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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press Series on Control Systems Theory and Applications
- Sprache: Englisch
Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)
Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.
Topics explored in this book include:
- Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and more
- Recursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithms
- Applications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis
This book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.
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Veröffentlichungsjahr: 2025
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List of Illustrations
Chapter 1
Figure 1.1 Schematic diagram of PMSM drive system.
Figure 1.2 Machine configurations of radial-flux internal rotor PMSMs: (a) surf...
Figure 1.3 Variants of IPM rotor configurations: (a) single V-type, (b) double ...
Figure 1.4 Stator winding topologies: (a) overlapping windings (12-slot stator ...
Figure 1.5 Representation of the three-phase PM machine model.
Figure 1.6 Phasor diagram of three-phase PM machine.
Figure 1.7 Incremental and apparent inductances considering magnetic saturation.
Figure 1.8 Illustration of cross-coupling effect based on a salient-pole synchr...
Figure 1.9 Representation of apparent and incremental reluctivities in non-line...
Figure 1.10 Intrinsic and normal curves of NdFeB magnet at different temperat...
Figure 1.11 -axis equivalent circuits of PMSM: (a) -axis and (b) -axis.
Figure 1.12 Schematic diagram of an electrical drive system for PMSM: (a) VSI-ba...
Figure 1.13 Phasor representation of eight basic space vectors.
Figure 1.14 Switching states and gate signals within one sampling period in Sect...
Figure 1.15 Overview of parameter estimation techniques.
Figure 1.16 Schematic diagram of online parameter estimation.
Figure 1.17 Outline of the book.
Chapter 2
Figure 2.1 DSP platform and experimental test rig.
Figure 2.2 Experimental results with and without filters [7], IEEE: (a) Scheme ...
Figure 2.3 Estimated parameters of schemes I and II [7], IEEE: (a) scheme I (no...
Figure 2.4 Estimated parameters of Scheme III [7], IEEE: (a) initial values far...
Figure 2.5 Estimated parameters of Scheme IV [7], IEEE: (a) A and A.
Figure 2.6 VSI-based three-phase PMSM drive system.
Figure 2.7 Switch on/off signals of space vector pulse width modulation.
Figure 2.8 Theoretical, equivalent, and real IGBT output voltages and drive sign...
Figure 2.9 Waveforms of and under control [9], IEEE:...
Figure 2.10 Measured and under control [9], IEEE.
Figure 2.11 Waveforms and FFT results of measured rotor speed with and without VSI...
Acquisition of high-frequency component from by using a first-order low-pass filter [9], IEEE.
Figure 2.13 Estimated caused by VSI non-linearity under control [9], IEEE.
Figure 2.14 Process of complete VSI non-linearity estimation/compensation method: (a)...
Figure 2.15 Estimated before and after VSI non-linearity compensation [9], IEEE.
Figure 2.16 -axis currents (a) without and (b) with compensation of VSI non-linearity [9], IEEE.
Figure 2.17 -axis currents (a) without and (b) with compensation...
Figure 2.18 Currents of phase-
a
(a) without and (b) with compensation of VSI non-linearity [9], IEEE.
Figure 2.19 System control diagram for PMSM.
Figure 2.20 Measured three-phase current waveforms [25], IEEE.
Figure 2.21 Schematic diagram of designed experimental investigation.
Figure 2.22 Estimated -axis inductance under control...
Figure 2.23 Estimated stator winding resistance and rotor flux linkage at 300 r/...
Figure 2.24 -axis currents and voltage with/without VSI compensation at 300 r/min [25], IEEE.
Figure 2.25 -axis currents and voltages with/without VSI compensation at 100 r/min [25], IEEE.
Figure 2.26 Estimated resistance and rotor flux linkage considering the dc-link ...
Figure 2.27 Estimated winding resistance and rotor flux linkage at 300 r/min [26...
Chapter 3
Figure 3.1 Online estimation of rotor PM flux linkage with the aid of thermocoup...
Figure 3.2 Prototype Machine 1 with buried thermocouples: (a) prototype PMSM an...
Figure 3.3 (a) Line back-EMF and its (b) FFT results under no-load condition at...
Figure 3.4 Estimated rotor PM flux linkage with and without VSI non-linearity c...
Figure 3.5 Correlation of measured stator winding resistance and temperature [4...
Figure 3.6 Comparison of estimated and measured rotor PM flux linkages at differ...
Chapter 4
Figure 4.1 Schematic diagram of current injection–based parameter estimation.
Figure 4.2 Schematic diagram of multi-parameter estimation scheme: (a) process ...
Figure 4.3 Iterative calculation of estimating , , and based on measured quantities.
Figure 4.4 Calculated variation of with -axis currents under various...
Figure 4.5 Measured variation of with -axis currents [15], IEEE.
Figure 4.6 Sampled electrical angular speed and -axis currents and voltages () [4]: (a) rotor speed...
