The Proceedings of 2022 International Conference on Wireless Power Transfer (ICWPT2022) 981990630X, 9789819906307
This book includes original, peer-reviewed research papers from the 2022 International Conference on Wireless Power Tran
276 85 155MB
English Pages 1212 [1213] Year 2023
Contents
Quadrature Six-Coils Wireless Charging with High Misalignment Tolerance and Constant Voltage Output
1 Introduction
2 The Proposed Hybrid IPT System
3 Magnetic Coupler
4 Experimental Verification
5 Conclusion
References
Inductively Coupled Power Transfer System Based Constant Voltage and Constant Current Charging for Rail Transit System
1 Introduction
2 Topology of ICPT System
3 Analysis of CV and CC Charging Mode
3.1 CV Charging Mode
3.2 CC Charging Mode
4 Simulation Results and Analysis
5 Conclusion
References
Modeling and Analysis of Bidirectional Wireless Power Transfer System with Asymmetric Parameters
1 Introduction
2 Basic Working Principle
2.1 Topological Structure of BWPT
2.2 3-Freedom Control Method
3 Power and Efficiency Model in Frequency Domain
3.1 Bidirectional Transfer Power Analysis
3.2 Maximum Efficiency Point Analysis
3.3 Asymmetric Parameters Analysis
4 Experimental Confirmation
5 Conclusion
Appendix
References
Design and Research on Coupling Mechanism of Inductive Power Transmission
1 Introduction
2 Coil Structure
3 Coupling Mechanism Materials
4 Optimization of Coil Parameters
5 Conclusion
References
Characteristics of Wireless Power Transmission Based on a New Spiral Resonant Coil
1 Introduction
2 Spiral Three-Coil WPT System
2.1 Structural Design
2.2 Simulation Results
2.3 Experimental Results
3 Spiral Four-Coil WPT System
4 Conclusion
References
Efficiency Optimization Method for Wireless Power Transfer System Between the Rocket and the Ground Based on Energy Compensation
1 Introduction
2 System Structure and Theoretical Analysis
2.1 Efficiency Analysis
2.2 Model of the Energy Receiving Processor
2.3 Characterisation of the Proposed WPT System
3 System Control Strategy
3.1 Control Strategy of Bus Voltage
3.2 Energy Management Scheme
3.3 Control Method for Efficiency Optimization
4 Simulation Analysis
5 Conclusion
References
Design and Modeling of Helmholtz Coil Based on Winding Method Optimization
1 Introduction
2 Helmholtz Coil Structure and Winding Methods
3 Parasitic Capacitance Between Windings
3.1 Litz Wire Model and Benchmark Example
3.2 Subdivision of Inter-turn and Inter-layer Capacitance
4 Theoretical Calculation for Stray Capacitance
4.1 Theoretical Calculation of Parasitic Capacitance
4.2 Effect of Turns and Layers on Equivalent Parasitic Capacitance Under Different Types of Winding
5 Experimental Verification and Result Analysis
5.1 Coil Design and Winding Optimization
5.2 Driving Experiment
6 Conclusion
References
Applicability Analysis of Coupled-Mode Theory Model in Capacitive Power Transfer System
1 Introduction
2 System Overview and Modeling
2.1 Circuit Structure of CPT System
2.2 Modeling Based on Coupled-Mode Theory
3 Transfer Efficiency and Power Based on Couple-Mode Theory
4 Simulation and Experimental Verification
5 Conclusion
References
Optimal Efficiency Control of Multiple Transmitting Array WPT System for Constant Power
1 Introduction
2 MTA-WPT System Model
3 Tx and Rx Coils Coupling Coefficient Simulation
4 Maximum Efficiency Control Strategy of MTA-WPT System for Constant Power
5 Simulation Experiment and Analysis of Maximum Efficiency Control Strategy
6 Conclusion
References
Optimized Design of the DD Coil for Improved Misalignment Tolerance
1 Introduction
2 Finite Element Analyses on the Coil Parameters
2.1 Analysis of the Spacing Between Magnetic Bars
2.2 Analysis of the Number of Turns of the DD Coil
2.3 Analysis of the Overlapped Edges of the DD Coil
3 Optimized Design of the DD Coupling Coil
4 Conclusions
References
Analysis of Geometric Characteristics of Three-Terminal Shaft Loosely Coupled Transformer Based on LCC-S Compensation
1 Introduction
2 ICPT System Structure Under LCC-S Compensation
3 Characteristic Analysis of Three-Terminal Shaft Loosely Coupled Transformer Three-Terminal Shaft Loosely Coupled Transformer Structure
4 Analysis of Geometric Characteristics of Three-Terminal Shaft Loosely Coupled Transformer Under LCC-S Compensation
4.1 Analysis of Axial Offset Influence of Three-Terminal Shaft Loosely Coupled Transformer
4.2 Comparative Analysis of Offset Characteristics of Three-Terminal and Single-Ended Axial Loosely Coupled Transformers
4.3 Optimization of Separation Distance Between Coils of Three-Terminal Shaft Loosely Coupled Transformers
5 Conclusion
References
Frequency Tracking Synchronization Technique for a Bidirectional Inductive Power Transfer System
1 Introduction
2 A Typical BD-IPT System
3 The Proposed Synchronization Technique
4 Experimental Validation
5 Conclusion
References
Analysis and Design of Magnetic Cores for Rotary Wireless Power Transfer Applications
1 Introduction
2 Magnetic Circuit Modeling from Geometry
2.1 Reluctance Model for a U-shaped Structure
2.2 Reluctance Model for a E-shaped Structure
3 Simulation and Experimental Results
3.1 FEM Analysis and Practical Design Considerations
3.2 Experimental Results
4 Conclusion
References
Electrical Characteristics of Magnetic Couplers in Inductive Power Transfer for Autonomous Underwater Vehicles
1 Introduction
2 Coupling Characteristics of Different Coil Structures
3 Coupling Characteristics with Different Misalignment
3.1 Misaligned at the Axial Direction
3.2 Misaligned at the Rotational Direction
4 Eddy Current Loss
4.1 Theoretical Analysis
4.2 Impact of the Frequency
5 Conclusions
References
Generation of an Airy Beam Based on a Holographic Scalar Metasurface
1 Introduction
2 Theoretical Analysis
2.1 Generation Principle of the Airy Beam
2.2 The Principle of the Holographic Metasurface
3 DESIGN oF the HOLOGRAPHIC METASURFACE aND tHE SIMULATION RESULTS
3.1 The Design of the Holographic Unit
3.2 The Simulation Result
4 Conclusion
References
Modulation of Deflected Bessel Beams Based on Reconfigurable Metasurface
1 Introduction
2 Theory and Design Methods
2.1 Theory of Bessel Beam
2.2 Design Method of the Metasurface
3 Design and Simulation of the Reconfigurable Metasurface
3.1 Design of the Metasurface Elements
3.2 Generation of the Bessel Beam
4 Conclusion
References
Simulation and Optimization Analysis of Magnetic Coupling Mechanism for Resonant Wireless Power Transfer
1 Introduction
2 Principles and Models
2.1 Principles of WPT
2.2 Mutual Inductance Coupling Models of Resonant Circuit
3 Parameter Design and Modeling Optimization of Magnetic Coupling Mechanism
3.1 Model Optimization
3.2 Coil Model
3.3 Magnetic Core Design
3.4 Electromagnetic Shielding Design
4 Electromagnetic Simulation Analysis
4.1 Magnetic Field Distribution of WPT
4.2 Effect of Coil Space Position Offset on WPT
5 Joint Simulation Analysis
5.1 Time Domain Simulation Analysis
5.2 Frequency Domain Simulation Analysis
6 Conclusion
References
Loss Analysis of Rectifier Circuit and Its Optimization Technique in Wireless Power Transfer System
1 Introduction
2 Loss Analysis of Rectifier Circuit
2.1 Loss Model of Full-Bridge Rectifier Circuit
2.2 Loss Model of Voltage-Doubler Rectifier Circuit
3 Loss Comparison of Full-Bridge Rectifier and Voltage-Doubler Rectifier
4 Experimental Verification
5 Conclusion
References
Simultaneous Wireless Power and Data Transfer System Using Parallel Injection Communication Method
1 Introduction
2 System Topology and Working Principle
2.1 Power Transfer
2.2 Data Transfer
3 Analysis of Crosstalk Between Power and Data Channel
3.1 Power Interference
3.2 Data Interference
4 Simulation Verification
5 Conclusion
References
A Magnetic Field Energy Harvester to Power Micro-power Sensors on the Freight Train for Railway Application
1 Introduction
2 System Analysis
3 Finite Element Simulation
3.1 Core Height
3.2 Metal Material
3.3 Saturation Limit of Core
4 Experimental Test
5 Conclusion
References
Coupling Comparison of Magnetic Couplers for Mid-range Wireless Power Transfer Systems
1 Introduction
2 Typical Magnetic Couplers for Mid-range WPT Systems
3 Shielding Scheme and Ferrite Layout of Cylindrical and Cuboid Couplers
4 Coupling Comparison of Typical Magnetic Couplers
4.1 Coupling Comparison in Unity Distance-To-Diameter Ratio Case
4.2 Impact of Pad Height on Coupling Coefficient
4.3 Impact of DDR on Coupling Coefficient
5 Conclusion
References
Model-Inverse-Based Output Control of the Multi-excitation-Unit WPT System
1 Introduction
2 Modeling of the MEU-WPT System
3 Controller Design of the MEU-WPT System
4 Experimental Results
4.1 Reference Tracking Experiment
4.2 Load Switching Experiment
5 Conclusion
References
The Impact of Metal Hull of AUVs for Underwater Wireless Power Transfer System
1 Introduction
2 Coupling Structure and Theory Analysis
3 Simulated and Experimental
3.1 Underwater Inductive Wireless Power Transfer System
3.2 Experimental Verification
4 Conclusions and Discussions
References
Synchronous Identification of Loads and Mutual Inductances for Multi-frequencies Multi-loads WPT System
1 Introduction
2 System Model and Identification Method
2.1 Analysis of Multi-loads Transmission
2.2 Primary Side Current Detection
2.3 Analysis of PSO Algorithm
3 Simulation Verification
3.1 Independent Control Verification of the MCR-WPT System
3.2 Parameter Identification Verification
4 Conclusion
References
A Cross-Shaped Solenoid Magnetic Coupler with High Lateral Offset Tolerance
1 Introduction
2 Magnetic Coupler Design
2.1 Coil Structure Optimization and FEA-Based Simulations
2.2 Analysis of the Mutual Inductance
3 Experimental Verification
3.1 Experimental Setup
3.2 Measurement of the Experiment
4 Conclusion
References
A Design of Secondary-Only Resonant Series-Series WPT System to Maintain Power Stability with Coil Misalignment
1 Introduction
2 Theoretical Derivation of Secondary-Only Resonant SS System
3 Simulation of SS WPT System and Experiment Results
4 Conclusion
References
Research on Constant Voltage Control Strategy of Dual Pick-Up Dynamic Inductive Coupled Power Transfer System Based on Optimal Efficiency
1 Introduction
2 Analysis of Transmission Characteristics of Dynamic ICPT System with Double Pickup
3 Constant Voltage Control Strategy Based on Optimal Efficiency
4 Experimental Analysis
4.1 Introduction to Experimental Platform
4.2 Analysis of Experimental Results
5 Conclusion
References
Analysis and Modeling of Response Characteristics Under Actual Rectifier Parameters in the Wireless Power Transfer System
1 Introduction
2 Fundamental Harmonic Equivalence Analysis
3 Analysis of Rectifier Load Equivalence and Its Influence
3.1 Modeling Method Under Actual Rectifier Parameters
3.2 System Characteristics Under Actual Rectifier Parameters
4 Experimental Verification and Analysis
5 Conclusions
References
Metal Object Detection for Electric Vehicle Wireless Charging Based on Fusion of Spectral and Texture Features
1 Introduction
2 Proposed Method
2.1 Target Segmentation and Classification
2.2 Hyperspectral Feature Extraction
2.3 Texture Feature Extraction
2.4 Feature Fusion
3 Experimental Results and Discussion
3.1 Experimental Configurations
3.2 Target Segmentation and Classification Results
3.3 Classification Results of SVM
3.4 Fusion Results of MOD
4 Conclusion
References
Study on the Performance of a Novel High Lateral Displacement Receiver Coil Based on Cross-Winding Method
1 Introduction
2 Anti-migration Ability Analysis of Stacked Coil Mechanism
3 Cross Wound Laminated Coil Structure
4 Verification of Inter-turn Voltage and Anti-migration Ability of New Laminated Coil
4.1 Simulation and Verification of Traditional Double-Layer Coil Inter-turn Voltage and New-Type Laminated Coil Inter-turn Voltage
4.2 Simulation of Anti-migration Ability of Stacked Coil
5 Conclusion
References
Anti-misalignment Improvement for SS Compensated IPT System Using Reconfigurable Rectifier
1 Introduction
2 Theoretical Analysis
2.1 Analysis of Detuned SS Compensation Topology
2.2 The Effect of Equivalent AC Load
3 Implementation of Ac Load Change
3.1 Structure of the Reconfigurable Rectifier
3.2 Analysis of the Efficiency
4 Experimental Results
5 Conclusion
References
Design and Icing Analysis of a Novel Magnetic Coupling Mechanism for WPT System on High-Voltage Transmission Lines
1 Introduction
2 Design of Magnetic Coupling Mechanism
2.1 Topological Analysis
2.2 Selection of Coil Parameters
2.3 Design of the Magnetic Core Structure
3 Application Analysis of Icing Performance
3.1 Calculation Principle of Iced Insulator
3.2 Influence of Icicle Length
3.3 Influence of Water Film Thickness
4 Conclusion
References
Research on Maximizing the Communication Capacity of OFDM-Based Simultaneous Wireless Transmission of Power and Information (SWTPI)
1 Introduction
2 Information Transmission Analysis
3 Communication Capacity Optimization Analysis
3.1 Subproblem I
3.2 Subproblem II
3.3 Overall Algorithm
4 Simulation Results
5 Conclusion
Appendix
References
Loss Analysis of Magnetic Core and Its Structure Optimization of Magnetic Coupling Structure in Wireless Power Transfer System
1 Introduction
2 The Flux Density and Core Loss Distribution Analysis of Magnetic Cores
2.1 Distribution of Flux Density in Disk Cores
2.2 Core Loss Analysis
3 Magnetic Core Layout Optimization Design of Magnetic Coupling Structure
4 Experimental Verification of Optimal Core Arrangement
5 Conclusion
References
Compact Mixed DC-DC Power Converters for Computing Server
1 Introduction
2 Multi-phase Series-Capacitor Buck Converter
3 Simulation Result and AC Losses Discussion
4 Conclusion
References
A Flexible Foreign Object Detection Method Based on Arrayed Vertical-Decoupled Coils for Wireless Power Transfer Systems
1 Introduction
2 Modeling of the Proposed Vertical-Coils-Based FOD Method
2.1 Basic Scheme
2.2 Circuit-Based Analysis of Detection Units
2.3 Theoretical Analysis of Vertical Detection Coil Array
3 Simulation and Analysis of Detection Coils
3.1 Analysis of the Number of Detection Coils
3.2 The Influence of Foreign Objects on the Magnetic Field of Coils
3.3 Simulation of Vertically Arranged Detection Coils
4 Experimental Measurement and Analysis
4.1 Experiment Setup
4.2 Detection Sensitivity Affected by Foreign OBJECt’s Positions
4.3 Decoupling Feature Between Power Stage Coupling Coils and FOD Coils
5 Conclusion
References
Optimal Efficiency Design of Single-to-Multiple Constant Voltage Based on LCC Compensation Topology for Wireless Power Transfer
1 Introduction
2 SIMO Circuit Model with LCC-S Topology Compensation
3 SIMO Efficiency Optimization Design
4 Simulation and Experimental Verification
5 Conclusion
References
Design of Dynamic Wireless Charging System Based on Coupling Coefficient Estimation
1 Introduction
2 System Modeling
2.1 System Introduction
2.2 Analysis of Magnetic Coupling Mechanism
2.3 Compensation Network Design
2.4 Optimal Load Modeling
3 Maximum Efficiency Tracking Model Based on Coupling Coefficient Estimation
3.1 Kalman Prediction Model
3.2 Triple Exponential Smoothing Model
3.3 Coupling Coefficient Estimation Optimization
4 Test Results
4.1 Validation of Maximum Efficiency Tracking Model Based on Coupling Coefficient Estimation
4.2 Coupling Coefficient Estimation Model Results Physical Platform Verification
5 Conclusion
References
Influence of Frequency on Transmission Performance of Multi-relay Wireless Power Supply System
1 Introduction
2 Equivalent Circuit Model
3 Simulation Analysis
4 Experimental Verification
5 Conclusion
References
Bidirectional Wireless Power Transfer System Control Strategy on Double-Sided LCC Resonant Network
1 Introduction
2 Steady-State Analysis of Double-Sided LCC WPT System
3 Dynamic Model
4 Control System Dynamic Analysis and Controller Design
5 Parameter Design of Passive Components
6 Simulation and Experimental Validation
7 Discussion
Appendix
References
Design of Underwater Wet Plug Connectors System Based on the Principle of Wireless Power Transfer
1 Introduction
2 Structure Design of Underwater Wet Plug Connector
3 Magnetic Coupler Design
4 Power Transmission and Control System of Underwater Wireless Power Transfer System
4.1 Power Transmission and Control System
4.2 Topology Theory Analysis of WPT System
4.3 Closed-Loop Control of WPT System
5 Test Verification and Analysis
5.1 Air Environment Test
5.2 Pool Environmental Test
5.3 Marine Environment Test
6 Conclusion
References
Metal Foreign Object Detection Algorithm Based on Multivariate Normal Distribution
1 Introduction
2 Detection Principle
2.1 Coupling Model Between MFM and Monitor Coil
2.2 Multivariate Normal Distribution Principle
3 Experimental Verification
4 Conclusion
References
Research on Parallel Circulation Suppression Strategy of High-Frequency Resonant Inverter Based on Improved Active Current Decomposition Method
1 Introduction
2 Analysis of High Frequency AC Inverter Level Parallel Circulation
3 Decomposition of Active Current
3.1 Definition of Active and Reactive Current
3.2 Decomposition of Active and Reactive Currents
3.3 Circulation Suppression Control Strategy for Parallel Inverters
4 Experimental Verification
5 Conclusion
References
The Power Control of a Multiple Pick-Up Bidirectional Wireless Power Transfer System
1 Introduction
2 System Model and Control
2.1 System Structure
2.2 BWPT System with One Pick-Up
2.3 BWPT System with Multiple Pick-Ups
3 Experimental Verification
3.1 Experiments of BWPT System with One Pick-Up
3.2 Experiments of BWPT System with Multiple Pick-Ups
4 Conclusion
References
Robust Regulation of Constant Current Wireless Charging System with Clamping Coil
1 Introduction
2 Output Characteristics of Proposed System
2.1 Analysis of CC Output Under Load Variation
2.2 Analysis of CC Output Under Mutual Inductance Variation
2.3 The Input ZPA Realization Analysis
3 Experiment
3.1 Experiment Platform
3.2 Experiment Result
4 Conclusion
References
Comparison of Wireless Power Transfer Systems with Multi-loads
1 Introduction
2 Analysis of Single Frequency WPT System
2.1 Modeling of the WPT System
2.2 Multi-load Analysis of the WPT System
3 Multi-load WPT Analysis Based on MFMA-PWM Principle
4 Experimental Verification
5 Conclusions
References
Multi-objective Optimization of IPT System Compensation Parameters for Improving Misalignment Tolerance
1 Introduction
2 Design and Analysis of LCC-S Compensation Topology
3 Multi-objective Optimization for Compensation Parameters
3.1 Overview of PSO Algorithm
3.2 Optimization Objectives
3.3 Setting Constraints
3.4 Optimal Design Procedure and Results
4 Experimental Results
5 Conclusion
References
Design of LCLC-S Impedance Matching Network for Ultrasonic Wireless Power Transmission System
1 Introduction
2 UPT System Structure
3 Mathematical Model Establishment of UPT System
4 LCLC-S Impedance Matching Network Design
4.1 Structural Design of Impedance Matching Network at Transmitter
4.2 Structural Design of Impedance Matching Network at the Receiving End
5 Simulation and Experimental Verification
5.1 Simulation Verification
5.2 Experimental Verification
6 Conclusions
References
A Switchable Modular AC~DC Buck-Boost Converter for the Wide Input Range in Energy Harvesting
1 Introduction
2 System Structure and Topology
3 Design Principle and Working Process of Switching Circuit
3.1 Loss of Converter
3.2 Switching Circuit
4 Prototype Design and Measurement Results
5 Conclusion
References
Research on Active Leakage Magnetic Field Suppression Techniques Applied in Electric Vehicle Wireless Chargers
1 Introduction
2 Active Suppression Method for Dual ASC Driven by Independent Inverters
2.1 Overall Design of the Dual ASC Active Suppression Method
2.2 ASC Current Control Strategy Research
3 Experiment of Dual ASC Active Suppression
3.1 Introduction to the Experimental Platform
3.2 Experiment of Leakage Magnetic Field Suppression Capability
4 Conclusion
References
The Solution of Power Frequency Electromagnetic Field for Parallel Transmission Lines Based on Superposition Algorithm
1 Introduction
2 Power Frequency Electromagnetic Field
2.1 Power Frequency Electric Field
2.2 Power Frequency Magnetic Field
3 Solution Method of Power Frequency Electromagnetic Field for PTL
3.1 Solution Method of PFEF
3.2 Solution Method of PFMF
4 Result Analysis of Power Frequency Electromagnetic Field
4.1 The Model of PTL
4.2 Measurement Experiment of Power Frequency Electromagnetic Field
4.3 Analysis and Comparison of Theoretical Values and Measured Values
5 Conclusion
References
Coupler Comparison of Inductive and Capacitive Power Transfer Systems
1 Introduction
2 Uniform IVS Model and Coupling Space
2.1 Uniform IVS Model
2.2 Peak Efficiency
2.3 Uniform Coupling Space
3 Optimization of Inductive Coupler
3.1 Variable Design of IPT Coupler
3.2 Simulation Results
4 Optimization of Capacitive Coupler
4.1 Variable Design of CPT Coupler
4.2 Simulation Results
5 Comparison
6 Conclusion
References
Design of Integrated Coil Structure for Simultaneous Wireless Information and Power Transfer Applied to Electric Power Inspection Robot
1 Introduction
2 Integrated Coil for SWIPT
2.1 Integrated Coil Structure and the Decoupling Principle
2.2 Decoupling Coupling Enhancement and Decoupling of Information Coils
2.3 Simulation Validation
3 Circuit Model of SWIPT
3.1 Power Transfer Equivalent Circuits
3.2 Information Modulation and Demodulation
4 System Experiments
5 Conclusion
References
Reconfiguration and Reuse of Receiver/Repeater in Wireless Power Transmission System
1 Introduction
2 System Description
3 System Modelling
4 Comparative Analysis
5 Conclusions
References
Improved Electromagnetic Halbach Array for Enhanced Efficiency in Wireless Power Transfer
1 Introduction
2 Improved Electromagnetic Halbach Array
2.1 Principle of the Electromagnetic Halbach Array
2.2 Magnetic Field of a Planar Square Coil
2.3 Proposed Design
3 Methodology
4 Results and Discussion
4.1 Magnetic Field
4.2 Power Transfer Efficiency
5 Conclusions
References
Robust Control of Ultrasonic Power Transfer System Under Parameter Perturbation
1 Introduction
2 Principle of Ultrasonic Power Transfer
3 Establishment of GSSA Model of Ultrasonic Power Transfer
4 Robust Controller Design Based on GSSA Model
4.1 Establishment of System Parameter Uncertainty Model
4.2 Controller Design of the System
5 Simulation Verification
6 Conclusion
References
Influence of Loop Impedance on Performance of Charging Power Supply Based on Battery Packs Connected in Series
1 Introduction
2 Mathematical Modeling of Cascade Charging Topology
3 Effect of Loop Resistance on Charging Current of Cascade System
3.1 The Reference Peak Current Imax is the Peak Current
3.2 Simulation Verification
3.3 The Reference Peak Current Imax is a Certain Value Which Greater Than the Peak Current When the First Battery is Connected in Series
3.4 Simulation Verification and Analysis
4 Analysis of Optimal Solution of Loop Resistance Parameters
5 Conclusion
References
Current Source Converter Optimization Method Based on Multi-step FCS-MPC
1 Introduction
2 Fundamental Theory
2.1 Construction of Multi-step Prediction Model
2.2 Conventional Multi-step FCS-MPC
3 The Proposed Method
3.1 Deadbeat Control
3.2 Multi-step Optimal Vector Sequence Selection
4 Simulation Verification
4.1 Reference Output Voltage Jump Analysis
4.2 Analysis of Output Voltage and Grid Current
5 Conclusion
References
A Fixed-Admittance Modeling Method of Power Electronic Switches Based on State Initializations
1 Introduction
2 L/C Equivalent Model
2.1 Classical L/C Equivalent Model
2.2 Virtual Power Loss
3 Virtual Power Loss Elimination
4 Factors Affecting Model Accuracy
4.1 Switch Device Characteristics
4.2 Equivalent Element Characteristics
5 Simulation Analysis
5.1 Example 1: A Boost Converter in Normal Conditions
5.2 Example 2: A Two-Level Bridge Converter in Fault Injection Conditions
6 Conclusion
References
Configuration Strategies of Reactive Power Compensation in Converter Stations with STATCOM
1 Introduction
2 Equivalent Circuit of AC-DC Systems
3 Equivalent Model of STATCOM
3.1 Steady-State Characteristics
3.2 Transient Characteristics
4 Reactive Power Compensation Strategy for Converter Stations
4.1 Constant Current Control Mode at Rectifier Side or Constant Voltage Control Mode at Inverter Side
4.2 Constant Current Control Mode at Rectifier Side or Constant Arc Extinguishing Angle Control Mode at Inverter Side
5 Case Analysis
6 Conclusion
References
SiC MOSFET Gate Drive Power Supply Based on Active Clamp Flyback
1 Introduction
2 Auxiliary Discharge Branch Hybrid Resonant DC/DC Active Clamp Flyback Converter
2.1 Circuit Topology
2.2 Circuit Analysis Under Mixed Resonance
3 Characterization Analysis and Parametric Design
3.1 Switch Realizes ZVS
3.2 Current Sag Process and Current Waveform of Hybrid Resonance
3.3 Component Parameter Design and Device Selection
4 Planar Transformer Design
5 Simulation and Experimental Verification
6 Conclusion
References
Analysis of Release Voltage Fluctuation Mechanism of Electromagnetic Relay with Bridge Polarized Magnetic System
1 Introduction
2 Research Object and Problem Description
2.1 Analysis of Research Object
2.2 Problem Posing
3 Establishment of Virtual Prototype Model
4 Analysis of Release Voltage Fluctuation Mechanism
4.1 Magnetic Flux Leakage of House
4.2 Analysis on the Mechanism of Release Voltage Reduction
5 Conclusion
References
Analysis and Optimization of a Three-Coil Coupler Based WPT System Featuring High Efficiency and Misalignment Tolerance
1 Introduction
2 Parameter Decoupling of the Three-Coil Coupler
2.1 Overview of the Three-Coil Coupler
2.2 Mutual Inductance Decoupling
3 Parameter Optimization of the Three-Coil Coupler
4 Experiment Verification and Discussion
5 Conclusion
References
Research on Interleaved DC-DC Converter with Extended CD Unit
1 Introduction
2 A New Topology and Its Principle Analysis
2.1 The Proposal of a New Topology
2.2 Working Principle Analysis
3 Steady State Characteristics and Performance of Topology
4 Validation of Experimental Results
5 Conclusion
References
Double Random PWM Method of DC-DC Chopper Converter Based on WELL Look-Up Table Method
1 Introduction
2 Well Algorithm
3 Double Random PWM Method for DC - DC Chopper Converter
4 Simulation and Experiment
5 Conclusion
References
Design and Analysis of a High-Voltage and High-Power ANPC Three-Level Power Module
1 Introduction
2 Analysis of Power Circuit
2.1 Voltage Stress of IGBT
2.2 IGBT Arrangement Analysis
3 Comparation of Different Topology Schemes
3.1 Power Loss Analysis
3.2 Influences of Three-Level Topology in Traction System
4 Experiment Result
4.1 Double-Pulse Experiment
4.2 Power Loss Experiment
5 Conclusion
References
Research on the Influence of Cable Capacitance of EMU Converter on IGBT Protection and Control
1 Introduction
2 Introduction to EMU Traction System
3 Generation of Cable Distributed Capacitance
3.1 Generation Mechanism and Calculation
3.2 Simulation Analysis
4 Influence of Cable Distributed Capacitance
4.1 Principle Analysis
4.2 Test Verification
5 Conclusion
References
Optimal Sampling Frequency of SVPWM for Multilevel Converter
1 Introduction
2 The n-cell Cascaded H-bridge Multilevel Converter
3 Reference Vector Trajectory and Space Vector Distribution of CHBMC
4 Optimal Sampling Frequency in SVPWM
5 Simulation Analysis
6 Optimal Sampling Frequency in SVPWM
References
Reliability Evaluation Method of Active Distribution Network Based on Optimization Model
1 Introduction
2 Model and Indices of Reliability Evaluation
2.1 Line Model
2.2 Multi-state Model of Combined Photovoltaic and Load
2.3 Reliability Index
3 Operating Rules and Model Assumptions
4 Reliability Evaluation Method Based on Optimization Model
5 Case Studies
6 Conclusion
References
A Review of the Current State of Development of High Precision AC Power Frequency Converter
1 Introduction
1.1 A Subsection Sample
2 Research Status of High-Percision AC Power Frequency Converter
2.1 Status of Foreign Research
2.2 Status of Domestic Research
3 Implementation of High Precision Inverter Power Supply
3.1 Power Amplifier Type AC Power Frequency Converter
3.2 PWM Type AC Power Frequency Converter
4 Control Strategy of High Precision Inverter Power Supply
4.1 PID Control
4.2 PR Control
4.3 Repeatitive Control
4.4 No Differential Beat Control
4.5 Other New Intelligent Control Methods
5 Conclusion
References
Electromagnetic Scattering Characteristics of Different Polarized Electromagnetic Waves by High Voltage Transmission Lines
1 Introduction
2 Passive Interference
3 Passive Interference Calculation Model
3.1 Calculation Model
3.2 Method of Moments
3.3 Polarization
4 Calculation Results
4.1 Different Frequencies
4.2 Different Distances
4.3 Tower Influence Coefficient
5 Conclusion
References
The Acquisition and Research of the Relative Complex Permeability of the Core Material of the Self-inductive Displacement Sensor
1 Introduction
2 Theoretical Analysis
3 Experimental Research Process
4 Conclusions
References
Current Sharing of Parallel IGBT Affected by Thermal Resistance
1 Introduction
2 Analysis Model
2.1 The Darlington Equivalent Circuits of IGBT
2.2 Current Unbalance Limits for Thermal Resistance
3 Simulation Result of Parallel Connected IGBTs
4 Conclusion
References
A Novel High Step-up DC-DC Converter Integrating Coupled-Inductor with Quasi-Symmetric Gain Feature
1 Introduction
2 Operation Principle
2.1 C-CCM Mode
2.2 C-DCM Mode
3 Steady-State Analysis
4 Experiment Result
5 Conclusion
References
A Behavior Model of Planar SiC MOSFET Considering Avalanche Breakdown
1 Introduction
2 Modeling
2.1 Cell-Level Physical Mechanisms of Avalanche Breakdown in Planar SiC MOSFET
2.2 Behavior Model Considering Avalanche Breakdown
2.3 Methodology for Junction Temperature Calculation
3 Calculation of Breakdown Voltage
3.1 Impact-Lonization Model
3.2 Electric Field Intensity Calculation
3.3 Breakdown Voltage Calculation
4 Verification of Proposed Model
5 Conclusion
References
Envelope Tracking Power Supply for Energy Saving of Mobile Communication Base Stations
1 Introduction
2 Hybrid ET Power Supply
2.1 Structure of the ET Power Supply
2.2 Hybrid ET Power Supply with Multi-level Converter
3 Control for Hybrid ET Power Supply
4 Experimental Design and Verification
4.1 Parameters Design
4.2 Experiment
5 Conclusions
References
Calculation of Turn-To-Turn Parasitic Capacitance
1 Introduction
2 Calculation of Parasitic Capacitance Between Turns of a Circular Wire Considering Insulation Materials
2.1 Segmented Solution Method
2.2 Equivalence Method
2.3 Simulation Verification
3 Conclusion
References
A Lag Compensation Method Based on All-Pass Filter
1 Introduction
2 Model of the Single-Phase Inverter with LC Filter
3 Stability Analysis of the Single-Phase Inverter with LC Filter
3.1 Number of Unstable Poles
3.2 Number of -180° Crossings
4 Lag Compensation Methods
4.1 Notch Filter
4.2 All-Pass Filter
5 Parameters Design
6 Simulation and Experimental Results
7 Conclusion
References
Characteristic Research of Magnetic Controllable Voltage Regulator
1 Introduction
2 Model of Magnetic Controllable Voltage Regulator and Its Working Principle
2.1 Model of Magnetic Controllable Voltage Regulator
2.2 Working Principle of Magnetic Controllable Voltage Regulator
3 Simulation Analysis of Magnetic Controllable Voltage Regulator
3.1 Modeling Method
3.2 Construction of the Simulation Circuit
3.3 Analysis of Output Voltage Characteristics
4 Conclusion
References
Space Vector Pulse Width Modulation Strategy for Cascaded Three-Phase Bridge Converters
1 Introduction
2 Cascaded Three-Phase Bridge Converters
3 Coordinate Transformation and Space Vector Distribution
4 Locating and Synthesizing Reference Vector
5 Simulation Verification
6 Conclusion
References
Design and Optimization of Totem Pole Bridgeless PFC Based on GaN
1 Introduction
2 Working Principle and Modeling
3 Control Strategy Optimization
3.1 Piecewise PI Compensation
3.2 Duty-Ratio-Feedforward Control
3.3 Optimization of Current Loop Bandwidth
4 Design of Control System and Main Circuit Parameter
4.1 Control System
4.2 Filter Inductance L
4.3 Output Filter Capacitor C
5 Experimental Verification
References
A Modular Multi-port Converter for Distribution of Vessel Integrated Power System
1 Introduction
2 Fundamental Topology
3 Control Strategy
3.1 Control Strategy of MMC
3.2 Control Strategy of DAB Power Channel
4 Simulation Results
5 Conclusions
References
Configuration Method and Parameter Impact Analysis of Parallel LCC Compensation WPT Systems
1 Introduction
2 Typical LCC Topology Parallel Structure
2.1 Problems of Traditional Structure
3 Zero Phase Angle LCC Topology Parallel Structure
4 Experimental Verification
4.1 Experimental Setup
4.2 Comparison of Traditional and Improved Configurations
4.3 Effect of Parameter Imbalance
5 Conclusion
References
Design and Comparative Analysis of Symmetric and Asymmetric Couplers for Underwater Wireless Power Transmission System
1 Introduction
2 AUV-WPT System
2.1 Coupler Structure Design of Symmetry and Asymmetry
2.2 Modeling Analysis of Circuit Topology
3 Performance Analysis of Symmetric and Asymmetric Couplers
3.1 Performance Analysis of Symmetric Coupler
3.2 Performance Analysis of Asymmetrical Coupler
4 Analysis of Electromagnetic Environment of Coupler
4.1 Electromagnetic Environment of Symmetrical Coupler
4.2 Electromagnetic Environment of Asymmetric Coupler
5 Comparison of Comprehensive Transmission Performance
6 Conclusion
References
Comparison and Analysis of Common Electromagnetic Field Numerical Computation Methods in Cable Model
1 Introduction
2 Analytic Model
2.1 Analytical Model of Cable
2.2 Analytical Solution of Magnetic Field
3 Numerical Calculation Method of Electromagnetic Field
3.1 FDM
3.2 FVM
3.3 FEM
3.4 Coupling Algorithm
4 Calculation Result Analysis and Algorithm Optimization
4.1 Numerical Solution of Magnetic Field for FDM (FVM)
4.2 Numerical Solution of Magnetic Field for FEM
4.3 Numerical Solution of Magnetic Field for Coupling Algorithm
5 Conclusion
References
Research and Design of Active Clamp Forward Converter
1 Introduction
2 Working Principle
2.1 Circuit Topology
2.2 Working Mode Analysis
3 Analysis of Soft-Switch and Synchronous Rectification
3.1 Soft-Switch
3.2 Synchronous Rectification
4 Design of Active Clamp Forward Converter
4.1 Key Parameters of Main Circuit
4.2 Selection of Control Chip
5 Experimental Result
5.1 Waveform of Switches
5.2 Output Analysis of Converter
6 Conclusion
References
Development of Calibration Device for Transformer Winding Deformation Tester
1 Introduction
1.1 A Subsection Sample
2 Design Scheme
2.1 Basic Structure
2.2 Selection of Key Components
3 Measurement Traceability
3.1 Measurement Traceability Method
3.2 Measurement Traceability Data
4 Evaluation of Measurement Uncertainty of Error [10]
4.1 Measurement Model
4.2 Evaluation of Uncertainty Sources and Components
4.3 Combined Standard Uncertainty
4.4 Expanded Uncertainty
5 Conclusion
References
A Novel APSO-GA Specific Harmonic Elimination Method for Nine Level Inverter
1 Introduction
2 Introduction Topology and Working Principle of Nine-Level MPUC Inverter
3 Basic Principles of SHEPWM
4 APSO - GA Algorithm
5 Simulation and Experimental Analysis
5.1 Simulation Comparison and Analysis
5.2 Experimentation
6 Conclusions
References
Suppression Method of DC Voltage Pulsation in Three - Phase Four - Wire APF
1 Introduction
2 DC Pulsation Analysis
3 Experiment
4 Conclusions
References
Energy Coordinated Control Method for High Power Density Power Electronic Transformers
1 Introduction
2 Topology and Control of PET
2.1 Topology of PET
2.2 Control of the Total Energy of the Primary and Secondary Sides of PET
2.3 Control of the Difference Between the Primary and Secondary Sides Energy of PET
2.4 Energy Coordination Control of Primary and Secondary Sides of PET
3 Simulation and Experiment of the System
4 Conclusion
References
Effects of Magnetic Field Shielding on UED Ultrashort Electron Pulses
1 Introduction
2 Magnetic Field Simulation
3 Particle Simulation
4 Conclusion
References
Asymmetric Five-Switch Cascaded Multilevel Inverter and Its Modulation Strategy
1 Introduction
2 New Inverter Topology
3 Asymmetric Two-Unit Cascaded Five-Switch Inverter
4 Modulation Strategy
5 Simulation Analysis
6 Experimental Analysis
7 Conclusion
References
Impedance Measurement Method for Obtaining the Accuracy of Current Transformers
1 Introduction
2 Definition and Analysis of Current Transformer Error
3 The Relationship Between Error and Impedance
4 Impedance Measurement Method Implementation
4.1 Impedance Measurement Method Implementation Process
4.2 Impedance Measurement Method Example
5 Conclusions
References
Fault Diagnosis Method of Cascaded H-Bridge Inverter Based on EEMD-MPE
1 Introduction
2 Principle of EEMD Multi-scale Sample Entropy
2.1 EEMD Signal Decomposition Principle
2.2 The Principle of MPE
3 Fault Diagnosis Process and Sample Structure of Cascaded H-bridge Inverter
3.1 H-bridge Cascaded Inverter Fault Process
3.2 Sample Set Construction
4 Analysis of the Effect of Fault Diagnosis
5 Conclusion
References
Development of All SiC EMU Charger Based on Vienna Rectifier
1 Introduction
2 Topology of Charger
3 Engineering Design of Charger
3.1 Vienna Rectifier Diode
3.2 Vienna Rectifier MOSFET
3.3 Phase Shifted Full Bridge MOSFET
3.4 Phase Shifted Full Bridge Diode
4 Control Strategy of Charger
4.1 Control Strategy of Vienna Rectifier
4.2 Control Strategy of Phase Shifted Full Bridge Converter
5 Simulation of Charger
5.1 Simulation Results of Vienna Rectifier
5.2 Simulation Results of Phase Shifted Full Bridge
6 Experiment of Charger
6.1 Static Test Results
6.2 Efficiency and Power Density
7 Conclusion
References
Research on Isolated DC/DC Converter with Frequency and Phase-Shift Adjustment Control Based on SiC Switches
1 Introduction
2 Operating Principle and Control Strategy
2.1 Operating Principle of the LLC Converter
2.2 Control Strategy of the LLC Converter
2.3 Operating Principle of SRDAB Converter
2.4 Control Strategy of the SRDAB Converter
3 Parameters Design
4 Experiment
5 Conclusion
References
Design of Increasing Dielectric Constant of Metallized Film Capacitor to Reduce Its Volume in MMC
1 Introduction
2 Modeling of Metallized Film Capacitors
2.1 Current Density Distribution
2.2 Thermal Field Model Establishment
2.3 Material Settings
3 Simulation Calculation Result Analysis
4 Conclusion
References
Prediction of Submarine Cable Probe Values Based on GA-BP Neural Network and Random Forest
1 Introduction
2 Overview
3 Prediction of Submarine Cable Probe Values Based on GA-BP Neural Networks and Random Forests
3.1 Data Sources
3.2 Construction of a Submarine Cable Probe Value Prediction Model Based on GA-BP Neural Network and Random Forest
3.3 Model Comparison
4 Conclusion
References
Research on High Gain Quadratic Boost Converter with Coupled Inductors
1 Introduction
2 Analysis of Converter Topology and Working Principle
2.1 Subsection
2.2 Circuit Operating Modal Analysis
3 Operating Characteristic Analysis
3.1 Voltage Gain
3.2 Switching Tube and Diode Voltage Stress
3.3 DCM Critical Conditions
3.4 The Performance Comparison
4 Experimental Analysis
5 Conclusions
References
A Simple and Effective Identification Method for Transient Pulse Wave Propagation Resulted from Overhead Transmission Line Fault
1 Introduction
2 The Pulse Identification Quantity Extraction Method
3 The Transmission Line Model
4 Results and Discussions
5 Conclusion
References
Multilevel Pulse Train Control Three-Phase Inverter Based on Power Reference
1 Introduction
2 PR-MPT Control Principle and Working Process
3 PR-MPT High and Low Power Pulse Design
3.1 Duty Cycle Analysis
3.2 High and Low Power Pulse Design Based on Power Reference
4 Simulation and Results
5 Conclusion
References
Power Characteristic and Phase Difference Analysis of Double-Ended PS Applied to ICWPT System
1 Introduction
2 Establishment of the System Model
3 Power Characteristic Analysis of Double-Ended PS System
4 Phase Difference Analysis of Double-Ended PS System
5 Verification
5.1 Verification of Double-Ended PS System Power Characteristic
5.2 Verification of Double-Ended PS System Phase Characteristic
6 Conclusions
References
Analysis of Transfer Characteristics of Magnetic-Valve-Type Current Transformer
1 Introduction
2 Basic Theory of MVCT
2.1 Structure of MVCT
2.2 Equivalent Model of MVCT
2.3 Transfer Characteristics of MVCT
3 Finite Element Simulation of MVCT
4 Experiment Results of MVCT Transfer Characteristics
5 Conclusion
References
Transient EMI Analysis of a Submodule of Modular Multilevel Converters Based on Discontinuous Galerkin Time-Domain Methods
1 Introduction
2 Formulations
3 Transient EMI Analysis of a Submodule of MMCs
3.1 Simulation Model
3.2 Numerical Results and Discussions
4 Conclusions
References
Investigations of the Influences of Parasitic Inductance on Modular Multilevel Converters
1 Introduction
2 Formulations
3 Investigations of the Influences of Parasitic Inductance on the Submodule of MMC
3.1 Simulation Model
3.2 Numerical Results and Discussions
4 Conclusions
References
Numerical Investigation on Frequency Dependence of Hysteresis Characteristics of Conducting Ferromagnetic Materials
1 Introduction
2 Measurement Devices and Measurement Results
2.1 Measurement Devices and Measurement Principle
2.2 Measurement Results
3 Theory Analysis
4 Calculation Model
5 Comparison of Calculation Results and Measurement Results
6 Conclusions
References
Design and Research of Distributed Coil Magnetic Levitation Platform
1 Introduction
2 Magnetic Levitation Platform and Electrolytic Force Analysis
2.1 Displacement Mechanism Design
2.2 Analysis of Electromagnetic Force
3 MFAC-PID Simulation Analysis
4 Conclusion
References
Adaptive Fast Power Control of Voltage Controlled Inverter Based on Timed Power Disturbance
1 Introduction
2 Power Response Analysis
2.1 System Structure and Control Scheme
2.2 Power Response
3 VCI Fast Power Control Strategy and System Characteristic Analysis
4 Adaptive Fast Power Control Strategy Based on Timed Power Disturbance
5 Experimental Verification
6 Conclusion
References
Research on Signal Extraction and Control Strategy of Single-Phase PWM Rectifier in d-q Coordinate Frame
1 Introduction
2 Topology and Mathematical Model of Single-Phase VSR
3 Control Strategy of Singe-Phase VSI
3.1 Design for Current Inner Loop Controller
3.2 Design for Voltage Outer Loop Controller
4 Discrete Extraction Method of Fundamental of Grid Voltage
5 Simulation Results
6 Conclusion
References
Loss Calculation and Deadtime Compensation for DPWMMIN in Voltage Source Inverter
1 Introduction
2 Loss Calculation of DPWMMIN Modulation Strategy
2.1 Topology of Motor Drive System
2.2 Calculation of Conduction Loss
2.3 Calculation of Switching Loss
2.4 Calculation of Switching Loss
3 Nonlinear Error Analysis of Phase Voltage
4 Simulation and Experimental Results
4.1 Simulation Results
4.2 Experimental Results
5 Conclusion
References
Single-Phase Grid-Connected Current Source Inverter Based on Control of DC-Link Current
1 Introduction
2 Topology and Mathematical Model of Five Switch Single-Phase Grid Connected Current Source Inverter
3 Control Scheme of DC Energy Storage Inductor Current
4 Control Scheme of Grid Connected Current
5 Simulation Results and Analysis
6 Conclusion
References
High Stability and Efficiency in Dual-Buck Inverter with Feedback Linearization Controller
1 Introduction
2 Topology Modelling
2.1 Double Buck Inverter Construction
2.2 System Model
2.3 Conditions of System Feedback Linearization
2.4 Input-State Feedback Linearization Controller Design
3 Simulation Results
References
Electromagnetic Compatibility and Insulation Performance of UHVDC Converter Valve After Implanting Sensor Detectors
1 Introduction
2 Theoretical Analysis
3 Simulation Results and Discussions
4 Conclusions
References
Modeling and Parameter Sensitivity Analysis of Inductor Used Multi-material Powder Core
1 Introduction
2 Modeling of Inductor Used Multi-material Powder Core
2.1 DC Superimposition Inductance
2.2 DC Superimposition Core Loss
2.3 Winding Loss
2.4 Thermal Resistor Network
3 Parameter Sensitivity Analysis
3.1 Powder Core Material
3.2 Air Gap
3.3 Core Size
3.4 Wire Size
3.5 Number of Turns
4 Conclusion
References
Optimized Design of T-type Three-Level Rectifier Based on Quasi-proportional Resonance Control
1 Introduction
2 Topology of T-Type Three-Level Rectifier
2.1 Topology
3 Control Strategy Design of T-Type Three-Level Rectifier
3.1 Control System
3.2 Current Inner Loop Design Based on QPR Controller
3.3 Voltage Outer Loop Design
3.4 Midpoint Potential Balance Control
4 Simulation and Verification
5 Conclusion
References
DC-Side Voltage Harmonic Control of a Three-Phase Current Source Rectifier Under Unbalanced AC Voltage Conditions
1 Introduction
2 Mathematical Model of CSR in the d-q Coordinate System
3 DC Voltage Harmonic Suppression Strategy
3.1 Unbalanced Grid Analysis
3.2 Suppress the Second Harmonic of DC Side Voltage
3.3 Positive and Negative Sequence Separation of Voltage
4 Simulation Results and Analysis
5 Conclusion
References
Active Clamp Flyback Converter with Variable Resonant Modes
1 Introduction
2 Analysis of ACF
2.1 Operating Principle
2.2 Mode of Resonance
3 ACF Converter with Variable Resonant Mode
4 Simulation Analysis
5 Conclusion
References
Magnetic Field Analysis of Inter-turn Short Circuit Fault in Hollow Reactor Based on Finite Element Simulation
1 Introduction
2 Equivalent Circuit Model of Hollow Reactor
3 Finite Element Model of Hollow Reactor
3.1 Establishment of Finite Element Simulation Model of Hollow Reactor
3.2 Magnetic Field Distribution of Hollow Reactor Under Normal Operating Conditions
3.3 Analysis of Inductance Variation of Inter-turn Short Circuit Fault
3.4 Analysis of Magnetic Field Variation of Interturn Short Circuit Fault
3.5 Magnetic Distribution Change with Fault Locations
4 Conclusion
References
Author Index
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Lecture Notes in Electrical Engineering 1018
Chengbin Ma · Yiming Zhang · Siqi Li · Lei Zhao · Ming Liu · Pengcheng Zhang Editors
The Proceedings of 2022 International Conference on Wireless Power Transfer (ICWPT2022)
Lecture Notes in Electrical Engineering
1018
Series Editors Leopoldo Angrisani, Dept. of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Dept. de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Lab, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dept. di Ingegneria dell’Informazione Palazzina 2, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Dept. of Electrical Engineering and Information Science, Technische Universität München, München, 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, Intell. Systems Lab, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, 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, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Dept. of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Federica Pascucci, Dept. di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA
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Chengbin Ma · Yiming Zhang · Siqi Li · Lei Zhao · Ming Liu · Pengcheng Zhang Editors
The Proceedings of 2022 International Conference on Wireless Power Transfer (ICWPT2022)
Editors Chengbin Ma Shanghai Jiao Tong University Shanghai, China Siqi Li Kunming University of Science and Technology Kunming, Yunnan, China Ming Liu Shanghai Jiao Tong University Shanghai, China
Yiming Zhang Fuzhou University Fuzhou, Fujian, China Lei Zhao Chongqing University Chongqing, China Pengcheng Zhang Tsinghua University Beijing, China
ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-0630-7 ISBN 978-981-99-0631-4 (eBook) https://doi.org/10.1007/978-981-99-0631-4 © Beijing Paike Culture Commu. Co., Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Contents
Quadrature Six-Coils Wireless Charging with High Misalignment Tolerance and Constant Voltage Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhaowei Gong, Jingang Li, Xiangqian Tong, and Ningchao Zhang
1
Inductively Coupled Power Transfer System Based Constant Voltage and Constant Current Charging for Rail Transit System . . . . . . . . . . . . . . . . . . . . Jixin Yang, Liming Shi, Zhenggang Yin, and Wenjing Tang
8
Modeling and Analysis of Bidirectional Wireless Power Transfer System with Asymmetric Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chenyang Wei, Bin Wei, Cheng Jiang, and Xiaokang Wu
18
Design and Research on Coupling Mechanism of Inductive Power Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Liu, Liangshun Sun, Mingwei Su, Fangrui Wang, Jian Long, Enxin Xiang, and Longlei Bai Characteristics of Wireless Power Transmission Based on a New Spiral Resonant Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haoyan Xi, Yihao Wei, Yong Dong, Yanhong Liu, Lijuan Dong, and Yunlong Shi
29
36
Efficiency Optimization Method for Wireless Power Transfer System Between the Rocket and the Ground Based on Energy Compensation . . . . . . . . Zhan Wang, Kun Lan, Jingang Zhang, and Da Yu
45
Design and Modeling of Helmholtz Coil Based on Winding Method Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xueting Zhao, Zihao Zhang, Xiaoyun Chen, Yi Zhou, and Deyan Lin
57
Applicability Analysis of Coupled-Mode Theory Model in Capacitive Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Zhou, Jingjing Yang, Yiming Zhang, Qingbin Chen, and Yanwei Jiang Optimal Efficiency Control of Multiple Transmitting Array WPT System for Constant Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boxiang Sun, Shui Pang, Jiayi Xu, Hongyu Li, and Xingfei Li
71
81
vi
Contents
Optimized Design of the DD Coil for Improved Misalignment Tolerance . . . . . Weijie Li, Weiyao Mei, Jiangjun Yuan, Zhonghao Dongye, and Lijun Diao
91
Analysis of Geometric Characteristics of Three-Terminal Shaft Loosely Coupled Transformer Based on LCC-S Compensation . . . . . . . . . . . . . . . . . . . . . Shijia Kang, Zewen Wang, Zijia Zhang, Yansong Li, and Jun Liu
99
Frequency Tracking Synchronization Technique for a Bidirectional Inductive Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bowang Zhang, Wei Han, Youhao Hu, and Weikang Hu
107
Analysis and Design of Magnetic Cores for Rotary Wireless Power Transfer Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Longyuan Fan, Zicheng Liu, Jiewei He, and Dong Jiang
117
Electrical Characteristics of Magnetic Couplers in Inductive Power Transfer for Autonomous Underwater Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiangjun Yuan, Weiyao Mei, Quan Yuan, Zhonghao Dongye, and Lijun Diao Generation of an Airy Beam Based on a Holographic Scalar Metasurface . . . . . Song Zhang, Hao Xue, Xiaonan Wu, Mingyang Chang, and Long Li Modulation of Deflected Bessel Beams Based on Reconfigurable Metasurface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shihao Zhao, Hao Xue, Song Zhang, Mingyang Chang, and Long Li Simulation and Optimization Analysis of Magnetic Coupling Mechanism for Resonant Wireless Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . Junjie Guo, Tao Ning, Kaijian Zhang, Xiaodong Zhang, Yuling Ma, and Yijia Shang
128
138
145
153
Loss Analysis of Rectifier Circuit and Its Optimization Technique in Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xu Zhang, Qingbin Chen, and Wei Chen
166
Simultaneous Wireless Power and Data Transfer System Using Parallel Injection Communication Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guangjie Bao and Linlin Tan
177
A Magnetic Field Energy Harvester to Power Micro-power Sensors on the Freight Train for Railway Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jin Tao, Bo Luo, Yongchao Wang, Zhuling Wang, and Ruikun Mai
190
Contents
vii
Coupling Comparison of Magnetic Couplers for Mid-range Wireless Power Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yousu Yao, Zixu Fang, Qinan Ni, and Xiufang Liu
199
Model-Inverse-Based Output Control of the Multi-excitation-Unit WPT System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiao Lv, Zi-yi Xia, Du-gang Kang, and Xin Dai
210
The Impact of Metal Hull of AUVs for Underwater Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lei Yang, Yuanqi Zhang, Xiaojie Li, Baoxiang Feng, Jingjing Huang, Darui Zhu, Aimin Zhang, and Xiangqian Tong Synchronous Identification of Loads and Mutual Inductances for Multi-frequencies Multi-loads WPT System . . . . . . . . . . . . . . . . . . . . . . . . . . . Dongxiao Huang, Qinwang Wei, Weidong Huang, Zequan Hong, and Fengxiang Wang A Cross-Shaped Solenoid Magnetic Coupler with High Lateral Offset Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chendawei Zhang, Wenzhou Lu, Jian Zhao, Qigao Fan, and Haiying Chen A Design of Secondary-Only Resonant Series-Series WPT System to Maintain Power Stability with Coil Misalignment . . . . . . . . . . . . . . . . . . . . . . . Yueyao Li, Xiaohua Wu, and Xiliang Chen Research on Constant Voltage Control Strategy of Dual Pick-Up Dynamic Inductive Coupled Power Transfer System Based on Optimal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anran Sun and Chenyang Xia
218
229
239
247
255
Analysis and Modeling of Response Characteristics Under Actual Rectifier Parameters in the Wireless Power Transfer System . . . . . . . . . . . . . . . . Binzhi Xie, Jinshuai Wang, Zhibin Lu, Wei Chen, and Qingbin Chen
264
Metal Object Detection for Electric Vehicle Wireless Charging Based on Fusion of Spectral and Texture Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zengpeng Zhou, Jindong Tian, Bo Liu, and Yong Tian
277
Study on the Performance of a Novel High Lateral Displacement Receiver Coil Based on Cross-Winding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . Chang Liu, Jinhai Jiang, Kai Song, Xiaoyan Li, Jianing Xu, and Chunbo Zhu
287
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Anti-misalignment Improvement for SS Compensated IPT System Using Reconfigurable Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Chen, Xiaofei Lyu, Yuhua Xiao, Xize Jiao, and Ruikun Mai Design and Icing Analysis of a Novel Magnetic Coupling Mechanism for WPT System on High-Voltage Transmission Lines . . . . . . . . . . . . . . . . . . . . . Shuyu Shen, Linlin Tan, Zhijun Wu, Heqi Xu, Tian Gao, and Xueliang Huang
299
308
Research on Maximizing the Communication Capacity of OFDM-Based Simultaneous Wireless Transmission of Power and Information (SWTPI) . . . . . Li Ji, Kaixin Yan, and Xudong Cao
323
Loss Analysis of Magnetic Core and Its Structure Optimization of Magnetic Coupling Structure in Wireless Power Transfer System . . . . . . . . . Yujie Lan, Feng Fan, Xiaolong Deng, Wei Chen, and Qingbin Chen
331
Compact Mixed DC-DC Power Converters for Computing Server . . . . . . . . . . . Zhiqiang Liu, Chaoqiang Jiang, Tianlu Mau, Jingchun Xiang, and Xiaosheng Wang A Flexible Foreign Object Detection Method Based on Arrayed Vertical-Decoupled Coils for Wireless Power Transfer Systems . . . . . . . . . . . . . Huishu Song, Xiaosheng Huang, Shuyi Lin, Ruping Lin, and Jing Huang Optimal Efficiency Design of Single-to-Multiple Constant Voltage Based on LCC Compensation Topology for Wireless Power Transfer . . . . . . . . Cang Liang, Renjie Zhang, Cheng Zhao, Huan Yuan, Aijun Yang, Xiaohua Wang, and Mingzhe Rong
341
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364
Design of Dynamic Wireless Charging System Based on Coupling Coefficient Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xuchi Xue, Zhitao Liu, Jia Liu, Wenjie Chen, and Hongye Su
372
Influence of Frequency on Transmission Performance of Multi-relay Wireless Power Supply System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhijun Wu, Linlin Tan, Shuyu Shen, and Heqi Xu
385
Bidirectional Wireless Power Transfer System Control Strategy on Double-Sided LCC Resonant Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuxuan Zheng, Kainan Chen, Yuchen Chen, Liqiang Yuan, and Zhengming Zhao
400
Contents
ix
Design of Underwater Wet Plug Connectors System Based on the Principle of Wireless Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jianduo Zhang, He Yin, Yudong Fu, Hai Lan, and Dan Li
415
Metal Foreign Object Detection Algorithm Based on Multivariate Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ying Sun, Kai Song, Tian Zhou, Guo Wei, and Chunbo Zhu
427
Research on Parallel Circulation Suppression Strategy of High-Frequency Resonant Inverter Based on Improved Active Current Decomposition Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Junfeng Liu, Mingze Ma, Hao Zhou, and Jun Zeng The Power Control of a Multiple Pick-Up Bidirectional Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhenggang Yin, Liming Shi, Jixin Yang, and Wenjing Tang Robust Regulation of Constant Current Wireless Charging System with Clamping Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Le Li, Bing Cheng, Houxuan Liu, Liangzong He, Wei Li, Tiejun Ma, and Yongjun Wang Comparison of Wireless Power Transfer Systems with Multi-loads . . . . . . . . . . Wei Deng, Zhiliang Yang, Jing Yin, Jie Wu, Pengfei Gao, Yafei Chen, and Zhanshi Lou Multi-objective Optimization of IPT System Compensation Parameters for Improving Misalignment Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Junfeng Yang, Junjie Guo, Qingbin Tong, Xu Yang, and Tianqi Hao Design of LCLC-S Impedance Matching Network for Ultrasonic Wireless Power Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kehan Zhang, Jiaming Feng, Baobao Lan, Xinyang Li, Zhengchao Yan, and Zhaoyong Mao A Switchable Modular AC~DC Buck-Boost Converter for the Wide Input Range in Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chunlong Li, Dengfeng Ju, Hui Huang, Kuan Ye, Hongjing Liu, and Jiayong Yuan Research on Active Leakage Magnetic Field Suppression Techniques Applied in Electric Vehicle Wireless Chargers . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ning Zhang, Xiaomin Zhou, Xianfeng Gong, Dawei Gao, and Guodong Zhu
436
444
455
463
472
482
496
506
x
Contents
The Solution of Power Frequency Electromagnetic Field for Parallel Transmission Lines Based on Superposition Algorithm . . . . . . . . . . . . . . . . . . . . Jiangong Zhang, Xiaofeng Yang, Zheyuan Gan, Zhibin Zhao, and Bo Tang
516
Coupler Comparison of Inductive and Capacitive Power Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siyi Yao, Minfan Fu, Heyuan Li, Yiming Yin, and Peng Zhao
523
Design of Integrated Coil Structure for Simultaneous Wireless Information and Power Transfer Applied to Electric Power Inspection Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chen Huang, Nenghong Xia, Xike Mao, Chengchao Hua, Xiaoying Xu, and Zhipeng Yuan
531
Reconfiguration and Reuse of Receiver/Repeater in Wireless Power Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Han Liu, Lingling Sun, and Wei Zhang
543
Improved Electromagnetic Halbach Array for Enhanced Efficiency in Wireless Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dibin Zhu and Tamuno-omie Gogo
550
Robust Control of Ultrasonic Power Transfer System Under Parameter Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kehan Zhang, Baobao Lan, Fan Dai, Jiaming Feng, and Zhaoyong Mao
559
Influence of Loop Impedance on Performance of Charging Power Supply Based on Battery Packs Connected in Series . . . . . . . . . . . . . . . . . . . . . . . Shikuo Cheng, Yinghui Gao, Jing Han, Kun Liu, Yaohong Sun, and Ping Yan
571
Current Source Converter Optimization Method Based on Multi-step FCS-MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hao Ding, Quanjie Li, Mingming Li, and Wei Wang
583
A Fixed-Admittance Modeling Method of Power Electronic Switches Based on State Initializations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bin Zhou, Guangsen Wang, Weichao Li, Kang Wang, and Guisheng Jie
592
Configuration Strategies of Reactive Power Compensation in Converter Stations with STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kanglong Yuan, Mingyu Han, Huansheng Zhou, Yan Li, Yu Huang, and Yu Liang
604
Contents
SiC MOSFET Gate Drive Power Supply Based on Active Clamp Flyback . . . . Dahan Deng, Jingwei Zhang, and Shuhao Li Analysis of Release Voltage Fluctuation Mechanism of Electromagnetic Relay with Bridge Polarized Magnetic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guilin Liu, Yong Xie, Huimin Liang, Zitong Wei, Junfeng Chen, and Manyun Huang Analysis and Optimization of a Three-Coil Coupler Based WPT System Featuring High Efficiency and Misalignment Tolerance . . . . . . . . . . . . . . . . . . . . Yousu Yao, Chunxu Zhang, and Qinan Ni Research on Interleaved DC-DC Converter with Extended CD Unit . . . . . . . . . . Rui Guo, Sen Yang, and Liying Jiang Double Random PWM Method of DC-DC Chopper Converter Based on WELL Look-Up Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guohua Li, Guangda Liu, and Yang Liu Design and Analysis of a High-Voltage and High-Power ANPC Three-Level Power Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yichun Zhang, Zechun Dou, Hangjie Fu, Jiayi Wang, Xiongbo Xie, and Yanping Chen Research on the Influence of Cable Capacitance of EMU Converter on IGBT Protection and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jianguang Yang, Jun Liao, Hangjie Fu, Mingyi Chen, and Shunmeng Xie Optimal Sampling Frequency of SVPWM for Multilevel Converter . . . . . . . . . . Wenjun Zeng, Cui Wang, Qiangsheng Dai, Zhanhao Zhao, Chenhang Wu, Zuojia Niu, and Haoran Li
xi
614
623
632
643
651
662
673
683
Reliability Evaluation Method of Active Distribution Network Based on Optimization Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Feng Zhao, Youzhong Miao, Chao Sun, Jing Wang, and Zongmin Yu
692
A Review of the Current State of Development of High Precision AC Power Frequency Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ruiqi Zhang, Li Liu, and Xiaohui Zhang
701
Electromagnetic Scattering Characteristics of Different Polarized Electromagnetic Waves by High Voltage Transmission Lines . . . . . . . . . . . . . . . Xianglin Ma, Yanxia Lu, Chaoqun Jiao, Jianggong Zhang, Zhibin Zhao, and Zheyuan Gan
714
xii
Contents
The Acquisition and Research of the Relative Complex Permeability of the Core Material of the Self-inductive Displacement Sensor . . . . . . . . . . . . . Zongqiang Ren, Xinwei Chen, Hongwei Li, and Wentao Yu Current Sharing of Parallel IGBT Affected by Thermal Resistance . . . . . . . . . . . Weifeng Tang and Changjiang Wang A Novel High Step-up DC-DC Converter Integrating Coupled-Inductor with Quasi-Symmetric Gain Feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yihai Li, Yan Zhang, and Jinjun Liu A Behavior Model of Planar SiC MOSFET Considering Avalanche Breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yifan Wu, Chi Li, Zedong Zheng, Lianzhong Wang, Tao Liu, and Guojing Liu Envelope Tracking Power Supply for Energy Saving of Mobile Communication Base Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaoguang Gao, Hao Wang, Linguo Wang, and Bin Zhang
723
731
739
748
766
Calculation of Turn-To-Turn Parasitic Capacitance . . . . . . . . . . . . . . . . . . . . . . . . Hao Wang, Peng Zhou, Zenan Xu, Zhijun Ye, Kaixiang Chen, Zongxuan Ma, and Jiliang Luo
775
A Lag Compensation Method Based on All-Pass Filter . . . . . . . . . . . . . . . . . . . . . Zhang Hongzhen, Hou Shiying, Robert M. Cuzner, and Ye Jiangdan
784
Characteristic Research of Magnetic Controllable Voltage Regulator . . . . . . . . . Guosheng Zhao, Xiaolei Zheng, Junpeng Pan, and Xiaohuan Hu
793
Space Vector Pulse Width Modulation Strategy for Cascaded Three-Phase Bridge Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yunhe Wang, Cui Wang, Qiangsheng Dai, Zhanhao Zhao, Chenhang Wu, Zuojia Niu, and Haoran Li Design and Optimization of Totem Pole Bridgeless PFC Based on GaN . . . . . . Mengyang Tang, Pengfei Xue, Zhangge Cheng, and Tao Yong
801
810
A Modular Multi-port Converter for Distribution of Vessel Integrated Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ZhaoJie Huang, Qiang Ren, Fei Xiao, JiLong Liu, and ZhiChao Zhu
819
Configuration Method and Parameter Impact Analysis of Parallel LCC Compensation WPT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao Cui, Xin Gao, Shumei Cui, and Qianfan Zhang
829
Contents
Design and Comparative Analysis of Symmetric and Asymmetric Couplers for Underwater Wireless Power Transmission System . . . . . . . . . . . . . Jiacheng Li, Jianing Feng, Xun Dou, Hanyu Yang, Xin Zhang, and Kai Ni Comparison and Analysis of Common Electromagnetic Field Numerical Computation Methods in Cable Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yanxin Ren, Nana Duan, Xinyu Ma, Weijie Xu, and Shuhong Wang Research and Design of Active Clamp Forward Converter . . . . . . . . . . . . . . . . . . Wang Zhou, Gaili Yue, Zijing Wang, Jiadong Yao, and Wenjie Gao
xiii
843
852
861
Development of Calibration Device for Transformer Winding Deformation Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pengfei Shi, Xuefang Luo, and Dazhi Ni
870
A Novel APSO-GA Specific Harmonic Elimination Method for Nine Level Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . He Qiao, Ziqi Zhao, and Zhaohui Shen
877
Suppression Method of DC Voltage Pulsation in Three - Phase Four Wire APF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haihong Huang, Weijie Zhao, and Haixin Wang
893
Energy Coordinated Control Method for High Power Density Power Electronic Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ziqing Cao, Yichao Sun, Liye Wu, Yinyu Yan, and Kai Yang
901
Effects of Magnetic Field Shielding on UED Ultrashort Electron Pulses . . . . . . Mengchao Li, Xuan Wang, Chuicai Rong, Wei Chen, Teng Gong, Menghao Tan, Jun Huang, and Xingquan Wang Asymmetric Five-Switch Cascaded Multilevel Inverter and Its Modulation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fei He and Wei Sun Impedance Measurement Method for Obtaining the Accuracy of Current Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hongsen You, Mengying Gan, Dapeng Duan, Cheng Zhao, Yuan Chi, Weiqiong Song, Fengming Lv, Jinjun Xie, and Jiansheng Yuan Fault Diagnosis Method of Cascaded H-Bridge Inverter Based on EEMD-MPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weiman Yang, Weinian Wang, Xinggui Wang, and Xue Sheng
909
916
929
938
xiv
Contents
Development of All SiC EMU Charger Based on Vienna Rectifier . . . . . . . . . . . Haiyang Li, Xuqiang Zhao, and Bowei Zhu
951
Research on Isolated DC/DC Converter with Frequency and Phase-Shift Adjustment Control Based on SiC Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nan Zhao, Zedong Zheng, and Yongdong Li
962
Design of Increasing Dielectric Constant of Metallized Film Capacitor to Reduce Its Volume in MMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hongyu Yu, Li Ran, Hao Feng, and Jinxiao Wei
975
Prediction of Submarine Cable Probe Values Based on GA-BP Neural Network and Random Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shaohua Chen, Dingcheng Guo, Qingyi Cui, Sitong Yi, and Jiameng Li
983
Research on High Gain Quadratic Boost Converter with Coupled Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rui Guo, Liying Jiang, and Sen Yang
992
A Simple and Effective Identification Method for Transient Pulse Wave Propagation Resulted from Overhead Transmission Line Fault . . . . . . . . . . . . . . 1004 Yue Yu, Longhao Liu, Zexin Zhou, Zhanpeng Du, Dingyu Qin, and Chongqing Jiao Multilevel Pulse Train Control Three-Phase Inverter Based on Power Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 Zhifu Wang, Jianping Xu, Yifan Wang, Yuxi Jing, and Xin Chen Power Characteristic and Phase Difference Analysis of Double-Ended PS Applied to ICWPT System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1020 Wenjing Tang and Liming Shi Analysis of Transfer Characteristics of Magnetic-Valve-Type Current Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1030 Shaojie Liu, Siming Wei, Yingying Zhao, Yue Tian, Yubo Fan, Baichao Chen, Cuihua Tian, and Zhexuan Zhang Transient EMI Analysis of a Submodule of Modular Multilevel Converters Based on Discontinuous Galerkin Time-Domain Methods . . . . . . . . 1038 Xiaoping Sun, Jiawei Wang, Fang Zhuo, Yanmei Zhang, He Chen, and Jinghui Shao
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xv
Investigations of the Influences of Parasitic Inductance on Modular Multilevel Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046 Yantao Lou, Pengcheng Zhu, Yanmei Zhang, He Chen, Xiaoping Sun, and Jiawei Wang Numerical Investigation on Frequency Dependence of Hysteresis Characteristics of Conducting Ferromagnetic Materials . . . . . . . . . . . . . . . . . . . . 1057 Zhang Yubo, Liu Tianyi, Liao Zhenyu, Li Dong, and Chen Dezhi Design and Research of Distributed Coil Magnetic Levitation Platform . . . . . . . 1069 Changzhou Jiang, Chaofan Du, and Zhengfeng Ming Adaptive Fast Power Control of Voltage Controlled Inverter Based on Timed Power Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076 Han Feng, Zhang Xing, Wang Jilei, Fu Xinxin, and Zhan Xiangdui Research on Signal Extraction and Control Strategy of Single-Phase PWM Rectifier in d-q Coordinate Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087 Lieqian Gong, Guanggang Fu, Xin Wang, Mengyang Tang, Wu Liao, and Yiru Miao Loss Calculation and Deadtime Compensation for DPWMMIN in Voltage Source Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096 Binbin Qiu, Huadong Zhang, and Guoyong Li Single-Phase Grid-Connected Current Source Inverter Based on Control of DC-Link Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112 Binbin Qiu, Huadong Zhang, and Guoyong Li High Stability and Efficiency in Dual-Buck Inverter with Feedback Linearization Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1121 Pingping Wen, Zengquan Yuan, Zhibao Yuan, and Haiping Xu Electromagnetic Compatibility and Insulation Performance of UHVDC Converter Valve After Implanting Sensor Detectors . . . . . . . . . . . . . . . . . . . . . . . . 1129 Zhiyao Luo, Siyuan Ma, Fei Du, Lei Shi, Shuai Yuan, and Tianyu Dong Modeling and Parameter Sensitivity Analysis of Inductor Used Multi-material Powder Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136 Yun Zhang, Zedong Zheng, Chi Li, and Qing Zhou Optimized Design of T-type Three-Level Rectifier Based on Quasi-proportional Resonance Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1150 Kemin Dai, Jinwu Gong, Xiaolu Ge, Shangzhi Pan, and Xiaoming Zha
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DC-Side Voltage Harmonic Control of a Three-Phase Current Source Rectifier Under Unbalanced AC Voltage Conditions . . . . . . . . . . . . . . . . . . . . . . . 1160 Jixuan Zhang, Wenping Cao, Wenjie Zhu, Huajian Zhou, and Cungang Hu Active Clamp Flyback Converter with Variable Resonant Modes . . . . . . . . . . . . 1170 Zhenye Dong, Qiang Zhang, Yuhui Yang, and Xueqin Zheng Magnetic Field Analysis of Inter-turn Short Circuit Fault in Hollow Reactor Based on Finite Element Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1180 Jieyi Luo, Yuanjia Li, and Rongfu Zhong Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1191
Quadrature Six-Coils Wireless Charging with High Misalignment Tolerance and Constant Voltage Output Zhaowei Gong1,2 , Jingang Li1,3(B) , Xiangqian Tong1 , and Ningchao Zhang2 1 School of Electrical Engineering, Xi’an University of Technology, Xi’an 710054, China
[email protected], {lijingang,xqtong}@xaut.edu.cn
2 School of Electronic Information Engineering, Xi’an Technological University, Xi’an 710021,
China [email protected] 3 Huaibei Huaming Industrial Frequency Conversion Equipment Co., Ltd., Huaibei 235100, China
Abstract. Aiming at improving the operating range of the wireless charging system with misalignment tolerance, a design method based on parameter optimization of wireless charging with wide range misalignment and constant-voltage output was proposed. The mathematical model of the proposed six-coils hybrid compensation network were established, and the output characteristics between load and mutual inductances were analyzed. The DD2Q (Double-D Quadrature) pad was proposed, which is beneficial to eliminate cross coupling and realize independent output of each channel. The results show that the system output current deviation is less than 5% when the coupling pads vary from 20 mm to 140 mm, and the efficiency is up to 94%. Keywords: Wireless charging · Misalignment tolerance · Constant voltage output
1 Introduction Inductive Power Transfer (IPT) is a method of energy transmission through highfrequency alternating magnetic field coupling, which has the advantages of safety, reliability, environmental friendliness and convenient operation. At present, it has been successfully applied to electronic products, medical electronic equipment and electric vehicles. Coupling coil is an important element of wireless charging system. The misalignment between the coupling coil will decrease the output power and efficiency. Therefore, wide range anti-offset output capability has become an important indicator of wireless charging system [1–5]. Aiming at improving the anti-offset ability, the optimization design is mainly from closed-loop control, magnetic coupling structure and high-order compensation network [6, 7]. The anti-offset output system based on closed-loop control usually requires additional wireless communication devices, but the wireless communication delay will © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 1–7, 2023. https://doi.org/10.1007/978-981-99-0631-4_1
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reduce the dynamic response of the system. DDQ coil structure, DD coil structure, I-type transmitting coil structure and 3D orthogonal coil structure were proposed in [8–11] to provide misalignment tolerance against coupling fluctuations. For example, a I-type transmitting coil is proposed in [9] to realize the fluctuation range of output voltage within 30% when the maximum offset in x direction is within 50%. A 3D orthogonal coil structure was presented in [11] to realize all-directional wireless charging, but the overall efficiency of the system is only 60%. Meanwhile, hybrid compensation network can also be used to provide better misalignment tolerance. A hybrid compensation network combining with LCC-LCC and S-S compensation network [12], could realize stable the power output when the system coupling coefficient varied from 0.2 to 0.3. However, this hybrid topology cannot operate without the secondary side. A series hybrid topology with the integrating compensating inductor into coupling coil was proposed in [13] to overcome the above mentioned issues. The operating principle of the hybrid compensation network was summarized in [14], and set up an experimental platform, which could limit the fluctuation range, when the coupling coefficient is 0.08–0.16. To sum up, the existing methods can achieve anti-offset wireless charging, but the range of coupling coefficient is relatively narrow. Considering different EVs, such as family cars, SUVs or trucks, the vertical height of the coupling coil is different, and the coupling coefficient varies widely, resulting in transmission power fluctuation and efficiency decline. Therefore, it is necessary to improve the operating range of vertical misalignment tolerance. The six-coil hybrid topology is presented in this paper. Firstly, the output characteristics of the topological circuit are analyzed. Secondly, the magnetic coupling coil structure of DD2Q is proposed to realize the mutual inductance decoupling between the same side coils. Finally, the experimental results show that the six-coil hybrid topology can achieve a wide range of anti-offset constant-current output, and the maximum efficiency of the system can reach 94%.
2 The Proposed Hybrid IPT System Figure 1 illustrates the six-coil hybrid topology circuit. Aiming at minimizing the VA rating, all resonant components should be tuned to the same angle frequency ω, therefore, we can get C1 C7 ω2 L0 C0 = ω2 L1 CC00+C = 1, ω2 L7 C7 = ω2 L4 CC44+C =1 1 7 (1) C8 =1 ω2 L2 C2 = ω2 L3 C3 = ω2 L6 C6 = 1, ω2 L8 C8 = ω2 L5 CC55+C 8 Then, the KVL equations can be obtained as ⎡ ⎤ ⎤ ⎡ U˙ out Z00 Z01 Z02 0 Z04 0 0 ⎡ ˙ ⎤ I 0 ⎢ ⎥ ⎢ Z10 Z11 Z12 0 Z14 0 Z16 ⎥ ⎥⎢ I˙ ⎥ ⎢ 0 ⎥ ⎢ 1⎥ ⎢ ⎢ ⎥ ⎥ ⎢Z Z Z ⎢ 20 21 22 0 0 Z25 Z26 ⎥⎢ I˙ ⎥ ⎢ 0 ⎥ ⎥⎢ 2 ⎥ ⎢ ˙ ⎥ ⎢ ⎢ 0 0 0 Z33 0 Z35 0 ⎥⎢ ˙ ⎥ ⎢ Uout ⎥ ⎥⎢ I ⎥ = ⎢ ⎥ ⎢ ⎢ Z40 Z41 0 0 Z44 0 Z46 ⎥⎢ ˙3 ⎥ ⎢ 0 ⎥ ⎥⎢ I4 ⎥ ⎢ ⎥ ⎢ ⎢ 0 0 Z52 Z53 0 Z55 Z56 ⎥⎢ ⎥ ⎢ 0 ⎥ ⎥⎣ I˙5 ⎦ ⎢ ⎥ ⎢ ⎣0 ⎦ ⎣ 0 Z61 Z62 0 Z64 Z65 Z66 ⎦ ˙I7 0 0 Z72 0 0 0 Z75 U˙ AC
(2)
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M12 I0
C0 Q1
Q3
E
U out
Q2
Q4
L0
I out
C3
C1 I1 L1
L2
C2 I2 # four-coil hybrid
M34 L7
I 4 C4
L3
I7
C7
L4
A U AB
B
I3
L8 C8
U AC
M56 C5 I 5 L5
Primary DD2Q Pad
I6
L6
Req
C6 U BC
# LCC-S
C
Secondary DD2Q Pad
Fig. 1. Proposed six-coil hybrid IPT system.
where Z00 = jωL0 + (jωC0 )−1 + jωL3 + (jωC3 )−1 , Z01 = Z10 = −(jωC0 )−1 , Z02 = Z20 = −jωM23 , Z04 = Z40 = −jωM34 , Z11 = jωL1 + (jωC0 )−1 + (jωC1 )−1 , Z12 = Z21 = −jωM12 − jωM16 , Z14 = Z41 = −jωM14 , Z16 = Z61 = −jωM16 , Z22 = jωL2 + (jωC2 )−1 + RAC + jωL6 + (jωC6 )−1 ,Z25 = Z52 = −jωM25 − jωM56 , Z26 = Z62 = RAC + jωL6 + (jωC6 )−1 , Z33 = jωL8 + (jωC8 )−1 , Z35 = Z53 = −(jωC8 )−1 , Z44 = jωL4 + (jωC4 )−1 + (jωC7 )−1 , Z46 = Z64 = −(jωC7 )−1 , Z55 = jωL5 + (jωC5 )−1 + (jωC8 )−1 , Z56 = Z65 = −jωM56 , Z66 = jωL7 + (jωC7 )−1 + RAC + jωL6 + (jωC6 )−1 ,Z72 = Z76 = RAC . In this paper, only the main mutual inductance is considered and the cross mutual inductance is ignored. Thus, we can get, U˙ AC =
L7 M12 U˙ out M56 U˙ out + L0 L7 + M12 M34 L8
(3)
From (3), the output voltage of the load is related with resonant inductor L 0 , L 7 , L 8 . If these parameters are well designed, the proposed IPT system can maintain stable voltage output.
3 Magnetic Coupler Figure 2 shows the DD2Q pad in this paper, and the Magnetic inductance distribution is shown in Fig. 3. It is clear that the cross coupling occurs when the lateral misalignment happens, while there is only main coupling when the vertical misalignment happens. Therefore, the proposed DD2Q can be used in these applications, such as medical implant and AGVs, which may has wide vertical misalignment.
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280m
m
0m m
L2 L4 L6
L3
28
L5 L1
100mm
Fig. 2. DD2Q magnetic coupler
(a) at centrosymmetric position
(b) at lateral offset position
Fig. 3. Magnetic inductance distribution of the DD2Q coil structure
4 Experimental Verification Figure 4 shows the wireless charging experiment platform, where the electronic load is used to simulate the changes in battery charging process. And Table 1 is the specific experimental parameters are shown in Table 1.
DD2Q Coils Inverter L7 L0 C5
C0
C2
C8 C6 C1 L8
C3
C4
Rectifier
C7
Fig. 4. Experiment platform
Figure 5(a) shows the output voltage curves with 80 and 160 load when vertical misalignment changes from 20 mm to 140 mm. It is obvious that the output voltage can remain relatively constant, The maximum output voltage is 104.5 V when the vertical
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Table 1. The parameters Parameter
Value
Parameter
Value
f L1
85 kHz
C1
24.9 nF
150.1 μH
C2
24.1 nF
L2
149.8 μH
C3
22.0 nF
L3
160.1 μH
C4
35.9 nF
L4
160.2 μH
C5
41.0 nF
L5
160.1 μH
C6
22.0 nF
L6
160.1 μH
C7
58.6 nF
L7
60.2 μH
C8
51.8 nF
L8
70.2 μH
Air gap
20 mm–140 mm
C0
388.4 nF
E
55 V
(a) output voltage
(b) efficiency
Fig. 5. Output voltage and efficiency curves at z-axis misalignment
misalignment reaches 100 mm, and the minimum output voltage is 95.66 V when the vertical misalignment reaches 140 mm. Figure 5(b) shows the system efficiency decreases when the vertical misalignment increases. Figure 6 shows the experimental waveforms of different z-axis misalignment when the load resistance is 80 . It can be obviously found that the variation of the output voltage is within 5%.
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Iout (5A/div)
Uout (50V/div)
Iout (5A/div)
UL=102.29V (50V/div)
UL=97.55V(50V/div)
IL=1.28A (1A/div)
IL=1.22A(1A/div)
t (10us/div)
t (10us/div)
(a) at 20 mm Z-axis misalignment Uout (50V/div)
Iout (5A/div)
(b) at 50 mm Z-axis misalignment Uout (50V/div)
Iout (5A/div)
UL=101.77V(50V/div)
UL=95.66V(50V/div)
IL=1.27A(1A/div)
IL=1.19A(1A/div)
t (10us/div)
t (10us/div)
(c) at 100 mm Z-axis misalignment
(d) at 140 mm Z-axis misalignment
Fig. 6. Experimental waveforms at RL = 80
5 Conclusion This paper presents a six-coil hybrid IPT topology. Firstly, the working characteristics of the system circuit are analyzed, and the variation rule of the output current is summarized. Secondly, DD2Q coupling coil structure is proposed to eliminate cross-coupling mutual inductance. Finally, the experimental results are consistent with the theoretical analysis. Acknowledgements. This work was supported by the Key Research Project of Shaanxi Province of China under Grant 2022GY-310, and the Natural Science Foundation of Shaanxi Provincial Department of Education of China under Grant 20JK0688.
References 1. Mai, J., Wang, Y., Yao, Y., et al.: High-misalignment-tolerant IPT systems with solenoid and double D pads. IEEE Trans. Ind. Electron. 69(4), 3527–3536 (2022) 2. Lee, Y., Han, S.: 2-D thin coil designs of IPT for wireless charging of automated guided vehicles. IEEE J. Emerg. Sel. Top. Power Electron. 10(2), 2629–2644 (2022) 3. Li, Y., Du, H., He, Z., et al.: Robust control for the IPT system with parametric uncertainty using LMI pole constraints. IEEE Trans. Power Electron. 35(1), 1022–1035 (2020) 4. Mai, J., Zeng, X., Yao, Y., et al.: Impedance analysis and design of IPT system to improve system efficiency and reduce output voltage or current fluctuations. IEEE Trans. Power Electron. 36(12), 14029–14038 (2021)
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5. Feng, H., Lukic, S.M.: Reduced-order modeling and design of single-stage LCL compensated IPT System for low voltage vehicle charging applications. IEEE Trans. Veh. Technol. 69(4), 3728–3739 (2020) 6. Dai, X., Li, X., Li, Y., et al.: Maximum efficiency tracking for wireless power transfer systems with dynamic coupling coefficient estimation. IEEE Trans. Power Electron. 33(6), 5005–5015 (2018) 7. Feng, H., Cai, T., Duan, S., et al.: An LCC-compensated resonant converter optimized for robust reaction to large coupling variation in dynamic wireless power transfer. IEEE Trans. Ind. Electron. 63(10), 6591–6601 (2016) 8. Budhia, M., Boys, J.T., Covic, G.A., et al.: Development of a single-sided flux magnetic coupler for electric vehicle IPT charging systems. IEEE Trans. Ind. Electron. 60(1), 318–328 (2013) 9. Park, C., Lee, S., Jeong, S.Y., et al.: Uniform power I-type inductive power transfer system with DQ-power supply rails for on-line electric vehicles. IEEE Trans. Power Electron. 30(11), 6446–6455 (2015) 10. Yao, Y., Wang, Y., Liu, X., et al.: A novel unsymmetrical coupling structure based on concentrated magnetic flux for high-misalignment IPT applications. IEEE Trans. Power Electron. 34(4), 3110–3123 (2019) 11. Zhang, Z., Zhang, B.: Angular-misalignment insensitive omnidirectional wireless power transfer. IEEE Trans. Ind. Electron. 67(4), 2755–2764 (2020) 12. Zhao, L., Thrimawithana, D.J., Madawala, U.K.: Hybrid bidirectional wireless EV charging system tolerant to pad misalignment. IEEE Trans. Ind. Electron. 64(9), 7079–7086 (2017) 13. Zhao, W., Qu, X., Lian, J., et al.: A family of hybrid IPT couplers with high tolerance to pad misalignment. IEEE Trans. Power Electron. 37(3), 3617–3623 (2022) 14. Li, G., Ma, H.: A hybrid IPT system with high-misalignment tolerance and inherent CC– CV output characteristics for EVs charging applications. IEEE Trans. Power Electron. 10(3), 3152–3161 (2022)
Inductively Coupled Power Transfer System Based Constant Voltage and Constant Current Charging for Rail Transit System Jixin Yang1,2(B) , Liming Shi1 , Zhenggang Yin1 , and Wenjing Tang1,2 1 Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering,
Chinese Academy of Sciences, Beijing 100190, China {jixiny,limings,yzhg,twj}@mail.iee.ac.cn 2 University of Chinese Academy of Sciences, Beijing 100049, China
Abstract. This paper focus on the constant voltage (CV) and constant current (CC) charging mode for rail transit energy storage by inductively coupled power transfer (ICPT) system. Firstly, the mathematical model of ICPT system based on LCC-S compensation network is established and analyzed, then a method of switching the parallel compensation capacitor of primary side to realize the switching of CV and CC charging mode is proposed in this paper, the zero voltage switching (ZVS) of MOSFETs can be realized in either CV or CC charging mode, and the method has the advantages of simple operation and high reliability. Finally, the simulation results are presented to verify the feasibility of the proposed method. Keywords: Constant voltage · Constant current · Rail transit system · Inductively coupled power transfer system · Zero voltage switching
1 Introduction At present, the third rail or overhead line and pantograph are the main power supply methods for rail transit system. However, these power supply methods have problems such as friction, electric sparks, electric shock risks and higher maintenance costs [1]. Therefore, the ICPT system has become an alternative to rail transit system power system power supply. The LCC-S compensation network has better advantages for ICPT charging system, such as constant transmitting coil current, high efficiency and low losses [2]. Another advantage for its application in rail transit system is the reduction of the total weight of the vehicle, because only one compensation capacitor is needed. The battery is the most commonly load as the energy storage in the rail transit system [3]. The battery charging process is mainly divided into two modes: CC charging mode and CV charging mode as shown in Fig. 1. First, the CC charging mode is used. When the battery voltage reaches the setting value, then the CV charging mode needs to be used. When the charging current is reduced to the charging cut-off current, the battery charging ends. The alternative CC and CV charging mode will prolong the © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 8–17, 2023. https://doi.org/10.1007/978-981-99-0631-4_2
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service life of the battery, and it is also important to the safety of the ICPT system. Therefore, it is necessary to switch between the CC charging mode and CV charging mode corresponding to the ICPT system used in the rail transit system.
Current /A
CC
Voltage /V
CV
t
Fig. 1. Battery charging process.
In order to realize the switching of CV and CC charging mode of the ICPT system, a method of switching working frequency of the inverter is proposed in [4, 5]. This method doesn’t require wireless communication, but this method is easy to cause the instability of the ICPT system with frequency bifurcation. In [6, 7], the closed-loop control method is adopted to realize the CV or CC charging mode of ICPT system, but closed-loop control method needs to transmit the voltage or current signal to the primary side, the data signal may be interfered by the energy signal, which will affect control accuracy. Meanwhile, the stability of the system using the closed-loop control also needs further research. In [8–10], a method of changing primary side or secondary side compensation structure is adopted, but more switching devices and compensation devices are used in this method, and the switching process between CV and CC charging mode is more complex. In this paper, the ICPT system based on LCC-S compensation network is researched. First, the mathematical model of the system is established, and the conditions for the system to realize the CV and CC mode are obtained through analysis. Then, the method of switching parallel compensation capacitor on the primary side is proposed, the ZVS of the MOSFETs can be realized. Finally, the feasibility of the proposed method is verified through simulation results.
2 Topology of ICPT System The topology of ICPT system is shown in Fig. 2. V dc is the input dc voltage, V ab and V cd are the input and output voltages of the compensation network, respectively, V o is the output dc voltage, I 1 is the input current of the compensation network, I p and I s are the current of the transmitting coil and receiving coil, respectively. L, C, C 1 , C p and L p are formed primary side of compensation network while L s and C s are formed secondary
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side of the compensation network. r p and r s are the inner resistance, M is the mutual inductance, C o is the output capacitor, R is the load, S1 ~ S4 are the MOSFETs of the inverter, D1 ~ D4 are the diodes of the rectifier.
S1
I1
S3
Is
Ip L
M
Cp
D1
D3
Cs Co
C1
Vab
Vdc
C S2
Lp rp
Vo
Vcd
Ls
R
rs
S4
D2
D4
Fig. 2. Topology of ICPT system.
If r p and r s are ignored, the equivalent circuit of the ICPT system is shown in Fig. 3. Each parameter in Fig. 3 is expressed as (1).
I1
Ip
L
Vab
Cp
C1
Lp Zm
Is
Ls
jωMIp
Cs Vcd
Re
C
Fig. 3. Equivalent circuit of the ICPT system.
√ ⎧ Vab = 2 2Vdc /π ⎪ ⎪ ⎨ Zm = (ωM )2 /(Re + jωLs + 1/jωCs ) 2 ⎪ R = 8R/π ⎪ √ ⎩ e Vcd = 2 2Vo /π
(1)
where ω is the resonant angular frequency of the system, Z m is the reflection impedance, Re is the ac equivalent resistance. Let Zeq = jωL + 1/jωC, ZC = 1/jωC1 , Zp = jωLp + 1/jωCp and Zs = jωLs + 1/jωCs , so the impedance of the primary side can be expressed as follows: Zin = Zeq + ZC /(Zp + Zm ) =
Zeq (ZC + Zp + Zm ) + ZC (Zp + Zm ) ZC + Zp + Zm
(2)
So, I 1 , I p , I s and V cd can be expressed as follows, I1 =
ZC + Zp + Zm Vab Vab = Zin Zeq (ZC + Zp + Zm ) + ZC (Zp + Zm )
(3)
Inductively Coupled Power Transfer System
Ip = Is =
ZC ZC Vab I1 = ZC + Zp + Zm Zeq (ZC + Zp + Zm ) + ZC (Zp + Zm )
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(4)
jωM jωMZC Vab Ip = Zs + Re (Zs + Re )Zeq (ZC + Zp + Zm ) + (Zs + Re )ZC (Zp + Zm )
(5)
jωMZC Re Vab (Zs + Re )Zeq (ZC + Zp + Zm ) + (Zs + Re )ZC (Zp + Zm )
(6)
Vcd = Is Re =
3 Analysis of CV and CC Charging Mode 3.1 CV Charging Mode When the conditions shown in (7) are satisfied by the ICPT system, the CV charging mode of the ICPT system can be realized. ⎧ ⎨ Zeq + ZC = 0 (7) Z + ZC = 0 ⎩ p Zs = 0 So, the impedance of the system in CV charging mode can be expressed as: Zin_CV =
ZC Zp Re = 2 Zm (ω MC)2
(8)
It can be seen from (8), the impedance Z in_CV is resistive. In order to realize ZVS of MOSFETs, the impedance of the system needs to be designed to be slightly inductive. In CV charging mode, V cd can be expressed as follows: Vcd =
ωM Vab ωLp − 1/ωCp
(9)
The curves of V cd with operation frequency f under different load are shown in Fig. 4, and the ICPT system parameters are shown in Table. 1. As can be seen from Fig. 4, when the working frequency is 30 kHz, the CV charging mode of the ICPT system can be realized. 3.2 CC Charging Mode On the basis of (5), I s can be further derived as follows: Is =
jωMZC Vab (Zs + Re )[Zeq (ZC + Zp ) + ZC Zp ] + (ωM )2 Zeq + (ωM )2 ZC
(10)
When the condition shown in (11) is satisfied by the ICPT system, the CC charging mode of the ICPT system can be realized. Zeq (ZC + Zp ) + ZC Zp = 0
(11)
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Vcd / V
12
f / kHz
Fig. 4. Curves of V cd with f under different load. Table 1. Parameters of the ICPT system. Symbol
Value
Symbol
Value
V dc
100 V
L
62 μH
C
0.52 µF
C1
3.57 µF
Lp
22.14 µH
Cp
1.97 µF
rp
0.033
Ls
980 µH
Cs
28.71 nF
rs
0.495
M
15 µH
Co
2000 µF
To simplify the structure of the ICPT system, only one part of the system is modified in this paper, so there are three solutions are shown in (12), (13) and (14), respectively. Zeq Zp Zeq + Zp
(12)
Zeq ZC Zeq + ZC
(13)
Zp ZC Zp + ZC
(14)
ZC = − Zp = −
Zeq = −
However, according to (7), in CV charging mode, Z eq + Z C = 0, Z p + Z C = 0, which will result in no solution to (13) and (14). Therefore, (12) is the only selection for the ICPT system to realize the CC charging mode in this paper.
Inductively Coupled Power Transfer System
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So, on the basis of (7) and (12), in CC charging mode, the capacitance of the parallel compensation capacitor C a can be derived as follows: Ca = C1
(15)
So, the impedance of the system in CC charging mode can be expressed as: Zin_CC =
−ZC Zm (ωM )2 Re + j2ωC1 (ωM )4 = 2Zm − ZC 4(ωC1 )2 (ωM )4 + R2e
(16)
It can be seen from (16), the impedance Z in_CC is inductive, so ZVS of MOSFETs can be realized. In CC charging mode, I s can be expressed as: Is = −j
Vab ωM
(17)
Is / A
The curves of I s with operation frequency f under different load are shown in Fig. 5. As can be seen from Fig. 5, when parallel compensation capacitor C a is added, when the working frequency is 30 kHz, the CC charging mode of the ICPT system can be realized. Therefore, the topology of ICPT system that can switch between CV and CC charging mode is shown in Fig. 6. When switch Sa is turned off, the CV charging mode can be realized, when Sa is turned on, the CC charging mode can be realized.
f / kHz
Fig. 5. Curves of I s with f under different load.
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S1
S3
L
Lp
Sa
R
Ls
rp
C S2
D3
Cs Co
C1 Vdc
D1
M
Cp
Ca
rs
S4
D2
D4
Fig. 6. Topology of ICPT system that can switch between CV and CC charging mode.
4 Simulation Results and Analysis Phase shift control is used in inverter of the primary side with the phase shift angle is 0°. Simulation results under CV and CC charging mode are shown in Fig. 7 and Fig. 8, respectively. Waveforms of V ab and I 1 are shown in Fig. 7 (a). When the resistance is changed from 40 to 20 , I 1 is increased, so the output power of the ICPT system is increased. R=40Ω
R=20Ω
Vab / V, I1 / A
Vab
I1
t/s
(a) R=40Ω
R=20Ω
Vo / V, Is / A
Vo
Is
t/s
(b) Fig. 7. CV charging mode of the ICPT system. (a) Waveforms of V ab and I 1 . (b) Waveforms of V o and I s .
Inductively Coupled Power Transfer System
15
Waveforms of V o and I s are shown in Fig. 7 (b). When the resistance is changed from 40 to 20 , I s is increased. Due to the existence of parasitic resistance, V o dropped by about 5 V, but it remains unchanged on the whole. Waveforms of V ab and I 1 are shown in Fig. 8 (a). When the resistance is changed from 40 to 20 , I 1 is decreased, so the output power of the ICPT system is decreased. Waveforms of V o and I s are shown in Fig. 8 (b). When the resistance is changed from 40 to 20 , I s remains unchanged on the whole, and V o when the resistance is 40 is almost twice that when the resistance is 20 . R=40Ω
R=20Ω
Vab / V, I1 / A
Vab
I1 t/s
(a)
Vo / V, Is / A
R=40Ω
R=20Ω
Vo
Is
t/s
(b) Fig. 8. CC charging mode of the ICPT system. (a) Waveforms of V ab and I 1 . (b) Waveforms of V o and I s .
The parallel compensation capacitance C a = 3.57 µF and the resistance R = 40 are selected. Simulation results of switching between CC and CV charging mode are shown in Fig. 9. Waveforms of V ab and I 1 are shown in Fig. 9 (a), waveforms of V o and I s are shown in Fig. 9 (b). Figure 9 (c) and Fig. 9 (d) show the detailed switching process under CC and CV charging mode, respectively. According to Fig. 9 (a) and Fig. 9 (b), when Sa is turned on or off, the switching between CC and CV charging mode of the ICPT system can be realized. As shown in
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CV
Vab / V, I1 / A
Vab
I1 t/s
(a) CC
CV
Vo / V, Is / A
Vo
Is
t/s
(b) Vab
Vab / V, I1 / A
Vab / V, I1 / A
Vab
I1
I1 t/s
t/s
(c)
(d)
Fig. 9. Switching between CC and CV charging mode. (a) Waveforms of V ab and I 1 . (b) Waveforms of V o and I s . (c) Switching process under CC charging mode. (d) Switching process under CV charging mode.
Fig. 9 (c) and Fig. 9 (d), ZVS of the MOSFETs is realized in either CC or CV charging mode.
Inductively Coupled Power Transfer System
17
5 Conclusion A method of the CV and CC charging mode of the ICPT system can be switched by switching parallel compensation capacitor on the primary side is proposed in this paper. When Sa is turned off, the CV mode can be realized, while Sa is turned on, the CC mode can be realized. The point of switching the two charging mode can be determined only by detecting the battery voltage. The feasibility of the method is verified by simulation results. The advantages of the proposed method include the reduction of wireless communication (compared to the closed-loop control), higher stability (compared to the change of working frequency of the inverter), and more easier operation. Through further optimization design, the proposed method in this paper can provide a certain reference for the ICPT system based CV and CC charging mode for rail transit system. Acknowledgments. This work was supported by the National Key Research and Development Program of China under Grant 2016YFB1200601-B21.
