resolution to avoid undesirable oscillations in steady state. One of the conditions for avoiding these phenomena requires that the resolution of the digital PWM signals be greater than the resolution of the ADC used to sample the signals from the electrical quantities to be regulated [4]. Unlike the resolution of an ADC which is fixed regardless of frequency, that of a PWM signal decreases as its frequency increases. To overcome this loss of resolution, one of the solutions consists in using counters with increased resolution. This enables the generation of high-resolution PWM signals (HRPWM), whose duty cycle can be adjusted with an accuracy of a few hundred picoseconds.
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Fig. 5 PWM signals generation principle for controlling the four phases of the interleaved converter
Fig. 6 ADC synchronization on the same timer used for PWM generation
3.3 Sensors Bandwidth and Propagation Delay Theoretically, the current increases linearly in the inductor as long as the PWM signal controlling the low side transistor (PWM1A) is in the high state. As mentioned in the previous section, as long as the PWM signals are generated symmetrically with respect to the high value of the counter, synchronizing the measurement to this value should allow sampling the average current . IL through the inductor, as depicted in Fig. 6. While voltage measurement at the input or output of a converter generally relies on a voltage divider, many techniques exist for current measurement [5]. In order to achieve the highest possible control bandwidth, current measurement requires the use of high-performance sensors with a bandwidth greater than the switching frequency. Also, these sensors must have a low propagation delay between their
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Fig. 7 Oscilloscope screenshot showing propagation delay and the effect of the bandwidth of an isolation amplifier (B) compared to a precision current probe (C)
input and their output. Furthermore, depending on the location of these sensors in the power circuit, they may require high immunity to common-mode transients given the voltage variations (dV/dt) associated with the very fast switching times of GaN transistors [6]. During this work, isolation amplifiers (ref. AMC13x) have been used. These sensors have a high propagation delay (typically 2.5 μs) and a bandwidth below 300 kHz. Figure 7, is a comparison between a high bandwidth oscilloscope current probe (C) (ref. Agilent 1147A) and a current feedback circuit based on this isolation amplifier (B) for a switching frequency of 250 kHz. (A) is the PWM signal controlling the low side FET of a Boost converter. The solution applied consists in shifting the synchronization of the measurement to the peak of the next counter and extending the acquisition window duration of the ADC. This way, the signal is sampled about 2.5 μs later.
3.4 Real-Time Management of Critical Tasks One of the main difficulties encountered during the implementation of the control of the IBC4 converter was to ensure the execution of different tasks on a single microcontroller, in a time interval strongly constrained by the switching frequency and the phase shift of the PWM signals. Indeed, in order to maintain a maximum control bandwidth, the various control loops were synchronized on the four counters (Timer 1 . . . 4) used for the generation of the PWM signals (c.f. Fig. 5). Due to the high switching frequency targeted (i.e. 250 kHz) and the 90◦ phase shift of the control of the four phases relative to each other, the time available between two consecutive PWM signals was then reduced to one microsecond (1/1000 kHz). During this microsecond, the microcontroller has to perform critical control tasks
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Fig. 8 Simplified timing diagram of the different tasks shared between CPU1 and its coprocessor CLA1 Table 1 Main steps of the different tasks performed on the coprocessor for controlling the four phases of the IBC4 Step (1) (2) (3) (4)
Description Read ADC EOC results Compute output voltage compensator Compute phase current compensator Update duty cycle
Phase 1
Phase 2 x
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(i.e. control loops), and also less critical tasks such as communication through different digital protocols (e.g. CAN, I2C, SPI . . . ). During this work, it was found that if these tasks were performed on only one of the processors (CPU1 or CPU2) of the TMS320F28379D microcontroller, the CPU used was overloaded and unable to control the converter. To solve this, critical control tasks were implemented on its coprocessor (i.e. CLA1), thus reducing drastically the load on the associated processor (i.e. CPU1). The main interactions between the processor and its coprocessor are represented in the form of a simplified timing diagram in Fig. 8. In general, the control of the converter is based on various interrupts. Four ADC modules (ADCA . . . D) are synchronized to the high value of the four counters (Timer 1 . . . 4) used for the generation of the PWM control signals. The end of conversion (EOC) of each ADC module triggers both an interrupt in CPU1 (which is immediately acknowledged) as well as the execution of a task in CLA1 through a DMA (Direct Memory Access) module. Each task represented in Fig. 8 is then dedicated to the control of one phase of the converter and comprises up to four main steps exposed in Table 1.
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Fig. 9 Architecture of the digital PI compensator used
3.5 Digital Compensator Selection Given this high switching frequency and the short time interval available between two successive PWMs (i.e. less than one microsecond), the use of a highlyoptimized compensator structure programmed in assembly language has proven to be essential to ensure the correct execution of the various control loops. Therefore, a digital Proportional-Integral (PI) compensator structure from a specific library optimized for this microcontroller reference was used. The architecture is shown in Fig. 9, where r(k) is the setpoint, y(k) the measurement, and u(k) the control effort. This parallel architecture facilitates the tuning of the proportional Kp and integral Ki coefficients independently. The compensator output has a saturation block as well as an anti-windup allowing the integrator to be reset as soon as the high and low limits of the saturation block are reached. For the voltage control loop, this saturation block is used to adjust the limit on the current setpoint at the converter input. This setpoint is then divided by four and is used as a setpoint for the four average current control loops in each of the inductors of the four phases of the DC/DC. For the inner current control loops, this saturation limits the value of the duty cycle (typically between 0 and 90%). This PI compensator offers one of the best execution times, measured at 169 ns, between receiving input data and updating the control effort.
4 Reverse Current Protection in DCM As mentioned above, the IBC4 converter consists of four elementary Boost converters connected in parallel which must ensure the transfer of electrical energy from the fuel cell to the battery pack. The use of synchronous switching cells implies that the converter can be bidirectional. Considering an elementary Boost converter, a reverse current may therefore be supplied from the battery pack to the fuel cell module through the high side transistor as illustrated in Fig. 10: Under non-fault condition, a Boost converter may operate according to three conduction modes, as long as the power supplied by the source increases. When it is started, the converter generally operates in discontinuous conduction mode
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Fig. 10 Diagram illustrating a reverse current through the high side FET of a Boost converter
(DCM), before transitorily operating in Boundary Conduction Mode (BCM), to finally operate in continuous conduction mode (CCM). Without any protection, a reverse current may occur when the converter operates in DCM.
4.1 Conduction Mode Detection Algorithm The simplest solution to avoid any reverse current would be to add a power Schottky diode at the input or output of the converter. However, this solution induces significant conduction losses (several tens of watts), when the fuel cell module operates at nominal power. With the objective of an electrical efficiency that must be as high as possible, another solution consists in implementing a control strategy to turn off the high side transistor, so that the latter operates only in reverse conduction (in a similar way to a diode) as long as the converter operates in DCM. Reference [7] caught our attention, presenting a method to detect the conduction regime of a synchronous boost converter. This method allows determining in real-time the conduction mode in which the converter operates and can easily be programmed on a microcontroller, without adding any electronic component. This article inspired the flowchart in Fig. 11, whose algorithm was programmed on the MCU of the IBC4 converter.
4.2 Gate Drive Considerations As soon as the discontinuous conduction mode is detected, the microcontroller must disable the control of the high side transistors of the four phases of the IBC4 converter. A total of eight gate drivers (ref. UCC27611) were used to build the IBC4 converter (i.e. a single driver for each GaN transistor). These drivers incorporate an AND logic gate, which enables and disables the transmission of the PWM control signal, as shown in Fig. 12. Thus, as soon as the DCM is detected by the algorithm, the microcontroller can disable the high side drivers using four digital outputs, and activate them again when the converter operates in continuous conduction mode.
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Fig. 11 Flowchart of the proposed conduction mode algorithm
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Fig. 12 Simplified diagram of a gate driver with an “Enable” input
5 Conclusions In this paper, some design and control considerations of an Interleaved Boost Converter based on GaN transistors are introduced. This research has highlighted the main challenges related to the use of GaN transistors in a power converter within a PEM fuel cell system. In addition, the use of synchronous switching cells involved the implementation of a functionality for detecting the discontinuous conduction mode (DCM). A digital solution without adding any component has been developed, thus avoiding any reverse current from the battery pack to the fuel cell module.
References 1. A. Lidow, “GaN as a displacement technology for silicon in power management,” in 2011 IEEE Energy Conversion Congress and Exposition, Sep. 2011, pp. 1–6, doi: 10.1109/ECCE.2011.6063741. 2. J. Millan, P. Godignon, X. Perpina, A. Perez-Tomas, and J. Rebollo, “A Survey of Wide Bandgap Power Semiconductor Devices,” IEEE Trans. Power Electron., vol. 29, no. 5, pp. 2155–2163, May 2014, doi: https://doi.org/10.1109/TPEL.2013.2268900. 3. A. Lidow, M. De Rooij, J. Strydom, D. Reusch, and J. Glaser, GaN transistors for efficient power conversion, Third edition. Hoboken, NJ: Wiley, 2020. 4. A. V. Peterchev and S. R. Sanders, “Quantization resolution and limit cycling in digitally controlled PWM converters,” IEEE Transactions on Power Electronics, vol. 18, no. 1, pp. 301– 308, Jan. 2003, doi: https://doi.org/10.1109/TPEL.2002.807092. 5. S. Ziegler, R. C. Woodward, H. H.-C. Iu, and L. J. Borle, “Current Sensing Techniques: A Review,” IEEE Sensors Journal, vol. 9, no. 4, pp. 354–376, Apr. 2009, doi: https://doi.org/ 10.1109/JSEN.2009.2013914. 6. B. Liu, R. Ren, Z. Zhang, B. Guo, F. (Fred) Wang, and D. Costinett, “Impacts of High Frequency, High di/dt, dv/dt Environment on Sensing Quality of GaN Based Converters and Their Mitigation,” CPSS TPEA, vol. 3, no. 4, pp. 301–312, Dec. 2018, doi: https://doi.org/ 10.24295/CPSSTPEA.2018.00030. 7. M. Kim, M. Shin, S. Choi, K. Bae, C. Won, and Y. Jung, “Reverse current control method of synchronous boost converter for fuel cell using a mode boundary detector,” in 2014 IEEE International Conference on Industrial Technology (ICIT), Busan, South Korea, Feb. 2014, pp. 359–364. doi: https://doi.org/10.1109/ICIT.2014.6894869.
Electromagnetic Transient Modeling of Power Electronics in Modelica, Accuracy and Performance Assessment A. Masoom, J. Gholinezhad, T. Ould-Bachir, and J. Mahseredjian
Abstract This paper presents the Electromagnetic Transient (EMT) modeling and simulation of power electronics in Modelica, a declarative equation-based language. In this paper, modeling of switching components such as diodes, insulated-gate bipolar transistors (IGBT) and multi-level converters using ideal and nonideal components are investigated. A three-phase three-level and a single-phase two-level converter with an open-loop controller are simulated in Modelica and EMTP® . The accuracy and performance of simulations are compared using the variable and fixedstep solvers. Analytical solutions are used for verification of results as well.
1 Introduction Power electronic components are widely used in high voltage DC (HVDC) networks, and the request for developing simulation tools to consider the detailed models including the nonlinearity of semiconductors is increasing. Currently, circuitoriented simulators e.g., EMTP® [1] are available and widely used. In EMTP, modified-augmented-nodal analysis (MANA) [1] is used to formulate companion circuits resulting from the conversion of differential equations from models; then an imperative language, e.g., Fortran, C is employed for numerical computations. The solution method is very efficient for large-scale circuits. The system matrix needs to be refactorized for switching and nonlinear models present in power electronics circuits. Power electronics circuits can cause numerical discontinuities, which creates complexities in the simulation algorithms. EMTP uses a combination
A. Masoom () · J. Gholinezhad · J. Mahseredjian Electrical Engineering Department, Polytechnique Montreal, Montréal, QC, Canada e-mail: [email protected]; [email protected]; [email protected] T. Ould-Bachir Computer and Software Engineering Department, Polytechnique Montreal, Montréal, QC, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_21
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of trapezoidal and Backward Euler integration methods to suppress numerical oscillations due to discontinuities. Modelica [2] is a declarative equation-based language developed for complex system modeling, in which the models are decoupled from the simulation engine. In addition, the language offers better efficiency for model development with concise and readable codes. Modelica models should be firstly flattened to construct the circuit equations. The equations have no pre-defined causality; thus, they should be sorted vertically and horizontally in an executable order. Finally, the C codes are generated and transferred to the selected solver. Modelica supports model exchange and co-simulation through the Functional Mock-up Interface (FMI) standard [3]. Modelica also supports a user-friendly graphical user interface (GUI) for designing network diagrams, building graphical tools such as component symbols, and visualizing results. For EMT simulations, Modelica was first used for transmission line simulations in [4]. Then, the Modelica Simulator of Electromagnetic Transients (MSEMT) [5], a library based on EMT models, was developed. The library includes power electric models such as transmission lines, synchronous machines, controllers, etc. used in large networks [6]. Dynaωo [7] is a hybrid simulation suite designed to speed up simulations in Modelica. The tool was also adapted for EMT simulations in [8]. Furthermore, a time-domain simulation of a grid-connected converter (average model) in Modelica was examined in [9]. However, simulation speed in Modelica tools, i.e., OpenModelica [10] and Dymola is a challenge in comparison with EMTtype codes, such as EMTP. This paper aims to investigate the accuracy and performance of power electronic models of diode, IGBT and multi-level converters with Modelica. These components are modeled with two approaches: (1) nonideal and (2) ideal characteristics. These approaches are used in two numerical tests to compare the results and performances. For this purpose, the simulations are run in Dymola and EMTP using variable step and fixed-step solvers, respectively. This paper is organized as follows. In Sect. 2, the power electronic models in Modelica are described and implemented. Section 3 is dedicated to numerical tests and validation of models.
2 Power Electronic Models in Modelica The MSEMT library is developed to cover the power electronic detailed nonideal and ideal models including diodes, IGBTs, and 2-level and 3-level converters, etc. All these models are packaged in “MSEMT\Electrical\Electronics” branch. Semiconductor switches including diodes, thyristors and IGBTs present nonlinearities during their transition from one state to the other. The model should be able to represent this switching of states appropriately. In this section, we deal with the key models used in power electronic simulations.
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2.1 Nonideal Diode Model The diode is a fundamental component in power electronics. In some simulators, the diode is modeled as an ideal component with a fixed small on and a large off resistance with a forward voltage drop. In MSEMT, like in EMTP, in addition to the ideal model, the diode is also modeled as a nonlinear resistor with a monotonically increasing piecewise linear representation of the voltage-current resistance (16 segments). In this model, the reverse recovery time is zero, Fig. 1a illustrates the symbol of a nonideal diode in MSEMT. The model can be dragged and dropped into the simulation page and easily connected in series or parallel to other components, e.g., resistor, sinusoidal voltage source, etc. without any mathematical constraints. Figure 1b shows the pieces of code for the diode model in Modelica. In these codes, the matrix T defines the current and voltage points of the nonlinear resistance curve of the diode (see Fig. 1c). OnePort is a class containing the generic equations of two-terminal devices [7]. The extends is used to specify inheritance from OnePort partial class into the diode model; a property that prevents the modeler to repeat equations in the model. The function linearinterpolate()interpolates the voltage, v, over the resistance curve, and returns the appropriate current, i. As one can observe, the model is explicitly expressed by its equations in an acausal form. The modeler has no concern about
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i = linearinterpolate(T[:,2], T[:,1], v); end Diode;
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Fig. 1 Nonideal diode model. (a): symbol of the model in MSEMT, (b): Modelica implementation coded as a nonlinear resistor with 16-segments. (c): v-i characteristics of nonideal diode
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the solution method. No input, output, or priority of equations are defined in the model. In the codes, the sign “=” defines the relationship between the variables, v and i.
2.2 Ideal Diode Model The ideal diode in MSEMT includes a Resistive Switch Model (RSM) controlled by the parameter forward threshold voltage, Vfw , whose default value is zero. The RSM uses a very small on-state resistance and off-state conductance (Ron = Goff ∼ = 0). The diode logic is coded to conduct when it is forward biased, i.e. (vak > Vfw ). When the diode is reverse biased or the current flow into the device becomes zero, the diode turns off. The exact instant of switching is computed using a root fining mechanism [11]. Figure 2 shows the symbol and v-i characteristics of the ideal diode in MSEMT. The functionality of the model is identical to the 2-segment diode model in EMTP.
2.3 Nonideal IGBT Model The IGBT is a semiconductor device controllable by the gate signal. Figure 3 represents the nonideal IGBT model [12]. The IGBT is modeled by an ideal controlled switch (SW), two nonlinear (series and anti-parallel) diodes, and the snubber circuit. This model reproduces switching and conduction losses and any topological conditions in the converter. The gate pin (G) is a Boolean variable that controls the opening and closing of the switch, SW.
2.4 Ideal IGBT Model Figure 4a shows the ideal IGBT block in MSEMT. The model consists of the series connection of a DC voltage source, Vfw , representing the forward biasing voltage drop, and an RSM controlled by logical signals. The IGBT logic is coded to conduct
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when the collector-emitter voltage, VCE , is positive and greater than Vfw and the Boolean signal G is true. It turns off if the vCE is positive and the Boolean signal G is false. The IGBT also turns off when vCE is negative (because of antiparallel diode). The voltage and current characteristics of the ideal IGBT are illustrated in Fig. 4b.
2.5 Three-Phase Three-Level Converter Model The three-phase three-level converter is used for renewable energy and microgrid interfaces. Figure 5a shows the block of a three-level neutral-point-clamped (NPC) converter implemented in Modelica. The converter is modeled with four nonideal IGBTs for each leg, controlled by firing pulses produced by a PWM generator as shown in Fig. 5b. In each leg, two diodes are connected to the common connection point of the two DC-link capacitors. The capacitors split the DC link voltage into 3 levels, +VDC /2, 0 and −VDC /2. If the switches Sa1 and Sa2 are triggered, the output voltage is +VDC /2, if the switches Sa2 and Sa3 conduct, the output voltage is 0 and if the switches Sa3 and Sa4 are fired, the output is −VDC /2. Assuming ma
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Fig. 5 Three-phase three-level converter. (a): symbol of model, (b): Modelica implementation of converter using nonideal IGBTs and diodes (16-segment) and SPWM
is the modulation index, the line-to-line RMS voltage at the fundamental frequency of the converter is obtained using VLLRMS =
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2.6 Three-Phase Two-Level Converter Model Figure 6a illustrates the block of a three-phase two-level converter in MSEMT. The converter consists of three legs, one for each phase, and the nonideal IGBTs are controlled by an SPWM (see Fig. 6b). One of the two switches in a leg is always in on-state at any instant. A similar model is available using the ideal IGBTs.
2.7 Single-Phase Two-Level Converter Model Figure 7 shows the model of a single-phase two-level converter implemented in Modelica. This converter consists of two half-bridge converters. In this model. The PWM with bipolar voltage switching is used; therefore, the diagonally opposite switches (L1–1, L2–2) and (L1–2, L2–1) from the two legs in Fig. 7 are switched as
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switch pairs 1 and 2, respectively. For the under modulation (ma ≤ 1), the RMS of the fundamental-frequency output voltage is obtained by [13]: VRMS =
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2.8 SPWM Generator (3-Level) The sinusoidal pulse width modulation (SPWM) generator (3-level) generates pulses for a three-phase three-level NPC converter. In this technique, the control signal is compared with two symmetrical level-shifted triangle carriers. The triangle block
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generates a symmetrical triangle waveform with the peak amplitude of ±1 and carrier frequency (fc ). The converter leg has three states: +1, 0, or − 1. When the control signal is greater than the positive carrier, the state of the leg is +1; when the control signal is smaller than the negative carrier, the state of the leg is −1; otherwise, the state is 0. For a three-phase bridge, three control signals are used to generate the 12 pulses. A similar technique is used for SPWM (2-level) for generating the 6 pulses.
3 Model Verification and Validation In this section, two case studies are used for the validation of modeling accuracy and comparison of simulation performances. For this purpose, the reference software is EMTP, since nonlinearity is fully considered. Moreover, both test cases are originated from EMTP examples. The two circuits are simulated using the nonideal and ideal components.
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Figure 8 shows the test case used for validation of the NPC three-level converter model. The converter is fed by a 1150 V DC link. The AC side of the converter is connected to the network of 34.5 kV through a Yd + 30 transformer and RL filter. The filter is used to mitigate high-frequency harmonics generated by the converter. The converter is controlled by an open-loop SPWM 3-level generator. The PWM switching frequency is set to 2500 Hz. The control voltage is a balanced three-phase voltage with the phases of −10◦ , −130◦ , and 110◦ respectively for phases a, b, and c. The modulation index, ma , is 0.89. Simulations of the circuit using nonideal and ideal models are run in EMTP with the trapezoidal/Backward Euler solver with the time step of 2 μs. The simulation time is 500 ms and the simultaneous switching option [14] is activated for nonideal models. The same circuits are also simulated using the DASSL [15] solver with the tolerance of 1e-6 in Dymola.
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Fig. 9 (a): Line-to-line voltage Vab of nonideal and ideal converter models (b): the zoom in view
Figure 9 shows the voltage of phase-a of the AC side of the converter. As it is observed, the results obtained from Modelica nonideal models agree with EMTP. As one can see, the results obtained from ideal models are very close to the nonideal ones. Analytical calculation of Vab, RMS as per (1) for the off-grid converter yields 626.7 V. The computed RMS values for Modelica and EMTP results obtained for nonideal models are 660.73 V and 710.62 V, respectively. The values in Modelica and EMTP ideal models are 678.21 V and 714.5 V, respectively. The RMS of Modelica nonideal model is closer to the analytical value. The precision is justified by the interpolation of exact points of discontinuities. Figure 10 shows the three-phase current waveforms of the converter. As it is observed a slight difference can be observed between the results of Modelica and EMTP nonideal (NI) models. The difference is due to different methods of discontinuity handling and solver precisions. Table 1 compares the RMS of converter current waveforms of Fig. 10a. A relative error of 1% is observed between Modelica and EMTP solutions for nonideal models. The differences between nonideal and ideal models are less than 3% and 5%, respectively for simulations in Modelica and EMTP. Table 2 compares the CPU time of simulations in Modelica and EMTP. For both types of simulations, it is observed that EMTP outperforms Modelica. The CPU time ratio of Modelica to EMTP for the simulation of nonideal models (16segment) is 1.8:1. The ratio for ideal models reaches 1.31:1. It should be noted that in the Modelica simulations, an amount of time is required for parsing and sorting equations. This procedure is not repeated in re-simulations unless the configuration of the circuit change.
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Fig. 10 (a): The output current of nonideal (NI) and ideal converter models (b): zoom view Table 1 The RMS values of three-phase converter phase currents
Phase Model Phase-a Phase-b Phase-c
Table 2 Comparison of runtime between Modelica and EMTP
Simulator Model type Solver t CPU time (s)
EMTP NI 1225.7 A 1215.0 A 1205.7 A
Ideal 1299.8 A 1249.3 A 1250.0 A
Modelica NI Ideal DASSL – 16.58 10.3
Modelica NI model 1215.0 A 1224.1 A 1228.9 A
Ideal 1254.7 A 1261.6 A 1262.6 A
EMTP NI Ideal Trap/BE 2 μs 9.2 7.81
3.2 Short-Circuit Simulation Let’s increase the complexity of the circuit by applying an unsymmetrical short circuit on phases a and b on the terminals of Winding 1 of the transformer YD + 30 at t = 300 ms. It is assumed the fault is cleared at t = 400 ms. The simulation is carried out using the non-ideal diode and saturable transformer (STC) models in both simulators. The fault is modeled by an ideal switch [5]. The fault switching drives the nonlinear inductors of transformer to operate in the saturation regions. The solvers parameters are like the previous case. Figure 11a, d compares the currents obtained from Modelica and EMTP solution methods at
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Fig. 11 (a): Grid-side current contribution. (b): Zoom-in plot of current before fault at the gridside (c): Zoom-in plot of current during the fault at the grid-side. (d): Converter-side current contribution. (e): Zoom-in plot of current during the fault at the converter-side. (f) Zoom-in view of the current after removing the fault at the converter-side
the grid and converter sides, respectively. As one can see, the simulation is finished successfully in Modelica without any numerical problem. Once again, it is observed that Modelica results are close to EMTP. Figure 11b compares the currents of phasea, −b and -c before the fault occurs. Figure 11c, e illustrate the currents injected into the fault from the gird and converter sides, respectively. It is observed that the gridside fault current contribution, i.e., 40 kA is much more than the converter-side fault current contribution, i.e., 5 kA. Figure 11f depicts the current waveforms after removing the fault in both simulators. In all cases, it is observed that the discrepancy between the two methods is negligible.
3.3 Single-Phase Two-Level Converter Figure 12 shows the circuit of a single-phase two-level converter connected to the grid through a three-winding 120 V/120 V/14.37 kV transformer (TR). The converter is supplied by a 360 V DC link. The modulation index, ma , and frequency modulation ratio, mf , are 0.95 and 75, respectively (the fundamental frequency is 60 Hz). The simulations are carried out with the same profile as the previous case. The analytical calculations of fundamental frequency and other harmonic components of output voltage as per (2) and the harmonic coefficients obtained from the interpolation for ma = 0.95 in Table 8–1 of [13] are as below: (Vo )h1 = 254.55 × 0.95 = 241.8 VRMS at 60 H z (Vo )h73 = 254.55 × 0.2935 = 74.71 VRMS at 4380 H z
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Fig. 13 Harmonic spectrum of output voltage of single-phase converter using nonideal models, Y1 and Y2 indicates the EMTP and Modelica values respectively
(Vo )h75 = 254.55 × 0.6552 = 166.78 VRMS at 4500 H z (Vo )h77 = 254.55 × 0.2935 = 74.71 VRMS at 4720 H z Figure 13 shows the harmonic components of the output off-grid voltage obtained from the FFT analysis of Modelica and EMTP solutions for nonideal models. The frequency range is limited to the first multiple of mf . As one can see, harmonic components obtained from both simulations are almost identical. It is observed that these values are almost equal to the analytical solutions. Figure 14 depicts the current waveforms of the converter. In this case, like the previous test, a slight difference between results obtained from Modelica and EMTP is observed. It is also observed that the solutions for nonideal models are very close to the ideal models. Table 3 shows the RMS of converter current waveforms of Fig. 14a. One can see that the differences between the results obtained for ideal and nonideal models are 4% in both simulators. The relative errors between EMTP and Modelica results are 0.4% and 0.2% for nonideal and ideal models, respectively. Table 4 compares the CPU time of simulations in Modelica and EMTP. For nonideal models, it is observed that the Modelica offers a CPU time close to EMTP. The simulation ratio of EMTP to Modelica for nonideal and ideal models
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Fig. 14 (a): Output current of single-phase converter supplying the grid (b): the zoom in view Table 3 The RMS values of single-phase converter phase currents
Phase Model Phase L1
Table 4 Comparison of runtime between Modelica and EMTP
Simulator Model type Solver t CPU time (s)
Modelica NI Ideal 31.43 A 32.72 A Modelica NI Ideal DASSL – 6.8 3.9
EMTP NI 31.56 A
Ideal 32.8A
EMTP NI Ideal Trap/BE 2 μs 7.05 4.59
are respectively 1:1.03 and 1:1.17. It is noted that the CPU time does account for the compilation time in Modelica.
4 Conclusions This paper presents the EMT modeling of power electronic components in Modelica and compares the accuracy of models with EMTP. The results show that simulation in Modelica is very accurate and associated with higher flexibility of modeling. The proposed modeling approach is very high-level and relies on expressing the equations of the model. The computational performances of simulations based on Modelica remain acceptable. In future work, the scalability of power electronic simulations in Modelica will be investigated. Also, the library will be extended to cover renewable energy sources.
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References 1. J Mahseredjian, S Dennetière, L Dubé, B. Khodabakhchian & L. Gérin-Lajoie, “On a new approach for the simulation of transients in power systems.” Electric power systems research, vol. 77(11), pp.1514–1520, Sep 2007. 2. Modelica – A Unified Object-Oriented Language for Systems Modeling Language Specification version 3.5, Feb 2021. 3. Functional Mock-up Interface. [Online] Available: https://fmistandard.org/ 4. A Masoom, T Ould-Bachir, J Mahseredjian, A Guironnet, “Simulation of electromagnetic transients with Modelica, accuracy and performance assessment for transmission line models.” Electric Power Systems Research, vol. 189, p. 106799, 2020. 5. A Masoom, J Mahseredjian, T Ould-Bachir, A Guironnet, “MSEMT: An Advanced Modelica Library for Power System Electromagnetic Transient Studies,“ IEEE Transactions on Power Delivery, DOI: https://doi.org/10.1109/TPWRD.2021.3111127. 6. A Masoom, J Mahseredjian, T Ould-Bachir, A Guironnet, “Electromagnetic Transient Simulation of Large Power Networks with Modelica” in Proc. 2021 14th International Modelica Conf. pp. 277–285. 7. Dynaωo, open-source simulator for power systems, [Online]. Available: https:// dynawo.github.io/. 8. A. Masoom, A. Guironnet, A. A. Zeghaida, T. Ould-Bachir, J. Mahseredjian “Modelica-based Simulation of Electromagnetic Transients Using Dynaωo: Current Status and Perspectives,” in Electric Power Systems Research, vol. 197, p. 107340, 2021. 9. LF Llerins, VA Lacerda, A Guironnet, Q Cossart Cossart, E. Prieto-Araujo, & O. GomisBellmunt, “ing and Simulation of Power Systems with Grid-Connected Converters in OpenModelica.” arXiv preprint arXiv:2112.00862. 10. P. Fritzson, A. Pop, K. Abdelhak, A. Asghar, “The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development,” in Modeling, Identification and Control, 41(4), 241–295, 2020. 11. H. Lundvall, P. Fritzson, and B. Bachmann. “Event handling in the OpenModelica compiler and runtime system,” Link¨oping University Electronic Press, 2008. 12. J. Peralta, H. Saad, S. Dennetiere, J. Mahseredjian and S. Nguefeu, ”Detailed and Averaged Models for a 401-Level MMC–HVDC System,“ in IEEE Transactions on Power Delivery, vol. 27, no. 3, pp. 1501–1508, July 2012 13. Ned Mohan, “Power Electronics: Converters, Applications, and Design”, Wiley; 3rd edition (Oct. 10, 2002) 14. W. Nzale, J. Mahseredjian, X. Fu, I. Kocar and C. Dufour, ”Improving Numerical Accuracy in Time-Domain Simulation for Power Electronics Circuits,“ in IEEE Open Access Journal of Power and Energy, vol. 8, pp. 157–165, 2021. 15. A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker & C. S. Woodward,” SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers.” in ACM Transactions on Mathematical Software (TOMS), 31(3), 363–396, 2.
Fuse on PiN Silicon Diode Monolithic Integration for New Fail-Safe Power Converters Topologies Amirouche Oumaziz, Frédéric Richardeau, Abdelhakim Bourennane, Emmanuel Sarraute, Eric Imbernon, and Ayad Ghannam
Abstract In this paper, a first concept of monolithic integration of a fuse on a silicon PiN diode is realized and experimentally characterized. An integrated fuse on PiN diode allows fast cut-off, with low I2 T (less than 2 A2 .s) and short prearcing times (4–6 µs). These fuse-on-diode components are intended for fail-safe topologies power converter, aiming for more compact and reliable applications. The fuses were electrothermally designed using Comsol Multiphysics™ and TCAD Sentaurus™ simulations were carried out to study their integration on PiN diodes. Characterization and experimental tests were carried out after components realization.
1 Introduction Fuses are simple, passive and inexpensive components, able to isolate faulty circuits paths in case of excessive current flow due to a failure. They allow in some faulttolerant power converters topologies [1–3] to avoid spreading failureby separating
A. Oumaziz University of Toulouse, INP, UPS, LAPLACE ENSEEIHT, Toulouse, France LAAS-CNRS, University of Toulouse, CNRS, UPS, Toulouse, France CNRS, LAPLACE, Toulouse, France F. Richardeau () · E. Sarraute University of Toulouse, INP, UPS, LAPLACE ENSEEIHT, Toulouse, France CNRS, LAPLACE, Toulouse, France e-mail: [email protected] A. Bourennane · E. Imbernon LAAS-CNRS, University of Toulouse, CNRS, UPS, Toulouse, France A. Ghannam 3DiS Technologies, Miniparc, Labège, France © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_22
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Fig. 1 Fail-safe topology based on dual-fuse (high-side and low-side fuse) and a crowbar switch (thyristor), with a back-up leg [4]
failed circuit parts, thus enabling the continuous operation of the system. In Fig. 1 [4] a representation of a fault-tolerant topology is presented. In case of internal short-circuit occurrence, the faulty leg is disconnected using the dual-fuse and the auxiliary crowbar switch, then a back-up leg (Fig. 1, red dashed box) is spontaneously connected, allowing continuity of operation. In order to improve the systems reliability and compactness, the used fuses could be integrated monolithically on power semiconductor [5, 6] components (IGBTs, MOSFETs, etc), as presented in Fig. 1 (Fuse-on-transistor, blue dashed box). The integration of the fuses on power the semiconductor component is carried out in two steps. First, fuses, called “Stand-alone fuses” (Fig. 1, green dashed box), made of thin copper layer (18 µm) electrodeposited on a silicon substrate have been realized in order to study the thermal and electrical behaviour of the components. Finite elements simulations using Comsol™ were carried out and experimental results allowed to validate the on-state operation of the components. Fast cut-off fuses with very low pre-arcing times (4–6 µs) under 200 VDC bus voltage have been reported, with low leakage currents ensuring high post-arc isolating resistance (up to 8 M) [7, 8]. Then, the fuses were integrated on silicon PiN diodes (Fig. 1, Fuse-on-diode, purple dashed box), which is the work presented in this paper. Table 1 gives a comparative overview between the monolithic fuse integration solutions, where several parameters are reported and compared. The clean room process based on electrolytic growth of copper, provides micrometer resolution, which is better than classical fuses, resulting in less dispersive I2 T values. In a previous work [8], the phase-leg dual-fuse function has been investigated in order to study the “Stand-alone” fuses symmetrical operation during a short-circuit. The characterization results showed well balanced post-arc voltages distribution between low-side and high-side fuses. The paper is organized as follows: first, the 3D structure of the “Fuse-on-diode” components, thermal and electrical requirements used to design the components are
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Table 1 Summary of the fuse designs integration characteristics, advantages and drawbacks Comparatives Design Purpose of use and flexibility
Stand-alone fuse
Fuse-on-diode
Fuse-on-transistor
Modular, could be placed in any part of the circuit Maximum protection Non-intrusive regarding the components
Fuse could be integrated either on anode or cathode side Fuse/component thermomechanical interaction during the arcing process
Integration issues Lifetime
Easy Expanded lifetime, thanks to the fuse integration +++ (more parasitic inductance) +++
Medium Diodes dissipate less power, so the lifetime could be expanded +
Fuse could be integrated only on the source side. The drain side will require a stand-alone fuse Fuse/component thermomechanical interaction during the arcing process Complex More constraints, because transistors dissipate more power +
++
+ (most compact)
Parasitic Occupied area in the circuit
discussed in Sect. 2. Section 3 is dedicated to the monolithic integration of the fuses on silicon PiN diodes. To that end, TCAD Sentaurus™ simulations were carried out to study this integration in different cases. In Sect. 4, the components realization detailing the main technological process steps is presented. Section 5 is devoted to experimental and characterization results.