Figure 4.7 Estimated parameters based on -axis current injection () [15], IEEE: (a) stator winding resistance...
Figure 4.8 Estimated parameters for tracking temperature variations of Prototype...
Figure 4.9 Estimation of and based on measured inputs and outputs under...
Figure 4.10 Measured variation of with different amplitudes of injected [16], IEEE.
Measured electrical angular speed and -axis currents and voltages [4]: (a) rotor speed, (b) -axis currents, and (c) -axis voltages.
Figure 4.12 Estimated (a) stator winding resistance and (b) rotor PM flux linkag...
Figure 4.13 Estimated parameters for tracking temperature variations of prototyp...
Chapter 5
Figure 5.1 Phasor diagram of PMSM with and without position offset .
Figure 5.2 Principle of POPE with associated FOC system under constant torque/s...
Figure 5.3 Iterative computation process of POPE for estimating and [3], IEEE.
Figure 5.4 Flowchart of compensation for position measurement error and...
Figure 5.5 Measured (a) rotor speed, (b) -axis current, and (c) -axis voltage...
Figure 5.6 Flowchart for estimation of under constant torque/speed control.
Figure 5.7 Measured -axis voltages and currents during estimation [3], IEEE...
Figure 5.8 Estimated rotor PM flux linkage and winding resistance with and witho...
Figure 5.9 Variations of estimated rotor PM flux linkages with against...
Figure 5.10 Estimation results after the addition of external resistors [3], IEE...
Figure 5.11 Measured and estimated rotor PM flux linkages and their variations w...
Figure 5.12 Estimation of -axis inductances at 300 r/min for non-salient-pole...
Figure 5.13 Estimation of -axis inductances at 200 r/min for salient-pole IPMSM...
Figure 5.14 Comparison of -axis inductances estimated by POPE and FEA with diff...
Figure 5.15 Measurement process of POPE under variable speed control: (a) princi...
Figure 5.16 Complete estimation method of POPE under variable speed control.
Figure 5.17 Measured electrical quantities for Prototype Machine 2 [4]: (a) ...
Figure 5.18 Estimated parameters based on POPE under variable speed control for ...
Figure 5.19 Comparison of estimated and FE-predicted variations of rotor PM flux...
Figure 5.20 Complete estimation flowchart for rotor PM flux linkage, inductance ...
Figure 5.21 Estimated parameters and -axis flux linkages errors against FEA re...
Figure 5.22 Estimated parameters and -axis flux linkage errors against FEA res...
Figure 5.23 Variations of measured/estimated rotor PM flux linkages with measure...
Figure 5.24 General POPE method with and under constant/variable speed...
Figure 5.25 Gain functions of and [8], IEEE: (a) gain functions of
Figure 5.26 Experimental platform and Prototype Machine 2.
Figure 5.27 Measured rotor speeds and reference -axis voltages under constant...
Figure 5.28 Estimated parameters under constant and variable speed operations [8...
Figure 5.29 FEA and POPE estimated -axis inductance maps with and at...
Figure 5.30 FEA and POPE estimated -axis inductance maps with and at constant...
Figure 5.31 Estimation errors of -axis inductance maps with and...
Figure 5.32 Variations of parameter estimation error with different dead time of...
Figure 5.33 Schematic diagrams of current loop before and after position offset ...
Figure 5.34 Typical I-type system [8], IEEE.
Figure 5.35 Variations of estimation errors with different amplitudes of injecte...
Chapter 6
Figure 6.1 Online parameter estimation of PMSM under variable speed control: (a...
Figure 6.2 Flowchart of estimation scheme under variable speed control.
Figure 6.3 Measured data under variable speed control [1], IEEE: (a) rotor speed...
Figure 6.4 Estimated parameters under variable speed control without compensati...
Figure 6.5 Estimated parameters under variable speed control with compensation ...
Figure 6.6 Estimated parameters under variable speed control with compensation ...
Figure 6.7 Estimation of -axis inductance under constant load torque [1], IEEE...
Figure 6.8 Measured data during variable speed control at load point ,...
Figure 6.9 Complete data recording process at different load points for estimat...
Figure 6.10 FE-predicted -axis flux linkage maps (end effect included):...
Figure 6.11 Fitness of ICQGA-based identification of -axis flux linkage maps [...
Figure 6.12 Identified -axis flux linkage maps and estimation errors [2], IEEE:...
Figure 6.13 Estimated -axis flux linkages at different speed regions () [2], IEEE:...
Figure 6.14 Estimated -axis flux linkages under uncertain circuit resistance [...
Figure 6.15 -axis inductance maps predicted by FE and ICQGA-based method [2], I...
Figure 6.16 -axis inductance maps predicted by FE and ICQGA-based method [2], I...
Figure 6.17 MTPA current trajectory and output torque [2], IEEE: (a) MTPA curren...