References 1. Shi, L., Yin, Z., Jiang, L., et al.: Advances in inductively coupled power transfer technology for rail transit. CES Trans. Electr. Mach. Syst. 1(3), 383–396 (2017) 2. Zhang, H., Chen, Y., Jo, C.-H., et al.: DC-link and switched capacitor control for varying coupling conditions in inductive power transfer system for unmanned aerial vehicles. IEEE Trans. Power Electron. 36(5), 5108–5120 (2021) 3. Zhong, W., Hui, S.Y.R.: Maximum energy efficiency operation of series-series resonant wireless power transfer systems using on-off keying modulation. IEEE Trans. Power Electron. 33(4), 3595–3603 (2018) 4. Lu, J., Zhu, G., Lin, D., et al.: Realizing constant current and constant voltage outputs and input zero phase angle of wireless power transfer systems with minimum component counts. IEEE Trans. Intell. Transp. Syst. 22(1), 600–610 (2021) 5. Lu, J., Zhu, G., Lin, D., et al.: Unified load-independent ZPA analysis and design in CC and CV modes of higher order resonant circuits for WPT systems. IEEE Trans. Transp. Electrif. 5(4), 977–987 (2019) 6. Li, X., Li, X.: Passivity-based control for movable multi-load inductively coupled power transfer system based on PCHD model. IEEE Access 8, 100810–100823 (2020) 7. Sheng, X., Shi, L.: An improved pulse density modulation strategy based on harmonics for ICPT system. IEEE Trans. Power Electron. 35(7), 6810–6819 (2020) 8. Zhang, Z., Zuo, Z., Zhu, J., et al.: Research on constant current and constant voltage control method for UAV based on switching of coupling structure. In: 2020 8th International Conference on Power Electronics Systems and Applications (PESA), Hong Kong, pp. 1–4. IEEE (2020) 9. Song, K., Li, Z., Du, Z., et al.: Design for constant output voltage and current controllability of primary side controlled wireless power transfer system. In: 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Chongqing, pp. 1–6. IEEE (2017) 10. Qui, X., Han, H., Wong, S.-C., et al.: Hybrid IPT topologies with constant current or constant voltage output for battery charging applications. IEEE Trans. Power Electron. 30(11), 6329– 6337 (2015)
Modeling and Analysis of Bidirectional Wireless Power Transfer System with Asymmetric Parameters Chenyang Wei(B) , Bin Wei, Cheng Jiang, and Xiaokang Wu Institute of Energy Storage and New Electrical Technology, China Electric Power Research Institute, Beijing 100192, China [email protected], {weibin,wuxiaokang}@epri.sgcc.com.cn
Abstract. Bidirectional wireless power transfer technology can realize the noncontact bidirectional flow of electric energy between devices. Compared with unidirectional wireless charging and wired charging, it is more intelligent, flexible and interactive. In high-power applications such as electric vehicle charging, bilateral LCC resonant networks are usually used. In this paper, a bidirectional wireless power transfer model of bilateral LCC with asymmetric parameters is established, and the power and efficiency characteristics of the system are analyzed in depth, and the approximate process and error analysis of the maximum efficiency point are given. Then the influence of parameter asymmetry on the system is also studied. The results show that the transferred power of the system is mainly affected by the resonant inductance, while the maximum efficiency is mainly affected by the parasitic resistance of the coil. Finally, the accuracy of the model is verified on a 1-kW prototype. Keywords: Bidirectional wireless power transfer · Bilateral LCC · Asymmetric parameters
1 Introduction Wireless power transfer (WPT) technology is a non-contact power transfer technology, which is widely used in the fields of underwater power supply, unmanned aerial vehicle, biomedical equipment and electric vehicles due to its ease of use, easy to realize automatic control and high security [1, 2]. In recent years, with the rise of concepts such as smart distribution network and vehicle-to-grid (V2G), bidirectional wireless power transfer (BWPT) technology has attracted more attention because of its ability to make energy flows in both directions [3, 4]. At present, many scholars have done some research on bidirectional wireless power transfer. Yeran Liu et al. proposed a novel primary-side parameter estimation method on the basis of establishing the transfer model for BWPT systems. This method can estimate mutual inductance at startup and monitor secondary-side phasor information continuously during operation [5]. And they proposes a multivariable control strategy © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 18–28, 2023. https://doi.org/10.1007/978-981-99-0631-4_3
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that uses the optimal combination of all control variables to maximize the efficiency of WPT systems [6]. However, the above research have adopted the simple S-S resonant network which is lack of robustness when disturbed. In order to achieve better system output characteristics, high order resonant network is usually adopted. Thrimawithana D.J. et al. established the steady-state model of LCL bidirectional wireless power transfer system, and analyzed the change of system induced impedance when the parameters change [7]. Chen K. and Zhao Z. studied three resonant topologies applied to bidirectional wireless power transfer, and believes that bilateral LCC topology is more suitable for bidirectional wireless charging of electric vehicles [8]. Zhang X. et al. derived the maximum efficiency point of bilateral LCC network, and the maximum efficiency control under the variation of bilateral voltage was realized [9]. However, existing studies usually set complete symmetry of bilateral parameters in modeling, but it is often difficult to achieve in practice because of engineering error and lack of standards. A more accurate model is needed to describe the power and efficiency characteristics of the system in the case of large differences in bilateral parameters. In this paper, a bidirectional wireless power transfer model of bilateral LCC with asymmetric parameters is established in the frequency domain. Considering the resonant inductance resistance and coil resistance, the power characteristics and the process of obtaining the maximum efficiency point of the system are analyzed in detail, and the influence of bilateral parameter asymmetry on the system is studied. Finally, a 1 kW prototype is built and relative experiments are designed to verify the correctness and accuracy of the model.
2 Basic Working Principle 2.1 Topological Structure of BWPT The structure of bidirectional wireless power transfer system using bilateral LCC resonance network is shown in Fig. 1. The left side is defined as the primary side while the right side as the secondary side. The bilateral structure is symmetrical and adopts the full bridge structure.
Fig. 1. Structure of BWPT system
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Where, U˙ 1 is the AC voltage output by the inverter on the primary side, L1 , C1 and Cp are primary side LCC resonant network, R1 is primary side resonant inductance parasitic resistance, Lp is primary side coil inductance, and Rp is primary side coil parasitic resistance. All parameters on the secondary side are the same. M is mutual inductance between two coils. 2.2 3-Freedom Control Method The full bridge control waveform and output waveform under 3-freedom control method are shown in Fig. 2 below. The phase shift angle between the two bridge arms of a single converter is defined as β1 and β2 and the phase shift angle between the inverters on both sides is defined as δ.
Fig. 2. Control and output waveform of BWPT system
In the figure, u1 (t) and u2 (t) are the output voltage waveforms of the inverter, and u1_1 (t) and u2_1 (t) are the fundamental component of the output voltage of the inverter. By adjusting β1 and β2 , the output voltage of the inverter can be adjusted, and by adjusting δ, the phase between the voltages on both sides can be adjusted, so as to control the system.
3 Power and Efficiency Model in Frequency Domain The frequency domain equivalent model of bilateral LCC resonant network is shown in the figure below. I˙1 is the output current of the inverter on the primary side, and I˙p is the coil current on the primary side. Both parameters on the secondary side are the same (Fig. 3).
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Fig. 3. Equivalent model of resonant network
Assume the frequency of U˙ 1 and U˙ 2 are ω, the frequency domain model of the circuit can be listed as: ⎧ ⎪ ˙ 1 = R1 + jωL1 + 1 I˙1 − 1 I˙p U ⎪ ⎪ jωC1 ⎪ jωC1 ⎪ ⎪ ⎨ 0 = Rp + jωLp + 1 + 1 I˙p − 1 I˙1 + jωM I˙s jωC1 jωCp jωC1 (1) 1 ˙ 1 1 ⎪ 0 = − R + jωL + + I I˙s − jωM I˙p ⎪ 2 s s ⎪ jωC jωC jωC s 2 2 ⎪ ⎪ ⎪ ⎩ U˙ 2 = R2 + jωL2 + 1 I˙2 − 1 I˙s jωC2 jωC2 In order to make the system work in the resonant state, the parameters of bilateral inductance and capacitance are set as: ⎧ 1 ⎪ jωL1 + jωC =0 ⎪ 1 ⎪ ⎪ ⎨ jωLp + 1 + 1 = 0 jωC1 jωCp (2) 1 1 ⎪ jωL + + s ⎪ jωC2 jωCs = 0 ⎪ ⎪ ⎩ jωL2 + 1 = 0 jωC2
Combining the Eq. (1) and (2), the expressions of output current of bilateral inverter and bilateral coil current can be solved as: ⎡ ⎤ b1 ⎡˙ ⎤ j da11 a1 I1 ⎢ ⎥ b2 j d2 ⎢ I˙2 ⎥ ⎢ ⎥ U˙ 1 a2 a2 ⎢ ⎥=⎢ ⎥ (3) ωC R d 1 1 1 R b ⎢ ⎥ ˙ ⎣ I˙p ⎦ 1 1 − a1 ⎣ jωC1 a1 − 1 ⎦ U2 I˙s jωC2 Ra22b2 − 1 − ωC2 R2 d2 a2
The expression of each coefficient a1 , b1 , d 1 , a2 , b2 and d 2 in the formula is shown in the appendix. According to Fig. 2, Assume U˙ 1 is the reference voltage, the vector form of bilateral voltage can be expressed as: U˙ 1 = U1 (4) U˙ 2 = U2 (cos δ − j sin δ) where U1 and U2 are the amplitudes of U˙ 1 and U˙ 2 respectively. Combining the Eq. (3) and (4), the energy transferred in both directions in the resonant mechanism can be expressed as: Pp = Re U˙ 1 I˙1∗ = ba11 U12 + da11 U1 U2 sin δ (5) Qp = Im U˙ 1 I˙1∗ = − da11 U1 U2 cos δ
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Ps = Re U˙ 2 I˙2∗ = ba22 U22 − da22 U1 U2 sin δ Qs = Im U˙ 2 I˙2∗ = − da22 U1 U2 cos δ
(6)
When sin δ ∈ (0, 1], the power is transferred forward from the primary side to the secondary side; When sin δ ∈ [−1, 0), the power is transferred in reverse and flows from the secondary side to the primary side. 3.1 Bidirectional Transfer Power Analysis The standard unitary method is adopted when analyzing the power. Assume the voltage amplitude U1 = U2 = 1, the transferred power is shown in the figure below (Fig. 4):
Reverse Transfer
Forward Transfer
Fig. 4. Transferred power with different δ
It can be seen that the value of reactive power transfer is maximum when the bilateral voltage has same phase, but the active power is still not 0. We think that this is caused by parasitic resistance during the establishment of electromagnetic field. 3.2 Maximum Efficiency Point Analysis The bilateral voltage amplitude ratio T is defined as follows: T=
U1 U2
(7)
Combining the Eq. (5)–(7), the efficiency of bidirectional transfer can be expressed as:
⎧ ⎪ ⎪ ⎪ ⎨ ηp−s =
−Ps Pp
=
⎪ ⎪ ⎪ ⎩ ηs−p =
−Pp Ps
=
b d − a2 + a2 T sin δ 2 2 b1 2 d1 a1 T + a1 T sin δ b d − a1 T 2 − a1 T sin δ 1 1 b2 d2 a2 − a2 T sin δ
, sin δ ∈ (0, 1] (8) , sin δ ∈ [−1, 0)
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Fig. 5. (a) ηp−s and ηs−p with different k (b) Efficiency ηp−s with different T and sin δ
According to Eq. (8), the change of system efficiency can be plotted as shown in the figure below where k is the coupling coefficient between the two coils: As can be seen from Fig. 5, the efficiency of bidirectional transfer is affected by T and sin δ when k is determined. Take forward transfer as an example, it is easy to discover that ∂ηp−s /∂ sin δ > 0. In order to find the maximum efficiency point Tηp−s max , assume that: ∂ηp−s =0 (9) ∂T Solution of Eq. (9) can be obtained as: b1 b2 + b21 b22 + b1 b2 d1 d2 (sin δ)2 Tηp−s max = (10) d2 b1 sin δ Since Eq. (10) is complex and contains mutual inductance coefficient M, it is difficult to be used for system control, so further simplification is required. We assume that Q12 1, Q22 1, k 2 1(Q1 , Q2 are the quality factor of L1 and L2 ), and the expression for Tη max can be reduced as: Q1 R1 Rs 1 + 1 + k 2 Qp Qs (sin δ)2 (11) Tηp−s max ≈ ωMQ2 R2 sin δ where Qp and Qs are the quality factor of Lp and Ls . We consider Eq. (11) as a first approximation. Since Eq. (11) still contains M, a further simplification is needed. Ignore the 1’s in the numerator on the right side of the Eq. (11), the expression for Tη max can be reduced as: L1 Rs (12) Tηp−s max ≈ L2 Rp We consider Eq. (12) as a secondary approximation. Similarly, the maximum efficiency point of reverse transfer can be expressed as: b1 b2 − b21 b22 + b1 b2 d1 d2 (sin δ)2 Tηs−p max = d2 b1 sin δ
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Q1 R1 Rs 1 − 1 + k 2 Qp Qs (sin δ)2 ≈
ωMQ2 R2 sin δ
L1 ≈ L2
Rs Rp
(13)
After two steps of approximation, the efficiency loss of the system is shown in the figure below (Fig. 6):
Fig. 6. Maximum efficiency point (MEP) and efficiency loss with different k: (a) Forward transfer when sin δ = 1 (b) Reverse transfer when sin δ = −1
It can be found that within the range of loose coupling coefficient, the efficiency loss caused by using secondary approximation to obtain the accurate point of the system is less than 0.5%. Therefore, we can use Eq. (12) for maximum efficiency control without large deviation. 3.3 Asymmetric Parameters Analysis The asymmetry of bilateral parameters is further analyzed using the standard unitary method. The ratio coefficients of bilateral parameters are defined as follows: kLm =
Rp L1 R1 , kRm = , kR = L2 R2 Rs
(14)
The influence of parameters ratio coefficients on transfer power and efficiency is shown in the figure below: According to Fig. 7 (a), the transferred power is mainly affected by resonant inductance L 1 and L 2 . When there is a certain difference between L 1 and L 2 , the system can transfer more power at the same voltage. According to Fig. 7 (b), the transferred efficiency is strongly Rp and Rs and weekly affected by L 1 and L 2 . Thus we prefer smaller Rs and smaller L 1 to improve the system’s efficiency.
4 Experimental Confirmation In order to verify the correctness of model derivation, an experimental prototype BWPT system was built in the laboratory settings as shown in Fig. 8. As for the controller, a
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Fig. 7. Influence on power and efficiency with different k Lm , k Rm and k R : (a) Influence on transferred active power (b) Influence on maximum transfer efficiency
digital signal processor (TMS320F28335) is used to accomplish the system control. An oscilloscope and a power analyzer are used to measure the waveform and the efficiency of the BWPT system. Both voltage sources are simulated by batteries. The specific parameters of the prototype are listed in Table 1.
Fig. 8. The experimental platform with bilateral LCC network BWPT system
Using Eq. (12) and (13) to achieve maximum efficiency control, the output waveform is shown below (Fig. 9): The maximum efficiency of the system is 93.2% in the case of forward transfer and 92.7% in the case of reverse transfer. Take forward transfer as an example, by changing control parameters β1 and system parameters L 2 , R2 and Rs , the power and efficiency curves of the system can be drawn as follows: It can be seen from Fig. 10 (a) that using Eq. (12) and (13) for system control can make the system work at the maximum efficiency point, and the difference between experiment and theory mainly comes from the loss of the converter. And we can find that a smaller L 2 caused bigger transferred power but smaller efficiency, and the influence of Rs on efficiency is bigger than R2 , as described in Sect. 3.3.
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Parameters
Symbols
Value
Resonant frequency
f
85 kHz
Resonant inductor
L1 , L2
48 µH, 45 µH
parasitic resistance of inductor
R1 , R2
35 m, 28 m
Self-induction of coils
Lp , Ls
210 µH, 167 µH
parasitic resistance of coils
Rp , Rs
96 m, 74 m
Mutual-induction
M
25 µH
Bilateral voltage amplitude
U 1, U 2
200 V, 200 V
Fig. 9. Output waveform of experiment: (a) Forward transfer when sin δ = 1 (b) Reverse transfer when sin δ = −1
Fig. 10. Output data of experiment: (a) Power and efficiency curves when β1 was changing (E means experimental data and T means theoretical data) (b) Power and efficiency curves when L 2 , R2 and Rs was changing
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5 Conclusion In this paper, a frequency domain model of bidirectional wireless power transfer system using bilateral LCC resonant network with asymmetric parameters was established. Through the research and analysis of the model, the following conclusions can be drawn: • When the bilateral voltage is in phase, the power supply still outputs active power, which can be considered as parasitic resistance loss in the establishment of electromagnetic field. • The maximum transfer efficiency point of the system can be approximately determined by the resonant inductance and coil resistance. • Bilateral parameter asymmetry will affect the performance of the system: The power is mainly affected by resonant inductance while efficiency is mainly affected by resonant inductance and coil resistance. Finally, a 1-kW prototype was built to verify the correctness of the model. The model can accurately describe the characteristics of the BWPT system and provide guidance for parameter design. Acknowledgment. This research is supported by The National Key Research and Development Program of China (2021YFB2501604).
Appendix The expression of the coefficients in Eq. (3) is shown below: ⎧ ⎧ 6 2 2 2 ω6 M 2 C 2 C 2 R1 R2 2 C 2 R R + 1 + ω M C1 C2 R2 R1 ⎪ ⎪ ⎪ ⎪ a2 = ω2 C22 Rs R2 + 1 + ω2 C 2 R1 R2 +1 a = ω 1 p 1 2 R R +1 ⎪ ⎪ 2 1 ω C ⎪ ⎪ 2 s 2 1 p 1 ⎨ ⎨ ω6 M 2 C 2 C 2 R ω6 M 2 C 2 C 2 R b1 = ω2 C12 Rp + ω2 C 2 R 1R 2+12 b2 = ω2 C22 Rs + ω2 C 2 R 1R 2+11 ⎪ ⎪ 2 s 2 1 p 1 ⎪ ⎪ 3 3 5 5 ⎪ ⎪ ⎪ ⎪ ⎩ d2 = ω3 C1 C2 M − ω 2MC21 C2 R1 Rp ⎩ d1 = ω3 C1 C2 M − ω 2MC21 C2 R2 Rs ω C R R +1 ω C R R +1 2 s 2
1 p 1
References 1. Ahmad, A., Alam, M.S., Chabaan, R.: A comprehensive review of wireless charging technologies for electric vehicles. IEEE Trans. Transp. Electrif. 4(1), 38–63 (2018) 2. Xue, M., Yang, Q., Zhang, P., et al.: Application status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(08), 1547–1568 (2021). (in Chinese) 3. Madawala, U.K., Thrimawithana, D.J.: A bidirectional inductive power interface for electric vehicles in V2G systems. IEEE Trans. Ind. Electron. 58(10), 4789–4796 (2011) 4. Liu, F., Chen, K., Jiang, Y., et al.: Research on the overall efficiency optimization of the bidirectional wireless power transfer system. Trans. China Electrotech. Soc. 34(5), 891–901 (2019). (in Chinese)
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5. Liu, Y., Madawala, U.K., Mai, R., He, Z.: Primary-side parameter estimation method for bidirectional inductive power transfer systems. IEEE Trans. Power Electron. 36(1), 68–72 (2021) 6. Liu, Y., Madawala, U.K., Mai, R., He, Z.: An optimal multivariable control strategy for inductive power transfer systems to improve efficiency. IEEE Trans. Power Electron. 35(9), 8998–9010 (2020) 7. Thrimawithana, D.J., Madawala, U.K.: A generalized steady-state model for bidirectional IPT systems. IEEE Trans. Power Electron. 28(10), 4681–4689 (2013) 8. Chen, K., Zhao, Z., Liu, F., et al.: Resonance topology analysis of bidirectional wireless charging system for electric vehicles. Autom. Electr. Power Syst. 41(2), 66–72 (2017). (in Chinese) 9. Zhang, X., et al.: A Control strategy for efficiency optimization and wide ZVS operation range in bidirectional inductive power transfer system. IEEE Trans. Ind. Electron. 66(8), 5958–5969 (2019)
Design and Research on Coupling Mechanism of Inductive Power Transmission Wei Liu1 , Liangshun Sun1 , Mingwei Su1 , Fangrui Wang2 , Jian Long3 , Enxin Xiang4 , and Longlei Bai1(B) 1 Yantai Research Institute, Harbin Engineering University, Yantai 264000, China
[email protected], [email protected]
2 Institute of Intelligence and Engineering, Harbin Engineering University, Harbin 150000,
China 3 Kunming Institute of Electrical Science, Kunming 650000, China 4 Yunnan Electric Power Research Institute, Yunnan Power Co., Ltd., Kunming 650000, China
Abstract. The original intention of wireless power transmission was to make the power supply more flexible, but compared with wired transmission, its efficiency has always restricted its application. Therefore, the performance characteristics of wireless power transmission have always been a research focus in wireless power transmission. As for induction power transmission, its coupling mechanism is the key part of the transmission system, and its optimal design directly affects the power, efficiency and transmission distance of the system. The research results of the coupling mechanism of an inductive power transmission system in recent years are reviewed, and the effects of coil structure, coupling mechanism material and coil parameter design on efficiency characteristics are analyzed. This paper analyzes the existing optimization methods and existing problems, and points out the direction for the optimal design of the coupling mechanism of a wireless power transmission system. Keywords: Inductive power transmission · Coupling mechanism · Efficacy characteristics
1 Introduction Wireless power transmission technology, as a non-contact power transmission technology, gets rid of the shackles of tangible media and can transmit power from the power supply terminal to the power consumption equipment terminal only by invisible soft media in space. Wireless power transmission realizes the portable and safe access to power supply, and solves the problems of plug-in and maintenance difficulty caused by traditional transmission mode, especially the hidden trouble of accidents in special cases [1]. It is considered a safe, convenient and effective power transmission method. Compared with the wired transmission, its efficiency characteristics are always insufficient, and it is difficult to meet the actual demand. As a key part of the inductive power transmission system, the optimal design of the coupling mechanism directly affects the © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 29–35, 2023. https://doi.org/10.1007/978-981-99-0631-4_4
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efficiency characteristics of the system. The influence of the coupling mechanism on the efficacy characteristics is expounded from three aspects: coil structure, coupling mechanism material and parameter design optimization, and the problems to be solved and development trends in the future are pointed out, to provide a reference for further research and design.
2 Coil Structure In the design of the coupling structure, the coil structure occupies an important position, which has an important influence on the coupling coefficient, anti-interference ability, transmission distance and efficiency characteristics of the coupling mechanism. It can be roughly divided into two categories: simple coil structure and complex coil structure. The simple coil structure is mainly represented by planar disk coil, rectangular coil and spiral coil, which have its advantages in different transmission occasions. Because of its simple structure, it is widely used in WPT. Its efficacy characteristics have a complete theoretical system, which is generally favored by people. This structure is shown in Fig. 1. With the in-depth study of the characteristics of IPT systems efficiency, the anti-deflection ability of coil has become a key problem to be solved, so it is a new solution to introduce a multi-coil structure.
(a) planar disk coil
(b) rectangular coil
(c) spiral coil
Fig. 1. Simple coil construction
The complex coil structure further shapes the magnetic field through the superposition of magnetic fields, effectively increases the coupling area, obtains better angle friendliness and space friendliness, solves the offset problem, and ensures transmission efficiency in the offset situation. The structure is shown in Fig. 2. The performances of each coil are shown in Table 1.
3 Coupling Mechanism Materials Copper has become the main coil material because of its low resistance, but in the case of high-frequency current, the skin effect will increase power loss and reduce system efficiency. To weaken the skin effect, in IPT systems, the Leeds line is used to reduce the loss and improve the transmission efficiency of the system [2]. High-temperature superconducting materials are characterized by almost no resistance. The coil design made of high-temperature superconducting material can reduce the resistance, Joule loss and energy loss in the process of electric energy transmission.
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(a)Flux pipe
(b)DD
(c)DDQ
(d)BP
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Fig. 2. Complex coil construction Table 1. Contrast of different structures Structure
Frequency (kHz)
Anti-deflection ability
Shielding performance
Coil loss
Power (kW)
Efficiency (%)
Flux pipe
20
Better
Large magnetic flux leakage
Larger
Middle
Low
DD
20
Better
Less leakage
So-so
Middle
High
DDQ
20
Better
Less leakage
Larger
High
High
BP
20
So-so
Less leakage
Smaller
High
High
Therefore, its energy consumption in wireless energy transmission increases the efficiency of the system. However, there will still be some AC power loss when AC power passes, and refrigeration will also bring energy loss [3]. Table 2 below compares the material properties of copper and high-temperature superconducting materials. Table 2. Coil material comparison Conductor material
Frequency
Efficiency
Costs
Copper
More than 20 kHz
High efficiency
Low
High-temperature superconductivity
Less than 20 kHz
High efficiency
High
Because the overall inductance of the coreless structure is small, it can only be used in high frequency, low power and short distance occasions. To face high power, long-distance and coil structure, adding a conductive magnet can effectively limit the
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magnetic field distribution, reduce the magnetic leakage of the system, reduce the impact on the environment, increase the magnetic flux density, improve efficiency and reduce the system volume. Different magnetic materials can play an important role in improving efficiency and power in different environments. Ferrite and metamaterials are discussed [4]. Ferrite is a kind of composite oxide sintered body, which has the characteristics of high resistivity, high permeability, medium magnetic induction, low loss, and low price. It is suitable for high-frequency circuits. It is widely applied in wireless power transmission [5]. The main parameters affecting the magnetic field distribution efficiency are the permeability and resistivity of ferrite, and the design size and thickness of the ferrite magnetic sheet. Due to the diversity of ferrite shapes, the square strip MnZn ferrite is commonly used in IPT systems, and the material characteristics are listed in Table 3. In addition, new nanocrystalline [6] and ferromagnetic oxide powder is also a good choice. Their high power density and low eddy current loss have great advantages in high frequency field. Table 3. Ferrite material comparison Material quality
Initial permeability Saturation flux μi density (mT) (25 °C; 100 °C)
Relative loss factor ×10−6 (100 kHz)
Resistivity ·m
PC40
2000 ± 25%
530
450
PLoad , PBat < PCh_Max , PWPT = PMax && PWPT = PLoad + PBat . Mode 3: PMax > PLoad , PBat = PCh_Max , PWPT < PMax && PWPT = PLoad + PBat . Mode 4: PMax > PLoad , PBat = 0, PWPT = PLoad .
3.3 Control Method for Efficiency Optimization When the load power PWPT is constant, the lower the input power Pin , the higher the transmission efficiency. From the analysis in Sect. 2.3, it is clear that there is an optimum input voltage U inopt to maximize the transmission efficiency. Therefore, this paper searches for the minimum input power of the system by perturbing U in to achieve the MEPT. The specific flowchart of this approach is shown in Fig. 10.
Fig. 10. Flowchart of P&O algorithm
The system applies a disturbance ΔU to the input voltage U in , and determines the direction of the next disturbance by comparing the input power before and after the disturbance. If the efficiency becomes higher, the direction of perturbation will be maintained. Otherwise, the system will change the direction of the perturbation.
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4 Simulation Analysis Based on the control strategy and circuit design proposed in Sect. 2, a simulation model of the WPT system between the rocket and the ground was built in MATLAB/Simulink as shown in Fig. 2 to verify the rationality of the optimisation design proposed in this paper. The basic parameters used in the simulation remain the same as in Table 1, and additional parameters are shown in Table 2. Table 2. Additional simulation parameters Symbol
Quantity
Value
C dc
Filter capacitors
1000 µF
C Bus
Filter capacitors
2200 µF
L Bus
Stream inductance
200 µH
SOC0
Initial SOC of the battery
90%
U bat0
Nominal voltage of the battery
7 × 3.7 V
T MEPT
Perturbation period of MEPT
30 ms
Firstly, the simulation verifies the variation of the system transmission efficiency η with the input voltage U in without the battery for optimisation, as shown in Fig. 11. The simulated results are consistent with the theoretical derivation (Fig. 5) in terms of trend, but the simulated values of transmission efficiency are lower than the theoretical values due to losses in the DC-DC variator and rectifier.
Fig. 11. Simulation curve of η with Uin
Fig. 12. Comparison of efficiency curves
The simulation verifies that the transmission efficiency η varies with the input voltage U in when the system outputs 0.5 kW, 0.9 kW and 2 kW power when only the WPT system supplies power and the battery does not participate in the discharge, as shown in Fig. 12. As can be seen from the figure, the simulation results are consistent with the theoretical results (Fig. 5) in the variation trend, but the simulation value of transmission efficiency is lower than the theoretical value due to the loss of the DC-DC changer and rectifier.
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To verify the optimization effect of the battery on the optimization of the MEPT, the simulation was designed for the following operating conditions. In 0–70 ms, the load power is stable at 0.5 kW and the input voltage U in is 50 V. At 70 ms, the load power is suddenly changed to 2 kW. After that, the system gradually reaches the maximum efficiency point and remains stable under the action of the MEPT control. The efficiency variation curve is shown in Fig. 12. The curves of the input voltage U in and the input power Pin during the MEPT search are shown in Fig. 13. When the battery does not participate in the energy supply, the system transmission efficiency drops from 86.4% to 53% when the load power changes abruptly. Under the control of MEPT, the maximum efficiency is achieved after 29 perturbation iterations. For the hybrid energy supply architecture, the transmission efficiency is reduced from 86.4% to 82% when the load power is suddenly changed. Under the action of MEPT control, the maximum efficiency is reached after 16 perturbation iterations. This simulation verifies the feasibility of the proposed hybrid power supply architecture and the optimisation effect of the MEPT algorithm.
Fig. 13. The MEPT search process (a) Hybrid energy supply system with battery; (b) General energy supply system without battery
5 Conclusion This paper explores the specific application of WPT technology in the field of launch vehicle, and presents a hybrid power supply architecture for WPT systems using batteries for energy compensation. Both theoretical derivation and simulation results show that this architecture can not only shorten the search range and time for the optimal operating point, but also weaken the problem of abrupt drop in transmission efficiency caused by sudden changes in load power. At the same time, the system does not require wireless communication and has high reliability.
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References 1. Peng, Y., Mou, Y., Song, J.: Research on the development of avionics and electrical system in Chinese next generation launch vehicle. Astronaut. Syst. Eng. Technol. 4(2), 13–24 (2020). (in Chinese) 2. Wang, G., Zhang, J., Geng, S., Zhou, G.: Development trend and key technologies of new generation measurement system for launch vehicles. Astronaut. Syst. Eng. Technol. 4(1), 1–7 (2020). (in Chinese) 3. Cui, S., Song, B., Wang, Z.: Overview of magnetic coupler for electric vehicles dynamic wireless charging. Trans. China Electrotech. Soc. 37(3), 537–554 (2022). (in Chinese) 4. Wu, X., Sun, P., Yang, S., He, L., Cai, J.: Review on underwater wireless power transfer technology and its application. Trans. China Electrotech. Soc. 34(8), 1559–1568 (2019). (in Chinese) 5. Wu, S., Cai, C., Chen, Y., Chai, W., Yang, S.: Research progress and development trend of multi-rotor unmanned aerial vehicles wireless charging technology. Trans. China Electrotech. Soc. 37(3), 555–565 (2022). (in Chinese) 6. Patil, D., Mcdonough, M., Miller, J., Fahimi, B., Balsara, P.: Wireless power transfer for vehicular applications: overview and challenges. IEEE Trans. Transp. Electrif. 4(1), 3–37 (2017) 7. Xue, M., Yang, Q., Zhang, P., Guo, J., Li, Y., Zhang, X.: Application status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(8), 1547–1568 (2021). (in Chinese) 8. Yeo, T., Kwon, D., Khang, S., Yu, J.: Design of maximum efficiency tracking control scheme for closed-loop wireless power charging system employing series resonant tank. IEEE Trans. Power Electron. 32(1), 471–478 (2016) 9. Li, H., Li, J., Wang, K., Chen, W., Yang, X.: A maximum efficiency point tracking control scheme for wireless power transfer systems using magnetic resonant coupling. IEEE Trans. Power Electron. 30(7), 3998–4008 (2015) 10. Mai, R., Liu, Y., Chen, Y.: Studies of efficiency optimization methods based on optimal equivalent load control in IPT systems. In: Proceedings of the CSEE, vol. 36, no. 23, pp. 6468– 6475+6613 (2016). (in Chinese) 11. Dai, X., Li, X., Li, Y., Hu, A.: Maximum efficiency tracking for wireless power transfer systems with dynamic coupling coefficient estimation. IEEE Trans. Power Electron. 33(6), 5005–5015 (2018) 12. Su, Y., Yang, J., Dai, X., Liu, J., Hou, X.: Load and mutual recognition of MCR-WPT system based on TensorFlow neural network. Autom. Electr. Power Syst. 45(18), 162–169 (2021). (in Chinese) 13. Zhao, J., Zhao, J., Zhang, J., Mao, L., Qu, K.: Maximum efficiency tracking study of active impedance matching network discontinuous current mode in wireless power transfer system. Trans. China Electrotech. Soc. 37(1), 24–35 (2022). (in Chinese) 14. Zhong, W., Hui, S.: Maximum energy efficiency tracking for wireless power transfer systems. IEEE Trans. Power Electron. 30(7), 4025–4034 (2015) 15. Li, Z., Song, K., Jiang, J., Zhu, C.: Constant current charging and maximum efficiency tracking control scheme for supercapacitor wireless charging. IEEE Trans. Power Electron. 33(10), 9088–9100 (2018) 16. Yang, Y., Zhong, W., Kiratipongvoot, S., Tan, S., Hui, S.: Dynamic improvement of seriesseries compensated wireless power transfer systems using discrete sliding mode control. IEEE Trans. Power Electron. 33(7), 6351–6360 (2017) 17. Zhang, W., Wu, X., Xia, C., Liu, X.: Maximum efficiency point tracking control method for series-series compensated wireless power transfer system. IET Power Electron. 12(10), 2534–2542 (2018)
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18. Guo, Y., Cui, N.: Research on optimal configuration and characteristics based on LCC-S type wireless power transfer system. Trans. China Electrotech. Soc. 34(18), 3723–3731 (2019). (in Chinese) 19. Huang, Y., Shinohara, N., Mitani, T.: Impedance matching in wireless power transfer. IEEE Trans. Microw. Theory Techn. 65(2), 582–590 (2017)
Design and Modeling of Helmholtz Coil Based on Winding Method Optimization Xueting Zhao, Zihao Zhang, Xiaoyun Chen, Yi Zhou, and Deyan Lin(B) Wuhan University of Technology, Wuhan, Hubei, China [email protected]
Abstract. Helmholtz coils are widely used in the calibration of magnetic probes and other research that requires standard uniform magnetic fields. Coils can be used as inductive loads as well. However, due to the parasitic capacitance among adjacent turns, the magnetic flux density is not in a strictly linear relationship with the driving current. Therefore, the parasitic capacitance needs to be mitigated. In this paper, the authors analyzed the influence of the parasitic capacitance of the coil wound by two conventional methods and two newly proposed methods. It is found that the inter-turn and inter-layer capacitances of the windings are subdivided, which has a great influence on the lumped parameters. The coil support frame has different effects on the turn-to-turn capacitance, so the electrostatic energy stored by the capacitance in each turn of the coil cannot be ignored, and so as the stray capacitance to the ground. The results are compared to those extracted from FEM electrostatic field simulation. Finally, we designed a capacitance-optimized Helmholtz coil over a nominal operating frequency range from 1 Hz to 100 kHz. Experimental measurements validated the proposed method and pointed out some design guides in the coil design. Keywords: Helmholtz coil · ANSYS maxwell 2D · Winding method · Parasitic capacitance
1 Introduction As a standard magnetic field generator, the Helmholtz coil is widely used in scientific experiments [1–3]. With a reasonably designed Helmholtz coil, ac or dc can be applied to generate the various magnetic field. The magnetic flux density is in a linear relationship with the driving current, and the uniform region of the magnetic field generated by the Helmholtz coil is large. The study pointed out that compared to multi-dimensions or other shapes of coil 1-D circular coils have the best uniformity of magnetic field in the center [4], with a simple structure, the 1-D circular Helmholtz coil has great advantages in the application of standard magnetic field generators. Therefore, its design optimization research is of great significance. However, when the frequency gradually increases, the parasitic parameters of a Helmholtz coil especially the parasitic capacitance cannot be ignored. When the Helmholtz coil is driven by a voltage source, the excessive stray capacitance is in shunt © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 57–70, 2023. https://doi.org/10.1007/978-981-99-0631-4_7
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to the load coil, which reduces the actual current passing through the coil inductance component and therefore influences the magnetic field at the center of the coil [5]. The existence of parasitic capacitance will also generate voltage or current spikes, which may damage the coil insulation [6]. At present, the operating frequency of Helmholtz coils on the market is generally 50 Hz or 60 Hz, narrow operating frequency range cannot meet the application of HF magnetic field. Therefore, the focus of this paper is to study the influence of the inter-turn and inter-layer parasitic parameters, improve the winding arrangement, and optimize the electric field distribution, eventually reducing the parasitic capacitance and increasing the self-resonant frequency. There are mainly three methods to get the global stray capacitance of a coil. The first method is based on the principle of electrostatic field energy storage. The finite element method(FEM) can be used to calculate the electrostatic energy storage between the windings, and then the parasitic capacitance is predicted [7]. The method regards each turn of the coil as an equipotential node; and most of the studies do not consider the non-adjacent capacitance [6, 8–10]. The second is the field-circuit combination method, that is, the capacitance is calculated by FEM or theoretical derivation, the equivalent circuit of the winding is established, and the resonant frequency of the coil is obtained by solving the circuit problems using basic KCL/KVL equations or simulation in MATLAB/Simulink, the equivalent circuit after the subdivision of the coil is a three-dimensional impedance network in practice, especially the coupling relationship between part of the inductors cannot be ignored, which makes circuit simplification complicated [11–13]. In addition, current research does not extend the equivalent circuit to different windings [14, 15]. The third is the experimental method, which establishes the HF model of the component, and then derives the winding distribution from the experimental results of the impedance test. This method is not suitable for the early design of the coil [16]. Based on the above analysis, this paper combines FEM simulation with theoretical derivation. The necessity of the multi-turn and multi-layer winding method for the Helmholtz coil is discussed in Sect. 2. For the accuracy of modeling, we considered the equivalent process of Litz wire to solid wire, and also the procedure of subdivision of inter-turn and inter-layer capacitance in Sect. 3. In Sect. 4 we proposed two new different winding arrangements based on conventional ones, then the lumped parasitic capacitance is calculated by the electrostatic energy method. The effect of turns and layers on equivalent capacitance under different types of winding is discussed. The influence of different winding methods on the final lumped capacitance of the coil is analyzed through theoretical analysis and experiments in Sect. 5. Designing and optimizing suggestions for the Helmholtz coil has given in this paper at last.
2 Helmholtz Coil Structure and Winding Methods The magnetic flux density at the center of the Helmholtz coil can be calculated through the superposition of partial magnetic fields generated by the current I of each turn. To meet the maximum field density value of the central area of the Helmholtz coil under a certain designed structure size, a multi-turn multi-layer configuration is generally used, as shown in Fig. 1(a). R represents the average radius of the two-layer coil, D represents the spacing between the two pairs of coils, and d p represents the layer spacing, where D = R.
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z D
dp
1/2dp
L
Rloss
R
I
O
x
Cw y
Incoming
(a)
Outgoing
Uw
(b)
Fig. 1. 1-D Helmholtz coil (a) Multi-turn multi-layer winding method, (b) Equivalent lumped circuit of a coil.
With Biot-Savart law, the magnetic field density at the central axis x of the two pairs of the coil is expressed as [4]: Bx =
μ0 N (R − dp )2 I μ0 N (R + dp )2 I + 2 3/2 2 [(R − dp + (x + (R − dp )/2) ] [(R + dp ) + (x − (R + dp )/2)2 ]3/2 (1) )2
where μ0 is the vacuum permeability, x is the coordinate at any point on the x-axis, and N is the number of turns of each layer of coils. It can be seen from theoretical formula (1) and simulation that when d p is much smaller than the R, the influence on the magnetic flux density and the range of the uniform filed region around the center point o is small. The multi-turn multi-layer coil winding method leads to the existence of inter-layer and inter-turn capacitance in the coil, and the impact at high frequency should be considered. Parasitic capacitance can be modeled accurately for the first resonance by a lumped equivalent capacitance connected between the terminals of the windings, as shown in Fig. 1(b). There are two conventional layer configurations for multi-layer coils [17], as shown in Fig. 2. The C-type (which is also called the standard type) is simple, and the potential distribution between adjacent layers is different. The maximum voltage difference between adjacent turns is large. The Z-type(which is also referred to as flyback winding) is more complicated, but the voltage difference between adjacent turns on the upper and lower layers of the coil is uniform [6, 17].
Fig. 2. Two conventional winding profiles and potential distribution. (a) C type (b) Z type.
In Fig. 2, N k represents the number of turns in a single layer, and N 1 represents the number of layers. According to the electrostatic field energy method, in the Z-type winding mode, the equivalent capacitance C w of the winding port is significantly lower
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than that of the C-type [17]. It can be seen that the winding method of the coil has a great influence on lumped equivalent capacitance. To further reduce the lumped capacitance of the coil, the winding method of the Helmholtz coil needs to be optimized [6].
3 Parasitic Capacitance Between Windings 3.1 Litz Wire Model and Benchmark Example In order to reduce the copper loss caused by the skin effect, the coil is generally wound with multiple Litz wire. Figure 3 shows the cross-section of a 7-strand Litz wire and equivalent solid wire. In this paper, the author adopt the equivalent method provided in [10]. The diameter of the Litz wire is d wire , the thickness of the paint layer is t L , the relative permittivity of the paint layer material PTFE is εL , the diameter of the outer layer is d 0 , the outer layer is wrapped by polyester wire, the thickness is t w , the relative permittivity is εw , and the number of strands is N S . The thickness of the insulating layer of the final equivalent solid wire is t eq , and the equivalent permittivity is εeq .
Fig. 3. Cross-section of Litz wire and equivalent solid wire.
Table 1 shows the parameters of the Litz wire in use. Table 1. Litz wire parameters used in this work d 0 /mm
3
d i /mm
2.9
d wire /mm
0.125
t w /mm
0.05
t L /mm
0.0125
εw
3.2
εL
2
NS
450
The relationships between the parameters are shown in formulas (2) and (3) [10]. teq = tL + tw
(2)
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εeq =
εw εL (tw + tL ) εL tw + εw tL
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(3)
Hence, we can obtain the equivalent solid wire parameters, the outer diameter d 0 of the solid wire does not change to 3 mm, the inner diameter of the solid wire d e = 2.875 mm, and the equivalent insulating layer thickness t eq is 0.0625 mm at this time. The equivalent relative permittivity of the effective insulating layer εeq is 2.86. The difference in inner diameter is 0.86%, and the difference in relative permittivity is 10.63%. Using ANSYS Maxwell 2D simulation, select the solution type as Electrostatic, and calculate the capacitance of the two conductors placed tangentially before and after the equivalent. The original capacitance is 136.33 pF, and the capacitance after the equivalent is 122.56 pF, a difference of 10.10%. Therefore, it is necessary to correct the relative permittivity of the Litz wire insulation and its inner size, which can significantly improve the accuracy of the calculation process [8]. 3.2 Subdivision of Inter-turn and Inter-layer Capacitance When the windings are wound tightly, the influence of the non-adjacent inter-turn capacitance on the parasitic capacitance cannot be ignored [10], so this paper will subdivide the inter-turn capacitance and the inter-layer capacitance. Because the insulating skeleton in the Helmholtz coil makes the electric field environment around the coil more complex than we thought, and the theoretical calculation of capacitance is not easy to obtain, the FEM simulation is used to extract the capacitance matrix to obtain the parameters we need. Taking the four-turn two-layer winding arrangement as an example, the subdivision capacitance parameters are shown in Fig. 4.
Fig. 4. Coil arrangement and parasitic capacitance.
The inter-turn capacitance includes the adjacent inter-turn capacitance C t1 and the non-adjacent inter-turn capacitance C t2 ; the inter-layer capacitance includes the interturn inter-layer capacitance C p1 at both ends, the middle-to-turn inter-layer capacitance C p2 , and the inter-layer diagonal capacitance C p3 . It can be seen from the simulation that when the inter-turn distance d t is large, the difference between the interlayer capacitances C p1 and C p2 is small. With the decrease of d t , the values of C p1 and C p2 gradually widen
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the gap, so it needs to be considered separately. When the interlayer spacing d p is large, C p3 is small and can be ignored when the voltage drop between turns of the layer is low. Using the solid wire parameters obtained in Sect. 3.1, and build an eight-turn twolayer model in ANSYS Maxwell 2D, assuming that the turns are closely tangentially arranged, that is, d t = 3 mm, d p = 4.5 mm, and add voltages excitations to each conductor according to the winding method. We set 5 times computational domain which can simulate the far-field environment in practice, and the capacitance matrix is obtained by electrostatic field solver. The matrix obtained by the FEM simulation is the capacitance per unit length, which should be multiplied by the mean length of each turn of the coil in actual use. When the number of turns increases, the average value should be taken. Extract the required capacitance parameters C tt1 = 142.96 pF, C tt2 = 1.04 pF, C pp1 = 17.08 pF, C pp2 = 10.15 pF, C pp3 = 2.05 pF (parameters in average).
4 Theoretical Calculation for Stray Capacitance 4.1 Theoretical Calculation of Parasitic Capacitance Studies show that the winding method with small equivalent capacitance has the advantage of making the potential distribution between layers as uniform and small as possible. Optimizing the type of winding is to minimize the parasitic capacitor energy storage; while reducing the equivalent capacitance [6]. This section will analyze two conventional winding profiles, and provide two new methods suited for grouping. Taking an eight-turn and four-layer coil as an example, Fig. 5 (a) is the square-wave-shaped combined Z-type, and Fig. 5(b) is the zigzag-shaped combined Z-type. The layer of these two winding arrangements must be an even number, and the two layers are regarded as a group. Assuming that the distances between layers are equal, the parameters C tt1 , C tt2 , C pp1 , C pp2 , and C pp3 are the average parameters corresponding to the capacitance matrix after simulation.
Fig. 5. Two newly proposed winding methods. (a) Square-wave-shaped combined with Z-type, (b) Zigzag-shaped combined with Z-type.
All the parasitic capacitance models of windings are based on the static turn-toturn capacitance, which could be measured at dc conditions between different turns, the voltage across the cross-section of a multi-layer multi-turn coil can be regarded as
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uniformly distributed [17]. Thus, the number in Fig. 5 indicates the winding sequence, and also the number difference indicates the potential difference between the windings. According to the principle of electrostatic energy storage, the relationship between lumped capacitance and stray capacitance of each winding is as follows [8]: Wtotall =
1 Cw,c Uw2 = 2
i=1,j=1(i=j)
1 Cij Uij2 2
(4)
where W totall represents the total energy stored by lumped capacitance C w,c , C ij represents the mutual capacitance of the ith and jth turns, C ij = C ji , which is only considered once in the calculation and does not consider the influence of self-capacitance(when i = j). U ij represents the potential difference coefficient between the ith coil and the jth coil. It is related to the winding method of the coil, the number of turns, and the number of layers. N toall represents the number of independent mutual capacitance, that is, the number of sums on the right side of the formula (4), and can be calculated as follow: Ntotall =
Nk N1 (Nk N1 − 1) 2
(5)
Based on formula (4), we consider the inter-layer and inter-turn capacitances subdivided in Sect. 3.2; and obtained the improved formulas of the two conventional methods and the two newly proposed methods. The calculation formula for the C-type can be improved as: (Nk −1) k −2) C + 4(N Ctt2 Nk2 N1 tt1 Nk2 N1 2 2(N −1)(2N −2N +1) + 1 N 2 Nk 2 k Cpp1 k 1 k −1)(2Nk −3)−3] + (N1 −1)[(Nk −1)(2N Cpp2 3Nk2 N12 4Nk (N1 −1)(Nk −1)(2Nk −1) + Cpp3 3Nk2 N12
Cw,c =
(6)
It can be seen that compared with the formulas that only consider the interlayer capacitance, after the subdivision process in this paper, the number of additional terms in the calculation formula increases, and the calculation result is larger than that of the existing research [8, 17]. As for other rest winding methods in this section, the formulas are too long. In particular, method (a) needs to be discussed according to the odd and even distribution of the number of turns of a single layer. Due to the limitation of the paper, it will not be shown here. If necessary, readers can contact the author by email. When the number of turns and layers are determined, the final parasitic capacitance has a linear relationship with each capacitance, so the lumped parasitic capacitance is calculated by: Cw = lw Cw,c
(7)
lw is the equivalent mean length of the coil, and C w,c is the theoretical results calculated by the formula (4).
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4.2 Effect of Turns and Layers on Equivalent Parasitic Capacitance Under Different Types of Winding Using the winding capacitance parameters of eight-turns and two-layers obtained in Sect. 3.2, change N k or N 1 , but keep the total number of turns N k × N 1 and d p , d t unchanged. Establish the model of four-turn and four-layer in ANSYS Maxwell 2D, and the parameters are obtained: C tt1 = 141.75 pF, C tt2 = 0.73 pF, C pp1 = 15.70 pF, C pp2 = 10.11 pF, C pp3 = 1.98 pF. Assuming the mean length of wire is 1m, calculate the theoretical equivalent capacitance according to Sect. 4.1, and explore the influence of the number of turns and layers on the equivalent capacitance. In Table 2, (a) represents C-type, (b) represents Z-type, (c) represents square-wave-shaped combined Z-type, and (d) represents zigzag-shaped combined Z-type. Table 2. Comparison results of lumped parasitic capacitance Nk
N1
Winding method
Equivalent stray capacitance
4
4
(a)
41.33 pF
(b)
25.35 pF
(c)
68.86 pF
(d)
54.20 pF
(a)
116.18 pF
(b)
52.74 pF
(c)
54.63 pF
(d)
44.53 pF
8
2
It can be seen from the comparison of the results that although the C-type winding is simple, it is not dominant when the number of turns is large. In methods (c) and (d), the potential difference between the even-numbered layer and the next layer is close to twice the potential difference between the Z-type layers, so if the two new methods proposed in Sect. 4.1 are to be used, the two layers can be regarded as a group, and the distance between the groups d p should be set reasonably. With the diversification of winding methods, such as unequally layer-spaced or when segmented windings are used, the difference between the turn-to-turn capacitances of windings of the inter layers obtained by the simulation is large, and the average value cannot be taken directly. The theoretical calculation should be discussed on a case-bycase based on formula (4).
5 Experimental Verification and Result Analysis 5.1 Coil Design and Winding Optimization Considering the manufacturing process of the Helmholtz coil, we design a coil with an operating frequency of 1 Hz−100 kHz, which adopts the square-wave-shaped combined
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C-type. It is noted that to the symmetry of the Helmholtz coil, only half of the crosssection of the structure is shown in Fig. 6(a), and the supporting skeleton is epoxy resin material with a relative permittivity of 3.5. The two layers of windings are arranged closely along with the skeleton as a group, and the distance d p between the two groups is 13 mm. Figure 6(b) is the coil prototype. The skeleton will lead to the complex distribution of the electric field environment around the coil, resulting in a large difference in capacitance between any two turns, so the mean value of turn-to-turn capacitance cannot be used. Thus, in this section, all the capacitors storage between any two turns of the coil are considered.
Fig. 6. Helmholtz coil winding method and physical structure (a) Cross-section of Helmholtz coil, (b) Helmholtz coil system prototype.
The equivalent circuit of any coil can be described in Fig. 1(b). Considering the coupling between two pairs of coils in Fig. 6(b), the equivalent circuit can be simplified into the following circuit:
Fig. 7. Equivalent circuit of the Helmholtz coil in Fig. 6(b)
In Fig. 7, L 1 and L 2 represent the self-inductance of the coil, where L 1 = L 2 , M is the mutual inductance between two pairs of the coil; and can be calculated by PEEC [9]. R1 = R2 , C 1 = C 2 , and C p is the opposite capacitance of the two coils, which can be calculated by FEM. The stray capacitance to ground C g is not marked in the figure, but the ground that exists everywhere in the building makes this part of capacitance unable to be ignored. In paper [18], self-resonance frequency can be estimated as: fr =
1 2π L(C + Cg )
(8)
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The global parasitic capacitance should be the sum of the coil lumped parasitic capacitance C and the ground capacitance C g . We built the model of the coil in ANSYS Maxwell 2D according to Fig. 6(a), then obtain the inter-turn and inter-layer capacitance matrix, then we can get C 1 , C p , and C g . Using the impedance measurement in Simulink and get the final C in formula (8). The average radius of the Helmholtz coil is 0.3 m, so the mean length of a single turn is 1.89 m. L 1 = L 2 = 1.43 mH, M = 0.063 mH calculated by PEEC. According to the theoretical calculation process mentioned in Chapter 4, C 1 = 106.85 pF, C p = 17 pF, C g = 18.2 pF. The final equivalent capacitance C w is 88.75 pF calculated by the proposed method. The Rloss of the coil is 0.6 , and the L in low frequency is 2.97 mH, obtained by LCR equipment. Figure 8 presents the experimental self-resonant frequency corresponding to the coil is around 321 kHz, the lumped parasitic capacitance is about 82.77 pF, and the error with the theoretical calculation is –7.2%.
Fig. 8. Experimental coil impedance and Rac varying with frequency
The error of the system comes from many aspects, such as the asymmetry of the skeleton, the influence of the connecting line between the two pairs of coils, and the setting of balloon boundary when solving the C g , but these errors are acceptable within the engineering scope. The designed 1-D Helmholtz coil meets the current working needs of HF magnetic fields. To further optimize the design of the Helmholtz coil and increase the self-resonant frequency, the equivalent capacitance values of the eight-turn four-layer winding with different winding methods under the same coil structure parameters are calculated and deduced. For the same system, C g remains the same, so only the C 1 is considered under the following winding methods. Table 3 shows that in the skeleton structure of Fig. 6(a), the C 1 of the square-waveshaped combined C-type is the largest, and the zigzag-shaped combined Z-type is the smallest. Under the four winding methods, the difference between the two methods (1) and (4) is 21.6%. Compare the electric field distribution under methods (1) and (4) in ANSYS Maxwell 2D, and the electric field range is set to 0–4000 V/m, as shown in Fig. 9.
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Table 3. Stray capacitance results from different types of winding with the same coil structure. No
Wingding method
C 1 calculated by
(1)
Square-wave-shaped + C type
106.85 pF
(2)
Square-wave-shaped + Z type
94.21 pF
(3)
Zigzag-shaped + C type
96.25 pF
(4)
Zigzag-shaped + Z type
83.82 pF
Fig. 9. Electric field distribution of coil (a) Method (1), (b) Method (4).
It can be seen from Fig. 9 that when method (4) is adopted, the global parasitic capacitance is not only the smallest, but the electric field distribution is also more uniform, and the insulation level of the coil can be improved. 5.2 Driving Experiment In order to compensate for the inductance of the coil at a high frequency, we use an RLC series compensation circuit. Figure 10 is the diagram of the coil drive system. The value of the variable capacitance part is determined by the state of the relay whether the capacitance can be connected to the main circuit. This part can be adjusted between 50 pF to 20 uF, which can be well compensated in the experiment. Table 4 shows the amplitude parameters of each group of current and voltage at the given frequencies. Figure 11 shows the I s and U s waveform under four different frequencies. The values in Table 4 are calculated by the FFT method. Therefore, voltage and current are the amplitude of the fundamental wave. The amplitude will be affected when there are spikes and oscillations in the voltage and current waveform. ϕUm −Im of four compensation situation are all smaller than 10°, it suggested that the compensated capacitance meet the working situation well. In Fig. 11 (d), we can see current spikes and oscillations due to the distribution parameters of the circuit at high frequency, so the operating range of the coil is limited to less than 100 kHz, or even lower. The self-resonant frequency of the coil should be more than 2 times or more than the highest operating frequency. If the self-resonant frequency needs to be further improved,
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Fig. 10. Diagram of Helmholtz coil drive system
Table 4. Experimental results in different frequencies fs
Im
Um
ϕUm −Im
800 Hz
4.48 A
3.61 V
2.78°
10 kHz
4.48 A
3.70 V
4.63°
80 kHz
0.44 A
17.21 V
2.28°
160 kHz
0.162 A
80.15 V
2.91°
Fig. 11. Voltage and current waveform under full bridge driving (a) f s = 800 Hz, (b) f s = 10 kHz, (c) f s = 80 kHz, (d) f s = 160 kHz.
it is necessary to increase the distance between each turn or select the insulating skeleton with smaller relative permittivity when the insulation ability meets the requirements of the conditions. At the same time, the skeleton of the Helmholtz coil should also be enlarged accordingly.
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6 Conclusion This paper summarizes the general steps for calculating the lumped parasitic capacitance of the Helmholtz coil, which combines FEM simulation and theoretical derivation. We designed a 1-D Helmholtz circular coil with a self-resonance frequency of 321 kHz. It can be seen from the experimental results that when the windings are closely arranged, the non-adjacent inter-turn capacitance and the inter-layer diagonal capacitance will have a great impact on the overall equivalent parameters. In addition, the skeleton of the coil should be modeled in the FEM situation because it influences turn-to-turn capacitance. The proposed method is in good agreement with the experimental results in this paper. The driving experiment shows that the parasitic parameters will bring current spikes and oscillations at high frequencies, and the stray capacitance needs to be further reduced. The two winding methods newly proposed in this paper can be extended to the optimization design of the equivalent parasitic capacitance of 2-D and 3-D Helmholtz coils, transmitter coils, or receiver coils in the WPT field, and other linearly wound inductors.
References 1. Shao, G., Guo, Y.X.: Hybrid wireless positioning and charging with switched field Helmholtz coils for wireless capsule endoscopy. IEEE Trans. Microwave Theory Tech. 68(3), 904–913 (2020) 2. Doan, V.D., et al.: Development of a broad bandwidth helmholtz coil for biomagnetic application. IEEE Trans. Magn. 57(2), 1–5 (2020) 3. Fontanet, A., Marcos, J., Ribó, L., Massana, V., Campmany, J.: Design and construction of 3D Helmholtz coil system to calibrate 3D Hall probes. J. Phys. Confer. Ser. 1350(1), 012167 (2019) 4. Chen, X., Luo, J., Lin, D.: Analysis and visualization of magnetic field for multi-dimensional helmholtz coils based on PEEC. In: 2021 IEEE 1st International Power Electronics and Application Symposium (PEAS), pp. 1–7. IEEE (2021) 5. Crotti, G., Chiampi, M., Giordano, D.: Estimation of stray parameters of coils for reference magnetic field generation. IEEE Trans. Magnet. 42(4), 1439–1442 (2006) 6. Zhiying, Z., Chunying, G., Haihong, Q.: Effect factors on stray capacitances in high frequency transformers. Proc. CSEE 28(9), 55–60 (2008). (in Chinese) 7. Yu, Q., Holmes, T.W.: Stray capacitance modeling of inductors by using the finite element method. In: 1999 IEEE International Symposium on Electromagnetic Compatability. Symposium Record (Cat. No. 99CH36261), vol. 1, pp. 305–310. IEEE (1999) 8. Wei, X., Zhengming, Z., Qirong, J.: Calculation method for parasitic capacitance of highfrequency transformers. J. Tsinghua Univ. (Sci. Technol.) 61(10), 1088–1096 (2021).(in Chinese) 9. Das, A.K., Fernandes, B.G.: Accurate capacitance calculation of multi-layer foil windings in a medium/high-frequency high-power transformer. In: 2020 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 5834–5841. IEEE (2020) 10. Dalessandro, L., Cavalcante, F., Kolar, J.W.: Self-capacitance of high-voltage transformers. IEEE Trans. Power Electron. 22(5), 2081–2092 (2007) 11. Zheng, C., Wang, Q., Wang, H., Bak, C.L., Shen, Z.: Uneven Inter-turn voltage distribution among windings of medium-voltage medium/high-frequency transformers. In: 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1–4. IEEE (2020)
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12. Nakahara, K., Kuroki, F.: Equivalent circuit model of multi-layered coils for integrated sensor applications in medium-wave frequencies. In: 2016 IEEE International Symposium on RadioFrequency Integration Technology (RFIT), pp. 1–3. IEEE (2016) 13. Grimaldi, D. : RLC parameter measurement of N-winding transformer. In: Proceedings of the 20th IEEE Instrumentation Technology Conference (Cat. No. 03CH37412), vol. 2, pp. 1571– 1576. IEEE (2003) 14. Mai, J., Zeng, X., Yao, Y., Wang, Y., Xu, D.: Improved winding and compensation methods for the multi-layer coil in IPT system. IEEE Trans. Ind. Electron 69(5), 5375–5380 (2021) 15. Bin, D., Ning, Y., Zhiping, W.: Simulation and measurement of inductor stray capacitance and resonance frequency. Transformer 47(9), 41–43 (2010). (in Chinese) 16. Lu, H., Zhu, J., Ramsden, V., Hui, S.: Measurement and modeling of stray capacitances in high frequency transformers. In: 30th Annual IEEE Power Electronics Specialists Conference, vol. 2, pp. 763–768 (1999) 17. Biela, J., Kolar, J.W.: Using transformer parasitics for resonant converters-a review of the calculation of the stray capacitance of transformers. In: Fourtieth IAS Annual Meeting. Conference Record of the 2005 Industry Applications Conference, 2005. vol. 3, pp. 1868–1875. IEEE (2005) 18. Ciurlo, S., Mariscotti, A., Viacava, A.: A Helmholtz coil for high frequency high field intensity applications. Metrol. Meas. Syst. 16(1), 117–127 (2009)
Applicability Analysis of Coupled-Mode Theory Model in Capacitive Power Transfer System Yang Zhou, Jingjing Yang, Yiming Zhang, Qingbin Chen, and Yanwei Jiang(B) College of Electric Engineering and Automation, Fuzhou University, 350108 Fuzhou, China {210127185,yangjingjing06046,zym,cqb,jiang_yanwei}@fzu.edu.cn
Abstract. Capacitive power transfer (CPT) technique has the advantages of negligible eddy-current loss, low cost and low weight, and so on. The circuit theory is currently used to model the CPT system to analyze its transfer characteristics, but the order of the circuit model is high and the analytical solution is complex. Coupled-mode theory model is a universal model that can be used to model coupled systems with low order and simple calculation. However, the coupled-mode theory has not been used to model the CPT system, and its applicability in the CPT system has not been analyzed. Therefore, this paper analyzes the coupledmode theory model of the CPT system. Firstly, the general coupled-mode model of the CPT system is derived from the circuit theory, and the relationship between coupled-mode parameters and circuit parameters are analyzed. Theoretical analysis shows that the coupled-mode theory model is equivalent to the circuit model when the coupling capacitance is far less than the compensation capacitance and the natural resonance frequencies of the transmitter and receiver are close. Then, the transfer efficiency and power of CPT are also deduced based on the coupledmode theory model. Finally, the simulated and experimental results verify the correctness of the theoretical analysis and the effectiveness of the coupled-mode theory model of the CPT system. Keywords: Capacitive power transfer · Coupled-mode theory · Mathematical model
1 Introduction Capacitive power transfer (CPT) system is generally composed of transmitter and receiver coupled by multiple metal plates. By high frequency electric-field, CPT can realize wireless power transfer with the negligible eddy current loss, the ability of transferring energy through metal barriers and the low cost and low weight of the metal coupling structure [1–4]. Therefore, CPT technology has been extensively studied in recent years [5, 6]. To analyze and acquire the transfer characteristics of the CPT system, its mathematical model is generally required. At present, the common modelling method is to use circuit theory to model [7–10]. The circuit theory is based on the equivalent lumped circuit. By using the voltage-current relationship between components, Kirchhoff’s law © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 71–80, 2023. https://doi.org/10.1007/978-981-99-0631-4_8
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and mutual inductance coupling model, the dynamic equation or impedance equation of the system can be obtained directly. Moreover, the transmission efficiency and power of the system can be analyzed accordingly. The model based on circuit theory can clearly describe the relationship between the various physical quantities of the CPT system. However, the order of the system equation is high and the corresponding calculation is complex. Coupled-mode theory is a perturbation analysis theory in mathematics, and its formula system is universal, which can be used to model and analyze two or more coupled systems. In the modeling process of coupled mode theory, firstly, a coupled resonant system is divided into two or more independent resonant units, and the energy modes and dynamic equations of each independent resonant unit are solved. Then, it is assumed that the perturbation in each element is generated by the energy coupling between the resonant elements; Finally, the energy dynamic equation of the whole system is obtained by superposition of the dynamic equation and perturbation of each resonant unit. Therefore, the coupled-mode theory modeling method is simple to calculate, and it models and analyzes the system from the perspective of energy, which can clearly describe the flow and dissipation of energy between each resonant unit. Coupled-mode theory modeling method has been proved to be able to correctly describe the magnetic-coupling wireless power transfer system, but its applicability has not been proved in the CPT system. Thus, this paper aims to analyze the applicability of the coupled-mode theory model in CPT system. The rest of the paper is organized as follows. The modeling process using coupled-mode theory for CPT system is described in Sect. 2. The transfer efficiency and output power of the CPT systems based on coupledmode theory is derived in Sect. 3. The simulated and the experimental results of the CPT system are provided to prove the effectiveness of the theoretical prediction in Sect. 4. Final conclusions are offered in Sect. 5.
2 System Overview and Modeling 2.1 Circuit Structure of CPT System Figure 1 shows an equivalent circuit of a double-sided LC-compensated CPT system, which consists of a transmitter and receiver [11]. The transmitter and receiver are coupled by a capacitor C M . In a practical CPT system, the capacitor C M is generally realized by multiple metal plates, such as copper or aluminum plates. The capacitor C T and C R are externally added to connected in parallel with the metal plates to reduce the required inductance of L T and L R . To indicate the coupling strength of the CPT system, the capacitive coupling coefficient k is often used, which is defined that k = C M /(C T C R )0.5 [12]. In addition, RST and RSR mean the internal resistances of the transmitter and receiver, respectively. 2.2 Modeling Based on Coupled-Mode Theory In this section, the coupled-mode theory model of CPT system is derived by starting from the circuit theory mode. Using the circuit theory, the dynamics of the CPT system
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Fig. 1. Equivalent circuit of a double-sided LC-compensated CPT system
in Fig. 1 can be described as ⎧ ⎪ diT vS vCT iT RST ⎪ ⎪ dt = LT − LT − LT ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ diR = − iR (RSR + RLoad ) − dt LR ⎪ dvCT ⎪ ⎪ ⎪ dt = ⎪ ⎪ ⎪ ⎪ ⎩ dvCR dt =
CR +CM iT CM iT
+
+
vCR LR
(1)
CM iR
CT +CM iR
where = C R C T + C M C T + C R C M . Equation (1) chooses the current and voltage of inductors and capacitors as the state variables, so it is a fourth-order equation. By using coupled-mode theory, the order of the model can be reduced. Assume that the energy mode in coupled-mode theory model is an , where subscript n can be T or R, referring to the transmitter or receiver. The relationship between energy modes and the circuit state variables can be expressed as [12] Ln Cn in + j vCn = An ej(ωt+θn ) = An cos(ωt + θn ) + jAn sin(ωt + θn ) (2) an = 2 2 where An and θ n are the amplitudes and phases of the energy modes. Therefore, the energy stored in the transmitter and receiver are |aT |2 and |aR |2 respectively. According to (2), the following equation can be acquired. ⎧ √ ⎪ ⎨ in = √ 2 An cos(ωt + θn ) Ln (3) √ ⎪ ⎩ v = √ 2 A sin(ωt + θ ) Cn n C n n
Then, the derivation of (2) is carried out by the follows.
d an d θn dAn = + jAn ω + ej(ωt+θn ) dt dt dt
(4)
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Therefore, to get the coupled-mode theory model, the unknows dAn /dt and dθ n /dt should be obtained. Substituting (3) into (1), we have ⎧ ⎪ dA vS ⎪ − √L1 C AT XST − RLST AT XCT ⎪ dtT XCT − YT XST = √2L ⎪ T T T T ⎪ ⎪ ⎪ ⎪ ⎨ dAR XCR − YR XSR = − 1 (RSR + RLoad )AR XCR − √ 1 AR XSR dt LR L C R R
√ √ ⎪ CM √CT dAT ⎪ M √CT ⎪ XST + YT XCT = CR +C A X + A X T CT ⎪ dt LT LR R CR ⎪ ⎪ ⎪ √ √ ⎪ ⎩ dAR CM √CR M √CR AT XCT + CT +C AR XCR dt XSR + YR XCR = L L T
(5)
R
where X CR , CT = cos(ωt + θ R,T ), X SR , ST = sin(ωt + θ R,T ), and Y R,T = AR,T (ω + dθ R,T /dt). From (5), assuming that vs = 20.5 V S cos(ωt) and using trigonometric function formula (double angle and product transforming sum and difference formula), the following equation can be derived. ⎧ √ ⎪ dAT CM √CT AR ⎪ ⎪ = [sin(2ωt + θT + θR ) + sin(θT − θR )] ⎪ dt LR 2 ⎪ ⎪ ⎪ √ ⎪ ⎪ M √CT ⎪ − √L1 C )AT sin 2(ωt + θT ) +( CR +C ⎪ ⎪ LT T T ⎪ ⎪ ⎪ ⎪ V RST S ⎨ + 2√L [cos(2ωt + θT ) + cos(θT )] − 2L AT [cos 2(ωt + θT ) + 1] T T (6) √ ⎪ dAR CM √CR AT ⎪ ⎪ [sin(2ωt + θT + θR ) + sin(θR − θT )] ⎪ dt = LT 2 ⎪ ⎪ ⎪ √ ⎪ ⎪ M √CR ⎪ − √L1 C ) A2R sin 2(ωt + θR ) +( CT +C ⎪ ⎪ LR R R ⎪ ⎪ ⎪ ⎪ 1 ⎩ − (RSR + RLoad )AR cos2 (ωt + θR ) LR
Since AT and AR are constant in a high frequency period, the high frequency terms in (6) can be ignored. Therefore, Eq. (6) can be approximated as ⎧ √ ⎪ VS ⎨ dAT = CM √CT AR sin(θT − θR ) − RST AT + √ cos(θT ) dt 2LT LR 2 2 LT (7) √ ⎪ ⎩ dAR = CM √CR AT sin(θ − θ ) − (RSR +RLoad ) A R T R dt 2LR L 2 T
Similarly, from (5), we have ⎧ √ ⎪ ⎪ d θT CR +CM √CT AT ⎪ A ω + = + √L1 C A2T T ⎪ dt ⎪ LT 2 T T ⎪ ⎪ ⎪ ⎪ CM √ C A V T R S ⎨ + √L 2 cos(θT − θR ) − 2√L sin(θT ) R T √ ⎪ d θR CM √CR ⎪ ⎪ AR ω + dt = 2 L AT cos(θT − θR ) ⎪ ⎪ T ⎪ ⎪ √ ⎪ ⎪ C C +C T M ⎩ + √L R A2R + √L1 C A2R R
R R
(8)
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According to (7) and (8), the four variables dAT /dt, dAR /dt, dθ T /dt and dθ R /dt can be solved. Thus, substituting them into (4), the coupled-mode theory model can be deduced as ⎧ √ ⎪ 1+CM /CT ⎪ M /CR +CM /CT ⎪ ddtaT = j 2+2C ωT aT ⎪ 1+CM /CR +CM /CT 2 ⎪ ⎪ ⎪ √ ⎪ ⎪ VS jωt 1 M /CR ⎨ √ −τST aT + j CMk/CR1+C +CM /CT +1 2 ωR aR + 2 LT e (9) √ ⎪ 1+CM /CR ⎪ M /CT +CM /CR ⎪ ddtaR = j 2+2C ω a R R ⎪ 1+CM /CR +CM /CT 2 ⎪ ⎪ ⎪ √ ⎪ ⎪ k /C (1+C ) 1 M T ⎩ −τR aR + j 1+CM /CT +C ωT aT M /CR 2 where ⎧ ⎪ ⎨ τST =
RST 2LT
⎪ ⎩ τ = RSR +RLoad R 2LR ⎧ ⎪ ⎨ ωT = √ 1 L (C +C ⎪ ⎩ω = R
T
√
T
M)
(10)
(11)
1 LR (CR +CM )
Fig. 2. Equivalent circuits of (a) the transmitter when C R = ∞, and (b) the receiver when C T = ∞
In coupled-mode theory, the variable τ ST and τ R mean the loss rates of the transmitter and receiver, respectively. Moreover, ωT and ωR are the resonant frequencies of the transmitter and receiver when the system is uncoupled that is the coupling strength k = 0. It’s worth to note that the expressions of ωT and ωR in the coupled-mode theory model of the CPT system are different with that of magnetic-coupled wireless power transfer system. The calculation of the frequencies ωT and ωR in the CPT system should consider the coupling capacitor C M . Since k = C M /(C T C R )0.5 , there are two cases to make k = 0 for the transmitter or receiver. In the first case when C M = 0, k = 0. In the
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second case, when C R = ∞ or C T = ∞, k = 0. Thus, for the transmitter, when C R = ∞, its equivalent circuit is shown in Fig. 2(a), and for the receiver, when C T = ∞, it’s the equivalent circuit is shown in Fig. 2(b). Therefore, from Fig. 2, the resonant frequencies of the transmitter and receiver in the coupled-mode theory should be expressed as (11). In a general CPT system, the coupled capacitor and coupling strength can satisfy that C M < < C T , C M n. Applying the Fourier transform to (4), a linear time-invariant (LTI) model is wirtten as: P x = Ax + Bu (3) y = Cx where A ∈ R17×17 , B ∈ R17×3 and C ∈ R1×17 are the GSSA model coefficient matrixes, u3×1 is input vector which includes three independent DC voltage sources, y is vdc , and x is below: x = [Rei1 1 Rei 3 1 Re up1 1 Re up3 1 vo 0 ]T
Imi1 1 Imi 3 1 Im up1 1 Im up3 1
Rei2 1 Rei s 1 Re up2 1 Reus 1
Imi2 1 Imi s 1 Im up2 1 Imus 1
(4)
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3 Controller Design of the MEU-WPT System According to (3), the transfer function matrix is obtained as: GMEU (s) =
Y (s) = C(sI − A)−1 B=[g11 (s) g12 (s) g13 (s)] U (s)
(5)
where U(s) = [u1 (s) u2 (s) u3 (s)]T , Y (s) = y1 (s). In this paper, u1 (s)-u3 (s) denote different excitation units E 1 -E 3 and y1 (s) denotes the output voltage vo . In ideal control of square systems, the controller matrix Gc (s) and the controlled object G(s) meets the relationship: G(s)GC (s) = I
(6)
For non-square system, use G+ (s) which is the Moore-Penrose pseudo inverse matrix of G(s) to replace G(s)−1 . G+ (s) can be calculated as: G+ (s) = GT (−s)[G(s)GT (−s)]−1
(7)
ˆ MEU (s) = [ 1/gˆ 11 (s) 1/gˆ 12 (s) 1/gˆ 13 (s) ] = G T
+T T T GMEU (s) = GMEU (−s)[GMEU (s)GMEU (−s)]−1
(8)
Then we have
+ + + = [ g11 (s) g12 (s) g13 (s) ]
where gˆ 1j , j = 1, 2, 3 represents the equivalent transfer function (ETF), which includes the interactions from other input-output loops. The ideal control objective for multivariable system G(s) is equivalent to that for multiple single systems, that is, I 1 ˆ ⇔ gc,ij (s)gˆ ji (s) = G(s)G C (s) = s s where GC (s) is the multivariable controller for G(s). The multivariable control problem with the goal of ⎡k
⎤
α,1
⎢ ⎢ G(s)GC (s) = ⎢ ⎢ ⎣
s
kα,2 s
..
(9)
⎥ ⎥ ⎥ ⎥ ⎦
.
(10)
kα,q s
can be solved by restructing the single loop controller: gc,ij (s)gˆ ji (s) =
kα,j s
(11)
where k α,j are regulating factors. Equation (11) can be rewritten as: 1 gc,ij (s)= Fji (s) s
(12)
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where Fji (s)=
kα,j gˆ ji (s)
(13)
It can be seen from (12) that the system model derived from GSSA model and ETFM are embedded into the controller in the form of inverse. Considering the order of the proposed MEU-WPT system (17 orders), the controller from (12) is of much high order (33 orders). Hence model order-reduction of controllers is necessary for engineering. Applying the Maclaurin series expansion to the above equation, the controller can be described as: gc,ij =
1 [Fji (0) + sFji (0) + s2 Fji (0) + ...] s
(14)
A standard PI controller is: gc,ij (s) = kP,ij +
kI ,ij s
(15)
where k P,ij and k I,ij are controller parameters. Comparing (14) with (15), the controller parameters are derived as: kP,ij = Fji (0) (16) kI ,ij = Fji (0) Hence a model-inverse-based controller for the MEU-WPT system is obtained which is a matrix (vector) that consists of three independent PI controllers.
4 Experimental Results The entire experimental setup established according to the diagram given in Fig. 1 is shown in Fig. 2. The output voltage vo is sampled by a voltage divider consisting of two resistors. Then the output voltage information is transferred to the primary aspect by a RF link. Once the voltage output information reaches the PI controller, three control signals will be given to the three buck choppers to accomplish the output voltage regulation. In our experiment, the PI controller matrix is realized by MCU (STM32F103VE). The model of oscilloscope used to record waveforms is Tektronix TPS 2024B. The parameters of the experimental system obey Table 1.
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Table 1. The Main Parameter of System Parameters
Values
Parameters
Values
L p1
115.3 µH
r1
0.2
L p2
119.2 µH
r2
0. 2
L p3
116.6 µH
r3
0.2
Ls
297 µH
rs
0.3
Cp1 Cp2 Cp3 Cs M14 M24 M34
61.03 nF 59.03 nF 60.3 nF 23.69 nF 13.25 µH 11.05 µH 13.47 µH
Cf RL M 12 M13 M 23 f
690 µF 10 4.2 µH 4 µH 4.05 µH 60 kHz
Fig. 2. Photography of the entire experimental setup.
4.1 Reference Tracking Experiment The reference voltage is set to be changed from 10V to 20V. As seen in Fig. 3 the dynamic response takes 90ms to track the reference input with an overshoot of about 20%. Besides, the waveforms of resonant currents i1 and the waveforms of control actions E 1 -E 3 are also provided in Fig. 3. As a result, the output voltage shows a excellent tracking performance.
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Fig. 3. System response waveforms under the condition of reference change.
4.2 Load Switching Experiment The load is set to be changed suddenly from 10 to 36 at the steady-state output of 20V. The experimental results under the control of the PI controller matrix are shown in Fig. 4. The settling time is about 55ms with some voltage fluctuations and the closed-loop MEU-WPT system can successfully keep the reference voltage. Hence the proposed PI controller matrix has a robust performance against load variations.
Fig. 4. System response waveforms under the condition of load switching
5 Conclusion Due to the cross-coupling MEU-WPT system is a high-order nonlinear system, the GSSA method is adopted to build a linear model of the MEU-WPT system in this work. For exactly describing the dynamic behavior of the closed MEU-WPT system, the concept of ETF is introduced. Then based on the ETF matrix, a model-inverse-based centralized controller matrix is set up for the MEU-WPT system which is a non-square system. Considering the engineering realizability, we use Maclaurin series expansion to reduce the order of the PI controller matrix to make it have the form of the classical PI controller. Consequently, the characteristics of the closed-loop MEU-WPT with multiple crosscoupling effect meet our demands which ensures its availability in wireless charging systems.
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Acknowledgment. This work is supported by science and technology planning project of state market regulatory administration of China (No.2021MK091) and Chongqing bureau of market supervision (No.CQSJKY2021033 and CQSJKJ2021046).
References 1. McDonough, M.: Integration of inductively coupled power transfer and hybrid energy storage system: a multiport power electronics interface for battery-powered electric vehicles. IEEE Trans. Power Electron. 30(11), 6423–6433 (2015) 2. Sallan, J., Villa, J.L., Llombart, A., Sanz, J.F.: Optimal design of ICPT systems applied to electric vehicle battery charge. IEEE Trans. Industr. Electron. 56(6), 2140–2149 (2009) 3. Chen, L., Nagendra, G.R., Boys, J.T., Covic, G.A.: Double-coupled systems for IPT roadway applications. IEEE J. Emerg. Selected Topics in Power Electr. 3(1), 37–49 (2015) 4. Zhu, Q., Wang, L., Guo, Y., Liao, C., Li, F.: Applying LCC compensation network to dynamic wireless EV charging system. IEEE Trans. Industr. Electron. 63(10), 6557–6567 (2016) 5. Ruddell, S., Madawala, U.K., Thrimawithana, D.J.: A wireless EV charging topology with integrated energy storage. IEEE Trans. Power Electron. 35(9), 8965–8972 (2020) 6. Dai, X., Jiang, J., Wu, J.: Charging area determining and power enhancement method for multiexcitation unit configuration of wirelessly dynamic charging EV system. IEEE Trans. Industr. Electron. 66(5), 4086–4096 (2019) 7. Chen, J., He, Z., Qi, X.: A new control method for MIMO first order time delay non-square systems. J. Process Control 21(4), 538–546 (2011) 8. Treiber, S.: Multivariable control of non-square systems. Ind. Eng. Chem. Process. Des. Dev. 23(4), 854–857 (1984)
The Impact of Metal Hull of AUVs for Underwater Wireless Power Transfer System Lei Yang1 , Yuanqi Zhang1(B) , Xiaojie Li1 , Baoxiang Feng1 , Jingjing Huang2 , Darui Zhu1 , Aimin Zhang2 , and Xiangqian Tong1 1 School of Electrical and Engineering, Xi’an University of Technology, Xi’an 710048,
Shaanxi, China {yanglei0930,zhudarui,Xqtong}@xaut.edu.cn, [email protected] 2 School of Automation Science and Engineering, Xi’an Jiao Tong University, Xi’an 710049, China [email protected], [email protected]
Abstract. Underwater wireless power transfer (UWPT) system has been widely studied in recent years. However, the material of metal plates and the shape which will affect the electromagnetic fields for the inductive wireless power transfer (IPT) system. This paper presents the effects of hull of the autonomous underwater vehicle (AUV) on the inductive underwater wireless power transfer system. The features of underwater wireless power transfer system have been carefully studied with the simulation and experimental work. The experiment was conducted in a 35‰ salinity water environment. The hull of AUVs has been respectively simulated and built with the rectangle metal plates and the curved metal plates. The original experimental data and phenomenon have been presented in this paper. This paper can provide reference for the application of AUV underwater wireless power transfer system. Keywords: Wireless power transfer (WPT) · Material · Underwater · Autonomous underwater vehicle (AUV)
1 Introduction The autonomous underwater vehicles (AUVs) have been widely used for exploring marine resources and monitoring infrastructure facilities. Most of AUVs are powered by batteries such as the lithium battery and lead-acid cell. Generally, there are two recharging methods. One is that it needs to be lifted out of the water to change the battery or recharge. The other one is that it is recharged with the physical wire which is put deep down to the AUVs in the marine environment. Their autonomy and work efficiency are quietly limited by the umbilical cable. The mother ship platform should be cruising around to provide the main technical and energy support. The underwater wireless power transfer method could provide a convenient and safety energy supply for AUVs [1–3]. The power could be transferred from the wireless © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 218–228, 2023. https://doi.org/10.1007/978-981-99-0631-4_23
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charging station to the AUVs without the physical wire restriction. The degree of freedom is greatly increased. The work efficiency is highly improved with the WPT technology. As the most promising underwater power feeding technique, the underwater inductive wireless power transfer technology meets the intractable challenges such as the eddy current loss, frequency splitting, magnetic waveforms attenuation in seawater, and ocean current disturbance, etc. [3]. For inductive wireless power transfer method, there are different kinds of coil structures, energy and power loss models and control methods have been proposed for marine applications. Z. Yan, et.al, [4] proposes a rotation-free wireless power transfer system based on a new coil structure to achieve stable output power and efficiency against rotational misalignments for charging autonomous underwater vehicles. J. Kim, et.al, propose an efficient modeling for the UWPT system using Z-parameters. Utilizing the electromagnetic analysis and two port network analysis, it could build an impedance model of coils considering the frequency and the conductivity of seawater [5]. The eddy current loss is detailed analyzed in [6] and [7] to provide the design guidance for underwater inductive wireless power transfer system. L. Yang, et.al, describes a new design method to deal with the misalignment and the changeable distance between the transmitter side and receiver side of the UWPT system to get the stable load regulation with the one cycle control method [8]. However, the underwater wireless power transfer system rarely considers the impact of the compatibility of the coil structure and the hull of the AUV, which can highly affect the hydrodynamic performance of the AUVs. In the marine environment, the hull will have the more impact on the power transfer and the electromagnetic fields or the electric fields for the conductive feature of seawater which compared with the air medium [9–13]. The impact of wireless power transfer system by the metal plate is surveyed and discussed in this paper. The impact of the metal hull of AUVs is analyzed and tested in this paper. A rectangle and curved hull-compatible metal plate structure is also studied in this paper to provide the reference for underwater inductive wireless power transfer system. The rest of paper is organized as follows: Sect. 2 provides the coupled structure and the theoretical analysis. Section 3 presents the simulated and experimental verification. Section 4 gives the conclusions and discussions.
2 Coupling Structure and Theory Analysis In this paper, the underwater inductive wireless power transfer system based on the electromagnetic fields are analyzed under the marine environment. For the underwater inductive wireless power transfer system, the coupled structure could be designed with the inductive coil and the model is shown as Fig. 1.
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Fig. 1. Model of underwater inductive wireless power transfer transfer system.
In the marine environment, DC resistance, AC resistance and radiation resistance constitute the total impedance of the coil. The radiation resistance in seawater is expressed as: 4 π 2π 2 (βR)3 + (βR)5 − · · ·] (1) RM rad = ωμM R[ (βR) − 3 3 15 M where ω is the angular frequency, β = μM ωσ , R is the radius of the coil. 2 According to [14], The equivalent resistance at the primary side of the underwater inductive wireless power transfer system can be expressed as: M M RP = RM DC + RAC + Rrad +R1
(2)
The equivalent resistance of the secondary side of UIPT system could be expressed as: M M RS = RM DC + RAC + Rrad +R2
(3)
The AC resistance can be calculated as [12, 13]: RM AC =
l×ρ π ×ω×δ
(4)
2ρ where l is the wire length of coil, ρ is electric resistivity, and δ is skin depth, δ = ωμ . M Based on the aforementioned discussion, the mutual inductance between Tx and Rx could be written as: −γ |RS −RP | e μo σ NP NS LM = (5) dlP dlS |RS −RP | 4π √ where γ ≈ jωμ0 δ, NP and NS are respectively turns ratio of transmitter coil and turns ratio of receiver coil,RP and RS are respectively equivalent resistance of primary side and the secondary side. σ is the is the conductivity of the medium, lP and lS are respectively perimeters of the two coils. Considering (5), the coupling coefficient is derived as: kM
LM = = Lp Ls
μo σ 4π NP NS
e−γ |RS −RP | |RS −RP | dlP dlS
Lp Ls
(6)
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The high-frequency alternating currents in the coil could generate the eddy current loss in the seawater condition. Based on [6], the eddy current loss could be presented as: Peddy−M ≈
2ω2 |Ba |2 π DR4 σM 3
(7)
where Ba is average magnetic flux density. The load voltage, coupling coefficient and angular frequency of Tx or Rx have a relationship as: jωKt/r VL =
jωL + Ro + RL +
1 1 R+jωL+ jωC
1 jωC
VR RL
2 L2 + ω2 Kt/r
1 1 (Re +jωL+ jωC )
(8)
where VL is load voltage, Ro is the internal resistance of Tx or Rx, RL is load resistance, VR is voltage of Rx, Re is equivalent resistance of Tx or Rx. The relationship between voltage of receiver and the voltage of transmitter could be derived as: VR =
(ωLM )RL VT (RL + RR )[RT RR + (ωLM )]2
(9)
Considering (4), the quality factor of a coil could be derived as: Q=
π ω2 δL ωL = RAC lρ
(10)
The output power of the UIPT system could be expressed as: Po =
ωI12 LM Q2 RL
(11)
where I1 is the current of the transmitter coil,Q2 is the quality factor of the receiver coil and RL is the load resistance. Considering (4) and (9), (11) could be rewritten as: Po =
π δω3 I12 LS LM ρlS RL
(12)
3 Simulated and Experimental To survey the impact of the AUVs’ hull for underwater wireless power transfer system. The different models for underwater inductive wireless power transfer system are constructed. The hull placement models for underwater inductive wireless power transfer system are shown Fig. 2. For the deep understanding of the feature of the impact of the hull, the rectangle metal plates, and the curved metal plates are taken as examples.
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Fig. 2. Models of AUV hull placement models for underwater inductive wireless power transfer system.
3.1 Underwater Inductive Wireless Power Transfer System The different kinds of metal plates are adapted in the simulation and experimental for underwater inductive wireless power transfer system. The parameters for iron, copper and aluminum are shown as Table 1. The tested parameters of coils are shown as Table 2. Table 1. Parameters of different metal plates Metal Plates
Conductivity
Permeability
Relative dielectric constant
Iron
10300000
4000
1
Copper
38000000
1.000021
1
Aluminum
58000000
0.999991
1
Table 2. Parameters of coils Parameters of coils Parameters
Transmitter
Receiver
Number of turns
5
5
Diameter of wire
1.5 mm
1.5 mm
Wire pitch
2.05 mm
2.05 mm
Inductance
1.88 μH
1.00 μH
Inner diameter of coil
20mm
10 mm
External diameter of coil
60 mm
40 mm
The achieved data is shown as Table 3. The parameter of coupling structure for underwater inductive wireless power transfer system is shown as Table 4.
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Table 3. Parameters of coils Metal Plate
Placement model
Inductance of Transmitter
Inductance of Receiver
Mutual Inductance
1.88 μH
1.00 μH
119.74 μH
Model 1
2.54 μH
1.22 μH
9.10 μH
Model 2
2.63 μH
1.29 μH
261.14 μH
Model 3
2.42 μH
1.28 μH
6.85 μH
Without metal plates Iron
Copper
Aluminum
Model 4
2.47 μH
1.28 μH
241.42 μH
Model 1
1.007 μH
685.42 μH
24.25 μH
Model 2
1.08 μH
763.97 μH
323.192 μH
Model 3
1.23 μH
704.97 μH
36.03 μH
Model 4
1.13 μH
750.8μH
698.19 μH
Model 1
1.01 μH
683.24 μH
23.45 μH
Model 2
1.07 μH
761.45 μH
321.45 μH
Model 3
1.21 μH
699.14μH
36.10 μH
Model 4
1.098 μH
750.32 μH
697.9 μH
Table 4. Parameters of coils with variable distance 1 mm
3 mm
5 mm
7 mm
Inductance of Transmitter
3.02 μH
2.71 μH
2.54 μH
2.32 μH
Inductance of Receiver
1.57 μH
1.39 μH
1.22 μH
1.17 μH
Mutual Inductance
6.39 μH
7.63 μH
9.10 μH
11.38 μH
In the simulation work, the resonant frequency is set 200 kHz and The distance between coils is set 20 mm. The simulation results are shown as Figs. 3, 4, 5, 6 and 7.
Fig. 3. The impact of placement conditions of IPT system.
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When the metal plates placed inside the coupling structure, the simulated results are shown in Fig. 3. The simulated results show that the power transfer will be prevented with the meatal plates. The electromagnetic fields will be exhibited. As a result, the power could not be delivered from the transmitter side to the receiver side.
Fig. 4. The impact of meatal plates of model 1.
However, as shown in Fig. 4, when the metal plates are placed outside the coupled structure, compared with the copper metal plates and the aluminum metal plates, the electromagnetic fields will be strongly enhanced with the iron meatal rectangle plates. What’s more, the leakage magnetic fields could be reduced with the metal plates. As a result, the EMI noises will be decreased.
Fig. 5. The impact of curved meatal plates of IPT system.
The simulated results are shown in Fig. 5. When the curved metal plates are placed outside of the couped structure, the electromagnetic will be highly enhanced, and the EMI noise will be restricted in the coupled structure area. When the curved metal plates placed inside the coupled structure, the power transfer will be prevented directly. When the inductive wireless power transfer system works in the marine environment, the eddy current loss will be generated. The eddy current loss is surveyed with the simulation. With the same placement model, the copper metal plates will have the highest eddy current loss as shown in Fig. 6. It can be seen in Fig. 7. The eddy current loss of the inductive wireless power transfer system is tested with the four placement models When
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Fig. 6. The impact of meatal plates on eddy current loss of IPT system.
the metal plates are placed outside of the coupled structure, the highest eddy current loss is generated with the rectangle metal plates.
Fig. 7. The impact of meatal plates on eddy current loss of IPT system.
3.2 Experimental Verification The correctness of the theoretical analysis is verified by experiments. The experimental platform is shown in Fig. 8. For the underwater inductive wireless power transfer system, A water tank is used to conduct the experiments with the 35‰ salinity water to simulate seawater conditions. The experimental results are shown as Fig. 9, Fig. 10, Fig. 11. Figure 9 shows that when a metal plate is added to the outside of the coil, the output voltage and current of the system are significantly reduced. The effect of iron plate on the output voltage and current of the system is obviously greater than that of copper plate
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Fig. 8. Experimental setup and the couped structure.
Fig. 9. Experimental results for model 2
and aluminum plate, and the output voltage and current waveforms of copper plate and aluminum plate are similar. In Fig. 10, when the metal plate is placed inside the coupling mechanism, the power transmission will be blocked. Figure 11 and Fig. 12 shows the system waveforms with arc-shaped aluminum plates placed inside and outside the coil. When the metal plate changes from a flat plate to an arc plate, the receiver coil still has no effective power output when the metal plate is inside the coil. When the metal plate is on the outside of the coil, the magnetic field absorbed by the metal plate increases because the effective area of contact between the
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Fig. 10. Experimental results for model 1.
metal plate and the magnetic field increases, and the output voltage of the receiving end is significantly lower than the output voltage of the system in the presence of the plate metal plate.
Fig. 11. Experimental results for model 3.
Fig. 12. Experimental results for model 4.
When the metal plates are injected inside the coupled structure, the power transfer will be blocked. What’s more, when the metal plates are placed outside the coupled structure, The influence on the transmission characteristics of the system is related to the material and shape of the metal. The influence of the metal with high permeability on the transmission characteristics of the system is obviously stronger than that of the metal with low permeability. At the same time, the larger the effective area of the metal shell contacting the magnetic field, the stronger the influence of the metal shell on the transmission characteristics of the system. The experimental results agree well with the theoretical analysis and simulation results.
4 Conclusions and Discussions This paper presents a survey of the impact of AUVs’ hull for undersea wireless power transfer system on electromagnetic fields and the eddy current loss. The simulation and experiments are conducted to test the performance of coupled structure and the power transfer capacity. The simulated and experimental results show that the electromagnetic
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field will be reduced when the metal plates placed inside the coupled structure. When the metal plates placed outside the coupled structure, the power transfer capacity of underwater wireless power transfer system will be enhanced. The rectangle metal plate and the curved metal plate are all tested in this paper with the four placement models. The simulated data and the experimental data show that the shape of the meatal plate has little effect on the power transfer of underwater wireless power transfer system and the capacity of power level.
References 1. Zeng, Y., et al.: Misalignment insensitive wireless power transfer system using a hybrid transmitter for autonomous underwater vehicles. IEEE Trans. Ind. Appl. 58(1), 1298–1306 (2022) 2. Zhou, J., Yao, P., Chen, Y., Guo, K., Hu, S., Sun, H.: Design considerations for a self-latching coupling structure of inductive power transfer for autonomous underwater vehicle. IEEE Trans. Indus. Appl. 57(1), 580–587 (2021) 3. Me¸se, H., Anılcan Budak, M.: Efficiency investigation of a 400 W resonant inductive wireless power transfer system for underwater unmanned vehicles. In: 2020 IEEE Wireless Power Transfer Conference (WPTC), pp. 223–226 (2020) 4. Yan, Z., Song, B., Zhang, Y., Zhang, K., Mao, Z., Hu, Y.: A rotation-free wireless power transfer system with stable output power and efficiency for autonomous underwater vehicles. IEEE Trans. Power Electr. 34(5), 4005–4008 (2019) 5. Kim, J., Kim, K., Kim, H., Kim, D., Park, J., Ahn, S.: An efficient modeling for underwater wireless power transfer using Z-Parameters. IEEE Trans. Electromag. Compatib. 61(6), 2006– 2014 (2019) 6. Zhang, K., Ma, Y., Yan, Z., Di, Z., Song, B., Hu, A.P.: Eddy current loss and detuning effect of seawater on wireless power transfer. IEEE J. Emer. Selected Topics in Power Electro. 8(1), 909–917 (2020) 7. Yan, Z., et al.: Frequency optimization of a loosely coupled underwater wireless power transfer system considering eddy current loss. IEEE Trans. Industr. Electron. 66(5), 3468–3476 (2019) 8. Yang, L., Zhang, B., Ju, M.: A fast dynamic response regulation method for undersea wireless power transfer system. In: 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp. 1162–1166 (2019) 9. Teeneti, C.R., Truscott, T.T., Beal, D.N., Pantic, Z.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Oceanic Eng. 46(1), 68–87 (2021) 10. Anyapo, C., Intani, P.: Wireless power transfer for autonomous underwater vehicle. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 246– 249 (2020) 11. Duarte, C., Gonçalves, F., Silva, M., Correia, V., Pessoa, L.M.: Experimental evaluation of coupling coils for underwater wireless power transfer. In: 2019 IEEE Wireless Power Transfer Conference (WPTC), pp. 557–560 (2019). 12. Dou, Y., Zhao, D., Ouyang, Z., Andersen, M.A.E.: Investigation and design of wireless power transfer system for autonomous underwater vehicle. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3144–3150 (2019) 13. Bana, V., Anderson, G., Xu, L., Rodriguez, D., Phipps, A., Rockway, J.: Characterization of Coupled Coil in Seawater for Wireless Power Transfer. In: SSC Pacific Technical Report 2026 (2013) 14. Kraichman, M.B.: Impedance of a circular loop in an infinite conducting medium. J. Res. Nat. Bureau of Standards D. Radio propagation 64, 499–503 (1962)
Synchronous Identification of Loads and Mutual Inductances for Multi-frequencies Multi-loads WPT System Dongxiao Huang1(B)
, Qinwang Wei1,2 , Weidong Huang2 , Zequan Hong1,2 , and Fengxiang Wang1
1 National Local Joint Engineering Research Center for Electrical Drives and Power
Electronics, Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Quanzhou 362000, China {dongxiao.huang,fengxiang.wang}@fjirsm.ac.cn 2 Fujian Key Laboratory of Intelligent Machining Technology and Equipment, Fujian University of Technology, Fuzhou 350118, China [email protected]
Abstract. The alteration of load and mutual inductance is an inevitable factor that limits the performance of the Wireless Power Transfer(WPT) system with multipickup coils. In the proposed synchronous identification method, a steady-state circuit model of mDulti-frequencies multi-loads WPT system is established and the sliding-window Discrete Fourier Transform(DFT) method is applied to extract primary current signals at different frequencies. Meanwhile, the Particle Swarm Optimization(PSO) algorithm is adopted to achieve the identification of loads and mutual inductances, which uses the deviations between experimental values and theoretical values of the output voltage as the objective function to turn the identificating process into an optimization problem. The result of simulation shows that errors of identification are within 4% and 3% respectively, which verifies the feasibility of the proposed identification method. Keywords: WPT · Multi-pickup coils · PSO · Load identification · Mutual inductance identification
1 Introduction Wireless Power Transfer(WPT) is a novel charging technology with the advantages of safety and convenience [1, 2], which realizes the contactless power transmission between the transmitter and the receiver through electromagnetic coupling. These years, Magnetic Coupled Resonant Wireless Power Transfer (MCR-WPT) technology has been developing rapidly due to the prominent performances of higher transmitted power, higher efficiency and longer distance [3]. The research and application field of WPT has gradually expanded from the common single-load energy supply system to the multiloads synchronous energy supply system, such as the simultaneous charging of electric vehicles [4] and electronic products [5]. However, load mutation and cross-coupling are © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 229–238, 2023. https://doi.org/10.1007/978-981-99-0631-4_24
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two significant issues of multi-receiver system, which directly influence the resonance and degrade the power transfer capability. Xue et al. [6] proposed a method introducing the Particle Swarm Optimization(PSO) algorithm to identify the load and mutual inductance with the state space equation of the secondary current as an identification model. Dai et al. [7] proposed a method to predict the value of mutual inductance between the trasmitting coil and two receiving coils using the transmitting voltage and current. Jin et al. [8] proposed a coupling coefficient identification method adopting the sliding window Discrete Fourier Transform(DFT) algorithm to improve the accuracy. Su et al. [9] designed a method suitable for any compensation topology by detecting the voltage and current of the primary side. Zhou et al. [10] proposed a mutual inductance identification method of a MCR-WPT steady-state model with the particle swarm algorithm, which only requires the data of input voltage and output voltage. The researches above mainly focuses on the identification of single load or single pair of mutual inductance parameters, which means that the research on the identification of multi-load and multi-mutual inductance parameters is still lack. In this paper, a novel method for synchronous identification of load and mutual inductance based on the multi-frequency multi-load MCR-WPT system is proposed. Firstly, the circuit model of the steady-state system is established to obtain the mathematical relationship between the load and mutual inductance. Secondly, the sliding window DFT is used to extract the primary side current at the different frequencies. Finally, the deviations between the actual value and the theoretical value of the output voltage is used as the objective function of the PSO algorithm to turn the identificating process into an optimization problem. The error of solution is limited to a small vaule by searching for the optimal solution of identified parameters.
2 System Model and Identification Method 2.1 Analysis of Multi-loads Transmission In this article, the topology of a multi-pickup WPT system based on a multi-frequencies compensation network [11] is proposed. The equivalent circuit at any single angular frequency ω for a system with n receivers is shown in Fig. 1.
Fig. 1. Equivalent circuit of multi-frequency multi-pickup MCR-WPT system.