2 Components Design Procedure 2.1 Fuse Characteristics and Design The “Stand-alone” fuses [7] (Fig. 2) are made of a thin layer of copper (18 µm) to form the fuses constrictions and pads, electrodeposited on an insulated silicon wafer (500 µm), using a thin nitride (200 nm) layer to prevent leakage currents once the constrictions are evaporated. The fuses constrictions are deposited on an insulating epoxy layer (25 µm). The purpose of this epoxy, with its low thermal conductivity (1.16 W.m−1 .K−1 ), is to provide a thermal insulation to the constrictions from the substrate (high thermal conductivity: ~130 W.m−1 .K−1 ) and concentrate the thermal energy during a short-circuit occurrence on this constrained area, thus improving the cut-off process. The epoxy layer also provides a mechanical protection to the substrate or the active area below during the cut-off process. Its thickness has been improved through simulations using Comsol Multiphysics™,
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Fig. 2 Stand-alone fuse designed by the authors and presented in [7] with a cutline along the constriction Table 2 Comparison between designed stand-alone fuses prototypes
Design Ns = Np = 1 Ns = 1 Np = 2 Ns = 2 Np = 1 Ns = Np = 2
I2 Tp (A2 .s) Theo. Exp. 1.53 1.93 1.45 1.71 1.01 0.7 0.47 0.55
Tp (µs)
Area (mm2 )
4.9 2.8 3.1 1.9
2.52 1.84 2.95 1.46
Ns number of constrictions in series, Np number of constrictions in parallel, [I2 Tp] normalized energy to evaporate fuse, Tp pre-arcing time
where 25 µm thickness is enough to induce a thermal decoupling between the constrictions and the silicon substrate. The fuses have been designed for 10 A nominal current, allowing a maximum temperature of 115 ◦ C at the constrictions center, while operating at an ambient temperature of 85 ◦ C. In the previous work [7], four prototypes of the “Stand-alone” fuses were designed, according to the number of the constrictions number and configurations (series/parallel). Table 1 summarizes the main electrical and geometrical parameters obtained from the electrothermal simulations based on Comsol™. When a shortcircuit occurs, the fuse’s current increases through the circuit’s stray inductance to reach a maximum value, in a time duration called Tp (pre-arcing time), that results in fuse melting. The required normalized energy to evaporate the fuse constrictions is defined by the I2 T ([A2 .s)]) parameter (Table 2).
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Fig. 3 First fuse-on-diode design approach
From Table 1, we can notice that the fuses I2 Tp parameter are very low and the difference between the theoretical and experimental values is very acceptable and some assumptions explaining the origin of this difference are explained in a previous work [7]. The pre-arcing times (Tp) are very short, making the fuses very fast in case of a short circuit occurrence. It has also been shown in [8] a reduction in the area of the fuse by a ration ratio of about five, and therefore in its compactness, as compared to the best commercially available SMD fuses.
2.2 Fuse-on-Diode Design Approach Once the “Stand-alone fuses” operation is validated, the technological process has been integrated within a vertical PiN silicon diode. Figure 3 shows a 2D representation of the “Fuse-on-diode” integration. Thanks to this PiN diode vertical architecture and its top-side aluminum electrode (anode here), the lateral fuse is realized through several materials depositions. One of the fuse’s pads is the diode’s electrode (anode), the second one must be fully isolated from the P+ region to withstand the full voltage after constrictions evaporation, therefore, avoiding leakage current flow between the pads. The electrical insulation is achieved using a thin nitride layer with optimized thickness. The pads thickness is about 43 µm. After depositing a first layer of copper (18 µm) to form the pads and the constrictions, the pads are thickened by compensating the epoxy thickness (25 µm) to obtain planar layers which is easier to make technologically.
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3 Simulations Results according to the circuit’s operating modes presented in Fig. 1, the “Fuse-ondiode” could be in three different states, either the fuse is conducting or not, the diode could be in off or on-state. Using 2D TCAD Sentaurus™ simulations, the different operating states have been studied in order to validate the feasibility of this integration. The PiN diode physical and geometrical parameters were those imposed by the IGBT process of the LAAS-CNRS micro and nanotechnology platform [9]. In these simulations, the Junction Termination Extension (JTE) has not been included since the process has already been validated during a previous work through several simulations and experiments [9].
3.1 Case 1- Fuse Conductive and Diode Off-State The most common case deals with the fuse conducting the nominal current though the active leg (Fig. 1), while the back-up leg is in off-state. The auxiliary diodes leg used during the back-up operation is as well in off-state, since no fault has occurred. Figure 4 shows the simulated circuit to validate this case. Figure 5 presents the electrostatic potential and the electric field distributions when 300 VDC were applied at the DC+ bus. In this case, the simulations allowed to validate that reverse biased diode sustains the rated DC voltage (300 V, Fig. 5a) with low leakage currents (8.5 µA). The simulated structure shows an electric field distribution around 8.9.10+4 V/cm (Fig. 5b), for the rated voltage (300 VDC ), which is under the silicon critical electric field (~2.10+5 V/cm).
DC+
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K (Cathode) +
A (Anode)
DC- (0V)
(a)
(b)
Fig. 4 Simulated circuit for case 1: Fuse is in on-state and diode in off-state
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Fig. 5 Electrostatic potential (a) and electric field distribution (b) for case 1 (fuse normally onstate and diode off-state) where a DC bus voltage of 300 V is applied on the diode’s cathode
Fig. 6 Simulated circuit for case 2: Fuse open and diode in on-state
3.2 Case 2- Fuse Open and Diode On-State In case of a short-circuit occurrence, the fuse’s current increases, therefore, the constrictions evaporated when the required melting energy is reached (I2 Tp). In this case, the diode could be in on-state with the back-up leg. Figure 6 shows the simulated circuit used to validate the components operation in this case.
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Fig. 7 Current density distribution (a) and diode’s on-state voltage drop while conducting 100 A/cm2 (b) for case 2 (fuse open and diode on-state)
The current density lines distribution when the diode is in on-state conducting 100 A/cm2 current density is presented in Fig. 7. Figure 7a shows a current density mostly focused on the diode section (right side), with a voltage drop of 0.78 V (Fig. 7b). Once the constrictions are evaporated and the diode is in on-state, the fuse pads sustain the rated voltage (300 VDC ) thanks to the insulating nitride layer, ensuring negligible leakage current (~9 nA). Given the nitride breakdown voltage (~10 MV/cm) and the components rated voltage (300 V), 350 nm nitride thickness has been designed using TCAD Sentaurus™ simulations.
3.3 Case 3- Fuse Open and Diode Off-State The last studied case takes into account a blown-up fuse and the diode in off-state, because the back-up leg’s high-side RC-IGBT is in on-state. In this case, the diode is reverse biased and supports few volts (simulated with 5 VDC ) due to the thyristor and IGBT on-state voltage drops, while the fuse supports almost the DC bus voltage (295 VDC ).
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Fig. 8 Simulated circuit for case 3: Fuse open and diode in off-state
Figure 8 shows the simulated electrical circuit for this case, where the fuse is open and the diode is in off-state. The simulations results presenting the simulated structure current density and electric field distribution are shown in Fig. 9. The leakage currents (Fig. 9) are mostly concentrated around the pads, but in steady state, very small values have been reported (~1 µA) between the pads. The electric field is higher around the nitride (Fig. 9b, c) sustaining the rated voltage between the pads, but still lower (8.55.10+6 V/cm) than the breakdown value (~10 MV/cm). Figure 10a, b show respectively the current density and lattice temperature distributions when the constrictions are evaporated. The boundary conditions consider a back-side temperature applied to the diode’s cathode of 85 ◦ C. Thus, simulated component’s temperature evolves following the physical models, which are temperature dependent. As presented in Fig. 3, the designed component comprises an anode contact covering partially the front side P+ region. This geometrical disposition causes a non-uniform current density distribution (Fig. 10a), concentrated at the diode side (right side). As a consequence, the component shows a slightly higher temperature (Fig. 10b) and mostly focused in the components front-side, where the current density is higher. On-going study focuses the work on an improved design where the front side P+ region could be fully exploited in order to obtain a homogenous current density distribution and thus improve components cooling. The component realization comprises two technological processes. First, the diode is realized using the LAAS-CNRS micro and nanotechnology platform. Then the fuse is realized by the company 3DiS technologies™ [10].
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Fig. 9 Current density (a) and electric field distribution (b, c) for case 3 (fuse open and diode off-state) where a DC bus voltage of 300 V is applied
4 Experiments and Results In order to validate the components operation under a short circuit occurrence, the electrical test circuit presented in Fig. 11 has been used. It is composed of a currentlimited voltage source, four parallel capacitors of 470 µF each and crowbar thyristor, used to induce a short-circuit. A 700 nH snubber inductance is added in order to limit the energy and the current variation (di/dt), avoiding the damaging of the thyristor. A freewheeling diode is added in parallel with the inductance. The diode prevents the fuse from having to dissipate all the energy stored in the snubber inductance. Only the energy stored in the stray inductance (~50 nH) will be dissipated in the fuse as in a real switching cell.
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Fig. 10 Current density distribution (a) and lattice temperature distribution (b) when the constrictions are evaporated and the diode is conducting 100 A
Fig. 11 Electrical test circuit used to validate the operation of the components
Once the thyristor is triggered, the stored energy in the capacitors is partially discharged through the fuse, causing the fuse voltage and current to increase until the required constrictions melting point energy is reached. The initiated electrical arc persists until the current reaches zero. No current restrike should be observed.
4.1 Cut-off Tests Several cut-off tests have been conducted on the realized components during a shortcircuit occurrence using the presented electrical test circuit (Fig. 11). Figure 12 shows some test results on a “Fuse-on-diode” component under a DC bus voltage of 100 VDC .
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Fig. 12 Electrical cut-off test results (a) with the associated leakage current (b)
When the short-circuit is initiated, the fuse current and voltage increase (Fig. 12a) to reach a maximum value, corresponding to the moment when the constrictions melting energy is reached, this after a pre-arcing time of ~7 µs. Once the current is cancelled, no current restrike was observed. The associated leakage current is very low (Fig. 12b), about 35 µA, leaving a very high post-arc isolation resistance (~3 M). Figure 13 shows a three parallel constriction “Fuse-on-diode” component before cut-off test (Fig. 13a) and the distribution of the constraints around the constrictions right after the cut-off test (Fig. 13b), where the released particles are trapped in
Fuse on PiN Silicon Diode Monolithic Integration for New Fail-Safe Power. . . Fig. 13 Pictures of the component before (a) and after (b) the cut-off test encapsulated in a silicone gel
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(b) the passivating silicone gel. The results (Fig. 13b) may suggest a good current distribution over the three constrictions, thanks to a well-managed technological process. Using an impedance analyzer (HP4294A), the parasitic inductance (ESL) brought by the integration of the fuse on this silicon PiN diode has been estimated. A measured value of 2.23 nH has been reported, which is very acceptable. Unfortunately, this 100 VDC was the maximum cut-off voltage obtained with these components. On-going components analysis suggest that the insulating nitride layer has to be optimized to sustain higher breakdown voltages. Rugosity of the deposited aluminum to form the diodes electrodes impacts the nitride layer thickness and causes non-uniform deposition, which weakens the nitride at some points.
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5 Conclusion In this paper, a new concept of vertical PiN diodes integrating monolithically lateral fuses are realized and experimentally tested. The devices are able to perform very fast cut-off (~7 µs) under a DC bus voltage of 100 VDC , with very low I2 T energies (1.35–1.55 A2 .s). The insulating post-arc resistances are very high (~3 M) ensuring very low leakage currents. The passivating silicone gel improved the cutoff by absorbing the excess of energy and avoiding its spreading towards the pads, thus avoiding any damage. Although, the cut-off voltage needs to be improved in order to cut-off higher voltages (around 200 VDC ) and fit commercial required applications. These good results suggest that design of more compact and reliable power converters combining these integrated fuses is possible. Future work will focus on the improvement of the components to support higher voltages and study their monolithic integration on power semiconductor transistors (IGBT, MOSFETs, etc). Acknowledgements Thanks to Céline Combettes and Vincent Bley for their participation in the fuses passivation process using the 3DPhi platform.
References 1. W. Zhang, D. Xu, P. N. Enjeti, H. Li, J. T. Hawke, and H. S. Krishnamoorthy, “Survey on faulttolerant techniques for power electronic converters,” IEEE Transactions on Power Electronics, vol. 29, no. 12, pp. 6319–6331, 2014, doi: https://doi.org/10.1109/TPEL.2014.2304561. 2. M. Gleissner and M. M. Bakran, “Fault-tolerant B6-B4 inverter reconfiguration with fuses and ideal short-on failure IGBT modules,” PCIM Europe 2016; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, no. May, pp. 683–690, 2016. 3. F. Richardeau, Z. Dou, J. M. Blaquiere, E. Sarraute, D. Flumian, and F. Mosser, “Complete short-circuit failure mode properties and comparison based on IGBT standard packaging. Application to new fault-tolerant inverter and interleaved chopper with reduced parts count,” Proceedings of the 2011 14th European Conference on Power Electronics and Applications, EPE 2011, pp. 1–9, 2011. 4. Z. Dou, “Sˆureté de fonctionnement des convertisseurs. Nouvelles structures de redoncdances pour onduleurs sécurisés à tolérance de pannes,”, Ph.D Dissertation, Toulouse INP, University of Toulouse, 2011. 5. S. E. Berberich, M. M¨arz, A. J. Bauer, S. K. Beuer, and H. Ryssel, “Active fuse,” Proceedings of the International Symposium on Power Semiconductor Devices and ICs, vol. 2006, pp. 0–3, 2006, doi: https://doi.org/10.1109/ispsd.2006.1666088. 6. J. vom Dorp, S. E. Berberich, A. J. Bauer, and H. Ryssel, “DC-arc behavior of a novel active fuse,” ESSDERC 2008 - Proceedings of the 38th European Solid-State Device Research Conference, pp. 67–70, 2008, doi: https://doi.org/10.1109/ESSDERC.2008.4681700. 7. A. Oumaziz et al., “Fast cut-off, low I2T and high temperature monolithic on-chip fuse on silicon substrate for new fail-safe embedded power switch,” Microelectronics Reliability, p. 114240, Oct. 2021, doi: https://doi.org/10.1016/j.microrel.2021.114240. 8. A. Oumaziz, Amirouche, Sarraute, Emmanuel, Richardeau, Frédéric, Bourennane, “Fail-safe switching-cells architectures based on monolithic on-chip fuse Keywords Fail-safe topologies
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using single-fuse or dual-fuse function,” in European Conference on Power Electronics and Applications (EPE 2020 ECCE Europe), 2020, p. 10. 9. É. Imbernon et al., “International Semiconductor Con-ference (CAS’2001),” 2001. [Online]. Available: https://hal.laas.fr/hal-01867591 10. A. Ghannam, “3Dis technologies.” https://www.3dis-tech.com/
Part III
Microgrids and Smart Grids
A Distributed Secondary Control for Autonomous AC Microgrid Based on Photovoltaic and Energy Storage Systems Sidlawendé V. M. Ouoba, Azeddine Houari, and Mohamed Machmoum
Abstract In this paper, a distributed control is proposed for Distributed Energy Storage Systems (DESSs) and Renewable Energy Sources (RESs) power management in islanded Microgrid (MG). The power management strategy is designed to maintain generation/consumption balance, to ensure State of Charge (SoC) balancing of the DESSs and MG frequency/voltage (f & V) regulation. A fully distributed control without leader-follower strategy is used to manage the power flow between renewable generators, energy storage and consumption (critical and non-critical loads), to balance the SoC of the DESSs and to restore the frequency and voltage to their nominal value only thanks to low bandwidth communication. The strategy framework of the power management set the islanded MG in 04 operations modes (normal mode, PV active power curtailment mode and load shedding and reconnection mode) in order to provide a high quality and reliable power source in the islanded MG. A MATLAB/Simulink simulation is performed with a system of two Batteries Energy Storage Systems (BESSs), three loads (a critical/variable load and two non-critical/constant loads) and photovoltaic (PV) generator, in order to verify the effectiveness and the resilience of the proposed power management method in several operation modes.
1 Introduction Distributed Energy Storage Systems (DESSs) are widely used in MG operation in order to assist RESs which have intermittent nature [1]. The mix of DESSs with RESs improves significantly the MG reliability, flexibility and power quality [2]. ESSs are vital in islanded MG in order to compensate the short-term mismatch power between RESs and loads [3].
S. V. M. Ouoba () · A. Houari · M. Machmoum IREENA – Nantes Université, Saint Nazaire, France e-mail: [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_23
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Fig. 1 Typical configuration for an AC microgrid system with distributed storage systems
Coordinated control is indispensable in this case to achieve power management between RESs, energy storage and loads in order to enhance the MG reliability, flexibility and power quality. This coordinated control is used to balance and maintain the SoC of DESSs in a certain range (20–90%), to maintain generation/consumption balance and to regulate frequency/voltage. DESSs and RESs power management strategy has many benefits. First, DESSs SoC balancing extends their lifetime by avoiding deep discharge and surcharge and reducing the BESSs charge/discharge cycles that caused premature ageing. Second generation/consumption balance allows to supply power to critical loads longer especially when a power mismatch between distributed generators (RESs and DESSs) and loads is observed. Coordinated control can be achieved by using a centralized (Fig. 1) or a distributed architecture controller. A centralized architecture uses a MGCC (Microgrid Central Controller) to achieve the power management between DESSs and RESs by exchanging data with all DGs while a distributed architecture controller only exchanges information between DGs through a sparse communication network. In a distributed architecture, each agent receives information from its neighbors. Unlike centralized control architecture which has a unique point of failure (MGCC default), the distributed architecture allows the continuity of system control when a communication failure happens and improves the system reliability and expandability. Many methods have been proposed to ensure coordinated control between RESs and DESSs. Conventionally, centralized control is used for the coordinated operation of DESSs, RESs units and loads. Reference [4] used a centralized control architecture for the coordinated operation, where SoC equalization is achieved
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between DESSs with different capacities by adjusting the frequency droop gain value. Nevertheless, centralized architecture control possesses the single point of failure that may cause loss of the coordination of the Microgrid and modifying the droop gain may bring stability issues. In [5], a distributed control based on leader-follower is implemented to ensure power management and DESSs SoC balancing. In order to maintain generation/consumption balance, load shedding and PV curtailment are introduced. However, since this strategy was used in DC MG, frequency regulation is not implemented. In this paper, a fully distributed control is used for coordinated operation of DESSs, RESs units and loads to ensure a reliable and stable operation of an AC islanded MG based PV-DESSs. The power management strategy achieves PV active power curtailment to prevent DESSs surcharge; loads shedding to avoid the storage systems from deep discharge and DESSs SoC balancing in order to reduce the storage systems charge/discharge cycles that caused premature ageing and to avoid uneven degradation. The Adaptive Frequency Droop based on Virtual Power (AFDVP) method is used for SoC synchronization. This method introduces a virtual power in the P- ω equation of the droop that is determined with a simple PI controller. In addition, frequency and voltage regulation is implemented in a distributed control architecture. In this proposal, active power curtailment, loads shedding, SoC balancing as well as frequency and voltage restoration are achieved in a fully distributed architecture controller therefore the proposed method is robust against communication failure. Information in this architecture is exchanged through a sparse communication network. The main contributions of this proposal are as follows: 1. The proposed coordinated control is fully distributed without a leader-follower strategy and is resilient to communication failure. 2. Frequency regulation is implemented in coordinated control with SoC balancing to maintain the frequency of the DGs at the nominal frequency of the MG. 3. Proposed algorithms for load shedding and PV curtailment are simple to implement. The rest of the paper is organized as follows: In Sect. 2, the studied system is presented. AFDVP and voltage/frequency regulation method implementation in a distributed control architecture are investigated in Sect. 3. In Sect. 4, coordinated control algorithm for PV-DESSs based islanded MG is explained. Simulation results are presented in Sects. 5 and 6 concludes this paper.
2 Studied System The general synoptic scheme of the studied system is presented in Fig. 2. This System represents an islanded AC Microgrid with two batteries and photovoltaic source supplying three loads (two non-critical and constant loads and one critical and variable load) connected the AC bus. All Distributed Generators (DESSs and
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PV) are relied to the AC bus through inverters. In the next section, the AFDVP strategy is presented, to ensure DESSs SoC synchronization.
3 SoC Balancing and Voltage/Frequency Regulation in a Fully Distributed Architecture Controller Distributed control is recently widely used in MG especially for secondary control. It is a promising approach to enhance islanded MG reliability, stability and performance [6]. Many works have been already proposed to ensure distributed secondary control [7–9]. Distributed control has many advantages such as reduction of the communication infrastructure cost, reduction of computational burden, is more reliable and adapted for large and complex MG compare to the centralized control. In this section, a fully distributed control architecture is used for DESSs SoC synchronization and voltage/frequency restoration.
3.1 Graph Theory and Distributed Control Based on Consensus The communication network can be expressed by a graph G = (V, E), with V = {v1 , v2 , . . . , vN }, the set of N nodes or N agents and E ⊆ V × V, the set of
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Agent 1
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Ar c( v2 ) v1 ,
D
ata
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Agent 3 Fig. 3 Graph with four agents
edges or arcs. Elements of E are denoted as (vi , vj ) and represent the arcs from node vi to node vj and are represented with arrows at unique or double direction depending on the information flow between the two agents (unidirectional or bidirectional) as represented in Fig. 3. Each edge (vi , vj ) is associated with a weight aij > 0 if vi receives information from vj else aij = 0. The adjacency matrix is defined as: A = [aij ] and the graph Laplacian matrix as L = D–A. D the diagonal matrix is defined as: D = diag {di } and .di = N j =1 aij . In order to bring all the agents (xj ) to converge to the same value (x0 ), the distributed control-based consensus protocol is defined as: μi =
N j =1
aij xj − xi + bi (xi − x0 )
(1)
where bi >0 if the agent vi has the information about the consensus value, otherwise bi = 0. With this protocol, the global dynamics of the consensus control protocol can be defined as: X˙ = K (−LX + B (X0 − X))
(2)
where X = [x1 , . . . , xN ] ; X0 = [x01 , . . . , x0N ] ; B = diag {bi }, the diagonal pinning matrix; L = D − A, the Laplacian matrix and K, the consensus gain. For the studied system defined in Fig. 2, the adjacency matrix A and Laplacian Matrix L can be defined respectively as: ⎛
⎞ ⎛ ⎞ ⎛ ⎞ 011 2 −1 −1 100 A = ⎝ 1 0 1 ⎠ , L = ⎝ − 1 2 −1 ⎠ ; B = ⎝ 0 1 0 ⎠ 110 − 1 −1 2 001
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3.2 DESSs SoC Balancing and Voltage/Frequency Regulation In this section, a distributed control-based consensus control is used for frequency/voltage regulation and the AFDVP method in [10] is used for DESSs SoCs synchronization. Equations for the distributed control-based consensus to calculate f & V compensators are designed as follows: X˙v = Kv −LV + B Vn − V
(3)
X˙ω = Kω (−LW + B (Wn − W ))
(4)
with .Xv = [x1v , x2v , x3v ] ; V = [V1 , V2 , V3 ] ; .Vn = [Vn , Vn , Vn ] ; Xω = [x1ω , x2ω , x3ω ] W = [ω1 , ω2 , ω3 ] ; Wn = [ωn , ωn , ωn ] ; where Kv , Kω : voltage and frequency consensus control gain respectively; L: Laplacian matrix; B: diagonal pinning Matrix and xiv , xiω : voltage and frequency compensator of the DESSi respectively. The global dynamic equations for voltage/frequency restoration and SoC equalization are as follows: Vi = Vn − ni (Qi − Qin ) + x iv
(5)
ωi = ωn − mi (Pi − Pin + P iSoC ) + x iω
(6)
PiSoC = KpSoC SoC i + KiSoC
SoC i dt
(7)
with PiSoC : the virtual power for SoC balancing; KpSoC : the PI proportional coefficient; KiSoC : the PI integrator coefficient. In the next section, proposed algorithms for PV active power reduction and load shedding are presented.
4 Proposed Fully Distributed Control for RESs and DESSs Coordinated Operation This section introduces a fully distributed control for coordinated operation of DESSs, RESs units and loads to ensure a reliable and stable operation of an AC Microgrid. The optimized power management strategy should ensure PV active power curtailment (during daytime when PV generation is maximum and DESSs are almost fully charged) to prevent DESSs surcharge and loads shedding in order to avoid deep surcharge during night (no PV generation). This proposal also includes a
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Non-Criticalloads Criticalloads Fig. 4 Algorithm for load shedding (mode 2) and reconnection (mode 3)
management for critical loads (CL) and non-critical loads (NL). Non-critical loads should be disconnected first when DESSs state of charge is below the minimum state of charge (SoCmin ). Then, critical load should be disconnected to the MG only when DESSs SoCs reach a critical value (SoCminc ). Loads are reconnected only when DESSs SoCs reach a value of safe reconnection (SoCr for non-critical loads and SoCrc for critical loads). The proposed method to ensure load shedding, uses signals based on DESSs SoCs (si and sci ) which are exchanged between the DESSs. Each DESS sends a signal to the loads according to its local information, information received from its neighbors and the loads (critical and non-critical). Loads are disconnected if one of the DESSs SoCs reach a minimum value (SoCmin _ NL , SoCmin _ CL ) and reconnected if all DESSs SoCs reach a safe range for reconnection (SoCr _ NL or SoCr _ CL ). The proposed strategy algorithm for load shedding is reported in Fig. 4. PV curtailment is ensured thanks to signals (ki ) that are exchanged between DESSs and PV. When DESSs states of charge reach the maximum value (SoCmax ), PV active power (Ppv ) is reduced according to the curtailment coefficient (kpv ) calculated using the loads total active power (PLoads ) sends by the loads to the PV unit local controller. kpv is determined in order to maintain the SoC of DESSs at SoCmax (SoCi = SoCmax , Ppv = PLoads , PDESSs = 0). Proposed algorithm for PV curtailment is represented in Fig. 5. All operational mode of the MG is reported in Fig. 6. The global communication network of the whole MG is represented in Fig. 7.
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if SoCi>SoCmax ki=0 else ki=1 end ki=ki*aij*kj
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Fig. 6 System stability margin depending on the capacitors (CPCC1 = 0.5 mF; CPCC2 = 0.4 mF; CPCC3 = 0.3 mF; CPCC4 = 0.2 mF; CPCC5 = 0.1 mF) for (RL = 0.8 et LL = 1 mH)
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Fig. 7 System stability margin depending on the line resistance (RL1 = 0.8 ; RL2 = 0.6 ; RL3 = 0.4 ; RL4 = 0.2 ; RL5 = 0.1 ) pour (LL = 1 mH et CPCC = 0.5mF)
Small Signal Stability Study for Island Distributed Generation System. . .
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LL1 0: the system needs more energy. Hence, the RZ must provide it by increasing its generation or by lowering its consumption. Thus, RZ provides ‘upward service’. – if .ACE < 0: the system presents surplus energy, so the RZ must provide it by stopping its generation or increasing its consumption. Thus, RZ provides ‘downward service’. An example of the Spanish AGC system operation with 4 RZ is presented in [9].
2.2 Market The Spanish electricity market has operated with no changes since 1998. The Iberian electricity market operator (known as OMIE for its Spanish acronym) manages the energy markets while REE leads the operation and settlement of ancillary services. Within them, aFRR service is provided by two market-based mechanisms: power band assignation and energy utilization. On the one hand, the power band assignment defines resources committed for the AGC. Every day, REE publishes the upward and downward reserve requirements (R) that depend on the expected demand (Lmax) as derived from: R=
.
10 · Lmax + 1502 − 150
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REE also publishes the hourly maximum and minimum values of aFRR band requirements per offer. Subsequently, a marginal auction starts at 14:45 h, after the publication of the day-ahead market resolution. This auction is launched to define the aFRR band for each hour of the following day. At it, the RZ submit their offers for each period and for each direction, indicating the bid price (e/MW) and the volume (MW). At 16:00, the auction closes and the power band allocation among zones is defined by another marginal process. Hence, the RZ with power assigned in a band period must provide AGC service in that period. As a result, their assigned power will be paid at the marginal price. On the other hand, the energy utilization depends on the real time needs derived from the ACE signal evolution. REE delivers every 4 s the CRR signals to those RZ
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that were matched in the running period. Therefore, they must build its own ACE and try to bring it to zero by modifying their generation or consumption program. Furthermore, in the event that the required aFRR power exceeds that matched in the market, those RZ whose initial bid was higher than their match will provide the extra aFRR power needs. The net energy supplied, calculated as the energy difference between the upward and the downward services, will be remunerated at the price of the tertiary regulation service that would had been required to call. If a RZ does not comply with the agreements in a power band assignation period, it will be penalized. The penalty factor is calculated as 50% of the band price for each hourly period. Consequently, the total cost of the non-compliance is: P enalty = 1.5 · P riceband · P owerassigned
.
(5)
Finally, note that REE can disqualify any RZ as an aFRR service provider if infractions become usual [17].
3 Strategy Within this framework and by means of the previous equations, the global aFRR response signal for the Spanish electricity system is reproduced in the following. Then, this will be used to simulate a potential operation of a BESS in this aFRR market and to analyze its economic viability.
3.1 Spanish aFRR Service Simulator As previously mentioned, each RZ receives every 4 s a CRR signal from REE. Then, the zones generate their internal ACE signal to provide the aFRR control. Note that given the confidentiality of these CRR signals, this work uses the global aFRR response signal generated by REE (PRR) and the frequency deviation signal (both signals shared by this TSO to allow this study). To validate the generated response signal for the whole system, this is compared with the total hourly aFRR response registered in the Iberian market and published by REE at [18]. Then, the simulation model of the aFRR service has been developed with ® ® .Matlab and .Simulink . Due to the aforementioned simplification of considering the whole Spanish system as a RZ, the PRR signal is used as the aFRR external requirement, as can be appreciated in Fig. 3. This model reproduces the ACE construction diagram indicated by Eq. 3. The frequency deviation signal multiplied by the K-factor is subtracted to PRR signal and the result is added to the NID divided by G. Once the ACE is built, a discretetime integrator with a time constant of 50 s is used to simulated the response of the
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Fig. 4 Response signals comparison
Fig. 5 Strategy diagram
RZ. This is defined according to the response time criteria imposed by REE [17], that fixes the RZ must behave as first order systems with time constants ranging from 4 to 100 s. As the PRR and the frequency deviation signals are updated every 4 s, the model generates a response with the same sampling period. However, in order to compare this signal with the actual global aFRR response, published by REE, the simulated response has to be re-sampled into accumulated hourly data. Once this is done, results can be compared as in Fig. 4. Note the similarity which can be evaluated by the mean absolute error value, which is 61.67 MW for June data and 134.58 MW for February data.
3.2 Battery Operation Once the aFRR service to be provided by a BESS conforming a RZ is generated, it is used as an input to the BESS operation simulator. The strategy assumed in this work is based on operating that BESS in parallel and continuously in both the aFRR market and the continuous intraday energy market. The participation in the latter will be mainly used to try to keep the state of charge (SOC) of the BESS around 50%, as summarized in Fig. 5. Hence, the BESS charges or discharges in accordance with the aFRR signal with an intensity being function of the power matched in the band assignment process,
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Fig. 6 Battery SOC evolution
Fig. 7 Power evolution
i.e. the aFRR response provided by the BESS keeps the proportion matched band vs total band distributed. Subsequently, the BESS operator must check the battery SOC to decide how much energy needs to be exchanged in the coming continuous intraday market sessions in order to track the 50% reference SOC. This decision must be made a few minutes before the closing time of the corresponding session. An example of BESS operation according to this strategy can be observed in Figs. 6 and 7. These show, respectively, the power exchanged by the BESS with the grid (detailing power flows corresponding to different markets) and the evolution of the BESS SOC for 10 consecutive hours. Note in Fig. 7 the ACE signal to provide aFRR power (purple line), the intraday energy signal to adjust SOC (brown line), the sum of these two signals (yellow line) and the actual signal exchanged with the grid (green line), which stays limited by the BESS power converter nominal capacity (.+− 4 MW in our case). If these two figures are analyzed together, it is easy to observe that a positive value of the green line implies BESS charge while a negative
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value means BESS discharge. Moreover, notice that the Iberian continuous intraday energy market has a lead time of 1 h, so the effect of the intraday participation is delayed by 1 h. In the first 2 h, the purple line has a positive value that would mean charging the BEES. However, given that the SOC was above 50% in the previous period, the BESS operator had decided to participate in the intraday market, selling energy, to reduce the SOC an approach it to its reference. Consequently, the total energy exchanged (green) is negative (BESS discharges with no saturation of the converter). The following hour, the ACE signal becomes negative what, coupled with the BESS discharge programmed for those intraday sessions, drives the SOC level down rapidly. Therefore, the operator of the RZ reacts by buying energy in the next intraday session available, starting at 14:00 (positive brown line in hour 14). This allows the BESS to be able to keep the provision of the aFRR service without losing control although this keeps asking for energy from the BESS until the end of hour 14. And so on, the future power exchanges with the intraday market are controlled by the operation system to avoid deviations in the aFRR service. Keeping the SOC level as close as possible to 50%.
4 Results The operation performance of the proposed control strategy defined for a RZ composed of a single BESS has been analyzed for a 4 MW battery with three different capacities: 4 MWh, 8 MWh and 16 MWh (i.e. 1, 2 and 4 h of accumulation). Also, the RZ operation is considered within the Spanish context, participating in the Iberian aFRR regulation market (with its power band assignation process and with its energy utilization process) and in the Iberian continuous intraday market (with 24 sessions per day, lead time of 1 h and hourly settlement periods). In addition, a maximum power of 8 MW (4 MW upward and 4 MW downward) are assumed as the RZ band assignment for each hourly period analyzed. The aFRR simulation model is used to provide and build the ACE signal. In this sense, note that the PRR and frequency deviation data used (with a time step of 4 s) correspond to the months of June 2019 and February 2020. However, the actual annual hourly data of the global aFRR response (available at the Esios website) is used to produce the economic feasibility study. Additionally, the following factors are taken into account: – Battery lifetime: 10 years. – Battery cost: 250 e per kWh. – Other costs (power converter, construction, credit).