Chapter 7
Figure 7.1 Illustration of incremental and apparent inductances.
Figure 7.2 Comparison of described injection sequences of HF voltage methods.
Figure 7.3 Time delay effects in HF voltage injection methods [26], IEEE.
Figure 7.4 Control diagram of HF inductance estimation based on HF rotating vol...
Figure 7.5 Demodulation of amplitudes of positive and negative sequence HF curr...
Figure 7.6 Sensorless position estimation based on HF rotating voltage injectio...
Figure 7.7 Estimation of HF inductances based on HF pulsating voltage injection...
Figure 7.8 Sensorless position estimation based on HF pulsating voltage injecti...
Figure 7.9 Estimation of HF inductances based on HF pulsating voltage injection...
Figure 7.10 Estimation of HF inductances based on combined HF rotating and pulsa...
Figure 7.11 Estimation of HF inductances based on combined HF rotating and pulsa...
Figure 7.12 Experimental setup.
Figure 7.13 Variation of estimated HF inductances by different HF signal injecti...
Figure 7.14 -axis current sequences under combined HF pulsating and ro...
Figure 7.15 Variation of measured HF inductances with different rotor positions ...
Figure 7.16 Comparison of HF inductances predicted by FEA and measured based on ...
Chapter 8
Figure 8.1 Flowchart of square-wave voltage-based estimation method.
Figure 8.2 Measured -axis voltage and -axis currents for Prototype Machine...
Figure 8.3 Comparison of estimated -axis flux linkages without (I) and with (II)...
Figure 8.4 Comparison of estimated -axis inductance against FEA reuslts.
Figure 8.5 Estimated -axis flux linkage maps with and : (a)...
Figure 8.6 Measured electrical quantities for estimation of and...
Figure 8.7 Estimation results at Position I: (a) estimated stator resistance ...
Figure 8.8 Estimation results at Positions II and III: (a) estimated stator resi...
Figure 8.9 Estimated winding resistance without compensating for VSI non-linearity.
Figure 8.10 Measured quantities for estimation of -axis inductances: (a) -ax...
Figure 8.11 Estimated and at standstill: (a) estimated and (b) estimated .
Figure 8.12 Measured rotor speed during HF current injections.
Figure 8.13 -axis HF currents and voltages: (a) measured -axis current, (b) m...
Figure 8.14 Estimation of winding resistance and rotor PM flux linkage by two-st...
Figure 8.15 Estimated rotor PM flux linkage and stator winding resistance under ...
Figure 8.16 Estimated rotor PM flux linkage and winding resistance of PMSM after...
Figure 8.17 Flowchart of three-step estimation method.
Figure 8.18 Measured electrical quantities at standstill with in
Step 1
: (a) me...
Figure 8.19 Estimation results at standstill in Step 1: (a) estimated distorted ...
Figure 8.20 Estimated rotor PM flux linkage at operating in Step 2.
Figure 8.21 Estimated stator winding resistance in Step 3.
Chapter 9
Figure 9.1 Transfer function of mechanical model of PMSM drive system [5], IEEE:...
Figure 9.2 Flowchart of fundamental motion equation–based estimation method.
Figure 9.3 Data measurement process of POPE.
Figure 9.4 Measured rotor speed and -axis current and detected zero-crossing p...
Figure 9.5 Estimation moment of inertia of PMSM rotor by MRAS with different per...
Figure 9.6 MRAS-based estimation of with different PI constant based on...
Figure 9.7 Estimation of PM flux linkage based on measured quantities of Prototy...
Figure 9.8 Estimation of PM flux linkage based on measured quantities of Prototy...
Figure 9.9 Comparison of estimated rotor PM flux linkages and FEA results [6], ...
Figure 9.10 Variation of estimated moment of inertia of dc load machine and PMSM...
Figure 9.11 Variations of estimated moment of inertia of dc load machine and PMS...
Figure 9.12 Block diagram of FOC-based mechanical parameter estimation system.
Figure 9.13 Transfer function of speed loop of field-oriented control [5], IEEE:...
Figure 9.14 Calculated at different rotor speeds [5], IEEE.
Figure 9.15 Step response of rotor speed in forward and reverse directions [5], ...
Figure 9.16 Performance comparison between designed speed regulators with and wi...
Figure 9.17 Comparison of rotor speeds and -axis currents by using proportional c...
Chapter 10
Figure 10.1 Schematic diagram of online parameter estimation.
Figure 10.2 Flowchart of three-step parameter estimation.
Figure 10.3 Simulated electrical quantities used for parameter estimation: (a) r...
Figure 10.4 Estimated -axis inductance, stator winding resistance, rotor PM fl...
Figure 10.5 Schematic diagram of parameter estimation based on Kalman filter.
Figure 10.6 Estimated -axis inductance, stator winding resistance, and rotor P...
Figure 10.7 Schematic diagram of MRAS estimator.