In Fig. 1, i (=1, 2, …, n) is used to represent the different working frequencies, loads, (i) (i) and receiving coils, U in and I p stand for the driving voltage phasors and current phasors,
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(i)
I sj (j = 1, 2, …, n) is the current phasor of the ith working frequency at the jth receiving coil. The selected multifrequency compensation network consists of a capacitor Cp1 and n − 1 parallel LC circuits, and L p1 is the self-inductance of the transmitting coil. The resonant circuits are composed of the receiving coils L s1 , L s2 and the compensation capacitors C s1 , C s2 . M psi is the mutual inductance between the transmitting coil and the ith receiving coil. Msisj as the mutual inductance between multipickup coils. Rp and Rsi are the equivalent series resistances of the transmitting coil and the ith receiving coils, respectively. Reqi = 8RLi /π 2 is the equivalent value of load resistance RLi form the full bridge rectifier. Analysis of a one-to-two MCR-WPT system without considering cross-coupling (i) effects. Zin is the input impedance of the system, which expressed as: (i)
Zin = Zp(i) + where
(i)
Zs1
⎧ ⎪ (i) ⎪ Z = R + j ωi Lp1 − ⎪ p ⎨ p ⎪ ⎪ ⎪ ⎩
(i)
2 ωi2 Mps1
(i)
+
2 ωi2 Mps2
(1)
(i)
Zs2
ωi Lp2 1−ωi2 Lp2 Cp2 (i) Zs1 =Rs1 + Req1 + j(ωi Ls1 − ωi 1Cs1 ) (i) Zs2 = Rs2 + Req2 + j(ωi Ls2 − ωi 1Cs2 ) 1 ωi Cp1
+
(i)
ωi , Zp , Zs1 and Zs2 is corresponded to the angular frequency, the equivalent impedance of the transmitter and receiver at the ith working frequency respectively. the input impedance angle is 0°, which indicates that both In the resonant state, (1) (2) Im Zin and Im Zin are 0. The parameters of 2-order Forster network can be foundin the following equations [11]: ⎤ ⎤−1 ⎡ ⎡ ⎤ ⎡ 2 γ 2 μ ω12 Mps1 ω12 Mps2 2 2 ω1 Lp1 − R2 +γ 2 − R2 +μ2 ⎥ ⎢ 1/Cp1 ⎥ ⎢ 1/ω1 ω1 / pω1 /ω2 − 1 ⎥ ⎢ 1 1 ⎥ (2) ⎦ ⎢ ⎣ ⎦=⎣ 2 υ 2 β ⎦ ⎣ ω22 Mps2 ω22 Mps1 Lp2 ω2 /(p − 1) ω2 Lp1 − R2 +υ 2 − R2 +β 2 1/ω2 1
1
where R1 = Req1 + Rs1 , R2 = Req2 + Rs2 , γ = ω1 Ls1 − 1/(ω1 Cs1 ) υ = ω2 Ls2 − 1/(ω2 Cs2 ), μ = ω1 Ls2 − 1/(ω1 Cs2 ), β = ω2 Ls1 − 1/(ω2 Cs1 ) p = ω22 Lp2 Cp2 is a constant that can be used to guarantee the algorithm can find the positive value of the Foster network parameter, which can be chosen as 0.95 or 1.05. According to (1), there is: ⎧ ⎪ ω2 M 2 ω2 R M 2 (1) ⎪ ⎨ 1 ps1 + 1 2 2 ps2 − Rp = Re Z 2 in R1 R2 +μ (3) 2 2 2 2 ω2 Mps2 ω R M ⎪ (2) ⎪ ⎩ 2 2 1 ps1 − R + = Re Z p in R2 R +β 2 1
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(1) (1) (2) (2) (1) (2) where Re Zin = Uin /Ip , Re Zin = Uin /Ip . Deriving from (3), the mutual inductance can be calculated as: ⎧ (2) (2) (1) (1) ⎪ ⎪ aR1 ω22 b Uin /Ip −Rp −ω12 R22 Uin /Ip −Rp ⎪ 1 ⎪ ⎨ Mps1 = ω1 ω2 ab−R2 R2 1 2 (2) (2) (1) (1) ⎪ ⎪ bR2 ω12 a Uin /Ip −Rp −ω22 R21 Uin /Ip −Rp ⎪ ⎪ ⎩ Mps2 = ω11ω2 ab−R2 R2
(4)
1 2
where a = R21 + β 2 , b = R22 + μ2 . 2.2 Primary Side Current Detection (1)
(2)
In the previous section, the primary side circuit current is superimposed by ip and ip . (1) (2) Since ip and ip need to be detected respectively when identifying different mutual inductance parameters, the sliding window DFT is adopted in this paper [8] to detect two current signals, whose expression is 2nπ k 2nπ k + Bn sin (5) ip (kTs ) = An cos N N where k is the natural number, N is the number of sampling points in an operation period of the system, Ts is the sampling period, An and Bn are the real and imaginary coefficients of current respectively, as shown below: ⎧ N −1 ⎪ ⎪ A = 2 i (kT ) cos n 2π k ⎪ p s ⎨ n N N k=0 (6) N −1 ⎪ 2 2π k ⎪ ⎪ i = B sin n (kT ) p s ⎩ n N N k=0
The coefficient iterative expression of the sliding window DFT transform can be concluded as: ⎧ ⎪ ⎨ An (k) = An (k − 1) + 2 ip (kTs ) − ip [(k − N )Ts ] cos n 2π k N N (7) ⎪ ⎩ B (k) = B (k − 1) + 2 i (kT ) − i [(k − N )T ] sin n 2π k n n s p s N p N According to (7), the flowchart is shown in Fig. 2:
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Fig. 2. Control block diagram of sliding window DFT.
The sliding window DFT current detection method is based on iterative calculation. It only needs to calculate the current sampling point instead of the sampling point in the whole cycle, which reduces the calculation amount and calculation time of DFT and improves the real-time detection. 2.3 Analysis of PSO Algorithm PSO algorithm is an artificial intelligence algorithm. By simulating the group behavior of birds flying foraging, the group cooperation among birds is analyzed to make the group reach optimal. PSO algorithm is essentially an iterative optimization process, and the flowchart is shown in Fig. 3.
Global optimal value gbest
Yes
Select the next particle pxi + 1
No
Meet the iterative conditions ?
No Complete an iteration
Input system parameters SDFT
Update adaptive weight k(n), update particle velocity v(n), position x(n)
Sampling Edc Ip(i) Vi(k)
Yes
Whether to traverse all particles
Evaluation of particle fitness by objective function fitness
No Select the optimal output
Yes
Meet the error requirements ?
Individual optimal value pbest Global optimal value gbest
Fig. 3. Flow chart of load and mutual inductance identification.
Particle swarm iteration is easy to fall into global optimum, in order to improve local optimization ability, the weight formula is improved as follows: k(n) = kmax −
(n − 1)(kmax − kmin ) nmax − 1
(8)
where kmax and kmin denote the maximum and minimum of inertia weight and nmax denote the maximum number of iterations. In order to reduce the ripple of DC signal output by the rectifier, the filter capacitor Cfi is used, as shown in Fig. 4.
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Fig. 4. Secondary side rectifier filter circuit diagram.
The relationship between the filter capacitor terminal voltage and the external input energy can be obtained according to the energy conservation law 2 − V2 Cfi Vi_fi i_in (9) Pi · T = 2 where Vi_in and Vi_fi are the initial and final voltage of RLi , respectively. T is the interval time, and Pi is the external input power. The relationship between the output voltage Vi (k − 1) and Vi∗ (k) at KT is obtained by discretization of (9) 2 2 V 1 (10) Pi (k − 1)T + Cfi Vi2 (k − 1) − i T Vi∗ (k) = Cfi 2 RLi where Vi (k − 1) is the sampling value of output voltage at (k-1) moment. In each update, all particles are calculated for fitness which is defined as fitness = Vi (k) − Vi∗ (k)
(11)
where Vi (k) are the sample value of the system at (k) T instant and the one with the least fitness is selected as the global optimal value.
3 Simulation Verification To verify the effectiveness of the identification method, the validating simulation model is built in MATLAB/Simulink, corresponding parameters are shown in Table 1. Table 1. The main parameters of the system model. Parameters
Value
DC supply
Edc
50 V
System operating frequency
f 1 /f 2
50 kHz/150 kHz
Inductance of transmitting coil
L p1
253.5 µH (continued)
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Table 1. (continued) Parameters
Value
Inductance of compensating coil
L p2
2 µH
Capacitance of primary side
C p1 /C p2
39.62 nF/567.6 nF
Resistance of primary side
Rp
0.7
Inductance of pickup coil
L s1 /L s2
186.29 µH/201.51 µH
Compensating capacitor
C s1 /C s2
54.39 nF/5.587 nF
Resistance of pickup coil
Rs1 /Rs2
0.49 /0.5
Mutual inductance
Mps1 /Mps2
15 µH/20 µH
Loads
RL1 /RL2
5 /10
3.1 Independent Control Verification of the MCR-WPT System Based on Table 1, if the amplitudes a1 and a2 of the two modulation waves are set to 0.55, the simulation waveforms of primary voltage, primary current, and secondary current are shown in Fig. 5 and Fig. 6.
Fig. 5. Simulation waveforms of the inverter output voltage and current.
Fig. 6. Simulation current waveforms of two receiving circuits when f 1 = 50 kHz and f 2 = 150 kHz based on the original circuit confifiguration.
As can be seen from Fig. 5, the primary voltage is a high-frequency mixed pulse voltage, the primary current is equivalent to the superposition of 50 kHz current and 150 kHz current components, and the primary voltage waveform is in the same phase as the primary current waveform. It can be seen from the secondary current waveform of Fig. 6 that the dual-load MCR-WPT system works in a resonant state, which verifies that the output power of the dual-frequency dual-load MCR-WPT system is independently controllable. 3.2 Parameter Identification Verification It can be seen from Fig. 7 that in the early stage of algorithm identification, a particle swarm is easy to fall into the global optimal state. Since the inertia weight changes with the number of iterations, the particle swarm is avoided to fall into the global optimum,
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and the load identification results tend to be stable at about 2 ms. The value of mutual inductance is calculated according to the value of the identified load, and the stability time of the identification results is relatively long. It can be seen from Fig. 7(a) that the identification errors of load RL1 and RL2 are 2.4% and 2.6%, respectively. From Fig. 7(b), the identification errors of mutual inductance Mps1 and Mps2 are 1.4% and 1.7%, respectively. The identification value is consistent with the actual value.
(a) Load identification result.
(b) Mutual inductance identification results.
Fig. 7. Load and Mutual inductance identification results.
To further verify the feasibility of the algorithm, other four group simulations of parameter identification are built. And the corresponding simulation results under load and mutual inductance are shown in Table 2 and Table 3, respectively. Table 2. Load identification results. Actual value RL1 /
Actual value RL2 /
Identification value RL1 /
Identificatin value RL2 /
Relative error RL1 /
Relative error RL2 /
10
15
10.24
14.82
2.4%
1.2%
10
15
10.11
15.37
1.1%
2.4%
15
20
15.38
20.20
2.5%
1.0%
15
20
15.32
19.36
2.1%
3.2%
It can be seen from Table 2 and Table 3 that the maximum relative errors of load and mutual inductance identification results are 3.2% and 2.7%. The identification results are very close to the simulation setting values.
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Table 3. Mutual inductance identification results. Actual value Mps1 /μH
Actual value Mps2 /μH
Identification value Mps1 /μH
Identification value Mps2 /μH
Relative error Mps1 /μH
Relative error Mps1 /μH
20
25
20.14
25.39
0.7%
1.5%
25
30
25.69
30.52
2.7%
1.7%
20
25
20.54
25.37
0.9%
1.4%
25
30
25.54
30.28
2.1%
0.9%
4 Conclusion This paper proposes a load and mutual inductance synchronous identification method of a multi-frequencies and multi-loads MCR-WPT system. Firstly, the relationship between the load and the mutual inductance is derived by establishing the steady-state model. Secondly, the sliding window iterative DFT is used to extract the specified fundamental signal of the mixing primary side current. Finally, the PSO algorithm is applied to achieve the process of the synchronous identification. After a series of simulation verification, the maximum identification error of load and mutual inductance parameters is 3.2% and 2.7%, and the identification value is very close to the actual value, which verifies the feasibility and effectiveness of the identification method. Acknowledgments. This research was supported by Quanzhou Science and Technology Program (2021C020R) and Fujian Science and Technology Program (2020T3016).
References 1. Li, Y., Shi, S.B., Liu, X.L., Ma, J.B., Huang, Y.P., Xu, R.: Overview of magnetic field coupling wireless energy transmission coupling mechanism. Trans. China Electrotech. Soc. 36(S2), 389–0403 (2021). https://doi.org/10.19595/j.cnki.1000-6753.tces.L90276. (in Chinese) 2. Xue, M., Yang, Q.X., Zhang, P.C., Guo, J.W., Li, Y., Zhang, X.: The application research status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(08), 1547–1568 (2021). https://doi.org/10.19595/j.cnki.1000-6753.tces.200059. (in Chinese) 3. Huang, X.L., Wang, W., Tan L.L.: Research trends and application prospects of magnetic coupling resonant wireless power transmission technology. Automa. Electr. Power Syst. 41(2), 2–14, 141 (2017). (in Chinese) 4. Swain, A.K., Devarakonda, S., Madawala, U.K.: Modeling, sensitivity analysis, and controller synthesis of multipickup bidirectional inductive power transfer systems. IEEE Trans. Industr. Inf. 10(2), 1372–1380 (2014). https://doi.org/10.1109/TII.2014.2307159 5. Bu, Y., Mizuno, T., Fujisawa, H.: Proposal of a wireless power transfer technique for lowpower multi-receiver applications. IEEE Trans. Magn. 51(11), 1–4 (2015). https://doi.org/10. 1109/TMAG.2015.2445318 6. Xue, M., Ma, S.T.: Identification method of WPT system load and mutual inductance based on SS-type compensation network. China Sci. Paper 15(11), 1277–1282 (2020). (in Chinese)
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7. Dai, X., Li, X., Li, Y.: Cross-Coupling Coefficient Estimation between Multi-Receivers in WPT System. In: 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 1–4 (2017) 8. Jin, R., Yang, Z., Lin, F.: Mutual inductance identification and maximum efficiency control of wireless power transfer system for the modern tram. In: 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 70–74. Chongqing, China (2017) 9. Su, Y., Chen, L., Wu, X., Hu, A.P.: Load and mutual inductance identification method of SStype magnetically-coupled WPT system based on genetic algorithm. Diangong Jishu Xuebao/Trans. China Electrotechn. Soc. 33(18), 4199–4206 (2018). https://doi.org/10.19595/j. cnki.1000-6753.tces.171088 10. Zhou, F., Huang, D.X., Wang, F.X.: A particle swarm optimization parameter identification algorithm based on model predictive control of wireless power transfer system. In: 2019 IEEE 3rd Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC). IEEE (2019) 11. Qi, C., Huang, S., Chen, X., Wang, P.: Multifrequency modulation to achieve an individual and continuous power distribution for simultaneous MR-WPT system with an inverter. IEEE Trans. Power Electron. 36(11), 12440–12455 (2021). https://doi.org/10.1109/TPEL.2021.308 1931
A Cross-Shaped Solenoid Magnetic Coupler with High Lateral Offset Tolerance Chendawei Zhang1 , Wenzhou Lu1(B) , Jian Zhao1 , Qigao Fan1 , and Haiying Chen2 1 School of Internet of Things Engineering, Key Laboratory of Advance Process Control for
Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China [email protected], [email protected] 2 School of Mechanical Engineering, Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, Jiangnan University, Wuxi 214122, China
Abstract. Wireless power transfer (WPT) technology has been applied in all walks of life on account of its advantages, but most WPT systems have low offset tolerance performance, which hinders its development. In order to further improve the lateral offset tolerance performance of a WPT system with asymmetric magnetic coupler, a cross-shaped solenoid magnetic coupler with higher lateral offset tolerance performance is proposed in this paper. Firstly, the coil structure of the proposed magnetic coupler is optimized and simulated through FEA-based simulations to obtain high lateral offset tolerance performance by making mutual inductance relatively stable with wide range of lateral offset. Then, the analysis of the mutual inductance is proposed to verify the method to reach the purpose. Finally, the LCC-S resonance topology is applied in the proposed WPT system, the experimental results show that the proposed magnetic coupler makes the system output power relatively stable around 51.95 W with a stable maximum efficiency of 72.4% when the lateral offset varies from −9 cm to 9 cm and the transfer distance is 2 cm. Keywords: Wireless power transfer (WPT) · Offset tolerance · magnetic coupler · LCC-S resonance topology · Power stability · Cross-shaped solenoid
1 Introduction Along with the rapid development of wireless power transfer (WPT) in recent years, this epoch-making technique has been applied in all walks of life, including EVs, implantable biomedical devices, and portable electronic devices [1]. But compared with the traditional wired power transfer system, most WPT systems have low offset tolerance, which is the major disadvantage. When the relative position of the transmitting and receiving magnetic couplers changes, the transmission power and efficiency of the system will be greatly affected [2]. The WPT system will not work properly when the offset reaches a certain distance [3], which greatly limits the development of WPT. Many magnetic couplers have been proposed for different applications. In [4], in order to reduce the mutual inductance decline caused by the coil lateral offset and to © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 239–246, 2023. https://doi.org/10.1007/978-981-99-0631-4_25
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stabilize the transfer efficiency of dynamic wireless charging, the length and width of the transmitting coil are optimally designed. [5] verified that the transmitting and receiving coils in series in the same direction have better anti-offset characteristics. In [6], the anti-offset performance of the magnetic coupler can be greatly improved by applying a third coil at the transmitting side. The compensation topology also influences the performance of WPT system. The properties of LCC-S resonance topologies were studied in [7], which concluded that LCC-S is suitable for low power (such as one to several hundred watts power level) applications. A switching hybrid compensation topology based on LCC-S resonance topologies for EV wireless charging is proposed in [8], which verified the LCC-S output characteristics of constant voltage (CV) and constant current (CC). In this study, in order to further improve the lateral offset tolerance of the WPT system with asymmetric magnetic couplers, a cross-shaped solenoid magnetic coupler with higher lateral offset tolerance is proposed. In Sect. 2, the coil structure of the proposed magnetic coupler is optimized and the magnetic field of system is simulated in FEA-based simulations, then the analysis of the mutual inductance is proposed to verify the method to reach the purpose. In Sect. 3, the LCC-S resonance topology is applied in the proposed WPT system and the experimental platform is set up to verify the lateral offset tolerance of the proposed magnetic coupler.
2 Magnetic Coupler Design 2.1 Coil Structure Optimization and FEA-Based Simulations This paper adopts COMSOL Multiphysics to design the magnetic coupler. In order to obtain higher lateral offset tolerance, a cross-shaped solenoid magnetic coupler is proposed, where the transmitting coils and receiving coils are wound on the manganesezinc ferrite core. The transmitting core size is set to 27 cm * 9 cm * 1 cm in rectangular shape and the receiving core size is set to 9 cm * 9 cm * 1 cm in square shape. Figure 1(a) shows the initial magnetic coupler model. In the transmitting magnetic coupler, the Middle Coil with single turn is wound along the short side at the center of the core; Offset-Compensated Coils (a) and (b) both with 7 turns are wound along the short side at 3 cm from both ends of the rectangle transmitting core; Lateral Coils with 9 turns is wound along the long side at the center of the rectangular transmitting core. In the receiving magnetic coupler, Receiving Coils (a) and (b) both with 10 turns are wound in the center of the square receiving core in a cross-orthogonal way. In the initial magnetic coupler model, Lateral Coils and Receiving Coils (a) enhance the mutual inductance in the same direction; Middle Coil, Offset-Compensated Coils and Receiving Coils (b) enhance the mutual inductance in another direction. The origin of lateral offset is defined as the position where the center of transmitting magnetic coupler is aligned with the center of receiving magnetic coupler. Measurement of the mutual inductance in the simulation is conducted from −18 cm to 18 cm with step size of 1 cm when the transfer distance between transmitting and receiving magnetic coupler is 2 cm. The result is shown in Fig. 2 when the Middle Coil has single turn. It can be found that the mutual inductance is obviously lower at the origin of lateral offset when the
A Cross-Shaped Solenoid Magnetic Coupler Receiving Coils (a)
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Receiving Coils (b) Receiving Core
Lateral Coils
Transmitting Core
(b) Middle Coils with 2 turns
Offset-Compensated Coils (a) Middle Coil Offset-Compensated Coils (b)
(a) Middle Coil with single turn
(c) Middle Coils with 3 turns
Fig. 1. Magnetic coupler modified by increasing the number of Middle Coils turns. 15
Mutual Inductance (μH)
Peak
Peak
Valley
Peak
Valley
10
Middle Coil with 1 Turn
5
Middle Coils with 2 Turns Middle Coils with 3 Turns
0 -18
-15
-10
-5
0 Lateral Offset (cm)
5
10
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Fig. 2. The mutual inductance when Middle Coils have different turns.
Middle Coil has just single turn. Meanwhile, Offset-Compensated Coils make the mutual inductance have two obvious peaks at the both ends of the rectangle transmitting core, which can enhance the mutual inductance when the lateral offset reaches a certain degree. In order to enhance the mutual inductance at the origin of lateral offset, the number of Middle Coils turns has been increased to 2 turns and 3 turns. Figure 1(b) and (c) show the modified magnetic coupler model in simulation. The results are shown in Fig. 2 when the Middle Coils have 2 turns and 3 turns. It can be found that the mutual inductance at the origin of lateral offset is enhanced when the number of Middle Coils turns is increased. Especially when the Middle Coils have 3 turns, the mutual inductance at the origin of lateral offset has been enhanced to be basically consistent with the mutual inductance at both ends. However, the valleys between the middle peak and peaks at both ends become more obviously in the meantime. In order to fill the valleys between the middle peak and peaks at both ends, ValleyFilled Coil (a) and (b) both with single turn are wound along the short side at the center of the valley, as shown in in Fig. 3(a). Same as the previous measurement, measurement of the mutual inductance is conducted from −18 cm to 18 cm with step size of 1 cm when the transfer distance between transmitting and receiving magnetic coupler is 2 cm, and the result is shown in Fig. 4. It can be found that the mutual inductance at the lateral offset of valley is obviously enhanced. However, the enhancement is not enough to reach the peaks at the both ends of the rectangle transmitting core. Therefore, the number of Valley-Filled Coils turns has been increased to 2 turns and 3 turns in the modified magnetic coupler model. Figure 3(b) and (c) show the modified magnetic coupler model in simulation. The results of the modified magnetic coupler are shown in Fig. 4. It can be found that the valleys between the middle peak and peaks at both ends are enhanced when the number of Valley-Filled Coils turns is increased. When
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the Valley-Filled Coils (a) and (b) both have 3 turns, the valleys almost reach the peaks at the both ends of the rectangle transmitting core, which provides a relatively stable mutual inductance when the lateral offset is from −9 cm to 9 cm (working plane). Receiving Coils (b) Receiving Core Transmitting Core
Receiving Coils (a) Lateral Coils
(b) Valley-Filled Coil 2 turns Offset-Compensated Coils (a) Valley-Filled Middle Coils OffsetValley-Filled Compensated Coil (a) Coil (b) Coils(b)
(c) Valley-Filled Coil with 3 turns
(a) Valley-Filled Coil with single turn Fig. 3. Magnetic coupler modified by increasing the number of Valley-Filled Coils turns.
Fig. 4. The mutual inductance when Valley-Filled Coils have different turns.
(T)
(a) -9cm
(c) 0cm
(b) -4.5cm
(d) 4.5cm
(e) 9cm
Fig. 5. FEA-based simulations on magnetic flux density at different lateral offset.
Figure 5 shows the FEA-based simulations on magnetic flux density when the lateral offset is −9 cm, −4.5 cm, 0 cm, 4.5 cm, and 9 cm when Middle Coils and ValleyFilled Coils both have 3 turns. It can be found that the magnetic field of system is evenly distributed with a relatively stable mutual inductance when the receiving magnetic coupler is on the working plane, which means the output power will be relatively stable on the working plane. In another word, the proposed cross-shaped solenoid magnetic coupler has a high lateral offset tolerance on the working plane, according with the design expectation.
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2.2 Analysis of the Mutual Inductance According to the Neumann formula, the mutual inductance can be expressed as: μ0 Ni Nj d li · d lj Mij = 4π Rij
(1)
where M ij represents the mutual inductance between the coil groups named by i and j. l i and l j represent the length vector of i and j coil groups. dl i and dl j are the infinitesimals of i and j coil groups. N i and N j are the turn numbers of i and j coil groups. Rij is the distance between dl i and dl j . μ0 is the magnetic permeability of a vacuum. According to the coil structure of the proposed magnetic coupler, the total mutual inductance can be expressed as: MTotal = ML + MM + MC1 + MC2 + MV 1 + MV 2
(2)
where M L is the mutual inductance between the Lateral Coils and the Receiving Coils (a). M M is the mutual inductance between the Middle Coils and the Receiving Coils (b). M C1 is the mutual inductance between the Offset-Compensated Coils (a) and the Receiving Coils (b). M C2 is the mutual inductance between the Offset-Compensated Coils (b) and the Receiving Coils (b). M V1 is the mutual inductance between the ValleyFilled Coils (a) and the Receiving Coils (b). M V2 is the mutual inductance between the Valley-Filled Coils (b) and the Receiving Coils (b). According to (1), M L , M M , M C1 , M C2 , M V1 and M V2 can be enhanced by increasing the turn number of their corresponding coil groups, so the mutual inductance at middle and valleys can be enhanced by increasing the turn number of the Middle Coils and the Valley-Filled Coils to get a relatively stable mutual inductance.
3 Experimental Verification 3.1 Experimental Setup The compensation topology of the proposed WPT system is selected as LCC-S. In [9], the LCC-S resonance topology is analyzed and concludes that the system output power Pout changes as the mutual inductance M changes when input voltage U IN , compensated inductance L 1 and load resistance RL are certain values. In order to maintain a stable output power, it is necessary to maintain a stable mutual inductance M. Based on the research of Sect. 2, the experimental platform is set up to verify the lateral offset tolerance of the proposed magnetic coupler, as shown in Fig. 6. DC power source (SS-6020KD) provides input voltage to the transmitter half-bridge inverter and the control circuit. The LCR meter (TH2832) measures the inductance of magnetic coupler. The voltage and current waveforms are measured by differential probes (Tektronix P5200A) and displayed on the oscilloscope (Tektronix TDS3040C). The DC electronic load (ITECH IT8514C) provides stable DC load and measures the output voltage and current. The MCU (STM32F030F4P6) provides the PWM required for invert. The Litz wires with specifications of 300 × 0.1 mm2 are employed to wind the coils.
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The resonant frequency f 0 is set to 150 kHz. In order to make the WPT system work in Magnetically Coupled Resonance (MCR) mode, the LCC-S compensation network is set as: on transmitting side, L 1 (4.56 µH) is the compensated inductance, C PP (246.88 nF) is the parallel compensation capacitor, C PS (9.97 nF) is the series compensation capacitor, L P (117.43 µH) is the inductance of transmitting magnetic coupler. On receiving side, C S (21.87 nF) is the series compensation capacitor, L S (51.48 µH) is the inductance of receiving magnetic coupler. LCR meter S network and rectifier
Oscilloscope Differential probes
Receiving magnetic coupler DC source DC electronic load
Transmitting magnetic coupler Proposed magnetic coupler Inverter and LCC network
Fig. 6. Experimental setup of the proposed magnetic coupler WPT system.
3.2 Measurement of the Experiment The mutual inductance between transmitting and receiving magnetic coupler can be calculated through the forward and reverse series inductance. The transfer distance (D) is set to 2 cm, 3 cm and 4 cm, the result of the mutual inductance under different transfer distance is shown in Fig. 7.
Fig. 7. The mutual inductance under different transfer distance.
The DC power source provides 24 V DC input voltage, the DC electronic load is set to 10 to measure the output parameters. The transfer distance is set to 2 cm, 3 cm and 4 cm, the result of output power and transfer efficiency is shown in Fig. 8(a) and (b).
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(a) Output Power
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(b) Transfer Efficiency
Fig. 8. The output parameters under different transfer distance.
From Fig. 8(a) the variation tendency of output power is consistent with mutual inductance, which verifies the conclusion in [9]. When the transfer distance is 2 cm the output power is relatively stable around 51.95 W on the working plane. When the transfer distance is increased to 3 cm or 4 cm, the fluctuation of output power is decreased, which provides a more stable output power on the working plane. From Fig. 8(b) the transfer efficiency on the working plane maintains stable enough under any transfer distance. When the transfer distance is 2 cm, 3 cm and 4 cm, the transfer efficiency on the working plane is about 72.4%, 69.6% and 64.3%. When the transfer distance (D) is 3 cm and the lateral offset is −9 cm, Fig. 9(a) shows the waveforms of inverter output voltage and current, Fig. 9(b) shows the waveforms of transmitting magnetic coupler output voltage and current, Fig. 9(c) shows the waveforms of voltage and current of series resonance compensation network (SRCN). The waveforms on the working plane are similar. From Fig. 9, both transmitting and receiving side of the proposed WPT system are working at the resonant state, and the working frequency is approximately 150 kHz. Voltage: 10V/div
Current: 1A/div Timebase: 2μs/div (a) Inverter output
Voltage: 250V/div
Current: 5A/div Timebase: 2μs/div (b) Transmitting magnetic coupler
Voltage: 10V/div
Current: 5A/div Timebase: 4μs/div (c) SRCN output
Fig. 9. The voltage and current waveforms when D = 3 cm and the lateral offset is −9 cm.
4 Conclusion In this paper, in order to improve the lateral offset tolerance of the WPT system with asymmetric magnetic couplers, a cross-shaped solenoid magnetic coupler with higher lateral offset tolerance is proposed. According to the simulation results, the number of coil turns can influence the mutual inductance where the coil is wound, and when Middle Coils and Valley-Filled Coils both have 3 turns the proposed cross-shaped solenoid
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magnetic coupler has the highest lateral offset tolerance on the working plane. The analysis of the mutual inductance is proposed to verify the method to reach the purpose. The LCC-S compensation topology is applied in the proposed WPT system. The experimental results show that the proposed magnetic coupler makes the system output power relatively stable around 51.95 W with a stable maximum efficiency of 72.4% on the working plane when the lateral offset is from −9 cm to 9 cm and the transfer distance is 2 cm. Acknowledgments. This research was funded by the National Natural Science Foundation of China (Grant No. 51407084), the China Postdoctoral Science Foundation (Grant No. 2017M610294), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 1701092B) and Sichuan Cuisine Development Research Center Planning Project (Grant No. CC22Z01).
References 1. Zhang, Z., Pang, H., Georgiadis, A., Cecati, C.: Wireless power transfer – an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019) 2. Tian, L., Yang, F., Cai, B., Li, S., Liu, K., Zhao, H.: High misalignment tolerance in efficiency of WPT system with movable intermediate coil and adjustable frequency. IEEE Access 9, 139527–139535 (2021) 3. Li, Y., Zhao, J., Yang, Q., Liu, L., Ma, J., Zhang, X.: A novel coil with high misalignment tolerance for wireless power transfer. IEEE Trans. Magn. 55(6), 1–4 (2019) 4. Dong, Y.F., Lu, W.Z., Chen, H.Y.: Optimization study for lateral offset tolerance of electric vehicles dynamic wireless charging. IEEJ Trans. Electr. Electr. Eng. 15(8), 1219–1229 (2020) 5. Lu, W.Z., Zhao, J., Dong, Y.F., Huang, F.C., Chen, H.Y.: Research on electric vehicle dynamic wireless charging system with two coils in series. J. Power Supply (2022). http://kns.cnki.net/ kcms/detail/12.1420.TM.20220209.1711.006.html (in Chinese) 6. Chen, Y., Mai, R., Zhang, Y., Li, M., He, Z.: Improving misalignment tolerance for IPT system using a third-coil. IEEE Trans. Power Electron. 34(4), 3009–3013 (2019) 7. Chen, Y., Zhang, H., Shin, C.-S., Seo, K.-H., Park, S.-J., Kim, D.-H.: A comparative study of S-S and LCC-S compensation topology of inductive power transfer systems for EV chargers. In: 2019 IEEE 10th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), pp. 99–104 (2019) 8. Chen, Y., Zhang, H., Park, S.-J., Kim, D.-H.: A switching hybrid LCC-S compensation topology for constant current/voltage EV wireless charging. IEEE Access 7, 133924–133935 (2019) 9. Guo, Y.G., Cui, N.X.: Research on optimal configuration and characteristics based on LCC-S type wireless power transfer system. Trans. China Electrotech. Soc. 34(18), 3723–3731 (2019). (in Chinese)
A Design of Secondary-Only Resonant Series-Series WPT System to Maintain Power Stability with Coil Misalignment Yueyao Li, Xiaohua Wu, and Xiliang Chen(B) School of Automation, Northwestern Polytechnical University, Xi’an 710072, China [email protected], [email protected]
Abstract. Wireless power transfer (WPT) technology has been a popular application in electric vehicle (EV) and unmanned aerial vehicle (UAV) charging. However, it is hard to keep transfer power stable or efficiency high with coil misalignment. In this paper, a method is designed based on the traditional fully resonant series-series (SS) WPT system to solve the power and efficiency problems above. With the optimal calculation of compensation capacitance in the primary circuit, this letter proposed a secondary-only resonant SS typology. The simulation results through ANSYS show that the transfer power plus (decrease) percentage is about 6% (26%) with the change percentage of coupling coefficient being 46.36%. In the whole offset period, the change percentage of horizontal displacement reaches 37.3% (100 mm). In addition, the average transfer efficiency is about 83%, which is maintained at a relatively high level. Keywords: Secondary-only resonant WPT · Stable transfer power · ANSYS
1 Introduction Magnetically coupled resonant wireless power transmission technology, also known as magnetic field resonance technology, involves microwave engineering, electromagnetic fields, power electronics, circuit theory, materials science, and other disciplines. It is a new field of research in academia and industry at home and abroad [1–3]. There are four types of compensation resonant structure: series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP). Consequently, in the case of working with low load resistance such as EV, UAV or mobile phone charging, the SS topology can be preferred [4]. However, in the actual wireless power transmission period, it is hardly avoided that horizontal or vertical misalignment happened to the coils. This will certainly cause the variation of the coupling coefficient so which will cause the variation in transfer power and efficiency. Nowadays, some research is used to keep power stable. On the one hand, some optimal topologies are put to regulate the power fluctuation. [5] adopted an optimized coupling structure to improve the displacement tolerance, whose insensitivity is possible by minimizing the variation of mutual inductance, but the tolerance is weak. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 247–254, 2023. https://doi.org/10.1007/978-981-99-0631-4_26
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In the roadway charging scheme, the primary coil constant current source is usually realized by LCL or LCC topology [6–8]. A new compensation-circuit is proposed that considers high-order current harmonics and results in inverter zero-current switching. The improved compensation capacitance network in [9] is optimized to have good resistance to large coupling changes, but higher-order compensation topologies enable better functionality and increase the complexity of the system. On the other hand, the coil structure like a three/four-coil coupling system [10] and orthogonal windings [11] are used to meliorate the power stability. In the above methods for stabilizing the transmission power, a relatively complicated compensation topology or a complex coil configuration is used, which limits the practicability of the system. In this letter, it is proved from theoretical analysis that the compensation capacitance of the primary side plays a crucial part in the fluctuation of transmission power. So a secondary-only resonant SS system is designed to maintain stable transfer power while keeping relatively high efficiency. Different from other methods, it does not need to change the structure of coil systems or topologies of transmitting and receiving circuits to get a more stable load power. Apart from the theoretical analysis, simulation is done with ANSYS Maxwell and Simplorer to support the method.
2 Theoretical Derivation of Secondary-Only Resonant SS System The topology of the traditional SS resonant WPT circuit is in Fig. 1. VS is the voltage of the AC supply. L1 , C1 , R1 are respectively inductance, compensation capacitance, and internal resistance of the primary-side circuit. L2 , C2 , R2 are respectively inductance, compensation capacitance, and internal resistance of the secondary circuit. RL is the resistance of the load. M is the mutual inductance of the transmitting coil and receiving coil. I1 , I2 are the current of two circuits.
I1
R1
Vs
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I2
R2
L2
C1
RL
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Fig. 1. SS circuit topology
Let the operation frequency of the SS circuit is f0 (ω0 = 2π f0 ). KVL is used in two circuits, as shown in (1). ⎧ 1 ⎪ ⎪ R I1 + jω0 MI2 = VS + jω L − j 0 1 ⎨ 1 ω0 C1 (1) ⎪ 1 ⎪ ⎩ R2 + jω0 L2 − j + RL I2 + jω0 MI1 = 0 ω0 C2
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Based on the formulas above and P = I 2 R, the input power and output (load) power are shown: ⎧
2 ⎪ ⎨ Pin = 2VS 2 · A · (R2 + RL ) + B · ω0 L2 − 1 ω0 C2 A +B (2) ⎪ ⎩ P = (ω0 MVS )2 · R out L A2 +B2 where, ⎧
⎨ A = (ω0 M )2 + R1 (R2 + RL ) − ω0 L1 − 1 ω0 L2 − ω C 0 1
1 ⎩ B = (R2 + RL ) ω0 L1 − 1 + R ω L − 1 0 2 ω0 C1 ω0 C2
1 ω0 C2
(3)
So the efficiency of SS WPT is: η=
(ω0 M )2 RL
2 1 R1 + (ω0 M )2 (R2 + RL ) (R2 + RL )2 + ωL2 − ωC 2
(4)
/W
For traditional resonant SS WPT, its output power decreases dramatically as the coupling coefficient increases, which is shown in Fig. 2.
Coupling coefficient
Fig. 2. The relation between the load transfer power and coupling coefficient
From the formula of efficiency, we can get the conclusion that the resonant state of the primary circuit does not affect the transmission efficiency of the system. Therefore, a new secondary-only resonance SS WPT system is proposed to maintain the stability of output√power. Also let d η/dRL = 0, the coupling coefficient of the two coils is k = M / L1 L2 , so that the optimal load resistance RLopt can be get, which is shown in Fig. 3(a) [12]. R2 ω02 k 2 L1 L2 (5) RLopt = R22 + R1
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/
(a) The relation between efficiency and load resistance
(b) The graph of the function f ( ρ )
Fig. 3. The graphs of efficiency and function f (ρ)
Suppose that the coupling coefficient varies from kmin to kmax when the coils offset. The reflection resistor of the secondary side Rf can be written as: Rf min =
2 L L ω02 kmin ω2 k 2 L1 L2 (ω0 M )2 1 2 ≤ Rf = ≤ Rf max = 0 max RL RL RL
(6)
The internal resistances of two coupling coils are ignored. When the secondary side is working at a resonant state, the variable X1 is expressed as the reactance of the primary side (X1 = ω0 L1 − 1/ω0 C1 ). α is expressed as the impedance angle. Let variable ρ be the tangent of impedance angle. ρ = tan α =
X1 Rf
(7)
The transfer power Pout is shown as follows: Pout =
VS2 Rf R2f + X12
=
VS2 VS2 = sin 2α X1 (ρ + 1/ρ) 2X1
(8)
From formula it can be seen that when the impedance angle α = 45° the load power gets maximum value, which also shows that the key to restraining power fluctuation is to modify the impedance and impedance angle of the primary side reasonably. The specific realization is to adjust the compensation capacitance of the primary side circuit. Assume kmax = λkmin to define the misalignment degree of the coil system. Apparently, when the central axis of two coils is coincident, the coupling coefficient gets a peak value. From (6) can draw the reflection resistance as Rf max = λ2 Rf min . Suppose the minimum tangent value of impedance angle is ρ0 , it’s easy to get the relationship which is ρ0 = X1 /Rf max . The variable ρ varies in ρ0 , λ2 ρ0 . In the formula (8), the only variable is ρ in a certain circuit. So a function of ρ is defined to describe fluctuations in output power, which is shown as follows: 1 (9) f (ρ) = , ρ ∈ ρ0 , λ2 ρ0 ρ + 1/ρ
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The graph of the function f (ρ) is shown as Fig. 3(b). A power fluctuation model is defined to describe the effect of coil misalignment: g(ρ) =
fmax (ρ) − fmin (ρ) fmin (ρ)
(10)
g(ρ) and its minimum can be calculated, as Table 1 shown. Table 1. Three cases of minimum fluctuation Cases
g(ρ)
gmin (ρ)
ρ0 < λ 2 ρ0 < 1
λ2 ρ02 +1 −1 2 4 λ ρ0 +1
λ2 −1 2λ2
λ2 −1 2λ2
λ4 ρ02 +1 −1 λ2 ρ02 +1
1 < ρ 0 < λ 2 ρ0
(ρ0 −1)2 1 2ρ0 , ρ0 < λ 2 2 λ ρ0 −1 , ρ0 > λ1 2λ2 ρ0
ρ0 ≤ 1 ≤ λ 2 ρ0
2
, ρ0 = 12 λ
2
, ρ0 = 1
(λ−1)2 1 2λ , ρ0 = λ
From the above table, it can be concluded that when ρ0 ≤ 1 ≤ λ2 ρ0 , g(ρ) takes the minimum value at ρ0 = 1/λ. Take this result in (7) to get the compensation capacitance: C1 =
λω02 L1 RL
λRL 2 L L − ω03 kmax 1 2
(11)
In the end, the compensation capacitance of the primary side is designed.
3 Simulation of SS WPT System and Experiment Results In order to verify the proposed design method above, the secondary-only resonance SS circuit is established with ANSYS Simplorer and Maxwell software. Firstly, the transmitting coil and receiving coil are designed in ANSYS Maxwell, which parameters are shown in Table 2. Table 2. Parameters of transmitting coil and receiving coil d/mm
D/mm
S/mm
w/mm
N
h/mm
L/μH
y/mm
120
268
2
1.8
20
60
90.04
0–100
The specific parameters are inner coil diameter d, external coil diameter D, turn spacing S, the diameter of a wire w, number of turns N, the distance between the transmitting
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(b)The magnetic field of the coil system in Max- well
(a)The coil system in Maxwell
Fig. 4. The coil model and the magnetic field in Maxwell
coil, and receiving coil h. Through finite-element analysis (FET), the inductance of the coil is 90.04 μH. The model and inducted magnetic field are shown in Fig. 4(a) and (b) respectively. To simulate the misalignment of coils, set horizontal displacement is y, which varies from 0 to 100 mm and the step length is 10 mm. The coil system is used in an SS topology which is simulated by ANSYS Simplorer, as shown in Fig. 5. Moving Average
Moving Average
W
WM1
C1
am1
C2
am2
Pout
+ A
+
A
Pin
WM2
W
RL
Mx_SS1 Vs
0
Winding1:src
Winding2:src
Winding1:snk
Winding2:snk
0
Fig. 5. The simulated circuit in Simplorer. Here, VS =30 V, f0 = 100 kHz, C1 = 35.79 nF, C2 = 28.13 nF, and RL in the range of [1 , 30 ].
A 30 V/100 kHz AC source is used for the primary circuit. The capacitance of the transmitting circuit is calculated through the formula (11). For secondary-only resonance SS WPT circuit, the compensation capacitor of receiving circuit is always working √ at a resonant state. Then the capacitance of C2 can be calculated by f2 = f0 = 1/2π L2 C2 . Also, a load resistance varied from 1 to 30 is set to simulate the influence of load. The output power changes under coil offset with different load resistances are shown in Fig. 6(a). In the case of an 8 load, the transfer power without misalignment (y = 0 mm) is 20.34 W. The simulated peak value and least value of transfer power are respectively 21.59 W (k = 0.184) and 15.02 W (k = 0.115) in the whole effective misalignment area. Then it can be calculated that the power raise and drop percentage is 6.15% and 26.1% respectively. With a horizontal displacement of 100 mm, the misalignment distance percentage is 37.3%. As to this, it can draw a conclusion that the actual power
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does not drop dramatically. Figure 6(b) shows the comparison of transfer power with a traditional fully resonant SS system with 6 load resistance. It is obvious that transfer power in traditionally full-resonant SS WPT has a sharp drop which is approximately 1/3 of starting value. Meanwhile, the secondary-only resonant SS system shows the tolerance of misalignment of coils.
(a) Transfer power versus k of different RL (b) The output power comparison diagram
misalignment optimal load area
(c) 3D graph of efficiency η versus k and RL
(d) 2D graph of efficiency η versus RL
Fig. 6. The graphs of results in simulation
Figure 6(c) displays the transfer efficiency under different horizontal displacements and various load resistance values. This shows the changing tendency of transfer power. Figure 6(d) is the 2D figure to show the optimal load resistances which are calculated by (5). Its theoretical values are 12.1 and 6.5 . It can be noticed that the efficiency drops more dramatic at RL = RLopt(kmax) = 12.1 . According to the results, the highest average efficiency is at RL = RLopt(kmin) = 6.5 , which is 83%.
4 Conclusion In this paper, a simple procedure is proposed to improve the insensitivity of system by optimizing the primary dynamic SS WPT compensation capacitor. The secondary-only resonant SS system consists of two circular coils with 20 turns. The simulation results show that the transfer power plus (decrease) is about 6% (26%). Within the whole offset period, the change percentage of horizontal is 37.3% (100 mm). Furthermore, the average power transmission efficiency is about 83%. We use carefully designed primary-side compensation capacitor to limit the influence of various coupling coefficients on transmitted power. This method actually reduces the
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capability of power transmission in WPT system because of the primary inductive reactance. However, no complicated compensation topology or a complex coil configuration requires a strategy.
References 1. Triviño, A., González-González, J.M., Aguado, J.A.: Wireless power transfer technologies applied to electric vehicles: a review. Energies 14(6), 1547 (2021) 2. Arif, S.M., Lie, T.T., Seet, B.C., Ayyadi, S., Jensen, K.: Review of electric vehicle technologies, charging methods, standards and optimization techniques. Electronics 10(16), 1910 (2021) 3. Liang, J., Wu, D., Yu, J.: A design method of compensation circuit for high-power dynamic capacitive power transfer system considering coupler voltage distribution for railway applications. Electronics 10(2), 153 (2021) 4. Ozkilic, S.O., Agcal, A., Toraman, K.: Comparison of compensating topologies in two coil resonant wireless power transfer system. J. Eng. Res. (2022) 5. Alshhawy, S., Barakat, A., Yoshitomi, K., Pokharel, R.K.: Separation-misalignment insensitive WPT system using two-plane printed inductors. IEEE Microwave Wirel. Compon. Lett. 29(10), 683–686 (2019). https://doi.org/10.1109/LMWC.2019.2935621 6. Hao, H., Covic, G.A., Boys, J.T.: An approximate dynamic model of LCL-T-based inductive power transfer power supplies. IEEE Trans. Power Electron. 29(10), 5554–5567 (2013) 7. Pantic, Z., Bai, S., Lukic, S.M.: ZCS LCC-compensated resonant inverter for inductive-powertransfer application. IEEE Trans. Ind. Electron. 58(8), 3500–3510 (2010) 8. Götz, T., Noeren, J., Elbracht, L.: Analysis of the eigenvalue distortion in a double-sided LCCcompensated stationary automotive WPT system during coil alignment. In: 2022 Wireless Power Week (WPW), pp. 503–508 (2022) 9. Lim, Y., Tang, H., Lim, S., Park, J.: An adaptive impedance-matching network based on a novel capacitor matrix for wireless power transfer. IEEE Trans. Power Electron. 29(8), 4403–4413 (2013) 10. Zhu, Q., Guo, Y., Wang, L., Liao, C., Li, F.: Improving the misalignment tolerance of wireless charging system by optimizing the compensate capacitor. IEEE Trans. Ind. Electron. 62(8), 4832–4836 (2015) 11. Chow, J.P., Chen, N., Chung, H.S., Chan, L.L.: Misalignment tolerable coil structure for biomedical applications with wireless power transfer. In: 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 775–778. IEEE, Osaka (2013) 12. Zhong, W., Hui, S.: Maximum energy efficiency tracking for wireless power transfer systems. IEEE Trans. Power Electron. 30(7), 4025–4034 (2014)
Research on Constant Voltage Control Strategy of Dual Pick-Up Dynamic Inductive Coupled Power Transfer System Based on Optimal Efficiency Anran Sun(B) and Chenyang Xia School of Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China [email protected]
Abstract. In order to realize the constant voltage and high-efficiency power output of dual pickup dynamic inductive coupled power transfer (ICPT) system, a constant voltage output control strategy based on optimal efficiency is proposed in this paper. By adjusting the buck modules of different pickup circuits, the output voltage and efficiency characteristics of the system are analyzed. According to the analysis of the characteristics, a constant voltage control strategy is proposed, so that the system can maintain the optimal state of efficiency while outputting constant voltage. Finally, an experimental platform is designed to verify the control strategy. The experimental results show that the control strategy proposed in this paper can achieve the two objectives of constant output voltage and optimal efficiency at the same time. The dynamic ICPT system with transmission power of 180 W can maintain the constant voltage output and the overall efficiency can be maintained above 93%. Keywords: Dynamic radio energy transmission · Dual pickup circuit · Constant voltage output · Optimal efficiency
1 Introduction Inductive Coupled Power Transfer (ICPT) technology is a non-contact power transfer technology, is a kind of energy by converting the power into other forms of energy (such as electromagnetic field energy, microwave, laser, etc.). Then the transmitter and receiver carry out point-to-point transmission of the transformed energy over a certain distance [1]. At present, it is gradually applied in household appliances [2], biomedicine [3] and electrified transportation. In the field of electrified transportation, vehicles can transmit power in static or dynamic ways through ICPT technology [4–6]. In the dynamic mode, the moving vehicle is charged by a series of transmitting coils on the road, and its normal running is ensured by designing the spacing between transmitting coils and the power transmission size [7]. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 255–263, 2023. https://doi.org/10.1007/978-981-99-0631-4_27
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Compared with static mode, vehicles in dynamic mode can be used stably for a long time and reduce the demand for battery capacity [8, 9]. For the double-pick dynamic ICPT system, on the one hand, the research is often on the optimization of coil parameters, taking multiple pick up coils as a whole to analyze the overall mutual inductance, but the influence of the mutual inductance of different coils on the system is less studied. On the other hand, most of the research focuses on parallel systems, and less on series systems. Literature [10] proposed a dual pick up parallel dynamic ICPT system that is suitable for low-speed moving conditions such as parking in a garage. By optimizing the coil structure, the mutual inductance of the system almost does not change when the lateral deviation is ±200 mm. Although the anti-offset property of the system is enhanced by coil design, the system may be detuned, and it is difficult to be used in practical engineering. Literature [11] proposed a control strategy for double-pick parallel ICPT system, which used PI controller to control the ratio of equivalent load resistance, so that the system always maintained constant power output and optimal efficiency during the moving process. However, the measurement of equivalent load resistance needed to be coordinated by multiple sensors, and the control target was not intuitive. Literature [12] further improved on the basis of literature [11], and changed PI controller control to directly calculate the duty cycle of two Boost circuits to improve the control speed of the system. However, it was still to control the equivalent load resistance of the system, and the process of achieving the control target was relatively tedious. In order to realize the constant voltage output and efficiency optimization of the dual pick up dynamic ICPT system simultaneously, this paper proposes a constant voltage control strategy based on efficiency optimization, which can maintain the constant voltage output and the optimal efficiency of the dynamic system under normal working conditions. In this paper, a mathematical model is established to analyze the relationship between the output voltage and efficiency of the system and the duty cycle of Buck modules of different pickups in series dynamic ICPT system. According to the analysis of output voltage and efficiency, a constant voltage control strategy is proposed to keep the system in the optimal state of efficiency. Finally, the feasibility of the control strategy is verified by experiments.
2 Analysis of Transmission Characteristics of Dynamic ICPT System with Double Pickup Dual pick up system according to the mode of connection can be divided into series connection and parallel connection, compared with the parallel system in series connection system is suitable for small load, and in the actual application, parallel connection system to prevent high pressure to low pressure charging, need through the DC/DC control module makes two pick up circuit output voltage equal, In addition, when a certain pick coil has a large offset, the normal operation of the system can only be ensured by cutting out the pick loop connection with the coil. In conclusion, series connection is selected as the connection mode between load and load in this paper. According to above analysis, this paper uses the LCC compound harmonic compensation the topology of the network as the original edge launch guide, S compensation
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network is adopted as a pair of side pick up coil compensation topology, ignore the mutual inductance between the pick up coil, DC/DC output control module connected in series with the load, the system structure and circuit model are shown in Fig. 1.
+
Edc
S2 -
M1 L1
C0
C1 S4
M1
C3
S3
S1
DC/ DC
L3 rL3
C2
I1 U
rL2L2 M2
I2
RL
C4
0
L1 C1
DC/ DC
L4 rL4
(a) system structure
C2
rL2
I C3 L3 3 RLeq1 rL3
L2
I C4 L4 4 RLeq2 M2
rL4
(b) System circuit model
Fig. 1. Structure and circuit model of dual pick up dynamic ICPT system
The Buck module is used as the voltage regulating module, and the duty cycle of the two Buck modules is set as D1 and D2 respectively, and the output voltage is U R1 and U R2 . Since the output terminals of the two Buck modules are connected in series, the voltage on the load is the sum of the output voltages of the two Buck converters, and the voltage on the load is shown in Eq. (1): URL =
π D1 ωM1 I2 π D2 ωM2 I2 + √ √ 2 2 2 2
(1)
When a constant output voltage is set for the load, the two pickup circuits can achieve the goal of constant voltage output in countless combinations by controlling the duty cycle of their respective Buck modules. The AC equivalent loads RLeq1 and RLeq2 are: ⎧ 8M1 ⎪ ⎪ RLeq1 = RL ⎨ 2 π D1 (D1 M1 + D2 M2 ) (2) 8M2 ⎪ ⎪ ⎩ RLeq2 = 2 RL π D2 (D1 M1 + D2 M2 ) Let the ratio of Buck module duty cycle of pick circuit 1 to Buck module duty cycle of pick circuit 2 be α. The total output of the system is the sum of the output power of the two pickup circuits, so the total output power of the system is: POUT =
ω2 I22 M1 (αM1 + M2 ) αRLeq1
(3)
Due to the existence of coil internal resistance in the primary side transmit guide and secondary side pick coil of the system, there is power loss in the system. Assume that the active power loss on the primary side transmit guide is PrL2 , the active power loss on pick up coil 1 is PrL3 , and the active power loss on pick up coil 2 is PrL4 . The system
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loss expression is: ⎧ 2 rL3 α 2 POUT ⎪ ⎪ P = ⎪ rL3 ⎪ 2 2 ⎪ ω I2 (αM1 + M2 )2 ⎪ ⎨ PrL2 = I22 rL2 ⎪ ⎪ ⎪ ⎪ P 2 rL4 ⎪ ⎪ ⎩ PrL4 = 2 2 OUT ω I2 (αM1 + M2 )2
(4)
And since the efficiency expression of the double-pick ICPT system is: η1 =
Pout Pout + PrL2 + PrL3 + PrL4
100
(5)
93.0
80 Pick up circuit 1 Pick up circuit 2
40
η/%
POUT / W
92.5
60
92.0 91.5
20 0
2.5
5.0
7.5 α
10
12.5
15
(a) Power comparison of pickup loops
91.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 α
(b) Comparison of efficiency of pickup loops
Fig. 2. System power and efficiency curve
Figure 2(a) shows that the output power of pick coil 1 increases with the increase of α, and the output power of pick coil 2 decreases with the increase of α, and the total output power of the system remains unchanged. When α increases, it indicates that the duty cycle of Buck module in pick up circuit 1 increases, and the output voltage of pick circuit 1 will increase accordingly. In constant voltage control mode, the duty cycle of Buck module in pick up circuit 2 will decrease, so as to reduce the output voltage of pick circuit 2 and ensure the stability of the total output voltage. Since the two pickup circuits are connected in series, that is, the output current is the same, the output power of the pickup circuit will be positively correlated with the output voltage, that is, the higher the output voltage, the more output power will be allocated. As can be seen from Fig. 2(b), with the increase of α, the efficiency of the system increases first and then decreases, and there is a maximum efficiency. That is, by adjusting the duty cycle of the Buck module of the two pickup circuits, the system can achieve the optimal efficiency while maintaining the constant voltage output.
3 Constant Voltage Control Strategy Based on Optimal Efficiency From the above analysis of efficiency, it can be seen that when the output voltage of the system is constant, there is an efficiency optimum. Therefore, this section will analyze
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the optimal efficiency advantage and propose a control strategy with optimal efficiency under constant pressure control. The total power of the system is mainly composed of the output power, the loss power of the transmitting guide at the primary side and the loss power of the secondary side pick up coil. Since the output voltage of the system is constant, the output power of the system is only related to the load resistance. When the load does not change, the output power of the system does not change. In addition, the original side coil adopts LCC resonant compensation network. According to the characteristics of the network, the current of the original side is only determined by the input voltage and the resonant frequency of the system. Therefore, the current flowing through the original side coil is a constant value, so the power lost in the transmitting guide of the original side should also be a constant value. To sum up, the variable loss of the system is only the loss of the pick coil. To improve the efficiency of the system and make it at the maximum, the pick coil loss of the system should be at the minimum value. Draw the relationship between the coil loss and the ratio α of the duty cycle of the Buck modules of the two pickup circuits, as shown in Fig. 3.
1.5
Pick up coil 1 loss Pick up coil 2 loss Total coil loss
PLOSS / W
1.0
0.5
0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 α
Fig. 3. Variation curve of system loss
When the value of α is close to 0 or infinity, one pick circuit will be short-circuited and the other pick circuit will work alone. Since the mutual inductance between each pick circuit and the transmitting guide is not the same, and different pick coils also have different internal resistance, the corresponding pick coil loss of the two pick circuits is different in each individual case. At the same time, it can also be seen from Fig. 3 that there is a value α in the system, which makes the system change the output voltage distribution strategy of the two pickup circuits at the same time of constant voltage output, so as to minimize the loss of the system and keep the system in the optimal efficiency state. When the loss power of the pickup coil of the system is the minimum, the corresponding system efficiency is the highest. The expression α max of the duty cycle ratio of Buck module of the pickup circuit that makes the system efficiency optimal can be obtained as follows: αmax =
M1 rL4 M2 rL3
(6)
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Then the voltage set values of pickup coil 1 and pickup coil 2 when the system efficiency is optimal, U SET1 and U SET2 , are: ⎧ M12 rL4 ⎪ ⎪ USET ⎪ USET1 = 2 ⎨ M1 rL4 + M22 rL3 ⎪ M 2 rL3 ⎪ ⎪ ⎩ USET2 = 2 2 USET M1 rL4 + M22 rL3
(7)
The control flow chart of the system is shown in Fig. 4. Start
Duty cycle is initialized (Duty cycle of Buck module is set to 50%)
Given the output voltage set value US ET, read the current position mutual inductance parameters
Calculate the output voltages US ET1 and US ET2 of each pickup circuit of the system under the optimal efficiency
The controller regulates the duty cycle of the BUCK circuit
Sample the output voltages UR1 and UR2 of each pickup circuit
US ET1-UR1 =0 US ET2-UR2 =0
End
Fig. 4. Flow chart of system control
4 Experimental Analysis 4.1 Introduction to Experimental Platform In order to further verify the feasibility and effectiveness of the control strategy, a set of experimental platform is built in this paper. The allowable displacement × range of the system is 50 cm–110 cm, and the transmission power is 180 W. The experimental platform is shown in Fig. 5 and the parameters are shown in Table 1.
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High frequency inverter Magnetic coupling mechanism
LCC resonant compensation network
S-type resonant compensation network and rectifier module
Buck module
PIController Electronic load
Fig. 5. Platform of system experiment
Table 1. System parameter table Parameter
Value
Parameter
Value
f /kHz
85
C 3 /nF
53.019
E dc /V
50
r L2 /
0.135
L 1 /μH
22
L 3 /μH
68.233
C 1 /nF
159.36
C 4 /nF
51.389
L 2 /μH
166.998
r L3 /
0.132
C 2 /nF
24.179
C f1 /μF
270
r L1 /
0.311
C f2 /μF
270
L 3 /μH
66.126
RL /
5
4.2 Analysis of Experimental Results When the system displacement x is 60 cm, α = 1.91, U SET1 = 23.65 V, and U SET2 = 6.35 V. Change the value of α to 2.37, then the output voltage of pick circuit 1 is set to 25 V, and the output voltage of pick circuit 2 is set to 5 V. The waveforms of current flowing in the pick coil for two different values of α are shown in Fig. 6. In Fig. 6, channel 2 is the current flowing through pick coil 1, and channel 1 is the current flowing through pick coil 2. It can be seen that the voltage distribution scheme corresponding to the optimal efficiency has a smaller loss. The load and output voltage are set to be constant. According to the proposed control scheme, the system efficiency curve obtained by experiment is shown in Fig. 7. It can be seen from Fig. 7 that the system efficiency in the experimental platform is similar to that in the simulation model, and the system efficiency can be maintained at about 93% when moving.
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Pick up coil 2
Pick up coil 2
Pick up coil 1
Pick up coil 1
(a) Optimal allocation scheme
α=1.91
(b) α=2.37
Fig. 6. Pickup coil current under different α values 94.5 94.0
η/%
93.5 93.0 92.5
Simulation value of system efficiency
92.0
Actual value of system efficiency
91.5
60
65
70
75
80 x/cm
85
90
95
Fig. 7. Variation curve of efficiency when the system moves
5 Conclusion Based on double dynamic ICPT pickup system, establish a closed-loop PI control, put forward a kind of constant pressure control strategy based on optimal efficiency, through the analysis of system efficiency, and found that the system output in the realization of constant voltage at the same time, the change of different pick up circuit for output voltage, which may lead to the loss of system changes, and there is a low loss is the most efficiency; The optimal efficiency is analyzed, and the value of the ratio of duty cycle of Buck module of two pickup circuits is obtained when the efficiency is optimal, and the effectiveness of the proposed scheme is verified by experiments.
References 1. Kurs, A., Karalis, A., Moffatt, R., et al.: Wireless power transfer via strongly coupled magnetic resonances. Science 317(5834), 83–86 (2007) 2. Wu, J.H.: Research on High Power Radio Energy Transmission Technology for Household Appliances. Harbin Institute of Technology (2013). (in Chinese) 3. Amasha, H.M., Ghazzawi, Z.K., Al-Nabulsi, J.I.: A wireless multi bundle concentric coil for charging the battery of a total artificial heart or a pacemaker. IEEE (2007) 4. Jeong, S., Jang, Y.J., Kum, D., et al.: Charging automation for electric vehicles: is a smaller battery good for the wireless charging electric vehicles. IEEE Trans. Autom. Sci. Eng. 16(1), 486–497 (2019)
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5. Fang, Z.Y., Zhang, X., Yang, Q.X.: Asymmetric coupling mechanism of wireless powered high-speed train. Trans. China Electrotech. Soc. 32(18), 18–25 (2017). (in Chinese) 6. Hu, C.: Study on Energy Efficiency Characteristics and Optimization Method Of Electromagnetic Coupling Mechanism for Electric Vehicle Wireless Power Supply. Chongqing University (2015). (in Chinese) 7. Wu, X., Li, G., Zhou, J.: A lightweight secure management scheme for energy harvesting dynamic wireless charging system. IEEE Access 8, 224729–224740 (2020). https://doi.org/ 10.1109/ACCESS.2020.3044293 8. Ma, J.M., Yang, X.: Simulation of coupling mechanism of wireless energy transfer system for sorting robot. Electr. Meas. Instrum. 58(3), 87–91 (2021). (in Chinese) 9. Yang, X.: Study on the Topology of Radio Energy Transmission System for Sorting Robot. Hebei University of Technology (2020). (in Chinese) 10. Zaheer, A., Neath, M., Beh, H.Z.Z., Covic, G.A.: A dynamic EV charging system for slow moving traffic applications. IEEE Trans. Transport. Electr. 3(2), 354–369 (2017). https://doi. org/10.1109/TTE.2016.2628796 11. Liu, Y., Mai, R., Liu, D., et al.: Optimal load ratio control for dual-receiver dynamic wireless power transfer maintaining stable output voltage. IET Power Electron. 12(10), 2669–2677 (2019) 12. Li, C., Zhou, K.Z., Shi, Z.H.: Research on control method of dynamic wireless power transmission system with double pickup. Res. Power Syst. Prot. Control 48(21), 149–156 (2020). (in Chinese)
Analysis and Modeling of Response Characteristics Under Actual Rectifier Parameters in the Wireless Power Transfer System Binzhi Xie1 , Jinshuai Wang1 , Zhibin Lu2 , Wei Chen1 , and Qingbin Chen1(B) 1 College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, China
{chw,cqb}@fzu.edu.cn 2 State Grid Fujian Ultra High Voltage Company, Fuzhou , China
Abstract. Wireless power transfer is widely used due to its safety and convenience. The rectification circuit is an important part of the WPT system. Different rectification circuits and input parameters may lead to different responses and output gains in the actual applications. Usually, the fundamental harmonic analysis method is adopted to analyze the WPT system’s performance. However, this method cannot present the differences between different parameter applications. It is because only the fundamental harmonic is taken into consideration. In this paper, the influence of harmonics is studied. Moreover, the equivalent impedance model of the rectification circuits is built. It can take the input and rectification circuit parameters into consideration, which is quite different from the traditional method. Based on the equivalent impedance model of the rectification circuits, the response model of the WPT system can be analyzed. Finally, a WPT system is used for the validation. The key waveforms calculation results are almost the same as the measured results. It verifies the proposed method to be correct and useful. It provides a good basis for WPT system optimization. Keywords: Wireless power transfer · Rectification circuit · Fundamental harmonic analysis
1 Introduction With the continuous development of science and technology, the problem of energy and environmental pollution is becoming more and more serious. In other words, people’s demand for WPT technology is increasing [1–3]. The continuous update and development of various resonant compensation methods make the non-contact power transmission more widely used [4, 5]. The WPT technology needs the rectifier to obtain the DC power required by the load. However, the nonlinear characteristics of the rectifier circuit make the circuit analysis of the whole WPT system more troublesome [6]. Many articles exist for LLC resonant converter, LC and C filter rectifier circuit research using fundamental harmonic equivalence [7, 8]. We can also broaden the output voltage gain characteristics of the resonant © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 264–276, 2023. https://doi.org/10.1007/978-981-99-0631-4_28
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converter from the perspective of fundamental harmonic analysis [9]. However, in practical application, there are many limitations in the whole circuit: inverter circuit output voltage and input current of the rectifier circuit can make a big harmonic component, leading to the use of traditional fundamental equivalent will bring the serious error. Therefore, this paper analyzes the influence of the fundamental harmonic equivalence of the rectifier load based on the S/SP compensation WPT network, points out the impact of the filter parameters and the input voltage of the rectifier bridge on the fundamental harmonic equivalence of the rectifier load, and analyzes the influence of the output voltage gain and input phase Angle of the system when the traditional harmonic equivalence is impure resistance.
2 Fundamental Harmonic Equivalence Analysis Establish the basic topology of the wireless charging system, as shown in Fig. 1. S3
S1
Cp
Lpk
Lsk
Cs
1:1 A
Uin S2
B
Lm
S4
+
Cm
Lf
id
iref D1
D3
vref
+ vd
− D2
D4
−
+ Cf
Uo
−
Fig. 1. S/SP resonant WPT topology.
The square harmonic voltage output by the inverter circuit can be shown as: Uin 0 ≤ t ≤ T2 uAB (t) = −Uin T2 < t < T
(1)
Square harmonic voltage uAB Fourier decomposition: uAB (t) =
∞ k=odd
∞ 4Uin sin(kωt) uAB_k (t) = kp
(2)
k=odd
Fourier decomposition shows that the excitation of the WPT system is composed of the fundamental harmonic and odd harmonic superposition. Therefore, according to the superposition theorem of the circuit, the system characteristics under the fundamental harmonic and harmonic excitation are analyzed, respectively and then superposition is carried out. Different filtering and load parameters influence the S/SP WPT system under rectifier load. The mutual inductance model of the magnetic coupling mechanism is transformed into the equivalent leakage inductance model. This paper sets the equal variation ratio to 1, and resonance compensation for the equivalent leakage inductance is carried out, as shown in Eqs. (3). ⎧ 2 ⎧ ⎪ ⎪ ⎨ ω Lm Cm = 1 ⎨ Lm = M Lpk = Lp − M , ω2 Lpk Cp = 1 (3) ⎪ ⎪ ⎩ 2 ⎩ Lsk = Ls − M ω Lsk Cs = 1
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The original site of the transformer is converted to the secondary side to obtain the equivalent circuit; Assuming that the filter inductance and capacitance are large enough, the input current of the rectifier bridge is approximately square harmonic, and its input voltage is approximately sine harmonic, as shown in Fig. 2. Lf
io
RE_LC
ilc
Io
ilc
D1
D3 Cf
V1c D2
Ro
ωt
vo vlc
D4
ωt (a)
(b)
Fig. 2. Fundamental harmonic equivalent circuit under S/SP compensation for wireless charging: (a) Inductance filter circuit structure; (b) Voltage current harmonic form.
When carrying out fundamental harmonic equivalence, only the fundamental harmonic component i1c_1 of rectifier bridge input current i1c is considered: RE_LC =
v1c V1c sin(ωt) = = 4 i1c π I0 sin(ωt)
π 2 V0 4 π I0
=
π2 R0 8
(4)
The rectifier filter circuit of the system designed in this paper adopts an LC filter circuit, as shown in Fig. 2. LC filter rectifier load can be equivalent to Eq. (4), It will need to meet the output filter inductor L f rectifier, filter capacitor C f large enough for square harmonic input current, the load resistance of the bridge voltage V 0 remains unchanged, the input voltage of the rectifier bridge for ideal sinusoidal AC voltage, ignore the diode forward voltage drop and parasitic parameters. However, in the actual working situation, When the filter inductance L f is not large enough or the input of the rectifier bridge is not the ideal sinusoidal voltage, the equivalence of Eq. (4) for the rectifier load will cause errors. Therefore, this paper will analyze the influence of filter parameters L f and C f and load resistance RL on the system’s actual rectifier circuit.
3 Analysis of Rectifier Load Equivalence and Its Influence 3.1 Modeling Method Under Actual Rectifier Parameters Firstly, the rectifier bridge input is AC sinusoidal voltage with constant amplitude, and the inductance current is in a continuous working state, but the current irec is not an ideal square harmonic. That is, the inductance is not large enough. Its circuit model, voltage, and current harmonic form are shown in Fig. 3. According to the characteristics of continuous input current and diode rectifier, the output voltage V d of rectifier bridge is: ∞
Vd = |Vrec | = |Vrec sin(ωt)| =
4Vrec 2Vrec + cos(2nωt) π (1 − 4n2 )π n=1
(5)
Analysis and Modeling of Response Characteristics Under Actual Rectifier Lf
id irec
id
io
vrec
D1 D3 vd
Cf
Ro
267
irec
vo
o
D2 D4
ωt (b)
(a)
Fig. 3. The rectifier bridge input is sinusoidal voltage, but the filter inductance is not large enough: (a) LC filter circuit structure; (b) Voltage current harmonic form.
According to Eq. (5), the circuit after rectification can be equivalent to the circuit shown in Fig. 4. id
Lf
Vd _ 2 n
Vd _ 4 Vd _ 2
Cf
Ro
V0
Z2n
Vd _ 0
Fig. 4. Rectifier bridge output equivalent circuit.
Figure 4. Shows that the post-bridge impedance of the rectifier bridge under the DC component and all even harmonics is: ⎧ ⎨ Z0 = Ro (6) Ro ⎩ Z2n = j2nωLf + 1 + j2nωCf Ro According to Eqs. (5) and (6), the output current of the rectifier bridge, namely the inductance current id , is: ∞ ∞ 4Vrec vd_0 vd_2n 2Vrec Im(Z2n ) ] + = + cos 2nωt − arctan[ id = Z0 Z2n pRo (1 − 4n2 )p|Z2n | Re(Z2n ) n=1
n=1
(7) The Voltage V 0 of the Load Resistor R0 is: ⎧
ZRC ∞ Im( ) Z 4V 2V ⎪ rec rec RC Z 2n ⎪v = cos 2nωt + arctan[ ⎪ + ] ⎨ o ZRC π (1 − 4n2 )π Z2n Re( Z2n ) n=1 ⎪ ⎪ Ro ⎪ ⎩ ZRC = 1 + j2nωCf Ro
(8)
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According to Eq. (8), the filter inductance and load resistance values remain unchanged. The larger the value of filter capacitor Cf is, the smaller the mode of ZRC /Z2n is, and the smaller the ripple of load voltage V O is, effectively filtering out the high harmonics to ensure the smooth load voltage. Similarly, when Z RC is constant, the filter inductance increases. The mode of Z2n increases, the harmonic component on the filter inductance will increase, and the harmonic of the load resistance decreases, so the ripple is small. When the rectifier load works in the state of continuous current, the current on the output side of the rectifier bridge (DC side) is converted to the input side of the rectifier bridge (AC side): ⎧ ∞ ⎪ 2Vrec Vd_2n T ⎪ ⎪ + cos(2nωt − φ2n ) , 0 ≤ t ≤ ⎪ ⎪ |Z | π R 2 ⎪ o 2n ⎪ n=1 ⎪ ⎪ ⎨ ∞ Vd_2n T (9) irec = − 2Vrec − cos(2nωt − φ2n ) , < t < T ⎪ ⎪ |Z | π R 2 o 2n ⎪ ⎪ n=1 ⎪ ⎪ ⎪ ⎪ Im(Z2n ) ⎪ ⎩ φ2n = arctan[ ] Re(Z2n ) The current irec is decomposed by Fourier transform. The iac_0 component of irec is a square harmonic, and its Fourier decomposition is: iac_0
∞ 8Vrec = sin(kωt) kπ2 Ro
(10)
k=odd
The component iac_2n of current irec is a periodic function and satisfies the Dirichlet condition so that it can be expanded into a convergent Fourier series, namely: iac_2n = B0_2n +
∞
Bk_2n cos(kωt + ϕk_2n )
(11)
k=1
⎧ 1 T ⎪ ⎪ ⎪ B = iac_2n dt 0_2n ⎪ ⎪ T 0 ⎪ ⎪
⎪ ⎪ ⎨B 2 2 k_2n = ak_2n + bk_2n ⎪ ⎪ −bk_2n ⎪ ⎪ ϕk_2n = arctan( ) ⎪ ⎪ ak_2n ⎪ ⎪ ⎪ ⎩ Bk_2n ejϕk_2n = ak_2n − jbk_2n
(12)
The input side of the rectifier bridge is AC without a constant DC component, so it can be known that B0 _2n = 0. Then ak_2n and bk_2n are solved, which meet: 2 T iac_2n · e−jkωt dt (13) ak_2n − jbk_2n = T 0 where ω = T/2π, after calculation simplification: Vd_2n 2n sin(φ2n ) + jk cos(φ2n ) ak_2n − jbk_2n = · (1 − e−jkπ )2 · |Z2n | p(4n2 − k 2 )
(14)
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After simplifying Eq. (14), it can be seen that current iac_2n contains only odd harmonics as Eq. (15).
0, k = odd ak_2n − jbk_2n = (15) V [2n sin(φ2n )+jk cos(φ2n )] , k = odd 4 |Zd_2n · π(4n2 −k 2 ) 2n | Therefore, the complete time-domain expression of the input current irec of the rectifier bridge is shown in Eq. (16). ∞ ∞ 8Vrec irec = sin(kωt) + Bk_2n cos(kωt + ϕk_2n ) (16) kπ2 Ro n=1
k=odd
To better analyze the amplitude and initial phase of the fundamental harmonic and harmonic components of the rectifier bridge input current, the details of the same frequency in Eq. (16) are added to obtain: irec =
∞
Ak sin(kωt + αk )
(17)
k=odd
When the filter capacitor value is large and φ2n = π/2 then ϕ2n = 0, and Z 2n = jωL f can be obtained: ⎧ ⎪ ∞ ⎪ 8Vrec 16Vrec ⎪ ⎪ ( 2+( ⎪ A = ) Bk_2n )2 , Bk_2n = 2 k ⎪ 2 ⎪ kπ Ro π (1 − 4n2 )(4n2 − k 2 )ωLf ⎪ ⎨ n=1 (18) ∞ ⎪ ⎪ B k_2n ⎪ ⎪ ⎪ n=1 ⎪ ⎪ ⎪ αk = arctan( 8Vrec ) ⎩ kπ 2 Ro
According to Eq. (18), the amplitude of fundamental and harmonic harmonics of rectifier bridge input current under different filter inductors and the simulation results of the initial phase and Saber circuit are calculated through Mathcad, as shown in Table 1. When the filter inductor is large enough, the output of the rectifier bridge side under the harmonic component of the impedance Z 2n is enough and id of the DC component is small enough, approximate to constant DC, so that the input side of the rectifier bridge is an approximate square harmonic, the Fourier decomposition every initial harmonic phase along with the increase of filter inductance is gradually approaching to zero. The smaller the filter inductance is, the larger the initial phase α k is. The larger the phase difference between the excitation voltage of the rectifier bridge and the greater the fundamental harmonic of the input current. Now, the equivalent of the fundamental harmonic analysis of the rectifier load is no longer pure resistance. According to Eqs. (17) and (18), the equivalent impedance of rectifier load fundamental harmonic is converted into phasor form: ZE1 =
Vrec sin(ωt) ⇒ ZE1 = A1 [cos(α1 ) − jsin(α1 )] A1 sin(ωt + α1 )
(19)
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Table 1. Theoretical calculation and simulation comparison of rectifier bridge input current under different filter inductors. Current irec
200 μH
300 μH
500 μH
Filtering Inductance Lf
Fundamental harmonic
Three harmonics
Five harmonics
Amplitude (A)
IP (°)
Amplitude (A)
IP (°)
Amplitude (A)
IP (°)
The theoretical calculation
14.93
-9.24
5.05
13.07
2.977
7.92
Saber simulation
14.89
-9.13
5.03
13.50
2.97
8.67
The theoretical calculation
14.83
-6.19
4.97
8.79
2.96
5.30
Saber simulation
14.68
-6.30
4.92
8.74
2.93
5.12
The theoretical calculation
14.76
-2.66
4.93
3.79
2.95
2.28
Saber simulation
14.87
-2.60
4.95
4.00
2.97
2.50
According to Eq. (19), if the filter inductance is not large enough and the rectifier load is equivalent to the pure resistive load π 2 Ro /8, an error will gradually decrease as α 1 it approaches zero. Secondly, when the input of the rectifier bridge is not the AC sinusoidal voltage with constant amplitude but the voltage on the shunt capacitance C m , as shown in Fig. 5. But the filter inductance of the rectifier output is large enough. id s
Lf
io
irec2
irec2
D1
vCm
D3 vd
vCm D2
D4
(a)
Cf
Ro o
t
(b)
Fig. 5. Rectifier bridge input non-sinusoidal voltage but output filter inductance is large enough: (a)The rectifier bridge input is not an ideal sinusoidal voltage circuit structure; (b) Rectifier bridge input voltage current harmonic form.
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When the filter inductance is large enough, the input current irec of the rectifier bridge is approximately a square harmonic, and its Fourier decomposition is: irec2
∞ 4Io sin(kωt) = kπ
(20)
k=odd
According to the equivalent circuit Fig. 6. The harmonic part of current irec2 is circuited through capacitor C m and rectifier load by shunt isobaric shunt in parallel according to the impedance. Zp_k
Zs_k 1:1
Uab_1
Z_k
Lm
Cm
is
ip
Fig. 6. Equivalent circuit of the rectifier bridge under harmonic input current.
Since the harmonic component of the current irec2 mainly flows through the shunt capacitor C m , it can be known that the voltage on the capacitor C m is the fundamental harmonic component superimposed harmonic component. Due to the operational characteristics of the diode rectifier bridge, it is known that the input voltage and current of the rectifier bridge have the same zero crossing. Under the input current of the rectifier bridge is zero, the input voltage rectifier bridge V Cm (0) is zero. Due to the harmonic current through the capacitor C m to produce advanced input current rectifier bridge π /2 phase, the C m on the fundamental voltage input current passing zero will lag rectifier bridge certain Angle, assuming that the actual voltage on the capacitor C m lag Angle of the voltage on the C m is β m , The voltage V Cm on C m is: ∞ vCm (t) = UCm_1 sin(ωt + βm ) + k=3,5,···
4Io π sin(kωt + ) k 2 π ωCm 2
(21)
where U Cm_1 represents the fundamental voltage amplitude on C m . Since the filter inductor current works in a continuous state when the square harmonic current crosses zero, the voltage on C m must also cross zero, so we can get: vCm (0) = 0 ⇒ UCm_1 sin(βm ) =
∞ k=3,5,···
4Io 2 k π ωCm
=
4Io π 2 − 1) ( π ωCm 8
(22)
The influence of harmonic voltage on C m on the current output current Io is ignored so that it can be obtained by simplification: βm ≈ arcsin(
π2 − 8 ) π2 ωCm Ro
(23)
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The equivalent impedance of rectifier load fundamental harmonic is converted into phasor form: ZE2 =
vCm_1 (t) π 2 Ro ⇒ ZE2 ≈ 1 − j tan(βm ) irec2_1 (t) 8
(24)
It can be seen from Eq. (23) that β m is inversely proportional to the parallel capacitance C m . When the shunt capacitance C m is large, and the output filter inductance of the rectifier bridge is large enough, the error of the fundamental harmonic equivalent to π 2 Ro /8 of the rectifier load is small. When the shunt capacitance C m is large, but the output filter inductance of the rectifier bridge is not large enough, the error decreases with the increase of the filter inductance L f . 3.2 System Characteristics Under Actual Rectifier Parameters To analyze the difference between the fundamental harmonic equivalence of the rectifier load and that of the traditional purely resistive load when the filter inductance is not large enough or the input voltage is not ideal sinusoidal voltage, the fundamental harmonic equivalence of the rectifier load is denoted as Z E = RE + jX E .To simplify the analysis, assume RE that the real part of Z E is π 2 Ro /8, and compare the effects of different X E on output voltage gain and input phase Angle through Eqs. (19) and (24) and considering the impact of magnetic coupling coil resistance, as shown in Fig. 7. The Eq. (25) of output voltage gain and input phase is: ⎧ ⎧ ⎡ Z ⎤⎫ ⎨ ∞ ⎪ ⎬ Im ZRC ⎪ Z 4 V 2 ⎪ 2n 0 RC ⎪ ⎣ ⎦ ⎪ G cos 2nωt + arctan + = = ⎨ inr ⎭ Vrec π (1 − 4n2 ) Z2n ⎩ Re ZZRC n=1 2n ⎪ ⎪ ⎪ Im(Z2n ) ⎪ ⎪ ⎩ θinr= arctan Re(Z2n ) (25)
0.82
Traditional fundamental wave equivalent method
XE is positive Traditional value fundamental wave equivalent method
10
Ginr
θinr /°
0.8
XE =0 Ω XE = ±3 Ω XE = ±5 Ω XE = ±7 Ω
0.78
0.76
20
40
Ro /Ω (a)
60
0
80
XE =0 Ω XE = ±3 Ω XE = ±5 Ω XE = ±7 Ω
XE is negative value
-10 20
40
Ro /Ω
60
80
(b)
Fig. 7. Effect of the imaginary part on the equivalence of fundamental harmonic of rectifying load: (a) Output voltage gain; (b) The input phase angle.
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It can be seen from Fig. 7 that when the equivalent load of the rectifier bridge is impure resistive, the voltage gain on the load decreases. As the value of X E of the imaginary part increases, the output voltage gain decreases gradually, and the constant voltage characteristic deteriorates. It also affects the input phase Angle of the system. The effect trend of virtual X E on the input phase Angle is consistent with output voltage gain. Among them, the decrease of the output voltage gain because when three or more harmonic current and input current of the rectifier bridge phase difference is very small, and harmonic current is mainly through the shunt capacitance Cm , makes the harmonic current in the shunt capacitance harmonic voltage produced by the C m π /2 phase shift relative to harmonic current, including the actual voltage on the Cm and three times harmonic voltage diagram as shown in Fig. 8. Therefore, when the half-period rectifier bridge is on, the average harmonic voltage on the shunt capacitor C m is almost zero, and the fundamental harmonic AC impedance is no longer pure resistance, so the fundamental harmonic voltage cannot be completely rectified to the DC side. Therefore, the actual output voltage is smaller than the traditional equivalent analysis of the fundamental harmonic. irec vCm
vCm_1 vCm_3
o t
Fig. 8. Input voltage and current of the rectifier bridge.
4 Experimental Verification and Analysis A WPT system based on S/SP resonance compensation is established to verify the correctness of theoretical analysis, as shown in Fig. 9. Detailed component parameters are shown in Table 2. Under the condition of load resistance Ro = 35 , we will collect the harmonic form points of transmitting and receiving coil current and rectifier bridge input voltage and current tested by the prototype through an oscilloscope and redraw them in Mathcad and compare them with theoretical calculation harmonic forms to obtain the comparison harmonic forms as shown in Fig. 10 and Fig. 11. Figure 10 shows that the measured harmonic of the transmitting and receiving coils conform with the theoretical calculation, and it illustrates that the theoretical analysis is verified with the existence of the parallel capacitor C m before the rectifier bridge. The rectifier loads nonlinear harmonic current mainly by capacitance C m, and the rectifier loads form closed loops, which have little impact on the front-end circuit. As we can see from Fig. 11 (a), the input voltage of the rectifier bridge measurement and theoretical calculation of harmonic has a certain error. The main reason is the error of the theoretical
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Magnetically coupled structure
Receiving side circuit
Fig. 9. WPT system based on S/SP resonance compensation.
Table 2. Wireless charging system parameters parameter
Types and Values
Inverter circuit IGBT
IKW40N120H3
Rectifier circuit diode
DSEP30-12ADSEP30-12A
Output filter capacitance C f
Two 3uF /1200 V film capacitors in parallel
The resonant capacitance
C p = 220.7 nF, C s = 288.2 nF, C m = 86.7 nF
Loosely coupled transformer
L p = 243.3 uH, L s = 260.4 uH, M = 188.3 uH
20
40
prototype tes t
is(t) /A
ip(t) /A
theoretical calculation
0
0 prototype tes t theoretical calculation
-40
-20 0
12.5
t /μs (a)
25
0
12.5
t /μs
25
(b)
Fig. 10. Comparison of magnetic coupling coil current harmonic form between prototype test and theoretical calculation: (a) Transmitting coil current; (b) Receiving coil current.
estimate because the input voltage rectifier bridge is a sinusoidal wave which is based on the filter inductor is large enough, namely the input current of the rectifier bridge, as an ideal square harmonic, but from Fig. 11 (b) known as the input current of the rectifier bridge is not a perfect square harmonic. Therefore, there is a certain error in calculating the input voltage of the rectifier bridge, which will decrease gradually with the increase of the filter inductance L f and the load resistance R0. In the same way, we can see from Fig. 11 (b) that rectifier bridge measurement and theoretical calculation of input current harmonic form is an error. On
Analysis and Modeling of Response Characteristics Under Actual Rectifier 1
20
275
protptype tes t
irec(t) /A
vrec(t) /kV
theoretical calculation
0
0
prototype tes t
-1
theoretical calculation
0
12.5
t /μs (a)
25
-20
0
12.5
t /μs
25
(b)
Fig. 11. Comparison between prototype test and theoretical calculation of rectifier bridge input voltage and current harmonic form: (a) Rectifier bridge input voltage; (b) Rectifier bridge input current.
the one hand, because of input current for rectifier bridge calculation is based on the input voltage of sine voltage rectifier bridge, and from Fig. 11 (a) is due to the presence of harmonic voltage on capacitor C m to make input voltage of the rectifier bridge is not the ideal sine. On the other hand, because the filter inductance under DC bias inductance changes and the influence of the parasitic resistance, the error between the measured and theoretical calculation of rectifier bridge input current will decrease gradually with the increase of capacitance C m , that is, the harmonic voltage on C m drops, and the accurate inductance of filter inductor under practical operation is consistent with the theoretical calculation. It is shown that when the input of rectifier load is not ideal, sinusoidal voltage or filter inductance is not large enough, there will be errors between theoretical analysis and practice when using traditional fundamental harmonic equivalence.
5 Conclusions In this paper, based on the S/SP compensation network, the limitation of the traditional fundamental harmonic equivalence is revealed, and the equivalence of the rectifier load and its influence are analyzed. When the output filter inductance is not large enough, or the input of the rectifier bridge is not ideal sinusoidal voltage, the specific expression of the equivalence of the rectifier load is given. The imaginary part of the equivalent fundamental harmonic makes the output voltage gain smaller and affects the input phase Angle of the system. Finally, a WPT system is built to verify the theory’s correctness. Acknowledgments. This research was partially funded by the National Natural Science Foundation of China under Grant 51407032 and the Natural Science Foundation of Fujian Province of China under Grant 2019J01251.
References 1. Yawan, Z., Ying, Z., Yanfeng, T., Shufen, H.: Design of a radio energy transmission device. In: 2021 4th International Conference on Electron Devices and Mechanical Engineering (ICEDME), pp. 67–70 (2021)
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2. Xiong, M., Liu, D., Zhang, Z., Li, W.: Design and effect analysis of wireless energy transmission device for an electric vehicle. In: 2021 International Conference on Information Control: Electrical Engineering and Rail Transit (ICEERT), pp. 91–94 (2021) 3. Kim, H.-J., Hirayama, H., Kim, S., Han, K.-J., Zhang, R., Choi, J.-W.: Review of near-field wireless power and communication for biomedical applications. IEEE Access, 21264–21285 (2017) 4. Yang, J., Jiang, D., Zhang, Y., Qu, R.: Harmonic optimization method by SHEPWM for contactless power transfer system with seriesseries compensation. In: 2020 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 1540–1545 (2020) 5. Liu, Z., Wang, L., Guo, Y., Li, S.: Primary-side linear control for constant current/voltage charging of the wireless power transfer system based on the LCC-N compensation topology. IEEE Trans. Ind. Electron. 8895–8904 (2022) 6. Guo, Y., Zhang, Y., Bo, Q., Liu, Z, Meng, J., Wang, L.: Approximate linearization of rectifier load in wireless power transfer systems. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 74–78 (2020) 7. Shen, H., Jun, L., Zhongliang, X., Gang, T.: Research on full bridge LLC resonant converter. J. Electric Power 32(05), 382–391 (2017) 8. Shufan, L., Lifang, W., Yanjie, G., Li, J., Yuan, Y.: Optimization of t-type impedance matching network design method for wireless charging System based on rectifying load compensation. Trans. China Electrotech. Soci. 32(24), 9–16 (2017) 9. Lie, Z., Yunqing, P., Xinhao, L., Wenjie, F., Yu, D.: Parameter design method of CLLC Resonant converter for vehicle charger based on fundamental wave analysis method. Chin. J. Electr. Eng. 40(15), 4965–4977 (2020)
Metal Object Detection for Electric Vehicle Wireless Charging Based on Fusion of Spectral and Texture Features Zengpeng Zhou1 , Jindong Tian1 , Bo Liu2 , and Yong Tian1(B) 1 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060,
China [email protected] 2 CVC Technology Co., Ltd., Guangzhou 510300, China
Abstract. Metal object intrusion would reduce the efficiency and stability of a wireless power transfer system, and even leading to safety concerns. Most of existing methods for metal object detection suffer from blind spots and/or cannot detect wrapped metal objects. In this paper, a method that combines hyperspectral features and texture features is proposed. Hyperspectral reflectance density is introduced to describe the spectral characteristics of materials, and Tchebishef moment is employed to capture the texture features of foreign objects, which are then both used to construct a feature vector. A YOLO v5 neural network is built to distinguish typical wrapped metal objects, while a support vector machine model is trained to further detect non-wrapped metal objects by combining the spectral and texture features. Experimental results show that the proposed method can detect both wrapped and non-wrapped metal objects effectively. For the test datasets, the detection accuracy at target level reaches 100%. Keywords: Metal object detection · Hyperspectral reflectance density · Wireless power transfer · Tchebishef moment · YOLO v5
1 Introduction Wireless Power Transfer (WPT) has the advantages of non-contact, simple operation, charging safety etc., and it has been widely concerned in consumer electronics, household appliances, electric vehicles and other fields [1]. WPT technology mainly can be divided into three types [2]: electromagnetic radiation, electric field coupling and magnetic field coupling (MF-WPT). Among them, MF-WPT is featured as high transmission power and high efficiency, which currently is the primary choice for electric vehicle wireless charging. However, the impact of metal objects (MOs) on charging efficiency and safety impedes the commercialization and promotion of the MF-WPT technology in electric vehicle applications. Accordingly, a number of metal object detection (MOD) approaches have been proposed in recent years. Generally, MOD methods can be divided into three types [3]: system parameterbased methods [4], magnetic field-based methods [5, 6], and wave-based methods [7, © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 277–286, 2023. https://doi.org/10.1007/978-981-99-0631-4_29
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8]. System parameter-based methods determine the presence of MOs by detecting the change of WPT system parameters. Ref. [4] developed a model of mutual coupling between the MO and primary coil, and analyzed the effect of the MO on system parameters. Magnetic field-based methods detect the change of magnetic field via additional coils and circuits to determine whether MOs intruded into the WPT system. Ref. [6] proposed a double-layer symmetric sensing coil based on the symmetrical distribution of the magnetic field generated by the transmitting coil in both horizontal and vertical directions, reducing the blind area of detection. Wave-based methods realize foreign object detection (FOD) by deploying extra sensors, such as thermal imaging camera, hyperspectral camera, and radar sensor. Ref. [7] proposed a real-time FOD method based on thermal imaging cameras, which can detect MOs and living objects simultaneously. In summary, system parameter-based methods have simple structure and low cost, but they are not suitable for high-power systems. Although magnetic field-based methods are not limited by transmission power of the system, additional sensors are required. In addition, both system parameter-based and magnetic field-based methods are low sensitive to small MOs. In contrast, wave-based methods have the merits of high speed, wide detection range, high sensitivity, and independent of system power. Based on the fact that metal and nonmetal materials have different spectral characteristics, our previous study [9] proposed a MOD method based on hyperspectral imaging, which can detect very small MOs. However, this method still has two limitations. First, it may detect wrongly under inhomogeneous lighting conditions, including different light intensity illumination, shadow areas and different reflective areas of three-dimensional objects, and because of the similar hyperspectral features of some specific nonmetal and metal materials. Second, it cannot detect MOs wrapped completely by non-metallic materials, which are called wrapped MOs in this paper. Aiming at the above two problems, this paper proposes a MOD method based on the fusion of spectral information and texture features. The concept of hyperspectral reflectance density is proposed for describing the spectral characteristics, while the Tchebishef moment (TM) is utilized to capture texture features of an object. Considering that typical wrapped MOs have unique shapes, such as plastic-wrapped paper clips, a YOLO v5 neural network is designed for foreign object (FO) segmentation and wrapped MO detection based on shape information directly.
2 Proposed Method The proposed method mainly includes three steps: (1) Target segmentation. The hyperspectral image of the charging area is collected and three channels are selected to form a RGB image, which is then segmented into wrapped MO and FO by a YOLO v5 neural network. (2) Feature extraction. The hyperspectral reflectivity density and the TM feature vector in the FO region are extracted. The former is unique and used to characterize the spectral properties of the material, and the latter is constructed to describe the texture features. (3) Data fusion. A support vector machine is trained to further classify FOs into MOs and nonmetal objects (NMOs), and the result is combined with that obtained by the YOLO v5 network to achieve the final MOD results.
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2.1 Target Segmentation and Classification A YOLO v5 network shown in Fig. 1 is used to segment and classify the object areas. The YOLO v5 network contains convolution layer and pooling layer, which can reduce the size of the image. It employs the strategies of up-sampling and down-sampling to strengthen the ability of feature fusion, and to acquire image semantic information while learning spatial information of the target. In this study, the network outputs three sizes of pictures (19 × 19, 38 × 38, and 76 × 76) to adapt different sizes of FOs. The input of the YOLO v5 contains a Mosaic data enhancement that enables the network to capture the local shape of the target and to improve its robustness to partially deformed objects. With this network, wrapped MOs can be detected firstly according to shape and texture features. In addition, FOs, i.e., regions of interest (ROI), can be extracted, so that the system only needs to focus on the ROI sections rather than on the whole image, reducing the computation cost.
Fig. 1. YOLO v5 network for target detection.
2.2 Hyperspectral Feature Extraction At present, hyperspectral images and hyperspectral reflectance images are widely used for target classification [10, 11]. However, the former ignores the proportion difference of light intensity of different wavelength bands, while the latter ignores the impact of different reflection surface inclination angles of stereoscopic objects and the influence of shadow on hyperspectral reflectivity. To this end, the concept of hyperspectral reflectivity density is proposed to better describe spectral properties of the material. Here, the hyperspectral reflectivity refers to the ratio of reflected light intensity to incident light intensity, that is: r0 (λ, x, y) =
R(λ, x, y) I0 (λ, x, y)
(1)
where I 0 (λ, x, y) denotes the measured reflecting light intensity of a white board without FOs, which is taken as the incident light intensity; (x, y) is the pixel coordinates; λ is the wavelength, and R(λ, x, y) represents the reflected light intensity with FOs.
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Considering object occlusion and ineffective reflection, the actual incident light intensity of the charging area is expressed as I(λ, x, y). Besides, incoherent light sources are used in this study, so we have: a(x, y) =
I (λ, x, y) I0 (λ, x, y)
(2)
Combining Eqs. (1) and (2) yields: r(λ, x, y) =
1 r0 (λ, x, y) a(x, y)
(3)
Due to the measured data in practice is discrete, the ration of r(λ, x, y) to the total reflectivity can be formulated as: r(λ, x, y) = λ
r(λ, x, y) λ /λ k =1
r(λ0 + kλ, x, y)λ
= k0
r0 (λ, x, y) k0 k =1
(4)
r0 (λ0 + kλ, x, y)
where k 0 = λ /λ, and λ is a selected wavelength range used to limit the value of the density function in an appropriate range. Since the dark current of the hyperspectral camera can be measured in total darkness, Eq. (1) can be rewritten as: r0 (λ, x, y) =
R(λ, x, y) − B(λ, x, y) I0 (λ, x, y) − B(λ, x, y)
(5)
where B(λ, x, y) is a correction image obtained by fully covering the lens, which is a constant for representing the dark current of the camera.
Fig. 2. Hyperspectral curves: (a) R and RD curves of the background plate at different shadow levels; (b) RD curves of different materials.
MOs are likely covered with dust particles and other impurities, so a template of size 9 × 9 is used to filter the hyperspectral images. Figure 2(a) shows the reflectivity (R) and reflectivity density (RD) of the background plate under different degrees of shadow. It is evident that the reflectivity of the background plate varies significantly with the shadow change, while the reflectivity densities at different shadow are very similar to each other. Figure 2(b) shows examples of RD curves of several typical materials. It can be seen that with the increase in wavelength, RD curves of nonmetal materials exhibit obvious fluctuations, while that of the metal keeps an approximate increasing trend.
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2.3 Texture Feature Extraction For MOs and NMOs with similar colors, their hyperspectral RD curves may be also very close to each other as shown in Fig. 3(a), making it difficult for the SVM to distinguish them accurately. Although a hyperspectral camera with a wider wavelength range and more channels can improve discrimination ability, it increases hardware cost and computation complexity significantly. Ref. [12] proved that hyperspectral images can provide both spectral features and spatial features, and the model accuracy can be further improved by feature fusion. Therefore, this paper introduces texture features to enhance the discrimination of similarly-colored MOs and NMOs based on the fact that metal and nonmetal often have significant texture differences. Moments are able to extract specific geometric information of an image and have been widely used to describe global shape and texture features of an object. In this study, TM is employed. The definition and calculation of the (p, q)-order TM of an image f (x, y) with a size of N × N can be found in Ref. [13].
Fig. 3. Hyperspectral and texture features: (a) RD curves of similar color materials; (b) Image of Tchebishef basis function ϕ pq (x, y; 8).
Taking 0 ≤ p ≤ 4, 0 ≤ q ≤ 4, and N = 8 as an example, the corresponding basis functions ϕ pq (x, y; N) are visualized in Fig. 3(b). It can be seen that T 0q , T p0 , T pq (p = q), and T 00 represent the horizontal, vertical, uniform, and direct current features of the image, respectively. Then, a total of 25 moments, T 0q , T p0 , T pq , and T 00 (p, q = 0, 1, 2,…, 8), are selected to construct a feature vector T to capture the texture information of FOs: T = [T01 , T02 , ..., T08 , T10 , T20 , ..., T80 , T00 , T11 , ..., T88 ]
(6)
Generally, the texture of a FO is related to its material and manufacturing method. There are three commonly used metal texture types: brushed, bright and matte. Their T features are plotted in Fig. 4(a)-(c), where each curve denotes the T value of one image area with a size of 16 × 16 pixels. The reflection surface of a three-dimensional object has a certain inclination angle, making the light intensity of each surface inconsistent, and both strong and weak light will weaken the texture, so the images are processed by
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Fig. 4. Feature vector T of 60 samples: (a) brushed type (can); (b) bright type (coin); (c) matte type (U disk); (d) nonmetal (A4 paper).
histogram averaging to exclude the effect of uneven light intensity. For comparison, here A4 paper is taken as an example of nonmetal materials as shown in Fig. 4(d). It can be seen from Fig. 4 that the T curves of brushed metal exist obvious valleys at (T 03 , T 05 , T 07 ), and peaks at (T 04 , T 06 ), as shown in Fig. 4(a). After processing, the bright metal presents a blocky texture, so elements representing the uniformly distributed texture will increase, whereas the inclination of the moment distribution will decrease compared with the brushed metal, as shown in Fig. 4(b). The matte metal is granular and performs more flat in distribution of T values, as shown in Fig. 4(c). In addition, the nonmetal (A4 paper) exhibits the flattest distribution of T values, meaning that the weight of each T element is approximately equal to each other, as shown in Fig. 4(d). Moreover, since the histogram averaging operation eliminates the difference in light intensity, T 00 remains around 7.6 consistently regardless of the material. 2.4 Feature Fusion Because manual labelling is tedious and time-consuming, usually only small sample of hyperspectral images can be acquired. According to kernel techniques, SVM maps original data to a high-dimensional feature space through nonlinear transformation on a small sample dataset, and tries to find a linear classification hyperplane to maximize classification ability, so it is employed to classify FOs in this study. The fusion process of hyperspectral and texture features is shown in Fig. 5. The hyperspectral reflectivity density image is sampled every 16 pixels to obtain the reduced highspectral density blocks. The segmented RGB region block of the FO by the YOLO v5 network is converted into a grayscale image. Each grayscale image is cut to a series of parts with a size of 16 × 16 pixels, and then T is calculated for each part to get the texture block. Then, the T and the hyperspectral reflectivity density are fused through splicing to obtain the fused feature image of the FO region, and preliminary classification results for the FO regions are obtained using SVM for each pixel of the fused feature image. Finally, the classification results are scaled to the original size.
3 Experimental Results and Discussion 3.1 Experimental Configurations A hyperspectral camera, SHIS VNIR, was used in this paper. Its working distance is 800 mm, and minimum resolution distance is 0.1 mm. There are 51 hyperspectral bands
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Fig. 5. Fusion process of hyperspectral and texture features.
in total, and the sampling interval is 10 nm/band from 450–950 nm. The image size is 2448 × 2048 pixels. The FO samples were collected according to SAE J2954TM (2017, September Edition) standard [14], including 13 kinds of common MOs, such as paper clips, stacks, coins, beverage cans, and aluminium sheets, etc. Common FOs in daily life were also added in experiments, including MOs such as U disk, painted metal clip, etc., and NMOs such as wooden strips, plastic bottle caps, cloth, etc. 3.2 Target Segmentation and Classification Results Due to the high cost of hyperspectral image collection, 90 ordinary RGB images with the size of 1280 × 1280 × 3 and 10 RGB images with the size of 2448 × 2048 × 3 extracted from hyperspectral images were collected. Since the training of the YOLO v5 network only requires a number of RGB images rather than complete hyperspectral images, the ordinary RGB images taken by mobile phones were employed to assist network training, while RGB images extracted from the hyperspectral images were used for MOD verification. The dataset including 190 FO and 30 MO targets was labeled by labelImg software. FO means that it needs to be further classified through the SVM model, while MO refers to typical wrapped MOs (plastic-wrapped paper clip) with special shape at this stage. The YOLO v5 network was trained 500 rounds, and the batch size is 10. After the 400 rounds of training, the loss curve becomes stable, indicating that the network has reached the convergence state. RGB images extracted from hyperspectral images were tested by the trained model with a confidence threshold of 0.5, and the results are shown in Fig. 6. It can be seen that the FOs are located accurately and the plastic-wrapped paper clips are recognized as MO successfully. Particularly, even the plastic-wrapped paper clip is twisted, it still can be recognized. It is worth mentioning that the test of a scene on this platform only takes about 0.02 s.
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Fig. 6. Target segmentation and wrapped MO detection using YOLO v5 network.