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Table 1 BESS economic results for June 2020 and February 2021 BESS size 1h 2h 4h February 2020 1 h 2h 4h
June 2019
Intraday (e) 7495 10,594 12,068 -2874 -3315 -7326
Band (e) 26,802 31,086 33,334 32,752 38,764 42,013
Utilization (e) 47,714 64,126 73,588 32,259 44,411 52,429
Penalty (e) Total (e) 6740 82,011 2457 105,805 209 118,990 9685 62,137 3673 79,860 424 87,116
Table 2 BESS annual economic results for 2019 and 2020 2019
2020
BESS size 1h 2h 4h 1h 2h 4h
Intraday (e) 148,056 180,046 213,160 72,672 90,576 113,474
Band (e) 440,100 537,315 577,639 453,705 554,811 605,053
Utilization (e) 282,919 410,344 470,269 213,003 312,331 370,714
Penalty (e) 149,449 45,234 4911 157,814 56,708 6466
Total (e) 871,076 1,127,705 1,261,068 739,380 957,717 1,089,240
Table 3 Feasibility study results: budget and payback on investment BESS size 1h 2h 4h
Budget (e) 1,676,263 3,032,048 6,095,051
2019 payback time (years) 3.45 5.41 13.74
2020 payback time (years) 4.33 6.99 19.33
4.1 Simulation Results Table 1 presents the economic simulation results using the aFRR simulator response for the indicated months, whilst Table 2 shows the annual economic simulation results using the real data available at Esios for 2019 and 2020. The meaning of each column is: – Intraday: the net profit of the BESS participation in the intraday continuous market as a result of the difference between sales and purchases. – Band: the benefit due to the power assignation band of 8 MW of power in all the periods analyzed minus the penalty due to the non-compliance of the service. – Utilization: the sum of upward and downward aFRR service energy utilization revenues. – Penalty: cost originated as a consequence of the failure in the provision of the aFRR service. – Total: the total net benefit obtained by the BESS. Finally, Table 3 offers the BESS assumed budget and the payback period derived from the economic study.
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4.2 Discussion According to the results shown in Table 1, it can be stated on the one hand that revenues are clearly higher in June than in February mainly due to three factors. First, the negative value in the intraday column in February indicates higher purchases than sales during that month, while June experienced the opposite. Likewise, June revenues from energy utilization service were greater than February revenues as a result of higher utilization prices in 2019 than in 2020. And the third and last factor is that penalties for the non-compliance of the service were also higher during the winter month, as reflected in the Penalty column. On the other hand, Table 2 shows that energy sales are higher than purchases in the continuous intraday market. This is due to the fact that BESS is more likely to charge than to discharge in annual terms by its participation in the aFRR service. In addition, note how the highest revenues in the 2 months analyzed are due to the power band assignment process. This is so because, although the energy utilization is significant, its income is calculated in a period as the net difference between the energy delivered upward and the energy delivered downward, ie. if 3 MWh are injected upward and 8 MWh downward in one period, only 5 MWh are remunerated to the RZ at the downward price. Lastly, Table 3 displays that the lower the BESS capacity, the lower the investment required. Nevertheless, check in Table 2 how increasing BESS capacity, reduces the penalties. These two considerations are used to define the best BESS size to be a aFRR provider. First, the smallest BESS analyzed, although presenting the best payback period, cannot be accepted as a service provider because it commits many service failures and, as mentioned above, this can force REE to deactivate the RZ for repeated non-compliance. Second, a 4-h BESS could be a suitable candidate from a technical point of view because it hardly fails to grant the services throughout the year. However, it involves a very high payback period due to the associated huge initial investment. Consequently, this BESS size would not be an appropriate option to become a aFRR provider. Finally, a 2-h BESS would result in the best option since it commits three times less service faults than the 1-h BESS and obtains a payback period also better than the assumed battery lifetime. Thus, this capacity would be the recommended BESS size to be part of a RZ.
5 Conclusion This paper introduces a model of the Spanish AGC system to be used to provide inputs for the simulation of the operation of a BESS that participates in the aFRR market. In this context, an economic feasibility study is elaborated to determinate the best BESS size. The simulated AGC system model provides an aFRR response that has been compared with the real aFRR data published by the Spanish TSO. Results show
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significant similarities and low error, validating the AGC system model. Moreover, interesting conclusions are derived from the results obtained with the BESS operation simulator. Firstly, the required aFRR response tends to charge rather than discharge the BESS because downward regulation energy is more demanded than the upward regulation energy. Secondly, the highest revenues come from the band assignation process. Finally, the analysis proves that the 2-h capacity batteries would be the best current option to provide aFRR service as a breakeven between the service interruptions committed, its cost, and the economic return with a payback lower than the assumed battery life. Further work on this topic will focus on refining the BESS operation by considering predictions of the aFRR service prices and of the aFRR energy requirements to develop new decision-making algorithms. Acknowledgments The authors would like to thank the financial support provided by the Universitat Jaume I (Spain), within the context of projects UJI-B2021-35, and grant number PREDOC/2020/35.
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tion of Hybrid Renewable Power Plants,” in 2021 International Conference on Smart Energy Systems and Technologies (SEST), 2021, pp. 1–6. 13. S. Zhang, H. Liu, F. Wang, T. Yan, and K. Wang, “Secondary frequency control strategy for BESS considering their degree of participation,” Energy Reports, vol. 6, pp. 594–602, 2020. 14. H. Beltran, P. Ayuso, J. Cardo-Miota, J. Segarra-Tamarit, N. Aparicio, and E. Pérez, “Influence of the intraday electricity market structure on the degradation of li-ion batteries used to firm photovoltaic production,” Energy Technology, vol. n/a, no. n/a, p. 2100943. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/ente.202100943 15. ENTSO-E, “P1-Policy 1: Load-Frequency Control and Performance [C],” Tech. Rep., 2009. 16. ——, “ENTSO-E Statistical Factsheet 2018,” Tech. Rep., 2019. 17. C. D. R. Nacional Los Mercados Y La Competencia, “P.O. 7.2. Restricciones técnicas,” 2020. 18. R. E. de Espa˜na, “E-SIOS.” [Online]. Available: https://www.esios.ree.es
Incremental Capacity Analysis as a Diagnostic Method Applied to Second Life Li-ion Batteries Lucas Albuquerque, Fabien Lacressonnière, Xavier Roboam, and Christophe Forgez
Abstract This work is inserted in the context of second life Li-ion batteries: for such storage devices, their first life characteristics are unknown and a simple capacity measurement might not be sufficient to fully characterize and get it ready for its second life. The Incremental Capacity Analysis (ICA) was used in this study to give a more intimate diagnosis of the batteries’ Degradation Modes (DMs), providing a link with physical degradation phenomena. This method was applied to a lithium-ion battery module (NMC/Graphite) which was used in an electrical vehicle and to a single cell from a similar module in order to verify its potential use in this context. Both IC curves were then compared to a DM simulation using the . Alawa software, capable of simulating different ageing phenomena and their effects on the IC curves. Moreover, this work gives an intrinsic view and explanation of the IC signature for the mentioned battery technology.
1 Introduction The increasing number of batteries produced and consumed nowadays can be attributed to the rise of electric vehicles (EVs) into the market. However, this step towards transport decarbonization created a problem of its own: what to do with these batteries after they are not suitable anymore to power said EVs? The answer to this question is either recycling or ending up in a landfill, creating another environmental problem in itself. Nonetheless, there are innovative projects nowadays, like ELSA [1] and Batteries2020 [2], that are striving to give a second life
L. Albuquerque () · F. Lacressonnière · X. Roboam LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France e-mail: [email protected]; [email protected]; [email protected] C. Forgez Roberval, CNRS, UTC, Compiègne, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_34
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to these batteries. Offering a second chance to these batteries would mean lowering their environmental impacts during their life cycle. The end of an EV battery life is defined by the US Advanced Battery Consortium as a 20% drop of cell capacity from the rated value, or a 20% drop from rated power density at 80% depth of discharge (DoD) [3]. In other cases, the battery end of life can be considered achieved when its resistance has doubled in value. Yet, after being used in an EV, these batteries can still be useful in other applications and can be selected and rebuilt for a new purpose, such as Energy Storage Systems (ESS) for stationary applications [4]. In order to have a homogeneous battery selection issued from various first lives, it is important to characterize the cells of a battery pack with respect to State of Health (SoH). However, in this study the Incremental Capacity Analysis (ICA) was here used to give a more intimate diagnosis of the batteries, pursuing a more precise characterization of the cells or modules for the assembly of the second life battery. This refine selection means a more homogeneous battery, in which the cells would age similarly during the second life. This paper is organized as follows. In the second part, a few diagnostic methods are presented and the feasibility of their use in second life applications is discussed. The third part presents the ICA as a diagnostic tool to determine with accuracy the battery DMs. The experimental procedure is detailed and the results are explained and compared to other studies. To further visualize the effects of degradation, the fourth part presents the results of a Hybrid Pulse Power Characterization (HPPC) test. The fifth and last part confirms the experimental results with a simulation toolbox for battery degradation called . Alawa.
2 Diagnostic Methods for Second Life Batteries There exist many diagnostic methods for Li-ion batteries, but some are better suited than others to characterize the cell for a possible second life. They mainly give as outputs the SoH in terms of capacity (1) or impedance (2) [3, 5]. SoH (Q)[%] = 100 ∗
.
Qpresent Qnominal
Zpresent SoH (Z)[%] = 100 ∗ 2 − Znominal
.
(1)
(2)
Where Q is the battery capacity in Ah and Z is the impedance in Ohms. Precise methods based on machine learning are employed in Battery Management Systems (BMS), but they track the battery usage since their beginning of life to estimate the SoH [6]. In a situation where the previous usage is unknown, these methods would lack precision or not be applicable due to the small sample or nonexistence of first life data. Other methods such as the electrochemical impedance spectroscopy have
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been proven to be precise and capable of determining the DMs occurring inside the battery [7], but it requires specialised equipment capable of exciting the cells in order to extract their reaction to the applied frequency spectrum. Since Li-ion battery degradation has been proven to be path dependent [8], meaning that their first life will influence the longevity and performance during their second life, two batteries can present the same SoH but have different degradation patterns. That is why, for a second life application, a diagnostic technique such as the ICA can be better suited to determine these degradation patterns in a battery cell or module. This method can be applied with simple laboratory equipment such as a power supply or an electronic load. With this technique, it is possible to estimate the Loss of Lithium Inventory (LLI ) and the Loss of Active Material (LAM) in the positive and the negative electrodes of a Li-ion cell. These DMs are a better representation of the battery first life when compared to a simple capacity measurement.
3 Incremental Capacity Analysis 3.1 Principle The ICA and Differential Voltage Analysis (DVA) are two similar methods that give an intimate view of the electrochemical processes inside the cell. Many papers have been previously published on these methods, but most of them focus on the estimation of the SoH during the first life [9–11]. In [9], it is possible to see how the Open Circuit Voltage (OCV) plateaus, which represent the convolution of the phase transitions inside the electrodes when being lithiated or delithiated, become peaks in the IC curve by applying Eq. (3) [9]. In which the tips represent the existence of two phases in one of the electrodes. IC =
.
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(3)
Where .dQcell is the variation in capacity with respect to the voltage .dVcell . As illustrated in [12], the effects of the DMs can be translated in a shift between the electrode potentials, in the case of LLI , or a contraction in the case of LAM, which can happen separately in each electrode (.LAMP E or .LAMN E ). These changes in the electrode OCV curves are ultimately going to change the overall signature of the IC curve and the amplitude and shift of the peaks can be used to estimate said DMs. In order to acquire the IC curve, it is necessary to measure the OCV for each State of Charge (SoC) value of the battery. However, to obtain this measurement, it is necessary to charge or discharge the battery with low currents. Lower currents improve the precision of the measurement by preventing high diffusion effects inside the electrode materials and thus the precision of the IC curve. These diffusion effects can mix the electrode phase transitions into one single indistinguishable curve, as
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seen in [13]. This study concludes that C/6 is a good compromise between time and precision, but there are studies that go as far as C/2, like [14].
3.2 Experimental Tests Two NMC/Graphite Li-ion batteries were studied in this work. One module is composed of 12 cells connected in series which had been used in an EV. The second battery is a single cell similar to the ones used in the module and it has also been used in an EV. The nominal capacity of the module and the cell is equal to 25 Ah, according to the manufacturer’s datasheet. Figure 1 shows the cell used in the module. First of all, several charge and discharge cycles were done with the module and the cell in order to determine and compare their discharged capacities. During the tests, they were both placed in a climate chamber at 25.◦ C. The charge protocol used was a CC–CV profile, in which a constant current (CC) is applied until the battery has reached its maximum allowed voltage (4.2 V per cell), then the power supply switches to constant voltage (CV) regulation until a low current of C/50 (0.5 A) is reached. The discharging process was stopped when the voltage across a cell was equal to 2.7 V (the discharge voltage limit). During the experimental tests, the twelve cells of the module were equilibrated (the voltage response for each cell was the same). Hence, in this study, the diagnosis of the module was based on one particular cell of the module (noted cell.m in this study). Figure 2 shows the discharge curves in volts by ampere-hours for the cell.m and the single cell. As shown, the discharge capacity of the module is equal to
Fig. 1 A NMC/G Li-ion cell tested in this work. The module consists of twelve of these cells in series
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Fig. 2 Discharge curves (with a C-rate of 0.2C) for a cell issued from the module and the single cell
27.5 Ah whereas it is equal to 23 Ah for the single cell, evidencing that this last has a lower SoH. Moreover, it is clearly visible that the phase transition voltage plateaus and the overall curves shift towards lower voltages, which indicates ageing and a resistance increase. These observations support the interest in using the ICA and a resistance measurement as diagnostic tools to understand the DM effects on the single cell. In order to obtain the DMs in both the cell.m and the single cell, the IC curve was plotted. As a first step to obtain the curve, a filtering on the voltage measurements is necessary before the derivative is calculated. As previously done in [15], the first filter applied to the voltage measurement was a moving average filter, giving a rough outline of the IC curve. Then the result was further smoothed by a Gaussian filter, in which the values of the averaging window are weighted with a Gaussian curve, where the center values have a bigger impact on the averaged value and the ones in the extremities have a lesser impact. The size of the averaging window is increased to smoothen the curve until its peaks start decreasing in amplitude.
3.3 Interpretations As previously said, the interest of the ICA is to analyze and identify the battery degradation phenomena intimately. To further understand and visualise the effects of ageing in the NMC/Graphite technology, the ICA method was applied to the single
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Fig. 3 Comparison between the IC curve of cell.m (from the module) and the single cell
cell in order to compare its signature with cell.m . Figure 3 shows both IC curves from a voltage measurement during the charging process. Several differences on the IC curves appear. These differences could be governed by ageing processes in the single cell. The analysis of the IC curves demands an understanding of both the graphite and NMC electrodes behaviour simultaneously. Since the pair of curves presented on Fig. 3 comes from the charge profile, starting from the lowest voltages where the graphite is almost fully delithiated until the end of the first peak (2.7 V until 3.55 V for cell.m or 3.6 V for the single cell): the negative electrode passes from .C6 to .LiC72 (diluted phases), then .LiC36 and finally transitioning to .LiC18 . At this point, the mentioned graphite intercalation stages coexist, especially under high currents where diffusion effects are intensified. The second big peak between 3.6 V and 3.75 V is mainly due to a NMC specific phase transition, where its structure changes from a hexagonal to monoclinic (H1 to M) lattice [16]. While so, the graphite transitions from .LiC18 towards .LiC12 corresponding to the end of the plateau between stage 3 and 2 in the graphite charge curve observed in the literature [17]. The third and last visible peak between 3.75 V and 4.1 V (shifted on the single cell IC curve) is primarily a result of the last phase change in the graphite electrode from .LiC12 to .LiC6 . This transition is the longest of all (kinetically slower). Due to the lack of a peak indicating the phase transition H2–H3 (hexagonal to hexagonal accompanied by a rapid volume contraction) towards the end of the charge, reported in Ni rich NMC cathodes, the NMC cathode present in the batteries is presumed to have a relatively good reversibility and this is translated into a good
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overall stability of the electrode [18], so in a first moment, .LAMP E does not seem to be the main cause of ageing. However, the lower first peak (3.5 V) amplitude can indicate small traces of active material loss of the positive electrode .LAMP E . Moreover, as a result of LLI , the cut off voltage (low SoC) of the positive electrode becomes higher as the lithium is consumed and it shifts both electrode potential curves away from each other. This means that at the end of a discharge or the beginning of a charge cycle, the positive electrode cannot reach lower voltage potentials due to the voltage limits (as in figure 8 from [19]). So, instead of having a strong peak between 3.6 and 3.75 V, its amplitude is considerably reduced. This indicates that LLI is the most prominent degradation mode at this stage of ageing. The consumption of lithium can also explain the overall shift of the IC curve towards higher voltages, since it is probably consumed during the thickening process of the SEI (Solid Electrolyte Interphase) layer.
3.4 C-Rate Influence on the ICA A study to further understand the influence of the C-rate on the IC curve was also conducted. Figure 4 shows IC curves plotted for several C-rates. The applied filters follow the same rule as explained in Sect. 3.2. It was checked that the peak amplitudes were not equally affected by the charge or discharge regimes. The influence of the C-rate on the IC curve can be explained by the difference in kinetics of charge transfer and diffusion reactions in the electrodes for the different current
Fig. 4 Comparison between different C-rates in charging and discharging modes for the cell.m
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Table 1 Comparison of peak amplitude and shift depending on the C-rates C-rates 0.2C 0.5C C
IC peaks for different C-rates in charging mode 1st peak: Amplitude 1st peak: Voltage 2nd peak: Amplitude 66.4 Ah/V 3.5 V 96.76 Ah/V 55.4 Ah/V (.−16.6%) 3.51 V (+11 mV) 89.91 Ah/V (.−7.1%) 51.8 Ah/V (.−22%) 3.54 V (+46 mV) 91.22 Ah/V (.−5.7%)
2nd peak: Voltage 3.64 V 3.65 V (+14 mV) 3.67 V (+35 mV)
values. This corroborates to choose a lower C-rate, in order to obtain an accurate IC plot. Hence, the choice of the C-rate has to be a compromise between the accuracy of the IC curve and the duration of the test for a rapid evaluation of the second life Li-ion batteries. The analysis of two peaks from the IC curve (charge regime) for different Crates was carried out and the results are summarized in Table 1. When the C-rate increases, the peak amplitudes are reduced and they shift toward higher voltages due to the voltage drop governed by the internal resistance. A reduction of peak areas is proportional to the number of exchanged amperes-hours during the charging process.
4 HPPC Profile Characterization As a complement to the ICA tests, a Hybrid Pulse Power Characterization (HPPC) test was carried out with both the module and the single cell in order to measure their internal resistances. One HPPC cycle profile consists on constant current charge and discharge pulses, followed by a 10% SoC constant current discharge and a 30 min pause between cycles. The cycles are repeated until 10% SoC. One sequence of the HPPC profile is shown in Fig. 5 where several current rates were imposed at 0.1C, 0.2C, 0.5C, 1C, 1.5C and 2C. The duration of the pulses was fixed at 10 s and the internal resistance was calculated by Ohm’s law. Figure 6 presents the internal resistances measured for several SoC values. These values were calculated for cell.m and the single cell for a discharge current of 1C. As depicted from Fig. 6, the single cell internal resistance is higher than the cell.m in a ratio of 1.7, regardless of the SoC value. This internal resistance increase may be associated with ageing mechanisms taken place in the single cell and can explain the overall shift of the IC curve for the aged cell (Fig. 3), as mentioned previously, and may be linked mainly to the growth of the SEI layer.
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Fig. 5 Current pulses and the voltage reactions during one sequence of the HPPC profile
Fig. 6 Internal resistance comparison between cell.m and the single cell
5 ICA Comparison with the Alawa Toolbox Figure 7 presents a comparison between the IC curves measured for cell.m and the single cell and IC curves obtained by using the . Alawa toolbox developed by Matthieu Dubarry et al. [20, 21]. This software is able to simulate the DMs through a model based on individual electrode potentials, in which LLI is translated into a
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Fig. 7 IC curves from . Alawa simulation of 0.032% of LLI and 0.01% of .LAMP E per cycle (top) and IC curves from both the single cell and cell.m (bottom). Q% is the percentage of the initial battery capacity Q in Ah
shift of the potentials and .LAMN E and .LAMP E are contractions of the electrode curves. The simulations are quantified based on a defined loss per cycle. In order to simulate the degradation as close as possible to the experimental results, a few parameters such as the electrode ratio, the initial resistance and the SEI offset were chosen. This last one is responsible for the initial shift between the electrode curves, consuming lithium-ions. These parameters were modified until the obtained IC profile was close to the experimental one from cell.m . The same methodology was applied to simulate the DMs. The optimal result was found when the toolbox was set to simulate 0.032% of LLI and 0.01% of .LAMP E per cycle during 500 cycles. These DMs result in a total of 16% of capacity loss and it is in accordance with the experimental value of 83.3% of SoH when dividing the capacity of cell.m to the aged one.
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Table 2 Comparison of the . Alawa simulations and the measurements. Note that LLI has been set to 0.032% per cycle and .LAMP E and .LAMN E were set to 0.01% per cycle
Case Experimental results LLI LLI + .LAMP E LLI + .LAMN E
DMs simulation and measured values Degradation Degradation Translation 1st 1st peak (%) 2nd peak (%) peak (V) 10.52 37.83 0.035 18.30 44.27 0.027 14.10 39.97 0.022 20.75 40.54 0.028
Translation 2nd peak (V) 0.049 0.045 0.038 0.043
The total amount of capacity loss is due to LLI (16%), but the active material loss from the positive electrode has an influence on the IC curve as this electrode capacity has been reduced. Generally, the lower voltages are limited by the negative electrode and the higher voltage is limited by the positive electrode. Table 2 summarizes the simulations results with . Alawa and compares them with the real measured values. The results presented in Table 2 show that with regard to peak degradation, the simulation with both LLI and .LAMP E combined are the closest to the experimental results, also supported by Fig. 7. The first peak is greatly reduced in the simulation with .LAMN E , as this peak is due to the first few phase transitions in the graphite, as mentioned in Sect. 3. The peak translation in volts show close results in all of the cases, mainly due to the formation of the SEI as previously said. However, the differences are minimal, thus the peak amplitudes seem to be more adequate to judge the accuracy of the simulations.
6 Conclusions In this paper, several tests were performed on a Li-ion module composed of 12 cells connected in series in order to estimate their state of health. These tests were also done with a single Li-ion cell. The capacity and internal resistance measurements allowed to distinguish a more important degradation for the single cell. An ICA was carried out to determine the degradation modes in the cell. It has been shown that the accuracy of the IC curves depends on the C-rate (amplitudes of the peaks decrease with the C-rate). To determine the degradation modes in the cell, the .‘Alawa toolbox was used. A comparison between the IC curves (simulated and measured) showed that the major degradation mode in the cell is the loss of lithium inventory and the loss of active material of the positive electrode. In the future, this study will be extended in order to develop an experimental method, based on the ICA, to determine with accuracy (and rapidly) the degradation modes in Li-ion modules. This diagnostic method will be applied in order to have a homogeneous module selection to develop a second life battery.
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Acknowledgments This work is funded by the B2LIVE project (Batteries de 2nd vie au Lithium Ion à Vieillissement caractérisé par Experimentation). This work has been supported by the OCCITANIE Region.
References 1. ELSA project. https://www.elsa-h2020.eu/Home.html. 2. Batteries2020 project. http://www.batteries2020.eu/. 3. Eklas Hossain, Darren Murtaugh, Jaisen Mody, Hossain Mansur Resalat Faruque, Md. Samiul Haque Sunny, and Naeem Mohammad. A comprehensive review on second-life batteries: Current state, manufacturing considerations, applications, impacts, barriers potential solutions, business strategies, and policies. IEEE Access, Vol 7:pages 73215–73252, 2019. 4. Shijie Tong, Tsz Fung, Matthew P. Klein, David A. Weisbach, and Jae Wan Park. Demonstration of reusing electric vehicle battery for solar energy storage and demand side management. Journal of Energy Storage, 11:200–210, 2017. 5. Honorat Quinard, Eduardo Redondo-Iglesias, Serge Pelissier, and Pascal Venet. Fast electrical characterizations of high-energy second life lithium-ion batteries for embedded and stationary applications. Batteries, 5(1), 2019. 6. Nina Harting, René Schenkendorf, Nicolas Wolff, and Ulrike Krewer. State-of-health identification of lithium-ion batteries based on nonlinear frequency response analysis: First steps with machine learning. MDPI Applied Sciences, Vol 8(5), 2018. 7. Carlos Pastor-Fernández, Kotub Uddin, Gael H. Chouchelamane, W. Dhammika Widanage, and James Marco. A comparison between electrochemical impedance spectroscopy and incremental capacity-differential voltage as li-ion diagnostic techniques to identify and quantify the effects of degradation modes within battery management systems. Journal of Power Sources, 360(ISSN 0378-7753):301–318, 2017. 8. Zeyu Ma, Jiuchun Jiang, Wei Shi, Weige Zhang, and Chunting Chris Mi. Investigation of path dependence in commercial lithium-ion cells for pure electric bus applications: Aging mechanism identification. Journal of Power Sources, 274:29–40, 2015. 9. Elie Riviere, Ali Sari, Pascal Venet, Frédéric Meniere, and Yann Bultel. Innovative incremental capacity analysis implementation for c/lifepo4 cell state-of-health estimation in electrical vehicles. MDPI Batteries, 5(2), 2019. 10. Yuan Ci Zhang, Olivier Briat, Jean-Yves Delétage, Cyril Martin, Nicolas Chadourne, and JeanMichel Vinassa. Efficient state of health estimation of li-ion battery under several ageing types for aeronautic applications. Microelectronics Reliability, 88–90:1231–1235, 2018. 11. Tiphaine Plattard, Nathalie Barnel, Lo¨ıc Assaud, Sylvain Franger, and Jean-Marc Duffault. Combining a fatigue model and an incremental capacity analysis on a commercial nmc/graphite cell under constant current cycling with and without calendar aging. MDPI Batteries, 5(1), 2019. 12. Christoph R. Birkl, Matthew R. Roberts, Euan McTurk, Peter G. Bruce, and David A. Howey. Degradation diagnostics for lithium ion cells. Journal of Power Sources, 341:373–386, 2017. 13. A. Fly and R. Chen. Rate dependency of incremental capacity analysis (dq/dv) as a diagnostic tool for lithium-ion batteries. Journal of Energy Storage, 29:101329, 2020. 14. E. Schaltz, Daniel-Ioan Stroe, K. Nørregaard, Lasse Stenhøj Ingvardsen, and Andreas Christensen. Incremental capacity analysis applied on electric vehicles for battery state-of-health estimation. IEEE Transactions on Industry Applications, 57:1810–1817, 2021. 15. Yi Li, Mohamed Abdel-Monem, Rahul Gopalakrishnan, Maitane Berecibar, Elise NaniniMaury, Noshin Omar, Peter van den Bossche, and Joeri Van Mierlo. A quick on-line state of health estimation method for li-ion battery with incremental capacity curves processed by gaussian filter. Journal of Power Sources, 373:40–53, 2018.
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A Li-Ion Battery Charger with Embedded Signal Generator for On-Board Electrochemical Impedance Spectroscopy Luigi Mattia, Giovanni Petrone, and Walter Zamboni
Abstract The development of a battery monitoring system is one of main tasks for applications needing an efficient and well-designed battery storage system. In this framework, a fast, on-board, non-invasive and low-cost diagnosis system has a primary importance. Among the large number of diagnosis techniques, the Electrochemical Impedance Spectroscopy (EIS) is one of the most powerful. It allows one to extract information about the overall state of an electrochemical cell by stimulating it with current or voltage signals with appropriate shapes and frequency. In this work, we present the changes made to a commercial Lithium-ion battery charger to implement a system for the generation of EIS stimuli, preserving large part of the native functions of the battery charger. The stimulation functions are implemented using a field-programmable gate array (FPGA) board, which ensures a good voltage resolution and an optimal frequency range for this kind of applications.
1 Introduction The Electrochemical Impedance Spectroscopy (EIS) is a well-known frequencydomain identification procedure that has experienced a growing interest in several power source fields, like batteries and fuel cells, thanks to the increasing demand for renewable sources and electric mobility. EIS can be used to observe the internal electrochemical reaction processes and states of a Lithium-ion (Li-ion) battery through the analysis of the so-called impedance plot in the Nyquist plane. Indeed, the shape and the size the impedance spectrum allow one to estimate battery properties like State of Charge (SoC), temperature, or battery ageing [1]. As it is well known, this method characterises the system at its electric terminals by measuring voltage and current signals in the presence of a particular stimulus, like a sinusoidal frequency sweep [2]. The experiment can be performed through
L. Mattia () · G. Petrone · W. Zamboni Università degli studi di Salerno, Fisciano, Italy e-mail: [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_35
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expensive laboratory equipment as well as with done less expensive experimental tools, making it suitable for online and on-board applications [3]. There are many attempts to realise efficient low-cost detection system with integrated on-board EIS [4–8]. Some of them are focused on methodologies and instruments for a drastic cost reduction of performed EIS identification activities, e.g., [4]. Other attempts propose compact solutions to gather EIS data, potentially operating online [5], while alternative solutions integrate a passive stimulation technique in battery charge balancers, already included in the battery management system. In some of these cases, they require a complex configuration of the battery charge balancer, which is suitable for EIS analysis of every single cell of the battery pack [6–8]. In this work, we present the design and implementation of a proof-of-concept for a low-cost on-board EIS stimulation system for EIS applications. The system is based on a commercial battery charger subject to simple changes to integrate the stimulation functions. The stimulation controller is a Field-Programmable Gate Array (FPGA), which ensures high quality of the stimulation in terms of amplitude and frequency resolution. The system operates on a single Li-ion cell having small capacity. The main advantage of the proposed contribution is that the approach is reliable, does not require complicated hardware, and its scaling up towards higher power and energy ratings is quite immediate, making it suitable in many application fields, from automotive to consumer electronics. The paper is organised as follows. Section 2 presents a description of the implementation of the sinusoidal stimulus generator; Sect. 2.1 focuses on the hardware layout, and Sect. 2.2 on the internal FPGA architecture. Section 3 presents the experimental results, and Sect. 4 draws some conclusions and outlines practical future perspectives.
2 Architecture of the Current Signal Generator For a good EIS analysis, an efficient stimulation system is required. In this work, we implement a sinusoidal stimulation system in a frequency range from .0.1 Hz to .7.5 kHz. In particular, this system works on a single Li-ion battery but, thanks to its simplicity, the system can easily be scaled down or up to whatever power ratings, from electrical mobility to nanoscale applications.
2.1 Hardware Implementation We start from a commercial battery charger with its own current control loop and an on-board microcontroller used for the implementation of the charging method, monitoring and fault detection. The change made to the battery charger is the exclusion of the internal voltage reference of the current control loop, by
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physically interrupting the printed-circuit-board trace and soldering a connector for an externally-fed reference, which is generated by an external on-board device. As it is well known, the voltage reference is a signal whose value must be followed by the charging current using a particular scale factor. In this application, the required charging current follows with a one-by-one ratio the reference value, therefore a sinusoidally-shaped voltage reference signal yields a sinusoidal charging current. Theoretically, the same on-board microcontroller can be reprogrammed to generate a sinusoidal voltage reference, but, in general, its performance may not be sufficiently high as required by an EIS application. Therefore, an external FPGA is used to generate a sinusoidal stimulus with a high resolution in voltage and frequency. The sine wave stimulus is generated from a digital pin according to the pinout of the FPGA, so the waveform is modulated using a PWM approach. The PWM signal, filtered by a Low-Pass (LP) filter, is converted in an analog signal .Vref . If the cutoff frequency .fLP of the filter is lower than the PWM frequency .fP W M , .fLP < fP W M , .Vref follows the filtered duty cycle trend, being sinusoidal. Figure 1 shows the architecture of the stimulation system, which is composed by a commercial battery charger, an FPGA device, and a LP filter. The microcontroller in the battery charger shown in the figure is still used for safety purposes, like overvoltage, over-current and over-temperature detection. The typical constant-current constant-voltage charging profile implemented in the internal microcontroller is temporary disabled, because the current loop is driven by the external board. The entire system is shown in Fig. 2. The regulation of .Vref is performed through the adjustment of the duty cycle D, defined by the ratio .D = Ton /TP W M between the time in which the signal is pulled up, .Ton , and .TP W M . In order to achieve a high resolution, the PWM period, namely .TP W M , must include an high number .NP W M of clock pulses .TCLK : TP W M = NP W M Tclk .
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Fig. 1 Block scheme of the stimulation system. A commercial battery charger and an FPGA device are used to generate the stimulus signal, the filter between the battery charger and the FPGA is a LP filter used to convert the PWM modulated signal to a sinusoidal signal. The main white block interacting with the stimulation system is the EIS data acquisition system and computation box
Fig. 2 Assembled prototype composed by an FPGA and a LP filter used to generate a sinusoidal stimulation signal which is converted in a current signal by the battery charger and injected in a Li-ion battery
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where .Ns is the number of samples per period of a sinusoidal waveform. Notice that, once .NP W M is fixed, f is a function of .Ns . The range adopted for .Ns determines the range of the stimulation frequency .f ∈ [fmin ; fmax ]. To meet the aforementioned resolution requirements, a very high clock frequency is required. The use of hardware frequency multiplier, which can effectively be programmed within an FPGA programming, allows us to successfully use an FPGA controller to manage the stimulus generation task. The description of the architecture we adopted is described hereinafter.