Figure 10.8 Estimated -axis inductance, stator winding resistance, and rotor P...
Figure 10.9 Structure of an ANN.
Figure 10.10 ANN-based estimation system for PMSM.
Figure 10.11 Subnet structures of designed ANN estimators: (a) -axis stator ind...
Figure 10.12 Estimated (a) -axis inductance, (b) stator winding resistance, and...
Figure 10.13 Estimated (a) -axis inductance, (b) stator winding resistance, and...
Figure 10.14 PSO-based parameter estimation.
Figure 10.15 Estimated (a) -axis inductance, (b) stator winding resistance, and...
Figure 10.16 Flowchart of GA algorithm.
Figure 10.17 Estimated (a) -axis inductance, (b) stator winding resistance, and...
Chapter 11
Figure 11.1 Block diagram of FOC for PMSM.
Figure 11.2 Complete transfer function of (a) -axis current loop and (b) speed...
Figure 11.3 Simplified transfer functions [3], IEEE: (a) -axis current loop an...
Figure 11.4 Exemplary estimation procedure for design of PI regulators.
Figure 11.5 Estimated results based on HF current injection–based offline ...
Figure 11.6 Estimated rotor PM flux linkage by fixing resistance ( A, A) [3], IEEE.
Figure 11.7 Estimated mechanical parameters [3], IEEE: (a) estimated friction co...
Figure 11.8 Step response of -axis currents by using designed current PI regul...
Figure 11.9 Step response of rotor speed by using designed speed PI regulator [3...
Figure 11.10 Block diagram of FOC-based MTPA control.
Figure 11.11 Derived MTPA trajectories and corresponding output torques consider...
Figure 11.12 Comparison of MTPA trajectories and output torques based on fixed no...
Figure 11.13 Block diagram of extended back-EMF-based sensorless control.
Figure 11.14 Variations of -axis apparent self- and mutual-inductances with currents [23]...
Figure 11.15 Estimation errors of the extend back-EMF-based sensorless control w...
Figure 11.16 Block diagram of -axis pulsating signal injection-based sensorless...
Figure 11.17 Comparison of FEA calculated and estimated coupling factors ...
Figure 11.18 Waveforms of voltage and current in signal injection-based sensorles...
Figure 11.19 Estimation performance of HF signal injection-based sensorless contr...
Figure 11.20 Error transfer issue of online parameter estimation under sensorless...
Figure 11.21 Block diagram of SWRPO-based online parameter estimation under senso...
Figure 11.22 Phasor diagram of SPMSM with stator resistance error under ...
Figure 11.23 Parameter estimation results based on Prototype Machine 3 at 30 r/mi...
Figure 11.24 Comparison of position-offset-based parameter estimation method wit...
Figure 11.25 Square wave voltage injection [39], IEEE: (a) vector diagram and (b)...
Figure 11.26 Torque estimation performance based on estimated HF inductances unde...
Figure 11.27 Estimated stator winding resistance and rotor PM flux linkage of pr...
Figure 11.28 Illustration of residual-based ITSC detection methods.
Figure 11.29 Waveforms and spectra of three-phase currents at healthy and ITSC co...
Figure 11.30 Illustration of irreversible demagnetization: (a) irreversible dema...
Figure 11.31 Simulated waveforms and spectra of winding flux linkage at healthy a...
Appendix A
Figure A.1 Cross-section of Prototype Machine 2: (a) cross section and (b) meshed view.
Figure A.2 Flowchart of FE calculation of inductances.
Figure A.3 FE-calculated three-phase and -axis flux linkages at and : (a)...
Figure A.4 Variations in average -axis flux linkages with currents: (a)...
Figure A.5 Variations in -axis apparent self- and mutual-inductances with cur...
Figure A.6 Variations in -axis incremental self- and mutual-inductances with ...
Appendix B
Figure B.1 Prototype PMSMs: (a) Prototype Machine 1, (b) Prototype Machine 2, an...
Figure B.2 Typical experimental platform.
List of Tables
Chapter 1
Table 1.1 Physical properties of PM materials.
Table 1.2 Correlation between voltages and corresponding space vectors.
Chapter 2
Table 2.1 Design parameters and specification of Prototype Machine 1.
Table 2.2 Summary of experimental results in four designed schemes.
Table 2.3 Relationship between current directions and -axis voltages.
Table 2.4 Typical electrical parameters of VSI from Mitsubishi PS21867 datasheet.
Chapter 5
Table 5.1 Features of POPE methods under different control strategies.
Table 5.2 Influence of position offsets on -axis back-EMFs for Prototype Mac...
Table 5.3 Main parameters of Prototype Machines 1 and 2.
Chapter 6
Table 6.1 Specification and measured parameters of Prototype Machine 2 – IPMSM.
Chapter 7
Table 7.1 Calculated HF inductances by various methods at A and A.