3.3 Classification Results of SVM In this paper, Gaussian function is selected as the kernel function of SVM. By adjusting the penalty coefficient C and γ , an optimal SVM model can be obtained. To train the SVM model, 2000 pixel-level samples (MO pixels: 1000, NMO pixels: 1000) were manually labeled. Three cases, including only the hyperspectral reflectivity (Model 1), only the hyperspectral reflectivity density (Model 2), both the hyperspectral reflectance density and moment (Model 3) are taken as input feature of the SVM model are compared. The results in two scenes are shown in Fig. 7(a)-(c), where red and green represent MO and NMO pixels, respectively.
Fig. 7. Results of object classification: (a) Model 1; (b) Model 2; (c) Model 3; (d) Fusion.
Figure 7(a) indicates that if only the hyperspectral reflectivity is used, the shaded parts around the FOs will be misidentified as MO, while the metallic U disk is mostly misidentified as NMO. Figure 7(b) indicates that when the hyperspectral reflectivity density is employed, the shadow pixels around the FOs and the metal area of the U disk can be more accurately classified. However, the SVM model is easy to misjudge the paper as MO. Based on Fig. 7(c), it is evident that by fusing the hyperspectral reflectance
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density and moment features, the MOs and NMOs with similar color can be recognized clearly. 3.4 Fusion Results of MOD The final MOD detection at a target level in the charging area is obtained by combining the results of YOLO v5 and SVM models, as shown in Fig. 7(d). It is indicated that the proposed fusion method can deal with the “elastic” lighting environment, and recognize plastic-wrapped paper clips as metal objects according to shape characteristics, thus improving the reliability of MOD. To further verify the generalization ability of the proposed method, a hyperspectral image dataset of 60 FO regions was tested (MO: 32, NMO: 28), and the results are summarized in Table 1. Also, the method proposed outperforms the other two models, and achieves an accuracy of 100%. Table 1. Comparison of the three models. Model
Accuracy (%)
Precision (%)
Recall (%)
F1 score (%)
Model 1
83.33
78.13
89.28
83.33
Model 2
90
100
84.21
91.42
The proposed Model 3
100
100
100
100
4 Conclusion In this paper, a metal object detection method for an electric vehicle wireless charging system based on the fusion of spectral and texture features is proposed. Based on the RGB image extracted from the hyperspectral image, a YOLO v5 neural network is developed to recognize the plastic-wrapped paper clip which is taken as an example of wrapped metal objects, and to segment the foreign objects. A SVM model is designed to further classify the foreign objects into metal objects and nonmetal objects according to both spectral and texture features. Then, the SVM classification results and the YOLO v5 detection results are combined to achieve the final detection results. Experimental results show that the proposed method can detect typical wrapped metal objects, and can distinguish metal objects and nonmetal objects with similar colors. Acknowledgement. This work was supported by the Key Research and Development Program of Guangdong Province, China (No. 2020B0404030004).
References 1. Mahesh, A., Chokkalingam, B.: Inductive wireless power transfer charging for electric vehicles: a review. IEEE Access 9, 137667–137713 (2021)
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2. Sun, L., Ma, D., Tang, H.: A review of recent trends in wireless power transfer technology and its applications in electric vehicle wireless charging. Renew. Sustain. Energy Rev. 91, 490–503 (2018) 3. Zhang, Y., Yan, Z., Zhu, J.: A review of foreign object detection (FOD) for inductive power transfer systems. eTransportation 1, 100002 (2019) 4. Jafari, H., Moghaddami, M., Sarwat, A.I.: Foreign object detection in inductive charging systems based on primary side measurements. IEEE Trans. Ind. Appl. 55(6), 6466–6475 (2019) 5. Jeong, S.Y., Kwak, H.G., Jang, G.C.: Dual-purpose nonoverlapping coil sets as metal object and vehicle position detections for wireless stationary EV chargers. IEEE Trans. Power Electron. 33(9), 7387–7397 (2019) 6. Xiang, L., Zhu, Z., Tian, J., Tian, Y.: Foreign object detection in a wireless power transfer system using symmetrical coil sets. IEEE Access 7, 44622–44631 (2019) 7. Sonnenberg, T., Stevens, A., Dayerizadeh, A.: Combined foreign object detection and live object protection in wireless power transfer systems via real-time thermal camera analysis. In: IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1547–1552. IEEE, Anaheim (2019) 8. Liu, X.Y., Liu, C.H., Han, W.: Design and implementation of a multi-purpose TMR sensor matrix for wireless electric vehicle charging. IEEE Sens. J. 19(5), 1683–1692 (2019) 9. Tian, Y., Li, Z., Lin, Y.: Metal object detection for electric vehicle inductive power transfer systems based on hyperspectral imaging. Measurement 168, 108493 (2021) 10. Wang, Y., Wang, C., Dong, F.: Integrated spectral and textural features of hyperspectral imaging for prediction and visualization of stearic acid content in lamb meat. Anal. Methods 13(36), 4157–4168 (2021) 11. Armacheska, R., Chiang, J.Y.: Multi-input deep learning model with RGB and hyperspectral imaging for banana grading. Agriculture 11(8), 1–18 (2021) 12. Houari, Y., Duan, H,. Zhang, B.: Cross spectral-spatial convolutional network for hyperspectral image classification. In: International Conference on Intelligent Control and Information Processing (ICICIP), pp. 221–225. IEEE, Marrakesh (2019) 13. Li, L., Lin, W., Wang, X.: No-reference image blur assessment based on discrete orthogonal moments. IEEE Trans. Cybern. 46(1), 39–50 (2017) 14. Wireless power transfer for light-duty plug-in/electric vehicles and alignment methodology, document SAE J2954TM (2017)
Study on the Performance of a Novel High Lateral Displacement Receiver Coil Based on Cross-Winding Method Chang Liu, Jinhai Jiang(B) , Kai Song, Xiaoyan Li, Jianing Xu, and Chunbo Zhu The Harbin Institute of Technology, The Electrical Engineering, Harbin 150001, China [email protected]
Abstract. In the wireless charging system of electric vehicle, the coupling mechanism of single-layer coil is often difficult to achieve the required mutual inductance value under the limitation of coil size. The mutual inductance and power density can be significantly increased by using the stacked coil, but the interlayer voltage stress of the stacked coil restricts the design of the coupling mechanism. In order to solve these problems, this paper presents a new type of stack receiver coil design method with strong anti-migration ability. By equivalent single-turn circuit analysis and voltage stress calculation, the maximum inter-turn voltage is reduced by more than 25% and the inter-layer voltage is reduced by more than 75% compared with the traditional double-layer coil. The simulation results show that the effective magnetic flux area of the structure increases by about 13% compared with the traditional single-layer square coil and decreases by 25.56% compared with the traditional double-layer coil under the same turns, compared with the second traditional double-layer coil down 55.14% At the same time, through the optimization of the coil design, in the same case of mutual inductance, the average mutual inductance volatility of the system decreased by about 2% . Keywords: Dynamic radio energy transmission · New type of laminated coil · Turn-to-turn voltage · Anti-deflection ability
1 Introduction In recent years, with the rapid development of electric vehicles, dynamic wireless charging technology can greatly reduce the capacity of vehicle batteries, infrastructure does not occupy land resources, and charging experience is good [1], so it has become a research hotspot. In the dynamic wireless charging system, the coupling mechanism is the link for the wireless transmission of electric energy, and it is one of the most important parts of the system. The anti-offset ability, efficiency and power density of the system can be improved by the rational design of the coupling mechanism [2–4]. At present, the common structure of receiver is square coil [5]. The advantage of this kind of coil is that it is simple in structure and easy to be wound, but the problem is that the mutual inductance between the coils decreases obviously with the displacement of the coil, which leads to the decrease of the efficiency of energy transmission between the © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 287–298, 2023. https://doi.org/10.1007/978-981-99-0631-4_30
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coils [6]. A new type of receiver used in the field of dynamic radio energy transmission is proposed in reference [7]. The receiver can improve the anti-offset ability of the coil, but the structure of the coil is complex, and the winding of the coil becomes very difficult. A new coupling mechanism based on TMR sensor is proposed in reference [8]. The magnetic field generated by the transmitting coil is detected by the TMR Sensor Array, and the offset position of the coil is judged according to the detection result, according to this result, the position of the coil is adjusted to obtain good anti-offset ability. However, this scheme requires the system to achieve real-time response and high control difficulty. In the design of the coupling mechanism of the magnetic field coupled radio energy transmission system, due to the restriction of the coil size and air gap, it is difficult to get the mutual inductance value of the system with the single-layer winding coil. At the same time, when the single-layer coil is wound inward, it will increase the diminishing returns and overall loss, thus reducing the efficiency of energy transmission. The doublelayer Coil (first winding the first layer, then winding the second layer) can obtain a larger mutual inductance value under the limit of limited physical size. However, the resonance voltage of the traditional single-layer coil is relatively large, and this double-layer coil not only has the same layer of turn-to-turn voltage, but also has a relatively large voltage between the upper and the lower layers [9]. According to the literature [10], the relatively large voltage of the coil in the transformer may cause insulation breakdown, which is harmful to people and equipment, and in order to increase the insulation performance, this is similar to the case in WPT coils, where the need to increase the insulation thickness of the wire results in increased costs and so on. In order to solve the above problems, a new type of laminated coil is proposed in this paper, which is based on the traditional winding scheme of double-layer coil, compared with the single-layer square coil, the self-inductance and mutual inductance under the same coil size and turn number are increased, and the anti-offset ability of the system is improved Compared with the method of coil winding proposed in [7], the method is simpler, and the coupling mechanism does not require real-time response and is less difficult to control. Firstly, the anti-offset ability of single-coil and double-coil is compared by analyzing the effective flux area, secondly, the self-inductance of single-coil and the mutual inductance between the two coils are compared, finally, the anti-offset ability and interturn voltage of the traditional double-layer coil and the new stacked coil are verified by ANSYS Maxwell software.
2 Anti-migration Ability Analysis of Stacked Coil Mechanism In practical applications, the most common structures of the receiving coil (assuming that the core and the coil are of the same shape and size) are round and square; it has been shown in [11] that, compared with the circular coil with the same size and the same number of turns, the square coil has obvious advantages in self-inductance, coupling coefficient and anti-offset ability. Therefore, this section mainly analyzes the advantages and disadvantages of the two-layer square coil and the single-layer square coil which is the most widely used in anti-migration ability. According to the formulas (1) and (2), the greater the magnetic flux, the greater the self-inductance of the coil under the given current flowing through the coil. The flux is
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positively correlated with the effective area of the coil, which means that the larger the effective flux area of the coil, the stronger the anti-offset ability of the coil. φ =L×I
(1)
φ = B × S × cos α
(2)
The angle between the normal direction of the effective area s and the direction of the magnetic field intensity. Therefore, this section compares the effective magnetic flux area s of the single-layer square coil with that of the double-layer square coil to analyze the strength of their anti-offset ability. The effective flux area of a single-layer square coil is calculated by the following formula: S=
i=n
Si
(3)
i=1
where Si is the effective flux area per turn of the coil and N is the number of turns of the coil. The effective flux area of a two-layer square coil is calculated by the following formula: S =2×
i=n/2
Si
(4)
i=1
In practical application, because the size of the coil is limited by the size of the chassis, the length of the coil can’t exceed a certain value. This section assumes that the outermost side of both coils is 900 mm × 900 mm in length, that the coil gap is 30 mm, and that the double-layer coil gap is 30 mm. All coils have 8 turns. The effective magnetic flux area of the single-layer square coil and the double-layer square coil are shown in Figs. 1.
S1 S2 S3 S4 S5 S6 S7 S8
S1 S2 S3 S4
(a)Single Layer Coil
(b)Double layer coil
Fig. 1. Schematic diagram of effective flux area.
According to Fig. 1, the effective magnetic flux area of a single-layer square coil and a double-layer square coil are shown in Formula (5) and (6). Ss = S1 + S2 + S3 + S4 + S5 + S6 + S7 + S8
(5)
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Sd = (S1 + S2 + S3 + S4) × 2
(6)
According to Fig. 1, S d > S s . According to the formula (5), the effective flux area of the single-layer square coil is 5094000 mm2 . According to the formula (6), the effective flux area of the double-layer square coil is 5857200 mm2 , which is 13.03% higher than that of the single-layer square coil. Therefore, under the same size and turns, the doublelayer coil has greater self-inductance and mutual inductance. At the same time, when the coil center offset distance is the same, because the double-layer coil has a larger effective magnetic flux area, the magnetic field area is larger, its relative offset is smaller, thus has a stronger anti-offset ability. However, compared with single-layer coil, traditional double-layer coil has inter-layer voltage stress, which is much higher than the inter-turn voltage of the same layer coil.
3 Cross Wound Laminated Coil Structure Taking the double-layer coil as an example, this section analyzes the inter-turn voltage distribution of the traditional double-layer coil winding the first layer and then the second layer and the cross-winding of the first and second layers. For example, a traditional two-layer coil structure with 8 turns is shown in Fig. 2. There are two main types of traditional double-layer coils. The first and the second type of traditional double-layer coils are shown in Fig. 3.
Fig. 2. Structure diagram of traditional double-layer coil.
n+1
n+2
n+3
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n+n
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n+3
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Fig. 3. Conventional double-layer coil numbering diagram.
if the number of coil turns is 8, The structure of the new stacked coil and the coil number diagram are shown in Fig. 4.
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2
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2n-1
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(a) The structure of the new stacked coil
(b) the coil number diagram
Fig. 4. The structure of the new stacked coil and the coil number diagram
According to reference [12], the equivalent circuit diagram of motor windings is shown in Fig. 5(a). In the dynamic radio energy transmission system, the coil equivalent circuit structure of the coupling mechanism is similar to that of the motor windings. However, in the coupling mechanism, the resistance and capacitance of the coil have little influence on the turn-to-turn voltage, the equivalent circuit diagram of the coil is shown in Fig. 5(b). R1
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L3
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(a) The equivalent circuit diagram of motor windings L1
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8 U8
(b) The equivalent circuit diagram of the coil Fig. 5. The equivalent circuit diagram
In the coupling mechanism, each turn coil is connected in series, and there is mutual inductance between each turn coil and the other turns coil. The voltage calculation formula of each turn coil can be found in Formula (7). ⎤⎡ ⎤ ⎡ ⎤ ⎡ L1 M12 · · · M1n i1 u1 ⎢ u2 ⎥ ⎢ M21 L2 . . . M2n ⎥⎢ i2 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ (7) ⎢ . ⎥=⎢ . .. . . .. ⎥⎢ .. ⎥ ⎣ .. ⎦ ⎣ .. . . ⎦⎣ . ⎦ . un
Mn1 Mn2 · · · Ln
in
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Since the current flowing through the receiving coil is the same, the voltage of each turn of the coil depends on the mutual inductance between the coil and the other coils and the sum of its self-inductance. This section aims to compare the size of mutual inductance and self-inductance between coils horizontally. Therefore, the relative size of the core can be compared and analyzed without considering the magnetic field and skin effect produced by the core and the original coil. The magnetic field of a square coil can be calculated according to Biot-Savart law. = dB
μ0 Idl sin θ μ0 Idl × r = 3 4π r 4π r2 → er μ0 I dl × − = B 2 r L 4π
The magnetic field intensity B. Where a is the side length of a square coil.
√ √ x2 +y2 x2 +(a−y)2 μ0 + B = I4π xy x(a−y) √ √ 2 2y+ (a−x) +y2 + (a−x)y The self-inductance of the coil is calculated according to Formula (11). ¨ 1 L= = Bdxdy I I D
(8) (9)
(10)
(11)
The self-inductance calculation formula (12) of the square coil whose side length is far larger than the wire radius is obtained by the integral calculation. μ0 a a 2 ln − 1.614 (12) L= π r According to this formula, it is found that the self-inductance values of each turn coil are not much different. According to the reference [13], the mutual inductance calculation formula (13) of rectangular coil without magnetic core is obtained. ⎡ l1 + l1 l1 − l1 μ0 ⎣ M0 = + l1 + l1 ln l1 − l1 ln π 2 l22 − l22 − l1 − l1 2 l12 + l12 − l1 + l1 ⎡ √ √ l2 + l2 μ 0 ⎣ l2 − l2 ln −2l1 ln( 2 + 1) + 2 2l1 − 2 2 l12 + l12 + π 2 l22 − l22 − l2 − l2 ⎤ √ √ − l l 2 2 2 2 ⎦ + l2 + l2 ln − 2l2 ln( 2 + 1) + 2 2l2 − 2 2 l2 + l2 2 2 2 l2 + l2 − l 2 + l2 (13) Since the square coil is used in this paper, l1 = l 2 , l1 = l2 .
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According to this formula, the mutual inductance value of the same layer coil is not much different from that of the same layer coil, because the inter-turn distance is much smaller than the side length of the coil. According to reference [13], the mutual inductance between the upper and lower coils is approximately equal when the turn-toturn distances of the coils are approximately equal. According to the above analysis, it is found that the self-inductance between the coils is approximately equal, the mutual inductance between the coils in the same layer is approximately equal, and the mutual inductance between the coils in the upper and lower layers is approximately equal. Therefore, the sizes of L 1 -L 2n and U 1 -U 2n are approximately equal. The first kind of traditional double-layer coil under the same position of the upper and lower levels of the number difference N, the same position between the upper and lower levels of voltage is: Utx = Ux+1 + Ux+2 + . . . . . . + Ux+n
(14)
Utx ≈ nU1
(15)
U TX is the interlayer voltage at the X turn of the first layer coil, where X has a range of 1-n. The interturn voltage under the same layer is U X , where the value range of x is 2-2n. The value of the turn-to-turn voltage is approximately U 1 . The second traditional two-layer coil under the same position of the upper and lower layers of the coil number maximum difference of 2n -1, the maximum inter-layer voltage is: Utm = U2 + U3 + . . . . . . + U2n
(16)
Utm ≈ (2n − 1) U1
(17)
The inter-turn voltage under the same layer is the same as that of the first traditional double-layer coil. The difference of number between the upper layer and the lower layer is 1, the interlayer voltage is U X , and the value range of x is 1-n, which is about U 1 . The maximum inter-turn voltage of the adjacent turns under the same layer is (x is the coil number) Unm = max {Ux+1 + Ux+2 + Ux+3 } x = 1, 3, 5 . . . . . .
(18)
Unm ≈ 3U1
(19)
The voltage of the upper and lower layers of the new stacked coil is much smaller than that of the traditional double-layer coil, and the reduction is more than 75%. Although the turn-to-turn voltage between some coils on the same layer of the new stacked coil will increase, it is still less than the voltage between two layers of the traditional double-layer coil. As a result, the maximum turn-to-turn voltage of the coil is reduced by about 25%.
4 Verification of Inter-turn Voltage and Anti-migration Ability of New Laminated Coil In this section, Maxwell simulation is used to compare the inter-turn voltage between the traditional double-layer coil and the new stacked coil, and the anti-migration ability
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of the single-layer square coil and the new stacked coil, so as to verify the excellent characteristics of the new stacked coil. 4.1 Simulation and Verification of Traditional Double-Layer Coil Inter-turn Voltage and New-Type Laminated Coil Inter-turn Voltage The self-inductance and mutual inductance of each turn of the double-layer coil are obtained by Maxwell software. The parameters of the coil used in the simulation are shown in Table 1 and the simulation results are shown in Table 2. Table 1. Parameters of the coil used in the simulation. Double coil parameters
Value
Side length of the outermost coil
900 mm × 900 mm
Wire radius
6 mm
Same layer coil turn spacing
30 mm
Layer spacing
30 mm
Upper coil turns
4
Lower coil turns
4
Current at transmitter
900 A*turn
Current at the receiver
10 A
Receiver’s magnetic core size
1000 mm × 1000 mm
Thickness of magnetic core at receiver
20 mm
Distance between receiving core and receiving coil
6 mm
The distance between the upper part of the launch track core and the receiving coil
300 mm
Table 2. Distribution table of self-inductance and mutual inductance among traditional doublelayer coils. L ij /M ij
i=1
i=2
i=3
i=4
i=5
i=6
i=7
i=8
j=1
4.88
2.92
3.04
2.54
2.21
2.00
1.68
1.58
j=2
2.92
4.20
2.55
2.57
2.02
1.95
1.59
1.53
j=3
3.04
2.55
4.55
2.82
2.85
2.10
2.05
1.87
j=4
2.54
2.57
2.82
3.83
2.4
2.10
1.87
1.81
j=5
2.21
2.01
2.85
2.40
4.22
2.62
2.65
2.20
j=6
2.00
1.95
2.40
2.40
2.62
3.54
2.21
2.22 (continued)
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Table 2. (continued) L ij /M ij
i=1
i=2
i=3
i=4
i=5
i=6
i=7
i=8
j=7
1.68
1.59
2.05
1.87
2.65
2.21
4.00
2.35
j=8
1.58
1.53
1.87
1.81
2.2
2.22
2.35
3.36
The data units in Table 2 are all µH. The current of the receiving coil is 10 A, and the voltages of each turn coil are calculated according to the results obtained in Table 2. The results are shown in Table 3. Table 3. The simulation result of the voltage per turn of coil. Coil voltage per turn
Value/V
U1
208.45
U2
193.07
U3
221.31
U4
202.35
U5
211.67
U6
193.19
U7
184.04
U8
169.07
According to the simulation results, the voltage between the upper and lower turns of the first traditional double-layer coil at the same position is 828.4 V, 828.52 V, 791.25 V, 757.97 V, respectively, the voltage between the upper and lower turns of the traditional two-layer coil at the same position is 211.67 V, 607.21 V, 1012.56 V, 1374.7 V respectively. The voltages of the new stacked coil are 193.07 V, 202.35 V, 193.19 V and 169.07 V from outside to inside respectively. The maximum inter-turn voltages of the upper and lower coils at the same position are about 75%lower than those of the first traditional double-layer coil, that’s about 88%less than the second. The maximum turnto-turn voltage of the first conventional double-layer coil is 828.52 V, and the maximum turn-to-turn voltage of the second conventional double-layer coil is 1374.7 V, the maximum inter-turn voltage (including the inter-turn voltage of the same layer coil) of the new stacked coil is 616.73 V, which is 25.56% less than that of the traditional double-layer coil, compared with the second traditional double-layer coil down 55.14%. 4.2 Simulation of Anti-migration Ability of Stacked Coil The simulation parameters of square coil and stacked coil are shown in Table 4.
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Parameter name
Square coil value
Numerical value of stacked coil
Coil turns
8 turns
The upper 4 turns The lower 4 turns
Receive coil current
10 A
10 A
Length of receiving coil side Wire radius Coil turn spacing Coil layer spacing Side length of magnetic core Core thickness Distance between core and coil
900 mm 6 mm 30 mm 1000 mm 20 mm 6 mm
900 mm 6 mm 30 mm 30 mm 1000 mm 20 mm 6 mm
After verification core is not saturated, after simulation, when the coil center is at the position of x = y = 0, the simulation results of self-inductance and mutual inductance of the stacked coil are shown in Table 5. Table 5. Initial simulation results of stacked coil. Parameter
Value/µH
Self-inductance of transmitting coil
627.683
Mutual affection
36.596
Self-inductance of receiving coil
157.907
In order to keep the self-inductance of the square coil and the receiving coil of the new stacked coil as same as possible, after iteration, when the turn spacing is 30 mm, when the number of turns of the square coil is 10, the self-inductance of the receiving coil is 10 mm, the self-inductance of the receiving coil is 10 mm, the self-inductance of the receiving coil is 10 mm, the self-inductance of the receiving coil is 10 mm, the self-inductance of the receiving The self-inductance of the receiving coil is similar to that of the stacked coil, and the self-inductance of the transmitting end is the same as that of the transmitting end. The simulation results of the square coil center at the position of x = y = 0 are shown in Table 6. According to the simulation results, under the same self-inductance of the receiver, the new stacked coil structure has smaller coil turns and uses less wires. In order to ensure the reliability of the result, the center point of the coil is selected in the direction y of the vehicle, and the anti-offset ability is compared and analyzed at Y = 400 mm, Y = 600 mm, Y = 800 mm. Because of the symmetry of square coil and stack coil, the offset direction is X-axis forward, the offset range is 0–400 mm, and the step length is 50 mm. The mutual inductance change diagram of these three positions is shown in Fig. 6.
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Table 6. Initial simulation results of square coil. Parameter
Value/µH
Self-inductance of transmitting coil
618.275
Mutual affection
39.119
Self-inductance of receiving coil
131.335
6
Square coil mutual inductance Mutual inductance of stacked coils 30
Mutual inductance(µH)
Mutual inductance(µH)
Square coil mutual inductance Mutual inductance of stacked coils 5
4
3
25
20
15
0
200
0
400
200
400
Offset distance (mm)
Offset distance (mm)
(a) Y = 400mm
(b) Y=600mm Square coil mutual inductance Mutual inductance of stacked coils
Mutual inductance(µH)
40
30
20
0
200
400
Offset distance (mm)
(c) Y=800mm Fig. 6. The equivalent circuit diagram.
According to the above simulation results, under the above three conditions, with the coil migration, the mutual inductance volatility of the stacked coil is smaller than that of the square coil, and the descending speed of the mutual inductance of the stacked coil is slower. It can be proved that the stack coil has better anti-migration ability when the self-inductance is close.
5 Conclusion In order to meet the requirements of X-axis offset tolerance and low inter-turn voltage for the dynamic wireless charging system of electric vehicle (EV), a cross-wound
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cascaded receiving coil is proposed in this paper, compared with the traditional square coil, the stack coil has stronger anti-migration ability, higher self-inductance at the same size, higher mutual inductance at the same number of turns, and greater power output Compared with the traditional double-layer coil, the voltage between the upper and lower layers is decreased by more than 75%, and the maximum turn-to-turn voltage is decreased by nearly 25%, which reduces the possibility of insulation breakdown. Acknowledgments. This work was funded by the National Natural Science Foundation of China (52007038).
References 1. Jinhai, J.: Research on dynamic wireless power supply technology using bipolar original side guideway. Harbin Institute of Technology (2019). (in Chinese) 2. Jie, R.: Research on anti-offset technology and its optimal design of radio energy transmission system. Southwest Jiaotong University (2019). (in Chinese) 3. Song, J., Liu, M., Fu, M., Ma, C.: High power density stacked-coils based power receiver for MHz wireless power transfer. In: 2019 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 244–249 (2019) 4. Futagami, D., Sawahara, Y., Ishizaki, T., Awai, I.: Study on high efficiency WPT underseas. In: 2015 IEEE Wireless Power Transfer Conference (WPTC), pp. 1–4 (2015) 5. Al-Saadi, M., Valtchev, S., Romba, L., Gonçalves, J., Craciunescu, A.: Comparison of spiral and square coil configurations in wireless power transfer system for contactless battery charging. In: 2019 Electric Vehicles International Conference, pp. 1–5 (2019) 6. Shi, H., Li, W., Yin, A., Wu, S.C.: Research on coil parameter optimization and offset characteristics of wireless charging system. J. Hefei Univ. Technol. Sci. 44(09), 1179–1186 (2021). (in Chinese) 7. Chang, Y., Wu, F., Chen, R., Duan, Q.: Study on anti-migration characteristics of two-layer overlapping coils for IWPT system. Power Electron. 55(08), 36-38 (2021). (in Chinese) 8. Liu, X., Han, W., Liu, C., Pong, P.W.T.: Marker-free coil-misalignment detection approach using TMR sensor array for dynamic wireless charging of electric vehicles. IEEE Trans. Magn. 54(11), 1–5 (2018). Art no 9. Li, C.: Research on high efficiency wireless charging technology based on magnetic coupling string resonance. Anhui University of Technology (2018). (in Chinese) 10. Jiang, Y.: Study on electromagnetic safety of magnetic resonance type radio energy transmission device. Wuhan University (2016). (in Chinese) 11. Yang, Y., Kim, L., Shin, C.: Study on coupling coefficient of magnetic coupling coil in electric vehicle wireless charging system. Smart Power 48(08), 56–62 + 115 (2020). (in Chinese) 12. Dan, L., Guanfang, L., Yonghong, J., Xiaojie, C., Xiaoqiang, Z.: Characteristics of transient overvoltage distribution in the windings of inverter-fed motors. Acta Dalian Jiaotong Univ. 42(01), 107–111 (2021). (in Chinese) 13. Kuang, H.-J., Jia, L.: Calculation of mutual inductance and interaction force between coaxial rectangular current-carrying coils. J. China West Norm. Univ. Sci. 38(04), 426–429 (2017). 072.2017.04.014. (in Chinese)
Anti-misalignment Improvement for SS Compensated IPT System Using Reconfigurable Rectifier Yang Chen1 , Xiaofei Lyu2 , Yuhua Xiao3 , Xize Jiao3 , and Ruikun Mai1(B) 1 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China
{yangchen,mairk}@swjtu.edu.cn
2 NARI Technology Company, Ltd., Nanjing 211106, China
[email protected]
3 State Grid Jiangsu Electric Power Company, Ltd., Nanjing 210003, China
{xiaoyh,jiaoxz}@js.sgcc.com.cn
Abstract. The output of the inductive power transfer (IPT) system can be dramatically influenced by coupling variations, greatly limiting the absorbing feature of flexibility. One effective solution is to optimize the parameters of compensation topologies to improve misalignment tolerance ability. However, the expected coupling range is still insufficient. In this paper, an IPT system with a detuned series-series (SS) circuit using a reconfigurable rectifier is proposed that can tolerate a large coupling range with stable output power. Switching the mode of the RR between the full-bridge rectifier mode and the half-bridge rectifier mode can change the value of the equivalent ac load, thereby increasing the coupling variation range of the system. The proposed method eliminates the complex control scheme, dedicated coupling pad design, and complicated circuit. The experimental results demonstrate that when the coupling factor varies in the range of [0.1, 0.4], the fluctuation of the transferred power in the proposed method is not more than 17.5%. Keywords: Inductive power transfer · Reconfigurable rectifier · Misalignment tolerance
1 Introduction Inductive power transfer (IPT) has the advantages of convenience and flexibility which is broadly employed in consumer electronics, biomedical implants, and electric vehicles [1]. However, the coupling variation is always unfixed because the place of the secondary coil might be random, which can reduce the transferred power and the system’s efficiency. To keep relatively stable output power, prior efforts principally focus on the coupling pad design and compensation circuits. In that way, the inductive power transfer system is equipped with the immanent ability of offset tolerance. As for the coupling pad design, the basic purpose is to change the distribution of the magnetic field by arranging the coil to form a nearly constant magnetic field for the secondary coil, such as the unsymmetrical © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 299–307, 2023. https://doi.org/10.1007/978-981-99-0631-4_31
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coil, double-D coil, and coil array [2–4]. However, these methods always have strict requirements for the coupling pad design, and most methods have one specific direction without considering the misalignment versus three directions. Besides, a hybrid compensation topology can mitigate power fluctuation by combining two different topologies with specific coupling pads. The output characteristics against the misalignment of the two topologies are opposite so that the superimposed output keeps stable within a wide misalignment range [5]. For instance, the hybrid compensation topology can consist of the SS and LCC-LCC circuits [6], or S-LCC and LCC-S circuits [7]. Nevertheless, these approaches need numerous passive components, and the coupling pads should be specifically designed. Moreover, compensation circuits with parameter optimization also can realize relatively constant output power versus misalignment. Any special coupling pad design, extra coil, or complex circuit is not required. The current of the primary coil can be automatically adjusted to maintain the output power nearly constant within the excepted coupling variation range with the help of the parameter design [8]. In papers [8] and [9], parameter optimization for LCC-S, X-type, and SS topologies are introduced, and power fluctuation is less than 20% with a 2 or 2.5 times coupling variation. Nevertheless, the desired coupling variation ranges of the methods are too small to accept. In addition, if the coupling coefficient varies, the efficiency could decrease since the impedance matching condition is lost. It might be better if there was a straightforward approach that could enhance the anti-misalignment ability and efficiency simultaneously. In this article, a detuned SS circuit for an inductive power transfer system using a reconfigurable rectifier (RR) is proposed to resist a large coupling range while maintaining stable output power. The RR can work in an asymmetric half-bridge rectifier mode or a full-bridge rectifier mode. The value of the ac load is changed by the RR, thereby enlarging the coupling variation range of the inductive power transfer system with the detuned SS topology. When the anti-offset ability is improved, the efficiency is also partly enhanced at the same time since the equivalent ac load is altered to the value near the system’s optimal equivalent ac load. A 400-W prototype was constructed, and the experimental results demonstrated that the proposed approach can improve the allowable coupling variation range.
2 Theoretical Analysis 2.1 Analysis of Detuned SS Compensation Topology An equivalent SS-compensated IPT circuit is shown in Fig. 1, where U p (U s ) and I p (I s ) are the high-frequency input (output) voltage and current of the SS topology. L p (L s ) and C p (C s ) are the primary (secondary) coil and compensation capacitor. Rp (Rs ) and Rac are the internal resistance of the primary (secondary) circuit and equivalent ac load, respectively. The fundamental harmonic approximation is employed to analyze the system. According to Kirchhoff’s voltage law, the SS topology can be expressed by −jXM j XLp − XCp + Rp Up Ip (1) = 0 −jXM j XLs − XCs + Rs + Rac Is
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where
XLp = ωLp , XCp = XLs = ωLs , XCs =
1 ωCp , XM 1 ωCs , M =
= ωM k Lp Ls
301
(2)
ω and k are the angular frequency and the coupling coefficient.
Fig. 1. An equivalent IPT system with an SS circuit.
The secondary capacitor C s fully compensates for the secondary coil, and a detuning design is used on the primary side to improve the misalignment tolerance [9], i.e., XLs − XCs = 0, α = 1 −
XCp XLp
(3)
where α is called the ratio of detuning. Substituting (3) into (1), the transferred power of the topology is yielded, i.e., XLs XLp Rac Up2 k 2 Ps = , 2 (R + R )2 + X X k 2 + R (R + R ) 2 α 2 XLp s ac Lp Ls p s ac
(4)
which shows that we can regard the transferred power as a function of the coupling factor k, i.e., Ps (k). Set dPs (k)/dk as 0, and an inflection point k inflec can be obtained,
1/4 √ Rs + Rac α 2 XL2p + R2p kinflec = . (5) XLp XLs When k > k inflec , Ps ’(k) < 0, and when k < k inflec , Ps ’(k) > 0, thus the transferred power has a peak value Psmax when k = k inflec . Rac Up2 α 2 XL2p + R2p
Psmax = (6) 2(Rs + Rac ) Rp α 2 XL2p + R2p + R2p + α 2 XL2p
2.2 The Effect of Equivalent AC Load To analyze the effect of the equivalent ac load on the transferred power of the detuned SS topology, the new ac load Rac-n is used to replace the prior one, and the relationship is described as Rac - n = nRac
(7)
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where n ≥ 1. Then, the output power Ps-n is represented by Ps - n =
nRac XLp XLs Up2 k 2 2 α 2 XL2p (Rs + nRac )2 + XLp XLs k 2 + Rp (Rs + nRac )
(8)
Substituting (7) into (5) and (6), a new inflection point k inflec-n and corresponding maximum value Psmax-n are given as
1/4 Rs + nRac α 2 XL2p + R2p kinflec - n = XLp XLs nRac Up2 α 2 XL2p + R2p
Psmax - n = 2(Rs + nRac ) Rp α 2 XL2p + R2p + R2p + α 2 XL2p √
(9)
Further, the ratio of k inflec-n to k inflec , and the ratio of Psmax-n to Psmax are defined as RAk and RAP , respectively, i.e.,
n−1 kinflec - n (10) RAk = = 1+ kinflec RARs - ac + 1 RAP =
Psmx - n n−1 =1+ Psmx n/RARs - ac + 1
(11)
where RARs-ac is the ratio of Rs to Rac . According to (10), when the equivalent ac load Rac increases, the new inflection point k inflec-n will get larger. It indicates that the fresh power vs coupling curve (P-k curve) shifts to the right region of the previous one. Based on (11), we can find that when Rac increases, the peak output power Psmax-n will become larger, which means the maximum value of the new Ps-n - k curve is bigger than that of the previous Ps - k curve. Figure 2 depicts the two curves, in which k min and k max are the minima and maximum of the allowable coupling factor variation range.
Fig. 2. The curves of the detuned series-series circuit with various equivalent ac loads.
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In Fig. 2, there is an intersection at k cross between the two curves, and it is acquired by setting Ps-n = Ps , i.e.,
nR2ac α 2 XL2p + R2p − α 2 R2s XL2p − Rp Rs kcross = (12) XLp XLs By substituting (12) into (4) or (8), the transferred power Pcross is derived, Pcross = Ps (kcross ) = Ps - n (kcross ) = Ps (kmin ) = Ps - n (kmax )
(13)
According to Fig. 2, if we properly design the circuit parameters, the proposed approach can work at the roof of the power-coupling curves. The volatility of the output power is nearly stable resisting a large misalignment range. The detuned SS-compensated IPT system is equipped with two curves’ small fluctuation parts when the ac load is changed from Rac to Rac-n .
3 Implementation of Ac Load Change 3.1 Structure of the Reconfigurable Rectifier Figure 3 illustrates the SS topology with a RR. Compared with the traditional full-bridge rectifier, the rectifier diode D4 can be substituted by a low-frequency switch Q5 . The proposed IPT system has two configurable structures. If the switch Q5 is kept in the OFF state, a full-bridge rectifier is formed, and the corresponding equivalent ac load Rac-f equals (8/π2 )Rdc . If the switch Q5 is turned OFF, an asymmetrical half-bridge rectifier occurs, and the equivalent ac load satisfies the condition of Rac-h = (2/π2 )Rdc . It
Fig. 3. (a) The SS topology with a RR. (b) Full-bridge rectifier on the secondary side. (c) Halfbridge rectifier on the secondary side.
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demonstrates that keeping the state of the switch Q5 ON or OFF can flexibly change the equivalent ac load to a large or small value. The relationship between the two ac loads is Rac - f = 4Rac - h
(14)
which means n is equal to 4 in this part. Therefore, based on the conclusion from Sect. 2-part A we can obtain that if the coupling coefficient k belongs to the range of [k min , k cross ], the asymmetrical half-bridge rectifier is active. If the coupling factor increases and the full-bridge rectifier works once the coupling satisfies [k cross , k max ]. 3.2 Analysis of the Efficiency The ac-ac efficiency of the IPT system is obtained as η=
XLs XLp Rac k 2 (Rac + Rs ) Rp Rs + XLp XLs k 2 + Rp Rac
(15)
When the equivalent ac load Rac reaches an optimal value Rac-opt , the efficiency can be the maximum value, and the corresponding optimal equivalent ac load is shown as
Rs Rac - opt = Rs Rp + XLs XLp k 2 (16) Rp Assuming that the two coils are almost the same, thereby Rp ≈ Rs . Usually, the internal resistances of the coils are minimal, so Rs · Rp is tiny, and we ignore it. Equation (16) is rewritten as Rac - opt ≈ k XLs XLp (17) On the base of (17), it can be concluded that if the coupling factor varies while the equivalent ac load is constant, the IPT system will miss the impedance matching condition. The efficiency will decrease significantly versus an extensive coupling range. Nevertheless, changing the load on the ac side to get closer to the optimal value obtains a higher ac-ac efficiency [10]. Thus, when the IPT system works in the full-bridge rectifier mode, Rac-f is designed as Rac - f ≈ kmax XLs XLp (18)
4 Experimental Results In order to verify the viability of the proposed concept, a 400-W system was built, and corresponding experimental parameters are listed in Table 1.
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Table 1. IPT system specification and parameter values. Symbol
Value
Symbol
Value
E Lp
120 V
f
250 kHz
38.16 μH
Ls
37.63 μH
Cp
13.05 nF
Cs
10.62 nF
k min
0.1
k cross
0.2
k max
0.4
Rdc
30
Figure 4 presents the experimental waveforms with different couplings, and the corresponding dc load is Rdc = 30 . The experimental waveforms indicate that the inductive input impedance can be obtained. The current I s is almost doubled to keep the power constant with the half-bridge rectifier operation because when the structure of the RR is altered from the full-bridge operation to the half-bridge operation, the voltage U s is halved. Up [CH1]
Ip [CH2]
Up [CH1]
Us [CH3]
(a)
Is [CH4]
Ip [CH2]
Us [CH3]
(b)
Is [CH4]
Fig. 4. Experimental waveforms under the condition of R = 30 : (a) half-bridge rectifier mode @ k = 0.15 and (b) full-bridge rectifier mode @ k = 0.29.
The proposed system’s transferred power and efficiency (dc-dc) against different couplings are depicted in Fig. 5. The rectifier is dormant so that half-bridge operation can be realized when the coupling factor varies from 0.1 to 0.2. The peak of transferred power can reach 393 W, and the minimum drops to 330 W. The rectifier is activated into full-bridge operation when the coupling coefficient changes from 0.2 to 0.4. The peak and minimum values of power are around 400 W and 330 W. The variation of the transferred power using the proposed approach is calculated as (400–330)/400 = 17.5%. However, if only the half-bridge operation (or full-bridge operation) operates with the coupling varying from 0.1 to 0.4, the fluctuation of the power is 71.7% (or 75.5%). The proposed method can significantly enhance the capacity of the offset tolerance. Figure 5(b) shows the efficiency, which under the mode of the hall-bridge rectifier is [87.5%, 92.4%] when the coupling factor varies from 0.1 to 0.2, while the efficiency with the full-bridge rectifier mode is [68.6%, 90.2%]. The efficiency is improved by 19.2% when the coupling is 0.1. Similarly, the efficiency under the mode of the full-bridge rectifier is [90.2%, 95.6%] when the coupling factor varies from 0.2 to 0.4, while the efficiency of the hall-bridge rectifier mode is [91.9%, 92.0%]. The efficiency is improved
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by 3.6% when the coupling is 0.4. Therefore, the introduced method can also enhance the efficiency of the detuned SS-compensated IPT system with misalignment, especially in the low coupling condition.
Fig. 5. The measured results in different coupling. (a) The transferred power. (b) the system’s efficiency.
5 Conclusion This paper proposes a detuned SS compensation topology adopting a RR to improve the ability of offset tolerance. It revealed that the stable transferred power of the detuned SS circuit could be maintained near the peak of the P-k curve with a restricted coupling variation range. Another P-k curve can be obtained for the detuned system if the load on the ac side is altered. With the help of these two curves, this paper achieves steady transferred power against a large coupling range utilizing a RR that can convert the equivalent ac load by switching between the full-bridge mode and half-bridge of the rectifier. When the coupling factor varies in the range of [0.1, 0.4], the variation of the power is not more than 17.5%, whereas that of the full-bridge or hall-bridge mode is greater than 70%. The experimental results prove that the proposed method can realize a good performance of offset tolerance. Generally, this approach focuses on small power scenarios demanding strong flexibility while the dc load is fixed.
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Acknowledgments. This work was supported by the Science and Technology Project of State Grid Corporation of China, “Research and Application of Safety Protection and Fault Early Warning Technologies for Shore Power System in Inland Port” (5400-202140167A-0-0-00).
References 1. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019) 2. Yao, Y., Wang, Y., Liu, X., et al.: A novel unsymmetrical coupling structure based on concentrated magnetic flux for high-misalignment IPT applications. IEEE Trans. Power Electron. 34(4), 3110–3123 (2019) 3. Song, K., et al.: Design of DD coil with high misalignment tolerance and low EMF emissions for wireless electric vehicle charging systems. IEEE Trans. Power Electron. 35(9), 9034–9045 (2020) 4. Joffe, C., Ditze, S., Rosskopf, A.: A novel positioning tolerant inductive power transfer system. In: 2013 3rd International Electric Drives Production Conference, pp. 1–7. IEEE, Nuremberg (2013) 5. Qu, X., Yao, Y., Wang, D., et al.: A family of hybrid IPT topologies with near load-independent output and high tolerance to pad misalignment. IEEE Trans. Power Electron. 35(7), 6867– 6877 (2020) 6. Zhao, L., Thrimawithana, D.J., Madawala, U.K.: Hybrid bidirectional wireless EV charging system tolerant to pad misalignment. IEEE Trans. Ind. Electron. 64(9), 7079–7086 (2017) 7. Chen, Y., Yang, B., Zhou, X., et al.: A hybrid inductive power transfer system with misalignment tolerance using Quadruple-D quadrature pads. IEEE Trans. Power Electron. 35(6), 6039–6049 (2020) 8. Feng, H., Dayerizadeh, A., Lukic, S.M.: A coupling-insensitive X-Type IPT system for high position tolerance. IEEE Trans. Ind. Electron. 68(8), 6917–6926 (2021) 9. Feng, H., Cai, T., Duan, S., et al.: A dual-side-detuned series-series compensated resonant converter for wide charging region in a wireless power transfer system. IEEE Trans. Ind. Electron. 65(3), 2177–2188 (2018) 10. Chen, S., Chen, Y., Li, H., et al.: An operation mode selection method of dual-side bridge converters for efficiency optimization in inductive power transfer. IEEE Trans. Power Electron. 35(10), 9992–9997 (2020)
Design and Icing Analysis of a Novel Magnetic Coupling Mechanism for WPT System on High-Voltage Transmission Lines Shuyu Shen, Linlin Tan(B) , Zhijun Wu, Heqi Xu, Tian Gao, and Xueliang Huang School of Electrical Engineering, Southeast University, Nanjing 210096, China [email protected]
Abstract. With the continuous progress of wireless power transfer (WPT) technology in the field of high-voltage (HV), this paper proposes a novel magnetic coupling mechanism fixed on the metal fittings at both ends of 500 kV insulator, which can further enhance the coupling between coils to provide stable electric energy for the online monitoring equipment on the HV tower. Firstly, suitable topological structure and coil parameters are selected for WPT system with long distance and small load. Then, the circular mesh magnetic coupling mechanism that acts as a fixed support is designed, and the finite element model is established. According to the simulation results, factors such as mutual inductance and volume are comprehensively analyzed to optimize the framework and ensure that it has no adverse effect on the original HV system. Finally, in order to prove its applicability, the performance of the designed coupling mechanism is analyzed under harsh environment of ice coating. It can be proved that the mechanism proposed is valid for WPT system on HV transmission lines, and several points for attention in monitoring and repairing HV system are offered. Keywords: Wireless power transfer (WPT) · Magnetic coupling mechanism · High-voltage insulator · Ice coating
1 Introduction As the steadily growing of economy and society, the safe operation of 500 kV highvoltage (HV) towers and transmission lines has become the essential link to ensure power transmission. Therefore, it is necessary to install online monitoring equipment to timely feedback the status information of transmission lines and prevent the occurrence of catastrophic accidents in advance. However, the traditional battery power supply must be frequently checked and replaced, and the new energy supply mode such as solar energy and wind energy is unreliable due to the constraints of natural conditions [1, 2]. At present, the development and application of current transformer (CT) energy extraction technology has been quite mature, which can collect stable and reliable energy from transmission lines [3]. Therefore, electrical energy of a given power can be obtained directly from the surrounding electric field environment through a special CT coil. After frequency conversion, the high frequency electromagnetic energy is transmitted from © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 308–322, 2023. https://doi.org/10.1007/978-981-99-0631-4_32
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the HV terminal to the low-voltage terminal across the insulation distance by means of magnetic coupling resonant wireless power transfer (MCRWPT) technology. Then it can be converted to supply the online monitoring equipment through rectification and voltage regulation. The system structure is shown in Fig. 1.
Fig. 1. WPT system for high voltage monitoring equipment.
A few pioneering researches have been involved in the application of wireless power transfer (WPT) technology for monitoring equipment on power towers over the last decade. Some scholars embedded resonant coils in insulators [4]. In [5], coil resonators were embedded inside totally sealed insulation sheds to form the new insulation string structure. The efficiency exceeded 60% for a transmission distance of 1.1m when 25 W power is transmitted. On this basis, a series of PCB resonators was embedded in the insulator sheds to transmit energy, and the feasibility was verified by a 110 kV composite insulator, whose maximum transmission efficiency was 11% [6]. Although these domino transmission structures can ensure HV insulating property, it is not conducive to be widespread promoted on account of the poor compatibility with the commercially available insulation strings. In addition, the damage of internal electronic devices is difficult to be noticed in time during maintenance, which brings hidden trouble to the stable operation of HV system. Another idea is to install the couplers outside the insulator. A barrel-shaped highpermeability material layer was added at a 110 kV insulator string to constrain the magnetic field distribution. The measured receiving power at 1.5 m distance was 16.7 W with a transfer efficiency around 15%, but the fixation of coils and layers were not mentioned [7]. After separating the elongated transmitter coil into two windings to improve the flux regulation flexibility, the efficiency reached 22.53% with 1.85 m distance, but an accurate position and angle is required of the coils [8]. It can be concluded that most of the studies are focused on the 110 kV voltage grade, whose insulation distance is less than 2 m. Whereas the WPT system proposed in this paper is applied in 500 kV HV environment with a distance of 5m, which means there will be a large leakage between the coils, causing the low transmission efficiency.
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Generally, in the long-distance WPT system, ferrite cores with high permeability should be added around the coupling coil to reduce the leakage inductance and improve the mutual inductance of the system, but how to fix the coupling mechanism at both ends of the insulator is ignored frequently in the above papers. Therefore, in view of the WPT system is applied to the tower at high altitude, the fixing mode and the balance of the magnetic core must be taken into consideration when designing the core. To sum up, in order to improve the power supply mode of online monitoring equipment on 500 kV towers, it is necessary to design a novel magnetic coupling mechanism for WPT system across insulation distance, which can improve mutual inductance while playing a role of fixation. In addition, performance tests are carried out to study the variation rule of electric field under different icing conditions, and analyze whether it can still meet the requirements of safe operation in the actual scene. The realization of this system will deliver stable electric energy for the online monitoring equipment on HV towers to strengthen the operation monitoring of transmission lines, and promote the development of smart grid.
2 Design of Magnetic Coupling Mechanism 2.1 Topological Analysis In the field of power supply for HV online monitoring equipment, overcoming the insulation distance is one of the ticklish problems that must be considered emphatically. The safe insulation distance of 500 kV power transmission lines is 3.878 m, and the length of commonly used 500 kV insulators is above 4 m. Considering the compatibility of different insulators, the transmission distance of the WPT system designed in this paper is 5 m. MCRWPT technology has the characteristics of wide transmission range and high power grade, which is suitable for wireless charging scenarios on HV transmission lines [9]. The intelligent monitoring equipment on the HV tower usually has a small internal resistance of about 10 ohms during normal charging process. For such a small load system, LCC-S resonant topology can achieve higher transmission power and effectively improve the dynamic capability of input voltage and current, as shown in Fig. 2 [10].
Fig. 2. Equivalent circuit of WPT system with LCC-S topology.
The equivalent power supply voltage vector U S flows through the LCC compensation network composed of L 0 , C 1 and C 0 , and transmits energy to the receiving coil L 2 in the form of high frequency electromagnetic field through the transmitting coil L 1 . The Stype series compensation network consisting of L 2 and C 2 at the receiving end transmits
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electrical energy to the load resistor RL . In the Fig. 2, R0, R1 and R2 are parasitic internal resistance of each inductor, and M represents mutual inductance between coils. 2.2 Selection of Coil Parameters It is worth noting that the MCRWPT system is a nonlinear multi-parameter crossinfluenced coupling system, and its transmission distance, output power, efficiency and other performance are easily affected by parameter offset. Therefore, it is significant to comprehensively consider the design indexes of the coupling coils to optimize the system transmission performance. First of all, in order to achieve relatively strong coupling performance and higher freedom of coil winding, vertical solenoid coils are selected for both transmitting and receiving terminals, located at both ends of the insulator, as shown in Fig. 3. The diameter of the transmitting and receiving coils is d and D respectively. The number of turns in both coils is N, whose height h = 10 cm, and the transmission distance L = 5 m.
Fig. 3. WPT system design diagram.
Next, an optimization analysis will be performed for the coil diameter and number of turns. According to coil design experience, the appropriate value range of parameters N, D and d is selected. When 20 ≤ N ≤ 50, the mutual inductance variation trend of coils with different sizes is obtained by finite element simulation. It can be concluded from Fig. 4 that: • In each coil scheme, M increases as N increases; • When D is the same, mutual inductance at d = 1.0 m is greater than that at d = 0.8 m; • When d is the same, the bigger D is, the bigger M will be. The above laws are consistent with the Neumann’s formula. However, when the number of turns and the diameter of the coils are too large, the inter-turn voltage also rises sharply. For example, when d = 1.0 m and N = 45 are determined, the interturn voltage is 1869 V when D = 1.2 m, while it increases to about 2.4 times when
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Fig. 4. Inductance variation of coils with different sizes and turns.
D = 1.4 m [11]. At the same time, in order to control the volume and weight of the coupling mechanism, to ensure that the coil will not be damaged by strong stress in the HV environment. Finally, the diameter of transmitting coil d = 1.0 m, the diameter of receiving coil D = 1.2 m, and the number of turns of two coils N = 45 are determined. 2.3 Design of the Magnetic Core Structure In the long-distance WPT system, a ferromagnetic material layer is suggested to be added between the coil and the insulator, because the magnetic effect of this material can be used to optimize the flux distribution, effectively constrain the magnetic field in the energy transfer region, and thus enhance coupling between the coils. At the same time, it plays the role of isolating the high-frequency magnetic field of the WPT system and the insulator string. In addition, since the system is applied in high altitude, the fixing method of coupling mechanism must be considered in the design. Construction of Finite Element Model. On account of the advantages of light weight, high tensile strength, and excellent anti-pollution flashover performance, 500 kV composite insulators are selected as the research object in this paper and the finite element model is built. The coils of the selected size are located at the fittings at both ends, as shown in Fig. 5. In the simulation analysis of this paper, the relative permittivity εr and electrical conductivity ρ of the main materials in the field are shown in Table 1 [12]. Selection of Magnetic Core Structure. In order to enhance the magnetic field coupling in the energy transfer region, the principle of increasing the reluctance in the self-coupling region is adopted to design a variety of magnetic core structures which can fix the coils at the metal fittings, including solid columnar core, upper and lower hollow disk core, bottom hollow lid core and annular mesh core. Their height is h, and the thickness is the same everywhere. the inner side is fixed on the insulator fittings, and the
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Fig. 5. Finite element model before adding core structure. Table 1. Main material properties. Material
Shed
Mandrel
Air
Core
Coil
Ice
Water film
εr
3
4.4
1
12
1
70
81
ρ/(s•m−1)
1 × 10–15
1 × 10–12
0.01
5.8107
1 × 10–6
0.03
0
outer side is close to the inner wall of the coil, as shown in Table 2. Wherein, the annular mesh magnetic core includes concentric rings and support frames. the concentric ring structure takes the center of the section of the insulator fitting as the center of the ring, and the distances between the rings are equal, which are equally spaced. the number of concentric rings is P (P ≥ 2). The support frame structure is evenly distributed in radiation, connecting the innermost and outermost magnetic core rings, and the number of which is Q. The annular reticulated cores in Table 2 take P = 6 as an example to compare the situation when Q = 6 and 12. In the Table 2, L t and L r are the inductance of transmitter and receiver respectively, k is the coupling coefficient, and V means the sum of volumes of core structures. It is found that when the volume of magnetic core is larger, the mutual inductance M of the coils is higher, and the values of L t , L r and k in the system are also improved, but this means the increase of the core weight and material cost. Therefore, S = M/V is taken as the reference index to represent the mutual inductance value generated by the magnetic core per unit volume. After calculation, it is found that S is relatively the largest when the annular mesh core structure with Q = 6 is used, indicating that the coil mutual inductance is high and the magnetic core volume is small at this time, which means the utilization rate of magnetic core is optimal. In addition, this hollowed-out design is not conducive to accumulation of water, snow and dirt, which is suitable for the application of WPT system across HV insulator. Optimization of Magnetic Core Structure. After determining the annular mesh core structure with Q = 6, the value of P also needs to be optimized. In order to find out the
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Colum
Disc
Lid
Annular mesh, P=6 Q=6 Q=12
Model
M/μH
4.1802
3.4303
3.5794
3.852
3.8898
Lt/μH
6383.7
5949.7
6064.1
6150.7
6169.5
Lr/μH
7868
7409.8
7527.6
7646.6
7657.6
k/10-4
5.8983
5.1663
5.2978
5.6169
5.6592
V/m
3
0.1876316 0.0128138 0.0128138 0.0137516 0.0166588
S/10-4
0.22279
2.6770
2.7934
2.8011
2.3350
Table 3. Simulation results with different P. P
2
3
4
5
6
7
8
9
10
11
M/μH
3.576
3.631
3.721
3.791
3.852
3.899
3.942
3.975
4.002
4.025
Lt/μH
6022
6045
6084
6118
6151
6180
6204
6224
6238
6253
Model
Lr/μH
7500
7523
7565
7606
7647
7675
7702
7727
7749
7766
k/10-4
5.322
5.384
5.484
5.557
5.617
5.662
5.703
5.732
5.756
5.776
influence rule of P value on system performance, finite element simulations are carried out for the magnetic core structure with 2 ≤ P ≤ 11 respectively, and the data in Table 3 is obtained. It can be seen that with the increase of P, the self-induction, M and k of the coils have been continuously rising. When P = 11, the coupling effect of the system is optimal, but the volume of the magnetic core is too large, which limits the application.
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It is easy to know that the volume of the annular mesh core increases in approximately equal proportion to P, so the difference between the mutual inductance values of the P ring and the (P-1) ring is calculated to obtain the differential mutual inductance (DM) at each P value, as shown in Fig. 6.
DMP = MP − MP−1 (3 ≤ P ≤ 11)
(1)
Fig. 6. M and DM of coils with different P.
The analysis shows that DM reaches the largest when P = 4, indicating that the M increases the fastest when the increase value of core volume is approximately the same, and the core weight and manufacturing cost are relatively low. Considering all aspects, it is suitable for application in HV engineering. Furthermore, the verification of the WPT system with transmission distance of 4m across the insulator also shows that the circular mesh magnetic core with four rings and six support frames has the best comprehensive effect. Therefore, the magnetic core structure has a certain universality in enhancing mutual inductance and can be applied to coils of various sizes. Verification of Insulating Property. After designing the novel coupling mechanism that can be fixed at both ends of the insulator, it is also necessary to verify whether the addition of the WPT system will destroy the insulation performance of the 500 kV insulator, and even interference the safe operation of the HV transmission lines. the comparison of electric field intensity and voltage distribution around insulator string before and after WPT system installation was obtained through finite element simulation, which are important references for HV insulating property [13]. The cloud image of y-z section is shown in Fig. 7. In the simulation, the effective operating voltage that HV transmission lines acts on the composite insulator is the amplitude of the phase voltage, so the voltage at the HV terminal is set as 408.2 kV. The low-voltage terminal is earthed, and its potential is set to 0 kV. In Fig. 7(a), the comparison is apparent that with the installation of the coupling mechanism, the electric field is concentrated around the insulator and the distant field
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Fig. 7. Cloud image with or without coupling mechanism.
strength is gradually diminished. At this point, the mutual inductance of WPT system is greatly improved by 48.24%. Whereas the voltage distribution is almost unchanged. It can be inferred that the WPT system improves the transmission performance without damaging the insulating property.
3 Application Analysis of Icing Performance 3.1 Calculation Principle of Iced Insulator 500 kV HV towers are mainly located in high altitude and cold regions, so the insulator sheds are often covered with ice, which leads to significant decline in both mechanical and electrical properties of insulators, and even flashover phenomenon, resulting in safety accidents [14, 15]. In order to verify the reliability of the proposed coupling mechanism under HV environment, the icing performance of the WPT system using this mechanism is analyzed below. There are various ice coating states, and its variables include ice thickness, icicle length, and icing type. Therefore, it is significant to analyze the potential distribution at the tip of insulator sheds under various ice coating conditions to determine whether the insulator performance meets the requirements of safe operation at this time.
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It is one of the common methods to solve the electric field of iced insulator by using complex number domain. This method uses the complex permittivity instead of the permittivity, namely ρ + jωε is used to replace ε in Laplace’s equation or Poisson’s equation, and converts the potential into a complex vector to solve, which is relatively simple and practical. In this paper, a two-dimensional axisymmetric model of iced insulator is established, and the potential distribution in this field satisfies the following: 1 ∂ ∂ϕ ∂ ∂ϕ + ρ =0 (2) (ρ + jωε) r ∂r ∂r ∂z ∂z The potential on the boundary between the HV terminal and the ground terminal is ϕ|l = f0 (p)
(3)
The potential on the axis of symmetry is ∂ϕ =0 ∂r The potential at the boundary of two dielectric materials is ⎧ ⎨ ϕ1 = ϕ2 ⎩ (ρ1 + jωε) ∂ϕ1 = (ρ2 + jωε) ∂ϕ2 ∂n ∂n
(4)
(5)
The potential at the model boundary is ∂ϕ + f1 (p)ϕ = f2 (p) ∂n
(6)
Among them, ϕ is potential, r and z represent the position in the column coordinates, ε and ρ are the permittivity and conductivity of the medium respectively, ω is the angular frequency of the power supply. On the basis of finite element method, the field distribution equation can be expressed as
⎧ 1 1 2 2 ⎪ ⎪ F(ϕ) = f d + ϕ − f ϕ d + jωε)(∇ϕ) + jωε) (ρ (ρ 1 2 ⎪ ⎪ 2 2 ⎪ =L1 ⎨ δF(ϕ) = 0 (7) ⎪ ⎪ ⎪ ϕ|l = f0 (p) ⎪ ⎪ ⎩ 0 ϕ|ab = 0 Based on the above calculation, this section uses finite element simulation software to explore the influence of icicle length and water film thickness on the electric field around the insulator. 3.2 Influence of Icicle Length In the freezing period, the surface of insulator sheds will be covered with ice of different thickness, especially its length will have a great influence on the surface potential
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distribution of insulator. The distance between the adjacent large umbrella skirts in the model is 90 mm, so the thickness of the ice coating on the upper surface is set to 10 mm, while the ice thickness on the lower surface is ignored. The icicle length T hanging from the tip of each shed is 0 mm, 15 mm, 30 mm, 45 mm, 60 mm and 75 mm in turn. To facilitate comparative analysis, only one side of the large sheds were covered with ice. The variation curve of its surface voltage U il and electric field intensity E il are obtained by simulation. Among them, the HV side bears the highest voltage and field strength, which is usually the beginning of the arc, so its changing trend is obvious and representative. Therefore, taking the first eight iced sheds near the HV side as an example, the influence law can be analyzed more clearly, as shown by the black line l in Fig. 8(a), and the voltage and field strength changes on l are shown in Fig. 8 (b), (c).
(a)The model of iced insulator
(b) Surface voltage Uil
(c) Electric field intensity Eil
Fig. 8. Simulation analysis of iced insulators with different T.
It is shown in Fig. 8 that with the continuous increase of T, the air gap between the ice edges decreases synchronously. Simultaneously, the decline rate of U il accelerates, while the peak value of E il rises rapidly and becomes more and more unevenly distributed. When 0mm ≤ T ≤ 60 mm, the distortion trend and increasing speed of E il are relatively slow. However, when T reaches 75 mm, E il rapidly reaches the maximum value of 7.82 × 106 V/m at the upper gap of the shed closest to the HV side, increasing by 257.57% compared with T = 60 mm. At this time, the minimum gap between the two icicles is only less than 3mm, where the voltage drop is extremely large. Through simulation data, E il of the first two air gaps close to the HV side exceeds the breakdown field strength of air (E air = 3 × 106 V/m), and the probability of flashover is greatly increased in this case, resulting in power safety accidents. This conclusion can also be visually verified by comparing the E il distributions around the icicles at T = 15 mm and 75 mm (as shown in Fig. 9). Therefore, if the insulator with the WPT system is applied in extremely cold regions, the icing situation should be monitored in real time. In particular, when the air gap between the icicles is less than 20 mm, maintenance and deicing must be carried out timely to guarantee the security and stability during the system operation. In addition to the electric field index, the mutual inductance value and coupling coefficient are obtained through the magnetic field simulation in order to ensure that the
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(b) T=75mm
Fig. 9. Electric field intensity distribution diagram.
icing state will not affect the normal operation of the WPT system, which are listed in Table 4. Table 4. WPT system parameters with different T. T /mm
Ice-free
0
15
30
45
60
75
M/µH
3.7205
3.7184
3.7153
3.7164
3.6907
3.7156
3.6695
L t /µH
6083.7
6080.5
6083.0
6081.8
6079.7
6081.1
6065.2
L r /µH
7564.6
7566.4
7553.1
7552.8
7438.8
7558.4
7622.1
k/10–4
5.4843
5.4821
5.4811
5.4834
5.4881
5.4805
5.3969
Although the M under the icing condition decreased slightly, it only descended by 1.27% at most. Similarly, k is reduced by only 1.58% at most, both at T = 75 mm. It illustrates that the icing influence on the transmission performance of proposed WPT system is negligible. 3.3 Influence of Water Film Thickness During the ice-melting period, due to the increase of ambient temperature and the effect of surface leakage current [16], the ice layer on the surface of the insulator begins to melt, forming a continuous water film. According to the operation experience, most insulators experience ice flash in the melting period. In order to further study the impact of water film thickness on the insulation and transmission performance of the system, an iced insulator model with an ice-covered thickness of 10mm and an icicle length of 60 mm is built on the upper surface of the large shed. The thickness of water film under natural conditions is generally less than 2 mm, so different thickness water film of 0 mm, 1 mm and 2 mm is added to the outer side of the ice. The variation curves of the electric field intensity E wf on l with the water film thickness t are shown in Fig. 10.
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(a)The model of iced insulator with water film
(b) Electric field intensity Ewf
Fig. 10. Simulation analysis of iced insulators with different t.
With the increase of water film thickness t, E wf at the each air gap between icicles also keeps rising. The highest point of the three curves, E wf, t=0,1,2 (max), are marked in the Fig. 10, which does not exceed E air . The highest field strength at t = 1 is 2.43 × 106 V/m, and the value at t = 2 becomes 2.81 × 106 V/m, which are 9.95% and 27.15% higher than that without water film, respectively. According to Table 1, the conductivity of the water film is much higher than that of ice and air, which makes the insulator surface show resistance and capacitance. The voltage drop in air gap is larger than that of dry ice, resulting in more uneven distribution of surrounding electric field and further increase of electric field distortion. Therefore, during the melting period of iced insulators, monitoring efforts and timely maintenance should be strengthened.
4 Conclusion In order to improve the performance of the WPT system across 500 kV insulator that supplies power for online monitoring equipment on HV tower, this paper designs a novel magnetic coupling mechanism that can be fixed on the metal fittings at both ends of the insulator, which can increase the coupling inductance while fixing the position of the coils. Then through the simulation and taking ice coating as an example, its validity and applicability are proved. The following conclusions can be drawn: 1. The MCRWPT system with LCC-S topology structure is used to analyze the mutual inductance variation trend obtained by finite element simulation, and the transmitting coil and receiving coil with the diameter of 1.0 m and 1.2 m are selected, respectively, with the number of turns being 45, considering the inter-turn voltage, volume weight and other factors; 2. Through the comprehensive analysis of mutual inductance and volume factors, an annular mesh magnetic core structure containing six support frames and four concentric rings is designed to fix the coils on both ends of the insulator, which is verified that the electric field is more concentrated without damaging the insulating property of HV transmission lines;
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3. In the icing state, it is obtained that in practical application, the mechanism proposed can reach a satisfying performance. And when the length of air gap between icicles is less than 2 cm or in the melting period, the monitoring and timely maintenance should be strengthened to ensure the security and stability of HV system. However, the size of the transmitting and receiving coil designed in this paper is relatively large. In the subsequent research, the size of the coils can be decreased by adding relay coils and more system experiments need to be conducted. Acknowledgments. Acknowledgments. This research is supported by the National Natural Science Foundation of China under Grant 51877036 and Southeast University’s Zhishan Young Scholar Support Program.
References 1. Xiao, Y., Guan, Y., Wang, Y., Xu, D.: Design and optimization of self-compensating multirelay wireless power transmission system with metal flanges. In: 2021 24th International Conference on Electrical Machines and Systems (ICEMS), pp. 716–721. IEEE, Gyeongju (2021) 2. Huang, M., Tang, N., Sheng, C., Lu, Q.: Zeng J: Composite Insulator Energy Transmission Structure for Power Supply of Intelligent Monitoring Instruments. High Voltage Engineering 46(2), 618–625 (2020) 3. Zhao, X., Keutel, T., Baldauf, M., Kanoun, O.: Energy harvesting for a wireless-monitoring system of overhead high-voltage power lines. IET Gener. Transm. Distrib. 7(2), 101–107 (2013) 4. Huang, Z., Zou, J., Wang, Y., Wang, L.: Application research of wireless power transmission technology in high-voltage equipment based on relay coil. Trans. China Electrotech. Soc. 30(11), 45–52 (2015). (in Chinese) 5. Zhang, C., Lin, D., Tang, N., Hui, S.: A novel electric insulation string structure with highvoltage insulation and wireless power transfer capabilities. IEEE Trans. Power Electron. 33(1), 87–96 (2018) 6. Qu, J., He, L., Tang, N., Lee, C.: Wireless power transfer using domino-resonator for 110-kV power grid online monitoring equipment. IEEE Trans. Power Electron. 35(11), 11380–11390 (2020) 7. Cai, C., Wang, J., Liu, R., Fang, Z., Zhang, P., et al.: Resonant wireless charging system design for 110-kv high-voltage transmission line monitoring equipment 66(5), 4118–4129 (2019) 8. Cai, C., Wang, J., Wang, L., Yuan, Z., Tang, N., et al.: Improved coplanar couplers based wpt systems for adaptive energy harvesting on power towers. IEEE Trans. Electromagn. Compat. 63(3), 922–934 (2021) 9. Huang, X., Wang, W., Tan, L.: Technical progress and application development of magnetic coupling resonant wireless power transfer. Autom. Electric Power Syst. 41(2), 2–14+144 (2017). (in Chinese) 10. S. Sasikumar, K. Deepa.: Comparative Study of LCL-S and LCC-S Topology of Wireless EV charging System. In: 2019 Innovations in Power and Advanced Computing Technologies (i-PACT), pp. 1–6. IEEE, Vellore (2019) 11. Song, H., Wang, Y., Liu, X., Wang, H., Han, X., et al.: Study on design and optimal control of long-distance wireless power supply system based on high-voltage lines. In: 2021 3rd International Conference on Electrical Engineering and Control Technologies (CEECT), pp. 114–120. IEEE, Macau (2021)
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12. Yang, Z., Jiang, X., Huang, Y., Hu, J., Han, X.: Influence of electric field on the ice-coating process of insulators with a different dielectric surface. IET Sci. Meas. Technol. 14(5), 585– 592 (2020) 13. Al-Gheilani, A., Rowe, W., Li, Y., Wong, K.L.: Stress control methods on a high voltage insulator: A review. In: 1st International Conference on Energy and Power (ICEP), pp. 95–100. Melbourne (2017) 14. Shu, L., Liu, Y., Jiang, X., Hu, Q., Zhou, L.: Analysis on the DC Discharge Path of Ice-Covered Disc Type Suspension Insulators under Natural Conditions. Trans. China Electrotech. Soc. 36(8), 1726–1733 (2022). (in Chinese) 15. Li, Y., Zhang, X., Jia, Z., Zhou, P., Sun, L., Liu, S.: Characteristic analysis of leakage current of insulator strings under different icing types. Power Syst. Technol. 41(11), 3691–3697 (2017). (in Chinese) 16. Li, W., Hao, Y., Xiong, G., Zhao, Y., Luo, B.: Simulation and analysis of potential distribution of iced composite insulator based on finite element method. Trans. China Electrotech. Soc. 27(12), 29–35 (2012). (in Chinese)
Research on Maximizing the Communication Capacity of OFDM-Based Simultaneous Wireless Transmission of Power and Information (SWTPI) Li Ji(B) , Kaixin Yan, and Xudong Cao College of Information Science and Engineering, China University of Petroleum, Beijing, China [email protected]
Abstract. Simultaneous wireless transmission of power and information (SWTPI) is an important research direction in the field of wireless energy transfer systems. In this paper, a two-channel transmission model with a single coil and multiple carriers is established by coupling a two-way information transmission communication channel into a wireless energy transmission system, and the impedance of each part in the transmission model and the channel gain during transmission are derived. To maximize the communication capacity of information transmission, orthogonal frequency division multiplexing (OFDM) is used to orthogonally decompose the information carrier, and the optimization problem of maximizing the communication capacity is established based on the water injection method. To solve this nonconvex problem, an algorithm based on alternating iterations of successive convex approximations and the Lagrangian pairwise method are proposed in this paper, and the optimal solution of this problem is finally found. Keywords: Simultaneous wireless transmission of power and information (SWTPI) · Channel capacity · Water injection theorem · Information transmission
1 Introduction Wireless power transmission (WPT) has received a lot of attention because of its advantages of efficiency, flexibility and reliability compared with traditional somewhat electrical power transmission, and the technology has been applied in many fields, such as electric vehicles, cell phones, implantable biomedical devices, wireless sensors, etc. In these applications, information and energy are usually required to be transmitted simultaneously to achieve their functions. So in recent years, simultaneous wireless transmission of power and information (SWTPI) has been extensively studied. There are four main ways to achieve simultaneous transmission of information and energy in WPT systems. The first one is to use radio frequency (RF) links for wireless communication in WPT systems [1-3], such as Bluetooth, ZigBee and Wi-Fi technologies for forward or backward information transmission in WPT systems. However, there © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 323–330, 2023. https://doi.org/10.1007/978-981-99-0631-4_33
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is an additional cost and low reliability. The second one is to add a set of induction coils for information transmission [4-9]. However, multiple links through two channels will generate additional magnetic interference, and strong power carriers can severely interfere with information signals and reduce the signal-to-noise ratio of the communication. The third one is the single carrier single channel for energy and information transmission [10-14], where the inherent inductive link used for power transmission is used as the transmission of information, however, the technique of using a single carrier for energy and information transmission can only be implemented in low power energy transmission systems. In response to the above, the fourth method of single-channel multi-carrier information and energy synchronous transmission is being widely studied. In this method, the information carrier and the energy carrier are transmitted synchronously through a shared channel, and since the information carrier frequency is usually higher than the power transmission frequency and no additional coils are required, this method is characterized by small equipment size, low cost and stable energy transmission. In the literature [15-17] proposes the use of frequency division multiplexing (FSK) techniques for information reception and transmission. A synchronous demodulation scheme based on ASK modulation is proposed in [18] to separate the forward and backward transmitted information by a Schmitt trigger. From the above studies, it can be seen that most of the current studies mainly focus on solving the problem of interference immunity of communication channels, lacking the analysis of the problem of maximizing the capacity of information transmission channels. In the literature [19], the use of the water injection method was proposed to achieve a trade-off between information transmission frequency and energy transmission frequency, but the article did not analyze the complete transmission system and the use of a single carrier single channel for transmission is not applicable to high-power energy transmission. To address the problems, this paper proposes an optimization method for maximizing the capacity of single coil multi-carrier mode energy-carrying communication in the face of multiple objectives. The information transmission carrier is partitioned into several subcarriers by OFDM method, and the optimization problem of maximizing the channel capacity is established based on the water injection method. The LCC topology is used in the topology as shown in Fig. 1 below to reduce the interference of the information transmission channel to the energy transmission channel.
2 Information Transmission Analysis This paper proposes an OFDM (orthogonal frequency division multiplexing) based information transmission method, which can ensure the information transmission channel system has a high signal-to-noise ratio and can obtain the maximum transmission channel capacity through the optimization analysis of the information transmission channel capacity maximization problem (Fig. 2). During information transmission, the channel capacity for information transmission is obtained from Shannon’s theorem as S (1) C = W log 2 1 + N
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Fig. 1. Synchronous transmission circuit based on single coil dual resonance structure.
Fig. 2. Simplified circuit diagram of energy interference during information transmission.
where W is the channel bandwidth, S is the information transmission power, and N is the noise power. From the previous analysis, we can get that the noise power mainly comes from the crosstalk from energy transmission to information transmission, and the energy carrier is a big noise for information communication. Therefore, the crosstalk from power transmission needs to be evaluated first. This section focuses on the forward transmission for the optimization analysis. The equivalent circuit diagram of power is shown below, and the impedance and transfer function of each part can be obtained by analysis as ⎧ ⎧ ⎪ ⎪ Gpf 1 = jwL1 s1 1 ⎪ ⎪ Z = + jwL ⎪ ⎪ c1 pf 1 jwC ⎪ ⎪ cr ⎪ Gpf 2 = jwM ⎪ ⎪ ⎪ ⎪ Z = w2 Mdt2 + jwLc1 − jwMdt2 ⎪ ⎪ ⎪ pf 2 ⎪ Z L c1 ⎪ pf 1 ⎨ ⎨ Gpf 3 = Zpf1 5 Zpf 2 (2) Zpf 3 = 1+jwCp1 Zpf 2 Zs Gpf 4 = Zs +Z ⎪ ⎪ ⎪ ⎪ pf 4 1 ⎪ ⎪ ⎪G = ⎪ Zpf 4 = Zpf 3 + Rc3 + jwCs1 ⎪ 1 ⎪ ⎪ ⎪ pf 5 1+jwCcr Zpf 2 ⎪ ⎪ Zs Zpf 4 ⎪ ⎪ ⎪ ⎪ Zpf 5 = jwLs1 + Zs +Z pf 4 ⎩ Gpf 6 = jwMd 2 ⎩ jwCcr Zpf 1 Then the energy noise gain of forward transmission is expressed as Gpf = Gpf 1 Gpf 2 Gpf 4 Gpf 5 Gpf 6
(3)
The signal-to-noise ratio of forward information transmission can be expressed as SNRp =
PGdp (w) Pf Gpf
(4)
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3 Communication Capacity Optimization Analysis In order to maximize the channel capacity of information communication, while avoiding mutual interference between frequency bands, the OFDM method can be used for information transmission of the communication part, the idea of the method is to talk about information communication split into a number of subcarriers, where in each bandwidth W = B/nF subcarrier channel capacity is PGdp (w) (5) C = W log 2 1 + Pf Gpf Then the total number of bits of information received at the receiving end is defined as U (P, S) =
nF
si W log 2
i=1
pi Gdp (w) 1+ Pf Gpf
(6)
where P = {Pi ≥ 0, ∀i} is the power allocation strategy for information transmission and S = {si ∈ {0, 1}, ∀i} is the subcarrier allocation strategy. Based on the above, the channel model for maximizing the channel capacity for information transmission can be obtained as maxU (P, S) P,S
⎧ n F si Ci ≥ Rmin , ⎪ ⎪ ⎪ i=1 ⎨ nF Pi si ≤ Pmax s.t. i=1 nF ⎪ Pi si ≥ Pmin ⎪ ⎪ ⎩ i=1 si ∈ {0,1},∀i.
(7)
Since the subcarrier allocation policy is a discrete variable, the problem (7) is nonconvex, so the problem is a multivariate nonconvex problem with mixed integers, which is difficult to solve using traditional optimization methods. In this paper, we use the alternating iteration method to solve this problem, and we decompose the original problem into two subproblems to obtain the power allocation policy P and the subcarrier allocation policy S for information transmission in an iterative manner. The optimization flow chart is shown in Fig. 3 below. 3.1 Subproblem I For any given information transmission power allocation policy P, , problem (7) can be solved by solving the following problem max S
nF i=1
pi Gdp (w) si W log 2 1 + Pf Gpf
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⎧ nF ⎪ i=1 si Ci ≥ Rmin , ⎪ ⎪ ⎨ n F Pi si ≤ Pmax s.t. i=1 nF ⎪ Pi si ≥ Pmin ⎪ ⎪ ⎩ i=1 si ∈ {0,1},∀i.
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(8)
For subproblem I, we can relax the binary variables to continuous variables to make problem (7) more tractable. At this point the problem is a standard linear programming (LP) problem that can be solved by optimization tools such as CVX. 3.2 Subproblem II For a given subcarrier allocation policy S, the original problem can be equated to optimize the following problem max P
pi Gdp (w) si W log 2 1 + Pf Gpf i=1 ⎧ n F si Ci ≥ Rmin , ⎪ ⎨ i=1 nF s.t. i=1 Pi si ≤ Pmax ⎪ ⎩ n F i=1 Pi si ≥ Pmin
nF
(9)
For this information transmission power allocation strategy subproblem, we can use the Lagrangian method to find the optimal solution. Defining the Lagrangian multipliers λ, β, γ ≥ 0, , the Lagrangian function of problem (9) can be written as U (P, S) =
nF i=1
pi Gdp (w) si W log 2 1 + Pf Gpf
(10)
By setting the first-order derivative of the Lagrangian function with respect to pi to zero and using the KKT condition, the minimum power distribution can pi∗ be obtained as follows
pf Gdf + wpf Gdf (λ − 1) ∗ − (11) pi = ln2Gdp (w)(β − γ ) Gdp (w) The Lagrange multiplier is iterated by the subgradient method, and the iterative expression is
λk+1 = λk + v1 Rmin −
nF
+ si Ci
(12)
i=1
β k+1
⎧ ⎡ F ⎤⎫+ n ⎨ ⎬ = β k + v2 ⎣ Pi si − Pmax ⎦ ⎩ ⎭ i=1
(13)
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γ
k+1
= γ +v k
3
Pmin −
nF
+ pi si
(14)
i=1
where v1 ,v2 ,v3 are small steps, λ, β, γ are Lagrange multipliers, the specific solution process is shown by Algorithm 1. Algorithm 1 Sub-gradient Method for Solving Problem (9). 1. 2. 3. 4. 5.
Initialize λ, β, γ . Repeat. Obtain the optimal pi∗ according to (11),respectively. Update Lagrange multipliers λ, β, γ according to (12), (13), (14). Until the objective function in (9) converges.
3.3 Overall Algorithm Based on the results of the above two subsections, we propose an overall iterative algorithm to solve the overall problem (shown in Algorithm 2). Since the information transmission channel capacity cannot be increased indefinitely, it will have an upper limit, which means that Algorithm 2 reaches convergence after a number of iterations. Algorithm 2 Alternating Optimization for Maximizing Channel Capacity 1. Initialize feasible solutions (S (0) ,P (0) ), set the parameters δ > 0, the iterate number t = 0, maximum number of iterations t max . nF 2. Calculate value of S (0) = O(S (0) ,P (0) ), where O(S, P) = i=1 si W log 2 (1 + 3. 4. 5. 6. 7. 8.
pi Gdp (w) Pf Gpf ).
Repeat. t = t + 1. According to (8), obtain the S (t) . Given (P (t−1) ,S (t) ), obtain the optimal P (t) of Problem (9) by applying Algorithm 1. With obtained (S (t) , P (t) ), calculate the objective value S (t) = O S (t) ,P (t) . Until |S (t) −S (t−1) |< δ or t > t max .
4 Simulation Results In this section, we provide simulation results to demonstrate the effectiveness of Algorithm 2. In the simulation experiments, the parameters are set to δ = 0.0001, t max =100, the maximum power of information transmission Pmax = 500W , and the minimum rate of information transmission Rmin = 400kbps. Figure 3 shows the convergence of Algorithm 2 for different times of information transmission bandwidth in the SWTPI system. The results show that the algorithm converges quickly in 50 iterations and after 50 iterations the information transfer rate plateaus and converges to its optimal value. In addition, when the bandwidth of the information transmission system is 1.5 MHz, the information transmission rate of the system can reach 965 kbps, which is 33% higher than the information transmission rate of the existing research.
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Fig. 3. Relationship between sum rate and different number of iterations.
5 Conclusion High-speed transmission of information is required in most SWTPI systems, and in the current study the external interference of information carriers, such as energy carrier interference and reverse information carrier interference, is mainly analyzed. In this paper, the energy and information transmission performance of the system is analyzed in detail in the dual-channel transmission model with single coil and multiple carriers, and for the information transmission rate problem, the optimization problem of maximizing the information transmission channel capacity is established, and this non-convex problem is solved analytically by alternating iterative method and Lagrangian dual method, and its feasibility is proved by theoretical analysis.
Appendix Proof of problem (9) as a convex problem. F p G (w) si W log 2 1 + iPf dpGpf , then its first order derivative is Suppose f (pi ) = ni=1 df fpi
= si W
1
ln2(1+
pi Gdp (w) Pf Gpf )
(15)
The second order derivative is (w)
G
d 2f dpi2
=
− PdpG f pf si W ln2 pi Gdp (w) 2 1+ P G f
From the above analysis, we can get that
d 2f dpi2
(16)
pf
≤ 0 holds constantly, and in problem
(9), we can see that the constraints of the problem are convex sets, so we can prove that problem (9) at is a convex optimization problem.
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References 1. Liu, S.B., Zhang, F.S., Ma, B.Y., et al.: Multiband dual-polarized hybrid antenna with complementary beam for simultaneous RF energy harvesting and WPT. IEEE Trans. Antennas Propag. 70(9), 8485–8495 (2022) 2. Basir, A., Yoo, H.: Efficient wireless power transfer system with a miniaturized quad-band implantable antenna for deep-body multitasking implants. IEEE Trans. Microw. Theory Tech. 68(5), 1943–1953 (2020) 3. Lu, P., Song, C.Y., Huang, K.M.: A compact rectenna design with wide input power range for wireless power transfer. IEEE Trans. Power Electron. 35(7), 6705–6710 (2020) 4. Choi, W.P., Ho, W.C., Liu, X., et al.: Bidirectional communication techniques for wireless battery charging systems & portable consumer electronics. IEEE Appl. Power Electron. Conf. Exposition 20(5), 2251–2257 (2010) 5. Wang, G.X., Wang, P.J., Tang, Y.N., et al.: Analysis of dual band power and data telemetry for biomedical implants. IEEE Trans. Biomed. Circuits Syst. 6(3), 208–215 (2012) 6. Yu, C.L., Lu, R.G., Su, C., et al.: Study on wireless energy and data transmission for long-range projectile. IEEE Trans. Plasma Sci 41(5), 1370–1375 (2013) 7. Narayanamoorthi, R., Juliet, A.V.: IoT-enabled home cage with three-dimensional resonant wireless power and data transfer scheme for freely moving animal. IEEE Sensors J. 18(19), 8154–8161 (2018) 8. Lee, W.S., Park, S., Lee, J.H., et al.: Longitudinally misalignment-insensitive dual-band wireless power and data transfer systems for a position detection of fast-moving vehicles. IEEE Trans. Antennas Propag 67(8), 5614–5622 (2019) 9. Najjarzadegan, M., Hafshejani, E., Mirabbasi, S.: An openloop double-carrier simultaneous wireless power and data transfer system. IEEE Trans. Circuits Syst—II 66(5), 823–827(2019) 10. Yilmaz, G., Atasoy, O., Dehollain, C.: Wireless energy and data transfer for in-vivo epileptic focus localization. IEEE Sens. J. 13(11), 4172–4179 (2013) 11. Sun, Y.S., Li, Y.G., Wu, J., et al.: Bidirectional simultaneous wireless information and power transfer via sharing inductive link and single switch in the secondary side. IEEE Access 8, 184187–184198 (2020) 12. Huang, C., Lin, C.: Wireless power and bidirectional data transfer scheme for battery charger. IEEE Trans. Power Electron. 33(6), 4679–4689 (2018) 13. Yu, T., Huang, W.H., Yang, C.L.: Design of dual frequency mixed coupling coils of wireless power and data transfer to enhance lateral and angular misalignment tolerance. IEEE J. Electromagn. RF Microw 3(3), 216–223 (2019) 14. Hirai, J., Kim, T.W., Kawamura, A.: Integral motor with driver and wireless transmission of power and information for autonomous sub-spindle drive. IEEE Trans. Power Electron. 15(1), 13–20 (2000) 15. Hirai, J., Kim, T.W., Kawamura, A.: Study on intelligent battery charging using inductive transmission of power and information. IEEE Trans. Power Electron. 15(2), 335–345 (2000) 16. Qian, Z.N., Yan, R., Wu, J.D., et al.: Full-duplex high-speed simultaneous communication technology for wireless EV charging. IEEE Trans. Power Electron. 34(10), 9369–9373 (2019) 17. Fan, Y.S., Sun, Y., Dai, X., et al.: Simultaneous wireless power transfer and full-duplex communication with a single coupling interface. IEEE Trans. Power Electron. 25(6), 6313– 6322 (2021) 18. Su, Y.G., Zhou, W., Hu, A.P., et al.: Full-duplex communication on the shared channel of a capacitively coupled power transfer system. IEEE Trans. Power Electron. 32(4), 3329–3339 (2017) 19. Grover, P., Sahai, A.: Shannon meets Tesla: wireless information and power transfer. In: IEEE International Symposium on Information Theory, 2363–2367 (2010)
Loss Analysis of Magnetic Core and Its Structure Optimization of Magnetic Coupling Structure in Wireless Power Transfer System Yujie Lan1 , Feng Fan1 , Xiaolong Deng2 , Wei Chen1 , and Qingbin Chen1(B) 1 College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, China
{chw,cqb}@fzu.edu.cn 2 State Grid Fujian Electric Power Co, Ltd Fuzhou Changle District Electric Power Supply
Branch, Fuzhou 350200, China
Abstract. Wireless power transfer (WPT) technology has been widely studied and used in academia and industry. However, the system’s efficiency is still the bottleneck of WPT technology. Moreover, the magnetic coupling system’s loss usually occupies much of the total loss. Furthermore, the magnetic coupling system’s core loss is hard to model and optimize due to the uneven flux density distribution in the magnetic core. Therefore, this paper analyzes the magnetic flux density inside the magnetic coupling system’s magnetic core with a spiral winding structure. It reveals that the flux density is quite uneven in the magnetic core, and the core loss dominates where the flux density peaks. Based on it, a new varied section of the magnetic core structure is proposed. An approximate even flux density distribution can be obtained with the proposed structure, and 37.14% can greatly reduce the core loss. Considering the proposed method’s manufacturing difficulty, a double-section improvement method of the magnetic core structure is proposed. With the double-section improvement method, the flux density can be evener compared to the traditional unique section method. The core loss can be effectively reduced. Finally, a 3kW electric vehicle’s WPT system is taken for experiments. The double-section method can improve the total efficiency by 0.8%, the machine maximum efficiency reaches 95.3%. It verifies the proposed method to be correct and useful. Keywords: Wireless power transfer (WPT) · S/SP compensation network · Magnetic coupling structure optimization · Core loss
1 Introduction In recent years, wireless power transfer (WPT) technology has a broad space for development in electric vehicles due to its advantages of flexibility, safety, and convenience, and therefore has become a research concern of scholars [1, 2]. Magnetically coupled resonant WPT is an efficient and practical mid-range wireless energy transmission technology [3, 4] and it affects the transmission efficiency of the WPT system to a large extent, so optimizing the magnetic coupling structure is particularly important. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 331–340, 2023. https://doi.org/10.1007/978-981-99-0631-4_34
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In [5–7], magnetic cores of different materials and shapes were proposed to improve the coupling coefficient and transfer efficiency, but the resulting core loss was ignored. In [9], it optimized the magnetic core structure under the condition of ensuring the coupling coefficient and reduced the weight of the magnetic coupler through finite element simulation (FEM) and experiment. However, it used the same size as the transmitter coil and receiver coil. To reduce the core losses, in [10, 11], the magnetic flux density distribution of different parts of the magnetic core, the structure of the magnetic switch and the size of the magnetic core are proposed, and the simulation results are given, but the proposed structure is difficult to operate in practice. Therefore, an optimal design scheme for the magnetic core structure is proposed in this paper. Based on the magnetic intensity distribution analysis in the core, a magnetic core structure with short strips stacked in the center of long strips is proposed, effectively reducing the loss of magnetic cores under the condition that the coupling coefficient is almost impossible to unchanged. This paper is organized as follows: Sect. 2 analyzes and simulates the composition of core loss and the magnetic induction intensity inside WPT magnetic core. Section 3 proposes the optimal design scheme for magnetic core structure. Section 4 verifies the correctness of the optimized structure through experiments. Section 5 draws the conclusion.
2 The Flux Density and Core Loss Distribution Analysis of Magnetic Cores 2.1 Distribution of Flux Density in Disk Cores The planar spiral coil is the most common coil structure in WPT system applications. Figure 1 shows the multi-turn simulation model of magnetic coupling structure with disk core. Z Rx coil
d0 b0
h0
R2xout R1xout R1xin R2xin
Tx coil
line1 line2 line3
Fig. 1. Multiturn simulation model of magnetic coupling structure with disk core.
Through FEM, the variation curves of the magnetic flux density inside the transmitter magnetic core with different Z-axis distances and the variation curves of the magnetic flux density inside the transmitter magnetic core with different R-axis distances can be obtained, as shown in Fig. 2, The specific parameters of the magnetic coupling structure are shown in Table 1.
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Table 1. Coil parameters and core parameters of the magnetic coupling structure Magnetic coupling structural model parameters
The numerical
Coil radius
R1xin = 100 mm
R1xout = 250 mm
Core radius
R1xin = 70 mm
R1xout = 280 mm
Conductor diameter and core thickness
d 0 = 4.2 mm
s0 = 5 mm
In Fig. 2, the flux density inside the transmitter magnetic core shows a similar quadratic function variation trend with R-axis distance, and there is a small flux density at the left and right boundaries. At the same R distance, the magnetic flux density at different z distances is roughly the same, but there is a great change at the core boundary.
Fig. 2. Magnetic flux density distribution in the disk core.
Based on the above analysis of the simulation waveform of magnetic flux density inside the magnetic core, this paper considers that the magnetic flux density inside the disk core is irrelevant to the z-axis distance but only with the R-axis distance. 2.2 Core Loss Analysis Since the current flowing in the magnetically coupled coil is approximately sinusoidal when the compensation circuit is well designed. The calculation method of core loss generally adopts Steinmetz formula proposed by C.P.Steinmetz, which is expressed as follows: β Pcv = K · f α · Bm
(1)
where Pcv represents loss per unit volume, f is the frequency; Bm is the maximum magnetic induction intensity, K, α and β are the undetermined coefficients related to the core material, α and β are non-integers, 1 < α < 3, 2 < β < 3. The core loss is also related to the structure and shape of the core.
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It can be seen from (1) that when the frequency and cross-sectional area (the core structure) remain unchanged, the core loss is proportional to the β times of the maximum flux density. The disk core can be evenly divided into five parts (each 42 mm), and the core losses of five different parts can be obtained through (1). The results are shown in Fig. 3. 2.581
P/W
2.5 2.0
1.991
1.698
1.5 1.0 0.5 0
0.419
0.35
1
2
3 Part
4
5
Fig. 3. Core loss distribution diagram of disk cores.
In Fig. 3, in the distribution rules of loss, the middle is high, and the sides are low. The reason is that the Bm in the middle part is too large, resulting in a large Pcore . Therefore, reducing the magnetic flux density in the middle region is very important to reduce the core loss. A variable sheet area optimization scheme to reduce core loss is proposed.
3 Magnetic Core Layout Optimization Design of Magnetic Coupling Structure In combination with the above analysis of core loss, the core loss is approximately β times the maximum magnetic flux density Bmmax . As shown in Fig. 3, Bmmax is usually very large in the case of uneven distribution of Bm , so the core loss Pcore is also very large. According to the magnetic flux formula: φ =B·S
(2)
Under the condition that the sheet S of the disk core above remains unchanged, Φ and Bm are approximately distributed in a quadratic curve, as shown in Fig. 3. On the contrary, if the distribution of S and Φ is similar, then Bm is roughly in a straight line, then the core loss will be greatly reduced. Due to this characteristic, this paper proposes an optimal arrangement scheme for magnetic core structure: the sheet area of the magnetic core is designed as a distribution like a quadratic function. In this paper, the magnetic flux of the two cores is considered nearly constant due to the nearly constant flux of the core structure. According to (2), Φ = 2πrh, r is the radius from the circle’s center, and h is the height of the core. Bm (r) of the traditional disk core
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is (2), and h is a constant h0 , while Bm of the improved core structure is a constant and h(r) is the height of the core (the rule is approximately (2)), so: Bm (r)2π r · h0 = B0 · 2π r · h(r)
(3)
It can be obtained from simulation experience that Bmmax = 94mT and h0 = 5mm, the average of the Bm conic is B0 = 62.7 mT, so h(r) can be calculated by: max 2 R + ( −4Bm a2
h(r) =
0
4Bmmax a0 R) · h0
B0
(4)
The magnetic coupling structure distributed according to the quadratic curve is shown in Fig. 4. (
Rx coil
Z R2xout R1xout
R1xin R2xin
Tx coil
O
R
Fig. 4. Magnetic coupling structure diagram distributed according to quadratic curve.
The magnetic flux density distribution of the optimized core structure can be obtained by (FEM). Line1 is the original core structure, and Line2 is the optimized core structure. 100
Line1 Line2
Bm1/mT
80 60 40 20 0
0
42
84 126 168 210 (R-R2xin )/mm
Fig. 5. The distribution of Bm inside the transmitter side under different (R-R2xin ).
In Fig. 5, the Bm of this structure approximates a straight line. Since the inner diameter of the circular core is smaller than the outer diameter, Bm will be close to the inner core of the disk. According to (1) and flux density distribution, Core loss distribution at the transmitter side with radius R can be obtained, as shown in Fig. 6. The simulation results show that the core loss density of the optimized core structure is greatly reduced.
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Fig. 6. Core loss distribution per unit area under different (R-R2xin ).
However, the magnetic core with the quadratic distribution has a complex structure, which is difficult to be realized in practical engineering applications. Moreover, the large area use of the magnetic core of the disk core will increase the volume and weight of the magnetic core and greatly increase the cost of making the coil. Therefore, this paper also puts forward an optimal arrangement of long strips of radial cores stacked with short strips.
Fig. 7. Schematic diagram of the magnetic coupling structure of strip stacked short strip.
The transmitter coil current is 12A; the receiving coil current is 18A. The basic working condition of scheme 1, the conic distribution is scheme 2, and the strip on top of the strip structure is scheme 3.
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The distribution of internal magnetic flux density of the transmitter side long strip magnetic core and the transmitter side short strip magnetic core under four different core arrangement schemes can be obtained through FEM, as shown in Fig. 8.
Fig. 8. Bm under schemes 3.
As seen from Fig. 7, the optimization scheme 3 increases the thickness of the magnetic core at the center by stacking short strip cores at the center of long strip cores, thus improving the problem of uneven distribution of magnetic flux density in the core. As shown in Fig. 8, compared with scheme 1, scheme 3 effectively reduces the magnetic flux density in the long strip core, while the magnetic flux density in the short strip core is relatively small, so it can still effectively reduce the magnetic flux density in the core. The core loss can be obtained under four different core layout schemes by FEM, as shown in Table 2. Table 2. Core loss on the emission side of the core arrangement scheme. Configuration scheme
Mutual inductance M/uH
Pcore /W
Scheme 1
305.87
14.606
Scheme 2
312.00
9.1807
Scheme 3
308.23
6.4936
It can be seen from Table 2 that the mutual inductance of the magnetic coupling structure in scheme 3 are roughly the same as those in other schemes, but the magnetic core loss of the long strip magnetic core on the transmitter side is greatly reduced compared with the original structure. The reduction of the core loss in Scheme 3 is because the magnetic flux density becomes uniform and the volume of the core in Scheme 3 becomes larger (with more short cores). In conclusion, when the thickness distribution of the magnetic core is like that of the radial magnetic core, the uneven distribution of the magnetic flux density inside the magnetic core can be improved, and the core loss of the magnetic coupling structure can be effectively reduced.
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4 Experimental Verification of Optimal Core Arrangement By establishing an experimental prototype of WPT, the correctness and feasibility of the above magnetic core structure arrangement optimization were verified in this paper, as shown in Fig. 9. The schematic diagram is shown in Fig. 10, wherein L pk , L sk , L m and n are equivalent leakage inductance of the primary side and the secondary side, and equivalent excitation inductance and equivalent ratio of transformer T model, respectively. C p and C s are the equivalent leakage inductance compensation capacitance of the primary side and the secondary side, C m is the parallel compensation capacitance of the equivalent excitation inductance. To verify the feasibility of the magnetic core arrangement optimization design proposed in this paper, magnetic coupling structures of two different magnetic core arrangement schemes were designed. The specification of short strip magnetic cores is 120 mm × 15 mm × 5 mm, and the number of short strips magnetic cores is 24.
Fig. 9. The experimental prototype of the WPT system and the core structure
Fig. 10. The schematic diagram of the WPT system circuit for S/SP compensation.
Waveform of inverter output voltage uab , transmitting coil current ip and receiving coil current is under 3 kW electric vehicle’s WPT system can be obtained through actual measurement of the prototype, as shown in Fig. 11. The efficiency curve of the whole machine under different turn schemes can be obtained by measuring the prototype, as shown in Fig. 12, where the DC output voltage U o = 380 V and the frequency of the system f = 40 kHz. It can be seen from Fig. 12 that the efficiency of the two schemes with additional short-strip cores is higher than that of the original scheme without additional short-strip cores, which indicates that adding magnetic cores not only improves the efficiency of the whole system by improves the mutual inductance of the magnetic coupling system
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Fig. 11. Measured voltage and current waveform.
Fig. 12. The efficiency curves of the whole machine under different schemes.
but also improves the efficiency of the whole system by reducing the loss of magnetic cores. At the same time, the efficiency of the optimal core loss arrangement scheme is higher than that of the common maximum mutual inductance arrangement scheme in the whole load range.
5 Conclusion This paper proposes an optimal design scheme of magnetic coupling structure based on the S/SP compensation network. The conclusions are as follows: 1. Through the analysis of magnetic flux density and core loss in magnetic core of magnetic coupling system with spiral wound structure, it is pointed out that the core loss is concentrated at the peak of magnetic flux density. 2. By analyzing the relationship between magnetic flux density and core loss, an optimal design scheme of variable cross section is proposed, and another optimal design scheme of a double cross section is proposed according to the actual engineering. 3. The WPT system model is established, and the correctness and feasibility of magnetic core structure optimization are verified through experiments.
Acknowledgments. This research was partially funded by the National Natural Science Foundation of China under Grant 51407032 and by the Natural Science Foundation of Fujian Province of China under Grant 2019J01251.