2.2 FPGA Waveform Generator Figure 4 shows the FPGA internal architecture, which is based on a vector of Ns = 1024 samples. Each sample represents the duty cycle D of a suitable point of the sinusoid. The .Ns samples represent a full single period of a sinusoid. A 10 bit representation is used for D, with data stored in a Block RAM (BRAM). We assume that the PWM period lasts 1024 clock pulses, that is, .NP W M = 1024. Now, we can define the base frequency .fb in correspondence of .NP W M = Ns = 1024:
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The stimulation signal generated at .fb is implemented in a very easy way, by using, one by one, the samples stored in the BRAM. In order to generate stimulus signals characterised by various frequency values, lower or higher than .fb , by picking values of D stored in the BRAM, we decide to play with two complementary approaches. The first approach implements the generation of a signal having frequency higher than .fb . The number of samples .Ns is reduced according to the power of two: 1024, 512, 256, and so forth, for a downsampling of the stored waveform. To implement this, the number of samples to skip .Nj is introduced:
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The downsampled waveform is smoothed by the LP filter located between the FPGA board and the battery charger current controller. The second approach is aimed at generating sinusoids having frequency lower than .fb , through the repetition of each sample according to an integer repetition factor .NR . The combined use of .Ns (.Nj ) and .NR allows us to obtain a specific frequency which is function of .Nj , .NR : .f (Nj , NR ). The set of frequencies f will be used for EIS. We store all the pairs .(Nj , NR ) to be used in an EIS generation loop in a look-up table (see Fig. 4). When the system starts working, the first value is selected by default from the multiplexer. During the EIS analysis loop, an external signal (“Change f.” in Fig. 4), coming from the EIS acquisition system, triggers the multiplexer output change to the successive value of .(Nj , NR ). The counter in the figure generates the BRAM address from .(Nj , NR ), and the corresponding D value is provided to the PWM generator. For the sake of example, Table 1 shows how the desired frequency .fdes within the decade 10-100 Hz are implement through the FPGA. Table 2 shows the main characteristics of the system. The frequency range indicated in the table is scanned with 8 points per decade, for a total of 40 points in the whole frequency interval. The amplitude range is chosen to achieve a C/10 stimulus current for a Li-ion cell of .2 A h rated capacity. The current resolution is computed according to (2). Table 1 Example of the computation of the actual frequencies in the range 10–.100 Hz
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Table 2 Characteristics of the stimulation system Parameter Type of EIS stimulation Frequency range Amplitude range Current resolution Analog filter Clock frequency .1/Tclk
Characteristics sinusoidal .0.1 Hz–.7498 kHz 0:.200 mA .0.195 mA 6th order Butterworth LP filter, cutoff frequency 15 kHz .374 MHz
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3 Experimental Results In order to evaluate the performance of the system and the quality of the signals, we perform a testing activity in which we acquire and analyse the sinusoidal stimulus signals. The test bench, shown in Fig. 5, is composed by the stimulation system already described in Sect. 2, a dc power supply, a Li-ion battery of .2000 mA h, an ad hoc designed Data AcQuisition system (DAQ) and spectrum analyser, used within several European projects, like [9], for online EIS on fuel cells (not optimised for Li-ion batteries) [10], and a personal computer collecting measurements from DAQ. A digital oscilloscope is added to the test bench to measure and check intermediate signals, which are sent to the computer. The stimulus signal is superposed to a dc bias of .100 mA, because the unidirectional battery charger does not manage negative currents, and therefore ac stimuli with zero offset cannot be processed. The first tests are aimed to evaluate the spectral purity of the generated stimulus. We choose to check the harmonic content of the generated waveform with the Total Harmonic Distortion (THD). Figure 6 shows the THD computed in the whole frequency span. The THD overtakes 2 % at high frequencies (.f > 200 Hz), but its value is always within 3.5 %. This THD increase can partially be ascribed to a small distortion of the time domain waveform near the zero voltage level, which becomes valuable when the frequency approaches the kilohertz range. Despite this aspect, the THD at low frequency is very small (within .0.1 %). For signals having frequency higher than .3 kHz, the LP-filter cutoff frequency is approached, and the secondary harmonics, which are out of the LP-filter pass band, are strongly attenuated. This yields a valuable THD reduction. Figure 7 shows three examples of current stimuli at 3905, 17.93, and .0.1365 Hz. For all of them, the first subplot (top of each subfigure) plots the time-domain signal acquired through the DAQ, while the second subplot (bottom of each subfigure) shows the waveform spectrum. The amplitude of the fundamental frequency is
Fig. 5 Experimental system used for testing the quality of the design
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Fig. 6 THD of current stimuli as a function of frequency used
almost constant from 0 to 418 Hz. After this frequency, the peak-to-peak amplitude suffers from an attenuation due to the overall load including the battery and the charger. As a final test, we perform a complete EIS loop for the analysis of the battery impedance response in a 5-decade range from .0.1 Hz to .7.8 kHz, scanned with 40 frequency points from the highest frequency to the lowest. Each decade includes 8 frequency points. At each frequency point, the impedance is computed by: .
˙ ω) = V (j ω) = R(j ω) + j X(j ω), Z(j I (j ω)
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where V and I are the fast Fourier transforms of the voltage and the current signals, respectively. Collecting all points, we plot the negative imaginary part .−X of .Z˙ versus the real part R, obtaining the so-called battery impedance plot. This method is simple and precise, but it require an accurate setting of the sampling frequency and of the number of samples in the acquisition time window. In our case, the best results are achieved with a sampling frequency 100 times higher than the sinusoidal one, and 2000 samples for each frequency stimulation. In order to show the capabilities of the system, Fig. 8 shows the comparison between the EIS computed with the proposed experimental system (namely, experimental) and a reference EIS plot (namely, reference), measured through a Biologic SP 200 spectrum analyser on the same battery [11]. Voltage and current resolutions of the acquisition system are respectively 5 µV and 2 nA. The comparison is aimed at showing a qualitative compatibility of the EIS spectrum, rather than an exact quantitative match, which would required a valuable improvement of the acquisition circuit including DAQ. In order to compare the responses, the initial SoC is estimated in both experiments and the EIS measurements of Fig. 8 are taken by starting from the same SoC value. Moreover, the experimental response has been compensated to remove the effect of the sensing circuit associated to the DAQ system. The latter effect is intrinsic with the topology and cannot be neglected.
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The high frequency part of the plots are almost superposed the one another. A small mismatch is observed for the four highest-frequency points. This phenomenon is probably due to a non negligible high-frequency inductive behaviour of the cables used in the low-cost system, which was also proved experimentally. The medium-tolow frequency part of the curves show similar tendency, even if a mismatch between them clearly appears. The mismatch can be explained in part by the longer time required by the low-cost stimulation system to make a satisfactory EIS analysis with respect to laboratory impedance analysers. During the test, a valuable SoC increase is achieved in all low frequency points, and therefore a quantitative comparison is definitely compromised. However, the right-hand-side shift of the experimental curve for low-frequency points is compatible with scientific literature [12].
4 Conclusions and Perspectives This work has presented the design and implementation of a low-cost system for onboard EIS sinusoidal stimulus generator in the range from hundred millihertz up to some kilohertz. Such a range is suitable for Li-ion batteries on-board EIS analysis. The generator is implemented through an FPGA device that interact with the current control loop of an off-the-shelf Li-ion battery charger. The experimental results prove the good generation performance of the system, with THD values always below 5 % on the whole frequency range. The main
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drawback of the EIS generator is the long time required by stimulation in low frequency range, which is estimated approximately in 20 minutes. This value came from the required acquisition time and from the time to transfer acquired data to the computer before next frequency stimulation. It is worth mentioning the several advantages of the architecture used for the stimulation. First, the architecture is fully compatible with several kind of more structured stimuli, like random noise, stochastic signals, or pseudo-random binary sequence, with wide spectra. In perspective, such kind of stimuli may provide a valuable time saving, but with a possible loss of resolution. Second, this kind of architecture can also be used to simultaneously analyse a whole battery module, made of series-connected cells. Third, comparing the system with those ones using on-board battery charge balancers to implement the EIS stimulation signals, the proposed system appears much simpler. Finally, the simplicity of the approach could easily be extended to every commercial battery charger whose dc/dc converter is equipped with an on-board current control loop the power ratings can be scaled-up according to the application. The work is in progress to develop an acquisition system based on a commercial product, like a battery monitor, to compute the EIS on board. The evaluation and testing of several promising low-cost solutions is still in progress. Acknowledgments This work was supported in part by funds of the projects “Holistic approach to EneRgy-efficient smart nanOGRIDS e HEROGRIDS” (PRIN 2017 2017WA5ZT3) within the Italian MUR 2017 PRIN programme, by the “Ex-WISCH e D-CODE” and FARB funds of the University of Salerno.
References 1. N. Al-Zubaidi R-Smith, M. Leitner, I. Alic, D. Toth, M. Kasper, M. Romio, Y. Surace, M. Jahn, F. Kienberger, A. Ebner, and G. Gramse, “Assessment of lithium ion battery ageing by combined impedance spectroscopy, functional microscopy and finite element modelling,” Journal of Power Sources, vol. 512, p. 230459, 2021. [Online]. Available: https://www. sciencedirect.com/science/article/pii/S0378775321009630 2. A. Waligo and P. Barendse, “A comparison of the different broadband impedance measurement techniques for lithium-ion batteries,” in 2016 IEEE Energy Conversion Congress and Exposition (ECCE), 2016, pp. 1–7. 3. W. Zamboni, “Eis diagnostics for fuel cells/vrfbs,” in Encyclopedia of Energy Storage, L. F. Cabeza, Ed. Oxford: Elsevier, 2022, pp. 568–581. [Online]. Available: https://www. sciencedirect.com/science/article/pii/B9780128197233001074 4. T. Serni, E. Locorotondo, L. Pugi, L. Berzi, M. Pierini, and V. Cultrera, “A low cost programmable hardware for online spectroscopy of lithium batteries,” in 2020 IEEE 20th Mediterranean Electrotechnical Conference (MELECON), 2020, pp. 57–62. 5. A. De Angelis, M. Crescentini, R. Ramilli, G. De Angelis, M. Tartagni, A. Moschitta, P. A. Traverso, and P. Carbone, “A compact system for on-line electrochemical impedance spectroscopy on lithium-ion batteries,” in 2020 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2020, pp. 1–6. 6. M. Koseoglou, E. Tsioumas, D. Papagiannis, N. Jabbour, and C. Mademlis, “A novel on-board electrochemical impedance spectroscopy system for real-time battery impedance estimation,” IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10 776–10 787, 2021.
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7. C. R. Lashway, G. Constant, J. Theogene, and O. Mohammed, “A real-time circuit topology for battery impedance monitoring,” in SoutheastCon 2016, 2016, pp. 1–6. 8. E. Din, C. Schaef, K. Moffat, and J. T. Stauth, “A scalable active battery management system with embedded real-time electrochemical impedance spectroscopy,” IEEE Transactions on Power Electronics, vol. 32, no. 7, pp. 5688–5698, 2017. 9. RUBY, “Robust and reliable general management tool for performance and durability improvement of fuel cell stationary unit (ruby),” https://www.rubyproject.eu/, 2020, accessed 2021-04-15. 10. G. Petrone, W. Zamboni, G. Spagnuolo, and R. Dessi, “Eis method for the on-board evaluation of the fuel cell impedance,” in 2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI), 2018, pp. 1–6. 11. “Biologic website,” accessed 2022-01-18. [Online]. Available: https://www.biologic.net/ products/hcp-1005/ 12. L. Ran, W. Junfeng, W. Haiying, and L. Gechen, “Prediction of state of charge of lithium-ion rechargeable battery with electrochemical impedance spectroscopy theory,” in 2010 5th IEEE Conference on Industrial Electronics and Applications, 2010, pp. 684–688.
A Survey of Energy Management Systems Considering Battery State of Health Preservation in Microgrid Applications Maria Carmela Di Piazza, Massimiliano Luna, and Giuseppe La Tona
Abstract Electrochemical storage systems play an increasingly central role in microgrids, providing several services which allow for more flexible and reliable operation. Lifetime of battery storage systems is a critical aspect to consider for their sustainable and cost-effective employment. In this paper a survey of energy management systems (EMSs) designed to contribute to battery lifetime extension is presented. To pursue this objective, the design of EMSs must rely on suitable battery degradation models, the most significant of which have been retrieved from the technical literature and described as well.
1 Introduction Climate change and environmental protection are global challenges which must be dealt with involving measures of political planning and technological transition, toward climate neutrality and a more sustainable economy. In this scenario, batteries are a key technology for energy storage, which can effectively contribute to the decarbonization process, e.g., through a more effective integration of renewable energy into the electricity grid and the electrification of transport [1]. With specific reference to microgrids, batteries can be used to perform several functions, all contributing to properly manage the variability of generation and demand, thus increasing the efficiency, the stability, and the resiliency of the electrical systems. Typical batteries’ use in microgrids is in providing services like voltage support, frequency regulation, synthetic inertia, renewable firming capacity, renewable energy time shift, arbitrage, distribution system upgrade deferral, grid resiliency, etc. The use of batteries in stationary application can take advantage of new promising technologies (e.g., flow batteries) and energy paradigms (e.g. vehicle-to- grid) [2, 3].
M. C. Di Piazza () · M. Luna · G. La Tona INM – Consiglio Nazionale delle Ricerche (CNR), Palermo, Italy e-mail: [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_36
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Fig. 1 Conceptual scheme of EMS operation in a microgrid
Energy Management Systems (EMSs) can be described as supervisory control systems dispatching power sources and battery storage systems (BSS) according to defined objectives; they are considered a crucial technical solution for the utilization of energy storage as a flexible grid asset that can both provide manifold grid services for efficient and sustainable operation and ensure safe operation [4]. Recent technical literature exhibits many EMSs for micro/nanogrids comprising renewables and batteries aiming at improving energy efficiency and economy by means of demand response or alternative optimization strategies. The EMSs for microgrids, if properly coordinated with the main power grid, can produce advantages for the DSO too, for example by limiting peaks of demand and power loss on electrical feeders and by preventing adverse occurrences like shortage of renewable-based power production, voltage limits breaches, electricity price fluctuations, etc. [5–7]. A conceptual scheme of EMS operation in a microgrid is shown in Fig. 1. Despite all the above-described advantages, it is worth observing that, for a sustainable integration of batteries in microgrids, the energy management strategy should consider the battery behavior in terms of state of health (SOH) by embedding in its formulation a suitable battery model; in this way, an improved exploitation and prolonged life for the battery is achievable. Indeed, from the sustainability standpoint according to EU Green Deal directions, batteries must be long-lasting, safe, traceable throughout their life-cycle and should be remanufactured, allowing also for a second-life application [1]. Recent works highlight that accounting for charge/recharge cycles alone leads to unsatisfactory energy management solutions, with a high rate of degradation; therefore, this is not the ideal way to extend battery life, which also depends, for example, on usage patterns [8, 9]. As a result, the appropriate contemplation within an EMS of the battery SOH, derived from reliable models or diagnostic prediction algorithms, is an issue which came to prominence in the last years. On such a basis, this paper wants to give a contribution in the considered technical area by proposing a survey of literature EMSs featuring a
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prolonged battery lifetime by properly considering battery degradation models in their formulation.
2 Battery Degradation Models Batteries are affected by several mechanical and electrochemical degradation processes causing capacity and power fading [10]. Aging caused by battery utilization, i.e., cycle aging, depends on ambient temperature (Ta ), state of charge (SOC), depth of discharge (DOD), charge/discharge current (C-rate), and number of cycles. Aging associated with the storage period, i.e., calendar aging, depends instead on storage temperature (Ts ), SOC, and time [11]. Both phenomena occur during the battery lifetime, but several modelling approaches consider them individually, either considering only one aspect at a time by adding both components, or by multiplying them [12]. The state of the battery with respect to its aging, compared with its off-the-shelf condition, is described by the SOH indicators, usually the battery capacity and the internal resistance, which reflect the energy and power capabilities, respectively [13]. Several battery degradation models have been proposed in the literature. The selection of the most appropriate models to pursue battery health preservation by an EMS is based on their usability for realtime running of energy management algorithms and should be driven by the best compromise between accuracy and complexity [14]. In this paper, only models that are usable on a control or management algorithm, referred as control-oriented models, are considered [15] [16]. Such models are classified according to their basic nature, into electrochemical, semi-empirical/empirical and physics-based nonelectrochemical models. In the following, a survey of models belonging to each category is presented. In addition, some recent review papers focused on battery degradation models are shortly surveyed. Table 1 shows an overview of selected relevant control-oriented battery degradation models, mainly referring to Li-ion batteries. Electrochemical models are a class of aging models related to the specific phenomena occurring during battery use; they aim at quantifying the impact of aging factors to obtain a reliable description of battery performance evolution [17]. The electrochemical model proposed in [18], usable for any type of lithium-ion battery, integrates the simplified single particle model (SSPM) and reduced-order model (ROM) for predicting solid electrolyte interphase (SEI) growth. It allows a good estimation of battery degradation over time considering the effect of several aging factors (current, SOC, DOD, temperature) on lifetime simulation results. Thanks to its simplified mathematical framework, the model is suitable to be implemented into the optimization framework of stand-alone renewable energy systems. A similar approach is followed in [19], where a capacity-loss ROM for graphite anodes of lithium-ion batteries is developed. Degradation mechanisms described by this model are the capacity loss due to SEI layer growth and the capacity loss due to isolation of active material. The model validation, performed
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Table 1 Synopsis of selected references on control-oriented battery degradation models References Authors Astaneh et al. (2018) [18]
[19]
[16]
[23]
[21]
[22] [24] [20]
[25]
[26]
Considered aging factors Current, SOC, DOD, Ta
Model type Battery chemistry Electrochemical Li-ion – validated on graphite/LiFePo4 Jin et al. (2017) Current, SOC Electrochemical Li-ion – validated on graphite/LiFePo4 Suri and Onori (2016) C-rate, SOC, Ts , Semi-empirical Any – validated Ah-throughput on graphite/LiFePo4 Petit et al. (2016) Current, SOC, Ts , Empirical Li-ion – validated on graphite/LiFePo4 and graphite/NCA Wang et al. (2014) C-rate, Ts , DOD, Semi-empirical Li-ion – validated Ah-throughput on graphite/LiNi1/3 Co1/3Mn1/ 3 + LiMn2 O Han et al. (2014) SOC, DOD Semi-empirical Any –validated on Li-ion Hoke et al. (2014) Ts , SOC, DOD Semi-Empirical Li-ion Guenther et al. (2013) State of Energy Electrochemical Li-ion (SOE), Ta , Time, DoD Wang et al. (2011) Ts , DoD, C-rate, Semi-empirical Li-ion – validated Ah-throughput on graphite/LiFePo4 Millner (2010) DoD, Avg SOC, Physics-based Li-ion Ta
with a lithium iron phosphate (LFP) cathode and graphite anode, demonstrates its ability to predict capacity degradation with a maximum error of 20%. Furthermore, the model computation rate is about 2400 times faster than that of other existing more complex electrochemical models. The control-oriented model proposed in [20] follows an energy-based approach and describes the reduction of the energy storage capability of the battery, accounting for both calendar and cycle aging. The main advantage of this modelling approach with respect to dynamic equivalent circuit models is the possibility to easily adapt the model parameters and to reduce the runtime of simulations. A semi-empirical battery degradation model is given in [16], where the Ah throughput is the factor considered to measure battery life and model identification is done over a dataset related to a hybrid electric vehicle (HEV). The model is intended for implementation in a multi objective control system aiming at minimiz-
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ing battery degradation along with vehicle fuel consumption. The main merit of this work relies in demonstrating that battery aging modeling can be advantageously exploited within system level optimization. A semi-empirical battery life model which inspired various modeling approaches in literature, is established in [21]. The model accounts for both calendar-life loss and cycle-life loss. As for the calendarlife loss, a square root of time relation is used to consider the capacity loss due to the diffusion-controlled lithium corrosion, and an Arrhenius correlation is used to describe the influence of temperature. As for the cycle-life loss, an exponential dependence on C-rate and a linear dependence on time are found. In [22], a practical semi-empirical battery wear model is proposed. It is derived from the achievable cycle count vs. DOD cycle life data. Since the return value of such a model is directly expressed in terms of wear cost, it is suitable to be used, in combination with other criteria, in multi-objective optimizations. An empirical aging model for Li-ion batteries, well suited for system level simulations, has been proposed and validated in [23]. The empirical model is coupled with an electro-thermal model and describes both calendar and cycle battery aging considering SOC, current, and temperature as stress factors. The battery lifetime model proposed in [24] aims at estimating both capacity and power battery degradation in the framework of a method for the optimization of electric vehicles (EVs) charging. The model considers temperature, SOC profile, and daily DOD as aging factors and has been tuned by comparison with a detailed model developed at NREL. This work resorts to one of the most used ways to formulate the cost of battery degradation cbd due to a charge cycle, expressed as: cbd = cb
L L
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where cb is the cost of battery replacement, L is the lifetime degradation evaluated per unit time, and L is the total battery lifetime if the charge cycle is repeated until the battery’s end of life (EOL). The effects of time, temperature, DOD and C-rate are studied in [25] through accelerated cycle-life tests on LiFePO4 batteries. According to the obtained results, the capacity fade is more significantly affected by time and temperature than by DOD for low C-rates; on the contrary, the effect of DOD is stronger for high C-rates. On such a basis, a simple battery life model, accounting for time, C-rate, and temperature and achieving agreement with measured data is developed. Physics-based models capture the physical processes underlying the operation of energy storage devices; thus, they are highly dependent on battery technology [4]. Such models are in principle unsuitable to be used in the framework of an EMS, due to their high computational requirements and implementation complexity. Although most of physics-based battery aging models are based on electro-chemical reactions, an interesting example of control-oriented non-electrochemical physics-based model is found in [26]. Here, the modelling approach considers crack propagation as the dominant mechanism of degradation and expresses the dependence of ion loss on aging factor like DOD, average SOC and temperature by an exponential law
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according to crack propagation theory. The obtained life parameter is related to ion concentration as a function of cycle life. The calculation of this aging parameter makes it possible to assess different usage patterns and charge control strategies. Several review papers focused on battery degradation models have been recently published, as well. In [6], aging models for different technologies, scales, and form factors of electrochemical storage devices are reviewed. Models are grouped by scale into cell, module, and pack-level models; moreover, the importance of using the right modelling approach for each scale is stressed. A review of battery degradation models focusing on plug-in hybrid electric vehicles (PHEVs) integration in smart grids is presented in [10]. Calendar aging effects are deemed non-negligible in PHEVs even when considering vehicle-to-grid (V2G) applications because of the long periods that they spend in parking. The authors of [27] reviews the degradation processes of different battery technologies and the battery monitoring and diagnosis techniques presented in the literature. Battery SOH monitoring methods for applications in smart BMSs are reviewed in [13], where a classification of methods into experimental and model-based estimations is presented and discussed. In [28], different battery degradation models are compared, and their applicability to system and control algorithm design is discussed. The review presented in [29] focuses, in turn, on temperature-dependent electrochemical properties, ageing, and performance of lithium-ion cells. Finally, [30] reviews and compares mechanical and chemical degradation models for Li-ion batteries. It is worth noting that, due the prevalent application of batteries to EVs and PHEVs, most literature contributions on battery degradation models refer to such an application. This paper, instead, is focused on the use of batteries in microgrids; to the best of the authors’ knowledge, a survey on microgrid EMSs including the battery lifetime extension objective has not been presented so far.
3 EMSs Considering Battery SOH Preservation A selection of literature contributions on EMSs considering battery SOH preservation is surveyed in this section. Most of them use battery degradation models described in the previous section. For each contribution, the case study, the considered aging factors, the main features of the EMS, and the used degradation model are identified. Table 2 presents a synopsis of the considered reference papers. Some of the retrieved contributions are focused on residential applications. In [31] an aging-aware model predictive control (MPC) for a building nanogrid, equipped with photovoltaic (PV) generation and battery storage, is developed. The control strategy finds the most economical solution that balances building utility and battery life-cycle costs. The electrochemical degradation model proposed in [19] is used, although suitably approximated to make it convex. A similar case study is investigated in [32] to achieve the best trade-off between battery aging and cost minimization. A nonlinear predictive EMS, performing weighted multi-objective optimization, is proposed, where aging of a second-life battery is modeled according
Authors Cai et al. (2019) Morin et al. (2019) Zia et al. (2019) Soleimani et al. (2019) Cardoso et al. (2018) Bordin et al. (2017) Leonori et al. (2016) Saez-de-Ibarra et al. (2016) Chalise et al. (2016) Sun et al. (2016) Su et al. (2014) Li & Danzer (2014) Khasawneh et al. (2014) Tran et al. (2013) Riffonneau et al. (2011)
Case study Building nanogrid Isolated microgrid Isolated microgrid Microgrid Microgrid Isolated microgrid Microgrid Microgrid Isolated microgrid Building nanogrid Microgrid Building nanogrid Isolated microgrid Microgrid Microgrid
Considered aging factors SOC, charge/discharge power n/s Ta , DoD DoD Cumulative output, time, Ta , E-throughput, cycles, DoD, SOC SOC, current, current derivative DoD DoD, SOC C-rate, Ah-throughput DoD Time, SOC Ta , SOC DoD, number of cycles SOC variation
EMS main features ♦ ♦• ◦ ◦ ◦ ◦ ◦ ♦ • ♦• • ♦ • ♦ •
Aging model [19] [21, 25] [39], Datasheet Datasheet [40, 41] Kinetic battery model n/a Datasheet Weighted throughput model [25] [45] [20] [26] [46] [48]
♦ Control/MPC approach; Optimization approach; • Forecasting-based; ◦ Only scheduling performed (no real-time update)
References [31] [34] [38] [9] [12] [35] [42] [43] [36] [32] [44] [33] [37] [46] [47]
Table 2 Synopsis of selected references on EMS accounting for battery degradation
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to [25]. A simple model of battery calendar aging is used in [33], where several strategies for optimal charge of a PV/battery system, based on a multi-objective formulation and solved by dynamic programming (DP), are proposed and compared. A number of the selected works is focused on the islanded microgrid case study. In [34], a MPC-based EMS that increases battery lifetime is proposed for an islanded microgrid with a PV generator and a hybrid battery-hydrogen energy storage. The method relies on the use of the wavelet neural network as a forecasting model, and includes, among its pursued objectives, the lifetime maximization of battery, electrolyzer, and fuel cell (FC). The authors of [35] develop linear programming-based models that include battery degradation in their formulation. Such models aim at optimizing the energy management of remote off-grid microgrids employing lead acid-batteries by finding out the battery cost/performance balance at which the microgrid operation become economic. A two-layer (schedule and dispatch) EMS for isolated microgrids is proposed in [36], where the battery lifetime cost model is considered with the aim of minimizing battery degradation. In such a paper, the scheduling model is formulated as a multi-objective optimization problem including both minimization of fuel consumption and battery degradation costs. An interesting contribution is found in [37], which refers to an isolated microgrid embracing distributed FCs and batteries to be used in an industrial scenario. The work assesses the battery life extension by a cooperative approach based on the so-called flexible distribution of energy and storage resources (FDERS) framework. FDERS is inspired by the V-shape formation of a flock of birds and realizes a variety of battery life balancing solutions by a ‘virtual’ reconfiguration approach and by controllable frequency/active power droop gains in the distributed generator’s controllers. A second-order cone programmingbased EMS (SOCP-EMS) aimed at minimizing the operating and emission costs of islanded microgrids is proposed in [38]. In such a paper, the economic operation of the microgrid is achieved by including battery degradation cost, derived from [39], in the management algorithm, which leads to a global optimal solution. Another group of EMSs accounting for battery SOH is focused on more general microgrid applications (grid-connected microgrids, multi energy power systems, active distribution networks, etc.). The authors of [9] propose an EMS scheme allowing for the efficient use of batteries in an active distribution network. The battery loss of health (LOH) along the simulation period is determined through the rain-flow cycle counting (RFCC) algorithm, and simulation results show that, when lifetime cost is considered, the batteries operate with a lower C-rate and do not utilize their maximum capacity. This leads to an optimal technical/economical tradeoff with an increase of battery lifetime of about 50%. In [12], the problem of microgrid optimal sizing, considering battery aging, is formulated by a mixed integer linear programming (MILP) approach. To incorporate both calendar and cycle battery aging, the lithium-ion battery capacity loss models proposed in [40, 41] are used. The study allowed to assess optimal capacity and operational patterns for storage units, energy costs savings, and actual use of renewable generation. The EMS proposed in [42] for a grid-connected microgrid is based on a fuzzy logic controller (FLC) optimized by a multi-objective genetic algorithm. It performs the
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maximization of both the profit in trading with the main power grid and the battery SOH. In this paper, the battery SOH is expressed as an index based on counting of how many times SOC, current, and its derivative go out of a safe interval. The authors of [43] compare different firming control strategies for market participation of PV generation and apply RFCC algorithm to get the expected battery lifetime under different management strategies. In [44], the formulation of a stochastic problem for microgrid energy scheduling, considering battery degradation cost [45], is presented. The proposed management strategy allows for the minimization of operational costs and power losses in the problem formulation. The EMS proposed in [46] improves energy efficiency and extends battery lifetime in a microgrid application. The problem is solved by stochastic DP. Moreover, Peukert lifetime energy throughput (PLET) model is proposed by applying Peukert’s law for cycle life and DOD of battery. Finally, [47] proposes a predictive control based on a DP approach, which optimizes power flows in a grid-connected PV/storage system and accounts for battery aging. Here, battery aging cost is associated to SOH variation through battery replacement cost. Furthermore, the SOH is assumed to vary linearly through a coefficient, as defined in [48].
4 Open Issues and Future Directions Microgrids are expected to evolve as flexible, efficient, and reliable systems accommodating multiple distributed generators (DGs) and storage systems and operating in dynamic market scenarios. Despite significant progresses have been achieved in modelling battery storage systems, open challenges still must be tackled. The need for defining physically-based models able to generalize any operating condition, featuring levels of computational efficiency and simplicity that make them suitable for control algorithm development is recognized [28]. As batteries continue growing in technology maturity and ubiquity for distributed energy applications, the assessment of SOH is unavoidable to set up analytical tools to drive system planning and decision making [12]. Further work on the analysis of battery degradation costs at module/pack level is needed to support the design of optimal system-level battery control. Indeed, available manufacturer data on battery SOH degradation are not ideal for predicting the cost of lifetime reductions deriving from given battery cycles [35]; furthermore, module/pack level battery life models developed for particular series/parallel combinations can hardly be adapted in case of different pack configurations [11]. A more effective use of batteries in microgrids under system-level intelligent management is strongly desired also to promote the return to investment for the deployed storage systems. This could enable massive integration of DGs, optimized production and use of energy in industrial factories and residential/commercial buildings, and optimal management of PHEVs. For this to happen, new robust EMSs are necessary to make microgrids evolve toward even higher levels of efficiency and reliability [4].
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5 Conclusions This paper presents a survey of the literature on EMSs providing for prolonged battery lifetime by implementing battery degradation models in their formulation. A selection of technical contributions in the literature on battery degradation models is presented, especially pointing out models that are suitable to be embedded within a control or management algorithm. Then, an overview of the literature on EMSs performing battery SOH preservation in microgrids is given, highlighting their specific peculiarities and main features. Open issues and future directions are finally outlined. Acknowledgements This research was funded by Italian Ministry of University and Research (MUR) grant number 2017WA5ZT3_004, program PRIN2017, project HEROGRIDS.
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Impedance Modeling for Multichannel EIS in Industrial Scale Vanadium Redox Flow Batteries Andrea Trovò, Walter Zamboni, and Massimi Guarnieri
Abstract The work provides early results obtained with a multichannel EIS system, which were used to identify an equivalent circuit of an Industrial Scale Vanadium Redox Flow Battery (IS-VRFB) stack with a rated power/energy of 9 kW/27 kWh. The single cell impedance is represented with three different models, including a series resistance and an RC loop (RRC model), or a constant phase element (CPE) loop (a ZARC element), or a ZARC element including also a Warburg impedance. The inclusion of the CPE constitutes a substantial improvement in the fit. Conversely, the addition of the Warburg element, which aims to model the mass transfer in the electrochemical process, does not produce significant effects for the frequencies at which we have experimental data. This numerical results are validated against EIS measurements taken on IS-VRFB. Very few analyses of this type are reported in the literature for such batteries. This study set the stage for developing advanced online State of Health (SOH) management for IS-VRFB.
1 Introduction Covering the entire global energy needs by using only renewable sources is not a simple challenge. To do this, it is necessary to have a flexible and efficient electricity transmission and distribution grid. Unlike traditional power plants, energy sources such as wind, sun and other renewable sources are intermittent because they generate electricity based on weather and climate availability [1]. The variability of energy
A. Trovò () · M. Guarnieri Department of Industrial Engineering, University of Padua, Padova, Italy Interdepartmental Centre Giorgio Levi Cases for Energy Economics and Technology, University of Padua, Padova, Italy e-mail: [email protected]; [email protected] W. Zamboni Dipartimento di ingegneria dell’Informazione ed Elettrica e Matematica applicata (DIEM), Università degli studi di Salerno, Fisciano, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_37
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passes from the hourly scale linked to the daily solar irradiation during the year, typical of photovoltaic systems, up to the minimum time scale characteristic of wind generators, susceptible to rapid climatic variations. For this reason, it is essential to pay attention to the design of electrical grids, which become unstable if the power of these intermitted energy sources exceeds 30% of the entire amount of power generated without adequate compensatory measures, i.e. without adequate energy storage [2]. Regarding the different technologies that can be used for energy storage, Redox Flow Batteries (RFBs) have proved to be a competitive solution. These types of batteries use liquid electrolyte to store electrical energy in the form of chemical energy. This conversion occurs due to redox reactions that take place inside the battery. Among RFBs, the all-Vanadium Redox Flow Batteries (VRFBs), presented in 1985 by Skyllas-Kazacos and coworkers of the University of New South Wales (UNSW) [3], are the most promising type. By using the same electrolyte for the positive and negative polarity, the VRFBs do not present crosscontamination problems that instead have been detected in batteries with redox pairs formed by different elements, such as: vanadium-bromine, zinc-bromine and hydrogen-bromine. The possibility of storing the fluid in separate tanks eliminates the problem of self-discharge. Room temperature and low pressure provide VRFBs with a high intrinsic safety. Indeed, the electrolyte, only needs a circuit consisting of pumps, polymeric pipes and cheap canisters [4]. As a result, some interesting features which make this technology particularly promising are the scalability, high cycle efficiency, very long lifecycle, rapid response and low environmental impact [5]. Electrochemical impedance spectroscopy (EIS) is largely used to investigate various types of properties and degradation phenomena occurring in electrochemical systems [6]. Regarding the use of EIS in RFBs, most published works are limited to studies of small single cells in the laboratory and, at the best of the authors knowledge, the direct use of this technique on pilot plants has only been explored. Trovò et al. aimed to reduce this lack by describing results obtained on a multichannel EIS on an Industrial-Scale VRFB (IS-VRFB) with a power/energy rating of 9 kW/27 kWh in [7]. In this case, power and signal connections, whose stray parameters affects measurements, required a careful optimization and calibration for the implementation of the measurement chain. The early results obtained with an EIS analyzer were used to identify an equivalent circuit of the whole stack, in which each cell is represented with a dynamic Thévenin equivalent, whose impedance is the series of a resistor and an RC loop, namely RRC impedance. This paper proposes an extension of the results published in reference [7], in which enhanced impedance models are analyzed. First, the capacitor in the RRC impedance is replace by Constant Phase Element (CPE) to implement the so-called ZARC loop, and then the Warburg element is connected in series to the charge transfer resistor. The inclusion of the CPE should constitute a substantial improvement in the fit, as it happens in small-scale RFBs [8]. To our knowledge, these are the first dynamic equivalent circuits of a whole stack which have been validated against EIS measurements taken on a real industrial-scale VRFBs. In these experiments, a multichannel measurement was carried out, which can be important in VRFB stacks, because it is capable
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of detecting imbalances and simultaneous misfeeding and of giving information on the design of the cells geometry [9]. It was found that the last cells of the stack were affected by insufficient flow at high power which compromized their performance. A continuous monitoring of the EIS measurements and the analysis of their evolution may allow one to detect the State of Health (SOH) of a VRFB and constitute a valuable application of the method [10].
2 Background A VRFB uses vanadium ions dissolved in sulfuric acid solution, which undergo the following electrochemical reactions in the electrochemical cell [11]: Positive electrolyte: − + 2+ + 2H2 O E0 = 0.99 V VO+ 2 + e + 2H → VO
(1)
Negative electrolyte: V2+ –e− → V3+
E0 = –0.26 V
(2)
2+ stored The battery charge level is directly linked to the percentages of .VO+ 2 and V in the tanks [12]. The reactor, or stack, is formed by a series of cells. Each of them contains two porous electrodes where the liquid electrolytes flow and a separator, which allows the diffusion of ions to balance the charge between the two half-cell. However, the separator is impermeable to electrons which are thus forced to flow in an external circuit supplying electric current. The voltage and the power of the system are related to the number of cells and the size of their active area. Piping circulate the liquid electrolytes between the stack and tanks to charge/discharge the battery according to Eqs. (1) and (2), being their flow rate modulated by two pumps and controlled by a system of valves.