Table 7.2 Comparison of HF inductance estimation methods.
Chapter 9
Table 9.1 Main design parameters of Prototype Machines 1 and 2.
Table 9.2 Estimation results of Scheme I.
Table 9.3 Estimation results of Scheme III.
Chapter 10
Table 10.1 Comparison of various estimation algorithms.
Chapter 11
Table 11.1 Estimated electrical/mechanical parameters and optimized PI constants.
Table 11.2 Temperature coefficients of copper and PM materials (%/°C).
Table 11.3 Summary of applications of online parameter estimation techniques.
Appendix B
Table B.1 Specifications of prototype PMSMs.
Table B.2 Typical characteristics of drive system and VSI (at 25 °C).
Guide
Cover
Table of Contents
IEEE Press Series on Control Systems Theory and Applications
Title Page
Copyright
Authors
Preface
List of Abbreviations
List of Symbols
Begin Reading
Appendix A: Finite Element Calculation of Winding Inductances
Appendix B: Specifications of Prototype Machines and Experimental Platforms
Index
End User License Agreement
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Parameter Estimation of Permanent Magnet Synchronous Machines
Zi Qiang Zhu
University of Sheffield, UK
Kan Liu
Hunan University, China
Dawei Liang
University of Sheffield, UK
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Library of Congress Cataloging-in-Publication Data:
Names: Zhu, Ziqiang, Ph. D., author. | Liu, Kan (Dean), author. | Liang, Dawei (Research associate), author.
Title: Parameter estimation of permanent magnet synchronous machines / Zi Qiang Zhu, Kan Liu, Dawei Liang.
Description: Hoboken, New Jersey : Wiley, [2025] | Series: IEEE Press series on control systems theory and applications | Includes bibliographical references and index.
Identifiers: LCCN 2025009543 | ISBN 9781394280421 (hardback) | ISBN 9781394280445 (epdf) | ISBN 9781394280438 (epub) | ISBN 9781394280452 (obook)
Subjects: LCSH: Parameter estimation. | Permanent magnet motors.
Classification: LCC QA276.8 .Z48 2025 | DDC 621.46—dc23/eng/20250326
LC record available at https://lccn.loc.gov/2025009543
Cover Design: Wiley
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Authors
Professor Zi Qiang (Z.Q.) Zhu received his BEng and MSc degrees from Zhejiang University, Hangzhou, China, in 1982 and 1984, respectively, and his PhD degree from the University of Sheffield, Sheffield, UK, in 1991, all in electrical engineering.
After working as a Lecturer/Assistant Lecturer at Zhejiang University from 1984 to 1988, he has been with the University of Sheffield since 1988, initially as a Visiting Research Fellow sponsored by the British Council (1988–1989), then as a Research Associate working with Philips (1989–1992), a Senior Research Scientist/Officer – an established university post (1992–2000), Professor (2000), Royal Academy of Engineering/Siemens Research Chair (2014–2023), and Head of the Electrical Machines and Drives Research Group (2008). As the Founding Director, he has helped several industries in establishing their research centres, most notably, Siemens Wind Power Research Centre at Sheffield (2009) and Midea Electrical Machines and Control Research Centres at Shanghai and Sheffield (2010).
His research interests include design and control of permanent magnet brushless machines and drives for applications ranging from electrified transportation (electric vehicles, fast trains, and more electric aircrafts) through domestic appliances to wind power generation, on which he has published >1500 papers including >600 IEEE and IET journal papers, as well as >200 patents.
He is a Fellow of the Royal Academy of Engineering, UK; the Institute of Electrical and Electronics Engineers (IEEE), USA; the Institution of Engineering and Technology (IET), UK; the Chinese Society for Electrical Engineering (CSEE); the China Electrotechnical Society (CES); and Editor-in-Chief of IET Electric Power Applications. He is the recipient of the 2024 Global Energy Prize, the 2021 IEEE Nikola Tesla Award, and the 2019 IEEE Industry Applications Society Outstanding Achievement Award.
Professor Kan Liu received his BEng and PhD degrees in automation from Hunan University, Changsha, China, in 2005 and 2011, respectively, and his PhD degree in electrical engineering from the University of Sheffield, Sheffield, UK, in 2013.
From 2013 to 2016, he was a Postdoctoral Research Associate in the Electrical Machines and Drives Group at the University of Sheffield. From 2016 to 2017, he was a Lecturer with the Control Systems Group, Loughborough University, UK. He joined Hunan University as a Professor of electromechanical engineering in 2017. He is currently the Director of the Engineering Research Center of Ministry of Education on Automotive Electronics and Control Technology, China, Chief Scientist of National Key Research and Development Program, China (2022), and Senior Member of IEEE.
His research interests include control, design, parameter identification, and state observation of permanent magnet synchronous machines and high-power density SiC inverters/converters for electric vehicles and locomotives. He has published 14 patents and >100 papers, including >40 IEEE transactions papers, and 3 Best Paper Awards of International Conference on Electrical Machines and Systems.