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References 1. Mahesh, A., Chokkalingam, B., Mihet-Popa, L.: Inductive wireless power transfer charging for electric vehicles–a review. IEEE Access 9, 137667–137713 (2021) 2. Sun, Z., Chen, Q., Zhang, L., Long, R.: Research on Bidirectional Wireless Power Transfer System for Electric Vehicles. Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp. 468–472(2019) 3. Liu, F., Yang, Y., Jiang, D., Ruan, X., Chen, X.: Modeling and optimization of magnetically coupled resonant wireless power transfer system with varying spatial scales. IEEE Trans. Power Electron. 32(4), 3240–3250 (2017) 4. Luo, Z., Wei, X.: Analysis of square and circular planar spiral coils in wireless power transfer system for electric vehicles. IEEE Trans. Ind. Electron. 65(1), 331–341 (2018) 5. Abdullah, A.A., Yusoff, S.H., Sulaiman, E. Nur Shahida Midi, Ahmed Samir Abed Badawi, Anis Farihah Fakhruddin.: Design of U and I Ferrite Core On Dynamic Wireless Charging for Electric Vehicle. 2021 8th International Conference on Computer and Communication Engineering (ICCCE), pp. 104–109 (2021) 6. Yusoff, S.H., Nanda, N.N., Midi, N.S., Badawi, A.S.A.: Mathematical design of coil parameter for wireless power transfer using NI multisims software. In: 2021 8th International Conference on Computer and Communication Engineering (ICCCE), pp. 99–103 (2021) 7. . Pearce, M.G.S, Covic, G.A., Boys, J.T.: Reduced Ferrite Double D Pad for Roadway IPT Applications. IEEE Trans. Power Electronics 36(5), 5055–5068 (2021) 8. Patil, D., McDonough, M.K., Miller, J.M., Fahimi, B., Balsara, P.T.: Wireless power transfer for vehicular applications: overview and challenges. IEEE Trans. Transp. Electrif. 4(1), 3–37 (2018) 9. Xiong, M., Wei, X., Huang, Y., Luo, Z., Dai, H.: Research on novel flexible high-saturation nanocrystalline cores for wireless charging systems of electric vehicles. IEEE Trans. Ind. Electron. 68(9), 8310–8320 (2021) 10. Ni, X., Long, R., Zhang, L., Chen, Q.: Optimization of magnetic core structure based on DD coils for electric vehicle wireless charging. In: 2020 16th International Conference on Control, Automation, Robotics and Vision (ICARCV), pp. 44–49 (2020) 11. Sanati, S., Vahedi, A., Alinejad-Beromi, Y.: Optimization of geometry and dimensions of magnetic switch core with approach of flux density uniformity. In: 2019 International Power System Conference (PSC), pp. 113–117(2019)
Compact Mixed DC-DC Power Converters for Computing Server Zhiqiang Liu1(B) , Chaoqiang Jiang1,2,3 , Tianlu Mau1,2,3 , Jingchun Xiang1,2,3 , and Xiaosheng Wang1,2,3 1 Department of Electrical Engineering, City University of Hong Kong, HKSAR, Hong Kong,
China [email protected] 2 State Key Laboratory of Terahertz and Millimeter Waves, City University of Hong Kong, HKSAR, Hong Kong, China 3 City University of Hong Kong, Shenzhen Research Institute, Shenzhen, China
Abstract. Various converters of new topology and multi-phase converter have emerged in response to the hugely demanding power requirement of the computer server. This paper introduces a 24–1 V four-module four-phase seriescapacitor buck converter for computing servers. This type of point-of-load converter achieves high voltage conversion ratios with four-time duty extension. It improves efficiency by reducing the switch’s drain-source voltage pressure. Furthermore, the multi-module approach will be analyzed to offer better performance for high output current stress. Besides, the fast response analysis is conducted via proper closed-loop design to achieve higher bandwidth. Moreover, in the exploration of achieving small size, the comparison of AC losses between GaN and MOSFET is investigated, where the GaN-based converter is allowed to work at a higher frequency providing more possibility of achieving compact. Keywords: DC-DC converter · Point-of-load · GaN · Series-capacitor buck converter
1 Introduction In the modern consumer electronics market, the demand for power supply is increasing because of an enormous number of transistors used in microprocessors (e.g., GPU, CPU). The trend of the microprocessor is concluded in Fig. 1 [1]. In general, the number of transistors used in the microprocessor has been more than 3–4 orders of magnitude since 2000. More current is consumed by the microprocessor as so many transistors are integrated. For instance, NVIDIA GP100 Pascal GPU released in 2016 consists of 15.3 billion transistors using 16 nm FinFET manufacturing process. Moreover, its power consumption is up to 300 W, which means it consumes nearly 300 amperes of current at 1V supply voltage. A solution to the conventional 48 V bus voltage power distribution is shown in Fig. 2. Point-of-load step-down DC-DC must satisfy high conversion rate (48 V to 24 V, 24 V © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 341–351, 2023. https://doi.org/10.1007/978-981-99-0631-4_35
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to 1 V) and high output current (up to several hundred amperes) both. Furthermore, it is essential to be able to deal with fast output current change due to the computation variation of the computer server.
Fig. 1. Microprocessor trend from 1970 to 2022 [1].
Fig. 2. Typical 48 V bus voltage power distribution flow for data center.
It is challenging to convert 24 V down to 1 V in a convential 48 V two-stage step-down solution. For example, a traditional buck converter’s duty cycle is limited to as little as 4% to achieve such a high conversion ratio. To solve the high step-down application issue, some novel DC-DC converters have been proposed [2]. A quadruple buck converter that cross-couple flying capacitors to extend duty cycle was introduced in [3]. As for high output current stress and fast transient response, paralleled multiple DC-DC converters and sophisticated closed-loop control are utilized to fulfill the two requirements. A fivephase synchronous buck converter and compensation method were investigated to deliver high output current [4, 5]. A 48–1 V two-stage converter also makes use of a multi-module multi-phase series-capacitor buck to cope with high output current pressure [6–8]. This paper introduces a 24–1 V DC-DC converter solution as shown in Fig. 3, which both meets the critical demands of computing server and improves the efficiency of the converter. This converter is made up of four identical modules (A, B, C, D), and each module contains a four-phase series-capacitor buck converter. It gains a high conversion ratio, fast transient response, and handles high output current stress. Meanwhile, a new generation of switching device GaN will be used for implementation instead of MOSFET,
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which can increase the operating frequency of the converter without losing too much efficiency because of its own advantages such as low on-resistance and low parasitic capacitance [9–11]. This paper is organized as follows: In Sect. 2, the working principle of this fourmodule four-phase series-capacitor converter will be discussed in detail, including operation analysis, steady-state analysis, and small-signal transfer function. In Sect. 3, a simulation verification will be carried out with projects on steady-state and transient characteristics, as well as the AC losses comparison between GaN and MOSFET. Finally, a conclusion will be made in Sect. 4.
Fig. 3. A 24-1V four-module four-phase series-capacitor buck converter.
2 Multi-phase Series-Capacitor Buck Converter A four-module four-phase series-capacitor buck converter with 24–1 V conversion ratio is present in Fig. 3. The purpose of applying four modules is to increase the current drive capability. In one single module, it only needs to drive 1/4 output current, which allows using a small size inductor. The action of one module is the same as others. So, the following circuit operation discussion only focuses on a single module. Typically, four independent synchronous buck converters are connected in parallel to form a four-phase buck converter shown in Fig. 4a. However, the four-phase series-capacitor (SC) buck converter used in this paper as shown in Fig. 4b is slightly different from the conventional four-phase buck converter. Firstly, each phase of the series-capacitor buck converter is in series connection. Besides, three additional capacitors C i1 , C i2 and C i3 are added to the first three-phase buck converter. In similarity to the conventional buck converter, each phase of SC buck converter consists of the main switch S m , a synchronous rectification switch S r and an energy storage element inductor L. Overall, the series-capacitor converter has advantages over the typical buck converter, including low voltage pressure on MOSFET, extended on-duty ratio, and automatic current balancing [12]. The periodic operation of four-phase series-capacitor buck converter could be divided into eight steps as shown in Fig. 4c. Among the eight steps, even-numbered steps are the same that output current is provided by the inductor storage energy.
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Fig. 4. Comparison of four-phase buck converter and gate control signal sequence diagram. (a) Conventional four-phase buck Converter. (b) Four-phase SC buck converter. (c) Gate control sequence diagram of four-phase SC buck converter.
The capacitor voltage V ci1 , V ci2 , V ci3 , and conversion ratio V out /V in can be derived as
VCi1 = 43 Vin , VCi2 = 24 Vin , VCi3 = 41 Vin Vout D Vin = 4
(1)
where D is the duty cycle of every phase’s high side switch. In this analysis, D is set to 1/6 to achieve 24–1 V conversion ratio. The duty cycle is divided into four, which yields duty cycle extension. Moreover, it should be restricted below 25% to prevent adjacent switches from conducting simultaneously. The switch voltage stress comparison of series-capacitor buck and conventional bulk is concluded in Table 1. It can be noticed that the series-capacitor converter can well ease the switch stress compared to the typical buck converter during steady-state. The efficiency of the four-phase SC converter has improved 9% compared with the typical one under the same simulation condition of f sw = 250 kHz, I load = 75 A. Furthermore, the efficiency gap will become even larger when the switching frequency goes up [12]. Table 1. Maximum switch voltage stress comparison in steady state Switch
Series-capacitor buck
Conventional buck
Sm1
Vin 4 Vin 2 Vin 4
Vin
Sm2 ∼ Sm4 Sr1 ∼ Sr4
Vin Vin
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For the optimal selection of component size, Eq. (2) is given to quantify the steadystate characteristics. ⎧ out )D ⎪ I = (Vin −4V ⎪ 4Lfsw ⎨ L,single m m+1 N (D− N )( N −D) (2) IL,multimodules = 4IL,single × D(1−D) ⎪ ⎪ I ⎩ V = L,multimodules cap
8Cout fsw
where ΔI L,single is single branch inductor’s current ripple, f SW is switching frequency, L is inductor value, ΔI L,multimodules is output current ripple for this four-module four-phase SC converter, N is the number of the phases, m is the maximum integer that does not exceed N × D, ΔV cap is the output voltage ripple(equivalent series resistance (ESR), equivalent series inductance (ESL) parts ignored), C out is the output capacitor. Furthermore, the averaged state-space equation can be described from every single step. After introducing perturbation of system state x, input voltage u and duty cycle d , the overall state space equation is defined as Eq. (3). ⎧ ⎨ X˙ + x˙ˆ = AX + BU + Aˆx + Bˆu + Bd dˆ (3) Y + yˆ = CX + C xˆ ⎩ −1 X = −A BU
where X = [iL1 ,iL2 ,iL4 ,vci1 ,vci2 ,vci3 ,vcout ]T , Y = vout , U = vin , and D is duty cycle. Here the nonlinear second-order term is eliminated. Besides, the state equation’s coefficients are defined as Eq. (4). ⎧ ⎪ ⎪ ⎨
A = A1 D + A3 D + A5 D + A7 D + (1 − 4D)A2 B = B1 D + B3 D + B5 D + B7 D + (1 − 4D)B2 ⎪ B = (A1 + A3 + A5 + A7 − 4A2 )(−A−1 BU ) + (B1 + B3 + B5 + B7 − 4B2 )U ⎪ ⎩ d C = C1 D + C3 D + C5 D + C7 D + (1 − 4D)C2 (4) where the value of A1 , B1 , and C 1 follow the step1 state matrix, A2~7 , B2~7 , and C 2~7 values correspond to the respective step state matrix. By using Eq. (4), the final state matrixes are derived as Eq. (5). ⎡ 0 − L1 0 0 0 −D ⎢ 0 L 0 ⎢ ⎢ ⎢ D −D 0 ⎢ 0 0 0 0 − L1 L L ⎢ ⎢ ⎢ D −D ⎢ 0 0 0 0 0 − L1 L L ⎢ ⎢ ⎢ D ⎢ 0 0 0 0 0 0 − L1 ⎢ L A=⎢ ⎢ ⎢ D − D 0 0 0 0 0 0 ⎢ Ci1 Ci1 ⎢ ⎢ ⎢ 0 D D 0 0 0 0 0 ⎢ Ci2 − Ci2 ⎢ ⎢ ⎢ D D 0 0 0 0 ⎢ 0 Ci3 − Ci3 0 ⎢ ⎣ 1 1 1 1 0 0 0 − RC1 Cout Cout Cout Cout out
⎡
⎤
⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥, B = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣
D L ⎥ ⎥
⎤
⎡
⎤
⎢ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ 0 ⎥ ⎥ ⎢ ⎥ , Bd = ⎢ ⎥ ⎢ ⎢ 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎢ ⎦ ⎣ 0
Vin 4L ⎥ ⎥ Vin 4L Vin 4L Vin 4L
0 0 0 0
⎡ ⎤T
⎢0⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎥, C = ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢0⎥ ⎥ ⎢ ⎥ ⎦ ⎣ ⎦ 1
(5)
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where C i1 ~ C i3 are additional capacitors, R is the load resistance. Through constituting Eq. (5) to Eq. (3), the small-signal transfer function of duty cycle and input voltage can be obtained as Eq. (6). ⎧ Vin ( LC1 ) ⎪ vˆ out (s) −1 B = out ⎪ G (s) = = C(sI − A) ⎪ vd d ⎪ s2 + RC1 s+ LC4 dˆ (s) ⎨ out out (6) ⎪ 1 ⎪ D( ) ⎪ (s) ⎪ = C(sI − A)−1 B = 2 1 LCout 4 ⎩ Gvv (s) = vˆvˆout(s) s + RC
in
out
s+ LC
out
Since four modules consist of the whole series-capacitor buck converter, one module is only responsible for a quarter of the output current. So, the Eq. (6) can be extended to Eq. (7) to represent the entire four-module four-phase series-capacitor buck converter’s small-signal transfer function. With proper design, the higher natural frequency can allow the converter to respond fast. ⎧ 4Vin ( LC1 ) ⎪ ⎪ ⎪ Gvd (s) = s2 + 1 s+out 16 ⎪ ⎨ RCout LCout (7) ⎪ ⎪ 4D( LC1 ) ⎪ ⎪ ⎩ Gvv (s) = 2 1 out 16 s + RC
out
s+ LC
out
From Eq. (7), it can be concluded that the series-buck converter owns a secondorder system which is like the conventional buck converter. And it is helpful to design closed-loop control as shown in Fig. 5 to regulate the output voltage.
Fig. 5. Closed-loop control of the 24–1 V SC converter.
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Although the 4-phase SC converter has three additional capacitors, it does not influence the small-signal transfer function. This can be explained as the additional capacitors only serve as a voltage source in the view of the averaged model, because the charge balance of capacitors always remains stable in every cycle. Unlike conventional multi-phase converters, with the application of these flying capacitors, multi-phase SC converters do not require branch current balancing control loops [13, 14].
3 Simulation Result and AC Losses Discussion In this paper, the simulation of the 24–1 V DC-DC buck converter is carried out by LTspice and MATLAB/Simulink. The steady-state characteristics and AC losses improvement with GaN device is verified in LTspice as it is easy to import the proper spice model of components. The transient response simulation is performed by Simulink since it provides well support for digital closed-loop control. Table 2 lists the values of the components used in this design. Table 2. The components used in the 24–1 V DC-DC buck converter simulation Components
Value
Switch
BSZ0506NS
Switching frequency
250 kHz
Additional capacitor
20 µF
Inductor
300 nH
Output capacitor
2 mF
Fig. 6. Steady-state waveforms in simulation. (a) Waveforms of input voltage, total inductor current, and output voltage. (b) Waveforms of main switch V gs , each phase inductor current, and module inductor current summation.
The steady-state simulation focuses on output voltage performance and inductor current cancelation between phases. Figure 6a demonstrates the converter’s output voltage
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1 V with 1 mV ripple at the input voltage of 24 V and the output current of 300 A. The interleaving phase performance is shown in Fig. 6b. The single inductor current ripple is 11.9 A, but the single module current ripple is reduced to 4 A owing to ripple-current cancellation. By adding the four modules’ current ripple together, the total current ripple can be seen as 15 A from the output capacitor. The transient simulation consists of input voltage transient response and output current transient response at the closed-loop control state. All PID parameters have been optimized by utilizing the transfer function derived in Eq. (7). The closed-loop structure is followed in Fig. 5. Considering the computing server’s sudden current variation, a simulation with current change from 300 A to 500 A in 20 A/us rate is done as shown in Fig. 7a. Both the undershot and overshot voltage do not exceed 0.1 V, which guarantees the microprocessor function properly. And the settling time is 28 µs (1% error). Figure 7b shows the output voltage changes when input voltage drop/rise 4 V in 10 us. The undershot/overshot voltage of 0.03 V is observed. And the output voltage is settled at 37 µs (1% error).
Fig. 7. Transient response waveforms. (a) Output current 300A ↔ 500A. (b) Input voltage 24V ↔ 20V.
It is reasonable to not give much thought to the alternating current (AC) losses when working at a relatively low operating frequency. However, to make this converter more compact, letting the converter operate at a higher frequency could be a good choice that can reduce the size of the inductor and output capacitor. In this case, the AC losses should be taken into account especially as a total of thirty-two MOSFETs are used in this 24–1 V SC buck converter. Compared to traditional power MOSFET, the GaN device has the advantages of low on-resistance and low parasitic capacitance. Moreover, a reverse recovery loss will occur when MOSFET body diode switches from forward-biased state to reverse-biased state. Due to the symmetric structure and none-body-diode properties of GaN, this reverse recovery loss can fall to zero [15]. Taking all the merits together, allowing the DC-DC converter to operate at a higher switching frequency is possible by using GaN instead of MOSFET [16].
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The detailed characteristic comparison of GaN and MOSFET is summarized in Table 3. In the VDS-30V level switch, compared to the latest generation MOSFET, the disincentive occurs on the on-resistance of GaN. However, the Total Gate Charge (Qg) and Output Charge (Qoss) related to parasitic capacitance are reduced by almost ½ while the Recovery Charge (Qrr) is disappeared. Table 3. Characteristic comparison of GaN and MOS FET Characteristic
Ron (m)
Qg (nC)
Qoss (nC)
Qrr (nC)
EPC2100 (GaN)
8.2
3.6
6.1
0
BSZ0506NS (MOSFET)
4.4
11
7.2
10
A gate drive circuit including dead-time generator, level-shifter, pre-drive, and bootstrap is constructed to investigate the difference in switching transient performance between GaN and MOSFET as shown in Fig. 8a. The dead-time is set large enough for a better observation of the difference.
Fig. 8. Loss comparison with the same gate driving ability (GaN and MOSFET). (a) Gate drive circuit used to drive power switch. (b) Gate charge loss. (c) Qoss + Qg loss. (d) Dead-time loss.
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It can be clearly seen that gate charge loss of GaN is reduced by comparing the discharge current area from Fig. 8b, Because of its lower C gs and C gd capacitance than MOSFET. This allows reducing the transition losses since the drain-source voltage will drop rapidly. As mentioned before, the Qrr is eliminated as shown in Fig. 8c. The disappearance of the reverse-recovery current not only decreases the AC losses but also mitigates the ringing effect when S r is off. Notably, Fig. 8d illustrates the dead-time loss of GaN is not superior to MOSFET. Owing to GaN’s third quadrant conducting feature, the drain voltage of S r reaches -2.6 V in the dead-time period, whereas MOSFET type switch’s drain voltage only comes to -0.7 V because of its intrinsic body-diode. It suggests that the dead-time should be optimized when GaN is used. Overall, it is possible that allow the GaN-used buck converter work at a higher frequency than MOSFET-used since its better performance on AC losses.
4 Conclusion In summary, this paper introduces a recent change in the power requirement of computing servers, whereas the conventional DC-DC buck converter may not function properly in high power density 24–1 V power distribution solution. A novel 24–1 V DC-DC converter is introduced, which can be realized by paralleling a four-phase series-capacitor converter. The point-of-load converter’s work principles are analyzed in detail, including voltage conversion ratio, steady-state characteristics, and transfer function. The simulation results indicate that the 24–1 V converter can meet high current stress and fast transient response. Moreover, by replacing the conventional switch device MOSFET with GaN, operating at a high frequency is allowed for GaN-based converter, meanwhile, the AC losses are well reduced. Acknowledgments. This work was supported in part by a grant (52107011) from the Natural Science Foundation of China (NSFC), China; in part by a grant (9667243) from the Applied Research Grant (ARG), City University of Hong Kong, Hong Kong SAR, China; a grant (ITS/068/21) from the Innovation and Technology Commission, Hong Kong SAR, China; in part by a grant (SGDX20210823104003034) from the Science Technology and Innovation Committee of Shenzhen Municipality, China.
References 1. Rupp, K.: 42 Years of Microprocessor Trend Data, https://www.karlrupp.net/2018/02/42years-of-microprocessor-trend-data/ 2. Ye, Z., Sanders, S., Pilawa-Podgurski, R.C.N.: Modeling and comparison of passive component volume of hybrid resonant switched-capacitor converters, IEEE Transactions on Power Electronics (2022) 3. Halamicek, M., McRae, T., Prodi´c, A.: Cross-coupled series-capacitor quadruple step-down buck converter. pp. 1–6 4. Gordillo, J., Aguilar, C.: A simple sensorless current sharing technique for multiphase DC–DC buck converters. IEEE Trans. Power Electron. 32(5), 3480–3489 (2016)
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5. Zhou, D.H., Elasser, Y., Baek, J., Chen, M.: Reluctance-based dynamic models for multiphase coupled inductor buck converters. IEEE Trans. Power Electron. 37(2), 1334–1351 (2021) 6. Chen, Y., et al.: Virtual Intermediate Bus CPU Voltage Regulator,” IEEE Transactions on Power Electronics (2021) 7. Zhao, H., Shen, Y., Ying, W., Qi, J., Jiang, C., Long, T.: Mixed Analog-Digital (MAD) converters for high power density DC–DC conversions. IEEE Trans. Power Electron. 35(8), 7742–7748 (2020) 8. Baek, J., et al.: Vertical stacked LEGO-PoL CPU voltage regulator. IEEE Trans. Power Electron. 37(6), 6305–6322 (2021) 9. Joshin, K., Kikkawa, T., Masuda, S., Watanabe, K.: Outlook for GaN HEMT technology. Fujitsu Sci. Tech. J 50(1), 138–143 (2014) 10. Jiang, Y., Shen, Y., Shillaber, L., Jiang, C., Long, T.: Split parallel semibridge switching cells for full-power-range efficiency improvement. IEEE Trans. Power Electron. 36(9), 10889– 10905 (2021) 11. Shen, Y., Jiang, Y., Zhao, H., Shillaber, L., Jiang, C., Long, T.: Quadrilateral current mode paralleling of power MOSFETs for zero-voltage switching. IEEE Trans. Power Electron. 36(5), 5997–6014 (2020) 12. Shenoy, P.S., Amaro, M., Morroni, J., Freeman, D.: Comparison of a buck converter and a series capacitor buck converter for high-frequency, high-conversion-ratio voltage regulators. IEEE Trans. Power Electron. 31(10), 7006–7015 (2015) 13. Roh, Y.-S., Moon, Y.-J., Park, J., Jeong, M.-G., Yoo, C.: A multiphase synchronous buck converter with a fully integrated current balancing scheme. IEEE Trans. Power Electron. 30(9), 5159–5169 (2014) 14. Shenoy, P.S., et al.: Automatic current sharing mechanism in the series capacitor buck converter, pp. 2003–2009 15. Jones, E.A., Wang, F., Ozpineci, B.: Application-based review of GaN HFETs. pp. 24–29 16. Zulauf, G., Guacci, M., Kolar, J.W.: Dynamic on-resistance in GaN-on-Si HEMTs: origins, dependencies, and future characterization frameworks. IEEE Trans. Power Electron. 35(6), 5581–5588 (2019)
A Flexible Foreign Object Detection Method Based on Arrayed Vertical-Decoupled Coils for Wireless Power Transfer Systems Huishu Song(B) , Xiaosheng Huang, Shuyi Lin, Ruping Lin, and Jing Huang School of Electronic, Electrical Engineering and Physics, Fujian University of Technology, Fuzhou, China [email protected]
Abstract. Wireless power transfer (WPT) has considerable advantages in electric vehicles, and implantable medical devices, depending on its reliability and flexibility. However, foreign objects (FO) can cause serious safety problems to the WPT system, and electromagnetic energy transfer is also affected. This paper presents a foreign object detection (FOD) method, which depends on measuring changes in the electromagnetic energy transfer between resonance detection coils. The proposed method differs from the conventional methods based on measuring impedance. Since the foreign objects detune arrayed resonant detection coils, the electromagnetic energy transfer between the detection coils varies significantly and can be measured sensitively, even if the foreign objects are very small. A coil array structure with the vertical configuration of dominoes is also proposed, which can be decoupled from the transmitting coil without affecting the transmission of the WPT system. By making the detection magnetic field horizontal, there is no blind zone on the surface of the detection coils. Experiments and simulations validate the proposed FOD method. The results show that, no matter what position and angle on the detection area, the FOD system can sensitively detect the one-yuan coin and the U-shaped needle. Keywords: Foreign object detection (FOD) · Wireless power transfer (WPT) · Resonance detection coil · Electromagnetic energy transfer · Vertical configuration
1 Introduction In recent years, compared with the traditional charging method, the wireless power transfer (WPT) system has gradually attracted the attention of scientific researchers. There is a high-power alternating electromagnetic field between the transmitting coil (Tx) and the receiving coil (Rx). Safety issues can arise if foreign objects such as metal or living objects can inevitably be present on the Tx pad [1–4]. The existing FOD methods can be divided into two categories according to the detection principle: one is based on the changes in system parameters, such as [5– 7] quality factor, frequency, and receiving coil’s current; the other method is based © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 352–363, 2023. https://doi.org/10.1007/978-981-99-0631-4_36
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on the appearance of the foreign objects, such as radar, real-time thermal camera and machine learning [6–8]. However, most FOD methods use additional detection coils to detect foreign objects. [7] proposed a two-layer symmetrical detection coil set, using the voltage difference detect the mutual inductance difference to judge the location of metal objects. The concept of symmetrical sensing coils based on magnetic field change sensing (MCFS) is proposed in [8]. The coils have many channels and each channel contains two induction coils that are symmetrical about the y-axis in the Tx pad. [9] proposes a non-overlapping coil set based on induced voltage sensing (IVS). The induced voltage difference judges the existence of metal objects. [10] applies a design of a selfinductance-based resonant circuit (SIRC) based on symmetrical sensing coils. According to amplifying the change of self-inductance to determine whether there are foreign objects. [11] proposes a sensor coil, to measure the change of mutual inductance between the sensing coil and the transmitting coil to judge foreign objects. [12] applies a method for detecting self-inductance with mistuned resonant circuits and utilizes a difference of self-inductance of a sensing pattern, which improves the detection sensitivity. This paper proposes a methodology to realize FOD by measuring the detection coil array’s electromagnetic energy transfer affected by foreign objects. This method can detect regardless of the existence of foreign objects with no blind zones. Since the detection coils are coupled, the output energy of the detection coils is superimposed in the energy transfer direction. The intervention of foreign objects will affect the electromagnetic energy transmission of the detection coils, so there is no blind zone. Furthermore, the system comprises a resonance detection coil array. By forming a “domino” detection coil array and arranging vertically on the surface of the transmitting coil, which is decoupled with power-stage coupling coils and cannot cause any power loss. A prototype is built to verify the proposed methodology. The presence of foreign objects is decided by the output voltage difference of the detection coil array. The performance of the proposed detection coil array was verified by theoretical analysis, simulation, and experiment.
2 Modeling of the Proposed Vertical-Coils-Based FOD Method 2.1 Basic Scheme High frequency excitation
Peak detection circuit
Fig. 1. The proposed FOD system
The schematic of the proposed FOD system is shown in Fig. 1. The FOD system includes a detection coil array, a high-frequency excitation source, and a peak detection
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circuit, which are omitted for simplicity. The detection coil set includes an excitation, a response, and relay coils. They all resonate at 6.78 MHz and arrange vertically on the Tx pad. The key idea of the FOD is based on the change in the energy transfer of the detection coil, which can be measured by the output voltage of the response coil. Take metal objects as an example. Metal objects will affect the electromagnetic energy transfer of the detection coil, but the change of electromagnetic energy is difficult to be directly detected in practical applications. By adding a compensation capacitor to resonate the detection coil, FOs will detune the resonant circuit and convert the change of electromagnetic energy into a voltage signal that can be easily detected by resonance induction coils. 2.2 Circuit-Based Analysis of Detection Units The equivalent circuit of foreign object detection is shown in Fig. 2. Us is the excitation source. In order to simplify the analysis, the internal resistance of the excitation source is ignored, RD and LD are the resistance and reactance of the detection coil, CS is the series compensation capacitor, MFOD is the mutual inductance between the detection coil or the foreign object and detection coil, LFO and RFO refer to the equivalent inductance and resistance of the foreign object. The equivalent loop impedance of the foreign object is ZFO = RFO + jωLFO .
Fig. 2. The detection resonance circuit with a foreign object.
The equivalent resonant loop impedance ZD of the detection coil is: ZD = RD + jωLD +
1 jωCS
(1)
Under normal circumstances the output power of the detection coil is: Us2 RD PD = RD + jωLD +
1 jωCS
2
(2)
When a foreign object falls on the detection area, the equivalent resistance and reactance of the detection coil affected by foreign objects are: ZDO = RDO + jXDO 2 ω2 MFOD
2 ω2 MFOD 1 = RD + 2 R + j ωLD − − 2 ωLFO 2 FO ωCS RFO + (ωLFO ) RFO + (ωLFO )2
(3)
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From Eq. (3), foreign objects can affect the equivalent impedance of the detection coil, the equivalent resistance increases, and the equivalent inductance decrease. At the same time, the output power of the coil is changed: 2 R ω2 MFOD Us2 FO PFOD = (4) 2 RD + 2 2 RFO + (ωLFO )2 ω2 MFOD 1 RD + jωLD + jωCS + RFO +jωLFO So when there is a foreign object, the output power ratio is: RDO ZD2 PFOD = 2 PD RD ZDO
(5)
When the detection coil is resonance, Eq. (5) simplifies to: PFOD RD RDO = 2 PD ZDO
(6)
Because the Q value of the coil is high,RD is approximately 0, so the above ratio is much less than 1. It can be seen that when the detection coil resonates, the intervention of foreign objects will significantly reduce the electromagnetic energy transmission of the detection coil. This detection method features high sensitivity. 2.3 Theoretical Analysis of Vertical Detection Coil Array The coil structure design of this paper has the following characteristics. 1. The detection coil must be decoupled from the power stage coil without affecting the power transmission efficiency of the WPT system. 2. The detection range must cover the entire charging area, and there is no detection blind zone. 3. The designed detection coil should have better sensitivity to objects of various sizes.
Fig. 3. Magnetic coupling system (cylindrical coordinate)
Figure 3 illustrates the magnetic field distribution of the vertically arranged detection coils and the WPT coupling coils. Since the magnetic field generated by the detection
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Fig. 4. The resonant link formed by a FOD coil array, the excitation coil and the response coil.
coil array and the coupling coils are nearly vertical in space, the detection coils and the WPT coupling coil are approximately decoupled. In addition, the detection coils are compensated to resonate at a much higher frequency than the coupling coils. The resonant circuit design of the detection coil of the FOD system is shown in Fig. 4.R1 ∼ Rn indicate the equivalent series resistance (ESR) of the loop of each coil,Mi,i−1 (i = 1, 2 · · · n) is the mutual inductance between the detection coils. Since the coupling coefficient of the spaced coils is much smaller than that of the adjacent coils, this paper only considers the coupling coefficient of adjacent coils. The High-Q resonance detection coils are arranged in sequence with equal spacing, and the mutual inductances between the coils are approximately equal, so M12 = M23 = M34 = ··· = Mn,n−1 = M . Due to the coupling between the coils, electromagnetic energy forms a transmission path. Using the KVL theory can obtain: ⎤⎡ ⎤ ⎡ ⎤ ⎡ I1 R1 −jωM12 ... 0 0 0 Us ⎥⎢ I ⎥ ⎢ 0 ⎥ ⎢ R2 −jωM23 ... 0 0 −jωM12 ⎥⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎢ ⎥⎢ ⎥ ⎢ 0 ⎥ ⎢ ... R −jωM ... 0 −jωM ⎥⎢ I3 ⎥ 23 3 34 ⎢ ⎥=⎢ ⎢ ⎥ ⎥ ⎢ ... ⎥ ⎢ ⎥⎢ ... ⎥ ... ... ... 0 ... −jωM34 ⎢ ⎥ ⎢ ⎢ ⎥ ⎥ ⎣ 0⎦ ⎣ −jωMn.n−1 ⎦⎣ In−1 ⎦ 0 0 ... ... Rn−1 0 0 0 0 ... −jωMn,n−1 Rn In (7) The impedance of the n-1 resonant loop can be expressed as: Rloop_n−1
2 ωMn,n−1 = Rn−1 + Rloop_n
(8)
When the resonant loops are all working in the resonance condition, make the resistance of each loop equal, and the impedance of the resonant loop n can be obtained: Rn + 4ω2 M 2 + R2n (9) Rloop_n = 2
A Flexible Foreign Object Detection Method ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
⎤ ⎡ −jωM12 ... 0 0 0 0 Us R1 ⎢ 0 ⎥ R2 −jωM23 ... 0 0 −jωMF2 ⎥ ⎢ −jωM12 ⎥ ⎢ 0 ⎥ ⎢ ... −jωM23 R3 −jωM34 ... 0 −jωMF3 ⎥ ⎢ ⎢ ... ⎥ 0 ... −jωM34 ... ... ... ... ⎥=⎢ ⎥ ⎢ 0 ⎥ ⎢ 0 0 ... ... Rn−1 −jωMn.n−1 0 ⎥ ⎢ 0 ⎦ ⎣ 0 0 0 ... −jωMn.n−1 Rn 0 0 0 −jωMF2 −jωMF3 ... 0 0 RFO + jωMFO
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⎤⎡
⎤ I1 ⎥⎢ I ⎥ ⎥⎢ 2 ⎥ ⎥⎢ ⎥ ⎥⎢ I 3 ⎥ ⎥⎢ ⎥ ⎥⎢ ... ⎥ ⎥⎢ ⎥ ⎥⎢ ⎥ ⎥⎢ In−1 ⎥ ⎥⎢ ⎥ ⎦⎣ I n ⎦
(10)
IFO
When a foreign object appears, the resonant frequency of the transmission path where the foreign object is located will shift, which causes the received power at the end of the path is decreased. The input power of the excitation will change. This method has no blind zone and this kind of coil has good expansion and cannot be affected by the area of the transmitting coil.
3 Simulation and Analysis of Detection Coils 3.1 Analysis of the Number of Detection Coils To better analyze the change of foreign objects on the electromagnetic energy transfer of the detection coil set, FEM simulations with detection coils and foreign objects are used for analysis and preparing for the acquisition of the sensitivity. The influence of the detection coils’ number on the sensitivity was explored. The number of detection coils was set as 4, 5, 6, 7, 8 and 9, and the coupling coefficients between coils were analyzed. By comparing the coupling coefficient in Table 1, when the number of coils is larger, the detection spacing is smaller, the coupling coefficient is larger, and the detection coil sensitivity is higher. However, when the number of detection coils is too large, the surface of the transmitting coil will be covered, thus the number of coils is selected as 6. Table 1. The coupling coefficient varies with the number of detection coils Number
4
5
6
7
8
9
Coupling coefficient
0.00154
0.00311
0.00545
0.00727
0.00978
0.01522
3.2 The Influence of Foreign Objects on the Magnetic Field of Coils Putting an iron block and a copper block of the same volume parallel at the same height above detection coils 2 and 3. The magnetic induction intensity of the coil on the XOY plane is shown in Fig. 5. Figure 5(a) shows that when there is under normal conditions, the distribution of the flux lines is very uniform. Figure 5(b) and (c) show the magnetic field change when an iron block and a copper block are present. It can be found that the flux lines in the space on the bottom and the left of the iron block seem to be “absorbed” by the iron block. The
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distribution of flux lines between coils is also sparse. Most of the flux lines surround the copper block, and the flux lines above the copper block become sparse. By comparing the coupling coefficient between coils 2 and 3 in Table 2, when there is a foreign object, the changes in k23 are particularly significant, and the others are changed. Hence, the energy transfer between the coils will be affected. Table 2. Coupling coefficients between detection coils Coupling coefficient
k 12
k 23
k 34
k 45
k 56
No object
0.00545
0.00545
0.00545
0.00537
0.00537
Iron
0.00539
0.00422
0.00548
0.00537
0.00537
Copper
0.00542
0.00476
0.00543
0.00537
0.00537
Fig. 5. FEM simulation results. (a) Coil set flux line distribution with no foreign object. (b) Flux line changes with an iron block. (c) Flux line changes with a copper block.
3.3 Simulation of Vertically Arranged Detection Coils The detection coil is placed vertically on the surface of the Tx pad. The litz wire diameter of the power stage coil is 2 mm, the excitation current is 1 A. The copper wire diameter of the detection coil is 0.15 mm, and the excitation current is 10 mA. The transmitting frequency is 3 MHz, and the resonant frequency is 6.78 MHz. In Fig. 6, in the XOY plane, comparing Fig. 6(a) and (b), When detection coils are arranged vertically on the transmitting coil, the flux lines around the detection coil have no distinguishable change, which still keeps radiating around. Therefore, there is negligible coupling between the detection coil and the transmitting coil. In practical systems, the detection coils may not perfectly decouple with the transmitting coil, especially on the edge. However, since the detection coils are compensated
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Fig. 6. FEM simulation results of flux lines. (a) The direction of the magnetic field lines between the Tx pad and Rx pad. (b) The direction of the magnetic field lines between the Tx pad and Rx pad when detection coils put vertically in the Tx pad.
to resonate at the resonant frequency, which is much higher than the operating frequency of power-stage coupling coils, the induced currents through detection coils are also negligible.
4 Experimental Measurement and Analysis 4.1 Experiment Setup In order to verify the feasibility of the proposed FOD system, an experimental device and the proposed coil array was built in Fig. 7. The experimental setup includes a WPT system and a FOD system. WPT system includes Tx pad and Rx pad, their size are 200 mm × 200 mm. The FOD induction coil array consists of 6 detection coils arranged vertically on the Tx pad in a “domino” pattern. Each coil is equal in size and has the same number of turns. The size of the coil is 150 mm × 5 mm × 3 mm, the white part is the 3D-printed coil frame choosing a copper wire with a diameter of 0.1mm, the number of turns is 6, and the resonance frequency of the coil is 6.78 MHz. The magnetic coupling resonant WPT prototype working at 3 MHz and 85 kHz, 85 kHz is the current wireless charging power for electric vehicles. The performance of the detection coil is verified using two experimental scenarios. The first is used to verify the sensitivity of the detection coils with different foreign objects. Figure 8 shows the foreign objects used in the experiment. One is a U-shaped needle, the other is a coin, their size is small, which can assist in detection coils’ sensitivity. The second is used to verify that the detection coil will not affect the transmission of the WPT system. 4.2 Detection Sensitivity Affected by Foreign OBJECt’s Positions The voltage difference expresses the sensitivity before and after whether there is a foreign object, and the expression of sensitivity is: V = |VO − VnO |
(11)
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Fig. 7. FOD device (left) and detection coil array arranged vertically on the surface of the transmitting coil (right).
Fig. 8. The size of a U-shaped needle (left) and 1-yuan coin (right).
VnO is the output voltage under normal conditions,VO is the output voltage when there is a foreign object, and V is the output voltage difference. First, a coin and a U-shaped needle are randomly placed at the same 9 positions of the Tx pad, as shown in Fig. 9(a), and the measured output voltage difference V corresponding to each position is shown in Fig. 9(b). Then is to verify whether the proposed FOD induction coil can detect foreign objects at different angles from the Tx surface. The measured position and angle θ ◦ are shown in Fig. 10(a) and (b). The angle θ ◦ between the foreign object and the surface of the detection coil set is different, and the relationship between the voltage difference and angle is shown in Fig. 10(c).
Fig. 9. (a) Floor plan of 9 inspection positions in Tx pad. (b) The output voltage change diagram of coin and U-pin at these 9 positions.
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In Fig. 10(c), the output voltage differences V are far more significant than 0, and the proposed detection coil array can detect the 1-yuan coin and the U-shaped needle well. The angle between the foreign objects and the Tx pad ranges from 0 to 180◦ . When θ ◦ is equal to 90◦ , V reaches a minimum value. When the angle θ ◦ is not equal to 90◦ , the detection voltage changes obviously. Through experimental analysis, the abovementioned foreign object detection system can detect small foreign objects well without a very dense coil configuration.
Fig. 10. Experimental results of different placement angles. (a) Top view of the FOD system. (b) Floor plan of foreign objects location (c) The relationship between θ ◦ and V .
4.3 Decoupling Feature Between Power Stage Coupling Coils and FOD Coils In order to verify the decoupling of the proposed detection coil and the power stage coupling coils, experiments are performed from different transmission frequencies and different transmission distances, respectively. The transmission frequency is set at 85 kHz and 3 MHz and the transmission distance at 20mm, 30 mm and 40 mm. When the transmission distance of the WPT system is changed, the change rate of the output voltage of the receiving coil is shown in Table 3. The transmission distance is set to 20 mm, 30 mm and 40 mm. Table 3. The rate of change of the output voltage of the receiving coil. Transmission distance
Voltage change rates in 85kHz
Voltage change rates in 3MHz
20mm
0.75%
0.89%
30mm
0.81%
0.88%
40mm
0.93%
0.95%
By observing Table 3, the resonant frequency of detection coils is much higher than the transmission frequency of power stage coupling coils, considering the measurement error, the influence of adding the detection coil to the system power-coupling coil is
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negligible. Therefore, the detection coil set can be decoupled with power stage coils of different transmission frequencies. Since the resonant frequency of the detection coil set is 6.78 MHz, the coils’ wire diameter is 0.1mm and much smaller than the wire diameter of the power stage coupling coils, which is much lower than the skin depth of 85 kHz and 3 MHz, and there is no proximity effect. Therefore, the measured results validate the impact on power transmission is minimal.
5 Conclusion This paper proposes a flexible FOD method, which is to detect foreign objects according to the variation of energy transfer within a vertical coil array. By using the vertically arrayed detection coils, the proposed FOD method has an extensible detection area and achieves blind-zone-free detection of foreign objects of various sizes. The simulation results validate that the excited vertically detection coils are sensitive to mental foreign objects of various sizes, and decoupled with the power-level coupling coils. A FOD prototype, of which detection coils are excited by a 6.78 MHz source, is built to verify the proposed method. The experiment shows that the FOD circuit realizes reliable detection of a coin and a U-shaped needle, regardless of the placement angle and location on the transmitting coil. Furthermore, the detection coil array does not affect the power transfer regardless of the operation frequency and transfer distance of the WPT system. Acknowledgments. This work was supported in part by the Natural Science Foundation of Fujian Province of China under Grants 2022J01949, in part by the Science and Technology Planning Project of Fujian Province under Grant 2021H0024, and in part by the Science and Technology Planning Project of Fuzhou under Grant 2021-P-051.
References 1. Sun, Y., Wei, G., Qian, K., He, P., Zhu, C., Song, K.: A foreign object detection method based on variation of quality factor of detection coil at multi-frequency. In: 2021 IEEE 12th Energy Conversion Congress & Exposition - Asia (ECCE-Asia). 1578–1582 (2021) 2. Deguchi, Y., Nagai, S., Fujita, T., Fujimoto, H., Hori, Y.: Sensorless metal object detection using transmission-side voltage pulses in standby phase for dynamic wireless power transfer. In: 2021 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW). 1–5 (2021) 3. Li, S., Li, H., Wu, Z., Bao, G., Qian, K., Li, Y.: Foreign object detection for LCC-S wireless power transfer system based on LSTM. In: 2021 IEEE International Conference on Emergency Science and Information Technology (ICESIT). 165–169 (2021) 4. Jeong, S.Y., Kwak, H.G., Jang, G.C., Rim, C.T.: Living object detection system based on comb pattern capacitive sensor for wireless EV chargers. In: 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC). 1–6 (2016) 5. Chu, S.Y., Zan, X., Avestruz, A.-T.: Electromagnetic model-based foreign object detection for wireless power transfer. IEEE Trans. Power Electron. 37(1), 100–113 (2022) 6. Gan, K., Zhang, H., Yao, C., Lai, X., Jin, N., Tang, H.: Statistical model of foreign object detection for wireless EV charger. In: 2019 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW). 71–74 (2019)
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7. Xiang, L., Zhu, Z., Tian, J., Tian, Y.: Foreign object detection in a wireless power transfer system using symmetrical coil sets. IEEE Access 7, 44622–44631 (2019) 8. Thai, V.X., Jang, G.C., Jeong, S.Y., Park, J.H., Kim, Y.-S., Rim, C.T.: Symmetric sensing coil design for the blind-zone free metal object detection of a stationary wireless electric vehicles charger. IEEE Trans. Power Electron. 35(4), 3466–3477 (2020) 9. Jeong, S.Y., Kwak, H.G., Jang, G.C., Choi, S.Y., Rim, C.T.: Dual-purpose non-overlapping coil sets as metal object and vehicle position detections for wireless stationary EV chargers. IEEE Trans. Power Electron. 33(9), 7387–7397 (2018) 10. Thai, V.X., Park, J.H., Jeong, S.Y., Rim, C.T., Kim, Y.S.: Equivalent-circuit-based design of symmetric sensing coil for self-inductance-based metal object detection. IEEE Access 8, 94190–94203 (2020) 11. Son, S., et al.: Foreign object detection of wireless power transfer system using sensor coil. In: 2021 IEEE Wireless Power Transfer Conference (WPTC). 1–4 (2021) 12. Jeong, S.Y., Thai, V.X., Park, J.H., Rim, C.T.: Self-Inductance-based metal object detection with mistuned resonant circuits and nullifying induced voltage for wireless EV chargers. IEEE Trans. Power Electron. 34(1), 748–758 (2019) 13. Zhang, H., Lee, J.-H., Iyer, N.M., Cao, L.: New analytical equations for skin and proximity effects in interconnects operated at high frequency. In: 2017 IEEE Electron Devices Technology and Manufacturing Conference (EDTM), 39–41(2017)
Optimal Efficiency Design of Single-to-Multiple Constant Voltage Based on LCC Compensation Topology for Wireless Power Transfer Cang Liang, Renjie Zhang, Cheng Zhao, Huan Yuan(B) , Aijun Yang, Xiaohua Wang, and Mingzhe Rong Xian Jiaotong University, Xian 710049, Shanxi, China [email protected]
Abstract. In order to achieve single-to-multiple high-efficiency wireless power transfer, this paper provides a design strategy for output efficiency optimization using the LCC compensation topology. To overcome the interference of the mutual inductance between the receivers to the current of the transmitter coil, the transmitter adopts the LCC topology and sets it to a load-independent constant current (CC) output mode. In order to further improve the coupling coefficient between the transmitting coil and the receiving coil, and achieve high-efficiency of both singleto- single and single-to-multiple energy transmission, a quasi-DD coil wound with the same magnetic polarity is designed. High anti-offset capacity, high-efficiency energy transmission can still be achieved when the receiving coil is offset or cut in and out. This paper provides a detailed hardware design strategy, analyzes the energy loss in the transmission process, uses SIMULINK software to simulate and verify the designed parameters, and builds an experimental prototype with 76% energy transfer efficiency. Keywords: LCC topology compensation · Single-to-multiple · Wireless power transfer · Constant voltage output efficiency optimization strategy
1 Introduction As a non-contact power transmission method, wireless power transfer (WPT) technology has received more and more attention in electric vehicles, electromechanical coupling, sensors, biomedical implants and other fields [1-5] in recent years. The existing wireless charging of small power consumer electronics stays in single input to single output (SISO) or multiple inputs to multiple outputs (SIMO) charging. In fact, SISO wireless charging greatly reduces the significance of WPT technology, because the transmitter still needs a charging line to connect with the socket. The existing SIMO wireless charging is essentially a combination of several SISO charging, requiring multiple inverters and power transmission equipment, which not only increases the cost of devices, but also complicates battery management. If we can develop a set of charging system that can be laid on the desktop, has strong anti-offset ability and can be single input to multiple outputs, and mobile phones, smart watches, laptops and other loads of different power © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 364–371, 2023. https://doi.org/10.1007/978-981-99-0631-4_37
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levels can be charged at the same time, we will really realize the convenience of wireless charging. As for SIMO, mutual inductances between receivers will greatly affect the overall working characteristics of the system and the overall power transfer efficiency. An efficiency optimization strategy is proposed in [6] when mutual inductance exists between multiple receivers. The optimal efficiency is achieved by adjusting the operating frequency. However, in this model, the mutual inductance between the receiver and the transmitter is considered to be constant, and in the process of energy transmission, it is difficult to identify the mutual inductances of the receivers in real time. The optimal load control strategy changes the equivalent load by adjusting the duty cycle of the DC-DC module on the secondary side, so as to achieve the optimal output efficiency [7]. In the field of consumer electronics, battery charging of consumer electronics usually requires constant current (CC)/constant voltage (CV) switching [8]. The optimal load regulation is not applicable to low-power consumer electronics. On the other hand, when the receiver is switched out/in, it will inevitably affect the transmission circuit. If the current of the transmitting coil is too small to suppress the induced voltage between receivers on the secondary side, the stabilized output voltage cannot be achieved. LCC topology can realize load independent CC input in the transmission coil [9], which is particularly suitable for SIMO WPT applications [10]. At the same time, the input current of the transmitter coil is constant and the induced voltage on the secondary side is constant, and the DC-DC voltage regulator module can maintain a stable working state. In this paper, LCC topology compensation is selected, and a simulation model and experimental prototype are built. Under the low power output of 5W, the transmission efficiency of SISO and SISO with offset can be more than 80%, and the size of the receiving coil is very small, which can be controlled within 3cm × 3cm. The overall efficiency is up to 76% at one transmitter to two receivers, which can provide stable power supply for a long time. It has unique advantages in overall efficiency and hardware design.
2 SIMO Circuit Model with LCC-S Topology Compensation The overall design scheme of this work is shown in Fig. 1. The DC input voltage V in outputs high-frequency ac voltage V 1 through the inverter, and the output current I 1 is shunted through LCC compensation topology, I 2 transmits power to receiver 1 and receiver 2 through the transmitting coil, the input current I 3 and I 4 of receiver 1 and receiver 2 transmit power to the load through the rectifier and DC-DC converter. L 1 , C 1 and C 2 constitute the LCC compensation topology on the primary side; Mutual inductances between transmitting coil L 2 and receiving coils L 3 and L 4 are M 13 and M 14 , respectively; Mutual inductance between Rx coils L 3 and L 4 is M 34 ; C 3 and C 4 are the series compensation capacitors of receiver 1 and receiver 2, respectively; The loads of receiver 1 and receiver 2 are represented as RL1 and RL2 , respectively, and their resistance values are 5 . Their output voltages are V L1 and V L2 , respectively. The system is composed of PWM generator, inverter, compensation circuits on the primary and secondary sides and transmitter/receiver coil. Generally, when the receiver
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Fig. 1. Diagram of SIMO WPT circuit with LLC topology.
compensation circuit is resonant, that is 1/ωC 3 = ωL 3 , 1/ωC 4 = ωL 4 , the front-end voltage V 2 and V 3 of rectifier can be expressed as: V2 = ωM13 I2 − ωM34 I4 (1) V3 = ωM14 I2 − ωM34 I3 When the number of receivers increases, if the transmission current I 2 is disturbed, the rectifier front-end voltage V 2 and V 3 will also be disturbed, which will not only affect the working state of the transmitter, but also make it difficult for the back-end DC-DC voltage stabilizing circuit to maintain stable operation. In order to realize the one to two wireless energy transmission of no less than 60%, the CC of the transmitting coil current is very important. By solving the KCL equation, it can be obtained that when the LCC compensation topology at the transmitter is 1/ωC 1 = ωL 1 , at this time, the transmission current I 2 is in the constant current working state independent of the load: I2 = V2 /jωL1
(2)
When mutual inductance M 34 between receivers exists, the transmitter needs a large transmission current I 2 to ensure that the voltage transmitted by the transmitter can effectively suppress the induced voltage between receivers, so as to ensure that each receiver can obtain a stable 5V output voltage. A typical LLC compensation circuit is shown in Fig. 1. In general, the LLC constant current topology needs to meet the following relationships: ⎧ 2 ω L1 C1 = 1 ⎪ ⎪ ⎪ ⎨ 2 ω L3 C3 = 1 (3) ⎪ ⎪ 2 C1 C2 ⎪ ⎩ ω L2 =1 C1 + C2 At this time, the transmission current I 2 flowing through the Tx coil can be expressed as Eq. (1). On the basis of Eqs. (1) and (3), the input current I 1 can be expressed as: I1 =
V2 (ωM13 )2 (ωM14 )2 (1 − − ) jωL1 jωL1 RL1 jωL1 RL2
(4)
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3 SIMO Efficiency Optimization Design The inverter generation circuit is a half bridge inverter circuit composed of EPC8009 GaN devices from EPC Company. Because the size of the Tx and Rx coil is small (7 cm × 7 cm, 3 cm × 3 cm). In the case of low mutual coupling, in order to meet 80% of the system energy transfer efficiency, the operating frequency needs to be increased to 1 MHz. Gallium nitride (GaN) devices have smaller size, lower drive loss and conduction loss at high frequency compared with traditional MOS tubes, and are more suitable for high frequency applications; Compared with the full bridge circuit, under the given 12V DC input voltage, the output voltage V 1 of the half bridge inverter circuit is a square wave with a peak to peak value of 12V (the full bridge circuit is 24V). Since the output current I 3 of L 2 in the LCC compensation topology is positively related to the inverter output voltage, reducing the output voltage V1 of the inverter circuit can effectively reduce the losses on L 2 and C 2 . The half bridge inverter circuit has more advantages than the full bridge inverter circuit. Considering the topology design of the receiver, the diode loss can generally be expressed as: 2π 2π I3 d ωt + 2Vd I4 d ωt (5) Ploss = 2Vd 0
0
where V d is the diode conduction voltage drop. When the output power is constant, the higher the rectifier front-end voltage, the lower the input currents I 3 and I 4 . At the same time, as the input currents I 3 and I 4 decrease, the diode conduction voltage drop V d will also decrease based on its physical properties. According to Eq. (5), the corresponding rectification loss will also be greatly reduced. S topology is also called series compensation topology. The induced voltage is the highest when 1 / ωC 3 = ωL 3 , 1/ ωC 4 = ωL 4 , which can meet the aforementioned low rectification loss. In order to achieve high efficiency wireless POWER transmission, it is necessary to reduce the loss of each link as much as possible, so the receiver compensation circuit selects S compensation topology.
4 Simulation and Experimental Verification To verify the efficiency, we used SIMULINK software to simulate and verify the designed WPT system. The loss of the simulation module was set as a fixed loss of 0.15W. The simulation diagram is shown in Fig. 2. Specific simulation parameters are shown in Table 1. The coil positive, offset and one to two simulation are mainly realized by changing the mutual inductances between the transmitting coil and the receiving coil, and the mutual inductances between multiple receiving coils. The circuit during SISO positive transmission is simulated (one transmitter and one receiver). The mutual inductance between transmitter and receiver is 12 uH. The simulated input current I 1 , output voltage V L and overall efficiency are shown in Fig. 3. The efficiency of SISO power transfer simulation can reach 84%, and the output voltage can also be stabilized at 5 V. It should be noted that in the initial state of the circuit, when the input current I 1 does not work in the steady state, there will be a high current peak.
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Parameters
Value
Parameters
Value
Parameters
Value
C 1‘ /nF
14.07
RL1 /
0.044
V F /V
0.2
C 2‘ /pF
287.2
RC1 /
0.056
L 1 /μH
1.8
C 3‘ /pF
1013.2
RL2 /
1
L 2 /μH
90
Vin /V
12
RL3 /
0.3
L 3 /μH
25
Fig. 2. Simulation diagram of proposed WPT system.
When designing the inverter circuit, special attention should be paid to the peak current of the MOS transistor to avoid device damage.
Fig. 3. Simulation diagram of SISO WPT system.
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The circuit with SISO offset of 1cm is simulated (one transmitter and one receiver). The input current I 1 , output voltage V L and overall efficiency obtained by simulation are shown in Fig. 4. When there is 1cm offset, the mutual inductance between transmitter and receiver is 10uH, the efficiency of one-to-one power transmission simulation can reach 83%, and the output voltage can also be stabilized at 5 V.
Fig. 4. Simulation diagram of SISO WPT system with offset.
For SIMO power transmission (one transmitter and two receivers), in order to facilitate analysis and verification, the parameters of the two receivers are set to be the same, as shown in Fig. 5. The mutual inductance between the transmitting coil and the receiving coil is 8uH, and the mutual inductance between the receiving coils is 1.5uH.
Fig. 5. Simulation diagram of SIMO WPT system.
The simulated input current I 1 , output voltage V L and overall efficiency are shown in Fig. 5. It can be seen that the output voltage can still be stabilized to 5 V under the condition of one transmitter and two receivers. At the same time, although the overall efficiency of the system is lower than 80% (only 78%), it can still meet the high output efficiency of more than 60% transmission efficiency. The peak value of input current I 1 decreases during one transmitter to two receivers transmission, but in specific design, MOS tubes should still be selected according to the maximum peak value of one transmitter to one receiver. The loss of each module of one-to-one positive transmission, one-to-one offset 1 cm transmission and one-to-two transmission is shown in Table 2. It can be found that in the low-power wireless power transmission, the loss mainly occurs in the inverter and rectifier links.
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Inverter
Rectifier
DC-DC
SISO
6.388W
5.922W
5.561W
5.402W
SISO + Offset
6.33W
5.869W
5.511W
5.361W
SIMO
12.79W
11.63W
10.864W
10.564W
5 Conclusion This paper proposes a design strategy based on LLC compensation topology, which has anti offset and SIMO functions. The power loss of the SIMO system is analyzed in detail, and a complete topology design and hardware design scheme are provided for the power loss of each part. In the low-power WPT system, power loss mainly occurs in the inverter and rectifier module. For the inverter module, the use of high-performance GaN devices and high efficiency drive modules can effectively reduce the inverter loss at high frequencies; For the rectifier module, when the back-end power output is constant, raising the receiver input voltage can effectively pull down the input current, thereby reducing the power loss of the rectifier module. It should be noted that the input voltage on the secondary side cannot be too high, which will lead to a low duty cycle of the back-end BUCK circuit and a significant increase in the loss of the BUCK regulator module on the secondary side. The theoretical analysis is validated by simulation and experiment.
References 1. Du, S., Chan, E.K., Wheatly, B., et al.: Wireless power transfer using oscillating magnets. IEEE Trans. Ind. Electron. 65(8), 6259–6269 (2018) 2. Li, Z., Zhu, C., Jiang, J., et al.: A 3-kW wireless power transfer system for sightseeing car supercapacitor charge. IEEE Trans. Power Electron. 32(5), 3301–3316 (2017). Author, F., Author, S., Author, T.: Book title. 2nd edn. Publisher, Location (1999) 3. Luo, B., Mai, R., Guo, L., et al.: LC–CLC compensation topology for capacitive power transfer system to improve misalignment performance. IET Power Electron. 12(10), 2626– 2633 (2019). http://www.springer.com/lncs. Accessed 21 Nov 2016 4. Li, K., Ni, W., Duan, L., et al.: Wireless power transfer and data collection in wireless sensor networks. IEEE Trans. Veh. Technol. 67(3), 2686–2697 (2018) 5. Wu, Y., Yuan, H., Zhang, R., et al.: Low-frequency wireless power transfer via rotating permanent magnets. IEEE Transactions on Industrial Electronics:1 6. Ahn, D., Hong, S.: Effect of coupling between multiple transmitters or multiple receivers on wireless power transfer. IEEE Trans. Ind. Electron. 60(7), 2602–2613 (2013) 7. Zhong, W.X., Hui, S.Y.R.: Maximum energy efficiency tracking for wireless power transfer systems. IEEE Trans. Power Electron. 30(7), 4025–4034 (2015) 8. Liu, Z., Su, Y., Zhao, Y., et al.: Capacitive power transfer system with double t-type resonant network for mobile devices charging/supply. IEEE Transactions on Power Electronics:1
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9. Tan, L., Pan, S., Liu, H., et al.: Load detection method for multiple-receiver wireless power transfer systems. IET Power Electron. 10(14), 1951–1958 (2017) 10. Jiang, Y., Wang, L., Wang, Y., Liu, J., Wu, M., Ning, G.: Analysis, design, and implementation of WPT system for EV’s battery charging based on optimal operation frequency range. IEEE Trans. Power Electron. 34(7), 6890–6905 (2019)
Design of Dynamic Wireless Charging System Based on Coupling Coefficient Estimation Xuchi Xue, Zhitao Liu(B) , Jia Liu, Wenjie Chen, and Hongye Su State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China [email protected]
Abstract. During the dynamic wireless charging process, the coupling coefficient between the wireless charging transmitter coil and the receiver coil varies greatly, thereby reducing the charging efficiency. Firstly, the change law of the magnetic coupling coefficient of the magnetic coupling mechanism in the process of dynamic wireless charging is analyzed. Secondly, the wireless charging network is analyzed to derive the relationship of the duty cycle under the optimal load. According to the changing law of the coupling coefficient, this paper analyzes the Kalman prediction model and the cubic exponential smoothing model, and proposes an improved error adaptive model based on the two algorithms. When the coupling coefficient changes rapidly, the error of the coefficient estimation can improve the efficiency of the whole wireless charging system. The method proposed in this paper can effectively improve the dynamic wireless charging efficiency by 9.5%, which is conducive to the popularization of electric AGV in the fields of transportation and logistics sorting. Keywords: Dynamic wireless power transfer · Bilateral LCC compensation · Coupling coefficient estimation · Maximum efficiency tracking
1 Introduction The traditional charging method of automatic guide vehicle (AGV) is wired contact charging. This charging method has many disadvantages, such as contacts being easily oxidized by moisture, potential safety hazards in the charging process, and fixed charging position. In order to improve the charging safety factor of AGV trolleys, the wireless energy transmission technology applied to AGV has been gradually developed and gradually matured [1, 2]. In the research of the magnetic coupling mechanism of wireless charging, there are mainly two types of long guide rails and segmented guide rails. Compared with the magnetic coupling mechanism of the long guide rail, the guide rail structure in the segmented form has a stronger magnetic field coupling ability [3, 4]. The current research on the magnetic coupling mechanism is mainly aimed at improving the coupling ability between the transmitting coil and the receiving coil, and improving the anti-offset ability [5, 6]. In terms of compensation structure, different charging modes correspond © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 372–384, 2023. https://doi.org/10.1007/978-981-99-0631-4_38
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to different circuit compensation structures. There are mainly four basic compensation topologies, namely series-parallel (SP), series-parallel (SS), series-parallel (PS) and series-parallel (PP) structures. The overall efficiency of the whole circuit is low due to the large and deep inductance of the circuit, so the research on high-order compensation topology has become popular in recent years [7, 8]. In the high-order compensation topology, the compensation structure of the LCC makes the system sensitive to changes in the parameters of the resonant circuit elements and improves the transmission efficiency of the system [9, 10]. In terms of maximum efficiency tracking, in the application of wireless charging, it is Generally necessary to make the system work at maximum efficiency to reduce system loss. However, the efficiency of wireless charging is affected by factors such as magnetic field coupling strength, compensation network parameters, and load characteristics, so there are many places to consider when tracking the maximum efficiency. In this paper, the composition and principle of the magnetically coupled resonant electric vehicle wireless charging system are firstly analyzed, and the rectangular coil array structure is simulated with the help of COMSOL software, and the variation trend of the coupling coefficient in the dynamic charging process is obtained. Secondly, in the set frequency range, through the analysis and derivation of the double-ended LCC compensation network, combined with MATLAB software, a set of suitable compensation parameters are deduced, and the optimal load model of the double-ended LCC is derived. Finally, the relationship model between the duty cycle and the coupling coefficient in the DC-DC impedance matching network was established estimated model. The estimated value is brought into the model between the duty cycle and the coupling coefficient to improve the efficiency of the entire wireless charging system when the coupling coefficient changes rapidly. The theoretical derivation is verified by Simulink software and physical platform.
2 System Modeling 2.1 System Introduction In the case of dynamic wireless charging, multiple transmitter coils can be coupled with single and secondary side receiver coils. The circuit structure of dynamic wireless charging in this paper is shown in Fig. 1.
Fig. 1. Dynamic wireless charging circuit structure
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As shown in Fig. 1, wireless charging consists of three parts: the inverter circuit, the compensation network and the magnetic coupling mechanism of the transmitter part; in the receiving part, it consists of the magnetic coupling mechanism, the compensation network, the rectifier circuit and the DC-DC active circuit composition. Impedance matching network composition. In terms of compensation network, both the transmitter and the receiver choose the LCC structure as the compensation network to improve the power quality. The DC-DC active impedance matching network at the receiving end is a Buck-Boost circuit. The output is a purely resistive electronic load. When the receiving coil is loaded on the motorized AGV and moves continuously, the coupling area between the transmitting coil and the receiving coil is constantly changing. When the coupling coefficient between the two coils fluctuates greatly, the power output at the receiving end will fluctuate, and the transmission efficiency will decrease. Therefore, this paper aims to suppress the efficiency fluctuation when the coupling coefficient changes in the dynamic wireless charging process and improve the overall transmission efficiency of the system. 2.2 Analysis of Magnetic Coupling Mechanism In dynamic wireless charging, the receiver coil moves on the transmitter coil array to pick up power from the adjacent transmitter coils. Therefore, the process of dynamic wireless charging in this paper can be equivalent to a power transmission model with dual transmitter coils, as shown in Fig. 2.
Fig. 2. Schematic diagram of the magnetic circuit structure of dynamic wireless charging
The derivation formula of the mutual inductance model between a single transmitter coil and the receiver coil is shown in formula (1). M13 = ψI13 = μN1lN3 S1 3 (1) ψ13 = N1 φ13 = N1 BS1 = N1 μ Nl3 I3 S1 = μN1lN2 S1 I3 In the formula, ψ13 is the number of flux linkages between the first coil of the transmitting end and the receiving coil of the receiving end; φ13 is the magnetic flux between the first coil of the transmitting end and the receiving coil; B is the magnetic induction intensity; ϕ is the magnetic permeability; l height between coils. The COMSOL software is used to simulate the mutual inductance between the transmitter coil and the receiver coil during the dynamic wireless charging process. The
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coil is a rectangular structure, its length is 30 cm, its width is 20 cm, each turn of the coil is 3 mm, a total of 16 strands, the coil self-inductance is 140 µH, and the vertical distance between the receiving coil and the transmitting coil is 10 cm. The horizontal distance between the two transmitting ends is chosen to be 10 cm. The change curve of the mutual inductance between the transmitting coil and the receiving end during the dynamic wireless charging process is shown in Fig. 3.
Fig. 3. Dynamic wireless charging coupling coefficient change diagram
In the dynamic wireless charging process, the change of the mutual inductance between the receiving end and the first transmitting coil and the second transmitting coil is a fluctuating process. According to this changing characteristic, this paper proposes a dynamic wireless charging coupling coefficient estimation model based on the improved exponential smoothing method. 2.3 Compensation Network Design In this paper, the dynamic wireless charging compensation network scheme selects the topology of the double-ended LCC. The double-ended LCC compensation network diagram is shown in Fig. 4.
Fig. 4. Double-ended LCC compensation network diagram
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Among them, the double-ended LCC network is in full resonance, the output power of the system can be obtained from the mesh equation. Pout = I02 RL =
M 2 Uin2 RL
(2)
ω2 L2f1 L2f2
Among them, M is the coupling coefficient, which can be derived from the sampled output power. It is pushed to the formula (3) Pout ω2 L2f L2f 1 2 (3) M = Uin2 RL The transmission efficiency of the double-ended LCC wireless charging system can be obtained through the formula of (total efficiency of the system = efficiency of the transmitting end and efficiency of the receiving end). The system efficiency can be obtained as: 1 1 · (4) ηLCC = L RL Cf2 RP 1 + ω2 M 2 (RS + RL Cf2f ) 1 + R2 L f2
2
2.4 Optimal Load Modeling Adding the impedance of the rectifier circuit, the equivalent impedance of the receiving end can be equivalent to Eq. (9). √ Uout 2 2Udc /π 8(1 − Dbb )2 = RL (5) Req = √ = 2 Iout π 2 Dbb π Idc /2 2 Taking the partial derivative of the transmission efficiency of the LCC compensation network system to the load RL . Then let ∂η∂RLCC = 0, and the formula (6) can be derived. L L2f2 RP Ropt = 2 (6) Cf2 Rs (ω2 M 2 + RP RS ) Combine the optimal load with an active impedance matching network. It can be deduced that the value of the duty cycle under the optimal load of the system is formula (7). 1 D= (7) π2 8RL
L2f RP 2
Cf2 RS (ω2 M 2 +RP RS )
+1
It can be seen from Eq. (7) that there is a relationship between the duty cycle under optimal load and the coupling coefficient in dynamic wireless charging. Therefore, the coupling coefficient in the dynamic charging process can be calculated by using the formula (3) through the state of the voltage and current in the circuit. Then use the coupling coefficient value of the previous moment to estimate. The estimated value is then combined with the derivation formula for the most loaded to obtain the duty cycle of the optimum load.
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3 Maximum Efficiency Tracking Model Based on Coupling Coefficient Estimation 3.1 Kalman Prediction Model The Kalman prediction part used in this paper mainly performs a priori estimation based on the current state, and then calculates the value of the current state variable and the estimated error covariance to construct a priori estimated value for the next time state; The prior estimates of the estimation process and the current measured variables establish a posterior estimate for the current state. Its process time update equation and state update equation are shown in Eqs. (8) and (9). Time update equation: − − X k = AX k−1 + BUk (8) Pk− = APk−1 AT + Q
State update equation: ⎧ ⎪ ⎪ ⎨ Kk =
Pk− H T
H Pk− H +R − − X k = X k + Kk (Zk − H X k ) ⎪ ⎪ ⎩ Pk = (1 − Kk H )Pk−
T
−
(9)
In the formula, X k represents the prior state estimate of the kth step when the state before the kth step is known; X k represents the posterior state estimate of the kth step when the measurement variable Zk is known; Pk represents the covariance; Pk− represents the predicted value covariance. In the COMSOL simulation, the prediction analysis is carried out according to the change data of the coupling coefficient during the dynamic charging process of the receiver. Since the dynamic wireless charging system changes in real time, it is necessary to predict and update the data in real time. The results of the real-time prediction of the model are shown in Fig. 5 (a).
Fig. 5. The result of the Kalman prediction model
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Comparing the predicted value of Kalman with the actual value of the coupling coefficient, the model has the effect of following the trend, but there is a large error. The difference between the Kalman predicted value and the actual value is analyzed. The result is shown in Fig. 5 (b). The Kalman forecast model has a strong hysteresis and is not sensitive to some small changes. 3.2 Triple Exponential Smoothing Model In the process of dynamic wireless charging, the transmitting coils are arrayed, and each coil is separated by a fixed distance. This makes the coupling coefficient between the transmitter coil and the receiver coil change periodically. Since time series can be used to describe the characteristics of phenomena changing with time, this paper introduces time series into the coupling coefficient estimation model. In time series, exponential smoothing can make predictions on data with periodic changes. In the exponential smoothing method, it is divided into three exponential smoothing. When the change of the time series is periodic, the triple exponential smoothing method can be constructed for prediction, and its calculation formula is formula (10). ⎧ ⎪ (1) (1) ⎪ ⎪ St = αyt + (1 − α)St−1 ⎪ ⎪ ⎨ (2) (1) (2) (10) St = αSt + (1 − α)St−1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ S (3) = αS (2) + (1 − α)S (3) t t t−1 (3)
In the formula, St is the triple exponential smoothing value. The prediction model of the triple exponential smoothing method is formula (11)
yt+T = at + bt T + ct T 2 , T = 1, 2, · · ·
In formula (11): ⎧ (1) (2) (3) ⎪ ⎨ at = 3St − 3St − St(1) (2) α bt = 2(1−α) [(6 − 5α)St − 2(5 − 4α)St + (4 − 3α)St(3) ] ⎪ ⎩ c = α 2 [S (1) − S (2) + S (3) ] t
2(1−α)2
t
t
(11)
(12)
t
In the dynamic wireless charging system, before estimating the coupling coefficient, the model parameter a needs to be determined first. Therefore, before making predictions, first perform the most valuable search on a. When the value of a is 0.13, the error of the whole system is the smallest. After the model parameters are determined, The comparison between the estimated results and the actual values is shown in Fig. 6.
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Fig. 6. Model result analysis based on three exponential smoothing methods
The one-time exponential smoothing method can predict the existing trend, but the one-time exponential smoothing is slow to respond to the changing trend, and the prediction result has a large error. The quadratic exponential smoothing method has a certain degree of identification of the changing trend, but the error is still very large. The triple exponential smoothing method is more sensitive to the changing trend, and can predict more accurately when the training samples reach a certain number. 3.3 Coupling Coefficient Estimation Optimization In the Kalman forecast, the forecast trend can be effectively followed, but with a certain lag. Compared with the first exponential smoothing method and the second exponential smoothing method, the error of the Kalman prediction model is smaller, and the accuracy of the model is higher. The error of the triple exponential smoothing method is slightly worse than that of the Kalman prediction model, but when the number of training samples reaches a certain number, the triple exponential smoothing model is more superior. The triple exponential smoothing method has poor prediction performance in the early stage, and can be combined with the Kalman prediction method to make up for it. Combining the two prediction methods, this paper establishes an improved error adaptive model based on the two algorithms. Ypre = kYker + (1 − k)Ysmo
(13)
Among them, Y pre is the predicted value of the optimization model, Y ker is the predicted value of Kalman, and Y smo is the predicted value of the exponential smoothing method. k is the error adaptive coefficient. The expression of Kalman coefficient is shown in formula (14). k = kadj
|Y − Ysmo | |Y − Yker | + |Y − Ysmo |
(14)
In the adaptive coefficient, the reliability coefficient k adj is introduced to correct the degree of trust between the models. The introduction of this coefficient can correct the
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large error existing in the early stage of the exponential smoothing prediction, increase the proportion of the Kalman prediction value, and reduce the overall error of the model. Use the search method to determine two parameters in the model. For the smoothing parameter a, the search range is 0–0.3, and the optimal value is searched with a step size of 0.01. When the smoothing coefficient is 0.13, the error of the triple exponential smoothing method is the smallest. Next, find the optimal reliability coefficient. Define the search range as 0.8–1.2 and the search step as 0.01. When the reliability coefficient is set to 0.97, the total error of the optimized model is minimized. Therefore, the reliability coefficient of the optimized model is set to 0.97. The values of the two parameters are brought into the optimization model for analysis, and the results are shown in Fig. 7.
Fig. 7. Comparison of the results of the three prediction models
The error of the model is shown in Fig. 7. The Kalman prediction model can make up for the large error caused by the lack of training samples in the exponential smoothing method in the early stage of prediction. The exponential smoothing method can follow the target well after the training samples reach a certain number. Therefore, in the later stage of the model, the reliability coefficient can be adjusted to make the predicted value of the model more inclined to the result of the exponential smoothing prediction model. Under the combined optimization of the two algorithms, the model is closer to the true value.
4 Test Results 4.1 Validation of Maximum Efficiency Tracking Model Based on Coupling Coefficient Estimation The coupling coefficient estimation model is simulated and verified by MATLAB/Simulink software, and the simulation adopts the circuit model and parameters verified in the second section. For each sub-process of dynamic wireless charging, the extraction of the coupling coefficient and the estimation of the coupling coefficient are
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carried out respectively, and the extracted data and the estimated data are compared and analyzed. When the estimated data error is within a certain range, the estimated value of the coupling coefficient is substituted into the calculation model of the optimal load to obtain the duty cycle of the buck-boost circuit when the system is optimally loaded. According to formula (2), the output power is 1000 W as the target amount, and the compensation network parameters are set. The parameters of the coil in the wireless charging system and the resonant frequency of the system are shown in Table 1 below. Table 1. Parameter selection of wireless charging circuit components Parameter name
Parameter value
Coil 1 Self-inductance LP /µH
140
Coil 2 Self-inductance LS /µH
140
Coil 1 resistance RP /
0.3
Coil 2 resistance RP /
0.3
Resonant frequency f /kHz
85
Input voltage Uin /V
100
Resistive load RL /
12.5
According to the system parameters in Table 1, the parameters of each compensation element in the double-ended LCC are obtained by solving, and the parameters are shown in Table 2. Table 2. LCC compensation network element parameter selection Parameter name
Parameter value
Transmitter compensation inductance Lf1 /µH
21.64
Receiver compensation inductance Lf2 /µH
21.64
Transmitter compensation capacitor Cf1 /nF
162.04
Receiver compensation capacitor Cf2 /nF
162.04
Transmitter compensation capacitor CP /nF
29.62
Receiver compensation capacitor CfS /nF
29.62
A dual-terminal LCC wireless charging simulation circuit is built in MATLAB/Simulink software, and Eqs. (3) and (7) are introduced for simulation. Figure 8 shows the comparison of the working efficiency of the dynamic wireless charging system when the coupling coefficient estimation model is introduced and the model is not added.
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Fig. 8. Coupling coefficient estimation model effect comparison chart
In Fig. 8, when the receiving end coil is between the two coils, the working efficiency of the system decreases. Compared with the case where the coupling coefficient estimation model is not added, the degree of decrease of the system work efficiency is suppressed. Compared with the model without coupling coefficient, the efficiency of the system is only about 50%. After adding the model, the working efficiency of the system has been greatly improved, and the degree of decline has been significantly suppressed. 4.2 Coupling Coefficient Estimation Model Results Physical Platform Verification In this paper, a 1 kW wireless charging experimental device is built as an experimental platform to verify the coupling coefficient estimation model. The experimental platform is shown in Fig. 9.
Fig. 9. Wireless charging rail device
In the physical verification part, this paper provides the condition of variable coupling coefficient by means of sampling points. During the test, during the offset process of the transceiver coil, the width of the coil is used as the maximum offset to divide into ten equal parts, and the output power of each ten equal point is calculated in turn to verify the validity of the model. The experimental results are shown in Fig. 10.
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Fig. 10. Physical output efficiency points
It can be seen from Fig. 10(a) that although the output power using the coupling coefficient estimation model is lower than that without the model, the average power is about 380 W, but the fluctuation range of the output power is small and the stability is high. The actual output efficiency sampling results are shown in Fig. 10(b). The output efficiency of the system is significantly improved compared with that without the model, and the overall efficiency is improved by 9.5% compared with the previous one. The experimental data can fully verify the validity of the coupling coefficient estimation model.
5 Conclusion The AGVs can be charged while working, thereby extending their battery life. However, during the dynamic wireless charging process of the electric AGV, the coupling coefficient between the transmitting coil and the receiving coil will change. The change of the coupling coefficient will affect the transmission performance of the system, so that the transmission efficiency and output power of the system will decrease accordingly. Therefore, a rectangular coil structure is designed in this paper, and the optimal load under different coupling coefficients is estimated based on the double-ended LCC network topology. By changing the DC/DC impedance matching network for impedance matching, the problem of system efficiency drop caused by the large change of the coupling coefficient during the dynamic wireless charging process is solved. Acknowledgments. This work was partially supported by Science Fund for Creative Research Group of the National Natural Science Foundation of China (Grant NO. 61621002), National Natural Science Foundation of China (NSFC: 62173297), Zhejiang Key R&D Program (Grant NO. 2022C01035), Fundamental Research Funds for the Central Universities (NO. 226-2022-00086).
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References 1. Tavakoli, R., Pantic, Z.: Analysis, design, and demonstration of a 25-kW dynamic wireless charging system for roadway electric vehicles. IEEE J. Emerg. Sel. Top. Power Electron. 6(3), 1378–1393 (2018) 2. Limb, B.J., Asher, Z.D., Bradley, T.H.: Economic viability and environmental impact of in-motion wireless power transfer. IEEE Trans. Transport. Electrif. 5(1), 135–146 (2018) 3. Choi, S., Gu, B.W., Jeong, S.Y., Rim, C.T.: Advances in wireless power transfer systems for roadway-powered electric vehicles. IEEE Trans. Industr. Electron. 63(10), 6533–6545 (2016) 4. Miller, J.M, Onar, O.C., Chinthavali, M.: Primary-side power flow control of wireless power transfer for electric vehicle charging. IEEE J. Emerg. Sel. Top. Power Electron. 3(1), 147–162 (2015) 5. Moon, S., Kim, B., Cho, S., et al.: Analysis and design of a wireless power transfer system with an intermediate coil for high efficiency. IEEE Trans. Industr. Electron. 61(11), 5861–5870 (2014) 6. Liu, J., Liu, Z.T., Su, H.Y.: Passivity-based PI control for receiver side of dynamic wireless charging system in electric vehicles. IEEE Trans. Industr. Electron. 69(1), 783–794 (2021) 7. Wu, H.H., Covic, G.A., Boys, J.T., et al.: A series-tuned inductive-power-transfer pickup with a controllable AC-voltage output. IEEE Trans. Power Electron. 26(1), 98–109 (2011) 8. Elliott, G.A.J., Raabe, S., Covic, G.A., et al.: Multiphase pickups for large lateral tolerance contactless power-transfer systems. IEEE Trans. Industr. Electron. 57(5), 1590–1598 (2010) 9. Li, H.L., Hu, A.P., Covic, G.A., et al.: Optimal coupling condition of IPT system for achieving maximum power transfer. Electron. Lett. 45(1), 76–77 (2009) 10. Zhang, Q., Huang, X., Chen, Z., et al.: Research on control strategy for the uniform charging of electric vehicle battery swapping station. Trans. China Electrotech. Soc. 30(12), 447–453 (2015)
Influence of Frequency on Transmission Performance of Multi-relay Wireless Power Supply System Zhijun Wu , Linlin Tan(B) , Shuyu Shen, and Heqi Xu Southeast University, Nanjing 210096, China [email protected]
Abstract. Frequency is an important parameter in the wireless power supply system. To explore the effect of frequency on the multi-relay wireless power supply system, the system is analyzed from three aspects: numerical calculation, finite element simulation, and experimental verification. In this paper, the relationship between the frequency and the system output power is calculated by using the equivalent circuit model. It is found that the coil internal resistance will increase with the increase of frequency due to the existence of skin effect and proximity effect. Then, a five-coil wireless power supply system model is built in the Ansys software. The output power and efficiency of the system are simulated, and the operating frequency range of the system is determined. Finally, a 5-coil wireless power transmission experimental platform is built, and four frequency points are selected as the working frequency to measure its output power and efficiency. The experimental results verify the rationality of the above theoretical analysis. Keywords: Relay coil · Wireless power transfer · Internal resistance
1 Introduction Compared with cable transmission, wireless power transmission (WPT) technology has been widely concerned by researchers because of its advantages of high security and flexibility without being bound by wires [1–5]. With the development of WPT technology, it is more and more widely used on special occasions requiring electrical isolation, high voltage insulation, and so on. For example, in terms of intelligent operation and maintenance in the high-voltage power system industry, WPT technology is used to supply power to intelligent devices on the transmission tower to ensure that the devices can work normally and achieve continuous monitoring of high-voltage transmission lines [6–9]. The resonant coil of WPT is installed based on the hardware of insulator string or embedded into the insulator to realize the power transmission from the transmission line side to the electrical equipment [10, 11]. However, the transmission distance of WPT system is limited. When the transmission distance is too long, the transmission power and efficiency of WPT system cannot meet the requirements. Therefore, to improve the energy transmission distance of the WPT system, the concept of the relay coil is introduced. As an extremely important part of the WPT system, the relay coil can effectively © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 385–399, 2023. https://doi.org/10.1007/978-981-99-0631-4_39
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focus the magnetic field, making the transmission distance of the WPT system longer. [12–14]. In the past, for the two-wire coil WPT system, when the mutual inductance remained fixed, the induced voltage on the receiving side could be increased by increasing the system operating frequency [15–18]. However, in the multi-relay wireless power transmission system, due to the existence of multiple repeater resonance links in the system, the slight deviation of the resonance frequency will lead to the reduction of transmission power and transmission efficiency, which makes the system become more sensitive to the operating point frequency. At the same time, the negative effects caused by the increase of internal resistance caused by high frequency and the loss of switching devices and circuit stray parameters cannot be ignored. In this paper, the relationship between the frequency and the system output power is calculated by using the equivalent circuit model. It is found that the coil internal resistance will increase with the increase of frequency due to the existence of skin effect and proximity effect. Then, a five-coil wireless power supply system model is built in the Ansys software. The output power and efficiency of the system are simulated, and the operating frequency range of the system is determined. Finally, a 5-coil wireless power transmission experimental platform is built, and four frequency points are selected as the working frequency to measure its output power and efficiency. The experimental results verify the rationality of the above theoretical analysis.
2 Equivalent Circuit Model The equivalent circuit model diagram of the multi-relay coil system is shown in Fig. 1. In Fig. 1, L1 , L2 , · · · Ln is the coil self-inductance, C1 , C2 , · · · Cn is the series resonant capacitor and the relay coils are equally spaced, so the mutual inductance values between adjacent coils are equal, M12 , M13 , · · · M1n is the mutual inductance between the transmitting coil and the nth relay coil, R1 , R2 , · · · Rn is the coil internal resistance, Us is the input voltage, and Rl is the load resistance.
Fig. 1. Equivalent circuit of multiple relay coils.
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From Fig. 1, the following equation can be written: ⎡ ⎤ ⎡ ⎤⎡ ˙ U˙ 1 Z11 Z12 Z13 · · · Z1n I1 ⎢ 0⎥ ⎢ ⎥ ⎢ Z21 Z22 Z23 · · · Z2n ⎥⎢ I˙2 ⎢ ⎥ ⎢ ⎥⎢ ⎢ 0 ⎥ ⎢ Z31 Z32 Z33 · · · Z3n ⎥⎢ I˙3 ⎢ ⎥=⎢ ⎥⎢ ⎢ . ⎥ ⎢ . . . . ⎥⎢ . .. ⎢ . ⎥ ⎣ .. .. .. . . ⎦⎣ .. . ⎣ . ⎦ Zn1 Zn2 Zn3 · · · Znn + Rl I˙n 0
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⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
(1)
In formula (1) Zii = Rpi + j(ωLi −
1 ) ωCi
(2)
Zij = jωMij
(3)
where i = j and satisfy i, j = 1, 2, 3, · · · , n. When the system is completely resonant, Eq. (2) can be expressed as Zii = Rpi
(4)
Substitute ω=2π f (f is the operating frequency) into Eqs. (1), (2), and (3) ⎡ ⎤ U1 ⎡ Rp1 ⎤⎡ ⎤ M M · · · M1n ⎢ ω⎥ I1 ⎢ ⎥ ⎢ ω Rp212 13 ⎥⎢ ⎥ ⎢ 0 ⎥ ⎢ M21 M · · · M I ⎥ 23 2n ⎢ 2 ⎥ ω ⎢ ⎥ ⎢ ⎥⎢ ⎥ Rp3 ⎢ ⎥ I3 ⎥ M M · · · M 31 32 3n ⎥ ⎢ 0 ⎥=⎢ ω ⎢ ⎥⎢ ⎢ ⎢ ⎥ ⎢ . . ⎥ ⎥ . . . ⎢ . ⎥ ⎣ . .. .. . . . .. ⎦⎣ .. ⎦ . ⎢ . ⎥ ⎣ . ⎦ R In Mn1 Mn2 Mn3 · · · ωeq 0 where Req = Rpn + Rl . From formula (5), the relay coil equation can be obtained as ⎡ ⎤ ⎡ ⎤⎡ Rp2 0 M M · · · M I1 21 23 2n ω ⎢ 0⎥ ⎢ ⎥⎢ Rp3 ⎢ ⎥ ⎢ M31 I ⎥ M · · · M 2 32 3n ⎢ ⎥ ⎢ ω ⎥⎢ ⎢ ⎢ 0⎥ ⎢ M ⎥ I M42 M43 · · · M4n ⎥⎢ 3 41 ⎢ ⎥=⎢ ⎢ .⎥ ⎢ . ⎥⎢ .. .. .. .. .. ⎢ .⎥ ⎣ ⎦⎣ .. . . . . . ⎣ .⎦ In M(n−1)1 M(n−1)2 M(n−1)3 · · · M(n−1)n 0 Let M = [ M21 M31 M41 · · · M(n−1)n ]T N = [ M2n M3n · · · M(n−2)n M(n−1)n ]T
(5)
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
(6)
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⎡
Rp2 ω
M23
M24 M34
Rp3 ⎢ M ⎢ 32 ω ⎢ Rp4 M M Z =⎢ 42 43 ω ⎢ .. .. .. ⎢ ⎣ . . . M(n−1)2 M(n−1)3 M(n−1)4
⎤ · · · M2(n−1) · · · M3(n−1) ⎥ ⎥ ⎥ · · · M4(n−1) ⎥ ⎥ .. ⎥ .. ⎦ . . Rp(n−1) ··· ω
Then, by solving Eq. (6), we can get, In =
−Uin Z21 (Z12 Z21 − Z11 Z22 )ω − Req Rp1 ω + Req Z11 + Rp1 Z22
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where Z11 = M T Z −1 M , Z12 = M T Z −1 N , Z21 = N T Z −1 M , Z22 = N T Z −1 N . The output power is Pout = In2 Rl
(8)
The system efficiency is Pout Uin I1
η=
(9)
The AC resistance can be expressed as Rac = Rdc (1+Rs )
(10)
where Rac is the AC resistance per unit length of the conductor at the standard operating temperature (/m), Rdc is the DC resistance per unit length of the conductor at the standard operating temperature (/m), Rs is the skin effect (SE) resistance. For a singleturn planar coil, the SE resistance is calculated as [19] Rs = Rdc
h 1 δ(1 − e−h/ δ ) 1 + h w
δ=
1 π μ0 σ f
(11) (12)
where f is the system frequency, h and w are the thickness and width of the wire, and σ is the conductivity of the wire. At the same time, studies have shown that the phenomenon of eddy current crowding can cause proximity effect (PE) resistance, that is, when the magnetic field generated by the coil outside a turn of wire passes through the surface of this turn of wire, eddy currents that hinder the change of the magnetic field will be generated in the wire. Eddy currents can cause uneven current distribution on the cross-section of the wire, resulting in PE resistance. In [20], the formula of the PE resistance of a multi-turn planar coil is: Rr =
N
n=1
Rrn =
N
4π ( ln n Hn2 ) σ n=1
(13)
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where Rrn is the PE resistance of the nth turn of wire, n is the curve fitting formula related to the coil size, and Hn is the magnetic field strength perpendicular to the conductor surface when excited by a 1 A current [21]. The total resistance of the coil is the sum of the SE resistance and the PE resistance [22], R = Rac + Rr
(14)
On the other hand, since there are multiple relay resonance links in the multi-coil structure, each resonance link has its own resonance frequency according to the coil inductance and compensation capacitance. Due to inaccurate measurement of coil inductance or errors in capacitance fabrication, the actual inductance and capacitance models are shown in Fig. 2.
Fig. 2. Actual capacitor-inductor model.
In Fig. 2, C is the equivalent capacitance error ( C = −(Cp2 + Cp C) C), and the series resonance model will be shown in Fig. 3.
Fig. 3. Equivalent circuit.
In Fig. 3, Lp is the ideal inductance, Cp is the ideal capacitance, L is the inductance error, and C is the equivalent capacitance error. Ideally, the system satisfies ω0 Lp −
1 =0 ω0 Cp
(15)
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Equation (4) no longer applies when inductive and capacitive errors are considered. When the system works as shown in Eq. (15), Eq. (4) is rewritten as Zii = Rpi + j(ω0 Li −
1 ) ω0 Ci
(16)
Let δL = L L be the error rate of the inductance, and its value is generally ±(0.1% − 0.25%). Let δC = C C be the error rate caused by the manufacture of the capacitor, and the allowable error of its design is generally ±(0.1% − 5%). When the above errors inevitably exist in the relay resonance links, there will be a certain deviation in the resonance frequency between the relay resonance links, and the impedance in the relay coil will be as shown in Eq. (16), which will greatly reduce the transmission power and efficiency of the system. To sum up, for the multi-relay coil system, frequency selection, parameter error, and coil internal resistance are the influencing factors that cannot be ignored when improving the transmission power and efficiency of the system. This paper will focus on analyzing the relationship between frequency, coil internal resistance, and system efficiency.
3 Simulation Analysis It can be seen from the analysis in the previous section that as the frequency increases, the internal resistance of the coil will also increase accordingly, resulting in a decrease in the efficiency of the system. Therefore, this section will take the 5-coil WPT system as an example to analyze the frequency, coil internal resistance, and system efficiency by means of simulation and numerical calculation. This paper builds 5 square coils in Ansys Maxwell, as shown in Fig. 4.
Fig. 4. 5-coil WPT system.
The mutual inductance between the coils is obtained through the finite element method simulation as shown in Table 1.
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Table 1. Mutual inductance simulation results. Coil number
Mutual inductance/µH
M 12
6.5743
M 13
1.6541
M 14
0.60075
M 15
0.27346
According to formula (14), the relationship between coil internal resistance and frequency can be calculated as shown in Fig. 5.
Fig. 5. The relationship between frequency and internal resistance.
Substitute the mutual inductance results between the coils obtained by simulation into Eq. (8), and calculate the changes in the input and output power of the system when the input voltage is constant, as shown in Fig. 6. It can be seen from Fig. 6 that under the condition of the same input voltage, the output power decreases with the increase of the frequency. Furthermore, the relationship between the efficiency of the system and the frequency is obtained as shown in Fig. 7.
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Fig. 6. The relationship between frequency and input power and output power.
Fig. 7. The relationship between frequency and efficiency.
As can be seen from Fig. 7, with the increase in frequency, the transmission efficiency of the system first increases and then decreases. It is because as the frequency increases, the AC resistance of the coil rises sharply, resulting in an increase in losses on the coil and a decrease in the efficiency of the system. To sum up, when the input voltage is constant, the output power will decrease as the frequency increases. The system efficiency will increase within a certain frequency range, but when the frequency is too high, the system efficiency will decrease instead. Therefore, in the process of system design, reasonable design of parameters should be carried out according to the input conditions and output requirements of the system and combined with the system efficiency.
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4 Experimental Verification To verify the above analysis, a 5-coil wireless power transmission experimental platform is built in this paper. First, PCB coils are used. The wire width is 8 mm and the thickness is 0.007 mm to meet the actual current demand. The turn spacing is 1 mm. The PCB coil is shown in Fig. 8.
Fig. 8. PCB coil.
The impedance analyzer was used to measure the coil internal resistance at the frequency of 2 kHz–3 MHz as shown in Fig. 9.
Fig. 9. Impedance measurement.
It can be seen from Fig. 9 that as the frequency increases, the coil internal resistance also increases sharply. According to the simulation result shown in Fig. 8, the transmission efficiency of the system is the highest when the operating frequency is 1.8 MHz. In
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order to verify the trend of the efficiency of the system changing with frequency, according to the measurement results shown in Fig. 9, four frequency points are selected for the experiment, and the measurement results of the coil internal resistance corresponding to the four frequency points are shown in Table 2. Table 2. Impedance values at different frequencies. Frequency/MHz
Internal resistance/
0.8
1.77
0.9
2.48
1.8
5.4
3.0
10.66
Referring to the parameters shown in Table 2, the experimental platform of the system built in this paper is shown in Fig. 10.
Fig. 10. Experiment platform.
By changing the operating frequency of the system and the corresponding component parameters, the AC-to-AC system efficiency and coil internal resistance of the system at different frequencies are experimentally measured as shown in Fig. 11.
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Fig. 11. The relationship between frequency and efficiency.
It can be seen from Fig. 11 that when the frequency increases, the AC resistance of the coil also increases correspondingly, which causes the efficiency of the system to first increase and then decrease with the increase of the frequency. To verify the influence of proximity effect resistance on the system, a space spiral coil is designed and wound in this paper, as shown in Fig. 12, with a turn spacing of 6 mm.
Fig. 12. Circular space spiral coil.
The measured impedance of the circular coil and the impedance of the PCB coil are compared as shown in Fig. 13.
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Fig. 13. The relationship between frequency and impedance.
As can be seen from Fig. 13, the circular coil has a smaller proximity effect resistance due to the larger turn spacing, and at the same time, the Litz wire also reduces the skin effect resistance, making the overall coil internal resistance smaller. The system efficiency of the circular coils is tested under the condition that the mutual inductance between the circular coils and the PCB coils are the same. The experimental platform is shown in Fig. 14.
Fig. 14. Experiment platform.
By changing the capacitance parameters and operating frequency of the system, the experimentally measured AC to AC operating efficiency of the system at different frequencies is shown in Fig. 15.
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Fig. 15. The relationship between frequency and efficiency.
It can be seen from Fig. 15 that, due to the small internal resistance of the coil, the efficiency improves as the frequency increases, but when the frequency increases to 3 MHz, the efficiency rises more slowly. It can be seen from Fig. 13 that the internal resistance of the coil is relatively large at this time. It can be seen from the two experimental results that the coil internal resistance is closely related to the system operating frequency and work efficiency. Therefore, when designing a multi-relay coil WPT system, the influence of high-frequency resistance on the system transmission efficiency should be fully considered. When the system inevitably needs to work under high-frequency conditions, the system impedance can be reduced from the SE resistance and the PE resistance to improve the system efficiency.
5 Conclusion Multi-relay wireless power supply system plays an important role in long-distance wireless power supply. However, due to the existence of multiple repeater resonant links in the system, the slight deviation of these repeater resonant frequencies will lead to the reduction of transmission performance, making the WPT system more sensitive to the operating point frequency. To select an appropriate frequency range for multi relay WPT system, the relationship between frequency and coil internal resistance is calculated in this paper. It is found that the operating frequency of multi relay WPT system cannot be infinitely increased due to the existence of SE and PE resistance. According to the calculation results, a five coil WPT system model is established in the finite element simulation software. With the transmission efficiency of the WPT system as the constraint condition, the operating frequency range of the five coil WPT system is determined. Finally, a five coil wireless power transmission experimental platform is built, and four frequency points are selected as working frequencies to measure its output power and efficiency. The experimental results verify the rationality of the above theoretical analysis. Acknowledgments. This work is supported in part by National Key Research and Development funded Project (2021YFB2501604).
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References 1. Shinohara, N.: Trends in wireless power transfer: WPT technology for energy harvesting, millimeter-wave/THz rectennas, MIMO-WPT, and advances in near-field WPT applications. IEEE Microwave Mag. 22(1), 46–59 (2021) 2. Hassen, T., Elzawawy, A., Alaskary, S.: A proposed trend toward capacitive coupling for wireless power transfer technology. In: 2021 International Telecommunications Conference (ITC-Egypt), pp. 1–9. IEEE, Alexandria, Egypt (2021) 3. Nigsch, S., Kyburz, F., Schenk, K.: Coil geometry modeling and optimization for a bidirectional wireless power transfer system. In: SMACD/PRIME 2021; International Conference on SMACD and 16th Conference on PRIME, pp. 1–4. VDE (2021) 4. Zakerian, A., Vaez-Zadeh, S., Babaki, A.: A dynamic WPT system with high efficiency and high power factor for electric vehicles. IEEE Trans. Power Electron. 35(7), 6732–6740 (2020) 5. Dang, X., Jayathurathnage, P., Tretyakov, S.A., Simovski, C.R.: Self-tuning multi-transmitter wireless power transfer to freely positioned receivers. IEEE Access 8, 119940–119950 (2020) 6. Werneck, M., Moreira D., Cosenza De Carvalho, C., Vieira Batista De Nazare, F., Celia Da Silva Barros Allil, R.: Detection and monitoring of leakage currents in power transmission insulators. IEEE Sens. J. 15(3), 1338–1346 (2015) 7. Medved, D., Pavlik, M., Zbojovsky, J.: Computer modeling of electromagnetic field around the 22 kV high voltage overhead lines. In: 2018 International IEEE Conference and Workshop in Óbuda on Electrical and Power Engineering (CANDO-EPE), pp. 289–294. IEEE, Budapest (2018) 8. Marius, P., Catalin L., Ovidiu B., Alexandru S.: Study on induced currents in an elliptical cylindrical model by overhead high voltage power lines. In: 2019 11th International Symposium on Advanced Topics in Electrical Engineering (ATEE), pp. 1–5. IEEE, Bucharest (2019) 9. Song, H., Wang, Y., Liu, X., Wang, H., Han, X., Wu, Z.: Study on design and optimal control of long-distance wireless power supply system based on high-voltage lines. In: 2021 3rd International Conference on Electrical Engineering and Control Technologies (CEECT), pp. 114–120. IEEE, Macau (2021) 10. Cai, C., et al.: Resonant wireless charging system design for 110-kV high-voltage transmission line monitoring equipment. IEEE Trans. Power Electron. 66(5), 4118–4129 (2019) 11. Zhang, C., Lin, D., Tang, N., Hui, S.: A novel electric insulation string structure with highvoltage insulation and wireless power transfer capabilities. IEEE Trans. Power Electron. 33(1), 87–96 (2018) 12. Zhong, W., Lee, C., Hui, S.: Wireless power domino-resonator systems with noncoaxial axes and circular structures. IEEE Trans. Power Electron. 27(11), 4750–4762 (2012) 13. Lee, C., Zhong, W., Hui, S.: Effects of magnetic coupling of nonadjacent resonators on wireless power domino-resonator systems. IEEE Trans. Power Electron. 27(4), 1905–1916 (2012) 14. Yan, Z., et al.: A monitoring equipment charging system for HVTL based on domino-resonator WPT With constant current or constant voltage output. IEEE Trans. Power Electron. 37(3), 3668–3680 (2022) 15. Zan, X., Avestruz, A.: Active segmentation at 100 MHz for 12W VHF wireless power transfer. In: 20th IEEE Workshop on Control and Modeling for Power Electronics (COMPEL). IEEE, Univ Toronto (2019) 16. Minki, K., Jungwon, C.: High-frequency, mid-range wireless power transfer system using critical coupling coefficient adjustment. In: 2021 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 714–719. IEEE, Phoenix (2021)
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17. Aldhaher, S., Mitcheson, P., Arteaga, J., Kkelis, G., Yates, D.: Light-weight wireless power transfer for mid-air charging of drones. In: 11th European Conference on Antennas and Propagation (EUCAP), pp. 336–340. IEEE, Paris (2017) 18. Li, J., Costinett, D.: Analysis and design of a series self-resonant coil for wireless power transfer. In: 2018 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1052–1059. IEEE, San Antonio (2018) 19. Wheeler, H.: Formulas for the skin effect. Proceedings IRE 30(9), 412–424. IEEE (1942) 20. Lope, I., Carretero, C., Acero, J., Alonso, R., Burdio, J.: AC power losses model for planar windings with rectangular cross-sectional conductors. IEEE Trans. Power Electron. 29(1), 23–28 (2014) 21. Kuhn, W., Ibrahim, N.: Analysis of current crowding effects in multiturn spiral inductors. IEEE Trans. Microw. Theory Tech. 49(1), 31–38 (2001) 22. Ferreira, J.: Improved analytical modeling of conductive losses in magnetic components. IEEE Trans. Power Electron. 9(1), 127–131 (1994)
Bidirectional Wireless Power Transfer System Control Strategy on Double-Sided LCC Resonant Network Shuxuan Zheng1 , Kainan Chen1,2(B) , Yuchen Chen1 , Liqiang Yuan1,2 , and Zhengming Zhao1,2 1 Department of Electrical Engineering, Tsinghua University, Beijing, China
[email protected], [email protected] 2 Sichuan Energy Internet Research Institute, Tsinghua University, Chengdu, China
Abstract. In bidirectional magnetic coupled resonant wireless power transmission system, in view of the difficulties in the cooperative control of high-frequency converters at the transmitting and receiving sides, as well as the problems of high resonance order and easy detuning of double-sided LCC resonance topology, the applicable conditions of the control strategy independent of real-time wireless communication in double-sided LCC resonance topology are analyzed. The highest efficiency working point of the system is deduced through the steady-state analysis of the circuit, and it is proved that the control method of phase shift angle disturbance observation at the receiving side is suitable for the double-sided LCC resonant topology. Then combined with the EDF and GSSA methods of the fullycontrolled full-bridge converter, the dynamic model of the double-sided LCC system is established, the control stability and dynamic performance are analyzed, and the PI regulator and filter parameters are designed. Based on the dynamic model, the influence of the parameter offset of the resonant element on the control performance is analyzed, and the parameters of the DC filter link are adjusted to improve the system controlling stability. The simulation and experimental results verify the correctness of the theoretical analysis. Keywords: Wireless power transmission · Double-sided LCC resonant topology · Independent of real-time wireless communication · Dynamic performance
1 Introduction Magnetic coupled resonant wireless power transmission (MCR-WPT) systems are showing promising application prospects in fields as electric vehicles, rail transit power supply and so on. Compared with traditional plug-in charging systems, WPT can achieve safer and more convenient power transmission performance [1, 2]. Early WPT systems mostly use four basic resonant networks, while the LCC resonant topology proposed in the literature [3] has the advantages of decoupling between load conditions and resonant frequency, coupling coefficient. LCC resonant also shows high © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 400–414, 2023. https://doi.org/10.1007/978-981-99-0631-4_40
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power transfer capability, meeting increasing power demands. Because of these advantages, it is gradually used in high-power system species. Although there have been many theoretical studies on such topology, they focus mainly on loss analysis [4], optimal design of passive component parameters [5, 6], and implementation of soft switching [7], and there are still deficiencies in control strategy and dynamic performance analysis. With the demand for power communication between electric vehicles and the grid, bidirectional WPT technology is expected. In the case of active converters at both transmit and receive sides, the system is usually controlled by Triple Phase Shift (TPS) which controls the two inward phase shift angles of the H-bridge converters at both sides and the outward phase shift angle between them. The literature [8] analyzed the operating conditions for the resonant network to achieve the highest efficiency point under TPS, which requires the outward phase shift angle to be maintained at 90°. However, it is difficult to achieve phase synchronization and cooperative control at both sides without real-time communication. To solve this problem, a control strategy independent of real-time wireless communication was proposed [9]. It implements perturbation observation of the inward phase shift angle at the receiving side under TPS control, and the control system achieves the maximum efficiency point with good results in SS resonant topology. Most of the current research in bidirectional WPT control is based on basic resonant topologies such as SS, while research in bilateral LCC resonance is still deficient in bidirectional power transfer control. The literature [10] verified the bidirectional power transfer capability of the bilateral LCC resonant network, but in terms of control, the receiving side is considered as a passive converter without control. There are more passive components in LCC resonant network and thus the resonance order is higher, making the deviation of individual component parameters easily leading to the system resonance point shift or loss of resonance. The disorder can cause current waveform distortion and affect the control stability. Therefore, it is necessary to analyze the dynamic performance of the WPT system with bilateral LCC resonance. This paper extends the idea of bidirectional WPT control independent of real-time wireless communication to the more complex bilateral LCC resonant topology. The first step is to obtain the converter control conditions for the LCC resonant network to achieve the highest efficiency with the circuit steady-state analysis. Then, by applying the Extended Description Function (EDF) and Generalized State Space Averaging (GSSA) methods, it establishes the dynamic models of the high frequency converter and resonant network, analyzes their dynamic performance and optimizes the controller parameters. Finally, from the perspective of system control stability, the design method of component parameters is proposed. The relevant theoretical analysis is verified by simulation and experiment.