3 The Experimental Set Up 3.1 Industrial-Scale VRFB The IS-VRFB test facility is a kW-class VRFB, where 9-kW power conversion is provided by a stack of 40 cells connected hydraulically in parallel, by means of internal manifolds, and electrically in series by means of Bipolar Plate (BP) interposed between cells [13].
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The cells have an active area of 600 cm2 and use two 5.7-mm thick (after compression) graphite felt as electrodes (produced by Beijing Great Wall, China) ® and a Nafion 212 membrane as separator. The electrolytes, or solutions, consist of 1.6 M vanadium ion dissolved in 4.5 M sulfuric acid. Two tanks 550 + 550 L of solutions which store the rated energy of 27 kWh (Fig. 1). Two centrifugal pumps, driven by induction motors whose ac brushless motors are controlled by two inverters on a PID feedback basis, circulate the solutions to match the required flow rates. The system is equipped with level sensors, differential pressure gauges, flowmeters and Resistance Temperature Detectors (RTDs). Two current probes measure the stack current, 41 voltage pick-ups detect the cell voltages, and a wattmeter measures the power supplied to the pump inverters. Power conditioning during charge/discharge is provided by the power conditioning system (PCS) unit, which consists of a two-quadrant ac/dc static converter rated ±75 A and 0–85 V. The operation of the PCS and pumps is controlled by the Flow Battery Management System (FBMS), based on the programmed operation and the State of Charge (SOC) [14].
3.2 Experimental Measurements EIS measurements were carried out with a dedicated multichannel EIS analyzer (MMulty SP by Materials Mates Instruments, Italy) that could ideally work in a frequency range f = 0–100 kHz [7]. Twenty cells have simultaneously been tested. The wiring diagram of the stack and the EIS analyzer used in these tests are schematized in Fig. 2. A real-time control system monitors and controls the EIS measurements. The core of the EIS analyzer consists of a waveform generator and a frequency response analyzer. It can work both in galvanostatic mode (i.e. as harmonic current source) or in potentiostatic mode (as harmonic voltage generator). Galvanostatic-mode stimuli i m (ω) at angular frequency ω = 2π f were added to a common bias dc load current I b . In each measurement sequence I b was kept constant to set the operating point of the cell where the EIS analysis was performed, while the frequency was varied in an array of values within a selected range. In these kind of measurements, stray parameters, such as inductance and resistance wiring, affect the measurements and make the procedure quite challenging to implement, particularly at high f. In our case, the size of the stack required long measurement connections which suffered from substantial electromagnetic interference (EMI). In addition, high bias currents, which were needed to study the behavior at high power, generated not negligible conducted disturbance. All such issues resulted in much more difficult optimization issues in comparison with small single cell experiments.
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Cells voltage sensors
Volumetric flow meter
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Differential pressure transmitter
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Fig. 1 IS-VRFB test facility and its main components: hydraulic circuits, stack, tanks, instrumentation: F1, F2: positive/negative electrolyte flow-meters, L1/L2: positive/negative electrolyte level sensors, DP1/DP2 positive/negative electrolyte differential pressure gauges. T1/T3: positive/negative electrolyte input temperatures, T2/T4: positive/negative electrolyte output temperatures, P1/P2 positive/negative electrolyte pumps, FBMS and PCS
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Fig. 2 Equivalent electric circuit of the multichannel EIS measurements equipment on IS-VRFB stack
4 Results and Discussion Figure 3 shows three impedance models for each single RFB cell [15]. The simplest one, called RRC and shown in Fig. 3a, has already been used in [7] for a multichannel EIS analysis. Its graph in the Nyquist plane is an half-circumference arc whose diameter is equal to the resistance Rat . Although the fitting achieved in [7] are good, the shape of the fitting arc yields real-axis intercepts far from the experimental ones. In order to improve the fit, the linear capacitor Cdl in Fig. 3a mainly representing the double layer effect, is replaced by a CPE (Fig. 3b, c), whose impedance is given by: −1 Z˙ (ω) = Y (j ω)n ,
(3)
where j is the imaginary unit, and Y and n are the fitting coefficients of the CPE. In particular, Y is the numerical value of the admittance (1/|Z|) at ω = 1 rad s1 . When n = 1, this is the equation for the impedance of a capacitor with capacity equal to Y. The R-CPE loop in Fig. 3b is often called ZARC element. Its response in the Nyquist plane is a depressed arc that is expected to better fit EIS data [8]. This may improve the fitting results both in terms of error as well as of the displacement of the fitted real-axis intercepts, as shown for instance in [16]. For an additional improvement of the model, the so-called Warburg impedance is connected in series to Rat in the ZARC loop (Fig. 3c) to investigate whether an arc rectification in the low-frequency region of the plot can help to improve the fit. The latter is named ZARC+W.
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Case 1 Case 2 Case 3 Case 4 Case 5
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The EIS tests were performed in five selected RFB operating conditions, by varying the battery SOC, electrolyte flow rates Q and stack bias current Ib , whose parameters are summarized in Table 1. The fitting procedure is performed in Matlab by using the Zfit function, which was specifically developed to fit complex impedance data [17]. In order to evaluate the quality of the fitting results, the Root Means Squared Error (RMSE) between fitted data and experimental results was computed. The results of the fitting procedure in Cases 1, 2, and 4 are plotted in Figs. 4, 5, and 6, respectively. In all figures, the black markers indicate the experimental data, the black solid line the RRC fitting curve, the blue arc the ZARC fit, and the red markers the ZARC+W fit. In Figs. 4 and 5, the fit with enhanced models almost coincide. The main difference
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Fig. 5 Impedance plot Case 2
Fig. 6 Impedance plot Case 4
between the enhanced ZARC and ZARC+W is achieved in Case 4 (Fig. 6), where a low-frequency tail on the right-hand side is present for the ZARC+W fit. It is worth noticing that, in this Case 4, such a result could be ascribed to the low frequency noise, whose level is higher than in the other cases. The RMSE values achieved by using the three proposed models in all experimental cases are shown in Table 2. They clearly shows that the use of a ZARC-based impedance model reduces the RMSE in all cases considered. In some of them, the improvement exceeds a 50% reduction. Conversely, no valuable improvement can be ascribed to the use of the Warburg impedance, whose inclusion seems not to
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Table 2 Root mean squared error RMSE of the fitting procedure Parameter RRC (µ) ZARC (µ) ZARC with (µ) Warburg (%)
Case 1 180 80.5 (−55%) 80.5 (−55%)
Case 2 171 120 (−30%) 120 (−30%)
Case 3 188 173 (−8%) 173 (−8%)
Case 4 83.4 82.7 (−1%) 80 (−4%)
Case 5 139 94 (−32%) 93.2 (−33%)
be necessary. The improvement of the fit yields a valuable change in the resistance values from RRC model to ZARC. Thanks to the change in the shape of the arc, the ohmic resistance R0 , which represents the high-frequency intercept of the fitting curve with real axis, decreases, while the charge transfer resistance Rat increases. In addition, experimental and numerical investigations in steady-state conditions where developed by Guarnieri et al. in [18], revealing that the major contribution to Ro , i.e. at least 70%, is due to the electrodes soaked with electrolytes, while the membrane contributes for about 20%, and the graphite bipolar plates for the remaining 10%. Conversely, the non-linear resistance Rat takes into account the activation and concentration overpotentials only dependent on the cell current, SOC and electrolyte flow rate Q.
5 Conclusions This study presents a characterization of a real 9 kW/27 kWh VRFB stack resorting to experimental data from a multichannel EIS analyzer. Early results on the cell passive elements identification by means of a numerical optimization procedure were presented. With the aim of investigating how transport losses affect the circuit parameters, several tests were performed at different operating conditions in terms of battery SOC, electrolyte flow rates and stack current. Three impedance models were evaluated: RRC model, ZARC model including CPE, ZARC+W model with a further Warburg impedance. The inclusion of the CPE provides a substantial improvement in the fit. Conversely, the addition of the Warburg element, which typically aims to model the mass transfer in the electrochemical process, does not produce significant effects for the frequencies at which experimental data were obtained. Building on the methodology here presented, advanced online state of health monitoring of industrial scale flow batteries can be developed and implemented. Acknowledgements The work was supported by funding from the project “Gridoptimized vanadium redox flow batteries: architecture, interconnection and economic factors” (GUARRICERCALASCITOLEVI 20-01) funded by the Interdepartmental Centre Giorgio Levi Cases for Energy Economics and Technology of University of Padua within its 2019 Research Program, from the project “Holistic approach to EneRgy-efficient smart nanOGRIDS – HEROGRIDS” (PRIN
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2017 2017WA5ZT3) within the Italian MUR 2017 PRIN program and from the University of Salerno FARB funds.
References 1. M. Ourahou, W. Ayrir, B. EL Hassouni, A. Haddi, “Review on smart grid control and reliability in presence of renewable energies: Challenges and prospects”, Mathematics and Computers in Simulation, Vol. 167, pp. 19–31, 2020. 2. A.Z. Weber, M.M. Mench, J.P. Meyers, P. N. Ross, J. T. Gostick, Q. Liu “Redox flow batteries: a review”, Journal of Applied Electrochemistry, Vol. 41, 1137, 2011. 3. M. Skyllas-Kazacos, “Performance improvements and cost considerations of the vanadium redox flow battery”, ECS Transactions, Vol. 89 (1–2), pp. 29–45, 2019. 4. L.F. Arenas, C. Ponce de León, F.C. Walsh, “Engineering aspects of the design, construction and performance of modular redox flow batteries for energy storage”, Journal of Energy Storage, Vol. 11, pp. 119–153, 2017. 5. A. Trovò, V. Di Noto, J. E. Mengou, C. Gamabaro, & M. Guarnieri, “Fast response of kWclass vanadium redox flow batteries”, IEEE Transactions on Sustainable Energy, Vol. 12, pp. 2413–2422. 6. J. Huang, Y. Gao, J. Luo, S. Wang, C. Li, S. Chen, J. Zhang, “Editors’ Choice Review— impedance response of porous electrodes: Theoretical framework, physical models and applications”, Journal of Electrochemical Society, Vol. 167, 166503, 2020. 7. A. Trovò, W. Zamboni, M. Guarnieri, “Multichannel Electrochemical Impedance Spectroscopy and equivalent circuit synthesis of a large-scale vanadium redox flow battery”, Journal of Power Sources, Vol. 493, 229703, 2021. 8. Y. Li, J. Bao, M. Skyllas-Kazacos, M. P. Akter, X. Zhang, J. Fletcher, “Studies on dynamic responses and impedance of the vanadium redox flow battery”, Applied Energy, Vol. 237, pp. 91–102, 2019. 9. J. E. Mengou, A. Trovò, C. Gambaro, M. Guarnieri, “A vanadium redox flow battery bracing the pilot microgrid at Eni Renewable Energy & Environmental R&DCenter,” 22nd IEEE International Conference on Industrial Technology (ICIT), pp. 298–303, 2021. 10. W. Zamboni, G. Petrone, M. C. Di Piazza, É. Monmasson, and B. Robyns, “Special Issue ELECTRIMACS 2019 ENERGY Modelling and computational simulation for control and diagnosis in renewable energy systems, energy storage, innovative devices and materials”, Mathematics and Computers in Simulation, Vol. 183, pp. 1–4, 2021. 11. N. Roznyatovskaya, J. Noack, H. Mild, M. F¨uhl, P. Fischer, K. Pinkwart, J. T¨ubke, M. SkyllasKazacos, “Vanadium Electrolyte for All-Vanadium Redox-Flow Batteries: The Effect of the Counter Ion”, Batteries, 5, 13, 2019. 12. A. Trovò, M. Guarnieri, “Standby thermal management system for a kW-class vanadium redox flow battery”. Energy Conversion and Management, Vol. 226, 113510, 2020. 13. A. Trovò, P. Alotto, M. Giomo, F. Moro, M. Guarnieri, “A validated dynamical model of a kW-class Vanadium Redox Flow Battery”, Mathematics and Computers in Simulation, Vol. 183, pp. 66–77, 2021. 14. A. Trovò, M. Guarnieri, “Battery management system with testing protocols for kW-class vanadium redox flow batteries,” 2nd IEEE International Conference on Industrial Electronics for Sustainable Energy Systems (IESES), pp. 33–38, 2020. 15. W. Zamboni, “Eis diagnostics for fuel cells/vrfbs,” Reference Module in Earth Systems and Environmental Sciences, Encyclopedia of Energy Storage, Elsevier, https://doi.org/10.1016/ B978-0-12-819723-3.00107-4, 2021. 16. W. Zamboni, G. Petrone, G. Spagnuolo, D. Beretta, “An Evolutionary Computation Approach for the Online/On-Board Identification of PEM Fuel Cell Impedance Parameters with A Diagnostic Perspective,” Energies, Vol. 12, 4374, 2019.
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17. Jean-Luc Dellis (2022). Zfit Online available at: https://www.mathworks.com/matlabcentral/ fileexchange/19460-zfit, MATLAB Central File Exchange. Accessed 24th Jan. 2022. 18. M. Guarnieri, A. Trovò, F. Picano. “Enhancing the efficiency of kW-class vanadium redox flow batteries by flow factor modulation: An experimental method” Appl Energy, Vol. 262, 114532, 2020.
Numerical Assessment of Cooling Systems for Thermal Management of Lithium-Ion Batteries Girolama Airò Farulla, Davide Aloisio, Valeria Palomba, Andrea Frazzica, Giovanni Brunaccini, and Francesco Sergi
Abstract Lithium-ion batteries have the advantages of high energy density, high charge-discharge efficiency, low self-discharge effect and long cycle life that make them suitable in both stationary and mobile applications. They are the most widely used solution in the field of electric vehicles and are increasing their application for stationary applications. Both the life-time and performances are negatively affected by high temperatures so the prevision of the thermal behaviour is a crucial step in the battery modelling. Based on an experimental setup, a simplified thermal model was developed to estimate the surface temperatures of a lithium titanate cell from current and voltage measurements. ® The model was implemented in the COMSOL Multiphysics Finite Element code. Charge and discharge cycles of the cell were performed and the predicted heat generation used as input of the thermal model. The calibrated model was lastly used to assess two thermal battery management (TBM) cooling systems, in this case applied to a single cell: a passive phase change material (PCM) system and a hybrid PCM/water system. The effects of the PCM thickness and velocity inlet of the water on the cell temperature were investigated. Results showed that, in comparison to the passively air cooled cell, both systems decreased the maximum surface temperatures, thus improving the uniformity of the temperature distribution and keeping the battery in a safe temperature range.
1 Introduction Lithium-ion batteries (LiBs) have several advantages, i.e., high energy density, high charge-discharge efficiency, low self-discharge effect, long cycle life that make them suitable in applications aimed at the clean energy transition [1].
G. A. Farulla () · D. Aloisio · V. Palomba · A. Frazzica · G. Brunaccini · F. Sergi Consiglio Nazionale delle Ricerche, Istituto di Tecnologie Avanzate per l’Energia “Nicola Giordano”, salita S. Lucia sopra Contesse, Messina, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_38
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Nowadays lithium-ion batteries have the dominant share among the rechargeable batteries [2]. Their use in electric vehicles (EV) could further increase their market share in the rechargeable batteries [3]. The operating temperature is a crucial parameter that can negatively affect the working performance of a LiB and its useful life. The heat balance between the cell dissipated and generated heat amount addresses the operating temperature of a battery. When a cell is heated above a certain threshold temperature, the rising overheating accelerates the chemical reactions, rather than the desired galvanic reactions, causing thermal runaway. TBM systems play a key role in safely temperature control (20–60 ◦ C) [4]. In literature, several TMB systems are proposed including air cooling, liquid cooling, phase change material based passive cooling and hybrid PCM/liquid configuration [5]. Many aspects of TBM have been theoretically and experimentally studied [6–9]. In literature, Computational Fluid Dynamic (CFD) is among the approaches utilized to achieve accurate and detailed results for modeling the temperature distribution of Lithium-ion batteries. Gumussu et al. [10] developed a fully predictive thermal model to investigate the thermal behaviour of lithium-ion batteries under natural convection. Thermal distribution was estimated only during discharge process and only using electrical parameters. The thermal dissipation of the battery was modelled using the wellknown heat generation model of Bernardi et al. [11]. Wang et al. [12] proposed a simplified CFD model of an air cooled lithium ion battery module to simulate the temperature field and flow field of the battery module in different inlet directions. Falcone et al. [13] employed a CFD approach to discuss TBM cooling methods with a focus on the comparison between air-cooling systems and liquid-cooling systems. In this paper, a simplified thermal model was developed to simulate a PCM-based passive cooling system and a hybrid PCM/water system. The model was validated with experimental data on charge and discharge cycles. This paper builds upon such existing literature and proposes different solutions, in terms of materials and hybrid systems, for the TBM under high current operating conditions.
2 Methodology A numerical model was developed to investigate the thermal distribution of a Li-ion battery based on the experimental charging/discharging tests carried out at CNR® ITAE. The numerical model was implemented in a COMSOL Multi-physics Finite Element code. A schematic of the geometry of the model is shown in Fig. 1.
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Fig. 1 Schematic of the model. (a) PCM/water cell Table 1 Main features of the tested cell
Table 2 Physical properties of the material battery
Nominal capacity Nominal voltage Dimensions
23 Ah 2.3 V W116 × D22 × H106 mm
ρ [kg/m3 ] λ[W/(m K)] cp[J/(kg K)]
Casing 1991 12 2138
PCM 778 0.151 2000
Water 1000 0.6 4186
The cell characteristics are listed in Table 1. In Table 2, material physical properties density ρ, thermal conductivity λ, and specific heat capacity (Cp) are reported [10, 14]. The following modeling assumptions has been made: • • • • •
The physical properties do not change with temperature variations; The properties of the PCM are equal for both solid and liquid phases; Heat exchange by radiation is negligible; Heat transfer inside the liquid PCM is dominated by conduction; Negligible thermal contact resistance between two different layers;
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Uniform heat source (battery heat dissipation); Convective heat flux condition on the outside of the cell; Newtonian fluid and no slip conditions on the walls in contact with the fluid; Laminar flow; The input parameters of the thermal model are determined from transient charging/discharging cycles of the cell.
During charging/discharging cycles, the cell dissipates heat generated by the complex electro-chemical processes taking place. In this work, the heat generated into the cell, Qbat [W], was estimated with the equation of Bernardi et al. [11]: Qbat = i (OCV − V ) − i T
d OCV dT
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Qrev = i T
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U (V) 120 150 160 165 170 175
Each substation current must respect the standard CEI1 46, namely I < In in steady state, I < 1.5 In for 2 hours and I < 3In for 1 minute. Lastly, the ground/rail potential difference must remain below the safety limits defined in the standards NF F 60–100 or NF EN 50163 (Table 2).
4 Optimization Method NSGA II 4.1 Problem Characteristics and Optimization Method Choice The optimization problem we are dealing with is characterized by discrete and continuous variables, by a nonlinear black-box model, constraints on the input and output of the model, and possibly antagonistic objectives. As we are interested in the compromise between these objectives, we need an optimization method based on the notion of Pareto dominance [5] and the non-dominated sorting genetic algorithm (NSGA-II) appears to be well suited [6, 7]. Genetic algorithms [8] are heuristic methods based on a population of individuals. Each individual corresponds to a point of the search space and is characterized by a chromosome. A chromosome is a set of genes, each one coding a feature of the individual. The population evolves from one generation to the next through selection, crossover and mutation operators. Selection is based on non-dominated sorting and keeps the best individuals while crossover and mutation generate new individuals in order to explore the search space. The next section explains how NSGA-II is implemented for our sizing problem: the genes are defined, as well as the crossover and mutation operators.
4.2 Genetic Algorithm Elements: Chromosome and Genes Individuals are points of the search space and their chromosome contains the genes corresponding to the different optimization variables. In our problem, the maximum number of each type of device (substations, feeders, equipotential connections) is specified in the problem formulation. The chromosome contains a fixed number of genes, enabling to code the information needed for the maximum number of devices.
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Fig. 3 Chromosome and genes of an individual
Each gene contains information about a specific device, this information being either a technical one or an indicator of non-existent device. As an example, Fig. 3 shows the chromosome and the genes for a problem with a maximum number of 4 substations, 8 equipotential connections and 3 feeders. Gene#1 contains the position of SST#1. Gene#4 contains the position of SST#4, if SST#4 exists. Gene#13 and gene#14 contain the positions of the ends of feeder#1, if feeder#1exists.
4.3 Crossover Operator The crossover operator creates an offspring from two parents randomly chosen in the mating pool [6, p. 89–90]. First, one of the parents is duplicated. Then, a gene of the offspring is randomly selected and updated with a new value calculated by a weighted average between the values of the parents’ gene, based on the fitness value of each parent. If the selected gene is non-existent, the operator randomly selects another one. Offspring that violate one of the problem constraints are attributed a very bad fitness score so that they will be eliminated at the next generation.
4.4 Mutation Operator The mutation operator is designed to increase the diversity of the population in order to avoid individuals trapped in local minima [6, p. 91–93]. First, an individual randomly selected in the mating pool is duplicated. Then one of his genes is randomly chosen and set to a new random value (including non-existent device).
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4.5 Influence of the Hyper-Parameters The quality of an offspring generation directly depends on the NSGA-II hyperparameters: mutation and crossover rates, population size and number of generations. The crossover (resp. mutation) rate defines the percentage of offspring created by crossover (resp. mutation) in a new generation. In the present work, offspring are generated either by crossover or mutation, so that the sum of the crossover and mutation rates is 100%. If the population size is small, the search space is poorly sampled and lacks diversity. This can lead to premature convergence towards a local minimum. On the other hand, a too large population may unnecessarily increase the computation time. The number of generations should be large enough to allow sufficient exploration of the search space, but again, a too large number may lead to unnecessary computation if the population does no longer evolve. The total number of evaluations of the model is the product of the population size by the number of generations, divided by 2 since 50% of the individuals are passed from one generation to the next. The next section presents the results obtained for a simple test case.
5 Results 5.1 Test Case For the test case we choose a 5 km bi-directional line, with a stop at each end, a +5% slope along the first 500 m and −5% slope along the last three kilometers (Fig. 4). The traffic consists of tramways departing every 6 minutes in each direction. Figure 5 shows (simulation result) the position and the traction power variations over time for a single tramway, traveling in one direction: the tramway accelerates, then moves at constant speed and finally decelerates. The maximum number of substations and equipotential connections are set to 5 and 1 respectively and there is no feeder. Hence, the individual chromosome contains six genes (Fig. 3), each one coding the position or the nonexistence of the corresponding device.
Fig. 4 Line profile and train traffic
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Fig. 5 Position and traction power time profile of a single tramway. All streetcar traveling in the same direction have the same profile, with a 6 mn shift
The two objective functions, cost and voltage security margin, have been described in Sect. 3.2. There is no position constraint and the electrical constraints are those described in Sect. 3.3.
5.2 Choice of the Hyper-parameters A parametric study was carried out in order to adjust the hyper-parameters of the algorithm. The necessity of a good initialization of the starting population, mixing empirical engineer knowledge and random choices, was also highlighted. The first step of the parametric study is to determine a good population size. All the other hyper-parameters being kept constant, the population size has been increased until a value that guarantees the convergence is obtained. For this example, a population of 100 individuals is large enough to obtain good convergence results. Starting population can be initialized using both random sampling or engineering rule of thumb. For instance, distance between successive substations is generally about 1.5–2 km depending on the traffic. The influence of the initialization was studied by comparing optimization processes starting with random initial population or a combination of random sampling and engineer knowledge. The later accelerate convergence as it enhances the number of viable individuals in the initial population. The second step of the parametric study is to assess the influence of the mutation rate, for a fixed population size Npop = 100. We have first tested constant mutation rates of 5%, and 10%. Then we have tested a dynamic mutation rate, as proposed in
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Table 3 Example of results of the parametric study, for Npop = 100 Mutation rate Fixed rate: 5% Fixed rate: 10% Dynamic rate: 0→100% Dynamic rate: 0→100%
Population initialization Random Random Random Knowledge + random
Maximum number of generations to reach convergence 500 No convergence 300 200
[9]: the mutation rate linearly increases from 0% at the first generation to 100% at the last one. Our test confirm that the dynamic rate improves the convergence. At this stage, we characterized the convergence by the reproducibility of the results with ten different runs and by the consistency of these results with the ones intuitively expected on this simple example. Table 3 reports some of the results of the parametric study that leads the following hyper-parameters for the considered test case. For this example, the best combination is a dynamic mutation rate with an initialization of the first generation with the half of individuals generated completely randomly and the rest generated based on engineer knowledge. We noticed that reproducibility of the optimization results can be reached with 200 generations.
5.3 Results Figure 6 shows results in the objective space. It represents the non-dominated individuals at each generation. Each point represents an individual that was nondominated at some point of the evolution process. The crosses represent the empirical Pareto frontier at the last generation. The color indicates at which generation the individual appeared. We can easily see that the performances of the non-dominated solutions constantly improve throughout generations. We also notice that the individuals of the final Pareto frontier appeared after the 60th generation. For better readability, the graph has been split into four parts. Each subgraph focuses on a group of individuals with the same number of substations (2, 3, 4 or 5). These groups do not overlap because the investment costs are very different for 2, 3, 4 or 5 substations. One should notice that the horizontal scales are slightly different. The behaviors of the solutions are quite different for 2 and 3 substations. In the case of 2 substations, the voltage margin is much more sensitive to the cost than in the case of 3 substations. The decision maker can either choose a solution with 2 substations and a low voltage margin, or a solution with 3 substations and a more comfortable voltage margin. This result is consistent with the engineer experience, but Fig. 6 provides quantified information to support this choice. In the next figures, we analyze the evolution of the non-dominated individuals in the solution space. To avoid overloading figures, we focus the analysis on the nondominated individuals with 2 substations. Figures 7 and Fig. 8 respectively show the
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Fig. 6 Non-dominated individuals in the objective space, for each generation. The crosses represent the empirical Pareto frontier at the last generation. The other points represent individuals that were non-dominated at some point of the evolution
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evolution of the substations and the positions of the equipotential connections. The points color indicates the cost. We notice the evolution of the devices position and the decrease of the total cost as the selection process progresses. Figure 9 plots the best scores of each objective, among the non-dominated individuals with 2 substations. The improvement mainly takes place during the first generations and until the 125th generation. As very close results were obtained for ten different runs, we are confident that the algorithm has converged.
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Fig. 8 Non-dominated solutions with 2 substations: evolution of the equipotential position. The points color indicates the cost (MA C)
Fig. 9 Non-dominated solutions with 2 substations: evolution of the best objective values
6 Conclusion The first optimization results are consistent with a trial and error approach. The Pareto fronts provide objective information on the possible trade-offs between cost on the one hand and power feeding quality on the other hand. The use of a simple example with a few optimization variables makes it possible to validate the tool with results that can be intuitively found. Obtaining the same results with ten different runs consolidates our confidence in the optimization results. The next step will be to apply this method to a more realistic and complex case.
References 1. M. Soler, J. López, J. M. Mera Sánchez de Pedro, et J. Maroto, « Methodology for Multiobjective Optimization of the AC Railway Power Supply System », IEEE Transactions on Intelligent Transportation Systems, vol. 16, no 5, p. 2531–2542, oct. 2015, https://doi.org/10.1109/ TITS.2015.2412460.
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2. T. Capuder, L. Lugaric, J. Brekalo-Strbic, et S. Krajcar, « Optimizing the train power system in Zagreb », in 2009 IEEE Vehicle Power and Propulsion Conference, sept. 2009, p. 41–45. https:/ /doi.org/10.1109/VPPC.2009.5289872. 3. R. Vial, « Vers un dimensionnement optimal structure-commande de système multiconvertisseurs.: Application aux réseaux de tramways », Thèse, Université de Grenoble, 2012. [En ligne]. Disponible sur: https://tel.archives-ouvertes.fr/tel-00734684 4. B. Desjouis, G. Remy, F. Ossart, C. Marchand, J. Bigeon, et E. Sourdille, « A new generic problem formulation dedicated to electrified railway systems », in 2015 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles (ESARS), Aachen, Germany, mars 2015, p. 1–6. https://doi.org/10.1109/ESARS.2015.7101437. 5. K. Deb et H. Gupta, « Searching for Robust Pareto-Optimal Solutions in Multi-objective Optimization », in Evolutionary Multi-Criterion Optimization, vol. 3410, C. A. Coello Coello, A. Hernández Aguirre, et E. Zitzler, Éd. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005, p. 150–164. https://doi.org/10.1007/978-3-540-31880-4_11. 6. K. Deb, Multi-objective optimization using evolutionary algorithms. Wiley, 2001. 7. K. Deb, S. Agrawal, A. Pratap, et T. Meyarivan, « A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II », in Parallel Problem Solving from Nature PPSN VI, vol. 1917, M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J. J. Merelo, et H.-P. Schwefel, Éd. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000, p. 849-858. https:/ /doi.org/10.1007/3-540-45356-3_83. 8. M. Mitchell, An Introduction to Genetic Algorithms. The MIT Press, 1998. https://doi.org/ 10.7551/mitpress/3927.001.0001. 9. A. Hassanat, K. Almohammadi, E. Alkafaween, E. Abunawas, A. Hammouri, et V. B. S. Prasath, « Choosing Mutation and Crossover Ratios for Genetic Algorithms—A Review with a New Dynamic Approach », Information, vol. 10, no 12, Art. no 12, déc. 2019, https://doi.org/10.3390/ info10120390.
A Comparative Study of Existing Approaches for Modeling the Incident Irradiance on Bifacial Panels Soufiane Ghafiri, Maxime Darnon, Arnaud Davigny, João Pedro F. Trovão, and Dhaker Abbes
Abstract Accurate modeling of bifacial module energy production is conditioned to the correct modeling of the front and rear irradiance. This paper compares the existing approaches used to estimate the incident irradiance on the back side and the front side of a photovoltaic (PV) bifacial module, by studying the performance of each model in terms of accuracy and computation time. In this study, we have selected three software with different approaches. We started with Bifacial_radiance which uses the ray-tracing technique. The second software is Sandia model which is a three-dimensional implementation of view factor method under MATLAB™. We complete our study with pvfactors that employs a two-dimensional configuration factor model. This study aims to propose the most time-efficient way to compute the irradiances received by bifacial panels, which will serve to predict the energy production of power plants. Having a fast model allows to develop efficient realtime management strategies for power supply systems that use bifacial modules.
S. Ghafiri () University of Lille, Arts et Metiers Institute of Technology, Centrale Lille, Junia, ULR 2697 – L2EP, Lille, France Institut Interdisciplinaire d Innovation Technologique (3IT), Université de Sherbrooke, Sherbrooke, QC, Canada e-mail: [email protected] M. Darnon Laboratoire Nanotechnologies Nanosystèmes (LN2) – CNRS UMI-3463 Institut Interdisciplinaire d Innovation Technologique (3IT), Université de Sherbrooke, Sherbrooke, Québec, Canada e-mail: [email protected] A. Davigny · D. Abbes University of Lille, Arts et Metiers Institute of Technology, Centrale Lille, Junia, ULR 2697 – L2EP, Lille, France e-mail: [email protected]; [email protected] J. P. F. Trovão e-TESC Lab, Université de Sherbrooke, Sherbrooke, QC, Canada Polytechnic of Coimbra, IPC-ISEC and INESC Coimbra, Coimbra, Portugal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_42
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According to this study, pvfactors has the lowest execution time and gives almost the same output results as Bifacial_radiance and Sandia model that use complex algorithms.
1 Introduction Bifacial modules are considered as an alternative to their monofacial counterparts. It is predicted that by 2030 the market share of bifacial modules will reach 70% of the total PV market [1]. Contrary to monofacial modules that receive only the front irradiance, bifacial modules are capable of receiving both front and rear irradiance, as shown in Fig. 1. With this feature of capturing the rear irradiance, the energy yield of a power plant can be increased up to 30% [2]. The key to precise modeling of bifacial modules energy production is to have an accurate model of the front and rear irradiance. These components are highly dependent on the weather, geographical and environmental conditions. As a function of the sun’s position rear and front irradiance can be deduced using an isotropic sky model such as the Perez model [3] or anisotropic model as described by Hay and Davies [4]. To prevent inaccurate predictions of the power plant production, it is preferred to have measured meteorological conditions data such as the Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DHI), rather than data collected from satellite-derived solar irradiance sources. Satellite-based sources have a high RMSE (Root Mean Square Error) value in clouded-sky and cold climates [5]. However, local meteorological data are not always available. Modeling techniques of the irradiance can be classified into three categories [6]. The first is the ray-tracing technique, based on complex algorithms that trace the path of the light and track the bouncing of each ray. The second technique uses the view factor model, it assumes that all radiation is scattered isotopically from any reflecting surface. The third and easiest technique to model the incident irradiance is the empirical model that uses the measured data (e.g., DNI, DHI, and albedo) to get a generalized approximation formula of the incident irradiance.
Fig. 1 Schematic of a bifacial module showing the source of irradiance on the front and back side
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The results of this study allow us to confirm the accuracy of the proposed techniques and to select the efficient tool that estimates the front and rear irradiance of a bifacial module. This paper is organized as follows. In Sect. 2, we introduce the main parameters and concepts of bifacial module technology. In Sect. 3, the existing tools for modeling the front and rear irradiance of a fixed tilt bifacial module are presented. In Sect. 4 we draw a synthesis of the simulations. Section 5 concludes the paper.
2 Bifacial Cell Modeling 2.1 Bifaciality Factor The major advantage of bifacial modules is their ability to capture the rear irradiance. However, the performance of the rear side of a bifacial cell is not as efficient as the front side. The bifaciality factor is defined as the ratio between the power produced by the module when its front side and when its back side are illuminated independently. This factor depends on the technology used. Typically, n-PERT bifacial modules have a bifaciality factor in the range of 70–95% while p-type PERC have a bifaciality factor of 60–70% [2]. The bifaciality factor is defined with the formula [6]: φ=
Pmaxrear Pmaxfront
(1)
where .Pmaxrear , Pmaxf ront are the maximum rear output power and the maximum front output power measured independently under standard test conditions, respectively.
2.2 Bifaciality Gain Compared to power plants that are using monofacial panels, those that utilize bifacial panels have a higher annual yield. To estimate this gain, the bifaciality gain is defined as follows: BG [%] = φ
Grear Gfront
(2)
where Gfront is front irradiance (W/m2 ) and Grear is rear irradiance (W/m2 ). The front and the rear irradiance depend on three main components which are: direct irradiance, sky diffuse irradiance, and ground reflected irradiance. For accuracy reasons, irradiance from the adjacent surfaces can be added.