Dr Dawei Liang received his BEng degree from Harbin Institute of Technology, Harbin, China, in 2014; his MSc degree from Karlsruhe Institute of Technology, Karlsruhe, Germany, in 2018; and his PhD degree from the University of Sheffield, Sheffield, UK, in 2022, all in electrical engineering. Since 2022, he has been a Postdoctoral Research Associate with the University of Sheffield, Sheffield, UK. His research interests include design and control of permanent magnet machines.
Preface
Parameter estimation is an essential requirement for high-performance permanent magnet synchronous machine (PMSM) drives. Indeed, many commercial industrial drives for PMSMs have embodied the features of the parameter estimation function, which many consider as a black box for online and/or offline parameter estimation. However, due to commercial sensitivity, most implemented techniques have been withheld from the public, and the estimation performance can vary significantly from one company to another. Nevertheless, how to develop reliable generic methods and reduce the errors in parameter estimation, particularly under wide speed and load variations and sensorless control, remains challenging.
Since 2005, I have been continuously working on various parameter estimation techniques for PMSMs together with my PhD students, particularly the co-authors of this book, Dr Kan Liu (2008–2016) and Dr Dawei Liang (2018–present) who obtained their PhD degrees and was/is a post-doctoral researcher at the University of Sheffield working on this important topic. We successfully addressed the issues of rank deficiency and inverter nonlinearity and have developed many new online electrical and mechanical parameter estimation techniques for PMSMs, including those with the aid of thermocouples in the stator windings, based on current/voltage injection, and based on position-offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs for various applications, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, etc. These parameter estimation techniques as well as those developed globally are comprehensively described in this book with examples of both experimental and simulation results.
Over the last few years, it has been interesting to see an increasing number of publications on modern control theory–based parameter estimation techniques for PMSMs. Therefore, such techniques, including recursive least squares, Kalman filter, model reference adaptive system, Adaline neural network, gradient-based methods, particle swarm optimization, and genetic algorithm, are systematically described with examples in this book.
It is anticipated that the new parameter estimation techniques of PMSMs will continue to be developed and more commonly employed in general industrial drives. They will be more extensively used for a wide variety of applications, including electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances; for improving control performance and sensorless control; and condition monitoring/fault diagnosis. Thus, applications of parameter estimation of PMSMs are also included in a separate chapter in this book.
I dedicate my thanks to our sponsors, including the UK government, particularly the UK EPSRC Prosperity Partnership (“A New Partnership in Offshore Wind” under Grant No. EP/R004900/1), Siemens, CRRC, and Midea. I also thank Mr Ian Parmenter for his proofreading of the book.
We sincerely hope this book will be useful to industrial engineers and researchers, university professionals, post-doctoral researchers, and students alike.
Professor Zi Qiang (Z.Q.) Zhu
FREng, FIEEE, FIET, FCSEE, FCES
August 2024, Sheffield, UK
List of Abbreviations
ac
Alternating current
AI
Artificial intelligence
AlNiCo
Aluminium–nickel–cobalt
ANN
Adaline neural networks
Back-EMF
Back electromotive force
dc
Direct current
DTC
Direct torque control
EA
Evolutionary algorithms
EMF
Electromotive force
EV
Electric vehicle
EKF
Extended Kalman filter
FFT
Fast Fourier transform
FE
Finite element
FEA
Finite element analysis
FOC
Field-oriented control
GA
Genetic algorithms
HF
High frequency
ICA
Immune clonal algorithm
ICQGA
Immune clonal–based quantum genetic algorithm
IPM
Interior permanent magnet
IPMSM
Interior permanent magnet synchronous machine
ITSC
Inter-turn short circuit
KF
Kalman filter
LMS
Least mean square
LPF
Low-pass filter
MMF
Magnetomotive forces
MPC
Model predictive control
MTPA
Maximum torque per ampere
MRAS
Model reference adaptive system
NdFeB
Neodymium–iron–boron
PI
Proportional integral
PM
Permanent magnet
PMSM
Permanent magnet synchronous machine
POPE
Position-offset parameter estimation
PSO
Particle swarm optimization
PWM
Pulse width modulation
QGA
Quantum genetic algorithm
RLS
Recursive least squares
SNR
Signal-to-noise ratio
SPM
Surface permanent magnet
SPMSM
Surface permanent magnet synchronous machine
SVPWM
Space vector pulse width modulation
SWRPO
Square wave rotor position offset
THD
Total harmonic distortion
VSI
Voltage source inverter
List of Symbols
Symbol
Description
Unit
State transition matrix
Control-input model
Remanence
T
,
Remanence at actual and reference temperatures