2 Steady-State Analysis of Double-Sided LCC WPT System A bilateral LCC resonant network WPT system is shown in Fig. 1. The transmitting and receiving sides both consist of a DC filter circuit, a high frequency converter, and a resonant network. L 1 and L 2 are the self-inductance of the transmitting and receiving coils, M is their mutual inductance, r 1 and r 2 are their internal resistance respectively, and
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C f1 and C f2 are the compensation capacitors on both sides. L f1 and C 1 are the resonant inductance and capacitance of the transmitting side, and r f1 is the internal resistance of L f1 . L dc1 and C dc1 are the DC filter inductance and capacitance of the transmitting side, and r dc1 is the internal resistance of L dc1 . The same for the receiving side, and the subscript is denoted by 2.
Fig. 1. Circuit diagram of WPT system of double-sided LCC resonant network
For the WPT system with TPS control, the transmission power control is achieved by adjusting the phase difference of the output voltage pulses of the bridge arm, i.e., the phase shift angle, as shown in Fig. 2. Where ϕ1 and ϕ2 are the internal phase shift angle at the transmitting and receiving sides, and θ the external phase shift angle.
Fig. 2. Waveform of bridges output voltage pulse in TPS control
There have been many studies on the steady-state analysis of WPT systems, and in terms of phase-shifting control strategies, reference can be made to those based on the SS resonant topology [9]. Applying this method, the maximum efficiency condition of the system in bilateral LCC resonant topology can be obtained. Only the key steps as well as the conclusions are written in this paper.
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The loop current equation for the resonant network part is listed. ⎧ 1 ˙ Zf 1 I˙Lf 1 − jωC I1 = U˙ 1 ⎪ 1 ⎪ ⎪ ⎨ − 1 I˙ + Z I˙ − jωM I˙ = 0 1 1 2 jωC1 Lf 1 1 ˙ ˙ ⎪ Zf 2 ILf 2 − jωC2 = −U2 ⎪ ⎪ ⎩ 1 ˙ −jωM I˙1 − jωC ILf 2 + Z2 I˙2 = 0 2
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(1)
1 1 , Z1 = ωL1 + R1 + jωC1 f 1 + jωC , Zf 2 = jωLf 2 + Rf 2 + where Zf 1 = jωLf 1 + Rf 1 + jωC 1 1 1 jωC2 , Z2
1 = ωL2 + R2 + jωC1 f 2 + jωC are impedance of each loop. 2 Solving the system transmission efficiency
η=
k 2 ReY11 + ReY22 P2 =1− 2 P1 k ReY11 − |Y12 | cos(θ + arg Y12 )
(2)
where k = U1 /U2 denotes the ratio of the AC voltage of the transmitting and receiving sides, and θ is the outward phase shift angle, i.e., the voltage phase of each side. Assuming the system is operating under resonant conditions, then arg Y12 = π2 . From the efficiency expression, it is easy to find that the system reaches the maximum power transfer efficiency when θ = π2 . And the ratio of voltage needs to meet kopt =
1 ReY11 |Y12 | sin θ
(ReY11 )2 (ReY22 )2 + ReY11 ReY22 |Y12 |2 sin2 θ + ReY11 ReY22
Next, the transmitter inward phase shift angle control command is obtained kopt Pref π φ1 = arcsin √ 2 2Udc1 kopt |Y12 | − ReY22
(3)
(4)
According to Eq. (2) and Eq. (4), at resonance, the sensitivity of ϕ2 to the θ is √ ∂U2 ∂U2 ∂ϕ2 π P2 k|Y12 | cos θ = / =− √ (5) 3 ∂θ ∂θ ∂ϕ2 2 2UCdc2 cos ϕ22 (k|Y12 | sin θ − ReY11 ) 2 The above equation shows that when θ is less than 90°, it decreases with the increase of ϕ2 ; when θ is greater than 90°, it increases with the increase of ϕ2 , and ϕ2 reaches minimum when θ is 90°. Therefore, a receiving side perturbation control strategy similar to literature [9] can be used in the bilateral LCC resonant topology, as shown in Fig. 3. The error of the load current iL is introduced into the PI regulator at the receiving side to generate the ϕ 2 control signal, which in turn realizes the regulation of the output power Pout . And by applying a disturbance to the outward phase shift angle θ, the θ that minimizes ϕ2 is found, and the control of θ is realized. At the transmitting side, the control command of the internal phase shift angle ϕ 1 can be calculated according to the circuit parameters or measurement results. The WPT system is controlled to work at the maximum efficiency point and achieve power stabilization control independent of real-time communication between the transmitting and receiving sides. It has the advantages of reliability, economy and efficiency,
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Fig. 3. Control diagram of (a) overall system (b) perturbation observation on receiving side
as it gets rid of the dependence of the bidirectional WPT control system on the real-time wireless communication of the primary and secondary sides, solves the phase synchronization problem and achieves the maximum efficiency point tracking at the same time. However, based on the characteristics of bilateral LCC itself, the aforementioned control strategy differs from SS resonant topology in terms of dynamic performance, stability analysis, and parameter design, which will be analyzed in the following.
3 Dynamic Model In order to examine the stability of the system under perturbations and to determine the perturbation observation execution period, a dynamic model of the WPT system is required. In the system shown in Fig. 1, each inductor current and capacitor voltage are selected as state variables and their state space models are established. The state equation of the DC filtering link is ⎧ ⎪ Ldc1 didtS = −rdc1 iS − uCdc1 + Vdc1 ⎪ ⎪ ⎨ Cdc1 Cdc1 dudt = iS − i01 (6) di L ⎪ L = −r i dc2 L + uCdc2 − Vdc2 ⎪ ⎪ dc2 dt ⎩ Cdc2 Cdc2 dudt = −iL + i02 The state equations of LCC resonant network are ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩
Lf 1
L1 didtL1
diLf 1 dt
= −rLf 1 iLf 1 − uC1 + u1 C1 dudtC1 = iLf 1 − iL1 du Cf 1 dtCf 1 = iL1 − M didtL2 = −r1 iL1 + uC1 − uCf 1
⎧ ⎪ ⎪ ⎪ ⎨
diLf 2 dt = −rLf 2 iLf 2 + uC2 − u2 C2 dudtC2 = −iLf 2 + iL2 , du ⎪ Cf 2 dtCf 2 = iL2 ⎪ ⎪ ⎩ diL2 L1 dt − M didtL1 = −r1 iL2 − uC2 − uCf 2
Lf 2
(7)
The GSSA method is used to linearize Eq. (7) to obtain its averaged state space model, and this expression is rather space-occupying so it is written in appendix Eq. (A1). The literature [11] developed a dynamic model of a fully controlled full-bridge converter based on the EDF method, which is
i01 uCdc1 = 21 u1 s iLf 1 s + u1 c iLf 1 c
(8) i02 uCdc2 = 21 u2 s iLf 2 s + u2 c iLf 2 c
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According to steady-state phase relationship, the sine and cosine components of the AC side voltage of the converter can be introduced. And then the linearization of small signals near the static operating point for DC currents and voltages are expressed as ⎧
⎨ ˆi01 = 1 ˆ ˆ U U I u ˆ u ˆ + + I + − I u ˆ i i 1 s Lf 1 1 c Lf 1 01 Cdc1 Lf 1 c 1 c 2UCdc1 Lf 1 s 1 s s c
⎩ ˆi02 = 1 ˆ ˆ U U I u ˆ u ˆ + + I + − I u ˆ i i 2 2 2 2 02 Lf 2 Lf 2 Lf 2 Lf 2 Cdc2 s c 2UCdc2 s s c c s
⎧ ⎪ uˆ 1 = ⎪ ⎪ ⎨ s uˆ = 1 c ⎪ uˆ 2 s = ⎪ ⎪ ⎩ uˆ 2 c =
c
(9) 4 π 4 π 4 π 4 π
sin 21 cos 1 · uˆ Cdc1 + π2 UCdc1 cos 21 sin 21 sin 1 · uˆ Cdc1 + π2 UCdc1 cos 21 sin 22 cos 2 · uˆ Cdc2 + π2 UCdc2 cos 22 sin 22 sin 2 · uˆ Cdc2 + π2 UCdc2 cos 22
cos 1 · ϕˆ1 − π4 UCdc1 sin 21 sin 1 · θˆ1 sin 1 · ϕˆ1 + π4 UCdc1 sin 21 cos 1 · θˆ1 cos 2 · ϕˆ2 − π4 UCdc2 sin 22 sin 2 · θˆ2 sin 2 · ϕˆ2 + π4 UCdc2 sin 22 cos 2 · θˆ2
(10)
The small-signal state space model of the system is obtained by combining Eq. (6), equation (A1), Eq. (9) and Eq. (10).
d xˆ A1 dt = A2 xˆ + Buˆ (11) y = C xˆ In which
xˆ = iLf 1 s , iLf 1 c , uC1 s , uC1 c , uCf 1 s , uCf 1 c , iL1 s , iL1 c , iLf 2 s , T
iLf 2 c , uC2 s , uC2 c , uCf 2 s , uCf 2 c , iL2 s , iL2 c , ˆiS , uˆ Cdc1 , ˆiL , uˆ Cdc2 T uˆ = θˆ1 , θˆ2 , ϕˆ1 , ϕˆ2 (12) yˆ = ˆiL A1 , A2 , B and C are the parameter matrices of 20 × 20, 20 × 20, 20 × 4, and 1 × 20, respectively. According to the state space model Eq. (11), the s-domain expression of the small signal transfer function from the control quantity to the system output quantity is derived. (13) Gθ2 (s), Gϕ1 (s), Gϕ2 (s) = C(sA1 − A2 )−1 B1 where Gθ2 (s), Gϕ1 (s) and Gϕ2 (s) represent the small signal transfer function from θˆ2 , ϕˆ1 and ϕˆ2 to ˆiL respectively. To facilitate the analysis, the actual prototype circuit parameters shown in Table 1 are used as an example to analyze the frequency characteristics of the transfer function derived from Eq. (13) and to compare the simulation results with those obtained from DSIM simulation software.
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Parameter
Value
Parameter
Value
L 1 , L 2 /μH
234.268, 237.657
L f1 , L f2 /μH
31.2, 31.1
M/μH
27.659
r f1 , r f2 /m
20
r 1 , r 2 /m
157.821, 343.978
L dc1 , L dc2 /μH
6.7
C 1 , C 2 /nF
115.3, 115.5
C dc1 , C dc2 /μF
100
C f1 , C f2 /nF
18.15, 18.17
V dc1, V dc2 /V
350
Fig. 4. Comparison of analysis and simulation of transfer function frequency characteristic
As can be seen from Fig. 4, the theoretical calculation is very close to the simulation results when the frequency is low (10 kHz), the error in the calculation results is larger. This is due to the fact that the dynamic model is based on the state space averaging method, which is difficult to handle the frequency characteristics close to the switching frequency of the converter. However, the control system analyzed in this paper does not require a high control bandwidth, and this model can meet the requirements of controller design and system dynamic performance analysis.
4 Control System Dynamic Analysis and Controller Design In the control strategy of the WPT system described in Section I, the digital controller of ϕ 2 includes four parts: sampling, zero-order retainer, PI regulator, and delay, whose s-domain model can be represented by the following transfer function [12] Ki 1 − 0.5sTs K (14) + Gd (s) = p s (1 + 0.5sTs )2 Then the open-loop transfer function of the system is G(s) = Gd (s)Gϕ2 (s)
(15)
The s-domain small signal model of the control system can be expressed as ˆiL (s) =
Gϕ1 (s) G(s) ˆ Gθ2 (s) θˆ2 (s) + ϕˆ1 (s) iref (s) + 1 + G(s) 1 + G(s) 1 + G(s)
(16)
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In which ˆiref = Pˆ ref /Vdc2 . The dynamic performance of this control system is analyzed below to examine the amplitude margin, phase margin, open-loop low-frequency gain (at 1 Hz), and closedloop bandwidth of the system in the frequency domain when the PI parameters are varied.
Fig. 5. Frequency domain performance of controller under different PI parameters
The following rules can be obtained from Fig. 5. 1) As K p increases, K g decreases and γ initially remains constant and then decreases rapidly. The system is unstable for larger K p . While |G(j2π )|and ωb remain almost constant. 2) As K i increases, K g first increases and then decreases, γ initially remains constant and then decreases rapidly. The system cannot reach stability when K i is large. |G(j2π )| and ωb increase significantly. Then, in terms of the time domain, K p and K i are extracted from the closed-loop characteristic equations and the generalized root trajectory diagram of the equivalent open-loop system is drawn. Considering only the dominant pole, its generalized root trajectory diagram is shown in Fig. 6.
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Fig. 6. Generalized root locus of controller under different PI parameters
Figure 6 indicates the following patterns. 1) The dominant pole distribution of the system is close to the second-order underdamped system. 2) In the process of increasing K p from 0.001 to 0.1, the damping coefficient of the system gradually increases. 3) In the process of increasing K i from 10 to 45, the damping coefficient of the system decreases and the natural oscillation frequency increases; in the process of continuing to increase K i to 1000, the system shows over-damping. Combining the results of time domain and frequency domain analysis, the values of K p and K i can be set as 0.005 and 100 respectively. The frequency characteristic curves of the open-loop and closed-loop transfer functions of ϕ 2 under this control parameter are shown in Fig. 7.
Fig. 7. Frequency characteristic of open-loop and closed-loop ϕ 2 transfer functions
The closed-loop transfer functions of θ 2 and ϕ 1 have significant amplitude spikes above 6 kHz, which may lead to high-frequency oscillations in the system under the disturbance of θ 2 and ϕ 1 and affect the normal operation of the controller. Therefore, low-frequency filters need to be added to the control loop. According to the frequency characteristics shown in Fig. 9 and the control bandwidth of the system, consider adding a pre-filter link to the control signal outputs of θ 2 and ϕ 1 , using a 4th-order Butterworth filter with the cut-off frequency set at 1000 Hz.
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The closed-loop transfer function frequency characteristics of θ 2 and ϕ 1 before and after setting the filter are shown in Fig. 8.
Fig. 8. Comparison of closed-loop frequency characteristics of controller with and without filtering
Figure 8 shows that there is a significant decrease in high frequency gain without a significant decrease in the closed-loop control bandwidth of the system, and the filter can suppress high frequency oscillations and guarantee the control stability of the system.
5 Parameter Design of Passive Components The problem of high order and easy detuning of the bilateral LCC resonant topology damages the system control stability, so it is necessary to analyze the effect of resonant element parameter offset on the system dynamic performance and propose passive element design requirements from the perspective of control stability. For a WPT system with the parameters shown in Table 1, assuming a 5% deviation in some of the component parameters, the control system performance indicators will change accordingly, as shown in Fig. 9.
Fig. 9. System amplitude margin with biased resonant element parameters
Figure 9 shows the effect of detuning due to resonant element parameter shifts on the control stability, and the following conclusions can be drawn.
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(1) Changes in the mutual inductance M of the coil do not affect the system amplitude margin. (2) Changes in compensation capacitance C f and coil inductance L have a small effect on the amplitude margin. (3) The change of resonant inductance L f has a large impact on the amplitude margin. (4) The error of the resonant capacitor C causes a significant decrease in the stability margin. Combined with the system circuit diagram Fig. 1 and the resonance condition, it can be seen that the resonant capacitor C is involved in both sides of the resonance, which is more important in the resonant network and therefore has a significant impact on the system stability. Priority should be given to ensure the accuracy of C during design. The DC filter suppresses the high-frequency oscillations of the system, and its element parameters can have an impact on changing the system stability. Figure 10 shows the effect of DC filter element parameter changes on the system amplitude margin.
Fig. 10. System amplitude margin with different DC filter element parameters
If the DC filter inductors and capacitors L dc and C dc at the transmit and receive sides are increased exponentially, the system stability margin is significantly increased, and vice versa. Since the DC bus capacitor is usually space consuming, priority should be given to improving system stability by increasing the DC filter inductor.
6 Simulation and Experimental Validation The control strategy studied in this paper is verified in Simulink simulation platform. The system circuit diagram is shown in Fig. 1, and the parameters are the same as those in Table 1. When the power command is changed, the system input and output power, phase shift angle, and voltage and current waveforms are shown in Fig. 11. Simulation results show that under this control strategy, the system can maintain the outward phase shift angle at 90° and achieve stable tracking and fast response to power commands. In this study, experimental verification was performed on an experimental platform. The prototype consists of the following parts: a fully controlled full-bridge converter
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Fig. 11. Simulation waveform of phase shift angle, voltage and current and transmission power
at the transmitting and receiving sides, a magnetic coupling mechanism, a bilateral LCC resonant network, and a DC power supply and waveform measurement equipment (Fig. 12).
Fig. 12. Actual photograph of principle verification prototype
A small power experiment verifies the phase synchronization and the stability of power transmission. The AC-side voltage and current waveforms of the converter at the transmitting and receiving sides are shown in Fig. 13.
Fig. 13. Small power experimental waveform of voltage and current
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The experimental results show that the system can operate stably with the voltage and current phases at the transmitting side leading the receiving side by 90°, and achieve phase synchronization and outward phase angle θ control without relying on real-time wireless communication. The 1 kW bidirectional power switching experiment verifies the ability of the control strategy to quickly switch the power transmission direction, and the experimental waveforms before and after switching are shown in Fig. 14.
Fig. 14. Power transmission direction switching experimental waveform
The experimental results show that the system can stably achieve bi-directional power transmission and dynamic switching of power transmission direction. During the switching process, the DC current quickly reaches the steady state and the transmitted power reaches the set value. It is pointed out that the control algorithm has good dynamic performance.
7 Discussion In order to realize the bidirectional power transmission of bilateral LCC resonant topology WPT system, this paper establishes a model to analyze it and draws the following conclusions. 1) The steady-state analysis shows that when the bilateral LCC resonant topology WPT system works in the resonant state, it can be controlled by perturbation observation to
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achieve phase synchronization at the transmitting and receiving sides without relying on real-time wireless communication, so that the system can reach the maximum efficiency point. 2) Based on the dynamic model, the stability of the above control strategy under bilateral LCC resonant topology is investigated and the controller and filter parameters are designed. The design method can be applied to different LCC resonant WPT systems. 3) The resonant element parameters as well as the DC filter design method are proposed in terms of the controller dynamic performance. It is proved that the above control strategy can overcome the adverse effects of LCC topology detuning on the control stability.
Acknowledgments. This work is supported by Science and Technology Project of State Grid (SGHB0000KXJS1900586).
Appendix State-space averaging equations for LCC resonant networks ⎧
d iLf 1 s ⎪ Lf 1 dt = ωLf 1 iLf 1 c − rLf 1 iLf 1 s − uC1 s + u1 s ⎪ ⎪ ⎪
⎪ d i ⎪ ⎪ Lf 1 Lfdt 1 c = −ωLf 1 iLf 1 s − rLf 1 iLf 1 c − uC1 c + u1 c ⎪ ⎪
⎪ ⎪ ⎪ C1 d udtC1 s = ωC1 uC1 c + iLf 1 s − iL1 s ⎪ ⎪
⎨ d uC1 c C1 dt = −ωC1 uC1 s + iLf 1 c − iL1 c
d uCf 1 s ⎪ ⎪ Cf 1 dt = ωCf 1 uCf 1 c + iL1 s ⎪ ⎪
⎪ d uCf 1 c ⎪ ⎪ Cf 1 dt = −ωCf 1 uCf 1 s + iL1 c ⎪ ⎪
⎪ ⎪ ⎪ L1 d idtL1 s − M d idtL2 s = ωL1 iL1 c − ωM iL2 c − r1 iL1 s + uC1 s − uCf 1 s ⎪ ⎪
⎩ d iL1 c L1 dt − M d idtL2 c = −ωL1 iL1 s + ωM iL2 s − r1 iL1 c + uC1 c − uCf 1 c ⎧
d iLf 2 s ⎪ Lf 2 dt = ωLf 2 iLf 2 c − rLf 2 iLf 2 s + uC2 s − u2 s ⎪ ⎪ ⎪
⎪ d iLf 2 c ⎪ ⎪ 2 iLf 2 c + uC2 c − u2 c ⎪ Lf 2 dt = −ωLf 2 iLf 2 s − rLf ⎪
⎪ ⎪ ⎪ C2 d udtC2 s = ωC2 uC2 c − iLf 2 s + iL2 s ⎪ ⎪
⎨ d uC2 c C2 dt = −ωC2 uC2 s − iLf 2 c + iL2 c
d uCf 2 s ⎪ ⎪ Cf 2 dt = ωCf 2 uCf 2 c + iL2 s ⎪ ⎪
⎪ d uCf 2 c ⎪ ⎪ Cf 2 dt = −ωCf 2 uCf 2 s + iL2 c ⎪ ⎪
⎪ ⎪ ⎪ L2 d idtL2 s − M d idtL1 s = ωL2 iL2 c − ωM iL1 c − r2 iL2 s − uC2 s − uCf 2 s ⎪ ⎪
⎩ d iL2 c L2 dt − M d idtL1 c = −ωL2 iL2 s + ωM iL1 s − r2 iL2 c − uC2 c − uCf 2 c (A1)
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References 1. Pusti, A., Das, P.K., Panda, A.K., Padhi, J., Kar, D.P.: Essential analysis of MRC-WPT system for electric vehicle charging using coupled mode theory. In: 2021 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON), pp. 1–5 (2021) 2. Patil, B.M., Gadgune, S.Y.: Review of wireless power transfer for EV with advancement in designs. In: 2021 5th International Conference on Electrical, Electronics, Communication, Computer Technologies and Optimization Techniques (ICEECCOT), pp. 44–48 (2021) 3. Li, S., Li, W., Deng, J., Nguyen, T.D., Mi, C.C.: A double-sided LCC compensation network and its tuning method for wireless power transfer. IEEE Trans. Veh. Technol. 64, 2261–2273 (2015) 4. Chen, K., Zhao, Z., Liu, F., Yuan, L.: Analysis of resonant topology for bi-direction wireless charging of electric vehicle. Autom. Electr. Power Syst. 41, 66–82 (2017). (in Chinese) 5. Su, Y.G., Wu, X.Y., Zhao, Y.M., Qing, X.D., Tang, C.S.: Parameter optimization of electricfield coupled wireless power transfer system with complementary symmetric LCC resonant network. Trans. China Electrotechn. Soc. 34, 2874–2883 (2019). (in Chinese) 6. Cheng, F., Liu, C., Shao, X., et al.: Parameter design method for symmetric dual LCC compensated wireless power transfer system. Adv. Technol. Electr. Eng. Energy 40(12), 64–72 (2021) 7. Fu, N., Deng, J., Wang, Z., Wang, W., Wang, S.: A hybrid mode control strategy for LCC– LCC- compensated WPT system with wide ZVS operation. IEEE Trans. Power Electr. 37, 2449–2460 (2022) 8. Nguyen, B.X., et al.: An efficiency optimization scheme for bidirectional inductive power transfer systems. IEEE Trans. Power Electr. 30, 6310–6319 (2015) 9. Tan, T., Chen, K., Jiang, Y., Lin, Q., Yuan, L., Zhao, Z.: A bidirectional wireless power transfer system control strategy independent of real-time wireless communication. IEEE Trans. Ind. Appl. 56, 1587–1598 (2020) 10. Mohammad, M., et al.: Bidirectional LCC–LCC-compensated 20-kW wireless power transfer system for medium-duty vehicle charging. IEEE Trans. Transport. Electrif. 7, 1205–1218 (2021) 11. Dong, W., Baguley, C.A., Madawala, U.K.: New modelling and control techniques for wireless power transfer (WPT) systems. In: 2020 8th International Conference on Power Electronics Systems and Applications (PESA), pp. 1–4 (2020) 12. Mei, T., Zhang, X., Liu, F., Chen, X., Kennel, R.M.: Multi-frequency phase-shifted angle control strategy for a two-phase MCR WPT system with multiple loads to achieve targeted power distribution and stable transmission power. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3117–3122 (2019)
Design of Underwater Wet Plug Connectors System Based on the Principle of Wireless Power Transfer Jianduo Zhang1 , He Yin1 , Yudong Fu2 , Hai Lan3 , and Dan Li1(B) 1 Yantai Research Institute of Harbin Engineering University, Yantai 264010, China
{zhangjianduo,ccy1824,davidlee}@hrbeu.edu.cn
2 College of Materials Science and Chemical Engineering, Harbin Engineering University,
Harbin 150000, China [email protected] 3 College of Intelligent Science and Engineering, Harbin Engineering University, Harbin 150000, China [email protected]
Abstract. To improve the low reliability while extending the service life of contacting underwater wet-plug connector, which is enslaved by the solve the issues such as low tightness and difficult insertion process, a wireless wet-plug connector system is designed based on magnetic coupling resonant wireless power transfer principle in this paper. Compared with existing researches, the proposed connector is superior in volume and weight, revealing excellent advantages in under water applications such as remotely operated vehicles (ROV). Correspondingly, a system circuit control method using underwater radio frequency communication is proposed to realize closed-loop control. The performance of the whole system has been tested in the air, pool and sea The maximum output power of the system is 1182 W and the maximum efficiency is 92.8%. It has been verified that, the prototype could always operate stably, and the system efficiency appears no significant difference in different environments. Keywords: Underwater wet-plug · Connector · Wireless power transfer · Radio frequency communication
1 Introduction Due to the various marine resources such as petroleum, there is huge development potential can be exploited in economic, science and military areas [1]. Underwater vehicles play an important role in ocean exploration. However, due to the size of the underwater vehicle, the battery capacity is restricted, therefore, the energy problem becomes one of the most significant factors restricting the working radius of underwater vehicles [2]. At present, there are mainly two traditional power supply methods for underwater vehicles [3]. The charging process of this method requires manual operation, and the cost and time of fishing are high, [4] in addition, when used for military purposes, © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 415–426, 2023. https://doi.org/10.1007/978-981-99-0631-4_41
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the degree of automation is low and the charging concealment is poor [5]. As to the other methods, ROV (remotely operated vehicle) carry underwater wet plug connector is usually employed to charge the equipment, This method can avoid the low safety and low concealment issue of the equipment salvage method. However, the cost of the wet plug connectors used is relatively high, and the life cycle is unsatisfactory due to the continuously weakened airtightness caused by the high-frequency insertion processes. For example, the electrical connectors of ODI Company in the United States can be plugged and pulled out 1000 times at a depth of 7000 m underwater [6] The well-known overseas manufacturers of underwater wet plug connectors include TRONIC and Hydro Group in the UK, GISMA and Siemens in Germany, etc. [7]. With the development of wireless power transfer technology, wireless power transfer technology has been gradually applied to the charging of underwater vehicles, which can enhance the safety of underwater vehicles and the degree of equipment automation, and increase the exploration radius of underwater vehicles [8]. Ocean and air environments are quite different, so not all wireless power transfer modes are suitable for marine applications. For example, although the electric field coupling wireless power transfer technology has the advantages of portability and low radiation, its transmission power is very small, so it is not suitable for underwater high-power transmission [9]. Microwave and laser wireless power transmission is inefficient and has serious impact on living organisms, so it is not suitable for marine environment [2]. Therefore, magnetic field coupling and ultrasonic coupling are two main methods used in underwater wireless power transmission at present. Ultrasonic radio can transmit electroacoustic transducer is the main principle of transmitter converts the high frequency AC inverter circuit for ultrasonic, the receiver uses the acoustoelectric transducer converts received ultrasonic energy to the high frequency communication, by rectifier circuit output to the load side, ultrasonic coupled wireless power transfer mode can achieve meter level energy transmission [5]. Ultrasonic coupled wireless power transmission needs efficient transducer, the transmission efficiency is low and the ultrasonic transducer is large, so it is not suitable for small volume equipment such as wet plug connector. Magnetic field coupling wireless power transfer is the most studied and widely used wireless power transfer mode at present [10]. Magnetic coupling resonant wireless power transfer mode has longer working distance and greater transmission capacity, which is more suitable for underwater wireless power transfer. At present, the docking of transmitter and receiver in underwater wireless power transfer system is mainly divided into mooring and non-mooring modes. The principle of mooring mode is to adopt mechanical arm and other mechanisms to lock the underwater vehicle after docking with the underwater charging platform, keep the relative position of the transmitter and receiver of the coupler unchanged, and then carry out wireless power transmission. Mooring docking mode can reduce the relative position deviation of coupler caused by ocean current impact and other factors, and keep the parameters of wireless power transfer system stable. However, due to corrosion and microbial parasitism in Marine environment, mechanical mechanism is easy to fail underwater, resulting in docking problems of mooring mechanism.
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Underwater wireless power transfer technology using magnetic field coupling radio energy transmission has been studied by many institutions at domestic and overseas. An underwater S-S compensation topology optimization design method was proposed by the Technical University of Denmark and applied to the 200 W IPT system design. An underwater WPT system with an operating frequency of 103.5 kHz in seawater has been established, and the system can achieve 200 W power transmission [11]. The research team of Zhejiang University designed a conical coupler with a 5 mm gap, which can achieve 300 W energy transmission with a maximum transmission efficiency of 88% [4]. The research team of Northwestern Polytechnical University proposed a three-phase AUV wireless charging system with three transmitter and three receiver couplers. The maximum output power of the system is 1.0 kW, and the DC efficiency is 92.41% [12]. The docking mode of the non-mooring radio energy transmission system does not require the docking mechanism to clamp the underwater vehicle, but it can only be used in the condition of small ocean current disturbance in the deep sea. In the shallow sea condition, the coupler is easy to shift under the impact of ocean current and cannot be charged. In 2019, Hiroyasu Kifune et al. from Tokyo University of Marine Science and Technology, proposed a scheme to optimize the coil layout of an underwater wireless power transfer system, the transmission efficiency of the system reaches more than 74% [13]. In view of the shortcomings of the two docking methods, this article is based on the principle of magnetic coupling resonant wireless power transfer and presents a system design of underwater wet plug connector. This method uses ROVs to carry underwater wet plug and pull connector launchers for docking with the underwater vehicle, avoiding complex docking mechanical structures and increasing the reliability of the charging system. The insertion structure can make the relative position of the transmitter and receiver fixed and avoid the dislocation of coupler caused by the impact of ocean currents. In addition, this method can avoid the complex mechanical structure design and physical contact between contacts of the traditional underwater wet plug and remove connector system. It can improve the reliability of the underwater wet plug and remove connector system, reduce the cost of the system, and improve the service life of the system.
2 Structure Design of Underwater Wet Plug Connector With reference to the existing wet plug connector shape on the whole structure design. The designed underwater wet plug connector mechanism is shown in Fig. 1, The left side of the figure is the transmitter end of the connector, which is designed with a handle that is convenient for ROV to carry. The circuit board and the coupler are sealed by the columnar cavity structure, and the end of the connector is the transmitter coil. The receiver coil is on the right of the figure.
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Fig. 1. Schematic diagram of Underwater wet-plug connector
3 Magnetic Coupler Design Putting the coupler into the wet plug connector needs to consider the size of the wet plug connector itself and the working scenarios such as portable movement and docking during the working process, Therefore, the following aspects should be considered in the design process: 1. The shape of the coupler should be as close as possible to the shape of the traditional wet-plug connector to facilitate docking [14]. 2. Under the condition of ensuring the working ability of the coil, the volume and weight of the coil should be reduced as much as possible to facilitate the carrying and docking of the ROV. 3. When there is axial rotation during the docking process, the coil can keep the parameters stable and achieve stable output [15]. 4. The influence range of the magnetic field generated by the coil is as small as possible to avoid the interference of the high-frequency magnetic field on the internal components of the underwater vehicle. The traditional coupler can be divided into two types: round coil and rectangular coil. Compared with rectangular coil, round coil has smaller magnetic flux leakage, less consumables and isotropy, and can still maintain relatively stable parameters in the presence of a certain axial rotation Angle [16]. Therefore, round coil is selected for comprehensive consideration coupler design. Coil winding exists in two forms: spiral and helix. Spiral winding is more suitable for such close-range applications, but due to the limitation of the diameter of the wet-plug connector, a laminated coil as shown in Fig. 2 is designed in this paper. The coupler’s transmitter and receiver are the same structure as the diameter; In order to reduce the diameter of the coil, a single line of 6 turns is used to create a four-turn single-plane spiral coil, which is the same 6 turn layer, forming a 48 turns of the laminated coil. In order to reduce the mass of the coil, the coil simplifies the tank core into a number of cuboid magnetic materials of 2.5 mm thickness. The last layer of the laminated coil structure is added with 2.5 mm magnetic shielding material, and the outer diameter of the coil is 80 mm. This design significantly reduces the mass of the whole coupler. Due to the large number of coil turns, the proximity effect of the system is relatively obvious. Therefore, an interval of 1 mm is added to increase the distance between the Litz wires, so as to reduce the proximity effect of the system.
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Fig. 2. Top view and side view of the coupler
In order to further verify the performance of the designed coupler, a physical magnetic coupler was built for verification. To make the skeleton of the coil, 0.01 mm * 300 Litz wire was selected for coil winding, and Mn-Zn ferrite with a thickness of 2.5 mm and a relative permeability of 2500 was used as the magnetic material. The parameters of the coupler were measured as shown in Table 1: Table 1. Coil parameters of coupler Parameter
Value
Diameter/mm
80
Height/mm
33
Weight/g
401.5
Working distance/mm
8–12
Self-inductance of the transmitter LP /uH
223.66
Self-inductance of the receiver LS /uH
233.95
Mutual inductance M/uH
64.77
Coupling coefficient k
0.28
4 Power Transmission and Control System of Underwater Wireless Power Transfer System 4.1 Power Transmission and Control System In this paper, the primary side control is used to adjust the power of the system. The primary side control is a power control method at the transmitter. The secondary side transmits output voltage, output current and other system parameters to the primary side through wireless communication, and the system power is regulated by the closed-loop control circuit of the primary side. The closed-loop topology of energy transmission and control of underwater wireless power transfer system designed in this paper is shown in Fig. 3. In the figure, UDC and CDC are the input DC source and the regulated filter capacitor of the system respectively. S1 –S4 are MOSFET; LP , LS and M represent the self-inductance of the transmitter, the self-inductance of the receiver and the mutual
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inductance of the coupler respectively. CP and CS represent the series compensation capacitors of transmitter and receiver respectively. T1 represents the impedance matching transformer of the system; D1 and D2 are two rectifier diodes; Capacitance C1 , C2 and inductor L1 constitute π-type filter circuit. The transmitter circuit system is composed of inverter circuit, primary side compensation circuit, drive and control circuit and transmitter magnetic coupler device. The inverter circuit converts the DC input into high-frequency AC under the control of the driving circuit, and the system adopts the frequency modulation mode to adjust the power control. The frequency modulation range is 85 kHz–110 kHz. In order to improve the power transmission capacity of the system, a compensation circuit is added to the transmitter and receiver of the system. Due to the limited space of the underwater wet plug connector and the inverter circuit of the system is voltage-type, in order to simplify the transmitter circuit as much as possible. This paper selects the primary side series compensation method. The receiver circuit is composed of receiver coupler, secondary compensation circuit, rectifier circuit and control circuit. The receiver compensation circuit also adopts series compensation with relatively simple structure to reduce the complexity and volume of the system and reduce the weight of the system.
Fig. 3. Energy transfer and control topology
The battery voltage is low, but in S-S topology, the impedance of the system will decrease when the voltage remains unchanged and the output current increases. In many cases, frequency splitting caused by too small system impedance cannot be avoided if the system achieves the desired output only by designing the coil, so that the frequency modulation mode is not monotonous. Therefore, the system added an impedance matching transformer to improve the problem. In addition, the addition of an impedance matching transformer allows the coil to have sufficient load capacity while ensuring that the system can achieve the rated output. 4.2 Topology Theory Analysis of WPT System The S-S type wireless power transfer system can be equivalent according to the model in Fig. 4. Uin is the voltage source voltage, which can be regarded as the equivalent circuit output of UDC after DC-AC transformation through the full-bridge inverter circuit. CP and CS represent the series compensation capacitors of transmitter and receiver, RP and
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RS are the internal resistance of transmitter and receiver coils, and RL is the load of receiver coils.
Fig. 4. S-S compensation equivalent model
The circuit equation of S-S wireless power transfer system is as follows: iP RP + uCP + LP
diS diT +M = uin dt dt
is + (RS + RL ) + uCR + M
(2)
duCR dt
(3)
duCS dt
(4)
iP = iCP = CP is = ics = CS
diS diP + LS dT dt
(1)
The dynamic characteristics of wireless power transfer system with S-S compensation can be obtained by solving Eqs. (1)–(4). When the system runs stably, it can be described by the following vector equation: 1 ˙ ˙ ˙ (5) Uin = RP + j ωLP − IP + jωM IS ωCP 1 ˙ jωM IP + RS + RL + j ωLS − (6) I˙S = 0 ωCS ˙ in is the phasor of input uin , ˙IP , ˙IS is the phasor of current iP , iS flowing through U the coils of transmitter and receiver, and ω is the angular frequency of uin . 4.3 Closed-Loop Control of WPT System The purpose of the closed-loop control of the wireless power transfer system is to realize the constant current and constant voltage output of the system, [17] so as to ensure that the wireless power transfer system can safely and reliably complete the charging of the battery and automatically cut off. Select frequency modulation mode for power regulation control. The principle is to change the output of the system by changing the operating frequency of the inverter bridge to keep the inverter circuit away from or close to the resonant frequency of the coupler. The system samples the output voltage VO
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and output current IO of the receiver and performs data compensation processing by the sampling circuit at the receiver, and then transmits the data to the transmitter through radio frequency communication, and is processed by the MCU (Microcontroller Unit) of the transmitter. Set the output value to adjust the frequency to realize the closed-loop control of the system.
5 Test Verification and Analysis 5.1 Air Environment Test A test system is built to test and verify the working ability of the designed wireless power transfer system. The circuit parameters of the system are shown in Table 2. Table 2. Circuit system parameter Parameter
Value
Compensation capacitance of transmitter Cp/nF
32
Compensation capacitance of receiver Cs/nF
17
Turns ratio
7:2:2
PWM duty cycle
0.5
Output voltage range/V
48–58.48
Output current range/A
1–18.80
Both the transmitter and receiver are designed with sampling circuits, and the data transmission between the transmitter and receiver is carried out by means of radio frequency communication. The transmitter and receiver control the output of the device at the same time to realize the closed-loop control of the system. The underwater wireless power transfer system before waterproof sealing treatment is shown in Fig. 5.
Fig. 5. Physical underwater wireless power transfer system
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The air environment test uses an electronic load to simulate the battery characteristics. Since the test system uses a deep-sea oil-filled battery, the voltage range is 48–58.48 V. In order to verify the characteristics of the constant current region of the system, the electronic load is set to 57 V. By changing the setting of the electronic load voltage value, the system can realize the transition from the constant current charging stage to the constant voltage charging stage, and can automatically shut down when the charging current is less than 1 A. It has been verified that the wireless power transfer system designed in this article can achieve the output voltage in the air environment 48–58.48 V, the output current can be adjusted in the range of 1–18.80 A, and the maximum output power in the constant current area is 1182 W, which meets the design requirements of the system. The underwater charging performance of the whole system is tested after the verification of the air environment working performance of the system is completed. 5.2 Pool Environmental Test In order to verify the working ability of the entire wireless power transfer system in seawater, the wireless power transfer system is connected to the battery, and a test device as shown in Fig. 6 is established. Under the depth of the 9 m pool, the system was tested underwater, and the test results obtained are shown in Fig. 7. It can be seen from the current-voltage curve of the system that when the underwater wireless power transfer system charges the battery in the constant current region, the charging current is stable at about 18 A, the output voltage rises slowly with the battery voltage, and turns to constant voltage when the battery voltage reaches 57.80 V. When charging, the system output voltage remains constant and the charging current decreases with time. It can be seen from the system power efficiency curve that in the first 240 min, the output voltage of the system keeps rising as the battery voltage rises, and the output current of the system is stable at about 18 A. Therefore, the output power of the system keeps increasing. At this time, the system is in the charging state of the constant current region. In this charging state, due to the voltage change of the battery, the impedance of the battery is in a state that changes at any time. Using radio frequency communication for closed-loop control, there is a delay in the adjustment of the system, resulting in
Fig. 6. Experimental equipment for WPT system
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fluctuations in the output current of the system. When the battery voltage is close to the constant voltage region, it can reach the maximum value of 1182 W, and the maximum system efficiency during the whole charging process is 92.8%. With the continuous decline of the output power, the working efficiency of the system also gradually declines.
Fig. 7. (a) System output current voltage curve (b) System output power and efficiency of system constant current region
5.3 Marine Environment Test The working performance of the system in the actual marine environment is verified through the marine environment test. The equipment can work stably in the marine environment of 2–8 m. The output efficiency and output power of the system in the three tests is shown in Fig. 8. The following conclusions can be drawn from the comparison of the efficiency curves of the system in the air environment, the pool environment and the marine environment:
Fig. 8. (a) System test efficiency comparison (b) System output power comparison
• In the three different environments, the efficiency of the system shows a gradual upward trend in the initial stage, and the efficiency reaches a stable level after a period of work. This is due to the process of system startup to stable output impedance;
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• In three different working environments, the efficiency curve fluctuates to a certain extent, but the efficiency of the entire wireless power transfer system is stable at more than 92% most of the time. • The parameters such as the output voltage and current of the system are read by the sampling circuit of the system and uploaded to the upper computer software, so there is some error in the efficiency of the system measurement. However, from the system efficiency curve, it can be observed that there are certain changes in the system efficiency under the three different working conditions of the air environment, the pool environment and the marine environment, but there is no obvious difference in the system efficiency. • It can be seen from the output power curve of the system that in the air and pool environment, the output power of the system has a trend of increasing with time, but there will be a decline process before each output power rises. This is due to the change of the battery’s impedance, which leads to the change of the system’s output current. The impedance matching of the system needs an adjustment process. • From the comparison of the output power curves of the air environment, the pool environment and the marine environment, it can be seen that in the first 40 min of the system, the output power of the three environments is not very different. After 40 min, the output power of the system in the marine environment is less than output power in air and pool environments.
6 Conclusion This paper proposes a new type of underwater wet-plug connector that uses magnetic coupling resonant wireless power transfer for underwater wet-plug power transmission. Aiming at the shape of traditional couplers and the docking requirements of wet-plug connectors, this paper proposes a stacked coupler with light weight, small volume, and high power transmission. In the underwater environment, the radio frequency communication method is used to realize the data transmission of the primary and secondary sides. The power is adjusted by the primary side to realize the closed-loop control of the system and almost not affected by seawater salinity. The power transmission circuit adopts S-S type compensation circuit for system compensation. By building a test platform, the whole system is charged in the air environment, pool and marine environment to verify the actual working ability of the equipment. The underwater wet-plug connector can achieve a power output of more than 1 kW in a marine environment with a maximum efficiency of 92.8%, and the efficiency of the wireless power transfer system changes little in three different media.
References 1. Ressurreicao, T., Goncalves, F., Duarte, C., et al.: System design for wireless powering of AUVs. In: OCEANS 2017 - Aberdeen, pp. 1–6 (2017) 2. Wen, H., Song, B., Zhang, K., et al.: Underwater magnetically-coupled resonant wireless power transfer technology and its applications: a review. J. Underwater Unmanned Syst. 27(04), 361–368 (2019). (in Chinese)
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3. Zheng, W., Xie, O., Ding, Y., Xing, M.: Research on contactless power transmission system of autonomous underwater vehicle. Equip. Manuf. Technol. 04, 85–87 (2019). (in Chinese) 4. Guo, K., Zhou, J., Sun, H., et al.: Design considerations for a position-adaptive contactless underwater power deliver system. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–6 (2019) 5. Wu, X., Sun, P., Yang, S., et al.: Review on underwater wireless power transfer technology and its application. Trans. China Electrotech. Soc. 34(08), 1559–1568 (2019). (in Chinese) 6. Chen, H.: Design and manufacture of underwater mateable electrical connector. School of Mechanical Engineering, Southeast University (2019).(in Chinese) 7. Guo, Q., Wang, Y., Han, J., et al.: Structural thermal stress and dynamic analysis of wet-mate electrical connectors. Shandong University (2021). (in Chinese) 8. Feng, L., Zhu, C., Zhang, J., et al.: Research on key technology based on wireless charging technology for unmanned underwater vehicle. Ship Sci. Technol. 42(23), 159–162 (2020). (in Chinese) 9. Gao, Z., Li, Y., Jing, Q., et al.: Study on the coupling structure of underwater wireless power transmission system via electric coupling. J. Hehai Univ. (Nat. Sci.) 46(04), 366–370 (2018). (in Chinese) 10. He, C., Gong, Y., Pu, S.: Application of wireless power transmission technology in military field. Inf. Commun. (02), 14–17 (2016). (in Chinese) 11. Dou, Y., Zhao, D., Ouyang, Z., et al.: Investigation and design of wireless power transfer system for autonomous underwater vehicle. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3144–3150 (2019) 12. Kan, T., Zhang, Y., Yan, Z., et al.: A rotation-resilient wireless charging system for lightweight autonomous underwater vehicles. IEEE Trans. Veh. Technol. 67(8), 6935–6942 (2018) 13. Sato, N., Kifune, H., Komeda, S.: A coil layout of wireless power transfer systems based on multicoil arrangement for underwater vehicles. Electr. Eng. Jpn. 207(2), 38–48 (2019) 14. Song, B., Wang, Y., Zhang, K., et al.: Research on wireless power transfer system for Torpedo autonomous underwater vehicles. Adv. Mech. Eng. 10(9), 1687814018802563 (2018) 15. Yan, Z., Song, B., Zhang, Y., et al.: A rotation-free wireless power transfer system with stable output power and efficiency for autonomous underwater vehicles. IEEE Trans Power Electron 34(5), 4005–4008 (2019) 16. Mohsan, S.A.H., Islam, A., Khan, M.A., et al.: A review on research challenges, limitations and practical solutions for underwater wireless power transfer. Int. J. Adv. Comput. Sci. Appl. 11(8), 554–562 (2020) 17. Han, D., He, Y., Chen, L., et al.: Underwater communication technology and its difficulties. Technol. Innov. Appl. 01, 155–159 (2021). (in Chinese)
Metal Foreign Object Detection Algorithm Based on Multivariate Normal Distribution Ying Sun(B) , Kai Song, Tian Zhou, Guo Wei, and Chunbo Zhu School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China [email protected]
Abstract. Aiming at the need of metal foreign object detection in wireless charging system, a metal foreign object detection algorithm based on multivariate normal distribution was proposed in this paper, which solves the problems of low detection sensitivity and blind area of single monitor coil in traditional method. This method has the advantages of low cost, high sensitivity, and strong applicability without changing the hardware circuit. First, the mutual inductance coupling model between metal foreign object and monitor coil was established. Also, the detection principle based on the variation of monitor coil impedance and multiple normal distribution algorithm were interpreted. Then, the corresponding monitor coil, circuit and signal processing were designed. Finally, the experimental verification was carried out on a 3.5 kW wireless charging prototype. As for 1-jiao coin at the position of the corner of the monitor coil, the eigenvalue output by the algorithm changed by 75.51 times compared with that without foreign objects. Thus, this algorithm can significantly improve the detection effect of small size foreign objects and which are in corner area of monitor coil. Keywords: Metal foreign object detection · Wireless power transfer · Multivariate normal distribution · Detection algorithm · Electric vehicle wireless charging
1 Introduction Varying from the traditional charging method of plug-in, wireless power transfer (WPT) can transfer the high electric power with high efficiency from the power supply equipment to power receiver equipment without electrical connection. Therefore, some safety hazards like plug wear and contact spark fires can be avoided perfectly. As a new generation of charging technology, wireless power transfer (WPT) technology has been deeply studied and widely utilized in variety applications. WPT is qualified easily for not only the traditional charging occasions, like electric vehicles (EV), but also the charging requirement in special environment, such as the implantable medical devices, underwater UUV charging [1–3]. However, it is precisely because the most distinct feature of WPT system is the non-contact between the transfer side and receiver side, foreign matters (FMs) could invade into the charging area easily where contains the alternating magnetic field with high power. If the FMs are metal foreign matters (MFMs) or include © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 427–435, 2023. https://doi.org/10.1007/978-981-99-0631-4_42
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metal materials, they will be heated under the effect of the eddy current. Consequently, MFMs will become the potential security risks for WPT system which can burn or ignite the WPT system. Therefore, to improve the security and stability of WPT system, the Foreign Object Detection (FOD) has become the most indispensable part in WPT system. The relevant standards of industry have clearly stipulated that the WPT system must contain the FOD function [4, 5]. At present, the commonly used methods include: primary and secondary side power loss method, machine vision detection, frequency modulation wave radar detection, infrared temperature detection and electromagnetic characteristics detection based on monitor coil, among which the primary and secondary side power loss method is suitable for low-power wireless charging occasions, such as: Qi standard mobile phone charging, wearable devices, etc. This method is not suitable for high-power wireless charging because the loss of FMs cannot be accurately measured by comparing the power difference between the transmitter and the receiver. Machine vision detection, frequency modulation wave radar detection and other methods require additional sensors, which will increase the cost of MFM system and make it vulnerable to environmental impact, and prone to misjudgment. The temperature detection method based on infrared camera will also increase the cost of the detection system, and there must be a significant temperature difference between the FMs and the transmitter before detection, and the detection speed of the system has a lag. Detection methods for FMs with electromagnetic characteristics based on monitor coils are mainly divided into magnetic flux detection methods and impedance detection methods. The above two methods achieve accurate and rapid detection of metal foreign matter by measuring the change of magnetic flux or impedance value of the monitor coil, but do not respond to other materials that will not be heated by eddy current effect or have no harm to the charging system, such as plastics. The principle of magnetic flux detection method is to detect the magnetic flux change and induced voltage of the monitor coil by measuring the MFM [6, 7, 10, 11]. Due to the inherent detection blind spots in its detection principle, the current solution is to lay multi-layer monitor coils to cover the blind spots of other layers of monitor coils. The principle of this detection method is relatively simple but the structure is relatively complex and the methods to improve detection sensitivity are limited, such as reducing the size of each sub-monitor coil. Impedance detection method is used to detect foreign matter by measuring the impedance change of the monitor coil under high frequency excitation [8, 9]. This method does not depend on the magnetic field of the transmitting end and can work independently. Because the excitation source frequency is different from the power magnetic field frequency, the detection signal in this method has strong anti-interference ability and is not susceptible to the original and secondary side migration. Meanwhile, a higher signal-to-noise ratio (SNR) can be designed to improve the detection sensitivity [8, 9]. At present, the above detection methods have the following problems [10–14]: 1) The detection sensitivity in some areas is low. When the MFM size is small or located at the edge of the monitor coil, the above method is difficult to achieve accurate detection or the solution is cumbersome, and the detection blind area will lead to potential security risks in the wireless charging system.
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2) The existing references mainly focus on the structure or circuit optimization of single-channel monitor coil, but lacks the research on the data processing algorithm of multi-channel monitor coil, that is, the research on detection algorithm is few. Based on the above analysis, this paper proposes a high-sensitivity metal foreign matter detection algorithm based on multivariate normal distribution, which makes full use of the correlation between the output signals and impedance changes of multiple adjacent monitor coils, and significantly amplifies the covariance of metal foreign matters to impedance changes of multichannel monitor coils. It solves the problems of low sensitivity and blind spot in the edge region of single monitor coil in traditional detection methods.
2 Detection Principle 2.1 Coupling Model Between MFM and Monitor Coil In alternating magnetic field, the metal matter can be equivalent as an inductance with the internal resistance. The relationship of mutual coupling inductance between the metal matter and monitor coil could be analyzed as built in in Fig. 1.
Fig. 1. The mutual coupling relationship between the MFM and monitor coil
In Fig. 1, L D and RD are the inductance and resistance of the monitor coil, L m and Rm are on behalf of the equivalent inductance and the internal resistance of MFM. M m is the equivalent mutual inductance between the metal matter and the monitor coil. Z NONE and Z FM are the whole impedance of the monitor coil under the condition where the foreign matters are absent and exist, respectively. According to the whole impedance change of the monitor coil, the MFM can be detected. ZNONE = RD + jωLD ZFM
Rm ω2 Mm2 Lm ω2 Mm2 RD + jω 1 − LD = 1+ · · RD R2m + ω2 L2m LD R2m + ω2 L2m
(1) (2)
2.2 Multivariate Normal Distribution Principle Suppose that n dimensional variables [x 1 , x 2 , …, x n ]T are independent from each variable, and the distribution model of each variable belongs to the normal distribution. When
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the total number of measurements is n, its mean value matrix μ = [μ1 , μ2 , …, μn ]T 2 , σ 2 , . . . σ 2 ]T can be calculated according to and its covariance matrix Σ = diag[σ11 nn 22 the definition. The covariance matrix is diagonal matrix because of the independent feature from each other. According to the independence of the n dimensional variables, the probability density can be calculated as (3). p(x1 , x2 , . . . , xn ) =
n i=1
p(xi ) =
n i=1
1
e √ 2π σi
−
(xi −μi )2 2σi2
(3)
Since the principle of the MFM detection system in this paper is based on the impedance change of the monitor coil to detect MFMs, the presence of MFMs will inevitably have varying degrees of influence on the impedance of the monitor coil where they are located and adjacent to them. Therefore, when the covariance matrix Σ is constructed with the impedance of the test coil or the output voltage signal of the detection circuit in which it is located, these variables are not independent of each other, but have a certain correlation. When the MFM is located at the junction of multiple monitor coils, the correlation is more obvious. Therefore, when n dimensional variables are not independent from each other, the above mean matrix can be still calculated as μ = [μ1 , μ2 , …, μn ]T , while the covariance matrix Σ is no longer diagonal matrix which contains the covariance between the mutual detection variables. Σ is updated as (4). When the n dimensional variables are correlated with each other, the general expression of probability density function p(x) is shown in (5). Where, the x = [x 1 , x 2 , …, x n ]T in (5). ⎡ 2 2 2 ⎤ σ11 σ12 · · · σ1n ⎢σ2 σ2 ··· σ2 ⎥ 2n ⎥ ⎢ 21 22 (4) = ⎢. . . . ⎥ . . .. ⎦ ⎣ .. .. 2 σ2 ··· σ2 σn1 nn n2 p(x1 , x2 , . . . , xn ) = √
1 1 T −1 e− 2 (x−μ) (x−μ) n (2π ) ||
(5)
Taking the bivariate multivariate normal distribution for example, its 2D cross profile model and 3D model are shown in Fig. 2(a) and Fig. 2(b). To simplify to calculate quickly and conveniently in FPGA, p(x) can be equivalent to calculate its exponential function y of natural logarithm e in p(x). The Σ and μ are utilized as the numerical value when there are no MFMs, the larger p(x) is, the smaller y is. While there exist MFMs, the smaller p(x) is and the larger y is. y = (x − μ)T −1 (x − μ)
(6)
When only one monitor coil Loop1 is separately taken into consideration for FOD, its normal distribution model of the measured values like detection system output p(x) is illustrated in Fig. 3. When the monitor coil impedance change caused by the MFMs is small, all the measured values basically conform to the normal output range of Loop1. Consequently, the existence of MFMs cannot be effectively detected only according to the single one monitor coil impedance.
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Fig. 2. 3D model and 2D cross profile model of the bivariate normal distribution
Fig. 3. The probability density model of the single monitor coil output
As the above analysis in Fig. 2, when the measured values of two monitor coils (Loop1&Loop2) are adopted, the distribution of the measured values conforms to the bivariate multivariate normal distribution which is illustrated in Fig. 4. The ellipse in Fig. 4 is the division boundary which determines whether the MFMs exist. The measured values without MFMs are all located inside the ellipse while the measured values with MFMs existence are outside the range of ellipse. Compared with Fig. 3, the points with MFMs existence can be distinguished easily by virtue of the correlation between multiple measured variables and the multivariate normal distribution model. It is assumed that the MFMs covering one coil has little influence on its impedance, and the MFMs covering the other coil has much influence on its impedance. When the output voltage of one detection circuit is close to the normal critical value of no MFMs, the output voltage of the other detection circuit will be close to the mean value without
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MFMs μ1 or μ2 . Therefore, abnormal points in the presence of MFMs can be detected by analyzing the correlation between multiple measured variables.
Fig. 4. The probability density model of the two-monitor-coil output
3 Experimental Verification The coil impedance detection circuit based on the parallel resonance is designed in Fig. 5. The detection circuit output U out-rms of multiple monitor coils are utilized as the multiple measured variables x = [x 1 , x 2 , …, x n ]T to calculate the characteristic value y. To highlight the improvement of detection algorithm on detection effect, the detection sensitivity S cir of detection circuit output signal and S y of detection algorithm output characteristic value are defined respectively, as defined in (7) and (8).
Fig. 5. The detection circuit of monitor coil impedance based on parallel resonance
Scir =
||UNONE | − |UFOD || |UNONE |
(7)
Sy =
||yNONE | − |yFOD || |yNONE |
(8)
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In the conditions without MFMs, each monitor coil is switched into the detection circuit by turns and their output signals U out-rms are gathered and adopted as the multiple variables x = [x 1 , x 2 , …, x n ]T . And Σ and μ are calculated under the conditions without MFMs. Also, the characteristic value of the algorithm y is calculated as yNONE which is regarded as the threshold without MFMs. When MFMs exist, the multiple variables x with MFMs are gathered and brought into (6) while the Σ and μ are still the value without MFMs. The new characteristic value y when MFMs exist is calculated and compared with the threshold yNONE to judge whether the MFMs exist (Fig. 6).
Fig. 6. The monitor coil array and test positions of MFM (1-jiao RMB coin)
When the coin is in the center area of monitor coil, the percentage variation of U out-rms , the corresponding detection sensitivity S cir of the detection circuit is 63.60%. While the coin is in the corner area of monitor coil, the detection sensitivity S cir is only 5.48%. It is hard to detect the existence of MFMs accurately due to the noise. Bring the above U out-rms detection data into (6). When the coin is in the corner area, the detection sensitivity S y of the characteristic value y is 7551% compared with the threshold of none MFMs, which is much higher than S cir 5.48%. More obviously, when the coin is in the center area, S y = 20982% is also much higher than S cir 63.60% (Fig. 7).
Fig. 7. The output of the detection algorithm
4 Conclusion A high sensitivity detection algorithm for metal foreign matters based on multivariate normal distribution is proposed in this paper to solve the problems of low sensitivity
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and blind detection spot. The proposed method has the advantages of low cost, high sensitivity, and strong application which does not need to change the hardware circuit. A 3.5 kW wireless charging prototype was established and verified. The experimental results demonstrate that when the 1-jiao coin is in the corner position of the monitor coil, the characteristic value of the algorithm output is 75.51 times higher than that without foreign matters. Without changing the parameters of the detection circuit, this algorithm can significantly improve the detection sensitivity of small foreign matters and the ones located in the corner area of the monitor coil. Acknowledgment. This academic research was supported and funded by General Program of National Natural Science Foundation of China No. 51977043.
References 1. Sun, L., Ma, D., Tang, H.: A review of recent trends in wireless power transfer technology and its applications in electric vehicle wireless charging. Renew. Sustain. Energy Rev. 91, 490–503 (2018) 2. Xue, M., Yang, Q., Zhang, P., et al.: Application status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(08), 1547–1568 (2021). (in Chinese). https://doi.org/10.19595/j.cnki.1000-6753.tces.200059 3. Wu, L., Zhang, B.: Overview of static wireless charging technology for electric vehicles: part II. Trans. China Electrotech. Soc. 35(08), 1662–1678 (2020). https://doi.org/10.19595/j.cnki. 1000-6753.tces.190107 4. SAEJ2954_201904, Wireless power transfer for light-duty plug-in/electric vehicles and alignment methodology wireless power transfer for light-duty plug-in/electric vehicles and alignment methodology (2019) 5. IEC 61980-1: 2015/COR1: 2017 corrigendum 1-electric vehicle wireless power transfer (WPT) systems-part 1: general requirements (2017) 6. Jeong, S.Y., Kwak, H.G., Jang, G.C., et al.: Dual-purpose non-overlapping coil sets as metal object and vehicle position detections for wireless stationary EV chargers. IEEE Trans. Power Electron. 33(9), 7387–7397 (2018) 7. Jang, G.C., Jeong, S.Y., Kwak, H.G., et al.: Metal object detection circuit with non-overlapped coils for wireless EV chargers. In: 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC) Auckland, pp. 1–6 (2016) 8. Jeong, S.Y., Thai, V.X., Park, J.H., et al.: Self-inductance based metal object detection with mistuned resonant circuits and nullifying induced voltage for wireless EV chargers. IEEE Trans. Power Electron. 34(1), 748–758 (2019) 9. Jeong, S.Y., Thai, V.X., Park, J.H., et al.: Metal object detection system with parallelmistuned resonant circuits and nullifying induced voltage for wireless EV chargers. In: 2018 International Power Electronics Conference (IPEC) Niigata, pp. 2564–2568 (2018) 10. Meichle, D.P.: Foreign object detection in wireless energy transfer systems, WO2017/0700227A1, 27 April 2017 11. Widmer, H., Sieber, L., Daetwyler, A., et al.: Systems, methods, and apparatus for radar-based detection of objects in a predetermined space: US, 977240125, 26 September 2017
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12. Zhang, X., Xing, Z., Xue, M., et al.:Overview of foreign object detection in wireless power transfer system. Trans. China Electrotech. Soc. 1–15, (2021) 13. Chen, C., Huang, X., Sun, W., et al.: Impact of metal obstacles on wireless power transmission system based coupled resonance. Trans. China Electrotech. Soc. 29(9), 22–26 (2014). (in Chinese) 14. Su, Y., Hou, X., Dai, X.: Review of foreign object detection technology in magnetic coupling wireless power transfer system. Proc. Chin. Soc. Electr. Eng. 41(2), 715–728 (2021)
Research on Parallel Circulation Suppression Strategy of High-Frequency Resonant Inverter Based on Improved Active Current Decomposition Method Junfeng Liu1(B) , Mingze Ma1 , Hao Zhou2 , and Jun Zeng3 1 School of Automation Science and Engineering, South China University of Technology,
Guangzhou 510640, China [email protected] 2 Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 511442, China 3 School of Electric Power, South China University of Technology, Guangzhou 510640, China
Abstract. In order to solve the circulation problem caused by the parameter difference of parallel high frequency resonant inverters, a current equalization control strategy is proposed. The mathematical model between the series and parallel resonant impedance of the parallel inverters and the circulation is deduced. Second, to get the amplitudes and phases of the output currents accurately and suppress the circulation of inverter system, the active and reactive components of inverter output current are defined. Based on the principle of periodic signal cross-correlation function, a current decomposition method without other additional sine and cosine signals is proposed. Finally, a control strategy of active power equalization and reactive power minimization is proposed to minimize the parallel circulation of inverters. And a 25 kHz high-frequency LCLC inverter parallel system is built. The feasibility and effectiveness of the control strategy are verified by experiment with rated output power of 250 W. Keywords: Parallel high frequency inverter · LCLC · Circulation suppression · Current decomposition · Cross-correlation function
1 Introduction With the progress of science and technology, power electronic technology is gradually developing to high frequency. High-frequency resonant inverter has been gradually applied to Inductive Power transmission [1] (IPT) system and Magnetic Coupling Resonance Wireless Power Transfer [2] (MCR-WPT) system, which have high research and application value. Among them, as the MCR-WPT system technology gradually becomes mature, the application of the system in high-power situations also gradually increases. And so do the control strategy of the inverters [3–6]. When the MCR-WPT system is applied in high-power scenarios, a single high-frequency inverter cannot meet © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 436–443, 2023. https://doi.org/10.1007/978-981-99-0631-4_43
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the high power requirements. Due to the limited power capacity or cost of switches, multiple high-frequency inverters are connected in parallel to meet the system output requirements. However, the difference of capacitance and inductance parameters of highfrequency inverters, inconsistent input voltage of DC power supply, delay of switching drive signal and other factors will lead to the inconsistency of amplitude and phase of output current [7, 8]. Make the parallel inverter module between a large circulations. On the one hand, it directly affects the output characteristics of the parallel system. On the other hand, it will cause damage to components and the system. The current decomposition method proposed in this paper has the following advantages: (1) Compared with the method proposed in reference [8], the current decomposition method proposed in this paper is applicable to a wide range of phase differences, and the extracted active and reactive currents are consistent with the actual phase differences of the current. (2) Compared with literature [9–11], the current decomposition method proposed in this paper does not need to provide additional sine or cosine signals to the controller, and does not need to build a low-pass filter, which further reduces the volume of control circuit. In view of this, the active and reactive components of the inverter output current are defined in this paper. Based on the cross-correlation function principle of periodic signals [10], a decomposition method of active current without providing additional sine and cosine signals is proposed, which effectively reduces the complexity of the decomposition algorithm. The experiments results show that the circulation of the system is significantly reduced after the control strategy added.
2 Analysis of High Frequency AC Inverter Level Parallel Circulation Figure 1 (a) shows the circuit parallel diagram of LCLC inverter [9]. In Fig. 1 (a) the modulation method of mosfets G1 , G2 , G5 and G6 adopts PWM modulation. And mosfets G3, G4 , G7 and G8 adopts PPM modulation. L s1 , C s1 , L s2 and C s2 are the series resonant inductance and capacitance of each inverter, respectively. L p1 , C p1 , L p2 and C p2 are the parallel resonant inductance and capacitance of each inverter, respectively. RLOAD indicates the load. Based on the substitution principle, the internal structure between inverters is ignored, and the parallel system of high-frequency inverters is further simplified into the equivalent model as shown in Fig. 1 (b). Where U 1B and U 2B represent the output voltage of the bridge arm of inverter 1 and inverter 2. Z 1s and Z 1p represent series and parallel resonant impedance of the inverter 1. Z 2s and Z 2p are the series and parallel resonant impedances of the inverter 2. U 1 and U 2 are the output voltage of the inverter, I p1 and I p2 are both output current, and I p is the total current. Z eq is equivalent load of inverter system.
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Fig. 1. LCLC inverter parallel topology and equivalent model of parallel inverters system.
According to Fig. 1 (b) and Kirchhoff’s voltage-current law: U0 U0 + I2 − U0 = Ip Zeq = u1b − I1 Z1s = u2b − I2 Z2s , Ip = Ip1 + Ip2 = I1 − Z1p Z2p
(1)
The circulation I H of the high-frequency inverter system is defined as Ip1 − Ip2 2 2Z1p Z2p Zeq (u1b − u2b ) + Z1p Z2p (u1b Z2s − u2b Z1s ) + 2Zeq (u1b Z1p Z2s − u2b Z2p Z1s ) = 2 Z1p Z2p (Z1s Zeq + Z1s Z2s + Z2s Zeq ) + Z1s Z2s Zeq (Z2p + Z1p )
IH =
(2)
According to Eq. (2), different series resonance parameters and parallel resonance parameters will generate circulation. When the series resonant impedance and the output voltage of the bridge arm of each inverter in the parallel system are equal, and the parallel resonant impedance is not equal, namely U 1B = U 2B = U B , Z 1s = Z 2s = Z s , Z 1p = k 1 Z 2p , then IH = ub
Zeq Z2p (k1 − 1) Z2p (2Zeq +Zs ) + (k2 + 1)Zs Zeq
(3)
When the parallel resonant impedance and the output voltage of the bridge arm of each inverter in the parallel system are equal, and the series resonant impedance is unequal, namely U 1B = U 2B = U B , Z 1p = Z 2p = Zp , Z 1s = k 2 Z 2s (Zp + 2Zeq )(1 − k2 ) IH = ub 2 Zp (Zeq +Z2s + Zeq ) + 2Z2s Zeq
(4)
According to Eqs. (4)–(5), in the parallel LCLC inverter system, when the series resonant impedance or parallel resonant impedance is unequal, the system circulation I H is not 0.
3 Decomposition of Active Current 3.1 Definition of Active and Reactive Current The output current of inverter 1 is I p1 , the output current of inverter 2 is I p2 , and the total output current of inverter is I p . Its angular frequency is the same as ω, with the
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total current I p as the reference current, current I p1 and the phase difference between I p2 and the reference current I p are angle F1 and angle F2 respectively. Its time-domain expression is: Ip = Ipm sin ωt, Ip1 = Ip1m sin(ωt + φ1 ), Ip2 = Ip2m sin(ωt + φ2 )
(5)
I pm , I p1m , and I p2m are the peaks of current I p , I p1 , and I p2 respectively. According to Eq. (5), the current I p1 and I p2 can be decomposed by phasor along the I p direction: Ip1 = Ia1 sin ωt + jIr1 cos ωt, Ip2 = Ia2 sin ωt + jIr2 cos ωt
(6)
where, define active current I a1 and I a2 , reactive current I r1 and I r2 . Ia1 = Ip1m cos φ1 , Ia2 = Ip2m cos φ2 ; Ir1 = Ip1m sin φ1 , Ir2 = Ip2m sin φ2 ;
(7)
According to Eqs. (6) and (7), the active current I an and reactive current I rn of inverter N contain the information of the inverter output current amplitude I pnm and phase difference Fn . By controlling the active and reactive current, the inverter output current amplitude and phase difference can be reduced, and then the system circulation can be minimized. The available active and reactive currents of the two-fold circulation 2I H of the inverter can be expressed as: 2IH = (Ia1 − Ia2 ) sin ωt + j(Ir1 − Ir2 ) cos ωt
(8)
Fig. 2. Diagram of active and reactive current decomposition.
Figure 2 is the phasor diagram of active and reactive current decomposition and circulation. According to Eq. (8) and Fig. 2, the system circulation can be minimized by controlling the active and reactive current difference between the output currents of the inverter. 3.2 Decomposition of Active and Reactive Currents The phase of the reference current I p is delayed by 0.5π, and the delayed reference current I pt is defined as Ipt = Ipm sin(ωt + 0.5π ) = Ipm cos(ωt)
(9)
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For signals with the same period T such as x(t) and y(t), assuming that the delay time between signals is zero, the cross correlation function is defined as follows Rxy
1 = T
T x(t)y(t)dt
(10)
0
Let x 1 (t) = I p1 , y1 (t) = I p , x 2 (t) = I p2 , y2 (t) = I p , x 3 (t) = I p1 , y3 (t) = I pt , x 4 (t) = I p2 , y4 (t) = I pt , substitute Eqs. (5) and (9) into Eq. (10), The cross-correlation function Rc1 between I p1 and I p , Rc2 between I p2 and I p , Rc3 between I p1 and I pt , and Rc4 between I p2 and current I pt can be obtained. 1 T 1 T Ip1m sin(ωt + φ1 )Ipm sin ωtdt; Rc2 = Ip2m sin(ωt + φ2 )Ipm sin ωtdt T 0 T 0 T T 1 1 Rc3 = Ip1m sin(ωt + φ1 )Ipm cos ωtdt; Rc4 = Ip2m sin(ωt + φ2 )Ipm cos ωtdt T 0 T 0
Rc1 =
(11)
where, T is the period of current I p1 , I p2 and I p . By calculating Eq. (13), it can be obtained 1 1 Rc1 = Ip1m Ipm cos φ1 , Rc2 = Ip2m Ipm cos φ2 2 2 1 1 Rc3 = Ip1m Ipm sin φ1 , Rc4 = Ip2m Ipm sin φ2 (12) 2 2 According to the definition of active current and reactive current in Eq. (6), active current Ia1 and Ia2 and reactive current Ir1 and Ir2 can be obtained. 2Rc1 2Rc2 2Rc3 2Rc4 Ia1 = , Ia2 = , Ir1 = , Ir2 = (13) Ipm Ipm Ipm Ipm Make the following definition. Ipp1 = Ip1 · Ip , Ipp2 = Ip2 · Ip , Ipp3 = Ip1 · Ipt , Ipp4 = Ip2 · Ipt
(14)
Fig. 3. Active and reactive current decomposition module.
Therefore, on the premise of knowing the working frequency of the inverter, the output current signals I pn , I p and I pm are extracted, and the active and reactive currents taking the total inverter current as the reference direction can be obtained after calculation as shown in Fig. 3. The decomposition process of active and reactive currents is simplified.
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3.3 Circulation Suppression Control Strategy for Parallel Inverters Figure 4 shows control part of the inverter system. In Fig. 4, K r (s) is a controller used for reactive current minimization. K a (s) is a controller used for active current equalization. K u (s) is the output voltage controller, and controllers K r (s), K a (s) and K u (s) are all PI controllers. U ref is the given value of output voltage, the reference value of reactive current is 0, and the reference value of active current is 0.5(I r1 + I r2 ). The output voltage value of the controller is sent to the PPM modulation module and PWM modulation module to generate the switching tube guide communication signal, so as to control the switching tube conduction of the inverter, and get the output voltage U pm and output current I pm .
Fig. 4. Inverter current control block diagram.
4 Experimental Verification To verify the feasibility of the control strategy based on the improved active current decomposition, the parameters of the inverter system in Table 1 and the parallel structure of the inverter shown in Fig. 1 are adopted. A high frequency parallel inverter platform is built for experimental verification. Figure 5(a) shows the experimental waveforms of output current I p1 of highfrequency inverter 1, output current I p2 of high-frequency inverter 2, total output current I p of the system and double circulation 2I H . In Fig. 5 (a), there is an obvious phase difference and amplitude difference between the output current I p1 of inverter 1 and the output current I p2 of inverter 2. And it can be seen that the output currents of two inverters have great differences not only in amplitude but also in phase. The two-fold circulation current 2I H of parallel inverter system is large with about ±4 A peak value. Figure 5(b) shows the experimental waveform after the control strategy is added. The output current amplitude I p1m of inverter 1 is about 6 A, and the output current amplitude I p2m of inverter 2 is equal to I p1m . And the amplitude difference is almost 0. In terms of phase, the output current I p1 of inverter 1 is almost the same as the output current I p2 of inverter 2, and the phase difference is almost negligible. According to the above analysis, I p1 and I p2 are equal in terms of amplitude and phase. The circulation of the parallel inverter system is small, and the peak value of the double circulation 2I H is about 0.5 A, which is much smaller than peak value of the system without the control strategy. It can be concluded that the control strategy can effectively reduce the circulation I H between inverters.
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Circuit parameters
Number of values Inverter 1
Inverter 2
Dc voltage V dc /V
100
Output frequency/kHz
25
Series resonant inductor L s /μH
110
Parallel resonant inductor L p /μH
17
Output voltage effective value U orms /V
28
Series resonant capacitor C s /nF
423
470
Parallel resonant capacitance C p /μF
1.62
1.8
Main control chip
TMS320F28335
Total output power/W
250
Fig. 5. Experimental waveform of parallel current and double circulation of inverter
Experiments show that the phase extraction method proposed in this paper can suppress the circulation of the system well. The circulation suppression control strategy can reduce the circulation and reduce the loss caused by the circulation in the inverter parallel system. The decomposition method can accurately extract the phase difference between the output signals, and has application prospect in the high-frequency AC inverter system.
5 Conclusion In order to solve the high frequency resonant inverter parallel system parameters caused by inconsistent circulation problems, this paper deduces LCLC parallel resonant inverter mathematical model of circulation, realize the output current of the active and reactive current decomposition, this method does not need additional sine, cosine signal with low pass filter, reduce the complexity of the algorithm, simplifies the hardware circuit. Based on this method, the control strategy of active current equalization and reactive current minimization is proposed. The experiment results show that the strategy can reduce the
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circulation of the inverter. The sinusoidal degree of the output current is high in the case of pure resistive load. Acknowledgments. This work was supported by Guangzhou science and technology program (No. 202002030373) and national natural science foundation of China (62173148, 51877085).
References 1. Lu, L.: Research on circulation elimination and frequency stability control of multi-inverter parallel IPT system. Chengdu: Southwest Jiaotong University (2017).(in Chinese) 2. Han, C., Zhang, B.: Characteristic analysis and parameter design of high frequency inverter in resonant radio energy transmission system. Trans. China Electrotech. Soc. 33(21), 5036–5050 (2018). (in Chinese) 3. Lan, Z., Hao, R., Jiao, H., You, X.: Optimal predictive control of three-phase inverter based on repetitive control and state feedback. Trans. China Electrotech. Soc. 37(06), 1473–1481 (2022). (in Chinese) 4. Xie, Q., Wang, R., Lin, K., Fan, X., Yang, G.: Parallel droop control strategy of inverter based on port voltage integral and variable droop coefficient. Trans. China Electrotech. Soc. 1–12 (2022). (in Chinese) 5. Ge, P., Xiao, F., Tu, C., Chen, L., Zhou, D.: Transient control strategy for sag inverter considering fault current limiting. Trans. China Electrotech. Soc. 1–12 (2022). (in Chinese) 6. Chen, Z., Wang, C., Cheng, Q.: Fast model predictive control for two-level inverter based on single vector. Trans. China Electrotech. Soc. 36(S2), 654–664+687 (2021). (in Chinese) 7. Liu, J., Cheng, K., Zeng, J.: A unified phase-shift modulation for optimized synchronization of parallel resonant inverters in high frequency power system. IEEE Trans. Industr. Electron. 61(7), 3232–3247 (2014) 8. Ye, Z., Praveen, J., Paresh, S.: A half-bridge hybrid resonant inverter with novel pulse phase modulation control. In: PESC Record IEEE Annual Power Electronics Specialists Conference (2006) 9. Ye, Z., Jain, P.K., Sen, P.C.: Circulating current minimization in high-frequency AC power distribution architecture with multiple inverter modules operated in parallel. IEEE Trans. Industr. Electron. 54(5), 2673–2687 (2007) 10. Yong, L., Mai, R., Lu, L., et al.: Active and reactive currents decomposition-based control of angle and magnitude of current for a parallel multiinverter IPT system. IEEE Trans. Power Electron. 32(2), 1 (2016) 11. Li, Y.W., Kao, C.N.: An accurate power control strategy for power-electronics-interfaced distributed generation units operating in a low-voltage multibus microgrid. IEEE Trans. Power Electron. 24(12), 2977–2988 (2009)
The Power Control of a Multiple Pick-Up Bidirectional Wireless Power Transfer System Zhenggang Yin1(B) , Liming Shi1 , Jixin Yang1,2 , and Wenjing Tang1,2 1 Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering,
Chinese Academy of Sciences, Beijing, China [email protected] 2 University of Chinese Academy of Sciences, Beijing, China
Abstract. When applying wireless power transfer technology in rail transit, multiple modular structure is preferred and bidirectional power transfer function is needed in order to increase the power and feedback the braking energy. This paper studies the bidirectional power control and module balance control of a multiple pick-up bidirectional wireless power transfer system. First, based on the secondary coil’s constant current characteristic of the primary and secondary both series compensated system, the control method that can determine the power direction by controlling the secondary voltage’s phase angle to be in-phase or anti-phase with secondary current is proposed, and the communication between both sides is no needed. For the unbalance problem of pick-up currents when the parameters of the pick-ups are different, the idea of adjusting the secondary inverter’s virtual impedance to compensate for the parameter difference between modules is provided. The phase angle of the secondary inverter voltages are adjusted by the phase difference between the module currents, and the phase shift angle of the secondary inverter voltages are controlled based from the magnitude difference between the module currents. The effectiveness of the bidirectional power control and secondary coil currents balance control are shown in experiments. Keywords: Bidirectional wireless power transfer · Multiple pick-ups · Current balance control · Phase angle · Phase shift angle
1 Introduction Wireless power transfer (WPT) technology has been widely applied in many applications such as consumer electronics and EVs. Most of the available rail transits use catenaries or power rails to get power, but they have some shortcomings, such as the mechanical abrasion, the need for regular maintenance, the risk of electric shock and so on. WPT technology can overcome these demerits, and this technology has been preliminarily applied in maglev, tram and railway train [1–3]. The inertia of rail transit is large. To make use of the braking energy, bidirectional power transfer WPT technology is needed. As the power rating of train is high, usually several pick-ups are used. In this paper, the bidirectional wireless power transfer (BWPT) © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 444–454, 2023. https://doi.org/10.1007/978-981-99-0631-4_44
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system with several secondary modules are studied, whose bidirectional power control and the secondary modules’ balance control are mainly studied. Bidirectional power flow can be realized by controlling the BWPT system as a unidirectional WPT in each direction [4, 5]. It can also be realized by active control of both primary and secondary sides. The power direction is controlled by setting the phase of the primary inverter voltage ± 90° ahead of that of the secondary, and the power magnitude is controlled by the voltage magnitude of the secondary inverter [6, 7]. All these controls need the information of both sides and often wireless communication is needed. To eliminate the wireless communication, voltage phase detection or estimation methods for the other side’s inverter are proposed [8–10]. For multiple pick-ups balance control, most of the available researches are about unidirectional system [11, 12]. The researches for bidirectional WPT with multiple pickups are relatively less [13, 14], and in these researches each of the secondary module output is connected to individual load. The balance control for multiple pick-ups in BWPT system with secondary outputs linked together has not been found out. Aiming at the high power BWPT system for rail transit, this paper studies its bidirectional power control and pick-ups current balance control. The system model is setup. Bidirectional power control without wireless communication is given for one pick-up BWPT system. The bidirectional power control is then extended to multiple pick-ups system, and the secondary currents balance control is proposed. Finally, the control effectiveness is shown by experiments.
2 System Model and Control 2.1 System Structure A BWPT system with multiple pick-ups for rail transit is shown in Fig. 1. The primary loops are laid on the ground. Several pick-ups are fixed on the vehicle. Each primary loop can cover several pick-ups. For the forwards transmission, the power from the grid is rectified and then pass through the BWPT system and is finally consumed by the motors. When the train is braking, the braking energy of the motors are fed back to the power grid through BWPT system.
Fig. 1. The rail transit powered by multiple pick-up BWPT system.
The structure of the studied BWPT system with multiple pick-ups is as in Fig. 2. Both the primary and the secondary coils are series compensated. The primary inverter and
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the secondary active rectifiers are all H-bridges. The outputs of the secondary rectifiers are parallel connected with a DC source.
Fig. 2. The structure of the multiple pick-up BWTP system.
2.2 BWPT System with One Pick-Up One Pick-up System Model and Analysis. To simplify the analysis, at first the parameters of multiple pick-ups are set to be the same, so the system with multiple pick-ups can be equivalent to that with one pick-up as in Fig. 3. Both the primary and the secondary coils are series compensated by capacitors. The system equations are: ⎧ dip 1 dis1 ⎪ ⎪ u + = i R + L ip dt − M1 p p p ⎨ p dt Cp dt (1) ⎪ di 1 di ⎪ ⎩ M1 p = is1 Rs1 + Ls1 s1 + is1 dt + us1 dt dt Cs1
Fig. 3. The structure of the BWPT system with one pick-up.
When both sides are in resonance, the steady state voltage equations are: U˙ p = I˙p Rp − jωM1 I˙s1 E˙ s1 = jωM1 I˙p = I˙s1 Rs1 + U˙ s1
(2)
Neglecting the primary coil resistance: · Is1
·
Up = jωM1
(3)
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The power received by the secondary coil is: ∗ Ps1 = Re I˙1s1 U˙ s1
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(4)
From (3) it can be concluded that if the primary inverter voltage is constant, the secondary coil current will also be constant. From (4) it can be seen that the secondary power can be adjusted by controlling the secondary inverter voltage while the secondary current is constant. For control implementation, the primary inverter voltage is kept constant, and by setting the phase of the secondary inverter voltage to be 0° or 180° relative to that of the secondary coil’s current the direction control of the power transfer is realized. The amplitude of the transferred power is controlled by adjusting the amplitude of the voltage of the secondary inverter. The control only need the secondary parameters so communication between both sides is not needed. The control system is shown in Fig. 4. The secondary coil’s current is sampled and its phase is derived by zero-cross detection. The Phase Angle (PA) stands for the leading angle of the secondary inverter voltage referring to the secondary inverter current. PA is set to 0° for forwards transmission or 180° for backwards transmission. The amount of transferred power is controlled by the Phase Shift (PS) angle between the drive signals for the two legs of the H-bridge. PS can be derived from the output power or current feedback control. Finally the secondary inverter voltage is produced from PS and PA by phase shift modulation.
Fig. 4. The bidirectional power control system of BWPT system with one pick-up.
2.3 BWPT System with Multiple Pick-Ups In this part, the bidirectional power control for one pick-up BWTP system will be extended to multiple pick-up system. Bidirectional Power Control for Pick-ups with Good Parameter Consistency. The structure of the multiple pick-ups BWPT system are as in Fig. 2. The steady state equations when both the primary and secondary sides are in resonance are: ⎧ ˙ ˙ ˙ ˙ ⎪ ⎨ Up = Ip Rp − jωM1 Is1 − jωM2 Is2 (5) jωM1 I˙p = I˙s1 Rs1 + U˙ s1 ⎪ ⎩ jωM2 I˙p = I˙s2 Rs2 + U˙ s2
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If all secondary coil currents are supposed to be the same for the good secondary ·
·
·
consistency or for the usage of the current balance control: Is1 = Is2 = Is . The Eq. (5) is transformed into: ⎧ ˙ ˙ ˙ ⎪ ⎨ Up = Ip Rp − jω(M1 + M2 )Is jωM1 I˙p = I˙s Rs1 + U˙ s1 ⎪ ⎩ jωM2 I˙p = I˙s Rs2 + U˙ s2
(6)
If the resistance of the primary coil here is neglected: · Is
·
Up = jω(M1 + M2 )
The output power of the secondary modules are: ∗ Ps1 = Re I˙s U˙ s1 ∗ Ps2 = Re I˙s U˙ s2
(7)
(8)
From (7) it can be seen that the secondary currents are fixed by keeping the primary inverter voltage constant. The secondary power control can be converted to the secondary voltages control based on (8). So the power control for the BWPT system with uniform pick-ups can be realized by setting the PA of secondary inverters to be 0° or 180° for power direction control and by adjusting the PS for power amplitude control. The Principle of the Current Balance Control for Pick-up Coils. When the parameters of the secondary coils are much different, the balance control of the secondary currents is needed in addition to the bidirectional power control. The uneven secondary parameters’ influence on the secondary currents will be analyzed. Take the two pick-ups system in Fig. 5 as an example. Suppose the 1st pick-up coil is fully compensated while the 2nd one has a reactance left after compensation:
jωM1 I˙p = E˙ 1 = I˙s1 Rs1 + U˙ s1 (9) jωM2 I˙p = E˙ 2 = I˙s2 Rs2 + jX2 I˙s2 + U˙ s2
Fig. 5. The equivalent circuits of two secondary modules.
From (9), the distribution of secondary currents can be deduced as (10). It can be seen that different induced voltage (mutual inductance), different coil internal resistance,
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or different resonant frequency can all lead to different secondary currents. · Is1
·
·
E1 − Us1 = Rs1
· Is2
·
·
E2 − Us2 = Rs1 + jX2
·
E1 · E2
=
M1 M2
(10)
To eliminate the difference among the second coil currents, a control method using virtual impedance of the secondary inverter is proposed as in Fig. 6. The each secondary ·
voltage Usi is controlled to be equal to the voltage drop on the corresponding load resistance Rldi , the compensation reactance jXi and compensation resistance Rldi as in (11). The adjustment of the secondary voltage can also be seen as the control of the virtual impedance of the secondary inverter for the constant secondary current. ⎧ · · · · ⎪ ⎪ jωM I = E = I R + I (Rld1 + Rld1 + jX1 ) ⎪ 1 p 1 s1 s1 s1 ⎪ ⎪ ⎪ ⎪ · ⎨ Us1 (11) · · · · · ⎪ ⎪ ⎪ jωM2 Ip = E2 = Is2 Rs2 + jX2 Is2 + Is2 (Rld2 + Rld2 + jX2 ) ⎪ ⎪ ⎪ ⎪ · ⎩ Us2
To keep the secondary currents balance, the virtual impedances for secondary inverters should be adjusted until the angle of the total serial impedance for each pick-up (which is constituted by the coil resistance and reactance, the compensation capacitor’s reactance and the inverter virtual impedance) are all the same. And the total serial impedance magnitude ratio between pick-ups is equal to the primary-secondary mutual inductance ratio between pick-ups. These relationships are shown in (12). ⎧ j(X2 + X2 ) jX1 ⎪ ⎪ = ⎨ Rs1 + Rld1 + Rld1 Rs2 + Rld2 + Rld2 (12) |R + R + R + jX1 | M1 ⎪ s1 ld1 ld1 ⎪ ⎩ = |Rs2 + Rld2 + Rld2 + j(X2 + X2 )| M2
Fig. 6. The principle of current balance control based on inverter’s virtual impedance.
The Implementation of the Current Balance Control for Pick-up Coils. The proposed control system can be divided into upper and lower layer as shown in Fig. 7. The upper control is responsible for the bidirectional power control, and it outputs the PS and PA for each secondary inverter. The lower control is for keeping the secondary currents balance, and it produces the adjustments PS and PA.
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The upper power control is the same as the power control for one pick-up BWPT. The power direction control is realized by setting the PAs of secondary inverters to be 0° for forwards transmission or 180° for backwards transmission relative with any one pick-up current’s phase. The power magnitude control is realized by the feedback control of the output current from all pick-ups, which generates PS for secondary inverters. The lower secondary currents balance control can be subdivided into magnitude difference control and phase difference control. The magnitude difference is reduced by adjusting the deviation of phase shift angle PS for each pick-up and phase difference by PA. Finally the PS from the upper control and the PS from lower control are added to get the phase shift angle PSi for each secondary inverter. The PA and the PA are added to get the voltage’s phase angle PAi for each secondary inverter.
Fig. 7. The bidirectional power control and module balance control of multiple pick-up WPT system.
3 Experimental Verification 3.1 Experiments of BWPT System with One Pick-Up The experimental platform of the BWPT with one pick-up is shown in Fig. 8. The DC side of the primary inverter and that of the secondary inverter are both connected with the DC source, so the capacity of the source can be reduced. The voltage of the DC source is 138V. Other parameters are shown Table 1 where the 1st pick-up corresponding to the pick-up used in the experimental system. The control system shown in Fig. 4 is used on the platform. The forwards power (output current) feedback control is as in Fig. 9. The secondary output current is set to be 8 A, and after about 3 ms, the output current settled to 8 A, and the corresponding power is 1.1 kW. The backwards power (output current) feedback control is as in Fig. 10. The secondary output current was set to be -8 and after about 3ms, the output current reached the set value after about 3ms. Here the corresponding power is -1.1kW.
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Fig. 8. The structure of the experimental platform of BWPT system with one pick-up.
Table 1. The parameters of BWPT system with two pick-ups. Parameter
Value
Primary coil resistance self-inductance/µH
24.33
Primary coil resistance/
0.0477
Primary coil compensate capacitor/µF
1.232
Mutual inductance between primary and 1st Pick-up coil/µH 1st pick-up coil self-inductance /µH
992.3
1st pick-up coil resistance/
0.742
1st pick-up compensate capacitor /µF
0.0302
Mutual inductance between primary and 2nd Pick-up coil/µH
14.20
2nd pick-up coil self inductance /µH 2nd pick-up coil resistance/
1004.9
2nd pick-up compensate capacitor/µF
0.02996
Working frequency/kHz
29.0698
DC sourve Voltage/V
100
14.20
0.773
Fig. 9. The waveforms of forwards control of BWPT system with one pick-up.
3.2 Experiments of BWPT System with Multiple Pick-Ups The experimental platform of BWPT with two pick-ups are shown in Fig. 11. The DC side of the primary inverter and two secondary inverters are all connected with the DC source. Parameters of this experimental platform are shown Tab.1. The forwards control is shown in Fig. 12. The inverters’ voltages are in-phase with their currents for both sides. The output current is 4A and has reached its set value.
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Fig. 10. The waveforms of backwards control of BWPT system with one pick-up.
Fig. 11. The structural diagram of the BWPT system with two pick-ups.
As to the balance of the secondary currents, Fig. 12(a) shows the system with the balance control where the 1st pick-up coil current is the same with the 2nd . The PSs and PAs for the two secondary inverters are different, which means the control system has adjusted the inverters’ voltages or the virtual impedances to compensate for the parameter differences between 2 pick-ups. The currents of pick-ups in Fig. 12(b) are different both in magnitude and in phase for the lack of balance control.
(a) with balance control
(b) without balance control
Fig. 12. The forwards transmission experimental waveforms of BWPT with multiple pick-ups.
The results of the backwards power control are shown in Fig. 13. The inverters voltages are anti-phase with their currents for both sides. The output current has reached the set value of -4 A. In Fig. 13(a), the secondary currents balance control is used, and the 1st pick-up coil current is the same with the 2nd and the PSs and PAs of the two secondary inverters are adjusted individually which can also be seen as the virtual impedances are regulated to compensate the parameter differences. Without balance control, the currents of pick-ups
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in Fig. 13(b) are different both in magnitude and in phase. The secondary coil currents become larger, so the transmission efficiency will also decrease.
(a) with balance control
(b) without balance control
Fig. 13. The backwards transmission experimental waveforms of BWPT with multiple pick-ups.
From above we can see that by using the proposed control system, the bidirectional power control can be realized only by the secondary information so the communication between the two sides can be eliminated, and all the pick-ups’ currents are balanced although their parameters are different.
4 Conclusion This paper proposes the bidirectional power control and the balance control of secondary modules for BWPT system with multiple pick-ups. The conclusions are: Controlling the secondary coil’s current to be in-phase or anti-phase with the secondary inverter’s voltage can set the power direction of the primary and secondary series compensated BWPT system, and the magnitude of the transferred power can be controlled by the phase shift angle of the secondary inverter. No communication between primary side and secondary side is needed. If the parameter difference between secondary modules is large, the currents of secondary coils will be unbalanced which can lower the power transfer capacity and efficiency. Setting the phase angle adjustment of the secondary inverters based on the phase difference between secondary coil currents, setting the phase-shift angle adjustment by the amplitude difference, and adding these adjustments into the output of the basic bidirectional power control system can keep the secondary coils’ currents balance bidirectionally. Acknowledgment. This work was supported by National Key R&D Program of China (2017YFB1201003–09, 2016YFB1200601-B21) and by Beijing Natural Science Foundation (3184060).
References 1. Deng, J., Zhang, Y., Wang, S., et al.: The design and coupler optimization of a singletransmitter coupled multireceiver inductive power transfer system for maglev trains. IEEE Trans. Transport. Electrific. 7(4), 3173–3184 (2021)
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2. Wang Z., Wang Y., Shi J., et al.: A 600kW wireless power system for the modern tram. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 214–217. IEEE, Seoul (2020) 3. Jiang, Y., Chen, K., Zhao, Z., et al.: Designing an M-Shape magnetic coupler for the wireless charging system in railway applications. IEEE Trans. Power Electron. 37(1), 1059–1073 (2022) 4. Nakadachi S., Mochizuki S., Sakaino S., et al.: Bidirectional contactless power transfer system expandable from unidirectional system. In: IEEE Energy Conversion Congress and Exposition 2013, pp. 3651–3657. IEEE, Denver (2013) 5. Dai, X., Sun, Y., Su, Y., et al.: Study on Contactless Power Bi-directional Push Mode. Proceedings of the CSEE 30(18), 55–61 (2010). (in Chinese) 6. Mohamed A. and Mohammed O.: Two-layer predictive controller for V2G and G2V services using on wireless power transfer technology. In: 2018 IEEE Industry Applications Society Annual Meeting, pp. 1–8. IEEE, Portland (2018) 7. Madawala, U., Thrimawithana, D.: A bidirectional inductive power interface for electric vehicles in V2G systems. IEEE Trans. Industr. Electron. 58(10), 4789–4796 (2011) 8. Tang, Y., Chen, Y., Madawala, U., et al.: A new controller for bidirectional wireless power transfer systems. IEEE Trans. Power Electron. 33(10), 9076–9087 (2018) 9. Jia, S., Chen, C., Liu, P., et al.: A digital phase synchronization method for bidirectional inductive power transfer. IEEE Trans. Industr. Electron. 67(8), 6450–6460 (2020) 10. Liu, F., Li, K., Chen, K., et al.: A phase synchronization technique based on perturbation and observation for bidirectional wireless power transfer system. IEEE Journal of Emerging and Selected Topics in Power Electronics 8(2), 1287–1297 (2020) 11. Lei, Y., Zhang, J., Song, K., et al.: Stability analysis of multi-load inductively coupled power transfer system. Trans. CES 30(S1), 187–192 (2015). (in Chinese) 12. Zhang, F., Shi, L., Yin, Z., et al.: A current balance control strategy applied in inductively coupled power transfer system with multiple parallel pickup modules. IEEE Trans. Veh. Technol. 8(3), 2207–2217 (2019) 13. Neath M., Madawala U. and Thrimawithana D.: Frequency jitter control of a multiple pick-up Bidirectional Inductive Power Transfer system. In: 2013 IEEE International Conference on Industrial Technology, pp. 521–526. IEEE, Cape Town (2013) 14. Dai, X., Wu, J., Jiang, J., et al.: An energy injection method to improve power transfer capability of bidirectional WPT system with multiple pickups. IEEE Trans. Power Electron. 36(5), 5095–5107 (2021)
Robust Regulation of Constant Current Wireless Charging System with Clamping Coil Le Li1 , Bing Cheng1 , Houxuan Liu1 , Liangzong He1(B) , Wei Li2 , Tiejun Ma3 , and Yongjun Wang4 1 Instrumental and Electrical Engineering Department, Xiamen University, Xiamen 361005,
China [email protected] 2 Xiamen Jinlong United Automobile Industry Corporation, Xiamen, China 3 Fujian Fuqing Nuclear Power Corporation, Fuqing, China 4 Xiamen Avida Electronics Corporation, Xiamen, China
Abstract. Constant current is desirable for some wireless power application such as LED driving and battery charging. In constant current wireless charging, the mutual inductance change caused by coil misalignment will lead to output current fluctuation. Aiming at the problem of insufficient robustness and low efficiency caused by mutual inductance change, the wireless charging system with clamping coil is proposed. The system maintains the output current constant under the coil misalignment by controlling semi-active rectification of the clamping coil circuit located on the transmitting side. Finally, an experimental platform with an output current of 2A is built. The results show that the system has good constant current output characteristics when the coil misalignment, and the maximum transmission efficiency can reach 94.3%. Keywords: Wireless charging · Constant current · Zero phase angle · Mutual inductance change
1 Introduction Wireless power transfer has been widely concerned on account of its convenience, safety, flexibility, non-contact. Which reduces the risk of electric spark in plugging in and on [1]. Hence, wireless power transfer is extensive used in many fields such as medical equipment [2], mobile phones [3], underwater device [4] and electric vehicles [5]. In recently years, aiming to improve the charging security and prolong the product life, constant current is required for charging the battery and driving the LED [6, 7]. Normally, the constant current output can be realized by designing suitable compensation topologies, such as series-series topology, which can maintain output constant current at resonance frequency point [8, 9]. However, misalignment between coupling structures weakens the output current stability and declines the system efficiency [10]. To attack above problem, many approaches have been put forward to efficiently reduce the influence of misalignment. These approaches are divided into coupling coil structure, compensation networks and control strategy. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 455–462, 2023. https://doi.org/10.1007/978-981-99-0631-4_45
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The first method is to optimize the coupling coil structure. Double-D(DD) coil and the DD quadrature (DDQ) coil are designed and analyzed in [11, 12], and the performance of misalignment tolerance is improved. However, the loss on the coil is increasing and the method of coil designing is complicated. The application of coil design is limited. The second method is applied control strategy. [13] proposes variable capacitor based on current feedback to achieve constant current output. The modulation method is complicated to realize. Regulated the duty cycle of the dc-dc converter can keep constant current stably when the coil position changes [14]. However, the addition converter makes system loss increase and the volume of the secondary side larger, which limits the application of this approach. Regulating the phase shift angle of the primary inverter can maintain stable current under the coil misalignment [15]. However, when the angle of phase shift becomes larger, the efficiency of the system will decrease sharply because this system cannot maintain zero-voltage-switching (ZVS) all the time. To solve above issues, a wireless charging system with clamping coil is proposed, which has the ability of constant current output. Besides, the zero phase angle (ZPA) could be achieved. In addition, the control on the semi-active rectifier ensures the constant current under the variation mutual inductance, which could improve stability of the wireless charging system. Finally, an experiment platform with 2A current output is established to demonstrate the feasibility of theoretical analysis.