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As Eq. (2) shows, a higher value of bifaciality gain implies higher values of rear irradiance and the latter depends on different parameters including: • Ground albedo • System Mounting (tilt, row to row spacing, module surface reflectivity, height, array azimuth) • Meteorological conditions (sun azimuth, sun zenith)
2.3 Electrical Model Bifacial modules can be modeled using similar models as monofacial modules, except that in the bifacial model we add a second current source that represents the back side of the module. The aim of this part is to present the module’s output power in function of the incident rear and front irradiance. Based on Fig. 2 we can calculate the power as follows: First, we calculate the load current using the expression: I = Iph − Id − Ip
(3)
Where Iph is the photocurrent, Id is diode current and Ip is current leak in parallel resistor. The photocurrent can be calculated using: Iph = Ifront + Irear =
Gf ront + α Grear Gref
Fig. 2 Equivalent circuit of a bifacial PV cell
Iphstc + μ (Tc − Tcstc )
(4)
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Where: Gfront front irradiance [W/m2 ] Grear irradiance [W/m2 ] Gref total irradiance at STC (Standard Test Conditions) [W/m2 ] α bifaciality factor T cell temperature [K] Tcstc cell temperature at STC [K] Iphstc photocurrent at STC [A] μ temperature coefficient of the short circuit current [A/K] The diode current is given by this equation: V + Rs I −1 Id = I0 exp Ns Vt
(5)
where I0 is the reverse saturation current, Ns is the number of cells connected in series and Vt being the junction thermal voltage Vt. Using the Fig. 2 the current in the parallel resistor is: Ip =
V + Rs I Rp
(6)
where V is the output voltage, I is the output current, Rs is the series resistance, Rp is the parallel resistance. The output power of bifacial module in function of rear and front irradiance is given by the expression: P=
Gfront + α Grear Gref
V + Rs I Iphstc + μ (Tc − Tcstc ) − I0 exp −1 − Ns Vt
V + Rs I V Rp
(7) proportional relationship with the front and rear irradiance. Therefore, what are the accurate techniques to model these irradiances? Section 3 addresses this question.
3 Tools for Modelling the Incident Irradiance This section presents different free-license tools that exist for modeling the front and rear irradiance, from the most complex to the simplest. The first category uses the ray-tracing approach which is based on advanced algorithms that analyze the ® light trajectory by tracking light scattering. RADIANCE is one of the existing ray-tracing tools, it was developed for research purposes. It has a wide range of applications e.g.; lighting design and graphic art. Bifacial-Radiance is a python-
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based tool that provides a set of functions and classes to make working with RADIANCE® easier. It is used for studying bifacial modules performance. The second category is the view factor models; these models rely on the calculation of the view factor also called the configuration factor which is defined as the fraction of radiation that leaves a surface (A) to reach surface (B). The cornerstone of this approach is the hypothesis that light scattering is isotopic which means that we have the same reflection properties from any surface. In the context of bifacial panels, the surface (A) may represent the ground or the adjacent surfaces, and the surface (B) can represent the front or rear surface of the PV module. The last category is the empirical models which refers to statistical models that use experimental observation to describe a phenomenon. In the literature, we can find several empirical model studies, for instance [7] that links the annual energy yield with tilt angle, ground albedo and module elevation.
3.1 Input Parameters Comparison between the three tools requires the same input parameters, namely the irradiance components (DNI, DHI and GHI) presented in Fig. 3, sun position angles (azimuth and zenith), array azimuth and the configuration parameters indicated in the Table 1. Figure 4 represents the input and output of the models. The weather data is collected from a station located in campus of the Université de Sherbrooke. The simulations are launched in a day (February 19th, 2021) with high albedo condition (0.6).
Fig. 3 DNI, DHI and GHI on 02-19-2021
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Table 1 parameters of the mounting system Parameter Albedo Type of module Number of modules per row Number of rows Height Row to row spacing surface azimuth tilt angle Panel width panel length Orientation
Value 0.6 LG395N2T-A5 10 6 1.5 m 4m 180◦ 45◦ 2.064 m 1.024 m Portrait
Fig. 4 Input and output parameters of the models
3.2 Raytracing: Bifacial_radiance The National Renewable Energy Laboratory NREL developed the Bifacial radiance which is a ray tracing tool that uses the core of Radiance. It provides both a line command and a graphical user interface [8]. There are other uses of Bifacial_radiance beside irradiance estimation, for instance the prediction of annual bifaciality gain or estimating the mismatch losses. The first step for using the Bifiacial_radiance is to define the ground properties and the weather condition; the tool uses the EPW format (EnergyPlus Weather Format) and gives the option to upload the climate file manually or automatically by selecting the latitude and the longitude of the station. The next step is defining the light source. Using the weather file, Bifacial_radiance generates the sky based on Perez sky model. The diffuse irradiance in this model takes this form [9]:
Idiffuse
1 + cos (θt ) = DHI (1 − F1 ) + F1 2
x + F2 sin (θt ) y
x = max (0, cos (Aoi)) y = max (cos (85◦ ) , cos (θz ))
(8) (9)
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πθz F1 = max 0, x11 + x12 δ + x23 180◦
(10)
πθz F2 = max 0, x11 + x12 δ + x 23 180◦
δ=
(11)
DHI AM Gon
(12)
Where AM is air mass, Gon is the extraterrestrial radiation or the solar radiation at the top of the earth’ atmosphere, θ t represents tilt angle, θ z is zenith angle, AOI is angle of incidence expressed in degrees ◦ , and xi are Perez model’s coefficients. For reducing the execution time Bifacial_radiance calculates the cumulative sky, that add all the generated skies for a time step and divides the sky dome into 145 patches. There is a step dedicated to scene description; in this step we specify the type of module used, tilt angle, row to row spacing, number of modules and number of rows. The final step is the analysis when the tool combines all the generated files to measure the irradiance received by the sensors located on both surfaces of the module. By default, the calculation is executed on the module in the center with 9 sensors. The drawback of ray-tracing technique is this approach is computationally intensive. Figure 5 shows the profile of the average front and rear irradiation received by the sensors of the panel located at the center (row = 3, position = 5) on 02-19-2021. From the datasheet of the module, the bifaciality coefficient is 0.76. On Feb. 19th, 2021, we would therefore have produced 12% more power with a bifacial than with a monofacial module.
(11,924.6882) Front Irradi...
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Fig. 5 Front and rear irradiance on 02-19-2021 – Bifacial_radiance
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3.3 Sandia View Factor Model Sandia view factor model is a three-dimensional configuration model under MATLAB™, with a command line interface. This tool discretizes the back side surface of the module into multiple elements and computes the incident radiance received by each element. The model assumes an isotropic sky diffuse and it considers the row’s shading. The front and the rear irradiance are defined as follows [10]: Ifront = Idirect + Idiffuse + Iground
(13)
Idirect = DNI cos (aoi)
(14)
Aoi = cos−1 cos (θz ) cos (θt ) + sin (θz ) sin (θt ) cos αs αp Idiffuse = DHI
1 + cos (θt ) 2
(16)
1 − cos (θt ) 2
Iground = GHI albedo
(15)
(17)
The reflected ground irradiance can be presented as function of the view factor: Iground = GHI albedo F1−2 F1−2 =
1 A1
cos (θ1 ) cos (θ2 )
1 S π 2
(18)
dA2 dA1
(19)
Equation (19) is the general formula of the configuration factor. We can reduce the space dimensionality and compute the view factor in two-dimensional space Fig. 6b thus, the new equation of the view factor is: 1 ( sin (φ2 ) − sin (φ1 ) ) 2
(20)
Irear = Idirectr + Idiffuser + Igroundr
(21)
F1−2 =
Idirectr =
−DNI cos (aoi)
cos (aoi) < 0 0
Idiffuser = DHI
1 − cos (θt ) 2
(22)
(23)
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Igroundr = GHI albedo FA−B
(24)
where θ t is tilt angle, θ z is zenith angle, αs and xi are sun azimuth angle and array azimuth angle, respectively, AOI is angle of incidence, Ifront is total front irradiance, Idirect is direct front irradiance, Iground is ground reflected irradiance towards the front surface, Idiffuse is Sky diffuse irradiance for the front surface, Irear is rear irradiance, Idiffuser is sky diffuse irradiance for the back surface, Igroundr is ground reflected irradiance towards the back surface, Idirectr is rear direct irradiance. The pairs of angles (θ 1, θ 2) and (φ1, φ2) are illustrated Fig. 6a and Fig. 6b, respectively. Sandia proposes an empirical model for the sky diffuse irradiance which adds a correction term to the isotropic diffuse irradiance. Thus, the sky diffuse irradiance will be expressed as follows: Idiffise = DHI
1 + cos (θt ) (1 − cos (θt )) (0.012θz − 0.04) + GHI 2 2
(25)
In this application we choose a discretization with 16 elements, The Fig. 7 shows the meshing of the panel situated in the center of the power plant.
(a)
(b) dA2 θ2
φ1
n2
A2
φ2
S
n1 θ1 dA1
dA1
Fig. 6 (a) View factor for two elemental areas in arbitrary configuration (b) View factor of differential element to surface generated by a line
Fig. 7 Generated mesh for the module in row = 3 position = 5
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Fig. 8 Front and rear irradiance on 19-02-2021 – SANDIA model
More elements provide further information about the non-uniformity distribution of the irradiance; however, it increases the program’s execution time. To estimate the rear incident irradiance, we compute the average of the received irradiances of all elements and the result is shown in the Fig. 8. With bifaciality factor of 0.76, the bifaciality gain was found to be 19.9%.
3.4 pvfactors Pvfactors is a free-license python library. It comes to minimize the computing time of other techniques while respecting the accuracy criteria. Pvfactors is characterized by a high computational speed which allows the user to get results of annual simulations in less than 10 s [11]. The trade-off between the simulation time and the precision is achieved by using a simplified configuration factor model in 2D space. Pvfactors provides two types of simulations: the full simulation which considers all the reflections between the surfaces and the fast simulation that uses some assumption to get less execution time. The mathematical model used in pvfactors is developed below [11]. Let’s consider a surface i, the radiosity of this surface can be expressed as: qi = qemitted,i + qreflected,i
(26)
Assuming that the surface absorption and the surface’s emitted flux is negligible compared to the reflected flux, the radiosity of the surface is: qi ≈ qreflected,i ⎛ qreflected,i = ρi ⎝
j
(27) ⎞
qj Fi,j + Skyi ⎠
(28)
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q0 = R ⎛⎛
ρ1 · · · ⎜⎜ . . ⎜ ⎝ . .. . ⎝ 0 ···
F q0 + Sky
(29)
⎞−1 ⎞−1 ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ 0 q1 Sky1 F1,1 · · · F1,n ⎟ .. ⎟ − ⎜ .. . . .. ⎟ ⎟ ⎜ .. ⎟ = ⎜ .. ⎟ ⎝ . . . ⎠ ⎠⎝ . ⎠ ⎝ . ⎠ . ⎠ qn Skyn Fn,1 · · · Fn,n ρn
(30)
where q0 is radiosity of the surface, which is the flux leaving a surface i, qreflected, i is reflected radiative flux, qemitted, i is emitted radiative flux, Fi, j is configuration factor, the term . j qo,i Fi,j in the (28) represents the radiations reflected from the surrounding surfaces (including the ground) toward the surface i, Skyi is the sky diffuse radiation received by the surface i and ρ i is the total reflectivity. For n surfaces the problem is reformulated as a linear system (30). The blue segments in Fig. 9 represent the bifacial modules row, the panels are facing the south with 180◦ azimuth angle, the yellow lines show the illuminated part of the ground. In contrast the grey segments represent the row shading. Using Fig. 10 with the bifaciality factor of 0.76, we find that pvfactors returns a daily gain equal to 21.5%.
Fig. 9 System representation under Pvfactors (11,889.2676) Front Irradi...
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Table 2 Results of simulations Model bifacial_radiance SANDIA model pvfactors
Sky model Perez Isotropic Isotropic
Mean Front Irr W/m2 152.3 150.3 139.9
Mean Rear Irr W/m2 Time [s] 25.8 130 s 39.5 97 s 39.7 5s
Gain [%] 12.9 19.9 21.5
4 Comparison In this section we compare simulations results in terms of two requirements, which are the accuracy and computing time. Concerning the front irradiance, the three models have almost the same profile with a maximum at 11:00 am. For the rear irradiance we notice a difference between Bifacial_radiance and the two other models. This is explained by a different sky model for bifacial_radiance. Indeed, Bifacial_radiance uses Perez model to compute diffuse irradiance while Sandia and Pvfactors assume an isotropic distribution of diffuse component. Perez sky model only uses DHI value, and therefore underestimates periods at low DHI but high GHI (e.g., shading from few clouds). The Table 2 summarizes the simulations results. To compute the execution time, we ran the simulations under the same computer with the following characteristics: processor Intel(R) Core (TM) i5-8265U CPU @ 1.60GHz 1.80 GHz with (8, G0 RAM). From the table below we can deduce that pvfactors has the lowest time complexity, while the other models have similar computation time (within 35%). In other hand Sandia model and Bifacial_radiance provide more information about the non-uniformity of the rear irradiance since they better capture situations with low DHI and high GHI.
5 Conclusion The main advantage of bifacial modules is their ability to capture the rear irradiance, which leads to a higher efficiency of the PV module and an increase of annual energy yield. This paper presents a comparative study between three free software that use different methodologies to estimate the bifacial gain based on the estimated front and rear irradiance. The study was done for a day with a high albedo condition and varying irradiance condition. The simulations confirm that using bifacial modules we can have a daily bifaciality gain between 13% and 21.5%. Pvfactors fulfils both accuracy and execution time criterion and is therefore recommended for real time production prediction. However, it does not cover certain effects such as the torque tube shading and the non-uniformity of the ground albedo. One of the perspectives of this study is to propose a real time simulation of bifacial module using the irradiances returned by pvfactors.
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Acknowledgements This work was supported in part by Grant 950-230672 from Canada Research Chairs Program. The support from the Natural Sciences and Engineering Research Council of Canada - NSERC (ALLRP558371-20), Prompt (project 144), Bell and STACE in the framework of the SAFE-TELECOM project is acknowledged. LN2 is a joint International Research Laboratory (IRL 3463) funded and co-operated in Canada by Université de Sherbrooke (UdeS) and in France by CNRS as well as Ecole Centrale de Lyon, INSA Lyon and Université Grenoble Alpes. It is supported by the Fonds de Recherche du Québec Nature et Technologie (FRQNT). SG acknowledges Hauts-de-France region for financial support.
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Self-Adaptive Construction Algorithm of a Surrogate Model for an Electric Powertrain Optimization Marvin Chauwin, Hamid Ben Ahmed, Melaine Desvaux, and Damien Birolleau
Abstract This article presents a generic and self-adaptive construction algorithm for a surrogate model. This method makes use of two major tools: Latin HyperCube, which serves to efficiently spread a large number of samples; and Kriging, which is very efficient for surrogate modeling in the domain of black box models. The efficiency of this method is investigated in the case of a finite element model of a surface permanent magnet synchronous machine. During this study, Kriging surrogate models are compared with various samples in terms of both accuracy of construction and calculation speed. Next, the self-adaptative algorithm is applied in order to derive an accuracy criterion in a minimal amount of time and compare one with a Kriging model built using the same number of samples, yet without our tool to determine any accuracy lost due to the black box feature of the model and the hypotheses used.
1 Introduction The optimization of a multiphysics system, like an electric car powertrain, is usually complicated to model [1, 2]. An electric powertrain contains just a few elements: battery, rectifier, electric machine, gearbox, and differential. Many principles of physics are required to produce such a model, including mechanical, electromagnetic and thermal [3]. The models used are typically time consuming, e.g. the model used in this case study of a surface permanent magnet synchronous machine takes approximately 59 s to compile (computer Quadcore ~3.7 GHz). Applying this kind of model in an optimization setting with 10–20 parameters and calling several
M. Chauwin () · H. Ben Ahmed · M. Desvaux SATIE Laboratory, ENS Rennes, Bruz, France e-mail: [email protected]; [email protected]; [email protected] D. Birolleau RENAULT S.A.S., Technocentre, Guyancourt, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_43
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models to obtain complementary information would lead to an overwhelming compilation time, which would need to be repeated for any modification of system specifications. For this reason, an approximation of the optimum tends to be employed, as is the case with analytical [4, 5] or semi-analytical models [6]. The objective here is to develop a generic and self-adaptive tool that constructs a surrogate model without simplifying the initial model, in order to help size or presize a system through an optimization process in a minimal amount of time. The aim is to keep the set-up generic to ensure a Plug and Play usage with all potentially associated models, even in contexts other than an electric powertrain. This article will first define surrogate modeling and the tools implemented before discussing the tool’s efficiency to reach an accuracy criterion.
2 Surrogate Modeling 2.1 Definition A surrogate model is a tool that estimates the evolution of a system (experimentation or a time-consuming model) based on just a few samples. It can then interpolate between the samples or else be used to extrapolate, though with less accuracy. An example of a surrogate model is shown in Fig. 1 through a least squares regression line that, once samples have been calculated or measured, allows estimating y for other values of x. A surrogate model can be applied in two contexts: • Create a model of a phenomenon without delving into the physics; • Create a fast-computing model of a system.
Fig. 1 Example of a least squares regression line
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An optimization context pertains to the second case; since the models used will be called thousands of times by the optimization algorithm, a fast-computing characteristic is essential. A 3-step approach is employed to construct a surrogate model, i.e.: (1) creation of a sampling plan, (2) computation of the model on each sample, and (3) optimization of the surrogate model parameters to fit the samples. One surrogate model is created for each value for purposes of subsequent estimation. To create a flexible and generic tool without bias, Kriging has been selected based on [7, 8, 13].
2.2 Sampling Plan Two methods serve to place the samples in space without adding random ones, namely: • Full Factorial design [9] • Latin HyperCube [10, 11] As observed in Fig. 2, the Full Factorial Design places samples at regular distances on each dimension, meaning that the number of samples are constrained to nD , in a D-dimensional problem. The Latin HyperCube however is more flexible, making it possible to choose precisely how many samples to start with. Yet the construction method is in no way unique, and all Latin HyperCube set-ups do not exhibit the same efficiency. To create an efficient Latin HyperCube, a Maximin criteria [10, 11] has been introduced to both maximize the distances between all samples and find a Latin HyperCube that most fully occupies the allowed D-dimensional space. Latin HyperCube will be used here to minimize the calls to time-consuming models, thus reducing the time required to construct a high-dimensional surrogate model. Once the sampling plan has been devised, our time-consuming models can be employed to calculate the values associated with the samples in order to construct the surrogate models.
Fig. 2 Distribution of 4 samples in a plan with: (a) Full Factorial design on the left, and (b) Latin HyperCube on the right
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2.3 Kriging D R →R Let’s consider .f : be the function we are seeking to approximate x → f (x) with surrogate models. Let Xech = {x1 , x2 , . . . , xn } be the samples placed in a Ddimensional space and Yech = {y1 , y2 , . . . , yn } the values associated with the samples such that yi = f (xi ), i ∈ 1; n. With Kriging, the value of f (x) can be estimated through .y, ˆ as in (1) below: y(x) ˆ =
N
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(2)
The parameters θ k in (1.2) determine the impact of each parameter in x and are found by maximizing the likelihood function (3): L (y1 , y2 , . . . , yn |μ, σ ) =
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In (3), μ denotes the mean value and σ the variance; they are estimated through .μˆ and .σˆ , respectively. Kriging allows estimating not only the value of a function but also the error introduced when using the function for each value of x, i.e.: sˆ 2 (x) = σˆ 2 1 − ϕ(x)t ψ −1 ϕ(x) +
1−l t ψ −1 ϕ(x) 1t ψ −1 1
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Kriging is a very powerful tool with multiple uses, as seen in (1) and (4). Both its value and error estimation capabilities will be displayed below. The tool can already be used to create our first surrogate model according to the diagram in Fig. 3. As shown in Fig. 3: it is possible to construct any surrogate model, like Kriging, since the tools are now available to draw up the sampling plan, as well as parameter optimization and estimation. Below is depicted a simple case to help better understand all this information. Figure 4 displays the function to be estimated, as well as the samples used for this purpose and the estimation. For each value of x, it is then known that the real value may lie between .yˆ − 3 × .sˆ and .yˆ + 3 × .sˆ , with an estimated 99% probability (Gaussian distribution) The estimated error tends to zero when moving closer to the samples; therefore, the number of samples used directly dictates the accuracy of the estimation.
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Fig. 3 Surrogate model construction steps
Fig. 4 Example of a Kriging estimation
2.4 Efficiency of Kriging All the tools developed in this article will be used on a finite element model of a surface permanent magnet synchronous machine. With this model, it has been decided to study the influence of 6 parameters: 3 related to the working point (magnetomotive force nI, torque angle , rotor speed N), and 3 geometric parameters with an impact on both the mesh and machine saturation (radius of the shaft and stator exterior, air gap), as clearly visible in Fig. 5. The finite element, as shown in Fig. 5, is used to estimate 3 values: the mean electromagnetic torque Tem , its peak-to-peak value Tempp , and the fundamental of the flux F1 . This model is computed on a 6-dimensionnal Latin HyperCube to obtain the values of all output to estimate. One surrogate model must be created for each output
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Fig. 5 2D ANSYS Electronic Desktop model, and the 3 geometric variables
value, since a surrogate model estimates a unique scalar. Will see on the case of the mean electromagnetic torque the huge impact that the number of samples has on the efficiency of the estimation. Figure 6 shows the estimation of the mean torque, with all parameters except current being set to their initial values; this step is performed by 3 surrogate models able to be constructed on a 6-dimensional sampling plan. Each model has a defined number of samples (12, 32 and 150) spread by the Latin HyperCube, hence not a single sample used to create the surrogate models is shown on the curve here. Let’s note that as the number of samples rises, the curves better fit the actual value calculated by the finite element model. The model thus transforms from an unusable one created from 12 samples to an accurate one based on 150 samples. Figure 7 relies on a 150 sample-based surrogate model of Tem in order to compute its behavior as a function of the evolution in both the magnetomotive force and shaft radius. To estimate this surface, 10,000 values were computed in 5.34 s, and the result was compared with 25 samples spread using a full factorial design computed with the finite element model in 537 s. The mean error recorded on these samples equaled 17.5 Nm. To compute such a surface with the finite element model alone, 1.99 · 105 s would be needed. This surrogate model is accurate enough to study the finite element model behavior and has been built in 3.04 · 103 s, hence 10,000 times faster to compute each value. Accuracy is important, but the time required to create a surrogate model and estimate the value is even more important, thus making time cost reduction our primary objective. The accuracy and time ratio of all Tem surrogate models have been evaluated, using 5000 samples spread by Latin HyperCube in the 6-
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Fig. 6 Estimation of electromagnetic torque vs. magnetomotive force
Fig. 7 Tem surface computed by a 150 sample-based surrogate model
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Fig. 8 Evolution of the computation time ratio and relative error vs. sampling plan size without enrichment
dimensional space as references computed with the finite element model (3 in parallel on a computer Quadcore @3.7 GHz) at an estimated time of 99,472 s. Figure 8 shows 2 values related to the surrogate models: – The time ratio on the 5000 samples (5) T ratio =
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The time needed to calculate the surrogate model is mainly the computation time of the finite element model, which is proportional to the number of samples to be computed. Meanwhile, the mean relative error decreases exponentially, meaning that a compromise can be found between accuracy and time cost when seeking an optimal Latin HyperCube to use. However, no prior knowledge of the timeconsuming model does not allow the user to efficiently chose the right sample amount. For this reason, an enrichment tool is necessary to help find an efficient sampling plan if the initially calculated plan is too sparse, thereby avoiding the need to once again compute the n initial samples.
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3 Enrichment Enrichment seeks to increase the accuracy of a surrogate model by adding new samples to it. The new samples can be determined by using either an element related to the surrogate model itself, making it an OFF-Line enrichment, or external information, making it an ON-Line enrichment.
3.1 Typical Methods OFF-Line is the simpler method; it solely relies on information from the surrogate model and mainly the error estimation. It can also rely on the maximum estimated error, e.g. [12], and add a sample at this point, in which case the new enriched surrogate model would have an error close to zero all around this sample. Figure 9 indicates that this method of enrichment reduces the error estimated within the entire design space. This finding means that the surrogate model can ultimately become very accurate and potentially used in an optimization process without making any changes, even if the problem were to change afterwards. Meanwhile, the time cost of such a method tends to be significant, as observed prior. The sample size defines the level of precision, yet the error made decreases exponentially, meaning that a large number of samples may be required. Another consideration is that the error tends to be higher further from the samples, so the border of the design space and the corner of the 6-dimensional HyperCube will then become preferred. With a high number of dimensions, hundreds to thousands of
Fig. 9 OFF-Line enrichment based on the error estimation
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Fig. 10 ON-Line enrichment based on the minimum estimated value
samples may be placed close to the border before any improvement occurs in other regions that may ultimately be more valuable to our optimization algorithm. In an optimization context, accuracy is only needed on the optimum. The ONLine enrichment tool makes use of external information that involves the model, along the lines of an optimization process, to determine the optimal value based on the surrogate model. After comparison with the real model, this sample can be added to the sampling plan for greater accuracy in the vicinity [14]. Figure 10 shows that the estimated error is greatly reduced around the minimum value found, thus leading to a precise definition of the minimum. This tool increases the accuracy in a specific region and can be fast-computing as well. While as stated in [14], if deployed on too sparse an initial surrogate model, this tool can get stuck at a local minimum. More sophisticated techniques exist with ON-Line enrichment to prevent it from getting stuck in a local minimum such as the Efficient Global Optimization [15]. It combines both the research of the optima and the minimization of the global error, and can be a sufficient tool. These tools are sequential, even if ON-Line tools such as EGO has multiobjective tool that have been developed [16]. The parallelisation options are limited. They require many iterations to converge if the initial surrogate model is too sparse. Then the tools can lead to an expensive time cost to reach the accuracy criterion in high dimension. For this reason, an OFF-Line enrichment method based on the Latin HyperCube has been developed, in the aim of computing many samples at once and occupying the space efficiently.
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3.2 Sub-Latin Hypercube This tool relies on the high efficiency of the Latin Hypercube method to spread samples in a D-dimensional space. From an n-sample Latin HyperCube, new Latin HyperCubes are sought that contain the initial one, yielding Sub-Latin HyperCubes (SHL). The new Latin HyperCubes now contain n = n + k × (n − 1) samples, with k belonging to N. Figure 11 exposes the initial points in red and points added by the enrichment in green. These new samples can be placed in many spots, hence their location can be optimized; the same Maximin criterion as discussed previously can now be used [10]. Let’s represent the SHL algorithm as follows: Figure 12 lays out all the enrichment steps. First, a few optimized Latin HyperCubes containing the initial one are calculated. Next, new surrogate models based on the initial one are then constructed merely to estimate the increased accuracy with these new samples. The new surrogate models are then compared based on a Full Factorial plan, whose creation is far quicker than that of a Latin HyperCube. {
By calculating the mean value of . ysˆ , an estimation of the mean relative error is therefore produced. The smallest error estimation reaching our accuracy criterion is then selected or, if none qualify, the most accurate one gets chosen. The new selected samples are computed based on the time-consuming model. Should the new surrogate model reach our criterion, then the loop is finished, else it becomes the new initial surrogate model of the next iteration. This tool is far less flexible than previous ones since it may add a very large number of samples at the same time, depending on the initial Latin HyperCube size. Achieving high accuracy with this tool would remain costly, which is why its use will be to reach a lower accuracy. Hence, an ON-Line enrichment based on an optimization problem could be performed without getting stuck at a local optimum.
Fig. 11 Initial 2D Latin HyperCube (k = 0) and those enriched with 1 (k = 1) or 2 (k = 2) new sections
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Fig. 12 Enrichment steps using SHL
3.3 SHL Results This enrichment tool is now applied to the previous surrogate model, as based on the finite element model of a surface permanent magnet synchronous machine (described in Sect. 2.4). Three surrogate models can therefore be constructed for each sampling plan in order to estimate all 3 values. Let’s first focus on the mean electromagnetic torque before discussing results covering all surrogate models. To estimate the efficiency of the tool based on the size of the initial sampling plan, the time needed to reach an estimated mean relative error of less than 15% will be studied for each initial sampling plan size. Figure 13 reveals the time required to attain our criterion; it is composed of 2 parts. In the first, the initial sampling is too sparse and needs to be enriched, like the one based on 12 and 22 samples enriched to 45 and 64 samples, respectively, and the one based on 2 samples enriched up to 49; with 4 iterations of SHL. For all other instances, the time needed once again becomes proportional to the number of samples initially used. The time spent due to SHL remains less than that of a 75sample based surrogate model (calculation based on extrapolation of construction time). However, let’s underscore the existence of an optimum sample size, which cannot be discerned without any computation. In lacking any prior information on how many samples are needed to achieve a defined accuracy, these results indicate the advantage of starting with a low number of initial samples and using an enrichment tool like SHL rather than choosing an overestimated number of samples like the one based on 150 samples.
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Fig. 13 Construction and compilation time for Tem using SHL compared to the time-consuming model, and mean relative error vs. the initial sampling plan size (i)
(i)
Table 1 Mean relative error of all 3 surrogate models: .Minit based on 2 samples, .Menr based on (i) (i) .Minit and enriched to 49 samples, and .Mcomp based on 49 Latin HyperCube samples Estimated parameter Tem Tempp F1 Construction time
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.Menr
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10.1% 17.1% 3.0% 1442 s
13.3% 14.3% 3.0% 1031 s
To obtain an overview of its efficiency and see whether this tool introduces any loss given that the SHL creates a more constrained Latin HyperCube that may prove to be suboptimal, the following table is proposed. It compares: an initial surrogate model based on 2 samples, then 4-times enriched by SHL up to 49 samples, and a surrogate model based on 49 samples spread by Latin HyperCube. Table 1 indicates that the enriched surrogate model has indeed attained our criterion for all data. Moreover, the mean error is of the same level on the surrogate model enriched to 49 samples as the one based on a 49-sample Latin HyperCube. Other elements may influence accuracy, like the localization of samples based on actual model evolution. Should the samples be placed where some event occurs in the model, then the surrogate model will be far more accurate in this specific region. In our case, which considers the time-consuming model as a black box, this takes place as a random phenomenon that cannot be used with the set of tools created.
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4 Conclusion The tools studied herein using both Kriging and Latin HyperCube have served to efficiently create a surrogate model with a self-adaptive method in order to attain an accuracy criterion. The surrogate models created in this case are not sufficiently accurate for use in an optimization algorithm. However, improving accuracy further would be very costly and may wind up being less competitive than using the finite elements themselves. An ON-Line tool will thus be employed to raise the level of local accuracy near the optimum. Without any prior information on a model’s behavior, it may be tempting to overestimate the number of samples needed to attain our accuracy criterion. Yet enrichment tools like SHL help limit the construction time required to satisfy our criterion provided it is agreed to start with a low number of samples. This would allow quickly achieving the construction of high-speed computing surrogate models.
References 1. Caillard, P. (2015). Conception par optimisation d’une chaine de traction électrique et de son contrôle par modélisation multi-physique (Doctoral dissertation, Ecole Centrale de Lille 2. Cisse, K. M., Hlioui, S., Belhadi, M., Mermaz Rollet, G., Gabsi, M., & Cheng, Y. (2021). Design Optimization of Multi-Layer Permanent Magnet Synchronous Machines for Electric Vehicle Applications. Energies, 14(21), 7116. 3. Bracikowski, N., Hecquet, M., Brochet, P., & Shirinskii, S. V. (2011). Multiphysics modeling of a permanent magnet synchronous machine by using lumped models. IEEE Transactions on Industrial Electronics, 59(6), 2426-2437. 4. de la Barriere, O., Hlioui, S., Ahmed, H. B., & Gabsi, M. (2013). An analytical model for the computation of no-load eddy-current losses in the rotor of a permanent magnet synchronous machine. IEEE Transactions on Magnetics, 52(6), 1-13 5. Rossi, M. (2016, June). Modèle Système de Machine Electrique pour l’Etude des Performances sur Cycle. In Symposium de Genie Electrique. 6. Caillard, P., Gillon, F., Hecquet, M., Randi, S. A., & Janiaud, N. (2014, October). An optimization methodology to predesign an electric vehicle powertrain. In 2014 IEEE Vehicle Power and Propulsion Conference (VPPC) (pp. 1-6). IEEE. 7. Simpson, T. W., Poplinski, J. D., Koch, P. N., & Allen, J. K. (2001). Metamodels for computerbased engineering design: survey and recommendations. Engineering with computers, 17(2), 129-150. 8. Hamdani, H., Radi, B., & El Hami, A. (2017). Métamodélisation pour une conception robuste des systèmes mécatroniques. Incertitudes et fiabilité des systèmes multiphysiques, 2(10). 9. George, E. P., Hunter, J. S., Hunter, W. G., Bins, R., Kirlin IV, K., & Carroll, D. (2005). Statistics for experimenters: Design, innovation, and discovery (Vol. 2). New York, NY, USA: Wiley. 10. Morris, M. D., & Mitchell, T. J. (1995). Exploratory designs for computational experiments. Journal of statistical planning and inference, 43(3), 381-402. 11. Keane, A., Forrester, A., & Sobester, A. (2008). Engineering design via surrogate modelling: a practical guide. American Institute of Aeronautics and Astronautics, Inc..
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12. Céline Scheidt. Analyse statistique d’expériences simulées : Modélisation adaptative de réponses non régulières par krigeage et plans d’expériences, Application à la quantification des incertitudes en ingénierie des réservoirs pétroliers. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2006. Franc¸ais. . 13. Peter, J., Marcelet, M., Burguburu, S., & Pediroda, V. (2007, September). Comparison of surrogate models for the actual global optimization of a 2D turbomachinery flow. In Proceedings of the 7th WSEAS international conference on simulation, modelling and optimization (pp. 46–51). 14. Leary, S. J., Bhaskar, A., & Keane, A. J. (2004). A derivative based surrogate model for approximating and optimizing the output of an expensive computer simulation. Journal of Global Optimization, 30(1), 39-58 15. Jones, D. R., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global optimization, 13(4), 455-492. 16. Jeong, S., & Obayashi, S. (2005, September). Efficient global optimization (EGO) for multiobjective problem and data mining. In 2005 IEEE congress on evolutionary computation (Vol. 3, pp. 2138-2145). IEEE.
Optimization of Neural Network-Based Load Forecasting by Means of Whale Optimization Algorithm Pooya Valinataj Bahnemiri, Francesco Grimaccia, Sonia Leva, and Marco Mussetta
Abstract Electric load forecasting is of utmost importance for governments and power market participants for planning and monitoring load generation and consumption. Reliable Short-Term Load Forecasting (STLF) can guarantee market operators and participants to manage their operations correctly, securely, and effectively. This paper presents the optimization of neural networks for power forecasting by means of whale optimization algorithm: two types of artificial neural networks namely, Feed-Forward Neural Network (FNN) and Echo State Network (ESN) have been used for STLF. ESN’s simplicity and strength have room for improvement. Therefore, an optimization algorithm called the Whale Optimization Algorithm (WOA) has been used to improve ESN’s performance. WOA-ESN was used for STLF of the first case study, namely Puget power utility in North America. The considered forecasting error indicators showed significant accuracy and reliability. WOA-ESN model and recursive approach resulted in better accuracy measures in terms of standard performance metrics.