T
Maximum energy product
kJ/m
3
,
Cognitive and social acceleration constants
Condition number
,
-axis gain functions of VSI nonlinearity
,
Average values of -axis gain functions of VSI nonlinearity
,
-axis extended back-EMF
V
Friction coefficient
Frequency of HF signal
Hz
First-order gradient
Coercivity
kA/m
Intrinsic coercivity
kA/m
Identity matrix
Three-phase currents
A
, ,
Three-phase currents
A
,
-axis currents
A
,
-axis HF currents
A
,
-axis currents
A
,
-axis HF currents
A
,
Amplitudes of -axis HF currents
A
,
Average values of -axis currents
A
Resolution of sampled current
A
Maximum current
A
,
Amplitudes of positive and negative sequence currents
A
,
Current perturbations in th and th coils
A
Variables of injected -axis current
A
Rotor moment of inertia
kg m
2
Index of discrete sampling instant
,
PI constants
, , , , ,
Gains of cost functions
Gain vector of RLS estimator
Self-inductance
H
Mutual inductance
H
Phase self-inductance
H
Phase leakage inductance
H
Second-order harmonic of self-inductance
H
,
-axis inductances
H
,
-axis HF inductances
H
,
-axis mutual inductances
H
,
-axis HF mutual inductances
H
,
-axis apparent inductances
H
,
-axis incremental inductances
H
,
-axis incremental self-inductances
H
,
-axis apparent self-inductances
H
,
-axis apparent mutual inductances
H
,
-axis incremental mutual inductances
H
Average mutual inductance
H
Second-order harmonic of mutual inductance
H
Overall time error
S
Sampling number
Pole pair number
,
Cost function
Covariance matrix
Model uncertainty matrix
Measurement noise covariance
Estimated synchronous rotating reference frame
On-state resistance of IGBT
Ω
On-state resistance of freewheeling diode
Ω
Iron loss resistance
Ω
Stator winding resistance
Ω
Error of estimated stator winding resistance
Ω
,
Winding resistance at actual and reference temperatures
Ω
Switching pattern of three-phase legs
Clarke transformation
Active durations of space vectors and
S
Actual duration of effective time
S
Commanded duration of effective time
S
Compensation time
S
Dead time of power device
S
Switch on/off time delay
S
Sampling time
S
Electromagnetic torque
N m
Estimated torque
N m
Load torque
N m
Control vector in KF
,
-axis voltages
V
,
-axis voltages
V
,
-axis reference voltages
V
,
-axis HF voltages
V
,
-axis HF reference voltages
V
Voltage vector reference
V
Maximum output phase voltage
V
HF voltage signal
V
System noise
Observation/measurement noise
Operator norm
Voltage vectors
V
, , ,
Reference three-phase voltages
V
, ,
Distorted three-phase voltage caused by VSI nonlinearity
V
On-state voltage drop of IGBT
V
Threshold voltage drop of IGBT
V
On-state voltage drop of freewheeling diode
V
Threshold voltage drop of freewheeling diode
V
Variable of injected -axis voltage
V
dc bus voltage
V
,
-axis distorted voltages due to VSI nonlinearity
V
Distorted voltage term due to VSI nonlinearity
V
Amplitude of injected HF voltage
V
Non-zero dc offset
V
Threshold voltage
V
Total stored energy
J
Weight in ANN estimator
Zero-mean white Gaussian system noise
Inertia weight in PSO estimator
,
Characteristic roots
,
Particle best and overall best locations in PSO estimator
Step variation
,
Measured and predicted output variables
Output matrix of RLS estimator
Temperature coefficient of copper
%/°C
Temperature coefficient of magnet
%/°C
Step length of Newton algorithm
Current advancing angle
Deg.
Finite positive constant
Least-square error
Optimal damping ratio
Tuning factor
Convergence factor
Stator actual temperature
°C
PM actual temperature
°C
Reference temperature
°C
Angle of injected HF signal
Deg.
Rotor position
Deg.
Unit electrical angle
Deg.
Position offset
Deg.
Injected rotor position offset
Deg.
Positive and negative position offsets
Deg.
Parameter vector in RLS estimator
Coupling factor
Forgetting factor of RLS estimator
Relative permeability
Predicted output in ANN estimator
Differential operator
Electrical resistivity
Ω m
Input matrix of RLS estimator
Phase delay between filtered HF current and demodulation signal
Deg.
Power factor angle
Deg.
Three-phase flux linkages
Wb
,
-axis flux linkages
Wb
,
-axis flux linkages
Wb
PM flux linkage
Wb
,
PM flux linkages at actual and reference temperatures
Wb
PM flux linkage error
Wb
HF angular velocity
Rad/s
Electrical angular velocity
Rad/s
Average electrical angular velocity
Rad/s
Variables of rotor angular velocity
Rad/s
Chapter 1General Introduction
1.1 Introduction
According to statistics from the US Energy Information Administration, electrical machines accounted for 43%–46% of the global electricity consumption in 2020 [1] and played an important role in industries and economics. Electrical machines have different types, e.g., direct current (dc) machines, induction machines, reluctance machines, and permanent magnet (PM) machines. Due to their high torque density and efficiency, permanent magnet synchronous machines (PMSMs) have been widely used in various applications, e.g., aerospace, electric vehicles (EVs), industrial drives, servo drives including robots and automation systems, domestic appliances, and wind power generation.