2 Output Characteristics of Proposed System
Fig. 1. The proposed three-coils WPT system with a semi-active rectifier.
The proposed three-coil wireless charging system is shown in Fig. 1. As shown in Fig. 1, L p , L c and L s are the self-inductance of transmitter, clamp and receiver coils, respectively. Rp , Rc and Rs are the parasitic resistance of three coils accordingly. C p is the compensation capacitor of L p . C c is the compensation capacitor of L c . C s is the compensation capacitor in series with L c . C s1 is the parallel compensation capacitor of L c . L s1 is the series compensation inductance in the secondary side. M ps , M pc and M sc are the mutual inductances between three coils, respectively. The fundamental approximation method is used to analyze this circuit, the relationship between input and output of the inverter, semi-active rectifier and full-bridge
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rectifier can be derived as follows [16]: ⎧ √ √ ⎪ 2 2Vdc 2 2Vdc ⎪ ⎪ V sin(D sin(Dc π ) = π ) V = ⎨ p p c π π √ ⎪ 2 2 π 8 ⎪ ⎪ Vo ; IB = √ IL Req = 2 RL ⎩ VB = π π 2 2
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(1)
where Dp and Dc are the equivalent duty cycle of the inverter and semi-active rectifier, respective. V p , V c , I s , are the root mean square(RMS) of V˙ p , V˙ c and I˙s , respectively. 2.1 Analysis of CC Output Under Load Variation
Fig. 2. The equivalent circuit of the proposed three-coils WPT system
Figure 2 shows the equivalent circuit of the proposed system. The following equations is calculated by Kirchhoff’s law: ⎧ 1 ⎪ ⎪ ⎪ V˙ p = (jωLp + jωC )I˙p + jωMps I˙2 + jωMpc I˙c ⎪ p ⎪ ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ )I˙c + jωMpc I˙p + jωMsc I˙s ⎨ V˙ c = (jωLc + jωCc (2) ⎪ 1 ˙ 1 1 ˙ ⎪ ˙ ˙ ⎪ jωM + jωM + + (jωL + + ) I = 0 I I I ps p sc c s1 s s ⎪ ⎪ jωCs1 jωCs jωCs1 ⎪ ⎪ ⎪ ⎪ ⎪ 1 ˙ ⎪ ⎩ (Is + I˙s1 ) + jωLs1 I˙s1 + Req I˙s1 = 0 jωCs1 The system compensation parameters meet the following conditions at operation frequency: ⎧ 1 1 ⎪ ⎪ ⎨ jωLp + jωC = 0, jωLc + jωC = 0 p c ⎪ 1 1 1 (3) ⎪ ⎩ jωLs + + = 0, jωLs1 − =0 jωCs jωCs1 jωCs1
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Substituting (3) into (2), the simplified equation is listed as: ⎧ ⎨ V˙ p = jωMps I˙s + jωMpc I˙c ,V˙ c = jωMpc I˙p + jωMsc I˙s 1 ˙ 1 ˙ ⎩ jωMps I˙p + jωMsc I˙c + Is1 = 0, Req I˙s1 + Is = 0 jωCs1 jωCs1
(4)
Derived from (4), the current of equivalent I˙s1 can be expressed as I˙s1 =
jωCs1 (Mps V˙ c + Msc V˙ p ) 2R −M j2ω3 Msc Mps Cs1 eq pc
(5)
According to Eq. (5), the load-independent current output can be achieved when crossing mutual inductance M sc is ignored. Then I˙s1 can be simplified as I˙s1 =
jωCs1 Mps V˙ c Mpc
(6)
Substituted (6) to (1), the output current I B can be derived IB =
ωCs1 Mps Vdc sin(Dc π) Mpc
(7)
The current expressions of other branches are deduced as I˙p =
V˙ p + ω2 C1 Mps Req I˙L V˙ c , I˙s = jωC1 Req I˙s1 , I˙c = jωMpc jωMpc
(8)
2.2 Analysis of CC Output Under Mutual Inductance Variation The misalignment between transmitter and secondary coils will affect the output current value fluctuation. From Eq. (7), it is known that the relationship between the equivalent duty cycle Dc and other parameters is deduced as Dc =
IB Mpc 1 ) arcsin( π ωCs1 Mps Vdc
(9)
From Eq. (9), it is obvious that the output current I B is in connection with Dc and M ps . As a sequence, maintaining constant I B by adjusting the duty cycle Dc under variable coil misalignment is reasonable. 2.3 The Input ZPA Realization Analysis Defining the ratio of voltage V p and current I p at the primary side and voltage V c and current I c at the clamping coil side as Z p and Z c respectively. The equations of Z p and Z c are expressed as Zp =
V˙ p jωMpc V˙ p = I˙p V˙ c
(10)
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2V ˙c jωMpc V˙ c = 2 2R V Mpc V˙ p + jω3 Cs1 Mps I˙c eq ˙ c
(11)
Zc =
When the angle of V c is ahead of V p 90°, which means the angle θ is equal to 90, then Z p and Z c are pure resistance without an imaginary part. At this time, the input ZPA of this system can be realized. The system reactive power can be reduced and the system transmission efficiency can be improved. Besides, the current stress of the whole circuit can be greatly reduced.
3 Experiment 3.1 Experiment Platform To verify the above analysis, a contactless charger experimental platform with 2A charging current has been constructed as depicted in Fig. 3. And the experiment parameters are listed in Table 1.
Fig. 3. The platform of the proposed system.
Table 1. Experiment parameters Parameter
Value
Parameter
Value
V dc f
72 V
C s1
71.96nF
85 kHz
L s1
48.7uH
Cp
15.7nF
M ps
22.5uH
Cc
33.6nF
M pc
35.12uH
Cs
59.75nF
Ls
107.4uH
Lp
225.7uH
Lc
104.8uH
3.2 Experiment Result Figure 4(a) shows the experimental waveforms of load equal to 15 at the coil wellaligned condition. The system output current is 2A, and the equivalent duty cycle Dc is
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0.395. When the angle of V c is 90° ahead of V p , the system input voltage V p has the same angle with the input current I P , meaning that the input ZPA is realized. And the angle between V c and I c is 180°, which means the clamp circuit is equivalent to the pure resistive at this time. Figure 4(b) shows the experimental waveforms of a load equal to 30 at the coil well-aligned condition. The system output current is still 2A, and the duty cycle Dc is 0.395 too. The input ZPA is realized too, which means the load variation does not affect input ZPA.
Fig. 4. Measured operating waveform of proposed system at M ps = 35.12uH (a) R = 15. (b) R = 30.
Figure 5 is the key voltage and current waveform under load variation. When the load is changed from 15 to 30, the power transmitted to the secondary side is increasing. During a short fluctuation, I B can be successfully maintained at 2A. I p keeps constant due to the clamping effect of the clamp coil, and it means that the input power of the system is constant. At the same time, I c is reduced caused by increasing load, the power delivered to the clamping side is decreasing. It meets the law of energy conversion.
Fig. 5. Measured operating waveform when load is changed from 15 to 30
Figure 6 shows the experiment waveforms under X misalignment. In this case of misalignment, the mutual inductance M ps is 41.09 uH. For maintaining output current I B is 2A, and the duty cycle Dc changes to 0.29. The input voltage and the input current have no phase difference, which means that the input ZPA is achieved under coil misalignment.
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Fig. 6. Measured operating waveform of proposed system at M ps = 35.12 uH and R = 15
Figure 7 shows the output current and system efficiency under load variation. And it is known that the output current has slight fluctuation when the load changed from 15 to 45, which is caused by the parasitic resistance of system. At the same time, the efficiency is positively related to the load. And the system transfer efficiency is improved from 73.8% to 94.3%. The reason is that when the system operated under light load condition, the system inherent losses including coil loss and rectifier’ s loss, taking a large portion of the input power. Nevertheless, when the system operated at the condition of heavy load, the inherent losses account for input power decreases, and the system efficiency will be significant increased.
Fig. 7. The output current and efficiency characteristic of proposed system
4 Conclusion A novel topology with a clamping side is proposed to realize constant current output under load variation. And the constant current output and input ZPA are analyzed. Then regulating the equivalent duty cycle Dc , constant current output is realized under the coil misalignment variation. Finally, a 180W system is established to prove the theoretical analysis. The constant current output and ZPA under coil misalignment are realized by regulating the semi-active rectifier circuit. And the maximum efficiency can reach 94.3%.
References 1. Fan, X., Mo, X., Zhang, Xn.: Research status and application of wireless power transmission technology. Process. CSEE 35(10),2584–2600 (2015). (in Chinese)
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2. Yin, C., Xu, P.: Wireless power transfer for implantable ventricular assistance: a review. Trans. China Electrotech. Soc. 30(19),103–109 (2015). (in Chinese) 3. Hui, S., Ho, W.: A new generation of universal contactless battery charging platform for portable consumer electronic equipment. IEEE Trans. Power Electron 20(3), 620–627 (2004) 4. Orekan, T., Zhang, P., Shih, C.: Analysis, design and maximum power efficiency tracking for undersea wireless power transfer. IEEE J. Emerg. Sel. Topics Power Electron. 6(2),843–854 (2017) 5. Song, K., Zhu, C., Li, Y., et al.: Wireless power transfer technology for electric vehicle dynamic charging using multi-parallel parimary coils. Process. CSEE 35(17),4445–4453 (2015). (in chinese) 6. Cheng, B., He, L.: High-order network based general modeling method for improved transfer performance of the WPT system. IEEE Trans. Power Electron 36(11), 12375–12388 (2021) 7. Li, Y., Hu, J., Li, X., et al.: Analysis, design and experimental verification of a mixed high order compensations-based WPT system with constant current outputs for driving multistring LEDs. IEEE Trans. Ind. Electron. 1(67),203–213 (2015) 8. Vu, V., Tran, D., Choi, W.: Implementation of the constant current and constant voltage charge of inductive power transfer systems with the double-sided LCC compensation topology for electric vehicle battery charge applications. IEEE Trans. Power Electron 33(9), 7398–7410 (2018) 9. Wei, Z., Mi, C.C.: Compensation topologies of high-power wireless power transfer systems. IEEE Trans. Veh. Technol 65(6), 4768–4778 (2016) 10. Villa, J.L., Sallan, J., Sanz Osorio, J.F., Llombart, A.: High-misalignment tolerant compensation topology for ICPT systems. IEEE Trans. Ind. Electron. 59(2),945–951 (2012) 11. Budhia, M., Boys, J.T., Covic, G.A., Huang, C.-Y.: Development of a single-sided flux magnetic coupler for electric vehicle IPT charging systems. IEEE Trans. Ind. Electron. 60(1),318–328 (2013) 12. Zaheer, A., Covic, G.A., Kacprzak, D.: A bipolar pad in a 10-kHz300-W distributed IPT system for AGV applications. IEEE Trans. Ind. Electron 61(7), 3288–3301 (2014) 13. Pan, X., Zhang,C., Niu, H., Zuo, Y., Zhao, F.: A PS/S Current-Fed IPT System With Variable Capacitors for Achieving ZPA Operation. IEEE J. Emerg. Sel. Topics Power Electron. 9(4), 4918–4931 (2021) 14. Li, Z., Zhu, C., Jiang, J., Song, K., Wei, G.: A 3-kW wireless power transfer system for sightseeing car supercapacitor charge. IEEE Trans. Power Electron 32(5), 3301–3316 (2017) 15. Song, K., Li, Z., Jiang, J., Zhu, C.: Constant current/voltage charging operation for seriesseries and series-parallel compensated wireless power transfer systems employing primaryside controller. IEEE Trans. Power Electron. 33(9), 8065–8080 (2018) 16. Jiang, Y., Wang, L., Fang, J., Li, R., Han, R., Wang, Y.: A high-efficiency ZVS wireless power transfer system for electric vehicle charging with variable angle phase shift control. IEEE J. Emerg. Sel. Topics Power Electron. 9(2),2356–2372 (2021)
Comparison of Wireless Power Transfer Systems with Multi-loads Wei Deng1 , Zhiliang Yang1 , Jing Yin1 , Jie Wu1(B) , Pengfei Gao1 , Yafei Chen1 , and Zhanshi Lou2 1 College of Electrical and Information Engineering, Zhengzhou University of Light Industry,
Zhengzhou 450002, China {2007046,joy,wujie,2019036}@zzuli.edu.cn, [email protected], [email protected] 2 China Eleventh Chemical Construction Company Ltd., Kaifeng 475002, China [email protected]
Abstract. Currently, wireless power transfer (WPT) system can reliably charge smart mobile devices, but in practice the need to charge multi-target mobile devices is increasing. In this paper, a multi-load magnetically coupled resonant WPT system is investigated. Through the comparison and theoretical analysis of the WPT system with single transmitter and multi-load transmitted at a single frequency, the results show that the increase or decrease of the load will have a great impact on other loads of the system. The limitations of single-transmitter and multi-load systems at a single frequency are described. The multi-frequency technology in the multi-load system can make each load form an independent system, reduce the interference between them, and improve the stability of the multi-load system. Then a multi-load system based on multi-frequency multi-amplitude pulse width modulation (MFMA-PWM) strategy is established. Finally, the correctness of the proposed method is verified by experiments. Keywords: Wireless power transfer · Magnetic coupling resonance · Multi-load · Multi-frequency
1 Introduction Wireless power transfer (WPT) is a safe, convenient and elegant way to transfer energy. In practical applications, due to the large number of electrical terminals, it is often necessary to charge multiple loads at the same time, such as wearable devices, mobile phones, notebook computers and other electrical terminals. At present, the single-load WPT technology is relatively mature and has been applied to fields such as electric vehicles, mobile devices, and implantable medical devices [1]. However, the single-load WPT system can only supply power to one load, and the system utilization rate is low [2, 3]. Multi-load WPT technology can just make up for the shortcomings of single-load WPT technology [4]. In recent years, researchers have studied the coil structure, power distribution, system efficiency, and frequency splitting of multi-load WPT systems. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 463–471, 2023. https://doi.org/10.1007/978-981-99-0631-4_46
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Kim et al. used time-division multiplexing for power distribution [5], that is, only supplying power to one load at each time. Although this method simplifies the multi-load system model, it cannot supply power to multiple loads at the same time. Wang et al. studied a single-transmitter, single-relay, and multiple-receive structure [6], which can enable multiple loads to receive power at the same time, but this structure cannot ignore crosscoupling, and the overall system design and control are relatively complex. Xie et al. proposed a method to achieve constant current output with cross-coupling compensation in multi-Rx WPT systems [7], avoiding tedious parameter measurement and communication between receivers. Zhou et al. studied an LCC-S compensated Bi-directional WPT system with multiple receivers, proposed the control strategy of maximum efficiency point tracking [8]. The above transmission schemes for multi-load systems all use a single frequency to transfer power. In this paper, the transmission scheme of the multi-load system is compared and studied, the relationship between the various loads in the multi-load system is analyzed, and the inherent defects and internal mechanism of the single-frequency multi-load WPT system are revealed, and a multi-frequency transmission scheme is proposed. The above findings and the feasibility of the proposed scheme are confirmed by experiments.
2 Analysis of Single Frequency WPT System In this section, the multi-load system of WPT is described. Firstly, the WPT system with the structure of transmitter and load is established, and the equivalent topology model is established. The method of WPT is analyzed. Then, assuming one transmitter and two loads, the multi-load system of WPT is analyzed under the condition of the same mutual inductance between the two receivers and the transmitter and the different mutual inductance between the two receivers and the transmitter. 2.1 Modeling of the WPT System In this part, The equivalent topology of single transmitter and single load is derived. The method of WPT is analyzed.
Fig. 1. (a) The dual-coil structure of WPT. (b) The equivalent topology of a single transmitter and a single receiver.
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According to Fig. 1(a). Through Kirchhoff’s voltage law (KVL), the circuit formula can be obtained: ⎧ ˙ ˙ ˙ ⎪ ⎨ V in = IP RP + jωM I s (1) 0 = V˙ L + I˙S R s + jωM I˙ P ⎪ ⎩˙ V L = I˙S R L where, V˙ in and I˙P are the voltage and current of the transmitter separately. V˙ L and I˙S are the voltage across the load and the current at the receiver end respectively. M is mutual inductance between two coils. L p , C p , and RP represent the inductance, capacitance, and coil resistance of the transmitter. L S , C S , RS , RL represent the inductance, capacitance, coil resistance and load resistance of the receiver. ∗ Assuming R L + R s = Rs , the terminal voltage V˙ in and the load current I˙S can be obtained by the above formula: ω2 M 2 ˙ jωM ), IS = − ∗ I˙ P V˙ in = I˙P (RP + ∗ Rs Rs
(2)
Therefore, the equivalent impedance Zrec of receiver conversion to transmitter can be obtained: Zrec =
ω2 M 2 R∗s
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Its equivalent topological structure model is shown in Fig. 1(b). The KVL equation is equivalent to the original equation, so the equivalent circuit is the same as the original circuit. The part outlined by the dotted line can be regarded as the equivalent impedance Zrec converted from the receiver to the transmitter. 2.2 Multi-load Analysis of the WPT System This section considers multi-load WPT. Assuming one transmitter and two loads, the cases where the mutual inductances of the transmitter and receiver are the same and different are analyzed. Then, its working process is deduced. The effects between different loads and the limitations of single-transmitter and multi-load systems at a single frequency are analyzed. In practical applications, the distance between multiple loads is relatively far, and the mutual inductance between them is very small, so it can be ignored. This paper analyzes the circuit based on this. According to Fig. 2. The KVL equation can be obtained: ⎧ V˙ in = I˙P RP + jωM (I˙ s1 + I˙ s2 ) ⎪ ⎪ ⎪ ⎪ ⎪ ˙ ˙ ˙ ⎪ ⎪ ⎨ 0 = V L1 + IS1 R s1 + jωM I P (4) 0 = V˙ L2 + I˙S2 R s2 + jωM I˙ P ⎪ ⎪ ⎪ ⎪ V˙ L1 = I˙S1 R L1 ⎪ ⎪ ⎪ ⎩˙ V L2 = I˙S2 R L2
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Fig. 2. Dual-load MCR WPT system with the same mutual inductance.
According to the above formula, assuming R L1 +R s1 = R∗s1 and R L2 +R s2 = R∗s2 , the ˙ in and the two load currents I˙S1 and I˙S2 are expressed as respectively: terminal voltage V 2 2 2 2 ˙ in = I˙P (RP + ω M + ω M ), I˙S1 = − jωM I˙ P , I˙S2 = − jωM I˙ P V R∗s1 R∗s2 R∗s1 R∗s2
(5)
According to Eq. (5), the approximate conversion impedance Zrec1 and Zrec2 of load 1 and load 2 be converted to the transmitter are respectively: Zrec1 =
ω2 M 2 ω2 M 2 , Z = rec2 R∗s1 R∗s2
(6)
When M of the transmitter coil and the receiver coil are the same, the load can be equivalent to the transmitter impedance in the form of ω2 M 2 R∗s . In this case it can be extended to multiple loads. When M of the transmitting coil and the receiving coil are different, the formula can be obtained: V˙ in = I˙P (RP +
ω2 M12 ω2 M22 + ) R∗s1 R∗s2
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In the case of multi-load, it can be concluded that: V˙ in = I˙P (RP +
ω2 M12 ω2 M22 ω2 Mn2 + + ······ + ) ∗ ∗ Rs1 Rs2 R∗sn
(8)
According to formula (7), it can beknown that the load impedance is approximately equivalent to ω2 M12 R∗s1 and ω2 M22 R∗s2 when the two loads and the emitter have different mutual inductance. In this case, we can deduce that in the WPT system with single transmitter and multi-load transmitted at a single frequency. If the number of loads keeps increasing, the amount of equivalent impedance ω2 Mn2 R∗sn converted from the receiving end to the transmitter will increase, as shown in Formula (8), so the total impedance will increase, and the voltage shared by each load will decrease sharply. Therefore, single-transmitter and multi-load WPT systems have limitations at a single frequency. It can be derived from the above formula: M1 R∗s2 R L1 I˙S1 M1 R∗s2 P L1 R L1 M12 R∗2 V˙ L1 s2 = , = , = M2 R∗s1 R L2 I˙S2 M2 R∗s1 P L2 R L2 M22 R∗2 V˙ L2 s1
(9)
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In the formula, V˙ L1 and I˙S1 are the voltage and current of load R L1 , where V˙ L2 and I˙S2 are the voltage and current of load R L2 , P L1 is the power of load R L1 , P L2 is the power of load R L2 , if the internal resistance R s1 and R s2 are ignored, it can be obtained: P L1 R L2 M12 = P L2 R L1 M22
(10)
We can see that the load current distribution is proportional to M and inversely proportional to the load R L . If the load R L increases and its mutual inductance M increases, the voltage distributed by the load will increase. In MCR WPT system with double load and single transmitter, the distribution of power, voltage and current is related to M and R L , and the change of M and R L in one channel will affect the other channel.
3 Multi-load WPT Analysis Based on MFMA-PWM Principle Section 2 compares and analyzes the multi-load situation, and shows that in the case of single-transmitter and multi-load at a single frequency, when each load has a great influence on each other. a load changes, which will affect the voltage and current of other loads, thus greatly affecting the stability of the multi-load system. Therefore, in the multi-load WPT system, multi-frequency transmission should be adopted to reduce the influence of the change of each load on other loads in the case of single frequency. There are many ways to generate multi-frequency. Among which [9] proposed multi-frequency Pulse width modulation (MFPWM) strategy can make the singlephase full-bridge inverter generate multiple frequencies. The idea of MFPWM comes from Selective harmonic elimination pulse width modulation (SHEPWM) [10, 11]. In traditional SHEPWM, the mode is programmed to output only fundamental waves, and the selected harmonic number is reduced to zero. Based on SHEPWM, MFPWM eliminates unnecessary harmonics and modulates selected harmonics to achieve power transfer. Another method to generate multi-frequency is to inject different frequencies generated by multiple single-phase half-bridge inverters in parallel to achieve multiple frequencies at the transmitter [12]. In [13], a multi-frequency and multi-amplitude pulse width modulation (MFMA-PWM) strategy was proposed. The principle of MFMAPWM is the control signal obtained by comparing the high frequency triangular carrier with the superposition wave. Superimposed waves are composed of sinusoidal waves of different frequencies and amplitudes. Like SPWM, the modulation method is based on the principle of equivalent area. Therefore, this paper uses a multi-load WPT based on MFMA-PWM strategy, as shown in Fig. 3(a). Through the MFMA-PWM strategy to control the inverter switch on and off time sequence to output the square wave voltage. The square wave voltage contains multiple sinusoidal signals with different target frequencies. The output of an inverter is expressed in the form of a compound frequency, which usually consists of multiple target frequency components. In addition, it inevitably contains the undesired harmonic frequency, caused by the inverter switching frequency, but it has the characteristics of low content, and small amplitude. The inverter output is connected to
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Fig. 3. (a) GaN inverter and its multi-frequency control signal. (b) Dual-load WPT system based on MFMA-PWM principle.
the transmitter end of different frequencies, and an independent WPT channel can be obtained through the LC resonant channel of the corresponding frequency. As shown in Fig. 3(b). It shows the dual load condition, which can make the dual load independent of each other with little interference and improve the stability of the system.
4 Experimental Verification In this section, the limitations of single-transmitter and multi-receiver system at single frequency and the feasibility of the multi-load WPT based on the MFMA-PWM principle are verified by experiments. This experiment verifies and compares three cases respectively. The first case is a single transmitter and a single load system, in which the frequency is 85 kHz, as shown in Fig. 5. The second case is a single transmitter and dual load system, where the frequency is 85 kHz, as shown in Fig. 6. The third case is a dual load system based on the MFMA-PWM strategy, where the frequencies are 85 kHz and 198 kHz, as shown in Fig. 7. The experimental platform is shown in Fig. 4. In order to ensure the accuracy of the experiment and avoid interference from other conditions, the size, shape, number of turns and self-induction of the transmitter and receiving coils used in the experiment are all the same, and the load is all 30 noninductive resistance. And the primary coil and secondary coil distance and contact area are consistent.
Fig. 4. Experiment platform. (a) Single frequency and dual load. (b) Dual load based on MFMAPWM
As shown in Fig. 5 and Fig. 6. in the case of single frequency. When a new load is added, the voltage of the other loads in the system will be greatly reduced which seriously affects the stability of the system. The limitations of single-transmitter and multi-load systems at a single frequency are verified. It can be seen from Fig. 5 and Fig. 7.
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That in the multi-load WPT system based on MFMA-PWM strategy, there is basically no interference between the loads and each load becomes an independent transmission channel. When the new load is added, the voltage of other loads in the system is unaffected basically. The feasibility of multi-load WPT system based on MFMA-PWM strategy is verified. It can improve the stability of system transmission.
Fig. 5. Single transmitter and single load system. (a) Inverter output waveform and FFT. (b) Load voltage waveform and FFT.
Fig. 6. Single transmitter and dual load system. (a) Inverter output waveform and FFT. (b) Load voltage waveform and FFT.
Fig. 7. Dual load system based on the MFMA-PWM strategy. (a) Inverter output waveform and FFT. (b) Load voltage waveform and FFT.
5 Conclusions In this paper, the single-transmitter single-load system and single-transmitter doubleload system are theoretically analyzed under the condition of single frequency. The
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analysis shows that in a multi-load system, the load of each transmission channel is connected in series in the circuit after being reduced to the transmitting side. Therefore, a change of any load will have an impact on the power transfer at the other channels. This paper analyzed the limitations of the single-frequency single-transmitter multi-load system and its internal reasons, and then proposed that each load can be involved in an independent system by using the multi-frequency technology, so that multiple loads can receive power simultaneously. Finally, the results of theoretical analysis and the effectiveness of the proposed method are verified by experiments. Acknowledgments. This work was supported by the Scientific and Technological Program of Henan Province under Grant 222102520039.
References 1. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Industr. Electron. 66(2), 1044–1058 (2018) 2. Stankiewicz, J.M., Choroszucho, A., Steckiewicz, A.: Estimation of the maximum efficiency and the load power in the periodic WPT systems using numerical and circuit models. Energies 14(4), 1151 (2021) 3. Fu, N., Deng, J., Wang, Z., et al.: A hybrid mode control strategy for LCC–LCC-compensated WPT system with wide ZVS operation. IEEE Trans. Power Electron. 37(2), 2449–2460 (2021) 4. Luo, B., Ma, D., Han, W., et al.: Extensible low-profile Coplanar Wireless Power transfer system for multi-load applications with load-independence constant current output. IEEE Trans. Ind. Electrons. 69, 11187–11197 (2021) 5. Kim, Y.J., Ha, D., Chappell, W.J., et al.: Selective wireless power transfer for smart power distribution in a miniature-sized multiple-receiver system. IEEE Trans. Industr. Electron. 63(3), 1853–1862 (2015) 6. Wang, W., Huang, X., Guo, J., et al.: Power stabilization based on efficiency optimization for WPT systems with single relay by frequency configuration and distribution design of receivers. IEEE Trans. Power Electron. 32(9), 7011–7024 (2017) 7. Xie, X., Xie, C., Wang, J., et al.: Constant current output control based on cross-coupling compensation in multi-receiver WPT system using active rectifier. IEEE Trans. Transp. Electrification. (2022) 8. Zhou, L., Liu, S., Li, Y., et al.: Efficiency optimization of LCC-S compensated multiplereceiver bi-directional WPT system for stackers in automated storage and retrieval systems. IEEE Trans. Power Electron. 37, 15693–15705 (2022) 9. Zhao, C., Costinett, D., Trento, B., Friedrichs, D.: A single-phase dual frequency inverter based on multi-frequency selective harmonic elimination. In: 2016 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3577–3584. IEEE, Long Beach (2016) 10. Ahmadi, D., Zou, K., Li, C., Huang, Y., Wang, J.: A universal selective harmonic elimination method for high-power inverters. IEEE Trans. Power Electron. 26(10), 2743–2752 (2011) 11. Du, Z., Tolbert, L.M., Chiasson, J.N.: Reduced switching-frequency active harmonic elimination for multilevel converters. IEEE Trans. Industr. Electron. 55(4), 1761–1770 (2008)
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12. Ding, Z., Liu, F., Yang, Y., et al.: High-efficiency design and close-loop power distribution control for double-frequency double-load magnetically coupled resonant wireless power transfer system. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3111–3116. IEEE, Long Beach (2019) 13. Wu, J., Bie, L., Kong, W., et al.: Multi-frequency multi-amplitude superposition modulation method with phase shift optimization for single inverter of wireless power transfer system. IEEE Trans. Circuits Syst. I Regul. Pap. 68(5), 2271–2279 (2021)
Multi-objective Optimization of IPT System Compensation Parameters for Improving Misalignment Tolerance Junfeng Yang1 , Junjie Guo1 , Qingbin Tong1(B) , Xu Yang1 , and Tianqi Hao2 1 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China
{yangjunfeng,20121437,qbtong,17117425}@bjtu.edu.cn
2 Department of Electrical and Computer Engineering, University of British Columbia,
Vancouver, BC V6T 1Z4, Canada [email protected]
Abstract. The capability of misalignment tolerance is a problem of great concern for inductive power transfer (IPT) system, especially with the simultaneous change of load. This paper presents a detailed multi-objective particle swarm optimization (MOPSO) -based parameters design method to minimize the output current fluctuation. Firstly, the parameter design of constant current output (CCO) type LCC-S compensated IPT system is derived in detail. Then, The multiobjective optimization reveals the Pareto trade-offs and performance limitations in the aspect of output current ripple, zero voltage switching (ZVS) demand and component stress. Two group optimal results are obtained with the algorithm, and one set parameters have the minimum output current fluctuation with high stress on components, and the other set parameters make the IPT system have excellent comprehensive characteristics. Finally, the effectiveness of proposed scheme are validated by experimental results. Keywords: Inductive power transfer (IPT) · Misalignment tolerance · Multi-objective particle swarm optimization (MOPSO) · Zero voltage switching (ZVS) · Pareto optimal solutions
1 Introduction As a result of the absence of electrical or mechanical contacts, inductive power transfer (IPT) system has many unique advantages, such as high safety, avoidance of bulky cables, simple charging process, and environment friendly [1, 2]. It uses alternating magnetic field as medium and transmits power through electromagnetic coupling in loosely coupled transformer. However, misalignment between the primary and secondary coupling coils is unavoidable [3] and the output voltage or current of IPT system is sensitive to the coupling coefficient. In order to enhance misalignment tolerance of IPT system, varies of design and optimization methods are proposed, including magnetic coupling mechanism design, control strategy, compensation topology and parameter optimization [4]. Among these methods, © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 472–481, 2023. https://doi.org/10.1007/978-981-99-0631-4_47
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compensation network is vital because it is related to resonant frequency, output characteristics and power factor. Traditional compensation parameters are designed to obtain stable output without considering coils tilt and dislocation. Basic SS topology using a single resonant capacitor to compensate inductance of the loosely coupled transformer on both side is widely promoted and applied. In [5] and [6], the anti-offset performance of SS topology was improved by parameter optimization. However, the results of improvement are insufficient and the input current is unbounded when the coupling coefficient is very small [7]. In [8], anti-offset optimization parameters for constant current output (CCO) type LCC-S compensation topology were obtained through complex derivative calculation, but load variation was not considered. Recently, the anti-offset optimization methods based on artificial intelligence have been studied for IPT system. In [9], a holistic comparison of four coupler forms are discussed with multi-objective Pareto method. A particle swarm optimization-based parameter analysis for constant voltage output type S-CLC compensated IPT systems featuring high tolerance of misalignment and load is presented In [10]. However, the primary side of S topology adopts series compensation, which will be affected by unbounded current when there is almost no coupling between the primary and secondary sides. A synchronous optimization of compensation network and parameters based on non-dominated sorting genetic algorithm III (NSGA-III) is proposed in [11], which optimizes the demand of constant output voltage but lacks the description of the compromise solution of output fluctuation and system efficiency. In order to obtain an IPT system whose output current is less sensitive to coupling coefficient and load variation, an LCC-S topology with CCO characteristic is adopted and optimized. Section 2 provides the overview of CCO type LCC-S compensation topology, where the structure and parameter resonant tuning method are presented. The detailed optimization process of MOPSO is described in Sect. 3 and the simulation experiments are presented in Sect. 4.
2 Design and Analysis of LCC-S Compensation Topology Figure 1 shows the circuit diagram of the LCC-S compensated IPT system, including voltage power supply U d , resonant tank and load RL . L P1 , C P1 , C P2 and C S make up the LCC-S compensation topology. L P and L S are the primary side and secondary side inductance of loosely coupled transformer. M stands for the mutual inductance between
Fig. 1. Circuit diagram of LCC-S compensated IPT system.
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two coils. Full bridge inverter consist of S 1 -S 4 MOSFETs. The secondary-side rectifier are composed of D1 -D4 diodes. A parameters method of LCC-S compensation topology with a good performance of load-independent current output is designed as follow. Base on T-type mode of the loosely coupled transformer, T equivalent model of LCC-S compensation topology can be obtained. In Fig. 2, LP and LS are the reflected leakage inductances of transmitting and receiving coils respectively. L M is the primary reflected mutual inductance. The following equations can be obtained ⎧ ⎪ ⎨ LP = (1 − k)LP (1) L = (1 − k)n2 LS ⎪ ⎩ S LM = nM where k denotes the coupling coefficient and n is turn ratio of loosely coupled transformer. CS and RE are the primary reflected values of the compensated C S and ac load RE .
Fig. 2. T model of LCC-S compensation topology.
In the design process, CP1 is tuned to resonate with L P1 at the system operating angular frequency ωS and CP1 is tuned to resonate with L M at ωS . Since CP1 and CP1 are in parallel, one capacitor C P1 can be used in the circuit to replace them. The expressions of CP1 and CP1 are given as follows: CP1 = 1 ωS2 LP1 (2) = 1 ωS2 LM CP1
Compensated capacitors C P2 and CS are determined as follows: CP2 = 1 ωS2 LP CS = 1 ωS2 LS
(3)
After the resonant tank composed of L P1 and CP1 , the load-independent current output ILCP1 after CP1 is yielded ILCP1 = −j
UAB ωS LP1
(4)
According to circuit resonance theory, the current on the RE load is equal to ILCP1 . Therefore, the output current I RO of actual load can be obtained as IRO =
8 nUd π 2 ωS LP1
(5)
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Equation (5) implies that the IPT system has a outstanding performance of constant current output and the system can achieve different current output levels by adjusting L P1 according to requirements. However, the system’s stable transfer power depends on the constant coupling coefficient of the magnetic coupler, which is inevitable. The output current with respect to the variational coupling coefficient and load is shown in the Fig. 3. The accrescent current is ineluctable, indicating that the currents flowing through the power supply also be large enough to be damaged at the misalignment. The tolerance performance of misalignment obviously cannot meet the system requirements. Improving the IPT system performance including both the coupling and load change operation state becomes important.
Fig. 3. The output current of CCO type LCC-S topology under misalignment.
3 Multi-objective Optimization for Compensation Parameters In order to broaden the charging region and reduce the current fluctuations, a multiobjective optimization framework based on PSO algorithm is utilized to search the optimal solution of LCC-S compensation topology. During the design procedure, the practical constraints and the targets of system capability are taken into account. 3.1 Overview of PSO Algorithm The PSO algorithm can converge to the optimal solution with high probability and has faster computation speed and better global search ability. Which is suitable for dynamic and multi-objective environment optimization. The algorithm firstly generates the initial solution, that is, in the feasible solution space, the population X = {X 1 , X 2 , X 3 ,· · · , X m } composed of m particles is randomly initialized. The position X i = {x i1 , x i2 , x i3 , …, x iD } of each particle stands for a solution. The new solution is calculated according to the objective functions. In each iteration, the particle will update itself by tracking with two extreme value, the best solution pid found by the particle itself, and the optimal solution pgd found over the whole population. In addition, the velocity V i = {vi1 , vi2 , vi3 , …, viD } is owned by each particle. If both optimal solutions are found, each particle updates its velocity and position according to the following formulas: vik+1 = ωvik + c1 r1 (pik − xik ) + c2 r2 (pgk − xik )
(6)
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xik+1 = xik + vik+1
(7)
where, ω is the weight of inertance. c1 and c2 are learning factors. r 1 and r 2 are independent random numbers, which are evenly distributed on [0, 1]. From the update formula of particles, it can be seen that the velocity of a particle depend on three parts: its original speed, the distance from its best experience and the distance from the group’s best experience. Their relative importance rest with the weight coefficient ω, c1 and c2 . 3.2 Optimization Objectives The optimization targets of the IPT system are described and summarized as follows: 1) Minimize output current fluctuation: In any state where k (k min , k max ) and RL (RLmin , RLmax ), the current I RL [k(i), RL (j)] across the load and the design value I RL_D is the lowest. k(i) and RL (j) represent the ith k and jth RL . Here, the square of the current difference is used to represent current fluctuation, and its mathematical description is defined as
2
(8) fIRL = IRL k(i), RL (j) − IRL - D 2) Zero-Voltage-Switching (ZVS): At hard turn-off mode, high reverse recovery loss occur in the body diode of the high-frequency inverter, which resulting in low system efficiency. Therefore, Soft switching of inverter should be implemented. The input impedance angle θ need to be greater than 0 and should be near 0 to achieve ZVS operation. The objective function is defined as: in ) arctan Im(Z Re(Zin ) θ ≥ 0 (9) fθ = Mpe θ 97% reduction in LMF intensity at the measurement point) in the case of positive coil alignment. In the literature [8], two ASCs in the shape of a semicircle at the transmitter were used and the effect of ASC geometry parameters and ASC current on the LMF intensity was investigated by theoretical calculations, but no specific hardware design was given and the effect of core, aluminum plate and coil offset was not considered. In this paper, the leakage magnetic flux density generated by the coil under unit current excitation (i.e., ic = 1 A) is referred to as the leakage magnetic flux density coefficient (LMFDC), and the concept of “leakage field proportionality” is proposed to qualitatively evaluate the LMF distribution characteristics. The system has “perfect leakage proportionality” when the magnetic induction lines generated by the transmitting coil, receiving coil and ASC coils coincide perfectly and the ratio of LMFDC of any two coils does not vary with the location of the measurement point [7]. The shortcoming of the existing active suppression methods for EV wireless charging systems is that the proportionality between the ASC and the LMF generated by the main coil is not high, resulting in the ASC only partially offsetting the LMF generated by the main coil, and thus the upper limit of the achievable LMF suppression capability is low, i.e., good LMF suppression can only be achieved at some measurement points in the protection area3. This deficiency in high-power systems may lead to LMF intensity exceeding the limit value in some areas.
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In this study, the active suppression technique based on independent inverter-driven dual ASC is used, and the control strategy of ASC current is mainly investigated. Firstly, the general design of the dual ASC active suppression method is introduced. Then, the LMF synthesis principle in the case of perfect magnetic field proportionality and the leakage magnetic flux density minimization condition in the case of non-perfect leakage field proportionality are analyzed according to whether the magnetic field conforms to perfect leakage field proportionality or not. Finally, experimental and simulation methods are used to verify the performance of the dual ASC active suppression technique driven by independent inverters.
2 Active Suppression Method for Dual ASC Driven by Independent Inverters 2.1 Overall Design of the Dual ASC Active Suppression Method The spatial right-angle coordinate system used in this paper is defined as follows: the origin is the position where the center of the transmitting coil is located when the coil is directly opposite, the positive direction of the x-axis (lateral) points to the right side of the vehicle, the positive direction of the y-axis (longitudinal) points to the front of the vehicle, and the positive direction of the z-axis (vertical) points to the roof of the vehicle. Figure 2 shows the schematic diagram of the system using the dual ASC active suppression method.
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(b) Coils arrangement form.
Fig. 2. Schematic diagram of the system using the dual ASC active suppression method.
The system consists of four coils, corresponding compensation (COM) circuits and driving voltage sources. L s1 and L s2 are ASCs arranged at the transmitting end, and their equivalent series resistance (ESR) is noted as Rs1 and Rs2 , respectively. LCC compensation circuits are used for all four coils, and the inductors and capacitors in the compensation circuits include L f1 , C f1 , C 1 , L f2 , C f2 , C 2 , L fs1 , C fs1 , C s1 , L fs2 , C fs2 and C s2 . U˙ INV , U˙ REC , U˙ INVs1 and U˙ INVs2 are the fundamental components of the four coil drive voltages, and their corresponding fundamental components of the AC currents are I˙INV , I˙REC I˙INVs1 and I˙INVs2 . The four coil current phase quantities are noted as I˙1 , I˙2 , I˙s1 and I˙s2 . The mutual inductance between the coils is denoted as M 1-2 , M 1-s1 , M 1-s2 ,
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M s1-2 , M s2-2 , and M s1-s2 . As shown in Fig. 2(b), the receiver coil L2 is located above the transmitting coil L1 , and the two active suppression coils Ls1 and Ls2 are distributed along the x-axis on both sides of the transmitting coil L1 . The two active suppression coils Ls1 and Ls2 are distributed along the x-axis on both sides of the transmitter coil L1 , and each coil is connected to a mutually independent compensation and rectifier (REC)/inverter (INV) circuit, where hg is the vertical spacing between the transmitter and receiver coils. In this paper, misx and misy are used to refer to the offset of L 1 with respect to L 2 in the x-axis direction and y-axis direction, respectively. The dual-ASC active suppression method has a high degree of control freedom, which is helpful to solve the problem of LMF suppression degradation caused by the left-right asymmetry of LMF distribution at lateral offset (misx = 0). The coil assembly proposed in this paper is an evolution of the coil assembly of a conventional single transmitter coil-single receiver coil wireless charging system, which differs from the latter in that the former has two symmetrically distributed ASCs at the transmitter end. The reason is that the increase has a weak effect on the magnetoresistance in the magnetic coupling path between the main coils. Our extensive simulation results show that the coupling coefficient between the transmit and receive coils is improved compared to the passive shielding scheme due to the elimination of the shielding aluminum plate at the transmit end of this scheme. 2.2 ASC Current Control Strategy Research ASC Current Control Under the Assumption of Perfect Leakage Magnetic Field Proportionality. Under the assumption of perfect LMF proportionality, the LMF suppression principle is shown in Fig. 3. bs1 ⋅ I s1
ψ uINVs1
b1 ⋅ I1
I s1 ψ uINVs1 I 1 b2 ⋅ I 2
I2
(a) The phase of magnetic flux density corresponding to each coil.
b1 ⋅ I1 π −ψ uINVs1 bs1 ⋅ I s1
b2 ⋅ I2 b2 ⋅ I2
bs1 ⋅ I s1
Bsum
Blimit
(b) Synthetic magnetic flux density phase volume.
Fig. 3. Basic principles of active suppression methods.
|b1 |· I˙1 , |bs1 |· I˙s1 and |b2 |· I˙2 are the magnetic flux density phase quantities generated by the three coils, respectively. LMF suppression can be achieved by regulating I˙s1 . In particular, when the relationship between the three coil currents is shown in Fig. 3(b), the proportion of LMF suppression approaches 100%, and this operating point is referred to as the perfect leakage magnetic field suppression (PLMFS) point in this paper. In Fig. 2(a), the fully resonant condition of the LCC compensation circuit is ω2 Lf1 Cf1 =
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ω2 Lf2 Cf2 = ω2 Lfs1 Cfs1 = ω2 Lfs2 Cfs2 = 1. Under this condition, the coil current only depends on the corresponding drive voltage. The currents in all coils are not affected by the mutual inductance between coils or the currents in other coils. The areas to the left and right of the aluminum plate at the receiving end within the protection area 3a are called the left half space (LHS) and the right half space (RHS) respectively. At misx = 0, the magnetic field distribution within the LHS and RHS is asymmetrical, and the LMF suppression process in the two half-space needs to be considered separately at this time. Under the assumption of perfect LMF proportionality, the LMF synthesis process within the LHS and RHS can be transformed into a superposition process of magnetic flux density phasor, as shown in Fig. 4. Where, b1 , b2 , bs1 and bs2 refer to the magnetic flux density coefficient vectors generated by the transmitter coil, receiver coil, ASC1 and ASC2 respectively Phase superposition of magnetic flux density in the LHS
Phase superposition of magnetic flux density in the RHS
bs1(L) ⋅ I s1
b1(L) ⋅ I1
bs2(L) ⋅ I s2
Bsum(L)
b 2(L) ⋅ I 2
bs2(R) ⋅ I s2 bs1(R) ⋅ I s1
b1(R) ⋅ I1
Bsum(R)
b 2(R) ⋅ I 2
Fig. 4. Phase superposition of the leakage flux density in the LHS and RHS.
The B˙ sum (denoted as B˙ sum(L) and B˙ sum(R) , respectively) at any measured point within the LHS and RHS is calculated as fellows. (1) B˙ sum(L) = bs1(L) · I˙s1 + bs1(L) · I˙s1 + b1(L) · I˙1 + b2(L) · I˙2 B˙ sum(R) = bs1(R) · I˙s1 + bs1(R) · I˙s1 + b1(R) · I˙1 + b2(R) · I˙2
(2)
where bs1(L) , bs1(R) , bs2(L) and bs2(R) refer to bs1 in LHS, bs1 in RHS, bs2 in LHS and bs2 in RHS respectively. so that Bsum(L) = Bsum(R) = 0, the ASC current corresponding to the PLMFS point can be obtained as follows. I˙s2 = bs1(R) · b1(L) − bs1(L) · b1(R) I˙1 + bs1(R) · b2(L) −bs1(L) · b2(R) I˙2 /(bs2(R) · bs1(L) − bs2(L) · bs1(R) ) (3) I˙s1 = b1(R) · bs2(L) − bs2(R) · b1(L) I˙1 + b2(R) · bs2(L) (4) −bs2(R) · b2(L) I˙2 /(bs2(R) · bs1(L) − bs1(R) · bs2(L) ) ˙ ˙ LMF suppression can be achieved by controlling Is1 and Is2 . Since bs1(L) bs1(R) and bs2(L) bs2(R) , the LMF suppression in the two half-spaces can be carried out
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approximately independently, i.e., the main control objectives of I˙s1 and I˙s2 are to reduce Bsum(L) and reduce Bsum(R) respectively. Leakage Magnetic Flux Density Minimization Condition Under Intersecting Magnetic Susceptibility Lines. The other manifestations of the non-perfect LMF proportionality is that the magnetic flux density vectors B generated by the ASC and the main coil at the same measurement point are not co-linear. Figure 5 gives a schematic diagram of the superposition process of three coplanar but non-parallel sinusoidal time-varying spatial magnetic flux density vectors (denoted as B1 , B2 and Bs1 respectively). The three vectors are generated by currents i1 , i2 and is1 . The angle between B1 and Bs1 and the angle between B2 and Bs1 are denoted as γ1 and γ2 respectively.
γ1 γ2
Fig. 5. Superposition process of B instantaneous values
Taking the direction of Bs1 as the x-axis, the angles of B1 and B2 with the x-axis are γ1 and γ2 The instantaneous values of the x-axis and y-axis components of Bsum (denoted as Bsum(x) and Bsum(y) respectively) are fellows: √ √ Bsum(x) (t) = |bs1 | · 2Is1 sin(ωt + ψis1 ) + |b2 | · 2I2 sin(ωt + ψi2 )cosγ2 +|b1 | ·
√
2I1 sin(ωt)cosγ1
√ √ Bsum(y) (t) = |b2 | · 2Is1 sin(ωt + ψi2 )sinγ2 + |b1 | · 2I2 sin(ωt)sinγ1
(5) (6)
From Eq. (6), it can be deduced that γ1 and γ2 having different sign is beneficial to improve the LMF suppression. The instantaneous value of |Bsum | is 2 2 |Bsum |(t) = Bsum(x) + Bsum(y) (7) Both Bsum(x) and Bsum(y) are sinusoidal quantities. By picking the appropriate I˙ s1 can make Bsum(x) = 0, but Bsum(y) can not be offset by Bs1 . Therefore, the lowest achievable value of the leakage magnetic flux density is √ √ |Bsum |min = |b2 | · 2I2 sinγ2 + |b1 | · 2I1 sinγ1 (8) Minimize |Bsum | required I˙
s1
for
−|b2 |I˙2 cosγ2 − |b1 |I˙1 cosγ1 I˙s1 = |bs1 |
(9)
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The I˙ s1 required to achieve Bsum(x) = 0 at different measurement points are different, so minimizing the I˙ s1 of |Bsum | in the full space is difficult to solve. In addition, the resolution results of the lowest |Bsum | that can be achieved in the whole region are difficult to obtain due to the complex pattern of variation of the B direction generated by different coils with the location of the measurement points. The above analysis results are suitable for qualitative analysis of the LMF suppression capability, and can also be used as a theoretical basis for system hardware parameter design and ASC current control.
3 Experiment of Dual ASC Active Suppression 3.1 Introduction to the Experimental Platform In this paper, we only study the system in the sinusoidal steady-state case, and the finite element (FEA) tool used is mainly the Maxwell module in ANSYS Electronics 2021 R2. The default excitation current frequency is 85 kHz. 10. A full-bridge inverter and a full-bridge active rectifier are used for AC-DC energy conversion at the transmitter and receiver sides respectively. The active rectifier combines the AC voltage and AC current sampling circuits proposed in the literature [9] with the AC impedance-based active rectifier synchronization scheme introduced in the literature [10]. The dimensions of the receiver-side body mock-up (i.e., aluminum plate) in the experimental prototype are 1.8 m in the transverse direction (x-direction) and 2 m in the longitudinal direction (y-direction). The definition of the spatial right-angle coordinate system can be found in the introduction section. 3.2 Experiment of Leakage Magnetic Field Suppression Capability This section compares three methods, namely passive shielding, unshielded and active suppression. In the passive shielding method, an aluminum plate is provided at the transmitter side (with dimensions of 1000 mm and 700 mm in the x-direction and ydirection respectively), the driving voltage of INVs1 and INVs2 is fixed at −5 V, and L s1 and L s2 are retained in the coil assembly but disconnected from the corresponding compensation circuit. In the unshielded method, there is no shielded aluminum plate at the transmitter side and the rest of the settings are the same as in the passively shielded method. In the active suppression method, no shielding aluminum plate is present at the transmitter side, INVs1 and INVs2 are in operation, and L s1 and L s2 are connected to the corresponding drive inverters via the compensation circuit. Compensation Circuit Parameters. All coils in the system are connected to the fullbridge converter through a fully resonant LCC compensation circuit. The circuit parameters measured in the coil-positive condition are listed in Table 1. The LCR tester used for the test was a HIOKIIM3536 with an excitation current of 85 kHz and an RMS value of 50 mA. Due to the presence of the aluminum plate at the emitter, the L 1 and L 2 values in the passive shielding method are lower than the corresponding values in the active suppression and unshielded methods.
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Table 1. Compensation circuit and coil parameters of the wireless charging system prototype Parameters
Value
Parameters
Passive shielding
Actively suppressed or unshielded
L 1 (µH)
149.5
163.8
L 2 (µH)
131.7
L f1 (µH)
19.2
Value Passive shielding
Actively suppressed or unshielded
L s1 (µH)
–
56.0
133.4
L s2 (µH)
–
55.4
19.2
L fs1 (µH)
–
27.0
L f2 (µH)
19.4
19.4
L fs2 (µH)
–
27.0
C f1 (nF)
182.5
182.5
C fs1 (nF)
–
129.8
C f2 (nF)
181.6
181.6
C fs2 (nF)
–
130.4
C 1 (nF)
26.8
24.3
C s1 (nF)
–
122
C 2 (nF)
31.4
30.8
C s2 (nF)
–
122
R1 (m)
162.6
118.9
Rs1 (m)
–
44.1
R2 (m)
116.6
115.0
Rs2 (m)
–
43.0
Experimental Measurement Results of System Efficiency and Leakage Magnetic Flux Density. In this section, the performance of the three methods is compared in terms of system efficiency and leakage magnetic flux density at 0mm coil offset and misx = 100 mm. The combination of the three methods with two coil offset situations are 6 operating points. Voltage and current waveforms at each operating point are observed by oscilloscope. The LMF intensity was obtained by an electromagnetic field analyzer (Narda EHP-50F). The measurement points within the LHS and RHS are symmetrical about the y-z plane. During the experiments, the desired Pbat was achieved by adjusting U DC . The experimental results are listed in Table 2, where |Bsum | is the valid value. In the active suppression method, the U˙ INV is chosen as the phase reference for the AC voltage phase volume, i.e. ψ uINV = 0°. At the OPe and OPf operating points, lower the |Bsum | at the measurement point by manually adjusting the INVs1 and INVs2 control volumes. The control volumes at the OPe operating point are: θ INVs1 = θ INVs2 = 78° and Table 2. ηDC and |Bsum | at the selected operating point under Pbat ≈ 2450 W. Working condition point
Type
misx (mm)
ηDC (%)
|Bsum(L) |(µT)
|Bsum(R) |(µT)
OPa
Passive shielding
0
94.40
1.23
1.24
100
94.13
4.19
8.03
0
94.34
3.28
3.17
100
94.63
7.25
3.94
0
94.23
0.18
0.17
100
93.94
4.40
2.91
OPb OPc
Unshielded
OPd OPe OPf
Active suppression
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= ψ uINVs1 = ψ uINVs2 = 155°. The control quantities for the OPf operating point are: θ INVs1 = 180°, ψ uINVs1 = 150°, θ INVs2 = 55°, ψ uINVs2 = 180°. The experimental results at the OPe condition point show the best LMF suppression achieved by the active suppression technique at misx = 0 mm. The following conclusions can be extracted from the test results listed in Table 2: the LMF suppression effect of the passive shielding method is significantly reduced when there is a large lateral offset of the coil, as shown in the comparison between OPb and OPd ; the effect of LMF suppression on ηDC is not significant. The distribution of the leakage magnetic flux density (RMS at Pbat = 2500 W) at several operating points obtained by FEA is given in Fig. 6, along with the RMS values of the coil current phases and the initial phase angle (where the phase reference is I˙ 1 ). |Bsum(L)| (μT)
|Bsum(R)| (μT) 5.8229 4.4656 3.1084 1.7511
3.4046 2.6265 1.8484 1.0704
z
I1 = 14.09 A, ψ i1 = 0° I 2 = 14.09 A, ψ i 2 = −102°
x
y
(a) OPb Passive shielding
|Bsum(L)| (μT)
|Bsum(R)| (μT) 2.2953 1.7812 1.2670 0.7529
I1 = 13.20 A, ψ i1 = 0° I 2 = 14.03 A, ψ i 2 = −96.8°
|Bsum(R)| (μT) 0.5588 0.4413 0.3238 0.2063
(b) OPf Active suppression I1 = 13.78 A, ψ i1 = 0° I 2 = 13.78 A, ψ i 2 = −96.8°
2.2139 1.7170 1.2202 0.7233
I s1 = 9.39 A, ψ is1 = 150° I s2 = 4.33 A, ψ is2 = 180°
|Bsum(L)| (μT)
I s1 = 14.62 A, ψ is1 = 146° I s2 = 4.44 A, ψ is2 = 189°
(c) Manual optimization results for active suppression
0.2963 0.2383 0.1802 0.1222
Fig. 6. |Bsum | distribution in different LMF suppression methods
For OPb , the peak value of |Bsum(L) | is 3.40µT and the peak value of |Bsum(R) | is 5.82µT. For OPf , the peak value of |Bsum(L) | is 2.21µT and the peak value of |Bsum(R) | is 2.30µT. For OPf , the |Bsum | can be further reduced by manually optimizing I˙ s1 and I˙ s2 , and the obtained |Bsum(L) | peak and |Bsum(R) | peak are 0.30µT and 0.56µT respectively. This optimization process only involves ASC current control, so the conclusion that can be drawn from Fig. 6 is that even if the LMF proportionality deviates more significantly from the perfect state, the active suppression technique still has a much higher LMF suppression capability than the passive shielding technique. Thanks to the high degree of freedom provided by the dual ASC, the LMF within the LHS and RHS can be effectively suppressed at the same time for misx = 0. When misx > 0, the proportionality of LMF within the LHS is higher than that of the RHS, and thus the peak of |Bsum(L) | is lower than that of |Bsum(R) | in Fig. 6(c).
4 Conclusion This paper analyzes the active suppression technique for leaking magnetic field of electric vehicle wireless charging system, mainly focuses on the control strategy of ASC current in the dual-ASC leaking magnetic field suppression method, and analyzes the
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magnetic field suppression capability of the independent inverter-driven active magnetic field suppression method under different magnetic field conditions. Simulation and experimental results show that the LMF suppression effect that can be achieved by the dual-ASC active suppression technique is much higher than that of passive shielding, and still has a better shielding effect when there is a large coil offset. Acknowledgments. This work was supported by the Beijing Natural Science Foundation (No. 3212030).
References 1. China Electricity Council.: Wireless Charging System for Electric Vehicles: Part 4 Electromagnetic Environmental Limits and Test Methods: GB/T 38775.4-2020. China Quality Inspection Press, Beijing (2020). (in Chinese) 2. Campi, T., Cruciani, S., De Santis, V., et al.: Numerical characterization of the magnetic field in electric vehicles equipped with a WPT system. Wireless Power Transfer 4(2), 78–87 (2017) 3. Campi, T., Cruciani, S., De Santis, V., et al.: Wireless power transfer (WPT) system for an electric vehicle (EV): how to shield the car from the magnetic field generated by two planar coils. Wireless Power Transfer 5(1), 1–8 (2018) 4. Lin, F.Y., Zaheer, A., Budhia, M., et al.: Reducing leakage flux in IPT systems by modifying pad ferrite structures. In: 2014 IEEE Energy Conversion Congress and Exposition, pp. 1770– 1777. IEEE, Pittsburgh (2014) 5. Campi, T., Cruciani, S., Maradei, F.: Near-field reduction in a wireless power transfer system using LCC compensation. IEEE Trans. Electromagn. Compat. 59(2), 686–694 (2017) 6. Choi, S.Y., Gu, B.W., Lee, S.W., et al.: Generalized active EMF cancel methods for wireless electric vehicles. IEEE Trans. Power Electron. 29(11), 5770–5783 (2014) 7. Zhu, G.D., Gao, D.W., Lin, S.L.: Leakage magnetic field suppression using dual-transmitter topology in EV wireless charging. J. Power Electron. 19(3), 625–636 (2019) 8. Campi, T., Cruciani, S., Maradei, F., et al.: Active coil system for magnetic field reduction in an automotive wireless power transfer system. In: 2019 IEEE International Symposium on Electromagnetic Compatibility, Signal & Power Integrity, pp. 189–192. IEEE, New Orleans (2019) 9. Zhu, G.D., Gao, D.W.: High-frequency voltage and current sense circuits for inductive power transfer systems. IEEE Trans. Power Electron. 35(11), 11352–11362 (2020) 10. Zhu, G.D., Gao, D.W.: Impedance-based synchronization of active rectifier in inductive power transfer systems. In: The proceedings of the 16th Annual Conference of China Electrotechnical Society, pp. 396–404. Springer, Singapore (2021). https://doi.org/10.1007/978-981-19-15284_40
The Solution of Power Frequency Electromagnetic Field for Parallel Transmission Lines Based on Superposition Algorithm Jiangong Zhang1 , Xiaofeng Yang2(B) , Zheyuan Gan1 , Zhibin Zhao3 , and Bo Tang2 1 China Electric Power Research Institute, Wuhan 430073, China 2 College of Electrical Engineering and New Energy, China Three Gorges University,
Yichang 443002, China [email protected] 3 College of Electrical and Electronic Engineering, North China Electric Power University, Beijing 100096, China
Abstract. The national standard specifies the electromagnetic field of a single line, but lacks the electromagnetic field algorithm and related regulations for parallel transmission lines (PTL). Using the electromagnetic field calculation method of transmission lines recommended by the International Conference on Large Power Grids, an algorithm for calculating the electromagnetic field strength of multiple lines in parallel is proposed using the vector superposition principle. Firstly, the algorithm is used to theoretically solve the horizontal distribution of the power frequency electric field (PFEF) and magnetic field (PFMF) of the PTL in China Three Gorges University (CTGU); then, according to the electromagnetic field measurement method stipulated by the national standard, the field measurement for the horizontal electromagnetic field distribution of the line is carried out; finally, the theoretical calculations are compared with the experimental measurements. The results show that the maximum error of the lateral distribution of the PFEF solved by the method in this paper is 0.45 kV/m, and the maximum error of the lateral distribution of the power frequency magnetic field is 0.0003 mT. Keywords: Power frequency electromagnetic field · Parallel transmission lines · Superposition algorithm
1 Introduction At present, with the increase of global electricity consumption, PTL have gradually become the research focus of designers both inside and outside China. The accompanying electromagnetic environment problems of PTL has also received more attention [1, 2]. China is a country with unbalanced energy distribution. The storage of coal resources is mainly concentrated in the economically backward northwest regions, which have less power load. This prompted the state to take measures to rationally allocate power resources, and the method of power transmission from west to east and mutual supply from north to south solved this problem to a large extent. As a result, most lines in China © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 516–522, 2023. https://doi.org/10.1007/978-981-99-0631-4_51
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adopt parallel or cross type, and the electromagnetic environment of PTL is relatively complicated [3–6]. For a PTL, reference [7, 8] proposes the method of finite element to solve the electric field strength, but this method is complex in theory and computational complexity for transmission lines occupying several hundreds of meters in space, so it is not widely used in engineering applications. For the PTL, the method of finite difference can be used for calculation, but the accuracy of this method is not high when the boundary is complex. Based on the principle of equivalent charge, this paper takes the PTL of CTGU as a case, to study the power frequency electromagnetic field of PTL. The algorithm based on the principle of vector superposition is proposed, and is used to solve the strength of PFEF and PFMF for the PTL in CTGU. Finally, the accuracy of the algorithm is verified by comparing the results of the algorithm with the measurement results.
2 Power Frequency Electromagnetic Field 2.1 Power Frequency Electric Field PFEF is generated by electrical charges on transmission lines or live equipment. The presence of an electric charge induces an electric field in the space around it. At this time, if the conductor is placed in the electric field, the charged particles on the conductor will move under the action of the electric field force, thus generating a new electric field in the conductor. The newly generated electric field will be superimposed with the original electric field, thus changing the electric field distribution near the conductor. The PFEF of the transmission lines is only produced by the three-phase conductors, and is affected by the terrain and surrounding objects. The arrangement of the line conductors determines the distribution of the electric field. 2.2 Power Frequency Magnetic Field PFMF is generated by the carrier fluid of the transmission lines. As long as currentcarrying conductors are existed, there is a magnetic field around the conductor. The magnitude of the magnetic field is proportional to the current of the carrier fluid, and the physical quantities that can describe the basic characteristics of the magnetic field are the magnetic induction strength and the magnetic field strength. In an isotropic linear medium, there is only a simple linear relationship between them, and the two are equivalent.
3 Solution Method of Power Frequency Electromagnetic Field for PTL 3.1 Solution Method of PFEF According to the principle of the equivalent charge method, to solve the PFEF of the transmission line, first, we need to solve the charges on the conductor per unit length, and then solve the electric field produced by these charges.
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As we can see from the above calculation steps, solve the space electromagnetic field produced by three-phase conductors of PTL, and obtain the vertical and horizontal components of the field strength projection on the ground, so that the space electric field of the PTL can be solved by vector superposition. Therefore, the electric field strength model of the PTL can be obtained as: m x − xi 1 x − xi Qi − Ex = (1) 2επ Li 2 L2i i=1 m y − yi 1 y − yi Qi − Ey = (2) 2επ Li 2 L2i i=1
For PTL, voltage is used as a time variable, and in the calculation process, the voltage of each conductor is usually expressed in the complex form. Besides the corresponding charges are also represented by complex numbers. The two are respectively: + Ui,I U˙ i = Ui,R
(3)
˙ = Qi,R + Qi,I Q
(4)
The solved components of electric field strength are also complex numbers, respectively are: E˙ x =
m
Eix·R +j
i=1
E˙ y =
m i=1
m
Eix.I = jEx.I + Ex·R
(5)
Eiy·I = jEy.I + Ey·R
(6)
i=1 Eiy.R +j
m i=1
represents the horizontal component of the field strength generated by the where, Eix.R represents the horizontal component real part of each conductor charge at this point; Eix.I of the field strength produced by the imaginary part of each conductor charge at this point; represents the vertical component of PFEF generated at this point by the real part Eiy.R represents the vertical component of each conductor charge generated at this point; Eiy.I of PFEF generated at this point by the imaginary part of each conductor charge. The composite field strength at this point in space is: + Ex.R )x + (jEy.I + Ey.R )y E = (jEx.I
(7)
represents the horizontal component of the resultant field strength produced where, Ex.R represents the horizontal at this point by the real part of each conductor charge; Ex.I component of the resultant field strength produced at this point by the imaginary part represents the real part of the vertical component of of each conductor charge; Ey.R the composite field strength generated by the conductor charge at a certain point; Ey.I represents the vertical component of the resultant field strength produced at this point by the imaginary part of each conductor charge.
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3.2 Solution Method of PFMF From the principle of vector superposition, it is known that the magnetic field strength generated by multiple conductors at any point in space is equal to the superposition of the magnetic field strength at this point when each conductor acts alone [9, 10]. Therefore, vector superposition can be used to solve the space magnetic field of PTL. The strength of PFMF generated by m conductors in a PTL solved by the superposition principle is: √ m m 2 y − yi Hxi = Ii (8) Hx = 2π ri2 i=1 i=1 √ m m 2 x − xi Hy = Hyi = Ii (9) 2π ri2 i=1 i=1 Finally, strength of PFMF for PTL is: H = Hx2 + Hy2
(10)
4 Result Analysis of Power Frequency Electromagnetic Field 4.1 The Model of PTL According to the actual parameters of PTL in CTGU, the established model is shown in Fig. 1, with a total of 15 phase conductors.
110kV A
110kV 10.5m A
110kV 10.2m
A B
B
11.7m
11.1m
B
12.1m
B C
C
110kV A
11.3m
C
C
39m 35kV B
36m 33m
6m 30m
A 5m
35m 32m
5m C
9m
22m 20m
19m
Ground
Fig. 1. The model of PTL in CTGU.
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4.2 Measurement Experiment of Power Frequency Electromagnetic Field According to the regulations of the reference [10] on the measurement instruments and measurement methods of the PFEF and PFMF of the AC high voltage overhead transmission lines and substations, we take the side phase conductor as the benchmark, we measured the transverse attenuation characteristics of the power frequency electromagnetic field in the direction perpendicular to the line path. During the measurement, measure the power frequency electromagnetic field strength within 50 m from the line side wire at an interval of 5 m point by point. The experiment uses the HI-3604 power frequency electromagnetic field strength measuring instrument, the measurement accuracy for the strength of PFEF is 0.05, and the measurement accuracy for strength of PFMF is 0.01. Figure 2 shows the picture of the power frequency electromagnetic field measuring instrument of the model.
(a) Measuring instrument of HI-3604
(b) field measurement diagram
Fig. 2. Power frequency electromagnetic field measuring instrument of HI-3604 type and field measurement diagram of power frequency electromagnetic field.
4.3 Analysis and Comparison of Theoretical Values and Measured Values The comparison between the theoretical and measured electric field strength of PTL is shown in Fig. 3(a). According to Fig. 3 (a), the variation rule of electric field strength measured results is basically the same as that of theoretical calculation results. However, there are still some errors between the theoretical calculation results and the measured values, of which the maximum error is 0.45 kV/m and the minimum error is 0.15 kV/m. The reasons for the error are as follows: 1) There is a certain error in the parameter measurement of the line model. Although the laser rangefinder has high accuracy, it is difficult to align the laser distance during measurement because the wire is tens of meters away from the line of sight.; 2) There is a certain accuracy error in the power frequency electric field measuring instrument; 3) Because the PFEF is generated by the electric charge, and the electric charge exists in the conductors, it also exists widely in nature. The air, human body, animals, plants, and the passing of the cars on adjacent
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roads will cause the change of PFEF at the measurement point. Therefore, the electric field measurement is greatly influenced by the outside world, which is also the main source of measurement error. Figure 3 (b) shows the comparison between the solved results and the measured results of this method. It can be seen from Fig. 3 (b) that the theoretical calculation results of magnetic field strength are consistent with the variation rule of measurement results with distance. However, there are still some errors between the theoretical calculation results and the measurement results, in which the maximum value of the magnetic field intensity error is 0.25 A/m, and the minimum value is 0.01 A/m, that is, the maximum value of the magnetic induction intensity error is 0.0003 mT, and the minimum value is 0.0001 mT. The theoretical calculation result of PFMF is more accurate than that of PFEF. The main reasons for the error are as follows: 1) PFMF is generated by current carrying conductor. The current exists in the conductor, which is less affected by external interference; 2) The measuring instrument of PFMF has high accuracy. As a result, magnetic field measurement is more accurate than magnetic field measurement.
(a) Electric field strength
(b) Magnetic field strength
Fig. 3. Comparison of theoretical and measured values
5 Conclusion In order to solve the power frequency electromagnetic field for PT, first the strength of electric and magnetic field produced by PTL three-phase conductors are solved; Then, the above electric field strength and magnetic field strength are projected on the ground to obtain their respective vertical and horizontal components; Finally, the above components are superimposed by vectors to obtain the space electromagnetic field of PTL. The superposition algorithm is used to solve the PFEF and PFMF of the PTL in CTGU. The maximum PFEF calculation error is 0.45 kV/m, and the maximum PFMF calculation error is 0.0003 mT.
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Acknowledgment. This work is supported by Joint Funds of the National Natural Science Foundation of China under Grant U20A20305.
References 1. Shi, S., Hao, J., Liu, H.: Simulation and verification of space charge density distribution of gas around wire in corona cage based on hybrid numerical model. High Volt. Eng. 48(06), 2434–2443 (2022) 2. Zheng, X., Tang, B., Zhang, S.: Prediction algorithm for radio interference of AC/DC parallel power transmission lines. South. Power Syst. Technol. 15(10), 72–79 (2021) 3. Ma, A., Chen, J.: Analysis on three-dimensional hybrid electric field and related electrostatic induction effect of ±800 kV DC and 500 kV AC parallel transmission line considering rainy days. High Volt. Eng. 43, 2114–2121 (2017) 4. Li,C., He, P., Wang, F.: A novel fault-location method for HVDC transmission lines based on concentric relaxation principle and wavelet packet. Recent Adv. Electr. Electron. Eng. 13, 705–716 (2020) 5. Sun, Z., Zhou, X., Liang, L.: Electromagnetic environment of transmission line based on full parameter online estimation. J. Inf. Process. Syst. 16(02), 394–405 (2020) 6. Zhang, B., Li, W.: Mehtod for measuring the electric field under UHV/EHV DC/AC hybrid transmission lines. High Volt. Eng. 38, 2157–2162 (2012) 7. Takuma, T., lkeda, T., Kawamoto, T.: Calculation of ion flow fields of HVDC transmission lines by the finite element method. IEEE Trans. PAS. PAS-100, 4802–4811 (1981) 8. Li, Y., Wang, H., Chen, K.: Effect of electrical trees on the distribution of electric field and space charge in cross-linked polyethylene cables. Recent Adv. Electr. Electron. Eng. 14, 114–121 (2021) 9. Campos, E., Hernandez, E., Barniol, P.: Phenomenographic analysis and comparison of students’ conceptual understanding of electric and magnetic fields and the principle of superposition. Phys. Rev. Phys. Educ. Res. 17(02) (2021) 10. Zhang, Y., Su, Z., Chi, M.: Magnitude and orientation error correction of a superimposed spatial universal rotating magnetic vector. IEEE Trans. Magn. 52(02) (2016)
Coupler Comparison of Inductive and Capacitive Power Transfer Systems Siyi Yao1 , Minfan Fu1,2(B) , Heyuan Li1 , Yiming Yin1 , and Peng Zhao1 1 School of Information Science and Technology, ShanghaiTech University, Shanghai 201210,
China {yaosy,fumf,lihy4,yinym,zhaopeng}@shanghaitech.edu.cn 2 Shanghai Engineering Research Center of Energy Efficient and Custom AI IC, Shanghai 201210, China
Abstract. Inductive power transfer (IPT) and capacitive power transfer (CPT) are two basic near-filed approaches for efficient wireless power transfer. Although they share similar system configurations, it is the coupler that determines power transfer characteristics and coupling efficiency. Given the same coupling space (i.e., coupler size constrains), this paper would study and compare the coupler characteristics for the inductive and capacitive coupler. The uniform induced voltage source is applied for both couplers, and the influence of the coupler size parameters and resonance frequencies are evaluated and used to optimize the coupler model parameters. The peak efficiency of the different couplers and their corresponding series-series compensated systems are used to judge the coupler performance. Finally, the design constrain is proposed to show the performance boundary of inductive and capacitive coupler. Keywords: Wireless power transfer · Inductive coupler · Capacitive coupler · Ansys simulation · Induced source model
1 Introduction Near-field coupling is an attractive approach for efficient wireless power transfer (WPT), which has been widely used to charge mobile devices, electric vehicles and medical implants [1–6]. Currently, both inductive power transfer (IPT) and capacitive power transfer (CPT) are valid for WPT system implementation. The main difference is the coupling field between the transmitter (TX) and the receiver (RX). Inductive coupler uses the magnetic field, and the coupling coil severs as a coupling unit for power exchange. Capacitive coupler uses the electric field, and the conductive plates serve as a coupling unit to construct the ac energy loop. From the system-level perspective, both types of systems require additional inverter, compensation, and rectifier to help the coupler. Considering the similarity between IPT and CPT, it is attractive to apply the same compensation theory and control algorithm for both systems. In the meantime, it is well known that the difference of the coupling mechanism would offer unique feature for various coupler. For example, the electric field coupling is usually much weaker than © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 523–530, 2023. https://doi.org/10.1007/978-981-99-0631-4_52
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the magnetic field coupling, and would not cause eddy-current issue for the nearby conductive objects. In the past few years, many IPT and CPT systems have been built to justify the claimed performance [7, 8]. In terms of power transfer capability and efficiency, it seems that IPT is more competitive from the system perspective (from dc input to dc output). However, the demonstrated systems have quite different system parameters, and coupler size. There are no fundamental comparisons on the coupler itself from the ac to ac point of view. This paper is devoted to a fair comparison between the inductive and capacitive coupler. The uniform induced voltage source (IVS) model is used to describe both couplers conveniently, which means the circuit parameters can be defined in the same manner. These parameters would help judge the coupler performance. For fair comparison, a uniform coupling space is defined for both couplers, which means the coupler size is identical. Given the size constrain, the size parameters for different couplers are defined and optimized for a single frequency. And then the influence of the frequency is included for further optimization. In this paper, both inductive and capacitive coupler would be optimized individually and then compared in terms of the peak efficiency.
2 Uniform IVS Model and Coupling Space This chapter is to introduce the uniform IVS model and to define the uniform coupling space, in which inductive and capacitive couplers can be fairly compared. 2.1 Uniform IVS Model Modeling of Couplers. A typical inductive coupler is composed of two coupling coils, where the primary side coil L tx is the transmitter and the secondary side coil L rx is the receiver. The voltage at the transmitter and receiver is defined as vi and vo respectively, and itx and irx are the network input and output current respectively. A typical capacitive coupler consists of four parallel metal plates. Coupling capacitance exists in each pair of the four plates, so the capacitive coupler has equivalent six coupling capacitance [9]. Therefore, the six-capacitance model is usually used as the circuit model of capacitive couplers. Due to the duality theory, both CPT and IPT can be described by a uniform IVS model as shown in Fig. 1. In this model, the self-impedances (Z tx and Z rx ) are used instead of self-inductances or self-capacitances, and the mutual impedance Z m is defined to replace the √ mutual inductance or capacitance, it has vtx = −Zm irx , vrx = Zm itx and k = Zm / Ztx Zrx 2.2 Peak Efficiency Peak Efficiency of Couplers. The loss in passive part of the system is mainly from the ESRs of the TX and RX self-inductors. The optimal efficiency of the coupler is determined by this loss. The quality factors of the TX and RX are defined as Qtx and Qrx respectively, and the quality factors of the inductors is expressed as Qtx = Ztx /rtx and Qrx = Zrx /rrx .
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Fig. 1. Uniform induced voltage source model.
For the resonant tank, the overall loss is Ploss , which is sightly larger than the loss caused by r tx and r rx , it has √ 2 Ploss ≥ Itx2 rtx + Irx rrx ≥ 2Itx Irx rtx rrx = Pmin , (1) where Pmin is the minimum loss. When the power transfer capability is maximized, it has ω2 Ltx Lrx 1 2P ·P· = √ . (2) Pmin = 2 · ωLm Qtx Qrx k Qtx Qrx Then, the efficiency of the coupler is η ≤ ηmax =
P 1 , = √ P + Pmin 1 + 2/(k Qtx Qrx )
(3)
where ηmax is the maximum efficiency of the coupler. It only depends on quality factors and coupling coefficient. The higher the quality factor, the higher the maximum efficiency of the coupler. In order to satisfy that power transfer capability is maximized, vrx and irx at the receiver need to be in phase, which means the impedance at the receiver is purely resistive. Similarly, vtx and itx at the transmitter are also in phase, which means that the impedance reflected from the receiver to the transmitter is also purely resistive [10]. Hence, the compensation network is necessary. Peak Efficiency of System with S-S Compensation. The simplest RX compensation network design is to use a series capacitor (or inductor) to resonate L rx and L tx (or C rx and C tx ), so that the input and output impedance of TX and RX can be purely resistive, which constitutes S-S compensation (see Fig. 2). The influence of S-S compensation on the efficiency is mainly from the ESRs. The ESR of the system r is composed of the ESR of inductor and capacitor (r L + r C ). Since the ESRs of inductors is much larger than the ESRs of capacitors, the influence of ESRs of capacitors on quality factors of the system can be ignored. Hence, for IPT, it has ηmax = ηmax
(4)
For CPT, it has ηmax =
1
1 + 2/(k QL1 QL2 )
= ηmax
where ηmax is the efficiency of system with S-S compensation.
(5)
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Fig. 2. Uniform IVS model with S-S compensation.
2.3 Uniform Coupling Space In order to compare the coupling characteristics of IPT and CPT couplers, a uniform coupling space, namely the volume constraints of the couplers, should be established. The shaded areas in Fig. 3.a and Fig. 3.b are the coupling spaces of IPT coupler and CPT coupler respectively. According to the practical application scenarios of the two couplers, the coupling space is selected as: cylinder space with outer diameter D = 100 cm and height H = 10 cm (see Fig. 3). Meanwhile, in order not to consider the influence of different materials, the coupling coil and metal plate are both selected as copper material.
Fig. 3. Couplers: (a) Uniform coupling space. (b) IPT coupler. (c) CPT coupler.
3 Optimization of Inductive Coupler In this chapter, two dimensional variables affecting the performance of inductive couplers are designed, and the couplers are optimized at a single frequency by sweeping parameter simulation. Then, the influence of frequency is considered to find the peak efficiency under a frequency range.
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3.1 Variable Design of IPT Coupler The IPT coupler is composed of two identical coupling coils on the TX and RX, and its physical model and the top view are shown in Fig. 3.b. The outer diameter of the coils is 100 cm, and the air gap between the TX and RX is 10 cm. The coupling coil has two free variables that affect the performance of the coupler: coil winding number N and the starting position of coil winding, which is defined as the distance d between the starting point and the center of the circle. By changing the values of the two variables, the values of the L and ESR can be obtained, and then the peak efficiency of the inductive coupler can be calculated. 3.2 Simulation Results A simulation is built in Maxwell. Figure 4 shows the relationship curves of the self inductance, mutual inductance, coupling coefficient and ESR with N and d. Since the size of the coils on TX and RX is the same and the self-inductance is only related to the properties of the coils, the self-inductances of TX and RX are the same. For the same reason, ESRs of TX and RX are also the same.
Fig. 4. Parameters at different N and d. (a) Self inductance L tx and L rx . (b) Mutual inductance L m . (c) Coupling coefficient k. (d) ESR r tx and r rx .
√ Therefore, the relationship curve √ of k Qtx Qrx with N and d at a fixed frequency of 100 kHz. At √ a given frequency, k Qtx Qrx has a peak value,which means that the peak value of k Qtx Qrx can be found at any frequency in this way, so as that the peak value of the efficiency of the coupler can be found too (see Fig. 5).
Fig.5. Peak efficiency from single frequency (100 kHz) to a frequency range.
According to the operating frequency and practical application of the coupler, the frequency range is set at 100 kHz–2 MHz. It can be found that the ESR increases
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√ with the increase of frequency at a fixed size. Taking the result into k Qtx Qrx , and the √ relationship √ curve of k Qtx Qrx with frequency can be obtained. When the frequency is 2 MHz, k Qtx Qrx reaches its peak value. Therefore, 2 MHz is the frequency point at which the maximum efficiency of the system can be obtained, as shown in Fig. 6.
4 Optimization of Capacitive Coupler In this chapter, two dimensional variables affecting the performance of inductive couplers are designed, and the couplers are optimized at a single frequency by sweeping parameter simulation. Since compensation inductance is too large in this condition. External shunt capacitors are helpful in reducing the required compensation inductance. After adding shunt capacitors, Then, the influence of frequency is considered to find the peak efficiency under a frequency range. 4.1 Variable Design of CPT Coupler The CPT coupler uses two disk plates with a small outer diameter and two circular plates with an outer diameter of 100 cm. The distance between the upper two plates and the lower two plates is 10 cm. The physical model and the top view are shown in Fig. 3.c. From the top view, there are two free variables affecting the performance of the capacitive coupler: radius R of the internal disk plate and spacing G of the internal and external plates. 4.2 Simulation Results A simulation is built in Maxwell. The self capacitance, mutual capacitance and coupling coefficient in the IVS model can be calculated, as shown in Fig. 6. Similar to IPT, the self-capacitance of the primary and secondary sides is equal due to the symmetry of the structure.
Fig. 6. Parameters at different R and G. (a) Self capacitance C tx and C rx . (b) Mutual capacitance C m. (c) Coupling coefficient k.
However, the ESR of the capacitor cannot be simulated using the existing simulation tool. Different from IPT system, and the Q value of the system is mainly from the QL of compensation inductor. Therefore, the ESR of the capacitor can be ignored here.
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The self-capacitance values of TX and RX are both tens of pF, so the inductance value of the series compensation inductor will be too large to obtain. Therefore, it’s necessary to improve the equivalent self-capacitance of the coupler by adding external shunt capacitors. Here, the impedance value of the equivalent self-capacitance is selected to be equal to the impedance value of the self-inductance corresponding to the maximum efficiency of the IPT in the above. That is, the self-impedance of the IPT and CPT couplers is consistent with Z tx and Z rx under the uniform IVS model of the coupler. As the calculation of impedance value involves frequency, the relationship between the new coupling coefficient k ’ and R and G at a fixed frequency is firstly found, as shown in Fig. 7.
Fig. 7. Equivalent coupling coefficient at different R and G (2 MHz).
5 Comparison Since the value of compensation inductance is too large to obtain, adding external shunt capacitor is considered when comparing. From formula (3), under a given system efficiency, when the coupling coefficient k reaches the maximum value, the minimum quality factor of series inductor is required. We can obtain the minimum inductance quality factors at different frequency, as shown in Table 1. Q value is far more than common high-frequency inductors, which is usually 50–300. The inductance that meets the condition cannot be obtained in practical application, which means that the optimal efficiency of CPT system in this case cannot be equal to that of IPT system. Table 1. Minimum QL at different frequency f (MHz)
k
Qmin
0.1
0.000033
6635191
1
0.000341
638646
2
0.000713
305782
3
0.001118
195023
4
0.001559
139790
5
0.002042
106767
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6 Conclusion This paper introduces uniform IVS model for both inductive and capacitive and define an uniform coupling space which helps a fair comparison of these two couplers. When optimizing the coupler parameters, the influence of the coupler size parameters and resonance frequencies are evaluated. Besides, for reducing the required compensation inductance, external shunt capacitors are also added to help the performance of capacitive couplers. After optimizing these two couplers, this paper obtains the peak efficiency of inductive coupler and the boundary conditions of capacitive coupler. Finally, this paper concludes that inductive coupler is better than capacitive coupler in peak efficiency.
References 1. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—An overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2018) 2. Munir, A., Ranum, B.T.: Wireless power charging system for mobile device based on magnetic resonance coupling. In: International Conference on Electrical Engineering and Informatics (ICEEI), Denpasar, pp 221–224. IEEE (2015) 3. Lee, C.H., Jung, G.H., Al Hosani, K., et al.: Wireless power transfer system for an autonomous electric vehicle. In: IEEE Wireless Power Transfer Conference (WPTC), Seoul, pp 467–470. IEEE (2020) 4. Qian, K., Li, J., Li, Y., et al.: Research on cooperative transfer technology of data and power in an electric vehicle wireless charging system. In: 3rd International Conference on Electrical Engineering and Control Technologies (CEECT), Macau, pp 250–254. IEEE (2021) 5. Sun, M., Xu, Q., Wang, T., et al.: Wireless power transfer and data communication for lowpower micro electronic devices deeply implanted within the human body. In: ACM International Symposium on Low Power Electronics and Design (ISLPED), Boston, p. 1. IEEE (2021) 6. Zhao, P., Zheng, G., Fu, M., et al.: A 45-W two-stage wireless fast charger using unregulated inductive power transfer. IEEE J. Emerg. Sel. Top. Ind. Electron. 2(3), 287–296 (2021) 7. Li, S., Li, W., Deng, J., et al.: A double-sided LCC compensation network and its tuning method for wireless power transfer. IEEE Trans. Veh. Technol. 64(6), 2261–2273 (2014) 8. Lu, F., Zhang, H., Hofmann, H., et al.: A double-sided LCLC-compensated capacitive power transfer system for electric vehicle charging. IEEE Trans. Power Electron. 30(11), 6011–6014 (2015) 9. Wang, S., Liang, J., Fu, M.: Analysis and design of capacitive power transfer systems based on induced voltage source model. IEEE Trans. Power Electron. 35(10), 10532–10541 (2020) 10. He, R., Zhao, P., Fu, M., et al.: Decomposition and synthesis of high-order compensated inductive power transfer systems for improved output controllability. IEEE Trans. Microw. Theory Tech. 67(11), 4514–4523 (2019)
Design of Integrated Coil Structure for Simultaneous Wireless Information and Power Transfer Applied to Electric Power Inspection Robot Chen Huang1 , Nenghong Xia2(B) , Xike Mao2 , Chengchao Hua1 , Xiaoying Xu2 , and Zhipeng Yuan2 1 Science and Technology on Electromagnetic Compatibility Laboratory,
China Ship Development and Design Centre, Wuhan 430064, China [email protected] 2 School of Electrical Engineering, Shanghai Electric Power University, Shanghai 200000, China [email protected]
Abstract. Wireless power transfer is gradually becoming a new choice for power supply for electric power inspection robots with its security and stability. In practical applications, in order to achieve autonomous charging of the robots, stable information interaction between the transmitting and receiving sides is required, among which magnetic near-field wireless information transfer technology can be an effective method for information interaction. However, cross-coupling between the power and information channels affects transmission efficiency. In this paper, we propose an integrated structure for simultaneous wireless information and power transfer based on magnetic near-field coupling. The circular coil is used for energy transmission. Two pairs of DD coils connected in series and vertically placed inside the circular coil for information transmission, which together form an integrated structure. The resulting integrated structure enables the decoupling of the power and information channels. The simulation results show that the interference between the power channel and the information channel is only 4nH, accounting for only 0.03% of the mutual inductance between the power channels. Through experiments, it is verified that the influence of the power channel and the information channel can be ignored. Keywords: Electric power inspection robots · Simultaneous wireless information and power transfer · Integrated coils · Charge control
1 Introduction With the rapid expansion of the scale of the power system, the complexity and uncertainty of the power grid has put forward higher requirements for the stable operation of the system, and the traditional manual inspection have failed to meet the requirements of accurate, real-time and high-frequency power inspection [1], and thus power inspection © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 531–542, 2023. https://doi.org/10.1007/978-981-99-0631-4_53
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robots have gradually become an efficient alternative means of detecting power equipment [2]. At present, the limited capacity of the battery causes the inspection robot to need frequent charging, and the traditional contact charging requires manual intervention, which has defects such as high labour intensity and safety hazards [3]. Wireless power transfer offers a new option for powering electric power inspection robots with the advantages of security, small occupied area and strong environmental adaptability [4–6]. In order to achieve autonomous charging of the robot, transmitting and receiving sides require stable and convenient information interaction. Traditional communication methods (such as Bluetooth, WiFi, ZigBee) require long handshake times, complex matching and higher costs. Research has shown that information transfer can be carried out on the basis of inherently wireless energy transfer channel. This magnetic near-field information transfer technology reduces system complexity while offering the advantages of low cost, low power consumption and good medium penetration. At present, near-field magnetically coupled simultaneous wireless information and power transfer (SWIPT) has been extensively studied. Traditionally, a single energy carrier has also been used for information transfer [7–9]. It has two schemes, the first is to transmit information by modulating the power waveform. The literature [7] addresses the shortcomings of the binary frequency shift keying modulation technique, such as insufficient resonance utilisation and low efficiency, by using a double resonant carrier, which greatly improves the transmission efficiency; the second is to inject information into the power coil. The literature [8] proposes an injection communication method based on a double D-coil structure, and in the literature [9], SWIPT is carried out by means of a combination of inductive and capacitive elements. However, achieving high power transfer and efficient information transfer using a single carrier approach is very challenging and we need to make a compromise between information efficiency and power efficiency. Unlike single-channel SWIPT, the multi-channel SWIPT model adds a new information transmission coil to the original power transmission channel. Power and information are transmitted through their respective channels [10, 11]. This model makes the coupling mechanisms of power and information independent of each other, and can control power and information transfer separately, reducing the control complexity to a certain extent. In addition, it shifts the interference of information and power from the circuit to the field, and the cross-coupling between the power and information coils needs to be considered for the two-channel SWIPT. The traditional approach to this problem is to increase the distance between the energy coil and the information coil, however, in most applications, the limited size of mobile devices makes it difficult to reduce crosstalk by increasing the distance. Therefore, this paper designs a new integrated energy and information coil structure based on the principle of magnetic coupling. The efficient decoupling between the energy and information coils reduces the crosstalk between the coils to a large extent, effectively ensuring quality and efficiency of SWIPT. This coil can be used for autonomous charging of power inspection robots for basic information interaction.
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2 Integrated Coil for SWIPT Dual-channel transmission technology is one of the ways to realize SWIPT. Due to the close distance between the power coil and the information coil, in addition to the self magnetic field coupling of the energy channel and the information channel, the magnetic fields between the two channels are also coupled with each other. Mp
Inverter
compensaon
compensaon M1
modulaon
M2
recfier
load
detecon
load
M3 M4
compensaon
compensaon Ms
Fig. 1. Structure diagram of dual channel SWIPT.
Figure 1 shows the structure of dual channel SWIPT. The mutual inductance of the power coil is Mp and the mutual inductance of the information coil is Ms. The crosstalk mutual inductance between the power channel and the information channel are M1, M2, M3, and M4. When the mutual inductance between the coils is large, the stability of power transmission and information transmission will be affected. 2.1 Integrated Coil Structure and the Decoupling Principle Based on the magnetic field distribution characteristics of various types of coils, a new integrated coil structure is proposed in this paper. The structure of the integrated coil is shown in Fig. 2. The PX coil is a large circular coil used for energy transmission; DX coil is composed of two sets of DD coils connected in series and perpendicular to
DX4 DX3
PX2
DX1
PX1
DX2 DX:For information transfer PX:For energy transfer
Fig. 2. Integrated coil structure.
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each other for information transmission. It placed at the center of PX coil to form an integrated coil structure. The crosstalk between two coils, i.e. the mutual inductance, is caused by the timevarying magnetic flux excited by coil PX1 across coil DX1, resulting in an induced electric potential. The expression for this is ˜ S2 Bd ψ12 = (1) M = I2 I2 The DD coil placed inside the power coil is bipolar, so the net magnetic flux generated by the power coil passes through the DD coil is zero When the coils are aligned. From the above formula (1), it can be seen that the mutual inductance of the power coil and the information coil is zero. That is to say, there is almost no crosstalk between them. 2.2 Decoupling Coupling Enhancement and Decoupling of Information Coils In order to increase the coupling strength of the communication coils, we use two sets of bipolar DD coils connected in series and stacked vertically on each side of the transmitter and receiver (Fig. 3). However, more cross coupling will be added when the coils are added. DX1 and DX4, DX2 and DX3 have unexpected coupling.
Fig. 3. Structure diagram of information coil.
Same as the above decoupling principle of energy coil and information coil, we stacked DX1 and DX2 vertically on top of each other. DX3 and DX4 combined in the same way. Therefore, the net flux generated by DX1 across DX2 and DX4 is approximately zero, making their mutual inductance close to zero; The mutual inductance of DX2 and DX3 can also be ignored. Therefore, only DX1 and DX3, DX2 and DX4 are coupled in the signal coil, which meets our requirements. 2.3 Simulation Validation In order to verify the correctness of the above theoretical analysis, the integrated structure was modelled and simulated. The modeling data refer to the size of the electric power
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inspection robot. In this simulation, the coupling of the integrated coil structure described above is analysed. Table 1 lists the structural parameters of the integrated coils. Table 1. Integrated coil simulation model parameters. Parameters
Values
PX coil outer radius/mm
70
PX coil inner/mm
50
PX coil turns
10
DX coil length/mm
60
DX coil width/mm
40
DX coil turns
5
Table 2. Simulation result. Parameters
Values/µH
MPX1–PX2
12
MDX1–DX3
0.7
MDX2–DX4
0.91
MDX1–PX1
0.003
MDX2–PX1
0.001
MDX1–DX2
0.005
MDX2–DX3
0.0031
MDX1–DX4
0.0036
Table 2 lists the mutual inductance between the coils obtained from the simulation. The mutual inductance of the main power channel is 12 µH. The total sum of mutual inductance between energy channel and information channel is about 4 nH, which is only 0.03% of the mutual inductance between the power channels. The mutual inductance of the information channel is 1.61 µH. The mutual inductance interference between the information coils is 9 nH, which is less than 0.6% of the mutual inductance of the information channel. Therefore, the integrated coils designed in this paper virtually eliminate the interference between the magnetic field induction of the energy channel and the information channel.
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3 Circuit Model of SWIPT Power and information transmission are divided into two modules. Power transmission uses magnetically coupled wireless power transfer with series compensation on both sides; information transmission uses ASK modulation technology to load the modulated signal into the information transmission coil, the signal is transmitted to the receiving side through the high frequency magnetic field, and non-coherent demodulation is used to filter and demodulate the induced voltage of the signal receiving coil to achieve signal restoration. 3.1 Power Transfer Equivalent Circuits The separation of the transmitting and receiving coils results in higher leakage inductance and induced reactive power, which reduces the transmission power and efficiency of the system. Therefore, matching capacitors are added on the transmitting side for compensation. The common compensation topologies are SS, SP, PS and PP. The SS structure has better immunity to interference and transmission in a high frequency environment [12], as shown in Fig. 4.
C1
R1
M
C2
R2
Rs TX
Vs
L1
L2
RX
I1
RL
I2
Fig. 4. SS topological structure.
3.2 Information Modulation and Demodulation From a technical point of view, wireless power transfer and near-field magnetically coupled information transfer are both based on the principle of electromagnetic coupling, but they have a different focus: wireless power transfer focuses on transmission power and efficiency, while near-field magnetically coupled wireless information transfer focuses on information modulation and demodulation. Information transmission based on power modulation technology is to load the information modulation on the energy waveform, and the power coupling mechanism receives the electrical information stream with signal characteristics, and then demodulates the information through the information stream characteristics to complete the information transmission. In this paper, the binary digital signal is reflected in the frequency of the inverter circuit switching tube, and the digital signal is modulated by switching the frequency of the inverter switching tube, using the difference between the power transmitted when the circuit is in a resonant state and a non-resonant state to reflect the
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binary signal. The demodulation circuits for amplitude modulation are coherent demodulation and non-coherent demodulation. Coherent demodulation requires the use of a baseband signal with the same frequency and phase as the carrier signal, which increases the complexity of the demodulation system and has no significant advantage in improving the transmitted signal, while Noncoherent demodulation is simple and easy. So, we use noncoherent demodulation. Figure 5 shows the equivalent circuit for information transmission.
Fig. 5. Information modulation and demodulation equivalent circuit.
The modulation and demodulation process of information used in this paper is as follows: the signal is modulated by controlling the PWM modulator to output pulses of different frequencies in accordance with the binary digital signals 0 and 1, while the signal is demodulated by detecting the induced sinusoidal voltage at the signal pick-up end. When the signal to be transmitted is 1, the modulator generates a PWM signal with a frequency of f1 to drive the switching tube, which causes the primary circuit to generate high-frequency alternating current, and f1 enables the circuit to work in a resonant state. When the signal to be transmitted is 0, the modulator generates a PWM signal with frequency f2 to drive the switching tube, and the circuit is taken out of resonance. Next, the carrier wave with information characteristics is demodulated using non-coherent demodulation, and the induced voltage at the pick-up end is envelope detector, then the detector voltage is passed through a low-pass filter to filter out interference from high frequency harmonics, and finally the amplitude of the comparator is set, and the change in carrier amplitude is extracted by the comparator for signal demodulation, thus realizing information communication from the original end to the secondary end. In order to verify the correctness of the theoretical analysis, simulations are carried out using SIMULINK. The simulation circuit is shown in Fig. 6 below, based on the wireless information transmission circuit. In the simulation model, binary digital messages are realized with square wave pulses and the message modulation is achieved by a selector switch. The coil mutual inductance and self-inductance are measured on the MAXWELL software and the data is input to the transformer model to replace the coil coupling structure, using a selector switch with a set comparison voltage to implement the comparator function.
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Fig. 6. Simulation circuit.
Figure 7 shows the simulation results. The waveforms from top to bottom are the signal square wave, primary coil voltage waveform, the voltage waveform after low-pass filtering and the voltage waveform after passing through the comparator.
Fig. 7. Simulation result.
4 System Experiments The geometric dimension of the experimental system is consistent with the simulation model. The system uses the WPT analysis software of the vector network analyzer (Keysight E5061b) to compare the coupling relationship between the energy coil and the information coil of the new structure and the conventional structure proposed in this paper. The experimental parameters of the system are shown in Table 3. The frequency of the system is 86.5 kHz, the input voltage of the system is 18 V, and the output load is
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set as 10 . Considering the skin effect and eddy current effect under the high-frequency magnetic field, The equivalent self inductance and resistance of various types of coils are measured by using a 400 strand Litz line and a LCR digital bridge. The transmission distance between the transmitting coil and the receiving coil is 60 mm. Table 4 and Table 5 are the geometric parameters of the two coil structures respectively (Table 6 and Figs. 8, 9). Table 3. Reference values of time-varying electric and magnetic fields. Parameters
Values
Vs/V
300
PN /W
350
f/kHZ
86.5
L1 , L2 /mH
15,16
C1 , C2 /nF
0.165,0.165
R1 , R2 /m
13.5,12
RL /
10
Table 4. Integrated coil structure 1 parameters. Parameters
Values
PX coil outer radius/mm
70
PX coil inner radius/mm
50
PX coil turns
10
DX coil length/mm
60
DX coil width/mm
40
DX coil turns
5
Table 5. Integrated coil structure 2 parameters. Parameters
Values
PX coil outer radius /mm
70
PX coil inner radius/mm
50
PX coil turns
10
DX coil length/mm
140
DX coil width/mm
120
DX coil turns
5
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Integrated coil structure 1.
Integrated coil structure 2.
Fig. 8. Two integrated coils.
Fig. 9. Comparison of radio energy transmission power between integrated coil 1 and integrated coil 2. Table 6. Power comparison of three coil structures. Parameters
Frequency/KHZ Values
Circular coils
86.5
364
Integrated coil structure 1 86.5
222
Integrated coil structure 2 86.5
374
According to the frequency scan of the vector network analyzer, the maximum power point of the wireless charging system built with the circular coil is at 86.5 kHz. The integrated coil 2 is not decoupled from the energy coil and the information coil, the mutual inductance of the energy coil and the information coil interferes with each other, the self-inductance of the energy coil changes under the influence of the crosstalk, thus the frequency of the resonance point changes. The transmission power of the power transmission system at 86.5 kHz changes from 364 W to 222 W, a reduction of 39%.
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Therefore, the mutual inductance of the energy and information coils of integrated coil 2 is not suitable for use in the parallel transmission system. The mutual inductance of the energy and information channels of the integrated coil 1 is only 0.4 nH, almost does not affect the power transmission, this wireless charging at 86.5 KH maximum transmission power is 374 W, so the integrated coil 1 realize the decoupling of energy channel and information channel.
5 Conclusion In this paper a new integrated coil structure for power and information transfer is designed, which can be applied to the power inspection robot to realize the information interaction of autonomous wireless charging. The integrated coil consists of a circular coil and two DD coils. The circular coil structure is used for power transmission. The two sets of DD coils are perpendicular to each other in the horizontal plane and are used for stable information transmission. The mutual inductance interference between the power channel and the information channel is only 4 nH, which is only 0.03% of the mutual inductance between the power channels, and it has been verified experimentally that the influence of the power channel and the information channel is negligible.