1 Introduction Around the world, energy systems are going through substantial changes to increase sustainability. One of the most important changes includes transitioning to electricity as the energy carrier in transportation sector and improving Renewable Energy Sources (RES) penetration in the grid [1]. An accurate Short-Term Load Forecasting (STLF) is crucial for power system networks to achieve higher efficiency, operations reliability, minimizing operating costs, improved scheduling, and contingency analysis. Many models have been proposed and employed. Some are conventional approaches and some are related to Artificial Intelligence [2]. The differences
P. Valinataj Bahnemiri () · F. Grimaccia · S. Leva · M. Mussetta Politecnico di Milano, Dipartimento di Energia, Milano, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_44
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between these models can be attributed to the data requirements, the algorithm, the computational requirements, and the availability of the real data sets [3]. Traditional load forecasting uses techniques such as regression, statistical analysis, and smoothing [4]. Although these models can be somewhat reliable, they are not able to adapt highly non-linear load patterns which can be as a result of unusual weather conditions or holidays activities. Occurrence of such events leads to unsatisfactory load predictions by conventional approaches. Some of the most famous conventional models are: Multiple Linear Regression model (MLR), General Exponential Smoothing model (GES), Stochastic Time Series model (STS); among these, Autoregressive Moving Average with Exogenous Variables model (ARMAX) and Autoregressive Integrated Moving Average with Exogenous Variables model (ARIMAX) take into account also exogenous variables such as weather and social variables into their stochastic processes. Computational intelligence approaches are more sophisticated means of load prediction that can map the correlation between all of the variables more satisfactorily. They use computational intelligence as a mean to have a better performance in presence of non-linearities for modeling of time series. Their biggest advantages with regard to conventional approaches are not requiring any correlation between inputs and outputs and not needing complex mathematical formulations. Some of the most frequently used models are Artificial Neural Network model (ANN), Fuzzy Logic model (FL) and Support Vector Machine for Regression model (SVR). In this work we will present a novel approach for STLF based on a recurrent neural network called Echo State Network (ESN) which will be tuned by means of the recently developed Whale Optimization Algorithm (WOA). The considered case study in this work addresses load forecasting focusing on 1-hour ahead. The reasons are attributed to its importance for the daily operations of a power utility such as load dispatch, energy transfer scheduling, and unit commitment of power stations.
2 Echo State Network Despite huge success of conventional neural networks as feed-forward (FNN), they have the limitation of being dependent on the assumption that training and testing data sets are independent [5] i.e., the connections between network neurons are not allowed to form cycles (information feedback). After each data point is processed, the past state of the network is lost. But, most often the data are related in time and space. Therefore, Recurrent Neural Networks (RNN) can be used, which allow the neurons to have directed cycles within their connections. In spite of these excellent capability, their performance is limited in nonlinear modelling for a long time, i.e., computationally expensive. Alternatively, reservoir computing (RC) appeared to be a suitable substitution [6]. Reservoir computing (RC) is considered as a new paradigm for RNN design and training. RC in contrast to gradient descent techniques only trains the weights between the reservoir and the readouts (outputs). The RNN in this case is referred
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to one fixed “reservoir” which is initially generated randomly, and the states within maintain a nonlinear transformation of the input signals. Then the linear aggregation of reservoir’s units results in the desired output, which can be obtained by linear regression using the teacher output (known output) as a target. RC was developed in 3 different methods such as Echo State Network (ESN), introduced by Jaeger in 2001 [7], Liquid State Machine (LSM) [8] and Backpropagation-Decorrelation (BPDC) learning rule [9]. ESN is one of the main favorites for RC where reservoir acts as a temporal memory of input .u(n). A generic ESN is a discrete-time recurrent neural network composed by K input units, a reservoir consisting of N internal units and M output units. The term echo means that the activation states of the reservoir’s internal neurons of an arbitrary recurrent neural network are a function of the inputs’ history presented to the reservoir. ESN was used in recent years in different areas, especially engineering [10–12]. A typical ESN structure is illustrated in Fig. 1. ESN are used for supervised machine learning tasks with 3 main signal types: .u(m) as input vector signals, m being the point in time; .x(m) as the reservoir neuron activation vector or network states; .y(m) as output signals. A very important issue about ESN training is the washout time .T0 , meaning that some initial network states of .x(m) are not considered for the training. Since the initial arbitrary setting of the .x(0) = 0 creates initial transient condition, which shows unnatural starting state and must be discarded. After neglecting the first .T0 states, a state collection matrix X, is obtained. It contains the concatenated reservoir/input states: X(m) = [x(m); u(m)]
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A linear format for the readout of .y target is used: y target = W out · X
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where .y target is the network output, and .W out is the output weight matrix. Calculation of output weight matrix is called the network readout. To obtain numerically stabilized values for .W out , the linear regression as a regularization regression technique is most commonly used. Even though ESN has simplicity in the sense of being highly practical, easy to conceptualize and implement, it has its own difficulty of needing some insights which can be acquired by experience. In particular, generation of the initial reservoir network requires some global parameters that need to be set justifiably. The socalled global parameters of ESN that effect its performance to a high degree are: network size .Nx , sparsity of the reservoir C, and spectral radius .ρ.
3 Whale Optimization Algorithm First introduced by S. Mirjalili [13], WOA is a very recent meta-heuristic evolutionary algorithm based on the behavior of humpback whales. It was found to be very competitive with other state-of-the-art optimization methods.
3.1 Exploration Phase From optimization point of view, the exploration phase of the search space happens when the whales are looking for the prey and the exploitation phase takes place while attacking. As a consequence, WOA employs two searching schemes and three sub-schemes to resemble the chasing and hunting behavior of whales: (1) bubble-net foraging maneuver (which includes the encircling prey and spiral-shape movement); (2) search for prey. The initial positioning is generated randomly through the following equation: Xi = r · (U B − LB) + LB
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where .Xi = [xi1 , xi2 , . . . , xiDim ] is the position of the i-th search agent, noting that .i = [1, 2, . . . , N ], with N the total number of search agents, and .Dim is the dimension of the problem. r is a random vector between .[0, 1]. .U B = [ub1 , ub2 , . . . , ubDim ] and .LB = [lb1 , lb2 , . . . , lbDim ] are the upper and lower boundaries vectors, respectively. They limit the movements of the search agents. In the following, mathematical modeling of the exploitation and exploration strategies is presented.
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3.2 Exploitation Phase This phase simulates the bubble-net attacking method of the whales. For hunting, whales exploit the search space around the candidate prey (so far optimum solution) in a shrinking circle and a spiral-shaped manner simultaneously. Therefore, it is assumed that there is a 50% possibility for each of these two behaviors. Consequently, a new parameter as p between [0,1] is introduced randomly for each agent to help the choice of the mechanism to update whales’ positions. Shrinking encircling mechanism: when Humpback whales conceive the location of the target prey, they consider that location as a clue and they tend to encircle those prey. This behavior is expressed by the following equations: Xi (t + 1) = X∗ (t) − A · D
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where .t = [0, 1, . . . , Tmax ] and .Tmax is the maximum number of iterations. .X∗ vector is the position of the best solution so far, and it must be checked at each iteration and updated if necessary. D is the distance vector and A and C are the coefficient vectors that are calculated as follows: A=2·a·r −a
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Decrease of this value throughout all the iterations causes the coefficient A to decrease as well, because A is a random value in the range of .[−a, a], considering that a decreases over the course of iterations from 2 to 0. Meaning that .0 ≤ |A| ≤ 2 can happen only at the beginning of the model execution and its range will reduce throughout the optimization. Therefore, it causes the shrinking behavior of the model, hence, it is a decisive parameter of the model. The spiral updating position mechanism tries to simulate the spiral path of the whales. Therefore, the following equations are applied: Xi (t + 1) = X∗ (t) + D ebl cos (2π l)
(9)
D = |X∗ (t) − X(t)|
(10)
.
.
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Fig. 2 Bubble-net search mechanisms: shrinking encircling
Where .D is the distance between the i-th search agent and the best agent, b is a constant to define the logarithmic spiral shape (taken as unit in this work) and l is a random vector between .[−1, 1]. Figures 2 and 3 illustrate the rationale behind the shrinking encircling and spiral movement of the search agents in a 2D space. The current position of the agent ∗ ∗ .(X, Y ) can be updated according to the position of the current best agent .(X , Y ). As shown in the figures, the random parameter A is the determining factor on where the next agent’s position can be located. In fact, just for the values of .|A| < 1, WOA cares about the exploitation, because in this way on the final half of optimization iterations WOA can focus only on the best solution found so far. For the next iteration, different positions around the best agent can be reached by the agent depending on the random parameters in the equations. The same notion can be generalized to an n-dimensional search space. Moreover, whales tend to search close to each other locations randomly. In this way, WOA cares about the exploration of new prey opportunities, allowing a global investigation. This mechanism, which is called the search for prey, is only employed when .|A| ≥ 1 (in contrast to spiral updating position which is applied when .|A| < 1). In this way, it just can happen in the first half of the iterations, allowing a wider search at the beginning of the optimization process. The search for prey mechanism is quite similar to encircling the prey, but in this case, agents search around a random previous search agent instead of the best agent. WOA considers this strategy when .|A| ≥ 1. It is formulated as follows: Xi (t + 1) = Xr (t) − A · D
.
(11)
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Fig. 3 Bubble-net search mechanisms: spiral updating
D = |C · Xr (t) − X(t)|
.
(12)
Where .Xr (t) is a randomly chosen search agent, and A and D are the coefficient vectors that were introduced before. Alike encircling the prey, search agents follow a shrinking circulating path. This behavior is represented in the figure, showing the possible positions around a randomly chosen agent for .|A| ≥ 1.
4 WOA-ESN Combined Model Despite the fact that ESN can be used as a powerful stand-alone method, its hyperparameters require fine tuning to maximize performance, as usual when dealing with computational intelligence techniques which depends on many parameters. Usage of a meta-heuristic global optimization algorithm can fulfill this need. In this study, WOA is utilized to optimize the hyper-parameters of ESN. However, reservoir size .Nx is selected by trial and error since it changes all of the matrices in ESN. Usually, it should be suitably tuned to avoid over-fitting and under-fitting problems. The rule of thumb is to choose in the range of .[T /10, T /2], while T being the time horizon of the input-output data set. The harder the task, the bigger the .Nx size should be [14]. In this work, the best performance was achieved when .Nx is chosen from the range .[500, 1500]. In this work, the following algorithm parameter settings were considered: – WOA settings: for all the case studies in this work, the considered WOA settings are as follows: number of search agents .N = 30; termination criteria .Tmax = 40; constant to define the logarithmic spiral shape .b = 1.
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– ESN settings: The number of inputs and internal units changes depending on the case study. In this work, only one output was considered in all of the cases. Therefore, the designed ESN is a Multi-Input-Single-Output method. Washout time .T0 was selected differently for each case study. Depending on the case, the hyper-parameters to be optimized might change. In general, the ESN optimization parameters were considered as spectral radius .ρ between .[0, 1]; input scaling and input shift ranging between .[−1, 1]; and weight matrices such as input weight .W in and internal weight W in the range of .[−1, 1]. To better understand the WOA-ESN procedure, the flowchart of the model is presented in Fig. 4.
5 Simulation and Results Puget power utility, Seattle, USA, is a real case [15] with hourly temperature and electricity load data over the period of more than 7 years, from 1 January 1985 to 12 October 1992. These hourly data for a span of 68,208 hours are shown in Fig. 5. The aim here is to compare the performance of WOA-ESN with other load forecasters in the literature [16–19] on the same dataset. We used input-output of years 89 and 90 as the training data set consisting 17,520 hours and last 2 years, i.e., year 91 and a part of year 92 as the testing data set with 15,624 hours [16]. The training and testing sections of the data sets are separated with dashes in Fig. 5. One-hour ahead STLF is considered in this case. The ESN has three inputs such as temperature, load and day index, and one output named the forecasted load. The day index is used here to differentiate the day types, meaning weekdays from weekends or holidays. Value of 0.25 is used for weekends or holidays and 0.75 is selected for weekdays to take into account how day type can affect the load pattern [17]. Actual temperature of the current hour .T (h), load of the current hour .L(h), and day index of the following hour .D(h + 1) are taken as the inputs of ESN, and 1-hour ahead load .L(h + 1) is considered as the output to be forecasted. This method of forecasting is called recursive type since the load of the current hour is also fed as one of the inputs to the neural network to forecast the 1-hour ahead load. The input and output data sets are normalized between [0,1] to be applied in WOA-ESN algorithm. ESN reservoir size, spectral radius and connectivity are taken as recommendations from Deihimi et al. [17] and are size .Nx = 910, connectivity .C = 0.011 and spectral radius .ρ = 0.94, respectively. However, input scaling, input shift, input weight, internal weight, teacher scaling, and teacher shift matrices which are ESN hyper-parameters are taken as WOA optimization parameters in this case. Number of search agent in WOA is considered as .N = 30 and maximum number of iterations is selected as .Tmax = 40. WOA-ESN algorithm was developed in MATLAB software. Raw source code of ESN is taken from Jaeger [14] and WOA raw source code was taken from Mirjalili [13].
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Fig. 4 The proposed WOA-ESN model flowchart
The forecasting performance metrics used for the preliminary case are Absolute Error (AE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). These metrics are chosen to be able to compare the results of WOA-ESN with the previous studies on the same real data sets Puget power utility [16–19].
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Fig. 5 Electric load and temperature data sets of Puget power utility
Table 1 represents the comparison between our WOA-ESN model results for 1hour ahead load forecasting of Puget power utility and the results obtained by the literature [16–19]. The resulting MAPE and MAE of 1-h ahead load for each day of the week and their average is reported in the table. As it can be seen, WESN [16] has the best performance between all models. However, our WOA-ESN model is the second best with only 0.068% difference in MAPE and 1.3 MW difference in MAE on the average basis with WESN. The third place belongs to ESN [17] with 0.442% difference in MAPE and 10.01 MW in MAE. WFNN [18] has the fourth place in the ranking with 0.734% difference in MAPE and 17.35 MW difference in MAE. Fifth place belongs to ARMAX [19] with 0.905% difference in MAPE and 20.85 MW difference in MAE. And the last place is owned by ANFIS [18] with 2.236% difference in MAPE and 50.94 MW difference in MAE. This shows how close to the best our WOA-ESN model is working without having complicated procedures and heavy computational burden of WESN which is described in [16]. In WESN, the authors used wavelet transform for the multi-resolution decomposition (approximation and details) of the load or temperature time series. Then, utilized ESN as the forecaster for each decomposed component individually. Furthermore, a shuffled frog leaping algorithm was used for optimizing each ESN model. Finally, the forecasted time series were reconstructed by sum of the outputs of all ESNs. WESN, as described in [16], is a very complex and time-consuming forecasting model, in contrast to our WOA-ESN model, with merely 0.068% better results in MAPE. These results show the great capabilities of WOA-ESN to learn the complex dynamics of electricity load time series and predict the near future loads with acceptable high accuracies and relatively fast method.
Average
Sunday
Saturday
Friday
Thursday
Wednesday
Tuesday
Days Monday
Error MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW) MAPE (%) MAE (MW)
WOA-ESN 0.8192 181.189 0.7215 163.049 0.6999 157.101 0.6981 156.452 0.7460 164.480 0.8399 171.676 0.8390 171.005 0.7662 166.422
WESN [16] 0.7416 163.520 0.6866 150.112 0.6553 145.443 0.6801 150.118 0.7246 157.970 0.6677 148.141 0.7261 158.627 0.6974 153.418
ESN [17] 11.840 262.178 11.005 246.863 10.734 241.308 11.651 258.993 11.554 256.348 11.007 245.032 12.011 264.402 1.14 253.589
Table 1 Comparison of 1-hour ahead WOA-ESN load forecast and other models ANFIS [18] 30.775 695.937 28.025 638.611 26.978 616.795 30.322 685.754 31.575 711.042 28.992 648.681 28.723 643.484 29.341 662.901
WFNN [18] 14.650 334.052 13.618 315.563 14.135 323.594 14.378 337.788 14.566 334.369 14.572 331.683 14.293 321.691 14.316 326.963
ARMAX [19] 16.179 368.847 15.661 354.679 15.704 353.078 16.488 372.286 15.966 360.601 16.418 369.016 15.773 355.328 16.027 361.976
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6 Conclusions The aim of this work was to improve STLF accuracy by optimizing ESN. Therefore, WOA as a global evolutionary optimization algorithm was combined to ESN to control and improve its performance. ESN hyper-parameters such as input scaling, input shift, input weight, internal weight, teacher scaling, and teacher shift matrices, and spectral radius were considered as WOA optimization parameters. Recursive approach was used to be comparable with previous works in the literature. The reported results have shown to be promising in comparison to the previous studies in the literature. Acknowledgments This research activity was partly supported by the EU Horizon 2020 project PLATOON (Grant agreement ID: 872592).
References 1. United Nations Development Programme, “Sustainable Development Goals. Goal 7: Affordable and clean energy,” [Online]. Available: https://www1.undp.org/content/brussels/en/home/ sustainable-development-goals/goal-7-affordable-and-clean-energy.html. 2. M. Mansoor, F. Grimaccia, S. Leva, M. Mussetta, “Comparison of echo state network and feed-forward neural networks in electrical load forecasting for demand response programs”, Mathematics and Computers in Simulation, Vol. 184, 2021, Pages 282–293. 3. European Union, “Energy roadmap 2050,” Publications Office of the European Union, 2012. 4. R. Blaga, A. Sabadus, N. Stefu, C. Dughir, M. Paulescu, and V. Badescu, “A current perspective on the accuracy of incoming solar energy forecasting,” Progress in Energy and Combustion Science, vol. 70, pp. 119–144, 2019. 5. Z. C. Lipton, J. Berkowitz and C. Elkan, “A Critical Review of Recurrent Neural Networks for Sequence Learning,” arXiv, 2015. 6. A. Bala, I. Ismail, R. Ibrahim and S. M. Sait, “Applications of Metaheuristics in Reservoir Computing Techniques: A Review,” IEEE Access, vol. 6, pp. 58012–58029, 2018. 7. H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks (2001),” 2001. 8. W. Maass, “Liquid State Machines: Motivation, Theory, and Applications,” Computability in Context, pp. 275–296, 2011. 9. J. J. Steil, “Backpropagation-decorrelation: online recurrent learning with O(N) complexity,” in 2004 IEEE International Joint Conference on Neural Networks, 2004. 10. G. Shi, D. Liu and Q. Wei, “Energy consumption prediction of office buildings based on echo state networks,” Neurocomputing, vol. 216, pp. 478–488, 2016. 11. M. A. Chitsazan, M. Sami Fadali and A. M. Trzynadlowski, “Wind speed and wind direction forecasting using echo state network with nonlinear functions,” Renewable Energy, vol. 131, pp. 879–889, 2019. 12. X. Yao, Z. Wang and H. Zhang, “A novel photovoltaic power forecasting model based on echo state network,” Neurocomputing, vol. 325, pp. 182–189, 2019. 13. S. Mirjalili and A. Lewis, “The Whale Optimization Algorithm,” Advances in Engineering Software, vol. 95, pp. 51–67, 2016. 14. H. Jaeger, “Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the “echo state network” approach,” GMD Report 159, German National Research Center for Information Technology, 2002.
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15. R. E. Abdel-Aal, “Hourly temperature forecasting using abductive networks,” Engineering Applications of Artificial Intelligence, vol. 17, pp. 543–556, 2004. 16. A. Deihimi, O. Orang and H. Showkati, “Short-term electric load and temperature forecasting using wavelet echo state networks with neural reconstruction,” Energy, vol. 57, pp. 382–401, 2013. 17. A. Deihimi and H. Showkati, “Application of echo state networks in short-term load forecasting,” Energy, vol. 39, pp. 327–340, 2012. 18. M. Hanmandlu and B. K. Chauhan, “Load forecasting using hybrid models,” IEEE Transactions on Power Systems, vol. 26, pp. 20–29, 2011. 19. C. M. Huang, C. J. Huang and M. L. Wang, “A particle swarm optimization to identifying the ARMAX model for short-term load forecasting,” IEEE Transactions on Power Systems, vol. 20, pp. 1126–1133, 2005.
Part VI
Modelling and Simulation of Electrical Machines and Electromagnetic Devices
Estimation of Steady-State Torque of Line Start Permanent Magnet Synchronous Motor Using Reluctance Network Approach Hamza Farooq, Nicolas Bracikowski, Patricio La Delfa, and Michel Hecquet
Abstract The efficiency of direct-start applications such as pumps or fans can be improved by replacing a squirrel cage induction motor (SCIM) with a line start permanent magnet synchronous motor (LSPMSM). LSPMSM is a super-premium efficiency class IE4 motor, which combines the features of both conventional SCIM and permanent magnet synchronous motor (PMSM). In this paper, a reluctance network approach (RNA) is devised to estimate the maximum steady-state torque of LSPMSM. A reluctance network (RN) in both nonlinear and linear conditions is utilized to investigate the effect of flux-bridge saturation on the computed back electromotive force (EMF). The value of back EMF calculated from RNA is used to calculate the steady-state torque of LSPMSM. Finally, a two-dimensional (2D) finite element method (FEM) simulation is performed to validate the results obtained by the proposed model.
1 Introduction Electric motors consume 43–46% of the electricity produced around the globe. A huge proportion of this electricity is used to drive motors for fixed-speed applications [1]. Currently, SCIM due to its self-starting ability is being widely used in these applications but due to its low torque density, there is a trend to replace SCIM with high efficiency class LSPMSM [2]. LSPMSM is composed of a stator similar to conventional SCIM while its rotor contains permanent magnets (PM) and a squirrel cage. It starts as SCIM due to rotor bars and then synchronizes at
H. Farooq · P. La Delfa · M. Hecquet University of Lille, Centrale Lille, Arts et Metiers ParisTech, Junia (HEI), -L2EP(EA2697), Lille, France e-mail: [email protected]; [email protected]; [email protected] N. Bracikowski () University of Nantes, IREENA, Nantes, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_45
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a constant speed to operate as a PMSM due to PM inside the rotor. Therefore, the design of LSPMSM consists of modelling both the transient regime and steady-state characteristics [3]. This study only focuses on the steady-state characteristics of the LSPMSM which heavily depends on the air-gap flux density due to PM. According to the literature [4–7], a recent trend is to use a linear RN based model to compute air-gap flux density to estimate the steady-state torque of LSPMSM. In [4–6] air-gap flux density considering the leakage paths was computed using a linear RN with saturated flux bridge. In [7], the saturation effect is included using a nonlinear least-square method which requires an iterative solving process. A purely analytical method is used in [8] to calculate air-gap flux density due to PM. The saturation effect due to the leakage flux in the rotor was not considered which increases the percentage of error in calculated flux density. In order to address the limitation in previous RN based model, the proposed RNA includes: (1) leakage flux effect in flux-bridge and rotor bar (2) nonlinear behaviour of the rotor flux-bridge. The RNA proposed in this study considers all the notable leakage flux paths in the rotor including flux-bridge. Further, RN in both linear and nonlinear condition is utilized. In the nonlinear RN, the flux-bridge reluctance is nonlinear as presented in Sect. 3.1. The air-gap flux computed value from nonlinear RN is used for the comparison purpose in Sect. 6. While in the linear RN case, the reluctances are considered as linear and flux-bridge is considered as saturated. A mathematical relation to obtain the air-gap flux is formulated, Sect. 3.2 presents the detailed procedure. The advantage of analytical expression based on linear RN is that it could be integrated in parametric analysis and optimization procedures. The computed value of air-gap flux allows to compute the back EMF which is then used to calculate the steady-state torque of LSPMSM. Section 4 presents the utilization of analytical expressions from literature to compute the synchronous torque. FEM modelling is performed to obtain the flux density, back EMF, and steady-state torque in Sect. 5. Finally, the torque characteristics obtained from RNA are being compared with the FEM based torque for verification. The adopted technique is meant to estimate steady-state torque which can lead to calculate the motor efficiency.
2 Studied Machine A series permanent magnet (PM) rotor topology of LSPMSM is utilized to implement the RNA and FEM model, and is presented in Fig. 1. The studied topology is radial flux type, so the proposed model only considers radial component of air-gap flux. The tangential component could be considered if there is variable or large air-gap [4]. The main motor characteristics and fixed parameters computed from the motor specifications are listed in the Table 1.
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Fig. 1 Half cross-section view of Series LSPMSM Table 1 Parameters of the studied motor
Parameter Rated power Phase voltage (RMS) Number of phases Number of pair poles Rated frequency Stator outer radius Rotor outer radius Number of stator slots Number of rotor bars Air-gap Stack length Relative permeability of PM Remanent flux density Saturated flux density (flux-bridge) Pole pitch Number of turns per phase Pole arc to pole pitch ratio Carter factor Winding factor Stator leakage reactance Q axis effective air-gap D axis effective air-gap
Symbol Prat V m p f Rstator ext Rrotor ext Zs Zr g ls μm Br Bsat τ pole Ntr ph α kc kw Xls lgq lgd
Value 7.5 kW 230 V 3 2 50 Hz 100 mm 61.9 mm 48 44 0.6 mm 200 mm 1.1 1.1 T 1.9 T 98.23 mm 124 0.95 1.34 0.96 1.65 0.732 mm 2.2 mm
3 Reluctance Network Approach (RNA) The procedure to estimate the air-gap flux density Bg and back EMF E from the RNA initially consists of the following steps: – Finding flux distribution pattern in open circuit condition – Reluctance components definition – Reluctance Network definition
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(a)
(b) Fig. 2 (a) Flux lines in the open circuit condition and (b) leakage flux through rotor elements
For the purpose of simplicity, the slotting effect of stator is neglected in RNA. While, Carter Factor is used to account the effective air-gap. The studied topology presented in Fig. 1 is being simulated in open circuit condition using a 2D FEM model in Ansys Maxwell commercial software. Open circuit simulation includes no stator winding excitation and it allows to observe the flux in the machine due to the presence of PM as depicted in Fig. 2a. This PM flux constitutes a major component of the steady-state torque and is the reason of LSPMSM having high torque density than SCIM [2]. As presented in the Fig. 2a, the flux lines from one half of the magnet north pole cross the air-gap, stator lamination and then again pass the air-gap to finally complete the loop at the half of the south pole magnet. This is the magnetizing flux contributing to the torque production. At the same time, by observing the flux distribution, a high flux density region of the rotor is located near the magnets ending and rotor bars presented in Fig. 2b. There are flux lines which does not cross the air-gap and remain in the rotor. These flux lines follow leakage flux paths available in the rotor to complete the loop at opposite magnet pole. The flux lines which remain in the rotor or stator and do not pass through the air-gap are not part of the main flux and are classified as leakage flux [9, 10]. These leakage flux lines cause saturation in the rotor near magnet edges. In order to estimate the
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Table 2 Representation of reluctance components Component Rotor bar
Formula Rbar = Rrect Rcir seg
Geometry
1 wbar μ0 Arect 1 2 .Rcir|seg = μ0 Acir|seg .Rrect
Flux barrier
=
=
.Rm
Flux-bridge
.Rbridge
Air-gap
.Rg
Surface area Arect
1 μ0
=
w hm ln 1+ w bt bs
Abarrier hm Am
1 μ0 μm
Permanent magnet
Table 3 Surface area equations for reluctance calculation
=
.Rbarrier
τbr 1 μ0 μr Abridge
1 kc g μ0 Ag
=
Formula =ls hbar
sin−1
Acir seg
.= ls
Abarrier Am
=ls 4 wbt =ls wm
bbar rbar
Rout|br Rin|br
Abridge
.= ls
Ag
=ls α τ pole
ln
+ sin−1
rbar rbar
leakage through these paths and its effect on the flux density following reluctance components are defined in the rotor: flux barrier reluctance Rbarrier , flux-bridge reluctance Rbridge (region between the flux barriers and the rotor bar), and rotor bar reluctance Rbar . The bar reluctance is composed of parallel equivlent of a circle segrment Rcir seg and rectangle Rrect reluctances. Rm and Rg are the reluctances of magnet and air-gap. The geometry and formulation of these reluctances are presented in the Table 2. The reluctance of a flux path depends on its material permeability, length, and surface area. The surface areas such as Abarrier , Abridge , Arect , and Acir seg for the respective reluctances are derived form [9, 11] and are listed in Table 3. For the Rbarrier being an air, the permeability is vacuum μ0 . While for Rbar the permeability is also estimated to vacuum μ0 as its material is aluminum. For the Rbridge , since it is the region of rotor core its relative permeabilty is the BH curve presented in Fig. 3.
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B(Tesla)
B1=1.9 T H1=2000 A/m
μr_sat≈1
B2=2.3 T H2=318
A/m
μr_lin
H(A/m) Fig. 3 Steel 1010 BH curve used for the stator and rotor core Fig. 4 Reluctance network according to the flux distribution
3.1 Nonlinear Reluctance Network Figure 4 presents the RN based on the flux distribution in Fig. 2a. As one pole includes half of the north pole of magnet and half of the south pole of magnet. The half of the remanent flux is utilized as the source of the RN. The RN in Fig. 4, is implemented with nonlinear bridge reluctance is refered as nonlinear RN. The BH curve from Fig. 3 is embeded in nonlinear reluctance element [12]. The air-gap flux density value is calculated directly from the implementation of nonlinear RN in MATLAB Simscape and is presented in Sect. 6.
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3.2 Simplified Reluctance Network A linear case of RN is used to formulate a simplified air-gap flux mathematical equation. In which stator and rotor core except the rotor bridge are considered as infinitely permeable. So, reluctances Rs and Rr in Fig. 4 are neglected. While the flux-bridge is considered as saturated having μr _ sat relative permeability and saturated flux density Bsat from Fig. 3. The flux through saturated flux-bridge is calculated using (1) [4, 5] and it acts as a source in the RN. The total flux source of the RN becomes ϕT in (2) where ϕr is the remanent flux depending upon Br . ϕbridge = Bsat Abridge ϕT =
(1)
ϕr − ϕbridge 2
(2)
By considering one equivalent magnet source and applying equivalent circuit rules a simplified RN is obtained as shown in Fig. 5. Further, by applying the flux divider rule from [9, 13] on Fig. 5, the air-gap flux expression is found as (3). To express the effect of air-gap to magnet reluctance in the flux expression, β is defined as air-gap reluctance ratio. While to present the leakage effect of each reluctance component, following ratios are defined: η is the flux barrier reluctance ratio. λ being the fluxbridge reluctance ratio and γ is the rotor bar reluctance ratio. The estimated values of the reluctance ratios are presented in Table 4.
φ g/2
+ 4Rm
2Rbarrier
Rbar
Rbridge
4Rg
φT
Fig. 5 Simplified equivalent reluctance network Table 4 Reluctance Ratios computed based on Linear RN
Parameter Reluctance ratio Barrier reluctance ratio Bridge reluctance flux ratio Bar reluctance ratio
Formula β = Rg /Rm η = Rm /Rbarrier λ = Rm /Rbridge γ = Rm /Rbar
Value 0.2657 0.1624 0.0053 0.0672
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Fig. 6 Average air-gap flux density due to magnets
The final expression of air-gap flux is presented in (3) shows that φ g depends on the total flux φ T by the reluctance ratios. ϕg = 2 ϕT ×
1 1 + β × (1 + 2η + +4λ + 4γ )
(3)
Utilizing the air-gap flux, the average air-gap flux density is found using the expression (4). Bg =
ϕg Ag
(4)
For the simplicity purpose, the slotting effect is neglected. Therefore, only the fundamental component of the air-gap flux will be evaluated for the validation. The average flux density curve in Fig. 6 is decomposed into the Fourier series to find the amplitude of the fundamental component using (5). θ in Fig. 6 is the mechanical angle presenting the air-gap position. α in (5) is the pole arc to pole pitch ratio.
Bg1
απ 4 = Bg sin π p
(5)
Inserting ϕg1 from (6) into (7), the root mean square (RMS) value of the fundamental component of the back EMF is estimated [10]. ϕg1 =
2 Bg1 Ag π
(6)
In (7) ω = 2πf is the electrical angular velocity. While Ntr ph is the number of series turns per phase and kw is the winding factor. All coefficients involve in expression (1) to (7) are presented in Table 1. ϕg1 E = kw Ntr|ph ω √ 2
(7)
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4 Steady-State Torque Characteristics The back EMF computed using RNA in Sect. 3 is used to calculate the steadystate torque in this section. In LSPMSM, after the synchronization at a constant speed, the asynchronous torque becomes zero. The torque used for motor rotation is a synchronous torque referred as steady-state torque [14]. This torque is estimated using the (8) where first term is permanent magnet torque and second term is the reluctance torque. δ in (8) is the load angle between back EMF E and phase voltage V [15, 16]. Generally, the load angle is varied by purpose for the maximum torque extraction in inverter fed motors [17]. As LSPMSM is a direct supply machine, its load angle is not used to the maximize the torque. Therefore, the computed response of torque in terms of load angle only serves to compute the maximum torque for the initial design of LSPMSM.
Tsyn =
3p E V 3p V 2 sinδ + ω Xd ω 2 Tmagnet
1 1 − Xq Xd
sin2δ
(8)
Treluctance
The relation (8) is obtained from modelling of LSPMSM in the d-q rotating reference frame in [15]. The synchronous reactance (Xd , Xq ) is calculated using relations (9) and (10) from [14]. These d-q axis reactance expressions do not consider the magnetic saturation effect. Because it only considers the reluctance of d-q axis effective air-gap. The motor parameters from Table 1 are used to calculate Xd and Xq values which are presented in Table 5.
2 2m τpole ls μ0 kw Ntr|ph ω + Xls lgd π 2p
(9)
2 2m τpole ls μ0 kw Ntr|ph ω + Xls lgq π 2p
(10)
Xd =
Xq =
Utilizing the expression (8), the steady-state torque response of the studied LSPMSM is presented in Fig. 7. This torque response allows to analyse the reluctance component and permanent magnet components of the torque separately. Whereas, the FEM provides the overall torque curve which is a sum of two torque components as presented in Sect. 5.2. Table 5 Analytically computed synchronous d-q axis reactance
Parameter D axis reactance Q axis reactance
Symbol Xd Xq
Value 16 47
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Fig. 7 Steady-state Torque components versus load angle
5 Finite Element Method Simulation For the validation of the proposed model the studied LSPMSM is modelled in 2D FEM solution. FEM is generally not used in the initial design because of high computing time. In the initial design stage, the RNA based solution is used for fast calculation and then FEM is utilized for validation of the computed results [5].