Accurate parameter estimation of PMSMs, including electrical and mechanical parameters, i.e., stator resistance, inductances, rotor flux linkage, and system inertia, is essential for determining the machine characteristics [2–4], improving general control performance [5–8], sensorless control [9–13], and thermal condition monitoring [14–18] for preventing potential irreversible demagnetization of PMs and damage of winding insulation and further improving torque density, as well as fault diagnosis, etc. For example, in EV applications, accurate electrical parameters are required for determining the machine saliency, the reluctance torque, the base speed, the maximum operating speed, the optimal current trajectories under maximum torque per ampere, and maximum power per voltage strategies. For the most common control methods, i.e., field-oriented control (FOC), direct torque control (DTC), as well as model predictive control (MPC), the accurate PMSM parameters are critical to ensuring system stability and improving efficiency and dynamic response. The mechanical parameters, e.g., moment of inertia and viscous friction coefficients, vary significantly with mechanical loads and are important in the design of speed-loop controllers.
Traditionally, the parameters are determined by static open-circuit and short-circuit tests and/or finite element methods. They have significant disadvantages: (a) the machine dimensions and material parameters should be pre-known, (b) there is a rank deficiency issue in most online parameter estimation techniques, (c) parameters are obtained under different operation conditions with conflicts, and (d) variations in speed and load cannot be tracked accurately, which will result in significant errors accounting for magnetic saturation and cross-coupling effect, etc.
In the last few decades, the techniques of parameter estimation have been extensively developed and the parameter estimation can be implemented both offline and online. Generally, offline parameter estimation is essential both in the machine and controller design and has been widely used and investigated [19], in which various computational methods can be employed, i.e., finite element analysis (FEA) and numerical, observer-, and artificial intelligence (AI)-based methods.
However, changes in operation conditions, temperature, mechanical stress, and other environmental factors may cause parameter variations in electrical machines, particularly PMSMs. These variations could result in deteriorated performance, reduced efficiency, and potential damage to the machine over time. To address these challenges, online parameter estimation techniques aim to acquire electrical, mechanical, or thermal parameters under real-time conditions using data gathered during the machine operation [19]. These techniques allow for the continuous monitoring and adjustment of the machine parameters, ensuring that the control system can adapt to changing conditions to maintain optimal performance, and monitoring that the winding and PM temperature cannot exceed the maximum allowable values. Indeed, many commercial industrial drives for PMSMs have embodied the features of parameter estimation functions to ensure efficient and reliable operation.
This book provides a comprehensive resource on basic and state-of-the-art online and offline parameter estimation techniques for PMSMs, including various new online parameter estimation techniques developed at the University of Sheffield and those developed globally, as well as modern control theory–based parameter estimation techniques, with examples of both experimental and simulation results. It addresses the issues of rank deficiency and inverter non-linearity and reports various new online electrical and mechanical parameter estimation techniques for PMSMs, including those with the aid of thermocouples in stator windings, based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter non-linearity, temperature effects, etc. Various applications of parameter estimation techniques of PMSMs for electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances are also reported for improving control performance and sensorless operation, condition monitoring/fault diagnosis, etc.
This chapter briefly describes PMSMs and drives and introduces mathematical models, machine parameters, and parameter estimation techniques accounting for the influence of magnetic saturation and temperature on parameters.
1.2 Permanent Magnet Machines
A typical electrical drive system for PMSMs mainly consists of an electrical machine, a power converter, a load, a rotor position sensor, and a control unit with an employed control strategy. A schematic diagram of a PMSM drive system is shown in Figure 1.1 and will be described in more detail in Section 1.4.
Figure 1.1 Schematic diagram of PMSM drive system.
In most PMSMs, PMs are usually located on the rotor for excitation. According to the directions of the magnetic flux in the air gap, the majority of PMSMs can be categorized into radial and axial flux machines, of which radial-flux rotor PM machines are the most common in terms of electromagnetic performance, manufacturability, cost, etc. The radial-flux rotor PM machines have either an internal or external rotor, while the PMs could be assembled either on the surface or in the interior of the rotor, as shown in Figure 1.2.
Figure 1.2 Machine configurations of radial-flux internal rotor PMSMs: (a) surface-mounted PM, (b) surface-inset PM, (c) I-type interior PM (radially magnetized), and (d) spoke-type interior PM (circumferentially magnetized).
In surface-mounted PM (SPM) machines, as shown in Figure 1.2a