References 1. Lu, S., Zhang, Y., Su, J.: Mobile robot for power substation inspection: a survey. IEEE/CAA J. Autom. Sin. 4(4), 860–847 (2017) 2. Alhassan, A.B., Zhang, X., Shen, H., et al.: Power transmission line inspection robots: a review, trends and challenges for future research. Int. J. Electr. Power Energy Syst. 118, 105862 (2020) 3. Wang, C.J., Yin, L., Zhao, Q.: An intelligent robot for indoor substation inspection. Ind. Robot Int. J. Robot. Res. Appl. 47(5), 705–712 (2020) 4. Mahesh, A., Chokkalingam, B., Mihet-Popa, L.: Inductive wireless power transfer charging for electric vehicles–a review. IEEE Access 9, 137667–137713 (2021) 5. Javan-Khoshkholgh, A., Farajidavar, A.: Simultaneous wireless power and data transfer: methods to design robust medical implants for gastrointestinal tract. IEEE J. Electromagn. RF Microw. Med. Biol. 6(1), 3–15 (2022) 6. Teeneti, C.R., Truscott, T.T., Beal, D.N., Pantic, Z.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Ocean. Eng. 46(1), 68–87 (2021) 7. Kim, J., Wei, G., Kim, M., Ryo, H., Zhu, C.: A Wireless power and information simultaneous transfer technology based on 2FSK modulation using the dual bands of series-parallel combined resonant circuit. IEEE Trans. Power Electron. 34(3), 2956–2965 (2019) 8. Wei, G., Feng, J., Zhang, J., Wang, C., Zhu, C., Yurievich, O.S.: An efficient power and data synchronous transfer method for wireless power transfer system using double-D coupling coil. IEEE Trans. Ind. Electron. 68(11), 10643–10653 (2021) 9. Li, X., Tang, C., Dai, X., et al.: An inductive and capacitive combined parallel transmission of power and data for wireless power transfer systems. IEEE Trans. Power Electron. 33(6), 4980–4991 (2018) 10. Ghovanloo, M., Atluri, S.: A wide-band power-efficient inductive wireless link for implantable microelectronic devices using multiple carriers. IEEE Trans. Circuits Syst. I Regul. Pap. 54(10), 2211–2221 (2007)
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11. Jow, U., Ghovanloo, M.: Optimization of data coils in a multiband wireless link for neuroprosthetic implantable devices. IEEE Trans. Biomed. Circuits Syst. 4(5), 301–310 (2010) 12. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2018)
Reconfiguration and Reuse of Receiver/Repeater in Wireless Power Transmission System Han Liu1,2(B) , Lingling Sun3 , and Wei Zhang4 1 College of Energy and Electrical Engineering, Hohai University, Nanjing 211106, China
[email protected]
2 Jiangsu Provincial Key Laboratory of Smart Grid Technology and Equipment, Southeast
University, Nanjing 210096, China 3 State Grid Zhenjiang Power Supply Company, Zhenjiang 212000, Jiangsu, China 4 PowerChina Qinghai Electric Power Design Institute Co., Ltd., Xining 810003, China
Abstract. Wireless power transmission technology has been widely applied in fields such as wireless sensor networks, consumer electronics, electric vehicles, implantable medical and etc., which is characterized as non-contact, convenience, safety, and strong environmental adaptability. In wireless power transmission systems with multiple coils, the coil plays a single role such as receiver or repeater, which leads to the lack of flexibility of system operation. To deal with this shortage, a reconfigurable wireless power transmission system is investigated in this paper. The coil can be selected as receiver or repeater by the circuit reconfiguration. The equivalent circuits of receiver operation mode and repeater operation mode are developed firstly. The expressions of receiving power and efficiency for two operation modes varying with the mutual inductances and loads are deduced according to the circuit theory. The corresponding system characteristics are studied comparatively. The receiving power and efficiency of the load in far end can be promoted through the reconfiguration and reuse of the near-end coil. Keywords: Wireless power transmission · Receiver · Repeater · Reconfiguration
1 Introduction Wireless power transmission technology is characterized as non-contact, convenience, safety, and strong environmental adaptability [1–5]. It has been widely applied in fields such as consumer electronics, electric vehicles, implantable medical, underwater devices, wireless sensor networks. Due to the advantages of wireless power transmission, this technology is gradually developing to the cooperative working mode with multiple coils. In order to achieve efficient long-distance wireless power transmission, the systems with multiple repeating coils is proposed to enhance the coupling between the transmitting coil and the receiving coil. A match adjustment method for the impedance network is proposed on the basis of impedance transformation with the relay coil in [6]. The number of relay coils for maximizing the system efficiency for a fixed end-to-end distance is derived and confirmed in [7]. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 543–549, 2023. https://doi.org/10.1007/978-981-99-0631-4_54
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This technology is also utilized to power for multiple loads. The self-oscillating source is used to overcome the shortage caused by the cross coupling between multiple loads in [8]. The one-to-multiple wireless power transmission topology is proposed to improve the system misalignment tolerance in [9]. In the existing research of wireless power transmission, the coils mostly play one fixed role such as transmitter, receiver or repeater. In [10], the receiving coil also acts as the relay coil in the positioning strategy for dynamic wireless charging system. In wireless power transmission systems with multiple coils, the receiving coil also can be used as the repeating coil to satisfy more power supply requirements. Therefore, we proposed a reconfigurable wireless power transmission system in this paper. The coil can be selected as receiver or repeater by the circuit reconfiguration. The equivalent circuits of receiver operation mode and repeater operation mode are developed firstly. The expressions of receiving power and efficiency for two operation modes varying with the mutual inductances and loads are deduced according to the circuit theory. The corresponding system characteristics are studied comparatively.
2 System Description The diagram of proposed system with reconfigurable receiver/repeater is shown in Fig. 1. Two loads are at same side of the transmitting coil. The transmitting coil is energized by high frequency inverter and compensated with the LCC topology circuit. The coil of near-end load is compensated with a series capacitor in both receiver mode and repeater mode. The roles of receiver and repeater can be switched through on-off control. The coil of far-load is also compensated with a series capacitor. When the switch is on, the near-end load is charged wirelessly and the far-end load is charged with a lower power
Transmitting coil
Near-end coil
C
LCC
0 1
Us
Far-end coil
C switch
RL1
RL2
Fig. 1. The diagram of proposed system with reconfigurable receiver/repeater
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rate. When the switch is off, the near-end load side is turned to repeating mode and the far-end load is charged with a higher power rate. Different wireless charging mode can be satisfied through the reconfiguration of receiver and repeater.
3 System Modelling The near-end operates as the receiver or repeater controlled by the switch. Therefore the system circuit models of different modes are developed as shown in Fig. 2 and Fig. 3. U s is the high frequency power source. L t and Rt represent the inductance and the equivalent resistance of transmitting coil, respectively. L f , C f and C t consists the LCC compensation circuit in transmitting side. L 1 , C 1 and R1 represent the inductance, the compensation capacitor and the equivalent resistance of near-end receiving coil, respectively. RL1 is the load at the near-end. At the repeating mode, C 1 is connected with L 1 in series. L 2 , C 2 and R2 represent the inductance, the compensation capacitor and the equivalent resistance of far-end receiving coil, respectively. RL2 is the far-end load.
Lf
Us
Cf
M2 C1
M1
Ct
L1
Lt Rt
RL1
R1
C2
L2
RL2
R2
Fig. 2. System circuit model of receiver mode
Lf
Us
Cf
M2 C1
M1
Ct
Lt Rt
C2
L1
L2
R1
R2
RL2
Fig. 3. System circuit model of repeater mode
As shown in Fig. 2 and Fig. 3, M1 and M2 are the mutual inductances between two adjacent coils. According to the design rules of LCC and series compensation topologies, the capacitor components of compensation circuit should satisfy the following equations. (1) ω2 Lf Cf = ω2 Lt − Lf Ct = ω2 L1 C1 = ω2 L2 C2 = 1
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Based on the circuit theory of mutual inductance, the circuit equations of receiver mode can be established. ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ZLf + ZCf −ZCf 0 0 If 2 Us ⎢ −ZCf ZLt + ZCt + ZCf + Rt −jωM1 ⎥ ⎢ I t2 ⎥ ⎢ 0 ⎥ 0 ⎢ ⎥·⎢ ⎥ = ⎢ ⎥ (2) ⎣ R1 +RL1 −jωM2 ⎦ ⎣ I 1 ⎦ ⎣ 0 ⎦ 0 −jωM1 0 0 −jωM2 R2 +RL2 I2 0 1 1 , ZLt = jωLt , and ZCt = jωC . f is the where ω = 2π f , ZLf = jωLf , ZCf = jωC t f operation frequency. By solving the equations above, the expressions of receiving power for two loads can be derived
P1 = P2 =
Us2 M12 (R2 + RL2 )2 RL1
2 L2f ω2 M22 + (R1 + RL1 )(R2 + RL2 ) Us2 M12 ω2 M22 RL2
(3)
2 L2f ω2 M22 + (R1 + RL1 )(R2 + RL2 )
The system efficiency when the near-end operates as receiver mode also can be deduced
ω2 M12 (R2 + RL2 )2 RL1 + ω2 M22 RL2 η=
2 ω2 M12 (R2 + RL2 )2 RL1 + ω2 M22 RL2 + Rt ω2 M22 + (R1 + RL1 )(R2 + RL2 ) (4) Comparing the system circuit models in Fig. 2 and Fig. 3, the repeater mode can be obtained easily by changing the load RL1 to 0. Therefore, the receiving power of far-end load in repeater mode can be derived. P2 =
Us2 M12 ω2 M22 RL2
2 L2f ω2 M22 + R1 (R2 + RL2 )
(5)
The system efficiency when the near-end operates in repeater mode also can be deduced η =
ω4 M12 M22 RL2
2 ω4 M12 M22 RL2 + Rt ω2 M22 + R1 (R2 + RL2 )
(6)
The expressions of receiving power and efficiency of different operation modes are derived according to the circuit models above. After changing the operation mode of the near-end, the system characteristics will be different. Therefore, the system comparative analysis will be investigated in detail based on the system modelling in the following part.
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4 Comparative Analysis In this paper, the relevant positions of multiple coils are considered fixed. The system characteristics of receiving power and efficiency in two different operation modes are investigated. According to the system parameters listed in Table 1, the characteristics of the receiving power and efficiency varying with the near-end load RL1 are studied comparatively in receiver mode and repeater mode. In the simulation, the near-end load RL1 changes between 1 to 50 . The comparative analysis results are shown in Fig. 4 and Fig. 5. Table 1. System parameters Parameter
Value
f (kHz)
100
U s (V)
20
L f (µH)
10
M 1 (µH)
4
M 2 (µH)
6
Rt ()
0.1
R1 ()
0.1
R2 ()
0.1
RL2 ()
5
Receiving power/W
25 20
15 Receiver mode
P1 P2 P1+P2
Repeater mode
P2'
10 5 0 0
10
20
30
40
50
RL1/ Fig. 4. The comparative analysis results of receiving power
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100
Efficiency/%
90 80 70 60 50
Efficiency of receiver mode Efficiency of repeater mode
0
10
20 30 RL1/
40
50
Fig. 5. The comparative analysis results of efficiency
As shown in Fig. 4 and Fig. 5, in receiver mode, the receiving power and the efficiency decrease with the increase of RL1 . As the resistance of near-end load increases, it is difficult for the far-end load to receive energy wirelessly in receiver mode. Therefore, this paper proposed the reconfiguration of receiver/repeater modes. In repeater mode, the RL1 is isolated by the reconfiguration. The receiving power of far-end load and the efficiency are promoted significantly in repeater mode. The system operation strategies will be enriched through the proposed reconfiguration.
5 Conclusions A reconfigurable wireless power transmission system is proposed in this paper. The circuit models of different operation modes are developed. The equivalent circuits of receiver operation mode and repeater operation mode are developed firstly. The expressions of receiving power and efficiency for two operation modes varying with the mutual inductances and loads are deduced according to the circuit theory. The corresponding system characteristics are studied comparatively. The receiving power and efficiency of the load in far end can be promoted through the reconfiguration. According to the research results in this paper, we will continue to study the related flexible control strategy in the future. Acknowledgments. This work was supported in part by the National Natural Science Foundation of China (52107003), in part by the Chinese Postdoctoral Science Foundation (2021M690867), in part by the Postdoctoral Fund of Jiangsu Province (2021K030A), in part by the Project of Jiangsu Provincial Key Laboratory of Smart Grid Technology and Equipment in Southeast University, in part by the Fundamental Research Funds for the Central Universities (B200201018), and in part by the Project of science and technology innovation for overseas returnees in Nanjing (B2004805).
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References 1. Wu, M., Yang, X., Chen, W., et al.: A compact coupler with integrated multiple decoupled coils for wireless power transfer system and its anti-misalignment control. IEEE Trans. Power Electron. 37(10), 12814–12827 (2022) 2. Jiang, J., Dai, X., Hu, A.P.: A dynamic tuning method for ZPA frequency operation of MEUWPT system by DC input voltages regulation. IEEE Trans. Power Electron. 37(9), 11369– 11381 (2022) 3. Zhang, Y., Pan, W., Wang, H., et al.: Misalignment-tolerant dual-transmitter electric vehicle wireless charging system with reconfigurable topologies. IEEE Trans. Power Electron. 37(8), 8816–8819 (2022) 4. Xia, C., Zhang, H., Wei, N., et al.: Simultaneous wireless power and multibit signals transfer system with hybrid modulation waves PWM control. IEEE Trans. Power Electron. 37(10), 12913–12928 (2022) 5. Khan, S.A., Ahn, D.: Automatic resonance tuning with ON/OFF soft switching for pushpull parallel-resonant inverter in wireless power transfer. IEEE Trans. Power Electron. 37(9), 10133–10138 (2022) 6. Li, Y., Song, K., Zhu, C., Wei, G., Lu, R.: Efficiency optimizing and load matching analysis for the weak-coupling wireless power transfer system using a repeating coil. In: 2016 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Knoxville, TN, USA, pp. 31–34 (2016) 7. Lee, J., Lee, K.: Effects of number of relays on achievable efficiency of magnetic resonant wireless power transfer. IEEE Trans. Power Electron. 35(7), 6697–6700 (2020) 8. Sun, S., Zhang, B., Rong, C., Shu, X., Wei, Z.: A multireceiver wireless power transfer system using self-oscillating source composed of zero-voltage switching full-bridge inverter. IEEE Trans. Ind. Electron. 69(3), 2885–2895 (2022) 9. Chen, J., Zhou, H., Deng, Q., et al.: Free-positioning wireless power transfer system based on one-to-multiple topology. IEEE Trans. Power Electron. 35(10), 9959–9964 (2020) 10. Liu, H., Huang, X., Tan, L., et al.: Dynamic wireless charging for inspection robots based on decentralized energy pickup structure. IEEE Trans. Ind. Inf. 14(4), 1786–1797 (2018)
Improved Electromagnetic Halbach Array for Enhanced Efficiency in Wireless Power Transfer Dibin Zhu1(B)
and Tamuno-omie Gogo2
1 Shanghai Jiao Tong University, Shanghai 200240, China
[email protected] 2 University of Exeter, Exeter EX4 4PY, UK
Abstract. This paper presents an improved design of an electromagnetic Halbach array that can be used as the transmitter of the wireless power transfer system for enhanced performance. An electromagnetic Halbach array consists of five coils, i.e. one base coil and four side coils forming a transmitter cube. Superposition of the magnetic fields generated by these five coils results in a stronger magnetic field in half of the cube. When the receiver coil is placed in the strong magnetic field half, higher power transfer efficiency can be achieved over longer transmission distances. It was found in the simulation that the magnetic field of the base coil distributed more densely in locations near its centre. Therefore, the proposed design moves the side coils closer to the centre of the base coil. It was verified in the ANSYS magnetostatic simulation that this method is able to increase the magnetic field strength of the electromagnetic Halbach array. Furthermore, co-simulation of ANSYS Maxwell and Simplorer has proved that using the improved electromagnetic Halbach array as the wireless power transmitter, higher power transfer efficiency is obtained when the receiver is placed inside the strong magnetic field half of the transmitter cube. Keywords: Wireless power transfer · Electromagnetic Halbach array · ANSYS maxwell · Simplorer
1 Introduction Wireless power transfer (WPT) as a flexible way of powering electronic devices has attracted significant attention over the last decades [1–3]. One of the most commonly used WPT methods is the inductive WPT where the transmitter and receiver coils are coupled inductively in close proximity to each other. The main drawback of this technology is that when the two coils are separated by a larger distance, the power transfer efficiency drops significantly. Existing solutions to address this issue includes domino resonators, metamaterials and single sided electromagnetic field. Domino-resonators refers to the concept of implementing additional coil resonators between the transmitter and for extended power transfer distance [4]. Metamaterials are artificially engineered materials which have © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 550–558, 2023. https://doi.org/10.1007/978-981-99-0631-4_55
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properties not naturally available from conventional materials. Metamaterials of negative index are one of the most promising solutions to addressing transmission distance limitation. When placing a specifically designed metamaterial slab between the transmitter and the receiver, it behaves like a “super lens” which can refocus the propagating waves from the transmitter to the receiver to enhance the power transfer efficiency [5–8]. Single-sided magnetic field is also a potential solution to extending the wireless power transmission range. One can achieve this by placing a ferrite tile at the back of the coil. However, as the operating frequency increases, eddy current in the ferrite may lead to heat problems. Therefore, ferrite-less single-sided magnetic field solutions were investigated to address this issue [9, 10]. Halbach-Type Coupler has also been used in wirelessly power linear motors [11]. Authors of this paper proposed an electromagnetic Halbach array which was developed based on the concept of permanent magnet Halbach array [12]. Based on this approach, an improved electromagnetic Halbach array for enhanced efficiency in wireless power transfer system is presented in paper. The paper is structured as follows. Section 2 introduces the principle of the electromagnetic Halbach array and the proposed method for improvement. Section 3 introduces the research methodology. Simulation results are presented and discussed in Sect. 4 followed by the conclusion.
2 Improved Electromagnetic Halbach Array 2.1 Principle of the Electromagnetic Halbach Array A typical Electromagnetic Halbach Array (EHA) consists of five coils as shown in Fig. 1. Four coils (C1–C4), a.k.a side coils, are placed vertically forming a box. The fifth one, C5, a.k.a base coil, is placed horizontally in the middle of the box and divides the box into two halves.
Fig. 1. An electromagnetic Halbach array.
The five coils are connected in series so that the magnetic fields generated by all coils are in phase. Superposition of these magnetic fields leads to a stronger magnetic field
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on one side of the Halbach array and a weaker magnetic field on the other side. When the current direction is as shown in Fig. 2a, magnetic fluxes in the upper half are in the same direction resulting in a stronger magnetic field as shown in Fig. 2b. The magnetic fluxes in the lower half are in the opposite directions resulting in a weaker magnetic field. If the current reverses its direction as shown in Fig. 2c, directions of all magnetic flux are also reversed. The upper half still has a stronger magnetic field, but its direction is reversed. If the EHA is driven by an AC current, the upper half will have a stronger AC magnetic field. Therefore, the EHA can be used as a transmitter of a wireless power transfer system. The receiver coil can be placed in parallel with the base coil, anywhere in the upper half; thus, the power transmission range can be increased.
Coil and current direcon Magnec flux
(a)
Stronger magnec field
Stronger magnec field
Weaker magnec field
Weaker magnec field
(b)
(c)
Fig. 2. (a) Side view of the electromagnetic Halbach array and its current and magnetic flux direction (b) stronger magnetic field in the upper half of the electromagnetic Halbach array (c) when the current reverses, the upper half still has the stronger magnetic field but with reversed direction.
2.2 Magnetic Field of a Planar Square Coil Figure 3b shows the simulation of the z component of the magnetic field generated by a square coil as in Fig. 3a. It is worth mentioning that since the receiver coil is typically parallel to the transmitter coil, only the magnetic field in the z direction is analysed here
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as contribution of the magnetic fields in x and y directions to power transmission in a WPT system is negligible. It was noticed that the z component of the magnetic field distributes around the centre and the edge of the coil with a zone in-between where the z-component of the magnetic field strength is minimum (highlighted with red dashed lines in Fig. 3b). Therefore, when building an electromagnetic Halbach array, the vertical coils can be placed in the weak magnetic field zone as highlighted in red in Fig. 3a to enhance the magnetic field strength in the stronger side, i.e. the upper half of the EHA.
Fig. 3. (a) an example planar square coil (b) Simulation of the z-component of the magnetic field generated by the square coil in (a) (side view).
2.3 Proposed Design The proposed design is developed from a conventional EHA as shown in Fig. 4a. The conventional EHA consists of five identical square coils whose parameters are listed as Coil A in Table 1. Based on the analysis in Sect. 2.2, decision is made to place the vertical coils in the red zone shown in Fig. 3a, i.e. between the second and the third
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turns from the outside of the coil. Parameters of these vertical coils are listed as Coil B in Table 1. The base coil in the proposed design is almost identical to Coil A. The only difference is that there is a slightly larger pitch (1.4 mm) between the second and the third turns to fit in the vertical coils. Its parameter is listed as Coil A1 in Table 1. Figure 4b shows the proposed EHA. The receiver coils used are Coil A for the conventional EHA and Coil B for the improved EHA.
Fig. 4. (a) Conventional electromagnetic Halbach array. (b) Improved electromagnetic Halbach array. The blue coils in both figures are the receiver coils.
Table 1. Coil parameters. Parameter
Coil A
Coil A1
Coil B
No. of turns
8
8
5
Pitch
1 mm
1 mm
1 mm
Wire width
1 mm
1 mm
1 mm
Resistance
19.46 m
19.38 m
9.91 m
Outer edge length
51 mm
51 mm
37 mm
3 Methodology Two sets of simulation were carried out in this research. The magnetostatic simulation in Ansys-Maxwell was firstly used to investigate the magnetic field generated by the two electromagnetic Halbach arrays as shown in Fig. 4. In this simulation, a DC current of
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1 A was applied. The coils’ resistances were obtained using the Maxwell-Eddy current simulation. The Maxwell-magnetostatic model was then imported into Simplorer and integrated into the wireless power transfer circuitry to study the power transfer efficiency. The circuit used in Simplorer is shown in Fig. 5. As the coils’ resistances are not part of the inductance matrix from Maxwell, all resistors were integrated as external resistors, i.e. RT and RR as resistances of the transmitter (electromagnetic Halbach array) and the receiver coil, respectively. The box located in the centre (labelled as EHA) contains the electromagnetic Halbach array and the receiver coil modelled in Maxwell and their terminals are connected to the corresponding transmitter and receiver circuits. The WPT system is structured with a series-parallel (SP) topology, where the value of Cp is fixed at 8 nF and Cs is variable. A parametric sweep was used to determine the optimum values of Cs and the load, RL . The AC/AC efficiency was calculated by connecting power meters at both transmitter and receiver terminals and derived as the ratio between the input and output power. The operating frequency is 200 kHz. The source internal resistance, RP , is 0.1 . The optimum power transfer efficiencies at various distances between the receiver coil and the base coil in the electromagnetic Halbach array were recorded. The power transfer efficiency of the EHA based WPT systems were also compared with the single coil transmitter WPT systems. More specifically, the conventional EHA is compared with the Coil A to Coil A WPT system and the improved EHA is compared with the Coil A to Coil B WPT system.
Fig. 5. Simplorer simulation circuit.
4 Results and Discussion 4.1 Magnetic Field Figure 6 compares the magnetic fields of the conventional and the improved electromagnetic Halbach arrays. It was found that the improved EHA has a stronger magnetic field
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in locations closer to the base coil (0–15 mm) which indicates that the decision to move the side coils closer to the centre of the base coil has positive effect on the magnetic field of the EHA. As the side coils in the improved EHA has smaller side lengths than that in the conventional EHA, the conventional EHA has stronger magnetic field than the improved design in locations further away from the base coil (>15 mm). 4.2 Power Transfer Efficiency Figure 7a compares the power transfer efficiency between the conventional EHA and the single-coil transmitter (Coil A) and receiver (Coil A) while Fig. 7b compares the power transfer efficiency between the improved EHA and the single-coil transmitter (Coil A) and receiver (Coil B). It was found that in both cases, the single coil transmitter has a higher power transfer efficiency when the receiver coil is closer to the transmitter coil. As the distance increases, the Halbach array-based transmitters outperform the single coil transmitters. When comparing the two electromagnetic Halbach arrays, it was found that as the receiver-transmitter distance is small ( 0, connecting the next battery pack at In = 0 will inevitably lead to the peak current less than the constraint current Imax. Therefore, if the peak current of each subsequent battery pack is connected to Imax, the connection time should be before In = 0. When the current is zero for the first time, the higher the capacitor voltage is, the lower the peak current is, and the more it needs to be connected in advance, so the smaller the current fluctuation is, that is, the smaller the ripple coefficient of the current is. At the same time, when the loop resistance is constant, the working process of each stage after the first stage can be regarded as a full response with the same initial value, that is, the corresponding In and Uc − (n − 1)e are the same at each series connection, so the time interval tgap of each battery series connection is the same. Considering the actual situation, as the battery pack is connected, the internal resistance of the battery pack will be superimposed step by step, the total resistance of the circuit will gradually increase with the series connection of the battery pack. From the analysis of the influence of the above loop resistance on the peak current of RLC circuit, it can be seen that the peak current of each RLC circuit will decrease with the increase of the resistance value. Therefore, if the battery pack is connected according to the time sequence corresponding to the original internal resistance of 0, the required restricted current will not be reached. Therefore, the following measures should be taken: increase the current In at the initial moment. Make the capacitor voltage Uc smaller at the initial time. It can be seen that this will lead to the advance of the timing, and with the gradual increase of the current when switching in, it will also lead to the gradual decrease of the interval tgap between the two times, and the greater the resistance change, the more obvious the phenomenon. 3.2 Simulation Verification Take the first peak current as the restraint current Imax , PSIM simulation is carried out for the 10 level cascade topology, and the specific parameters are: e = 550 V, R0 = 0, n = 10, L = 0.05 H, C = 2 F, R are 0.6 , 0.25 and 0.15 respectively (corresponding to different damping ratios), and the simulation waveform is shown in Fig. 7 (Fig. 6). The simulation results show that when In = 0 is over-damped, when the resistance is 0.2 5 and 0.15 , it is under-damped, and when In > 0 is over-damped, it is earlier than In = 0. The smaller the damping ratio is, the more the earlier the time is, the smaller the fluctuation is, and the time interval t of each series connection.
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Fig. 6. The corresponding charging current waveforms when R is 0.6 (overdamping), 0.25 and 0.15 (underdamping)
Considering the influence of the internal resistance of the battery, R0 = 0.05 is chosen, and the peak current imax1 reached by the first-stage battery pack in series is still taken as the constraint current Imax. The simulation is carried out when R = 0.15 and R = 0.25 (the corresponding constraint currents are 1670 A and 1320 A, respectively), and the charging time and ripple coefficient of charging current when the pulse capacitor is charged to 4000 V are studied. Table 1. The parameters of simulation Parameter
Value
Total series of lithium battery
n = 10
Voltage of lithium battery per stage
e = 550 V
Equivalent internal resistance
R0 = 0.05
Loop inductance
L = 0.05 H
Pulse capacitance
C = 2F
Constrained current
Imax = imax1
Cutoff voltage
UC = 4000 V
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Fig. 7. The charging current and voltage waveforms when R = 0.15 and R = 0.25
with simulation data ξR=0.15 = IP − Iavg /Iavg = 0.16, ξR=0.25 = Combined IP − Iavg /Iavg = 0.2. It can be seen from the above simulation analysis that, taking into account the influence of the internal resistance of the battery, the total resistance in the circuit is gradually increasing with the series connection of the battery pack. The current of each stage of the battery pack is gradually increasing, that is, the time sequence of the connection is ahead of the time sequence when the internal resistance is ignored, and the time interval of the connection is tgap decreases gradually; Under the condition of under damping, the ripple coefficient ξ decreases with the reduction of the loop resistance R gradually decrease. 3.3 The Reference Peak Current Imax is a Certain Value Which Greater Than the Peak Current When the First Battery is Connected in Series If the peak current of the first group of batteries in series is small, which can’t reach the restricted current Imax, it needs to be connected in two or more stages to reach Imax. Conclusions from the previous section, the greater the loop resistance of the system, the smaller the peak current. Therefore, when the new battery pack is connected in series, the larger the loop current In and the smaller the capacitor voltage Uc should be, that is, connected in series. The larger In is, the closer the loop current is to the peak current when the new first-class battery pack is connected in series, resulting in the decrease of current fluctuation, ripple coefficient and average current. However, considering the limitation of battery series, with the increase of resistance, the time of series connection will be advanced. When the resistance is too large, it will lead to all battery series connection into the system prematurely. After that, the loop current will continue to decrease until the capacitor voltage reaches the set value, which may lead to the decrease of average current and the increase of charging time. Therefore, an appropriate increase in resistance will increase the average current and shorten the charging time, but an excessive resistance may reduce the average current and prolong the charging time. At the same time, because the resistor is an energy-consuming device, it is easy to know that increasing the resistor will consume more energy, thus reducing the charging efficiency of the power supply. 3.4 Simulation Verification and Analysis Considering the double factors of charging speed and maximum current, the constraint current Imax = 1400 A, other parameters unchanged, and the simulation of R = 0.5
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and R = 0.25 by PSIM, respectively, to study the charging time and charging efficiency when the pulse capacitor is charged to 4000 V. The simulation waveform diagram is shown in Fig. 8.
Fig. 8. The charging current and voltage waveforms when R = 0.25 and R = 0.5
The simulation results show that when R = 0.25 , it takes 7.41 s (average current is 1081 A, average power is 2.16 WM) to charge the capacitor to 4000 V; When R = 0.5 , it takes 6.83 s to charge the capacitor voltage to 4000 V (average current is 1164 A, average power is 2.33 WM); Through the above simulation data, the ripple coefficient of charging current can be obtained when the loop resistance R = 0.25 and R = 0.5 I −I is ξR=0.25 = maxIavg avg = 0.3, ξR=0.5 = (Imax − Iavg )/Iavg = 0.203. Charging efficiency is 1 1 CUR2 CUR2 16000000 16000000 = 86.1%, ηR=0.5 = 2tn = 76.3% = = ηR=0.25 = 2tn 18583042 20969855 0 Ut Idt 0 Ut Idt
It can be seen that when the constraint current Imax is 1400 A, the charging time is shortened by 7.8%, the ripple coefficient is reduced by 32% and the charging efficiency is reduced by 11.3% when the loop resistance is R = 0.5 compared with R = 0.25 . To sum up, with the increase of resistance, the average current increases to a certain extent, and the ripple coefficient, charging time and charging efficiency decrease, which verifies the above theoretical analysis.
4 Analysis of Optimal Solution of Loop Resistance Parameters According to the above analysis, when the system constraint current I_max is greater than the peak current of the first-stage battery pack, with the gradual increase of the loop resistance, the charging efficiency will gradually decrease and the charging time will be shortened, but with the further increase of the loop resistance, the charging time may increase. Therefore, it is necessary to quantitatively analyze and comprehensively consider the influence of loop resistance on both of them, so as to obtain the most suitable loop resistance parameters. Because the variable is only the loop resistance, and considering that it will not be too large in the actual situation, the parameter scanning method is used to study it by using MATLAB combined with the above theoretical analysis process. The flow chart is shown in Fig. 8. R is 0.2 –2 (Fig. 9).
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Fig. 9. Flow diagram of parameter scanner
Fig. 10. The variation curve of charging time (left) and charging efficiency (right) with loop resistance R
Through parameter scanning of the loop resistance R, the curves of charging time and charging efficiency with R are obtained, as shown in the following figure (Fig. 10). It can be seen from the above figure that with the increase of the loop resistance R, the charging time first decreases and then increases, and the charging efficiency η continues to decrease. When R = 0.9 , the charging time is the shortest, which is 6.55 s Therefore, the loop resistance R should be less than 0.9 in terms of charging time and charging efficiency. According to the curve of the change of charging time with resistance, when the resistance increases from 0.25 to 0.4 , the slope of the curve is larger, the time decreases obviously, and the charging efficiency is higher at this time. Therefore, considering the trend of the influence of the loop resistance R on the charging time and charging efficiency, R = 0.4 can be regarded as the optimal solution. At this time, the charging time is 7.05 s, the average power is 2.3 MW, and the charging efficiency is 81%.
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Using PSIM to build a simulation circuit for verification, the resistance is R = 0.4 , and other parameters are taken according to the data given in Table 1. The simulation results are shown in the figure (Fig. 11).
Fig. 11. Charging current and capacitor voltage waveform when R = 0.4
The simulation results show that when R = 0.4 , it takes 7.01s to charge the capacitor voltage to 4000 V, and the average current is 1140 A; Charging efficiency is η=
1
CU 2 0 Ut Idt
2t
=
16000000 19583843
= 81.7%.
Comparing the optimization results with the simulation waveforms, the charging time and charging efficiency are in good agreement, which proves the effectiveness of the scheme.
5 Conclusion In this paper, the cascade charging topology is modeled and analyzed, and the influence of loop resistance on the charging current and charging efficiency of power supply under different conditions is studied based on the balance equation of the system. The following conclusions are obtained: 1) The larger the resistance, the smaller the peak current of the loop and the shorter the time to reach the peak current. 2) When the peak current of the first group of batteries is just the constraint current Imax, under the condition of underdamping, the smaller the loop resistance, the smaller the current ripple and the closer the current is to the constant current. 3) If the peak current of the first group of batteries in series is small, which can’t reach the constraint current Imax, and it needs two or more series to reach Imax, with the increase of the loop resistance R, the charging time first decreases and then increases, and the charging efficiency continues to decrease gradually. 4) By analyzing the influence of loop resistance on system performance, a technical scheme of appropriately increasing loop resistance to improve charging rate is proposed, and the correctness of the scheme is verified by simulation.
References 1. Jiang W.: Repetition rate pulsed power technology and its applications: (I) summary. High Power Laser Part. Beams 25(24(01)), 10–15 (2012). (in Chinese)
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2. Yang, S., Ren, S., Lai, D.: High power high voltage constant current capacitor charging power supply. High Power Laser Part. Beams 27(9), 943–948 (2016) 3. Jiang, P., Dong, L., Liu, X.: Research on high voltage charging and energy storage device based on series resonance 21(10), 52–57 (2021). (in Chinese) 4. Li, H.R., Zhang, Z.L., Wang, S.: A 300-kHz 6.6-kW SiC bidirectional LLC onboard charger 67(2), 1435–1445 (2020) 5. Ren, R.: Research on high power pulsed charging power supply based on cascaded topology. Xidian University (2020). (in Chinese) 6. Zhou, J., Ding, H., Liu, Y.: A high power charging power supply for capacitor in pulsed power system. In: 21st IEEE International Conference on Pulsed Power, England, pp. 421–430. IEEE (2017) 7. Zhang, G., Zhu, X., Zou, Y.: HVDC power supply of high power based on resonant softswitching. Electr. Syst. 18(5), 130–131 (2018). (in Chinese) 8. Tan, Q., Sun, Y.H., Gao, Y.: A novel closed-loop control method for li-ion batteries connected in series power supply based on the time sequences recalculation algorithm. Symmetry 13(8), 1201–1213 (2021) 9. Tan, Q., Gao, Y., Liu, K., Han, J.: Research on current control method of high-voltage and constant current. Adv. Technol. Electr. Eng. Energy 39(9), 48–55 (2020). (in Chinese) 10. Li, C., Lu, J.Y., Wang, H.: Comparison of charging methods of multilevel hybrid energy storage for electromagnetic launch. High Power Laser Part. Beams 27(7), 234–239 (2015). (in Chinese) 11. Huang, F., Han, A.: Research on lithium-ion battery models and model parameter identification methods. Electr. Switchg. (3), 37–41 (2020). (in Chinese) 12. Yan, L., Chen, J.: Study and design of lithium battery equivalent model. Electr. Tool 3, 1–4 (2020). (in Chinese) 13. Chen, J., Wang, L.: RLC series circuit of two order mathematical model analysis and circuit design research. Autom. Instrum. 03, 12–15 14. Iman-Eini, H., Liserre, M.: DC fault current blocking with the coordination of half-bridge MMC and the hybrid DC breaker. IEEE Trans. Ind. Electron. 67, 5503–5514 (2020)
Current Source Converter Optimization Method Based on Multi-step FCS-MPC Hao Ding(B) , Quanjie Li, Mingming Li, and Wei Wang School of Electrical Engineering, Yanshan University, Qinghuangdao 066004, China [email protected]
Abstract. Three-phase current source converters have the advantages of bidirectional energy flow, controllable output current, inherent short-circuit protection and fast dynamic response capability. Meanwhile, FCS-MPC has attracted much attention because it exhibits significant advantages when dealing with complex constraints and control objectives. Therefore, it is of great research interest to study the combination of current source converters and FCS-MPC. However, the delay caused by the large online computation, the difficulty of filtering design due to the variable switching frequency, the influence of model parameter variation on the control effect, and the need for higher sampling frequency to achieve better control performance are the bottlenecks that hinder the further development of FCS-MPC. To this end, this paper proposes an optimized multi-step FCS-MPC that combines multi-step FCS-MPC with deadbeat control and duty cycle control to reduce the computational effort while also achieving an approximately fixed frequency, thus reducing the harmonic of grid current and improving the performance of system. Keywords: Multi-step FCS-MPC · Three-phase current source converter · Vector advance screening
1 Introduction The power converter is the core equipment in the system for the development and exploitation of electrical energy. Depending on the energy storage link of the circuit, electrical energy converters can be classified into voltage-source converters and current-source converters. Due to its advantages such as controllable output current, low voltage stress of switching pipe and fast dynamic response capability, current source converter has attracted more and more attention in many fields such as uninterruptible power supply, electric vehicles, new energy generation system and active power filtering, Uninterruptible Power Supplies [1–3]. Current research on current source converters focuses on operation under different working conditions, controllable power factor, low AC current distortion, DC-link ripple suppression, front and rear stage coordinated control. To improve the performance of current converters, many control strategies have been proposed. Among them, FCS-MPC considers various constraints of space state, using discrete characteristic of the circuit © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 583–591, 2023. https://doi.org/10.1007/978-981-99-0631-4_58
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and traverse the switch state in the interrupt execution time take cost function minimum corresponding state the multi-objective control effect of these significant advantages let it become a hot spot in the field of power electronics, however, traditional FCS-MPC just realized the optimality of the single control cycle control variables, unrealized control variables in a number of control cycle optimality. Compared with the single-step model predictive control, the multi-step model predictive control is more suitable for highvoltage and large-capacity situations with lower switching frequency and better control performance. Theoretically, the more the number of prediction steps, the better the control of the system, however, as the number of prediction steps increases, the control algorithm of the system becomes more complex, more computationally intensive and steady state limited [4–6]. For these problems, the literature [7] proposes to take the two vectors with the best performance at the previous moment as alternative vectors for screening the best multistep performance vector at the next predictive period and to choose the best multi-step performance vector that has minimum error at different moments by the cost function, but its switching frequency is not fixed and the selected vectors are not multi-step optimal. The literature [8] proposes to take the optimized solution obtained from single-step predictive control as a basis to construct a finite set of multi-step FCS-MPC, thus significantly reducing the amount of cyclic prediction required, but its computational effort is interconnected with the cascaded modules, thus creating a scenario that is not suitable for a large number of modules. Literature [9] proposed an optimization strategy combining neural networks with multi-step predictive control. Through the control, the zero error tracking between the given value and the output value can be quickly realized, and the performance of AC current is great. When the power grid is unbalanced, the output current can still be balanced and stable output. However, the vector selected by the cost function is still a single vector acting on a single period, so it has the problem of unfixed switching frequency. The literature [10] proposes a new optimization scheme combining duty cycle control with model predictive control, which trades a significant increase in computational effort for a scheme with better grid-side current performance and better steady-state performance, and thus the scheme is not suitable for wide application. In this paper, an optimization multi-step FCS-MPC with good dynamic and steady state performance and small computation is proposed. Compared with the above literatures, the proposed multi-step FCS-MPC is a process of transforming the solution of the best performing vector into the solution of the best performing active vector under the condition of multi-vector action. In addition, the proposed multi-step FCS-MPC can quickly select the best performing vector to reduce the computational burden through the deadbeat control.
2 Fundamental Theory 2.1 Construction of Multi-step Prediction Model The circuit structure is shown in Fig. 1 below. U a , U b , U c are three-phase grid voltages, L, C are AC side filter inductors and filter capacitors, S1–S6 are IGBTs, each IGBT is connected in series with a diode, which is equivalent to building a reverse resistance device, L p , C dc are DC side inductors and capacitors, RL is load, I a , I b , I c are three-phase
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grid currents, isa , isb , isc are current source converter input currents, U ca , U cb , U cc are voltages across the filter capacitors, io is DC side output current.
Fig. 1. Current source converter
The conversion equation of the αβ stationary coordinate system to the three-phase abc coordinate system is as follows: 2 xa + ej2π/3 xb + ej4π/3 xc (1) x = xα + jxβ = 3 The circuit is modeled and discretized using Kirchhoff’s law and Heun’s discretization method, which can derive to the following prediction model. ⎡ ⎤ c (k) U 2 Ts Ts Ts ⎢ ⎥ c (k + 1) U 1 − Ts2 /2LC C 2LC − C ⎢ I (k) ⎥ = (2) 2 2 ⎣ Ts Ts Ts Ts I (k + 1) (k) ⎦ U −L 1 − 2LC L 2LC i(k) c (k + 1) are the predictor variables obtained at moment k + where I (k + 1) and U 1 by using discretization, i(k) is the space current vector of the circuit, each vector corresponds to a different two switches on and are classified into active current vectors and zero current vectors depending on whether the on-off switches are in the same bridge arm. It is worth noting that the grid voltage and grid reference current are rotated and changed at the angular frequency ωg , so the prediction model is as follows: (k + N ) (k) U U = Y ∗ (3) I ref (k + N ) I ref (k) where Y = ejN ωg Ts , N is prediction step size. 2.2 Conventional Multi-step FCS-MPC The essence of traditional multi-step FCS-MPC to find the optimal switching function combination is to list all vector combinations and then find the vector combination with the minimum error from them, thus leading to the following problem:
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(1) By traversing each switch state during the interrupt execution time, the vector combination with the minimum error corresponding to the minimum cost function is selected, so the computation is large. (2) It is difficult to select filter because of the unfixed switching frequency of single vector control in switching period. (3) The condition of screening the multi-step optimal vector is that only one vector is acted in a single switching period, so that the selected best performance muti-step vector still cannot follow the reference current vector at different moments.
3 The Proposed Method See Fig. 2.
Fig. 2. Schematic block diagram of the proposed solution
3.1 Deadbeat Control The math model of converter at k + 2 moments can be obtained from the principle of multi-step FCS-MPC:
c (k + 3) U I (k + 3)
=
Ts 1 − Ts2 /2LC C Ts2 − Ts 1 − L 2LC
Ts2 2LC Ts L
⎡ ⎤ c (k + 2) U ⎢ ⎥ − Ts C ⎢ I (k + 2) ⎥ ⎣U Ts2 (k + 2) ⎦ 2LC i(k + 2)
(4)
When acting on different current vectors, the corresponding predicted values are different, where the predicted value when the zero vector i0 acts:
c (k + 3) U I0 (k + 3)
=
Ts 1 − Ts2 /2LC C Ts Ts2 −L 1 − 2LC
Ts2 2LC Ts L
⎡ ⎤ c (k + 2) U ⎢ ⎥ − Ts C ⎢ I (k + 2) ⎥ ⎣U Ts2 (k + 2) ⎦ 2LC 0
(5)
According to the principle of deadbeat control, a general expression for all vector errors can be constructed with the help of the errors generated by the zero vector as
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follows: I (k + 3) =
− Ts L 1−
Ts2 Ts Ts2 2LC L 2LC
i(k+2) = I0 (k + 3) + 2LC/Ts 2 ⇒ ε = I ref − I
⎛⎡ ⎜⎢ ⎜⎢ ⎝⎣
⎤⎞ ⎤ ⎡ 0 Uc (k + 2) ⎥ ⎢ I (k + 2) ⎥⎟ 0 ⎥⎟ ⎥+⎢ ⎦ ⎣U (k + 2) ⎦⎠ 0 i(k + 2) 0 (6)
⇒ ε(k + 3) = I ref (k + 3) − I0 (k + 3) − = ε0 (k + 3) −
i(k+2) 2LC/Ts2
i(k+2) 2LC/Ts2
From the principle of deadbeat control, it is known that the space current vector closest to ε0 (k + 3) is the best performing active vector, and then the corresponding zero vector can be obtained by checking Table 1. Table 1. Optimal vector combination in different sectors Sector
Zero vector
Active vector
I
1(0–30°)
i7
i1
II
2(30°–60°)
i9
i2
i8
i3
i7
i4
i9
i5
i8
i6
i7
i1
3(60°–90°) III
4(90°–120°)
IV
6(150°–180°)
5(120°–150°) 7(180°–210°) V
8(210°–240°) 9(240°–270°)
VI
10(270°–300°)
I
12(330°–360°)
11(300°–330°)
3.2 Multi-step Optimal Vector Sequence Selection Figure 3 shows the flow chart of vector selection of the proposed scheme at different times. The proposed scheme combines vector advance selection and deadbeat control, so that only six different spatial current vector combinations need to be discriminated in this paper, and the predicted current values of different vector combinations are replaced into the Eq. (7): g(x) = |ε(k + 2)| + |ε (k + 3)|
(7)
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The space current vector combination with the best multi-step performance represents the one that minimizes the error generated at different moments: − → I (selceted ) ⇔ min{g(x), x ∈ [1 ∼ 6]}
(8)
After selecting the best multi-step performance vector, the corresponding zero vector can be directly obtained by looking up Table 1. Finally, the zero vector and the selected best multi-step performance active vector are substituted into the control to synthesis the reference current vector.
Fig. 3. Flow chart of vector selection
4 Simulation Verification In order to better verify the effectiveness of the proposed scheme and the correctness of the theoretical analysis, we write the model prediction algorithm in MATLAB and build the simulation of the three-phase CSR system, whose parameters can be seen in Table 2. Table 2. System parameters System parameters
Value
Phase voltage
220 V
Ts
33 μs
Lp
5 mH
Cdc
940 μF
L
2.5 mH
C
20 μF
4.1 Reference Output Voltage Jump Analysis We can see from Fig. 4 that the reference DC output voltage jump command is executed within 0.3 s. Both the proposed FCS-MPC strategy and the conventional multi-step
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Fig. 4. Output voltage jump (a) Proposed strategy (b) Traditional multi-step FCS-MPC
FCS-MPC take only 0.05 s to complete the process, so the proposed scheme does not degrade the dynamic performance. It is worth noting that the proposed scheme reduces the computational effort while keeping the dynamic performance unchanged. In order to better demonstrate the superiority of the proposed scheme, we take the current source converter as an example and compare the computational effort between the proposed scheme and other multi-step predictive control schemes in Table 3. From the table, it can be seen that the proposed FCS-MPC strategy reduces the number of calculations significantly and also ensures that the performance of the chosen vectors is the best over multiple prediction periods. Table 3. Computational comparison Method
Number of calculations
Whether the selected vector is multi-step optimal
Traditional multi-step FCS-MPC
90
Yes
[7]
27
No
[8]
11
No
Proposed
12
Yes
4.2 Analysis of Output Voltage and Grid Current Figure 5 shows the output voltage and grid current waveforms of different schemes. We can see from the Fig. 5 that the proposed scheme presented a lower output voltage ripple 0.3V versus the 1V obtained with the traditional multi-step predictive FCS-MPC, which means a 70% reduction in output voltage ripple. It is worth noting that the proposed scheme with duty cycle control not only has a better performance of output voltage, but also the grid-side current performance is improved with a lower degree of grid-side current distortion [11]. As shown in Fig. 5, the proposed scheme presented a lower THD 2.31% versus the 3.58% obtained with the traditional multi-step predictive FCS-MPC, which means a better performance of grid current.
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Fig. 5. Diagram of output voltage and grid current (a) Proposed strategy (b) Traditional multi-step FCS-MPC
5 Conclusion In this paper, an optimization method that combines deadbeat control, duty-cycle control and multi-step FCS-MPC is proposed. The proposed optimization scheme achieves a significant reduction in computational effort by realizing deadbeat control and dutycycle advance screening, while ensuring that the selected vector is multi-step optimal. Moreover, the control algorithm of the proposed scheme is simple and easy to implement. Acknowledgments. This project was supported by the National Natural Science Foundation of China (61903321), the Science and Technology Program of Higher Education Institutions of Hebei Province (QN2019016).
References 1. Liu, P., Wang, Z., Xu, Y., Xiao, H., Li, Y.: Optimal overlap-time distribution of space vector modulation for current-source rectifier. IEEE Trans. Ind. Electron. 68(6), 4586–4597 (2021) 2. Xing, L., Wei, Q., Li, Y.: Transformerless series-connected current source converter. IEEE Trans. Power Electron. 37(8), 8811–8815 (2022) 3. Yang, Y., et al.: Zero dynamic DC-link voltage control for current source converter under grid disturbances. IEEE Trans. Power Electron. 37(1), 855–864 (2022) 4. Hu, J., Shan, Y., Cheng, K., Islam, S.: Overview of power converter control in microgrids— challenges, advances, and future trends. IEEE Trans. Power Electron. 37(8), 9907–9922 (2022) 5. Chen, Z., Qu, W.: Model predictive current control for permanent magnet synchronous motors based on PID-type cost function. Trans. China Electrotech. Soc. 36(14), 2971–2978 (2021). (in Chinese) 6. Liu, Z, Du, G., Du, F.: Research status and development trend of finite set model predictive control in power electronic system. Trans. China Electrotech. Soc. 32(22), 58–69 (2017). (in Chinese) 7. Xu, Y., Sun, Y., Hou, Y.: Multi-step model predictive current control of permanent-magnet synchronous motor. J. Power Electron. 20(1), 176–187 (2019). https://doi.org/10.1007/s43 236-019-00024-3
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8. Guo, P, He, Z., Luo, A., et al.: Circulation control strategy of modular multilevel converter based on multi-step model predictive control. Autom. Electr. Power Syst. 41(16), 137–143+157 (2017). (in Chinese) 9. Yu, Y., Wang, X.: Multi-step predictive current control for NPC grid-connected inverter. IEEE Access 7, 157756–157765 (2019) 10. Xue, C., Song, W., Wu, X., Feng, X.: A constant switching frequency finite-control-set predictive current control scheme of a five-phase inverter with duty-ratio optimization. IEEE Trans. Power Electron. 33(4), 3583–3594 (2018) 11. Wang, Z., Zhang, Y., Tong, C.: Research on an improved model predictive control method of three-phase PWM rectifier. Electr. Mach. Control 24(7), 73–81 (2020). (in Chinese)
A Fixed-Admittance Modeling Method of Power Electronic Switches Based on State Initializations Bin Zhou, Guangsen Wang, Weichao Li(B) , Kang Wang, and Guisheng Jie National Key Laboratory For Vessel Integrated Power System Technology, Naval University of Engineering, Wuhan 430033, China {guangsenwang,zhenyujie}@sina.com, [email protected]
Abstract. The constant admittance model of power electronic switches adopt an inductance and a capacitance to simulate the on-off state of the switch respectively, which is also called L/C equivalent model. Its constant switching admittance is conducive to simplifying the simulation calculation while its virtual power loss affects the accuracy of the model seriously. Therefore, a modeling method of constant admittance of power electronic switches based on state initializations is proposed in this paper, where initial state values of the equivalent LC elements of the switch model are obtained through voltage and current relationships between the ideal switch and the external circuit, then an accurate L/C equivalent model with the ability of simulating fault injection is built. The factors affecting the accuracy of the L/C equivalent model are analyzed, and three typical circuits’ off-line simulations under normal and fault conditions are carried out. Simulation results show that the switch model established based on the proposed method solves the problem of virtual power loss of the classical L/C equivalent model and simulates the short-circuit and open-circuit faults of switches correctly. Compared with the existing virtual power loss elimination methods, our method is based on a single switch directly rather than specific topologies, and has better universality and simple implementation. Keywords: Power electronic switch · Fixed admittance model · Virtual power loss · State initialization · Fault injection
1 Introduction With the advancement of semiconductor technology, power electronic switches have evolved into the key components for power conversion in new energy microgrids, rail transit, and other fields [1, 2]. The modeling of power electronic switches is a challenging subject in the small step electromagnetic transient (EMT) simulation. On the one hand, the switch circuit’s complex and flexible topologies and its nonlinear characteristics make it difficult and time-consuming to solve circuit equations; on the other hand, the special high-frequency properties of power electronic switches and the application trend toward high-frequency have extremely strict requirements for the simulation step size. © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 592–603, 2023. https://doi.org/10.1007/978-981-99-0631-4_59
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For wide bandgap devices like SiC and GaN, whose working frequency has exceeded 100 kHz, a simulation step size of a sub-microsecond or even a hundred nanosecond is required [3]. The two primary switch models employed in the present EMT simulation are the binary-value resistance model and the L/C equivalent model. To resolve the issue of the ideal switch model making the circuit topology and equation order time-varying, Dr. H. W. Dommel proposed the binary-value resistance model [4], but its admittance still change with the switch state. Therefore, this model is mostly used for offline EMT simulation with low real-time requirements [5–7]. Hui et al. proposed [8, 9] and Pejovi et al. developed [10] the L/C equivalent model, which is widely applied in mainstream realtime simulation platforms like RT-Lab and RTDS. Due to the constant switch admittance, the L/C equivalent model simplifies the calculating of circuit equations to a straightforward matrix-vector multiplication operation. Its drawback is that, for switching frequencies higher than 10 kHz, the virtual power loss is significantly higher than the real switching loss [11]. The L/C equivalent model has been optimized by many researchers. To minimize the power loss, Razzaghi R et al. optimized the switch’s equivalent admittance value by defining the virtual power loss as the energy lost by the analogous LC element [12–14]. By matching the system’s greatest damping point, XU J et al. suggested a generalized parameterized L/C equivalent model hastens the convergence of the error response [15– 17]. Although the concept of the method restricts its range of use, it can remove virtual power loss. Larijani M R et al. applied a comparable approach to examine the system state-space equation’s characteristic root distribution [18]. Additionally, several studies use the technique of altering the L/C equivalent model’s circuit configuration. In [19], the R-C series branch replaced the equivalent capacitance branch to minimize numerical oscillation when the switching state changed, however, it is challenging to determine the properties of the damping resistance. In [20, 21], a negative impedance or a compensation source was introduced to the switching equivalent circuit, which may change the stability of the system or relies on the topology of the circuit seriously. This paper proposes a state initialization-based method for power electronic switch constant admittance models. In addition to resolving the virtual power loss issue of the classical L/C equivalent model, the accurate L/C equivalent model constructed by methodology also can simulate a single switch’s fault injection.
2 L/C Equivalent Model 2.1 Classical L/C Equivalent Model In classical L/C equivalent model, the switch is equivalent to an inductance branch L when it is on, and to a capacitance branch C when it is off. After being discretized by the numerical integration method, the differential circuits of L and C can be unified as the same Norton equivalent circuit, where an equivalent admittance Gs is parallel with a historical current source ish [9]. The Gs of the switch will keep constant while the ish updates with switch state changes.
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The ish and Gs based on BE discrete are as follows, taking into account that Backward Euler (BE) method can reduce numerical oscillations: ish (t) = s(t)is (t − T ) − s˜ (t)Gs us (t − T )
(1)
Gs = s(t)T /L + s˜ (t)C/T
(2)
where, us (t − T ) and is (t − T ) are the switching voltage and current of the previous step size, s(t) is the switch’s on-off state (“1” means on, “0” means off), and T is the simulation step size. Finally, the L/C equivalent model’s voltage-current relationship can be written as: is (t) = us (t)Gs + ish (t)
(3)
2.2 Virtual Power Loss Assume that the switch has been in a steady state before the operation, and its on and off voltage have steady-state values of 0 and U s (t), respectively, its on and off current have steady-state values of I s (t) and 0 respectively. When the switch is at the initial time of conduction, the historical current source’s initial value, ish (t+), is 0, as is (t − T ) is equal to 0. Similarly, when the switch is at the initial moment of turning off, us (t − T ) is equal to 0, therefore the corresponding ish (t+) is also 0. Equation (4) has illustrated the steady-state value I sh (t) of the historical current source of the L/C equivalent model. Evidently, the difference between ish (t+) and I sh (t) is enormous. Ish (t) = s(t)Is (t) − s˜ (t)Gs Us (t)
(4)
In other numerical integration methods, such as the trapezoidal method, ish (t+) may not necessarily be 0, but the difference between ish (t+) and I sh (t) is prevalent. It is this difference that causes abrupt changes in us (t), is (t), and other state quantities, namely “over pulse”. In the process of us (t) and is (t) converging to the steady state value, the switch will generate a virtual power loss much greater than the actual switching loss. From an energy standpoint, the energy in LC is transferred step by step in the simulation process in the form of ish (t). If ish (t+) is 0, the stored energy is discarded [18, 20]. From the perspective of the transient response of dynamic components, if ish (t+) is 0, then the LC only has zero state response. The convergence process is to reconstruct the correct zero input response. The faster the convergence, the smaller the power loss. In addition to the over pulse amplitude, system damping characteristics, and other factors, the minimum pulse width is crucial in determining whether us (t) and is (t) can recover to the steady state before the switch activates once more.
3 Virtual Power Loss Elimination In this paper, a fixed-admittance modeling method of power electronic switches based on state initialization has been proposed. The voltage-current relationship between the
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is ideal switch
us
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the external circuit uref (t)={uin(t), uload(t-T), us_i(t-T)...} iref (t)={iin(t), iload(t-T), is_i(t-T)...}
Fig. 1. The method of this paper
ideal switch and the external circuit is used for figuring out the initial state value of a single switch. As shown in Fig. 1, based on the ideal switch model, the relationships between the switching voltage us (t) and the external circuit voltage, as well as the switching current is (t) and the external circuit current, are analyzed. Then, using the relationship to figure out the reference voltage uref (t) and reference current iref (t) that can be used as the initial state value of swithes. The historical current source of the switch is derived using the formula shown below. ish (t) = s(t)iref (t) − s˜ (t)Gs uref (t)
(5)
uref (t) can be input voltage uin (t), load voltage uload (t − T ), and voltage of other switches us_i (t − T ) or their combination. Similarly, iref (t) can be the input current iin (t), load current iload (t − T ), and the current is of other switches is_i (t − T ) or their combination. For example, a Boost converter in a current discontinuous state and a neutral point clamped (NPC) three-level converter are typical topologies that do not meet the condition that the number of switches is paired and the on-off state is complimentary, but they can complete the state initialization of each switch according to the uref (t) and iref (t) listed in Table 1 and Table 2. Table 1. Reference initial values of switches in the Boost converter s(t)
0 (current continuous)
0 (current discontinuous)
1
Diode
−uload (t − T )
uin (t) − uload (t − T )
iL (t − T )
IGBT
uload (t − T )
uin (t)
iL (t − T )
In the table, uref (t) and iref (t) can also be other values, which are not unique. iL (t − T ) in Table 1 is the inductance current of the previous step. In Table 2, Q1–Q4 and D5–D6 correspond to 4 IGBTs and 2 diodes of a three-level half-bridge from top to bottom respectively. The iref (t) of Q2 and Q3 and the uref (t) of D5 and D6 have more than one value. Their actual values are according to the working state of the circuit. For example, when Q2 is on, iload (t − T ) may flow out in the forward direction through Q2, or it may flow in the downstream direction through D6. In some cases, the uref (t) of D5 and D6 is 0, which is based on the assumption that the voltage of the two supporting
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s(t)
Q1
Q2
D5
Q3
Q4
D6
0
uin (t)/2
uin (t)/2
− uin (t)/2 or 0
uin (t)/2
uin (t)/2
− uin (t)/2 or 0
1
iload (t − T )
iload (t − T ) or 0
iload (t − T )
− iload (t − T ) or 0
− iload (t − T)
− iload (t − T)
capacitors (C1 and C2) on the DC side is balanced. The theoretical value should be: (VC1 − VC2 )/3
(6)
The method proposed in this paper expands the application domain of state initialization to a single switch, enabling to simulate fault injection. Switches S1 and S2 can be initialized using the reference values in the following table in the two-level half-bridge circuit, for instance, when taking into account open circuit and short circuit circumstances, where S(t) is the combination of their on-off states (Table 3). Table 3. Reference initial values of switches in the two-level half-bridge circuit S(t)
01
10
00
11
S1 S2
uin (t)
iload (t − T )
uin (t)/2
iload (t − T ) + uin (t)GS1 /2
− iload (t − T )
uin (t)
uin (t)/2
− iload (t − T ) + uin (t)GS2 /2
4 Factors Affecting Model Accuracy 4.1 Switch Device Characteristics The on-off state of fully controlled switching devices is entirely under the control of their pulse signals. However, uncontrolled and semi-controlled switching devices commutate naturally, it is important to choose whether to turn them on or off based on the polarity of their voltage and current. Taking the uncontrolled device diode as an example, its on-off state expression in numerical simulation is [24]: s(t) = s(t − T )(i(t − T ) > 0) + s˜ (t − T )(u(t − T ) > 0)
(7)
Because the on-off state of current step is dependent on the on-off state of the previous step and the polarity of the voltage or current, the on-off state of the diode always lags behind the theoretical value. Therefore, the diode will appear delayed on and delayed off in the simulation. The historical current source based on the wrong on/off state will
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deviate from the steady state value, which will cause the switching voltage and current to produce an over pulse. Taking Boost converter as an example, this paper introduces the idea of initializing uncontrolled and semi controlled switching devices. In Fig. 2, the subscripts “D” and “T ” stand for diode and IGBT, respectively. S(t) stands for the combination of diode and IGBT on-off states, and “00” and “11” stand for the combination of diode’s delayed on-off and delayed on-off, respectively. S(t)={sD(t), sT(t)} Y
= S(t-T) N
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uD(t-T), iD(t-T) uT(t-T), iT(t-T)
Fig. 2. Reference initial values of switche histiry currents in the Boost converter
Firstly, detect whether S(t) has changed at the start of each simulation step. If it changes, start the state initialization process. If not, the switching voltage and current from the previous step will be used to update the historical current source normally. Secondly, correct the on-off state of the diode such that it is treated as on when S(t) is “00” and as off when S(t) is “11”, respectively. Because S(t) will also be “00” when the inductance current is discontinuous, the requirement that the inductance current iL be larger than 0 distinguishes it from the delayed conduction of a diode. Finally, the reference value for the Boost converter’s switching history current source is obtained. Semi-controlled thyristors will postpone shutdown rather than delay conduction. As to IGBT anti-parallel diode module, if it is seen as a whole and the on-off status is updated by Eq. (8) [24], it will postpone switching on and delaying switching off when the diode is freewheeling. Similar to how diodes are handled, these circumstances can also be handled. s(t) = g(t) + s(t − T )(i(t − T ) ≤ 0) + s˜ (t − T )(u(t − T ) < 0)
(8)
4.2 Equivalent Element Characteristics The on-off state of the switch is equivalently represented by inductance L and capacitance C in the L/C equivalent model. The voltage and current of the L/C equivalent model
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satisfy the following criteria based on the volt-ampere characteristics of LC elements: us (t) = (is (t) − is (t − T ))/Gs (9) is (t) = Gs (us (t) − us (t − T )) It can be determined that the creation of the on voltage occurs simultaneously with a change in the switch on current and that a change in the off voltage likewise result in a change in the off current. In other words, the L/C equivalent model’s on voltage and off current may not be zero. Equation (7) may typically determine the switch status when the conduction voltage produced by the equivalent inductance is more than zero; if the conduction voltage is less than zero, it will not meet the criterion of switch conduction in Eq. (7). Similar to this, if the equivalent capacitor’s turning off current is less than zero, it does not satisfy the equation’s switching off condition. The on-off state of uncontrolled and semi-controlled switching devices therefore cannot be determined by the polarity of voltage or current, and corresponding changes must be performed after taking into account the device characteristics of a single switch. For example, the expression of diode on-off state can be changed to: s(t) = s(t − T )(i(t − T ) > IsON ) + s˜ (t − T )(v(t − T ) > UsOFF )
(10)
wherein, U sON and I sOFF are the maximum amplitudes of the switch on voltage and turn off current respectively.
5 Simulation Analysis 5.1 Example 1: A Boost Converter in Normal Conditions To verify the accurate L/C model built with the proposed method has a wider range of applications, this section takes the Boost converter under discontinuous current as simulation examples. Set the simulation model parameters of the Boost converter according to the following table to ensure that it works in the discontinuous inductance current state (Table 4). Table 4. Parameters of the Boost converter Parameters
Values
U in /V
24
L/mH
0.05
C/mF
0.2
R/
10
Duty cycle/%
50
Switching frequency/kHz
10
The following three switch models are used to conduct off-line simulation of the calculation example, and the simulation step size is 1us.
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1) Binary-value resistance model (Ron /Roff equivalent): Use the switch module in the Simulink/Specialized Power Systems toolbox to build the converter model, the size resistance of the switch takes the default values: infinity and 1 m. Since the model is close to the ideal switch, it will be used as a benchmark below. 2) Classical L/C equivalent model: EMT simulation process is established in the Sfunction of Matlab, the converter constant admittance model based on the classical L/C switch model is built. The Gs values of diode and IGBT are set as 0.35S and 1.35S respectively according to the method in literature [19]. 3). Accurate L/C equivalent model: The accurate L/C switch model established by the proposed method is used to replace the switch model in 2). The Gs value is set to 1S, and the U sON and I sOFF of the two switches are approximately set to 1.0 V and 0.2 A.
t Fig. 3. On-off state, voltage and current of the Diode
Figure 3 displays the voltage and current waveforms of a diode in the on-off state while the Boost converter’s inductance current is discontinuous. When the current is cut off, the voltage of the classical L/C equivalent model has not yet crossed zero and is still on. This means that the voltage does not change to zero in the classical L/C equivalent model immediately from off to on but instead begins to naturally exchange current and maintains the off state until the voltage crosses zero. This demonstrates that when the current is discontinuous, the classical L/C equivalent model can no longer accurately represent the genuine on-off state of a diode.
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p
Additionally, the voltage and current of the classical L/C equivalent model have a significant overshoot when a diode is turned on and off since the initial value of the state is zero. The dual value resistance model and the correct L/C equivalent model, however, have more uniform waveforms. It is properly shut off when the current is sporadic. As soon as the switch is activated, it reaches the steady state without experiencing an over pulse. The two L/C equivalent models in the enlarged detail drawing have a turn-off current of 0.025 A and a conduction voltage of roughly −0.6 V. Despite having modest values, they are sufficient to influence how the switch’s on-off state is determined. After about 10 simulation steps, the conventional L/C equivalent model’s voltage and current over-pulse converge, resulting in a significant power loss. As seen in Fig. 4, the maximum power loss even approaches 1.2 kW. The exact L/C equivalent model also has a maximum instantaneous power of no more than 15 W when the switch is engaged. Because the initial value of the switch’s state is taken from the previous simulation step and cannot be exactly equal to the actual value of this step, the voltage and current of the switch fluctuate dramatically.
t Fig. 4. Diode instantaneous power of the Boost converter
Because the switch has on voltage and off current, the L/C equivalent model has a power of nearly 1.4 W after waveform convergence, while the power corresponding to the dual resistance model is less than 0.02 W. 5.2 Example 2: A Two-Level Bridge Converter in Fault Injection Conditions Take a two-level bridge converter as another example with the Gs set to 0.302S [19]. The pulse signal of tube S1 on phase a half-bridge is set to 0 in 42.5–47.5 ms of simulation time to mimic the open circuit fault and to 1 in 70–100 ms to simulate the short circuit fault to test the applicability of the exact L/C model developed using the method suggested in this research. Based on the binary-value resistance model and the accurate L/C equivalent model, Fig. 5 shows the a-phase output voltage and current of the two-level bridge converter. The anti-parallel diode of S2 begins to freewheel after the fault occurs because the phase current is greater than 0 before the open circuit fault happens. S2 will always be on and the phase voltage will always be −120 V before the phase current passes through zero. After the phase current crosses zero, S2’s pulse signal once more controls its on-off status while the phase voltage synchronously alternates between −120 V and 0 V. The phase voltage switches between 0 V and 120 V with the on-off state of S2 following the
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occurrence of the short circuit fault, and the phase current waveform as a whole shift to the positive direction.
i
t
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Fig. 5. Current and voltage comparisons of phase a from two-level bridge converter
The two switching models’ phase voltage and current waveforms are fairly similar. The accurate L/C equivalent model’s current error is kept at 0.1 A in comparison to the dual value resistance model during normal operation and rises to a maximum of 0.54 A after an open circuit fault. In general, even under fault situations, the accurate L/C equivalent model built using the technique in this study still maintains high simulation accuracy.
6 Conclusion This paper presents a modeling method of power electronic switch constant admittance based on state initialization The initial state value of the equivalent LC of the constant admittance switch model is determined through the relationship between the ideal switch and the voltage and current of the external circuit. The typical topology simulation model is built with the proposed L/C equivalent model, and the off-line simulation is conducted under both normal and fault situations. The simulation results demonstrate that the accurate L/C equivalent model has no virtual power losses and performs better in terms of universality and implementation than existing optimization strategies.
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References 1. Wang, X., Zhang, B., Qiao, P., et al.: A block hierarchical parallel method for real-time simulation of microgrid. Trans. China Electrotech. Soc. 32(7), 104–111 (2017). (in Chinese) 2. Hao, Q., Ge, X., Song, W., et al.: Microsecond hardware-in-the-loop real-time simulation of electric traction drive system. Trans. China Electrotech. Soc. 31(8), 189–198 (2016). (in Chinese) 3. Biela, J., Schweizer, M., Waffler, S., et al.: SiC versus Si-evaluation of potentials for performance improvement of inverter and DC-DC converter systems by SiC power semiconductors. IEEE Trans. Power Electron. 58(7), 2872–2882 (2011) 4. Dommel, H.: EMTP Theory Book. Microtran Power System Analysis Corporation, Vancouver, British Columbia, 2nd edn. (1992) 5. Wang, C., Gao, F., Li, P., et al.: Adaptability analysis of typical models of power electronic devices. Power Syst. Autom. 36(6), 63–68 (2012). (in Chinese) 6. Hadizadeh, A., Hashemi, M., Labbaf, M., et al.: A matrix-inversion technique for FPGA-based real-time EMT simulation of power converters. IEEE Trans. Ind. Electron. 66(2), 1224–1234 (2018) 7. Wang, C., Ding, C., Li, P., et al.: Research on FPGA-based transient real-time simulation of distribution network (1): realization of functional modules. Proc. Chin. Soc. Electr. Eng. 34(1), 161–168 (2014). (in Chinese) 8. Hui, S., Christopoulos, C.: A discrete approach to the modeling of power electronic switching networks. IEEE Trans. Power Electron. 5(4), 398–403 (1990) 9. Hui, S., Morrall, S.: Generalised associated discrete circuit model for switching devices. IEE Proc. Sci. Meas. Technol. 141(1), 57–64 (1994) 10. Pejovic, P., Maksimovic, D.: A method for fast time-domain simulation of networks with switches. IEEE Trans. Power Electron. 9(4), 449–456 (1994) 11. Jin, X.: Research and application of general power electronics real-time simulation method. Shanghai Jiaotong University (2019). (in Chinese) 12. Razzaghi, R., Foti, C., Paolone, M., et al.: A method for the assessment of the optimal parameter of discrete-time switch model. Electr. Power Syst. Res. 115, 80–86 (2014) 13. Mu, Q., Zhou, X., Wang, X., et al.: Small-step switching error analysis and parameter setting for real-time simulation. Proc. Chin. Soc. Electr. Eng. 33(31), 120–129 (2013). (in Chinese) 14. Tang, Y., Guo, X., Zhang, Z., et al.: Parameter optimization method of ADC model based on real-time simulation. Electr. Power Autom. Equip. 40(03), 214–218 (2020). (in Chinese) 15. Xu, J., Wang, K., Li, G., et al.: A general small time-step model based on the parameterized history current sources. Chin. Soc. Electr. Eng. 38(6), 1647–1654 (2018). (in Chinese) 16. Xu, J., Wang, K., Li, G., et al.: Fixed-admittance modeling of power electronic converters using response-matching technique. Chin. Soc. Electr. Eng. 39(13), 3879–3889 (2019). (in Chinese) 17. Wang, K., Xu, J., Li, G., et al.: A generalized associated discrete circuit model of power converters in real-time simulation. IEEE Trans. Power Electron. 34(3), 2220–2233 (2018) 18. Rezaei Larijani, M., Zolghadri, M.R.: Design and implementation of an ADC-based real-time simulator along with an optimal selection of the switch model parameters. Electr. Eng. 103(5), 2315–2325 (2021). https://doi.org/10.1007/s00202-021-01237-1 19. Maguire, T., Giesbrecht, J.: Small time-step (Rout2
Yes
Rin30 & M13m>0, M23 VC2 , k > 0.5, k*t(V01n ) > 0.5t(V01n ), then the action time of V01n increase, and then the decreasing trend of VC1 increases, and the increasing trend of VC2 . If VC2
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> VC1 , k < 0.5, k*t(V01n ) < 0.5t(V01n ), then the action time of V01n decrease, which weakens the decreasing trend of VC1 and the increasing trend of VC2 . If the ia direction is negative, the converter is in the inverter state, and V01n discharges capacitor C2 and charges C1 . If VC1 > VC2 , k > 0.5, k*t(V01n ) > 0.5t(V01n ), then the action time of V01n increase, so that the decreasing trend of VC2 increases, and the increasing trend of VC1 increase. If the action time of V01n is not changed, the purpose of voltage sharing cannot be achieved. VC1 will increase to the voltage tending to the DC bus, and VC2 will approach 0. At this time, if k1 = 1 − k, k1 *t(V01n ) < 0.5t(V01n ), then the trend of VC2 decreasing will be weakened, and the trend of VC1 increasing will be weakened, so as to realize the purpose of NP voltage balance. If VC2 > VC1 , k1 < 0.5, k1 = 1 − k, k1 *t(V01n ) > 0.5t(V01n ), the action time of V01n increase. In turn, the increase trend of VC1 is strengthened, and the decrease trend of VC2 . Since the total Vdc is unchanged, the capacitance voltage error is generated and then adjusted through PI control, and finally the capacitance voltage error becomes 0, that is, the midpoint potential balance of upper and lower capacitors is achieved.
4 Simulation and Verification The design is carried out under the conditions that the switching frequency is 20 kHz, the three-phase power grid voltage amplitude is 380 V, the rated power is 5 kW, and the output DC voltage is 650 V. In order to verify the engineering practical and application-oriented in this paper, the simulation design is shown in Table 1. Table 1. Experimental parameters of T-type three-level rectifier. Experimental parameters
Value
AC inductor
1.3 mH*3
Output DC capacitor
1000 μF*2
Current limiting resistance
17.5 *3
Load
84.5
Voltage outer loop proportional coefficient/resonant frequency
4.2658/15 Hz
Proportional coefficient of current inner loop/cut-off frequency/resonant frequency
8.2224/20πHZ/200 Hz
Figure 10 shows the waveform of DC voltage and three-phase AC current obtained in the soft start experiment. The process of soft starting is to cut off the series resistance in 0.04 s, so that the voltage increases in the process of just starting is gentle, and then the control of double closed loops is switched to quickly stabilize the voltage. The peak current of soft start is limited within 40A by current limiting resistor, which is 80% lower than that without soft start circuit. The overshoot of output voltage is also reduced by 85%.
Optimized Design of T-type Three-Level Rectifier 1200 800 400
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Fig. 10. Influence waveform of soft start circuit.
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Fig. 11. DC output voltage waveform.
Figure 11 shows the DC output voltage waveform of different control loops. The DC output voltage waveform of QPR control is stable in 0.07 s, and the overshoot of double PI control is greater under the same circuit parameters, and it is stable in about 0.1 s. The comparative simulation verifies the fast dynamic response brought by QPR control loop. The waveform of capacitor voltage is placed in Fig. 12. The DC side capacitor achieves voltage sharing and the neutral point potential is basically balanced. 350 300 250 200 150 100 50 0
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Fig. 12. DC capacitor voltage waveform.
Figure 13 shows the waveform of output voltage and AC current obtained from the load switching experiment. In 0.19 s, when the load suddenly changes and the resistance is switched from 84.5 to 60 , the DC side output voltage drops 2 V, which is about 0.3% of the stable value. It was basically stable in 0.24 s, and the recovery time was 0.05 s. The load shedding experiment proves that the DC side voltage has good stability and anti-interference performance.
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650
Vo
649 648
0.12 0.14 0.16 0.18 0.20 0.22 0.24 Time (s)
20 10 0 -10 -20
Ia Ib Ic
0.12 0.14 0.16 0.18 0.20 0.22 Time (s)
Fig. 13. Waveform diagram of output voltage and current in load shedding experiment.
5 Conclusion In terms of the defects of the traditional PI controller, the current inner loop takes a double closed loop control strategy based on the QPR controller, which effectively achieves the following of the current with no static error and enhances the adaptability of the controller to the fluctuations of the fundamental wave and harmonic frequency of the grid voltage. The design scheme of control loop parameters is provided. At the same time, the necessary simulation verification is carried out to verify the reliability of the design which provides a good reference value for the relevant control of T-type three-level rectifier.
References 1. Lim, Y., Lee, J., Lee, K.: Advanced speed control for a five-leg inverter driving a dual-induction motor system. IEEE Trans. Industr. Electron. 66(1), 707–716 (2019) 2. Hu, Y., Huang, S., Wu, X., Li, X.: Control of dual three-phase permanent magnet synchronous machine based on five-leg inverter. IEEE Trans. Power Electron. 34(11), 11071–11079 (2019) 3. Wang, R., Yuan, S., Liu, C., Guo, D., Shao, X.: A three-phase dual-output T-type three-level converter. IEEE Trans. Power Electron. 38, 1844–1859 (2022) 4. Jin, Y., Zhang, F., Liang, L.X., et al.: Research on planning optimization of electric vehicle charging station. Autom. Instrumentation 2017, (02). (in Chinese) 5. Wu, H.H.: Research on fault diagnosis method of power electronic rectifier. Anhui University of technology (2017). (in Chinese) 6. Long, L.J.: Research on three-phase three wire Vienna rectifier. Zhejiang University (2019). (in Chinese) 7. Ma, F.J., Kuang, D.X., Tian, X., Zhu, Z., Wang, Y.C., Wang, L.N.: A natural switching current peak control strategy for three-phase rectifiers. J. Hunan Univ. (Natural Science Edition) 49(02), 169–175 (2022) 8. Zhou, S.Q.: Research on the control strategy of T-type three-level inverter. Huazhong University of Science and Technology (2019). (in Chinese) 9. Zhou, J.Y., Ojo, J.O., Tang, F., et al.: A carrier-based discontinuous PWM for single and parallel three-level T-type converters with neutral-point potential balancing. IEEE Trans. Ind. Appl. 57(5), 5117–5127 (2021) 10. Zhao, R.D., Wang, C., Loh, P.C., et al.: A practical core loss estimation method for three-phase three-level grid-connected inverters. IEEE Trans. Power Electron. 35(3), 2263–2267 (2020) 11. Zhao, X.K.: Chen Y.D.: Design of dynamic weighted optimal switching vector MPC for three-level rectifier. Power Electron. 55(1), 116–120 (2021). (in Chinese) 12. Schweizer, M., Kolar, J.W.: Design and implementation of a highly efficient 3-level T-type inverter for low-voltage application. IEEE Trans. Power Electron. 28(2), 899–907 (2013)
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13. Choi, U.M., Lee, H.H., Lee, K.B.: Simple neutral-point voltage control for three-level inverters using a discontinuous pulse width modulation. IEEE Trans. Energy Convers. 28(2), 434–443 (2013) 14. Park, Y., Sul, S.K., Lim, C.H., et al.: Reliability improvement of a t-type three-level inverter with fault-tolerant control strategy. IEEE Trans. Power Electron. 30(5), 2660–2673 (2015) 15. Lee, J.S., K. Lee, B.: Time-offset injection method for neutral-point AC ripple voltage reduction in a three-level inverter. IEEE Trans. Power Electron. 31(3), 1931–1941 (2016) 16. Adhikari, J., Prasanna, I.V., Panda, S.K.: Reduction of input current harmonic distortions and balancing of output voltages of the vienna rectifier under supply voltage disturbances. IEEE Trans. Power Electron. 32(7), 5802–5812 (2017) 17. Du, W.C.: Design of T-type three-level rectifier system based on quasi proportional resonance control. Automation and instrumentation (2017) (11). (in Chinese) 18. Meng, J.H., Shi, X.C., Fu, C., et al.: Optimal control of photovoltaic grid connected current based on PR control. Power Automation Equipment 34(2), 42–47 (2014). (in Chinese) 19. Wang, S.: Research on three-phase voltage source three-level PWM rectifier. Beijing Jiaotong University (2015). (in Chinese) 20. Zhang, Y.Y.: Research on low power modular three-phase Vienna rectifier power supply. Beijing Jiaotong University (2020). (in Chinese)
DC-Side Voltage Harmonic Control of a Three-Phase Current Source Rectifier Under Unbalanced AC Voltage Conditions Jixuan Zhang(B) , Wenping Cao, Wenjie Zhu, Huajian Zhou, and Cungang Hu School of Electrical Engineering and Automation, Anhui University, Anhui 230000, China [email protected]
Abstract. This paper proposes a control strategy that can suppress the doublefrequency fluctuation of the DC-side voltage for a three-phase current source rectifier under unbalanced ac input conditions. The proposed method obtains the reference value of the grid voltage and current at any time by extracting the positive and negative sequence components of the grid-side voltage, at the same time, starting from the complex power of the three-phase current source rectifier unbalanced system, set the power and reactive power that generate the double frequency fluctuation of the DC voltage to zero, then solve the given value of the grid current. The given value is used to calculate the control quantity at the next moment, so as to remove the second harmonic of the DC-side voltage and ensure that the grid side voltage and current being in the same phase. The proposed control strategy does not need to sample the three-phase input current, it can eliminate the double-frequency fluctuation of the DC-side voltage. A simulation model is built in MATLAB to verify the effectiveness of the proposed method. Keywords: Current source rectifier · DC-side harmonics · Unbalanced grid voltage
1 Introduction Three-phase current source rectifiers (3ph-CSR) are widely used in communication, building power supply and other low-voltage DC power distribution systems due to their desirable features [1], such as unity power factor, constant dc bus voltage, and sinusoidal input currents [2]. Compared with the three-phase voltage source rectifier(3ph-VSR), the 3ph-CSR not only has a wider range of output voltage, but also has a small starting current, which has a good application prospect [3]. In practical applications, the three-phase input voltage is often in an unbalanced state, which will lead to the appearance of odd harmonics of the rectifier input current and even harmonics of the output voltage ripple, it will reduce the performance of the three-phase rectifier. In order to improve the performance of the three phase PWM rectifier under the condition of unbalanced AC input, scholars have proposed various control strategies [4– 7]. In [4], by changing the DC side topology of the voltage source rectifier, the original capacitive filter is replaced by an active compensator, and the DC side voltage ripple is © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 1160–1169, 2023. https://doi.org/10.1007/978-981-99-0631-4_116
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suppressed by controlling the compensator. In [5], based on the analytical expressions for the input and output instantaneous power, a simple cascaded PI control scheme is developed to ensure that the DC link voltage remains constant. In [6], proposed resistance simulation control for suppressing inrush current under unknown input. Furthermore, to deal with power oscillations caused by unbalanced grids, extended resistance simulation control is proposed in [7]. It is worth noting that the above control methods are all suitable for VSRs, and whether it can be extended to 3ph-CSR under the condition of unbalanced grid input remains to be discussed. Recently, with the in-depth research on 3ph-CSR, some scholars have proposed targeted control strategies [8, 9]. In [8], A simple transfer matrix is derived from the sampled input voltage. The differential operation of the sampled voltage realized by the discrete control of the digital controller can effectively suppress the even harmonics of the output voltage ripple and the odd harmonics of the input current. Subharmonic. Whereas in [9], the proposed method constructs a virtual voltage pair with two separate adaptive parameters, one to regulate the oscillating power between active and reactive power, and the other to control the average reactive power. Then, the rectifier simulates the variable conductance under the virtual voltage pair to adjust the average active power, so as to achieve the purpose of eliminating the current harmonics on the grid side. This paper proposes a control strategy that can suppress the double-frequency fluctuation of the DC side in view of the problem that the voltage of the DC side will appear double-frequency fluctuation when the 3ph-CSR works under the unbalanced grid voltage. This paper firstly develops a mathematical model of 3ph-CSR, and the control strategy to suppress the voltage fluctuation of DC side is proposed. Secondly, the positive and negative sequence voltages are separated by the second order generalized integration method. Starting from the mechanism of the second harmonic generation of the 3ph-CSR DC side voltage, the active and reactive powers that generate the second harmonic are set to zero. Calculate and solve the grid-side current control quantity to suppress the double-frequency fluctuation of the DC-side voltage. Finally, a 3ph-CSR circuit and control system are built using MATLAB to verify the correctness of the proposed method.
2 Mathematical Model of CSR in the d-q Coordinate System The 3ph-CSR is generally used as the front stage rectifier of the DC power distribution system, and the rear stage is connected to the DC/DC system [10]. D is the flyback diode, Lo is the DC side inductance of the rectifier, Co is the DC side capacitance of the rectifier, RL is the load; ex , ix , Lx , ucx , ipx (x = a, b, c) are the AC-side input voltage, AC-side input current, AC filter inductor, AC filter capacitor and rectifier input current; iL is the inductor current, vdc is the rectifier output voltage, idc and vo are the current flowing through the load and the voltage across the load. The topology of the 3ph-CSR is shown in Fig. 1. The 3ph-CSR mathematical model based on the d-q coordinate system is, d L dt id + rid − ωLiq + uCd = ed (1) d L dt iq + riq + ωLid + uCq = eq
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Fig. 1. The topology of the 3ph-CSR.
d uCd − ωCuCq + ipd id = C dt d iq = C dt uCa + ωCuCd + ipq
(2)
where r is the AC filter inductance and the line equivalent resistance; L and C are the AC filter inductor and AC filter capacitor, which are used to filter out high frequency components; ed , eq are the d-q component of the grid voltage; uCd , uCq are the d-q component of the capacitor voltage; ipd , ipq are the d-q component of the rectifier input current; ω is the electromotive force angular velocity. The control objects of the 3ph-CSR are id and iq . Under the low frequency model, id and iq are controlled by the modulated wave. ipd and ipq are the control quantities. From (1) and (2), the relationship between ipd , ipq and id , iq can be obtained, and this relationship is discretized as (3). In the case of grid voltage balance, (3) can be used to perform predictive control on CSR, so that the control amount at time k can track the predicted value at the next time, to realize the rapid response of the control system. However, when the grid voltage is unbalanced, using (3) for predictive control will cause the output performance of the rectifier to deteriorate or even fail to work normally, so the control process should be improved. ⎧ LC id (k) − id (k − 1) id (k − 1) − id (k − 2) ⎪ ⎪ − ]− ⎪ ipd (k) = T [ ⎪ Ts Ts ⎪ s ⎪ ⎪ iq (k) − iq (k − 1) id (k) − id (k − 1) ⎪ ⎪ 2ωLC[ ] + RC − ⎪ ⎪ ⎪ T Ts s ⎪ ⎨ 2 ωRCiq (k) + (1 − ω LC)id (k) + ωCeq (k) (3) LC iq (k) − iq (k − 1) iq (k − 1) − iq (k − 2) ⎪ ⎪ i (k) = [ − ]+ ⎪ pq ⎪ ⎪ Ts Ts Ts ⎪ ⎪ iq (k) − iq (k − 1) id (k) − id (k − 1) ⎪ ⎪ ⎪ 2ωLC[ ] + RC + ⎪ ⎪ Ts Ts ⎪ ⎩ ωRCid (k) + (1 − ω2 LC)iq (k) − ωCed (k)
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3 DC Voltage Harmonic Suppression Strategy 3.1 Unbalanced Grid Analysis The mathematical model of the positive and negative sequence components of the 3phCSR based on the two-phase synchronously rotating d-q coordinate system is shown in (4): ⎧ P ⎨ E P = L dIdq + rI P − jωLI P + uP dq dq dq Cdq dt (4) dI N ⎩ N N − jωLI N + uN Edq = L dtdq + rIdq dq Cdq Based on the instantaneous reactive power theory, the expression of complex power on the side of three-phase CSR can be obtained as follows: S = Eαβ Iαβ = p + jq
(5)
The electric quantity has the following relationship in the two-phase stationary α-β coordinate system and the two-phase rotating d-q coordinate system: P + e−jωt E N Eαβ = ejωt Edq dq (6) P N jωt Iαβ = e Idq + e−jωt Idq Substituting (6) into (5), the instantaneous active power p and reactive power q of the three-phase CSR can be obtained as: p(t) = p0 + pc2 cos(2ωt) + ps2 sin(2ωt) (7) q(t) = q0 + qc2 cos(2ωt) + qs2 sin(2ωt) where p0 and q0 are the average value of active and reactive power on the grid side of the rectifier; pc2 and qc2 are the harmonic peaks of the secondary active and reactive power cosine terms on the grid side of the rectifier; ps2 and qs2 are the harmonic peaks of the secondary active and reactive power sinusoidal terms on the grid side of the rectifier. It can be seen from (7) that when the grid voltage is unbalanced, the active and reactive power of the 3ph-CSR grid side not only contains the fundamental component, but also contains the second harmonic component. Expanding (7), each power component can be obtained as follows: ⎧ P P N N P P N N ⎪ ⎪ p0 = 1.5(ed id + eq iq + ed id + eq iq ) ⎪ ⎪ pc2 = 1.5(edP idN + eqP iqN + edN idP + eqN iqP ) ⎪ ⎪ ⎪ ⎨ p = 1.5(eN iP − eN iP − eP iN + eP iN ) s2 q d q d d q d q (8) ⎪ q0 = 1.5(eqP idP − edP iqP + eqN idN − edN iqN ) ⎪ ⎪ ⎪ ⎪ qc2 = 1.5(eqP idN − edP iqN + eqN idP − edN iqP ) ⎪ ⎪ ⎩ qs2 = 1.5(eqP idN + eqP iqN − edN idP − eqN iqP )
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Express it in matrix form as follows: ⎤ ⎡ ⎡ P ed p0 ⎢p ⎥ ⎢ eN ⎢ c2 ⎥ ⎢ d ⎥ ⎢ ⎢ N ⎢ ps2 ⎥ 3 ⎢ eq ⎥= ⎢ P ⎢ ⎢ q0 ⎥ 2 ⎢ eq ⎥ ⎢ ⎢ N ⎣ qc2 ⎦ ⎣ eq qs2 −edN
eqP eqN −edN −edP −edN −eqN
edN edP −eqP eqN eqP edP
⎤ eqN ⎡ ⎤ P eqP ⎥ ⎥ id ⎥⎢ iP ⎥ P ed ⎥⎢ q ⎥ ⎥⎢ ⎥ −edN ⎥⎣ idN ⎦ ⎥ −edP ⎦ iqN eqP
(9)
3.2 Suppress the Second Harmonic of DC Side Voltage Equation (7) shows that when the grid voltage is unbalanced, the active power and reactive power of the 3ph-CSR grid side both contain second harmonics. Therefore, the DC side voltage of the 3ph-CSR also has a second harmonic component and constraining ps2 and pc2 can suppress the second harmonic of the DC side voltage. Substitute q0∗ = ∗ = p∗ = 0 into (9) to obtain the current command expression for suppressing the ps2 c2 DC side voltage harmonics: ⎤ ⎤ ⎡ ⎡ edP idP∗ ⎢ iP∗ ⎥ 2p∗ ⎢ eP ⎥ ⎥ ⎢ ⎢ q ⎥ (10) ⎢ N∗ ⎥ = 0 ⎢ q N ⎥ ⎣ id ⎦ 3D ⎣ −ed ⎦ iqN ∗ −eqN where D =
P 2 P 2 2 2 ed + eq − edN + eqN 0. p0∗ is the average active power
command value of the 3ph-CSR, which is related to the average value of the DC side voltage. The traditional method is to use the PI regulator to adjust the active power component in the system. The realization process is shown in (11). p0∗ = [(kvp +
kvi ∗ )(vdc − vdc )]vdc s
(11)
where kvp and kvi are the proportional and integral gains of the PI controller. If the positive and negative sequence components of electric quantity are controlled separately in the control process, it will increase the control difficulty and increase the control complexity. Therefore, a synthetic operation is performed for the positive and negative sequence components of the grid-side voltage and current of the 3ph-CSR to simplify the control process, such as (12) and (13). N ∗ p ed∗ (ed ) cos 2ωt sin 2ωt (ed )∗ = (12) p ∗ + eq∗ (eq ) − sin 2ωt cos 2ωt (eqN )∗ N ∗ p id∗ (id ) cos 2ωt sin 2ωt (id )∗ = (13) p ∗ + ∗ iq (iq ) − sin 2ωt cos 2ωt (iqN )∗
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3.3 Positive and Negative Sequence Separation of Voltage From the analysis in the previous section, the accurate separation of positive and negative sequence components of 3ph-CSR network side voltage will directly affect the overall control effect under the condition of unbalanced grid voltage. At present, the commonly used methods for separating positive and negative sequences of voltages are notch method, T/4 delay method, and second order generalized integral method (SOGI-QSG).
Fig. 2. SOGI-QSG separates positive and negative sequence processes.
Compared with the other two methods, the voltage positive and negative sequence separation module of SOGI-QSG is simple in principle and easy to implement in structure, and the integral link can well suppress the low-frequency harmonics of the system. Therefore, SOGI-QSG is used in this paper to separate the positive and negative sequence components of the grid-side voltage. The process of SOGI-QSG separating positive and negative sequence voltages is shown in Fig. 2. The overall control flow of the 3ph-CSR is shown in Fig. 3. In Fig. 3, the positive and negative sequences of the sampled grid voltage are separated, and four voltage quantities edP , eqP , edN , eqN are obtained, and the operation of (12) is performed to form the command voltage ed∗ , eq∗ . At the same time, these four voltage quantities are combined with the average active power command p0∗ and the command to ∗ = p∗ = 0 via (10) suppress reactive power and second harmonic active power q0∗ = pc2 s2 ∗ ∗ and (13), and the calculation can get the command current id , iq . Finally substituting the ∗ , i∗ . command voltage and command current into (3) to get the control current iPd Pq
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Fig. 3. Three-phase CSR overall control process.
4 Simulation Results and Analysis In order to verify the correctness of the above theory, a 3ph-CSR system is simulated by MATLAB/Simulink. The simulation parameters are shown in Table 1. Table 1. 3ph-CSR simulation parameters. Quantity
Symbol
Value
Unbalanced input voltage
ea , eb , ec
115 Vrms , 125 Vrms , 115 Vrms
Unbalanced phase angle
θa , θb , θc
0 , 130 ,240
AC input frequency
f
50 Hz
Output voltage
VO
200 V
Output Power
Po
5 kW
AC filter inductor
La , Lb ,Lc
150 μ H
AC filter capacitor
Ca , Cb ,Cc
4.7 μ F
Output inductor
Lo
150 μ H
Output capacitor
Co
150 μ F
Switching frequency
fs
100 kHz
◦
◦
◦
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Figures 4, 5 and 6 show the simulation results of 3ph-CSR running under different control strategies. Figures 4 and 5 show that when the grid voltage is unbalanced, but we still use the control strategy of grid voltage balance, the AC side current of the 3-ph CSR will have serious distortion, and the DC side output voltage will show double frequency fluctuation. However, the control strategy proposed in this paper can well suppress the DC side voltage fluctuation, keep the grid side current sinusoidal and always keep the same phase with the grid side voltage.
(a)
(b)
Fig. 4. Output voltage (a) without the proposed control strategy (b) with the proposed control strategy.
(a)
(b)
Fig. 5. Phase a voltage and three phase input current (a) without the proposed control strategy (b) with the proposed control strategy.
Figure 6 shows that the control strategy proposed in this paper can effectively reduce the grid-side current harmonics, and the THD is reduced from 7.67% to 4.35%, which meets the IEEE 519 standard (THD > C o /n2 , where C C is the clamping capacitance and C o /n2 is equivalent value of the output capacitance to the primary side). At this point, the output capacitor will play a key role in the resonance process, which can prevent the wrong turn-off of the © Beijing Paike Culture Commu. Co., Ltd. 2023 C. Ma et al. (Eds.): ICWPT 2022, LNEE 1018, pp. 1170–1179, 2023. https://doi.org/10.1007/978-981-99-0631-4_117
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secondary rectifier and reduce the effective value of the primary current, thus reducing the conduction loss [10]. In addition, when secondary-side resonance is used, LC filtering is needed because the output capacitance is small and the output voltage ripple is large. In the meanwhile, the mixed-resonance occurs C c capacitance is comparable to C o /n2 , making the resonance process more complicated and more possibilities for optimization.
2 Analysis of ACF 2.1 Operating Principle Figure 1 shows the converter topology of active clamp flyback and its steady-state operating waveforms of primary-side resonant mode. Where C c is clamp capacitance, SH , SL and SD are clamp switch, main switch and secondary switch respectively, C H_oss and C L_oss are parasitic capacitances of clamp switch and primary switch respectively, L k and L m are leakage inductance and magnetizing inductance of transformer respectively, C D_oss and C o are parasitic capacitances of secondary switch and output capacitances respectively. n:1 is the ratio of turns of primary and secondary side winding of equivalent ideal transformer model. Lk Cc
CH_oss
CD_oss
n:1
iLk
SL
Lm
SD
Co
Vo
SL
iLm
i
iLk
Vin
vCc SH
SH
Vgs
isec
nvo
vSL CL_oss
SL
a: topology of ACF
isec
t0
t1 t2 t3
t4
t5
t6
t7 t
b: waveforms in primary resonant DCM mode
Fig. 1. Active clamp flyback converter
2.2 Mode of Resonance According to the resonance principle, the resonance mode can be divided into primaryside resonance, secondary-side resonance. When C c > C o /n2 , the system occurs secondary-side resonance. The circuit is equivalent to Fig. 2(b). At this time, the resonance is dominated by C o /n2 and L k . iLk and iLm as shown in (2). As shown in Fig. 3(b), when the secondary-side resonance occurs, the leakage current iLk magnetizing current iLm will not meet before the reverse, which avoids the false shutdown of SD . nVo Io iLk (t) = −K2 sin(ω2 t + ϕ2 ) + ILm(max) − − t (2) n Lm Lk 1 Z2 = ω2 = 2 2 C o /n Lk × Co /n ϕ2 = tan−1 K2 =
Io n − ILk(ini) nVo −VCc(ini) Z2
ILm(max) − nVo ω2 Lm
nVo nVo − VCc(ini) + ω2 Lm Z2
+
2
2 Io + ILm(max) − − ILk(ini) n
In the primary-side and secondary-side resonant mode, there is a paradoxical problem: if ZCS of Sd needs to be implemented, the resonant frequency of LC needs to be reduced, and in the case of fixed L k , we can only change the value of C c . However, in order to achieve ZCS, decreasing the value of C c will increase the peak of iLk , which may make iLk meet iLm ahead of time. When the input voltage and output voltage are fixed, the value of iLk will only change a little if load current varies. On the contrary, the value of iLm and duty cycle D will vary significantly if load current or input voltage varies. In the light load current, iLm will be close to iLk so that improve the possible of meeting the iLk in unexpected case.
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iLk
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iLm
t
t
a: primary-side resonance
b: secondary-side resonance
Fig. 3. Waveforms of leakage inductance current and magnetizing current
If the C c capacitance is comparable to C o /n2 , both primary resonance and secondary resonance named as mixed-resonance happens, as shown in Fig. 4. The mixed-resonance can use to adjust the waveform of current when input or load varies. As shown in Fig. 4. The relationship is shown below: Lk
Cc
Co/n2 Lm
Io/n
Fig. 4. Equivalent circuit of mixed-resonance
ipri (t) ≈
nVo (t) nVo (t) − VCc(ini) Io sin(ω3 t) ILm, max − − Ipri(ini) cos(ω3 t) + ωLm Z3 n nVo (t) Io + ILm, max − − t n Lm (3) Cc + Co /n2 Lk (Cc + Co /n2 ) ω3 = Z = 3 Lk Cc Co /n2 Cc Co /n2
3 ACF Converter with Variable Resonant Mode To solve the problems in Sect. 2, according to the working characteristics of ACF under two resonant modes described in the previous section, a multi-resonant ACF converter is proposed, as shown in Fig. 5. The capacitor-switching cell is added to the secondary side, and the LC filter is added to the output side to decouple, where C 1 /n2 >> C c , C c close to C 2 /n2 . When the switch Sdc is off, mixed-resonance occurs, which means that L k ,C 1 and Cc are in resonance. ACF works in the primary resonance mode when switch Sdc is on. The input of C 1 can be determined according to the variable input or output. Since the input of C 1 changes the capacitance value involved in the resonance,
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so as to ensure the ZVS of SL and ZCS of SD . From the analysis in Sect. 2, it can be seen that under the mixed-resonance, the false shutdown of the secondary rectifier can be effectively avoided. Therefore, the ACF with variable resonant mode in Fig. 5 is set to the mixed-resonant mode. When the input or output of the converter change, Sdc is switched according to the demand. The influence of capacitor C 1 on dead time is analyzed as follows. CD_oss
Lk i Lk Cc Vin
Lo
isec
CH_oss Lm iLm
SD S dc C1
C2 C3 Vo
SH CL_oss
SL
Fig. 5. ACF with variable resonance mode
The average current of the magnetizing inductor I Lm has the following relationship with the input and output, where η is the converter efficiency, D is the duty cycle of SL and fs is the switching frequency, the equation can be shown as follows: ILm =
Po Io + ηVin N
(4)
iLm, max = ILm +
Vin D 2fs Lm
(5)
iLm, min = ILm −
Vin D 2fs Lm
(6)
Lk Cc
CH_oss Lm
Vin SH
Sdc
IH
ILm C1/n^2 IL
SL
CL_oss
C2/n2
Fig. 6. Equivalent circuit in dead time
As shown in Fig. 6, in the dead time t D1 before the clamp switch SH is on, the parasitic capacitor is discharged by the positive magnetizing inductance current. In the dead time t D2 before the main switch SL is on, the parasitic capacitor is discharged by the negative magnetizing inductance current, so: iLm,max · tD1 = Ceq · Vsw
(7)
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(8)
V sw refers to the node voltage that the switch bears when it is turned off. In [t 2 -t 3 ], both the secondary rectifier and the primary switch SH is on. In this case, the magnetizing inductor L M is clamped and no longer participates in resonance, while the output capacitor participates in resonance. The charging process of the parasitic capacitor of the main switch tube is as follows, and the equivalent circuit is shown in the Fig. 7: Lk Cc
CH_oss Lm
Vin
Sdc
IH
ILm C1/n^2 IL
SL
CL_oss
C2/n2
Fig. 7. Equivalent circuit in [t 2 -t 3 ]
According to (4) and (8), in the analysis of the above conditions, t D1 decreases and t D2 increases as the output current increases. When the input voltage rises, both t D1 and t D2 increases. Therefore, the size of C eq can be controlled by changing the on-off state of Sdc to adapt to soft switching conditions.
4 Simulation Analysis In this paper, ACF with the maximum output power of 60 W, input voltage of 90– 240Vrms and output voltage of 20 V was designed for simulation verification, in which the switching frequency f S is 450 kHz. As in traditional flyback design, the transformer turns ratio is calculated. The magnetizing current needs to flow in both directions. So, L m must meet (10). Then set the L k to 4.5% of the L m : Lm