5.1 Flux Density in the Air-Gap and Back EMF To calculate the air-gap flux density, a 2D FEM model of the studied LSPMSM is simulated in open circuit condition. A polyline in the air-gap is used to trace the radial component of flux density in terms of space (air-gap position θ). The flux density in the air-gap versus θ is presented in Fig. 8a. It contains the slotting effect of the rotor bars and stator slots. To find the fundamental component of flux density, fast fourier transform (FFT) is perfomed in terms of spatial distribution and is presented in Fig. 8b. As the studied motor contains 4 poles, harmonic components of the flux denisty are present at every 4 spatial order. The back EMF value from FEM contains the slotting effect similar to as depicted in flux density response in Fig. 8a. To observe the fundamental component of back EMF the FFT is presented is presented in Fig. 9. The fundamental component at 50 Hz is the 328.74 V peak value and rms value is 232.46 V.
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(a) X =2 Y=0.721
X =6 Y=0.2
X =10 Y=0.1
(b) Fig. 8 (a) Spatial air-gap flux density and (b) corresponding FFT
Fig. 9 FFT of back EMF calculated by FEM
5.2 Steady-State Torque Calculation To validate the torque obtained by relation (8), the FEM based simulation in the steady-state is performed using Ansys Maxwell. A parametric analysis was
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Fig. 10 Steady-state torque response calculated by FEM and RNA Table 6 Comparison between RNA and FEM results
Symbol Bg1 E (RMS)
Nonlinear RN 0.6999 T 221.24 V
Simplified RN 0.69982 T 221.22 V
FEM 0.721 T 232.46 V
performed by varying load angle to find the evolution of the mean value of steadystate torque. A refined mesh with 38,000 elements was applied to have a smooth steady-state torque. The time-step was 200 points per period (20 ms). Therefore, simulation time to compute FEM characteristic for one load angle was 6 hours 9 minutes using a 32 GB RAM core i7 processor computer. The torque response from both FEM simulation and RNA are depicted in Fig. 10.
6 Comparison of the Results The values of Bg1 and E calculated from nonlinear RN, simplified RN, and FEM are listed in Table 6. The nonlinear RN based values are obtained from the implementation of Fig. 4 in MATLAB. Whereas the simplifed RN based values are computed from analytical expression (5) and (7). The values of Bg1 from the nonlinear RN and simplifed RN are identical beacause of the consideration of saturated flux-bridge in simplified RN. In FEM simulation the material core is nonlinear with permeability characteristics shown in Fig. 3 and the values are calculated in Sect. 5.2. The difference in the values from RNA and FEM is due the difference in computation method. FEM computation is based on Maxwell Stress Tensor Method while RNA is based on analytical resolution of RN. According to the Fig. 10, maximum torque from FEM simulation is 80.58 N.m at 105◦ load angle while the RNA based maximum torque is 71.38 N.m at 115◦ load angle. There is 10◦ shift in the load angle between both cases because the FEM simulation accounts the rotation of the rotor due to which the d-q inductance varies. The d-q axis reactance does not remain constant like in the RNA case. The difference
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in magnitude of torque is due to the fact that calculation technique is different in both models. Further, FEM computation of torque includes all the harmonic component of E. Whereas RN based torque computation only involves fundamental component of E.
7 Conclusions An RNA to compute steady-state torque of LSPMSM was proposed in this work. Firstly, the back EMF of the motor was calculated using RNA. A RN adapted for the studied LSPMSM was analyzed using nonlinear flux-bridge and saturated fluxbridge. Flux-bridge in the studied LSPMSM rotor always remain saturated which significantly affects the back EMF of the motor. It was found that the analytical resolution of RN with saturated flux-bridge provides the back EMF value similar to the one from nonlinear RN. Therefore, analytical resolution because of its simple integration in the optimization procedure, will be utilized in further design stages. All the notable rotor leakage flux components were included in the RN, and a new reluctance ratio γ for the rotor bars was introduced. The approach presented in this work can help to identify the rotor leakage flux in the early design stage using the reluctance ratios. RNA could also be adopted for different LSPMSM rotor topologies provided that a new RN is defined. Secondly, maximum steady-state torque of the studied LSPMSM was estimated. The torque response computed by RNA exhibits agreement with the torque obtained by FEM. Because of less computation time the proposed technique is useful for fast parametric analysis, such as to observe the effect of magnet size on the steady-state performance of the motor. In order to design the LSPMSM rotor, parametric analysis and optimization based on this RNA will be performed in future work.
References 1. P. Waide and C. U. Brunner, “Energy-Efficiency Policy Opportunities for Electric MotorDriven Systems,” IEA, Paris, 2011. 2. R. F. McElveen, R. A. Holub, and W. E. Martin, “Replacing Induction Motors With CagedRotor Permanent Magnet Motors: Application Considerations and Cost Analysis,” IEEE Ind. Appl. Mag., no. August, pp. 67–75, 2020. 3. A. U. Ganesan and L. N. Chokkalingam, “Review on the evolution of technology advancements and applications of line-start synchronous machines,” IET Electr. Power Appl., vol. 13, no. 1, pp. 1–16, Jan. 2019. 4. A. Waheed and J. S. Ro, “Analytical Modeling for Optimal Rotor Shape to Design Highly Efficient Line-Start Permanent Magnet Synchronous Motor,” IEEE Access, vol. 8, pp. 145672– 145686, 2020. 5. M. M. Ghahfarokhi, A. D. Aliabad, S. T. Boroujeni, E. Amiri, and V. Z. Faradonbeh, “Analytical modelling and optimisation of line start LSPM synchronous motors,” IET Electr. Power Appl., vol. 14, no. 3, pp. 398–408, 2020.
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6. J. G. Lee and D. K. Lim, “A Stepwise Optimal Design Applied to an Interior Permanent Magnet Synchronous Motor for Electric Vehicle Traction Applications,” IEEE Access, vol. 9, pp. 115090–115099, 2021. 7. X. Lu, K. L. V. Iyer, K. Mukherjee, and N. C. Kar, “Development of a novel magnetic circuit model for design of premium efficiency three-phase line start permanent magnet machines with improved starting performance,” IEEE Trans. Magn., vol. 49, no. 7, pp. 3965–3968, 2013. 8. R. T. Ugale and B. N. Chaudhari, “Rotor Configurations for Improved Starting and Synchronous Performance of Line Start Permanent-Magnet Synchronous Motor,” IEEE Trans. Ind. Electron., vol. 64, no. 1, pp. 138–148, 2017. 9. C. C. Hwang and Y. H. Cho, “Effects of leakage flux on magnetic fields of interior permanent magnet synchronous motors,” IEEE Trans. Magn., vol. 37, no. 4 II, pp. 3021–3024, 2001. 10. J. Pyrh¨onen, T. Jokinen, and V. Hrabovcová, Design of Rotating Electrical Machines. 2008. 11. J. Perho, “Reluctance Network for Analysing Induction Machines,” Doctoral Thesis, Helsinki University of Technology, 2002. 12. “Nonlinear reluctance with magnetic hysteresis - MATLAB- MathWorks.” https:// fr.mathworks.com/help/physmod/sps/ref/nonlinearreluctance.html (accessed Dec. 06, 2021). 13. W. Bin Tsai and T. Y. Chang, “Analysis of flux leakage in a brushless permanent-magnet motor with embedded magnets,” IEEE Trans. Magn., vol. 35, no. 1 PART 2, pp. 543–547, 1999. 14. V. Elistratova, “Optimal design of line-start permanent magnet synchronous motors of high efficiency,” Doctoral Thesis, Ecole Centrale de Lille, 2015. 15. T. Ding, “Study and optimization of line-start Permanent Magnet Motors,” Doctoral Thesis, University of Lorraine, 2014. 16. A. D. Aliabad, M. Mirsalim, and N. F. Ershad, “Line-start permanent-magnet motors: Significant improvements in starting torque, synchronization, and steady-state performance,” IEEE Trans. Magn., vol. 46, no. 12, pp. 4066–4072, 2010. 17. E. Uygun et al., “Influence of the load angle on magnetic radial forces and torque ripple of a low power permanent magnet synchronous machine,” Math. Comput. Simul., vol. 184, pp. 153–164, 2021.
An Overview of High-Speed Axial Flux Permanent Magnets Synchronous Machines Hoda Taha, Georges Barakat, Yacine Amara, and Mazen Ghandour
Abstract With the development of axial flux technology and industrial evolution, traditional machines cannot fit application requirements. Radial flux machines represent the majority of machines in high-speed application but they are not always an optimal solution according to the criteria of the considered applications. The design of the high-speed axial flux machines is challenging where many multi-physics critical issues remain to be solved. This paper reviews the highspeed axial flux machines in terms of different features such as machine types and designing structure, mechanical constraints, specific losses, materials, and application domains. The purpose is to give an overview of different technics and solutions in the literature to meet the needs of the high-speed axial flux machines to investigate their development and integration in different applications.
1 Introduction High-speed (HS) technology in electrical machines is experiencing remarkable improvements and it is gaining interest in various fields. Despite being used in the electromobility sector and extending to some generators and motors, it attracts a growing attention for various applications, such as civil, industrial, aerospace, emerging applications, and portable power generation [1, 2]. Nowadays, many applications require high-speed machines such as centrifugal compressors, micro gas turbines, pumps, energy storage, machine tools, drills, etc. [3–7]. The (HS) machines have the advantages of a reduced size, volume, and weight, higher power density, and higher efficiency compared to their low-speed counterpart machines, which reflect in a space-saving, an axial bulk length reduction, and more reliability in the machine [3].
H. Taha () · G. Barakat · Y. Amara · M. Ghandour Le Havre Normandy University, Lebanese University, Le Havre, France e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Pierfederici, J.-P. Martin (eds.), ELECTRIMACS 2022, Lecture Notes in Electrical Engineering 993, https://doi.org/10.1007/978-3-031-24837-5_46
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Usually, the electrical machines could be classified into two main categories (based on the direction of the magnetic field passing through the air gap with respect to the rotational axis): the axial flux machines (AF) and the radial flux machines (RF). The latter is more popular, their development is very mature, and they dominate in the most high-speed application [8]. However, the high-speed radial flux machines are not always the best choice especially for some applications which require a great demand for integration, the elimination of the mechanical gears, and the direct coupling to reduce the system volume and components and the cost of manufacturing and maintenance [6, 9, 10]. High-speed axial flux machines (HSAF) have recently attracted more attention and interest, and they represent a valid alternative of the traditional radial flux electrical machines due to their higher torque to weight ratio (lightness) and higher diameter to length ratio (compactness) [11, 12]. Reaching the high rotational speeds is still a significant challenge for axial flux machines. It is limited by the mechanical problems and constraints that can occur due to the centrifugal forces, the vibrations, the unbalance and displacement of the rotor, the high strong attraction force between stator and rotor, and the inability of the used materials to withstand tremendous pressure that lead to the fatigue, crack, and deterioration of machine. Thermal problems are linked directly to high speed, high operating temperature, and high frequency resulting in different critical losses, thus reducing machine efficiency [3, 13–15]. Unlike HSAF machines, where few articles discuss the essential design limitations, many research papers have already studied the various techniques, problems, and solutions for the electromagnetic, mechanical, and thermal problems, limiting the HS in RF machines and improving the performance of their designs. Therefore, additional research is required to solve the problems that limit the high speed in AF machines and improve it to be close to RF machines. This article aims to give an overview of the different constraints and solutions discussed in the literature to meet the needs of HSAF machines. The paper is organized as follows: firstly, the possible high-speed axial flux machine’s topologies are presented. Secondly, the mechanical constraints are discussed, some additional high-speed losses are highlighted, some corresponding high-speed materials types are given, and finally, some application domains of high-speed axial flux machines are reported.
2 Possible High-Speed Topologies Identifying the speed, which is considered as a decisive factor to designate an HS machine, is necessary. It would not be reasonable to take rotational speed as the only criterion. HS pushes the designer to think in terms of high fundamental frequencies and reduced dimensions, driving high power densities and cooling systems. The tangential speed at the outer rotor radius can be taken as a criterion to define the HS since it takes into account the machine size. One of the main limiting factors of the rotational speed is the rotor mechanical stress, which depends on
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the tangential rotor speed. HS machines can also be classified according to the correlations between the operating power and the rotational speed. The design and the choice of the typology of HSAF machine depend on the specifications and performances expected for a specific application, which are the density of the output power, the speed, and the machine power supply frequency. The most desirable ones present a higher power density, rotor stiffness, minimum volume, losses, and better heat dissipation. Moreover, when designing HSAF machines, it is essential to consider the electromagnetic aspect, mechanical constraints, and thermal problems, which affect the choice of materials and overall structure efficiency. The design and the control are both critical. It is possible to make some initial choices in the preliminary design phase, then check the mechanical limits and thermal behavior and adjust the geometrical and physical parameters and recheck again to get an optimal compromise between these different aspects simultaneously. The various collected literature data show that the applications, which require high speed, are performed at relatively low torque and vice versa; this is caused by the high-speed limitations, especially the mechanical stresses exerted on the rotor [2, 16–21]. Furthermore, the analysis shows that most of the reported HSAF machines structure in the literature are permanent magnet synchronous machines (PMSM), induction machines, and switched reluctance machines [2, 14]. There are also some other types of machines used at HS for specific applications like wound-field synchronous machines, claw-pole machines, flux switching synchronous machines, etc. They are less familiar than conventional machines and are not suitable for highvolume production [18, 20]. Induction machines have a robust and simple rotor structure. The absence of permanent magnets puts them in the low-cost design option, they require a little maintenance, and are easy to manufacture. The high resistance to mechanical stresses permits to withstand the high centrifugal forces and reach high speeds, especially for medium and large powers [20]. They are characterized by a low power factor and larger size when compared with other machine types. Joule losses increase rapidly with speed, resulting in high rotor core losses and hence low efficiency [22]. Switched reluctance machines also have the advantage of high reliability due to their solid rotor structure, resulting in the savings in the materials and in, the ability to resist the various thermal and mechanical problems in the rotor, and the absence of excitation losses. Eddy current losses are high in the massive rotor at high speed since (SRM) requires a high excitation current to magnetize the air gap. This reduces (according to the power supply command type), the power factor, and the machine’s overall efficiency and results in the vibrations due to the torque ripple and, therefore, some acoustic problems [18, 23]. Bearings are more worn out, due to the high air friction losses. There is an increasing interest in considering permanent magnet synchronous machines (PMSMs) for high-speed applications [22]. This goes back to rare-earth magnet types with high energy density [24]. PMSM offers good efficiency compared to other machines, high power density, superior controllability, and compact
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size at high speed. However, the design of their rotor is complex. There must be a tendency to undergo strong centrifugal forces to hold the permanent magnets on the rotor and to minimize the eddy current losses generated in the permanent magnets due to the temperature increasing to avoid their demagnetization [25]. PMSMs are mostly employed for HS operations; thus, in the following sections, only permanent magnet machines are discussed. Different types of structures of axial flux permanent magnet synchronous machines can be adopted at high speed. The choice of machine configuration depends on the conditions of the intended application and the integrity and mechanical rigidity of the rotor. The description of the different stacking topologies is based on the number of stators and rotors. The first topologies are the simplest and the least expensive to fabricate a single stator and a single rotor. It is mainly suited to low torque requirements. A large axial force is constantly acting between the rotor and the stator, demanding particular bearings and a considerable thickness of the rotor yoke. The strong axial pull can seriously harm the motor and deform the machine. This machine is less widespread than others, but it can be found in specific low-power applications [26]. It is possible to add a second stator to take advantage of the inductive field on both sides of the rotor. The resulting topology is composed of a central rotor and two stators. The rotor flux is better utilized and produces better torque. Axial forces exerted on this rotor are balanced by the opposing attraction of the two stators. The rotor is, therefore, in a stable equilibrium position. The coils are easily accessible and, therefore, easier to cool. However, the two wound stators implied more joule losses [27]. The most popular AFPM structure comprises two rotors and a central stator. The torque to mass ratio produced is the strongest of the two air gap topologies. A larger volume of iron is required, leading to more significant iron losses. This configuration produces less joule loss, but the stator is more challenging to access, so it is more challenging to cool. A strong axial attraction exists between the stators and the rotors, and the mechanical parts are then firmly stressed continuously. The last topology is the multistage one. It is achieved by stacking the previous topologies together to achieve the desired performance [28]. It is characterized by a high torque and power in the same radial length of the machine. The machine axial length is then increased.
3 Mechanical Constraints Analysis Designing HSAF machines is a technological challenge. Keeping the rotor’s integrity and the mechanical rigidity is of paramount importance. Avoiding rotor eccentricities and vibrations and overcoming mechanical stresses are some critical design issues. Due to the high operating speed, efficient mechanical sizing at the rotor in HSAFPM machines has to be considered, thus imposing constraints on the
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machine dimensions (outer rotor diameter) and having direct consequences on the electromagnetic performance.
3.1 Centrifugal Forces and Corresponding Stresses The rotor yoke and permanent magnets are applied to strong centrifugal forces at high speeds, which must be studied to avoid structure destruction and ensure a safe operation [29]. The centrifugal force is given by: Fc = m..ϑ
(1)
ϑ = rr .
(2)
Where m is the rotor’s mass, is the rotational speed, ϑ is the linear speed at the end of the rotor, and rr is the radius of the rotor. This force acts along the radius of rotation and tries to pull the permanent magnets radially outward. Therefore, the radius of the rotor must be minimized as possible to limit the linear speed, which is an essential factor when adopting the rotor dimensions [3]. The mechanical stresses of the centrifugal force and frequency limit the maximum speed and the output power. The maximum stress created by the centrifugal force is expressed by σmec = C .ρ.rr2 .2
(3)
Where C is a constant related to the Poisson’s ratio, and ρ is the material density. The rotor components should essentially derive from high strength to density ratio materials. Defining a maximum rotor yoke diameter is mandatory to limit the mechanical tensile stress in the rotor to be less than the maximum elastic stress that the rotor material can withstand [30].
3.2 Permanent Magnets Preserving the bond between the permanent magnets and the rotor core is necessary to prevent their shuttering and protect them from corrosion and demagnetization. This latter can be avoided by a rotor cooling method and a suitable design according to the required application. The permanent magnets can either be held in place by inserting them into the rotor, burying them, or gluing them. Fixing the permanent magnets with a retention sleeve helps hold and fix them and increases the rotor stiffness. The life and reliability of the retention sleeve are some critical factors, particularly in situations where the rotor rotates at high speeds for a long time [31].
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3.3 Attraction Forces Strong axial magnetic attraction forces exist between the stator and rotor and lead to difficulties in the machine fabrication and keeping the air gap uniform. This can be accentuated by the fact that the force is distributed in an unbalanced manner on the parts of the machine. Unbalanced back-electromotive forces are the principal consequence of eccentricity fault and rotor tilt in HSAFPM machines. These forces also lead to the large pressures loads on the bearings, which are more susceptible to significant harmonics in air gap magnetic flux density. Therefore, the study of the rotor movements and vibrations produced by the attraction forces between the stator and rotor disks constitutes an essential part of the design and optimization process of HSAFPM machines. These vibrations could be reduced significantly if the attraction forces produced do not stimulate the mechanical resonances of the designed structure. High-strength magnetic materials are then required to keep the magnetic pull as minimum as possible [10, 32, 33]. The magnitude of attraction forces applied on the stator magnetic disk by to the rotor’s strong permanent magnets (axial pull) is given by:
Fz =
Bg2 .S 2μ0
(4)
Where Bg is the Air gap flux density, S is the active stator surface facing the air gap area, .S = π. (Dse4−Dsi ) with Dse and Dsi the outer and inner stator diameters respectively, and μ0 is the permeability of the free space. One can conclude that to reduce axial attraction force as much as possible, permanent magnet sizing must be chosen in a way to keep Bg low, and the stator dimensions must be fixed where S is minimum. Note that when designing HS machines, the rotor resonance is an important element to take into consideration to avoid its damage by making the shaft as thick as possible and by reducing the distance between the bearings. In the same mode of vibration, this phenomenon occurs once the frequency of the force ripple applied on the rotor is close to the resonance frequency of the latter. Hence, it is necessary to predict the rotor resonance frequencies, the forces applied on the rotor, the torque ripples as well as the vibration modes. In addition, the rotor stress distribution, the electromagnetic force, and the degradation of the material’s properties must also be taken into account in order to avoid its deformation and its failure. 2
4 High-Speed Additional Losses The generated losses in HSAF machines are significant compared with low-speed machine losses. This requires ensuring an efficient thermal based sizing and a
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precise calculation for specific losses at high speed, such as winding, eddy current losses, and mechanical losses. Eddy current losses are significant since they are proportional to the frequency square. These losses are generated in the stator and the rotor yoke, permanent magnets, and magnetic conductive sleeve if any. They are also present in windings due to both skin and proximity effects. The latter is predominant at high speed since the conductors are exposed directly to the magnet magnetic field [34]. The use of Litz strand wires can be beneficial. It helps reducing these losses and serves to increase the torque. The optimal choice between Litz wires and conventional conductors depends on the specifications of the intended application [3, 35, 36]. Magnetic losses in the stator and rotor yoke appears in the form of iron and hysteresis losses (generated by the fundamental and harmonic components of the rotating magnetic field) and eddy current losses, especially in permanent magnets. At high speeds, the addition of a conductive sleeve prevents the high-frequency field from entering the rotor yoke and magnets. This reduces the losses in magnets and concentrates them in the sleeve [36]. The rotor can be also designed by using a copper shield between the permanent magnets and the retaining sleeve. In this case, much of the rotor-eddy current loss passes from the permanent magnets to the copper shield. Even if additional eddy current loss occurs in the shield, since the conductivity of the copper shield is high, this loss is not significant compared to the reduction of eddy current losses in the permanent magnets. Segmenting the pole magnets into small blocks can also be a good solution to minimize the eddy current losses in the rotor. To assess the overall losses in HS machines, one needs to estimate the mechanical losses accurately. These losses are represented in the form of friction losses in the bearings and aerodynamic losses from the air friction on the rotor circumferential surface at the air gap and on the two side faces [37]. These losses depend on the rotor dimensions, the properties and the nature of the airflow in the air gap, and the rotational speed. The friction losses are proportional to the rotational speed and depend on the nature and type of the used bearing system. Mechanical losses are limited by the maximum rotational speed, diameter, and mechanical stresses of centrifugal forces [38]. These additional losses force the machine to overheat and can lead to the demagnetization of permanent magnets, the degradation of the conductor insulations, and, consequently, affect the efficiency [8]. Hence, an accurate estimation of the losses seems critical to choose the suitable materials for the design, suitable cooling method, and predict the thermal behavior of the machine.
5 Suitable Materials for High Speed In high-speed applications, the materials are an essential design part. However, a compromise between various multi-physical aspects and costs is required. From the magnetic side, the material should withstand high flux density.
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Mechanically, rigid material resisting the high strengths and stresses is a priority. In addition, these materials must have high electrical and thermal conductivity and must be suitable for reducing losses. Soft and hard magnetic materials and conductors produce the magnetic field. Insulators are used to ensure proper operation and improve the performance [39]. A high permeability, a low mass losses, and a high magnetic flux density at saturation represent a good magnetic material.
5.1 Soft Magnetic Components To reduce the magnetic losses generated by the eddy current, soft magnetic materials of low conductivity can be used either in steel sheets of very thin thicknesses electrically insulated or in the form of iron particles separated by an electrical insulator constituting the soft magnetic composite (SMC). Several types of magnetic laminated materials are dedicated to the design of HS machines. They are made from three families of magnetic alloys: Iron-Nickel, IronSilicon, and Iron-Cobalt [40]. The materials have different multi-physical properties, and their prices depend on the desired performance and thickness of chosen steel sheets, whose price increases as their thickness decreases. Iron-Silicon Alloys, especially at 3% of Silicon, are the most used in HS machines. The addition of Silicon increases the electrical resistivity and reduces the mass losses. These alloys have a high saturation level and a good permeability. Steel sheets of the stator magnetic circuit must be chosen relatively thin to limit the magnetic losses. Manufacturers offer thin sheets in the range from 0.05 to 0.35 mm [18]. Iron-Cobalt alloys have some exciting characteristics, high cost, very high saturation level, moderate mass losses, and the highest Curie temperature [41]. These alloys are mainly used in sophisticated applications that require a low weight and a good mechanical rigidity. They can be found in the form of thin sheets in order of 0.1–0.3 mm, in aeronautical, military, and aerospace applications [42]. Iron-Nickel alloys are made with 36% and 80% of Nickel. They are used in small quantities in the high-speed machines due to their high cost and lower saturation level when compared to other alloys [42]. Iron-Nickel steel sheets are reserved for specialized applications due of their price and performance. The fabrication of SMCs by molding and compression helps to form complex shapes and increases thermal and magnetic properties. Compared to the conventional steel sheets materials, SMCs have a low relative permeability and the lower saturation level. Increasing the permeability of SMC can be done by increasing the compressive force, thus bringing the iron particles together, increasing contact between them, and overall conductivity. Reduction in the hysteresis losses can be achieved by increasing the treatment temperature. But, if the maximum temperature of the dielectric insulation is exceeded, the latter can burn, and the material conductivity increases. The design of SMCs must therefore follow a compromise
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between the conductivity, permeability, and hysteresis losses by modifying the composition and parameters of the production process [41]. The use of SMCs in HS machines is important according to the application specifications since the high magnetic losses in SMCs at low frequencies are compensated at high frequencies due to the substantial reduction in eddy currents. The total magnetic losses in SMCs, dominated by hysteresis losses, increase linearly with the frequency and become less than those in steel sheets. Given their low permeability, these materials seem to be more suitable for HSPMSMs where the magnetic air gap is large [41, 43, 44].
5.2 Permanent Magnets In HSAFPMSMs, rare earth-type Neodymium-Iron-Boron NdFeB and SamariumCobalt SmCo magnets are the most widely used [45]. NdFeB magnets are more powerful and perform better than SmCo because their energy density and remanence are higher and their cost is low. SmCo magnets are used in the applications where thermal conditions impose significant constraints due to their excellent resistance to high temperatures but higher cost. At high speeds, the resistivity of rare-earth type magnets is not negligible. It leads to a significant eddy current losses, which must be taken into account during sizing. Increasing the temperature for NdFeB magnets, which are more thermally sensitive, decreases the remanence and coercive magnetic field and lowers the demagnetization field. Magnets can be more susceptible to power loss by undergoing reversible demagnetization. To improve the efficiency of the HS machine, it is good to try almost to obtain the ideal sinusoidal counterelectromotive force by a special shaping of the permanent magnets or by varying the magnet angle, or moving them [7, 14, 46, 47].
5.3 Conductors The excitation frequency in the stator-winding conductors is high for HS machines. The appearance of eddy currents within the conductors results in an additional Joule losses due to the skin and proximity effects [48]. The control of these losses depends on the type of conductor used and its section. Two types of conductors are generally used for several classes of insulation: (i) Standard copper conductors: which are used in the majority of electrical machines. (ii) Litz Wires: These are copper conductors made up of a set of finer strands electrically insulated from each other and which are braided or stranded. They reduce the losses caused by the skin and proximity effect. The diameter of the strands should be less than the skin depth corresponding to the penetration of the eddy currents for an operating frequency. The major disadvantage of Litz
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wire conductors, which can be either round or square, or rectangular, is the decrease in the stator fills factor compared to standard conductors. During the machine design phase, the choice of the conductors depends on a compromise between the fill factor of the slots and the influence of Joule losses. In other words, an optimal compromise is therefore required between the stator linear current at load condition and the dissipated heating due to the additional Eddy current losses. To use Litz wires, the first consideration in any design is the operating frequency of such applications. This frequency is also used to determine the gauge of the individual wire.
5.4 Retaining Sleeve PMSM machines are able to have a larger air gap; the rotor-retaining sleeve can be designed with sufficient thickness since the motor is less susceptible to air gap irregularities due to manufacturing issues. Three types of mechanical sleeves are used in HSPM machines, and they can be made from several types of materials: (i) Non-magnetic and non-conductive sleeves: made from pre-stressed materials such as carbon fiber and fiberglass... those materials have good mechanical and electrical performance [49]. (ii) Non-magnetic conductive sleeves: conductive materials such as copper, aluminum, stainless steel, or titanium. Their drawback is the additional losses by induced eddy currents [49, 50]. It can cause significant warming up due to the dissipating rotor heat difficulty. (iii) Sleeves obtained from magnetic materials: such as amorphous ribbons. They increase the induction in the air gap, but they are less used because they can short circuit the sides of the permanent magnets, increase the leakage fluxes, and limit the main flux [51]. If the retaining sleeve is made of non-magnetic material, the machine’s electromagnetic air gap becomes larger, resulting in lower flux density and power density. Since a non-metallic retaining sleeve has low thermal conductivity, the rotor heat dissipation will be difficult, thus causing a rise in the rotor temperature. Sleeve resistance should be studied to avoid the thermal dilation of the rotor parts due to the change in the sleeve properties once the rotor heats up. The retaining sleeve choice depends on both the electromagnetic machine losses, its thermal behavior, and the mechanical rotor stresses.
5.5 Bearings Selection Various bearings are widely developed in the last decade and are available for HS applications: contactless or contact bearings such as magnetic bearings, oil bearings, air bearings, ceramic ball bearings . . . etc. choosing the suitable bearings
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depends on the rotational speed, the axial and radial pressures loads to which they are submitted and the environmental requirements. This choice affects the rotor dynamics (resonance frequency, vibration...etc.), air friction losses, and the life of the bearing itself due to the continuous excitation of pressures loads on them and their own characteristics and rigidities. Predicting and analyzing the rotor dynamics according to the chosen bearing and its properties is then an essential factor to consider for HS machines.
6 Application Domains of High-Speed Axial Flux Machines The applications where HS technology is adopted require compactness and lightness, whether for small, medium, or large power ratings, in a range from a few watts to hundreds of kilowatts, and operating as a motor or a generator. Rotating at high speeds is possible due to improvements in power electronics and magnetic materials. Note that the power electronics and control aspects were limited before the development of HS machines. The higher the rotational speed of the machine, the higher the fundamental power supply frequency and, thus, the switching frequencies of power electronic devices. In addition to the rapid development of high-energy magnets and reliable lubricated bearings, reductions in components and failure, maintenance-free operations, and lower cost are also remarkable advantages. Many recent researches are concerned with the development of high-speed axial flux machines and their integration into different applications. Some of them impose the presence of high speed due to external gears; others impose high energy and reduced torque. This results in a significant increasement in speed and an exciting reduction in mass. High-speed machines are widely spread in the pharmacology field in the form of machine tools used in high-speed machining (milling, drilling, cutting, turning), having precise speed and torque control and practical design due to the reduced diameter and volume [2, 6, 14]. They are also found in small microscale applications, centrifugal compressor drives, heat pumps in the power stations, and automotive turbochargers implanted in different industries for low power applications, refrigeration, direct-drive turbines, and air conditioning applications [3, 52]. Furthermore, their demand is increasing in the field of spindle applications where the need of high precision and mechanical rigidity [2] and in the electromobility sector like road transport applications, flywheel energy storage directly driven by high-speed machines [53], air fact drive, electric and hybrid vehicles and submarine ship drive, etc. High-speed generators are also implemented on many applications and mobile power generation units. Gas turbines and microturbines usually drive them. Among these applications, one can cite among other: Generation systems embedded in hybrid cars, all-electric boats, aerospace applications, starter-generation applications for aircraft engines, electromagnetic energy storage devices used in hybrid vehicles, portable power generators, etc. [1, 2, 54, 55].
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Some applications may require a dual-mode system: motor and generator, such as a gas turbine engine. High-speed power plants can drive some ordinary-speed electrical generators (micro gas turbines). Table 1 shows the rated power versus speed of some high-speed applications. For example, a parametric study is carried out in [1] to investigate the influence of some parameters on the geometry of a multi-disc axial flux synchronous generator and its performance, such as permanent magnet size and the inner/outer rotor diameter. Then, at a given speed, the number of poles turns per phase, and modules (stators and rotors) are studied. They showed that optimizing the rotor radius leads to study the bundle diameter, strand diameter, number of strands per bundle, and the impact on the eddy currents and stator copper losses. In [3], the authors design and test an AFPMSM. Four permanent magnets (NdFeB) were mounted on the rotor’s steel back iron surface with a carbon fiber ring to hold them against centrifugal force; a slotless stator made from powder composite materials was used. To improve efficiency, the magnetic air gap length has been increased to reduce the thrust force and hence bearing losses. Multi-stranded Litz wires were chosen to reduce the eddy current losses. Tested efficiency was about 67%. A new design of an AF surface-mounted SM is presented in [7, 13] for aerospace flywheel energy. Their goal is to obtain an ideal sinusoidal back EMF through a particular shape of the permanent magnet. The stator is slotless with a two-phase
Table 1 Rated power versus speed of some high-speed applications References [1] [3] [5] [6] [7][13] [15] [14][31]
Power (W) 50K 100 100K 62.8 230 70 1K
Speed range (Krpm) 50 50 70 30 32 30 50
Fig. 1 Examples of high-speed machines
Structure 2 stators, 3 rotors 1 stator, 1 rotor Multi-section 1 stator, 1 rotor 1 stator, 2 rotors 1 stator, 1 rotor 1 stator, 2 rotors
Application Modular design generator Centrifugal compressor Micro gas turbine plant Low power applications Energy storage Low power applications Portable power platform
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winding. Two magnets in the form of rings with the entire rotor surface are used in the basic model to be compared with a sinusoidal magnet shape. In the first comparison model, the stator is wound to fill the inner surface with 15 turns per coil. The back EMF induced at each turn is sinusoidal but out of phase one with the other. The base model was further compared to a second model, where the winding is inserted like a bundled coil. The second model’s performance is even better than the others. Paper [14] presents the design and analysis of an HSAFPM motor. To minimize cogging torque and iron losses, a slotless stator (non-oriented silicon steel with 0.35 mm thick lamination) is adopted, and ultra-high-strength steel is used for the rotor core. To protect rotor magnets from corrosion, high centrifugal force, and for better rotor integrity, buried quad magnets (NdFeB) were utilized. Concentrated winding with the shortest possible turns to reduce winding losses was used. They tried to make the back EMF as close to sinusoidal as possible by varying magnet angles and using the technique of moving magnet and they improved the machine efficiency to 93%. In [15], an HSAFPM generator was designed. The air-core stator configuration helps to reduce losses, and the adopted structure facilitates heat extraction through natural cooling. Eight circular permanent magnets (NdFeB) were mounted circumferentially on the surface of the steel back iron with a reinforced epoxy resin to attach and protect them, and carbon fiber retaining sleeves held them against centrifugal force. Three-phase single-layer circular armature coils are arranged around the stator, supported by non-magnetic non-conductive materials (Teflon). Fine-stranded insulated Litz wires were used to minimize the eddy current losses. Other loss studies were done to evaluate machine performance. Efficiency was about 85%.
7 Conclusion The paper aimed to present a general overview of high-speed axial flux permanent magnet synchronous machines technology by highlighting the various multi-physics obstacles for a multidisciplinary approach where an optimal compromise between the different electromagnetic, mechanical and thermal aspects simultaneously is a principal necessity for the environment multi-domain applications. Some techniques and solutions were discussed to meet the high efficiency and performance demand, low cost, high operating materials, and innovative design methods.
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