Investigation of PWM-induced rotor harmonic losses in IPMSMs considering axial leakage effects of step-skews

국문 초록 (Abstract)

최근 시스템 성능 향상을 위한 모터의 고출력밀도화가 요구되고 있다. 이로 인해 고에너지밀도를 갖는 희토류 영구자석형 모터 중 고속 구동 시 출력 향상에 유리한 매입형 영구자석 동기 전동기 (interior permanent magnet synchronous motors, IPMSMs)에 대한 연구, 개발이 활발히 이뤄지고 있다. 모터의 고출력밀도화는 손실밀도의 악화를 초래하여 발열량을 증가시키게 된다. 모터의 발열은 영구자석의 불가역 감자로 인한 영구적인 성능 악화 등 모터 성능에 영향을 미치게 된다. 따라서 고성능 모터의 설계를 위해 모터의 열원으로 작용하는 전자계 손실에 대한 고려가 필수적으로 나타나게 된다.
전자계 손실 중, 영구자석 와류손은 전체 손실 중 큰 비중을 차지하지는 않지만, 영구자석의 직접적인 열원으로 작용하게 된다. 따라서 모터의 고출력밀도화에 따라 해당 손실 고려의 중요도가 상승하게 된다. 하지만 해당 손실의 고려를 위해서는 3차원 수치해석이 요구되어 많은 계산 비용이 요구된다. 뿐만 아니라 해당 손실의 주요 원인으로 나타나는 pulse-width modulation (PWM) 인버터에 의한 전류 고조파 성분을 고려가 필요하게 되어 계산 비용이 급증하게 된다. 이로 인해 설계 단계에서의 영구자석 와류손에 대한 고려가 실질적으로 불가하게 된다. 따라서 본 논문에서는 고성능 IPMSM의 설계 시, PWM 전류 고조파에 의해 유도되는 영구자석 와류손의 고려를 위한 해석 기법의 연구를 수행하였다. 먼저, 자기 등가회로를 기반으로 IPMSM의 step-skew 구조로 인해 발생하는 3차원
자속 경로에 의한 d-q 축 인덕턴스 변화에 대한 연구를 수행하였다. 이를 통해 d-q 축 인덕턴스에 의한 PWM 전류 고조파의 모델링을 수행하였다. 이후 T-Ω 기법과 영구자석 분할로 인한 3차원 형상에 따른 영구자석 와류손의 분석을 통해 2차원 수치해석 기반의 영구자석 와류손 모델링과 산정 결과의 검증을 수행하였다. 3차원 수치해석 결과와의 비교와 모터 부하 시험을 통한 검증을 수행하였으며,
검증 결과 약 90%의 계산 비용 저감과 10% 내외의 오차 발생을 통한 정합성을 확인하여 연구기법을 통한 IPMSM의 영구자석 와류손 산정의 효용성을 검증하였다. 뿐만 아니라 연구기법을 적용한 IPMSM의 에너지효율 최적설계를 수행하여 연구기법을 통한 단일 모델의 손실 산정 뿐만 아닌 설계 단계에서의 영구자석 와류손 검토의 효용성 또한 검증하였다.

다국어 초록 (Multilingual Abstract)

Recently, the demand for high-power density motors has been increasing to enhance system performance. Consequently, intensive research and development have been conducted on interior permanent magnet synchronous motors (IPMSMs), which are advantageous for improving output characteristics during high-speed operation due to rare-earth permanent magnet (PM) with high-energy density. However, the increase in power density leads to the deterioration of loss density, thereby causing an increase in heat generation. The resulting temperature rise affects motor performance by inducing irreversible demagnetization of the PMs. Therefore, consideration
of the electromagnetic losses acting as heat sources is essential for the design of high-performance motors. Among the electromagnetic losses, the PM eddy current loss (PMECL) does not occupy a large proportion of the total losses but serves as a direct heat source for the magnet. Therefore, its consideration becomes increasingly
important as motor power density increases. However, accurate evaluation of this loss requires three-dimensional numerical analysis, which entails a high
computational cost. Moreover, since the dominant cause of this loss is the current harmonics generated by the pulse-width modulation (PWM) inverter, additional consideration of these harmonics further increases the computational burden. As a result, it becomes practically infeasible to consider
PMECL during the design stage. Therefore, this study investigated an analysis method for considering PMECL induced by PWM current harmonics in the design of high-performance IPMSMs. First, the variation of the d–q axes inductances caused by three-dimensional flux paths generated by the step-skew structure of the IPMSM was analyzed based on a magnetic equivalent circuit. Using these results, the PWM current harmonics were modeled as functions of the d–q axes inductances. Subsequently, the T–Ω method and analysis of three-dimensional geometries resulting from magnet segmentation were employed to evaluate PMECL. Based on this, a two-dimensional numerical-analysis based modeling and estimation method for PMECL was proposed and validated. The proposed method was verified through comparison with three-dimensional numerical analysis and experimental load tests, demonstrating approximately 90% reduction in computational cost while maintaining an estimation error within 10%, thereby confirming the validity of the proposed approach for PMECL estimation in IPMSMs. Furthermore, an energy-efficiency optimization of the IPMSM incorporating the proposed method was performed, verifying not only the accuracy of loss estimation for a single model but also the practicality of applying PMECL evaluation during the design stage.

목차 (Table of Contents)

• 1. Introduction 1
• 1.1 Research background 1
• 1.2 Previous research 7
• 1.2.1 Research related to design methodologies 7
• 1.2.2 Research related to analysis methodologies of electromagnetic losses 10
• 1.3 Objective of research 12
• 1.4 Organization of dissertation 13
• 2. Fundamental Theory 14
• 2.1 Electromagnetic Analysis of PMSM 14
• 2.1.1 Characteristics of PMSM 14
• 2.1.2 Governing Equation of PMSM 17
• 2.1.3 Electromagnetic Losses of PMSM 20
• 2.2 Thermal Analysis of PMSM 29
• 2.2.1 Lumped Parameter Thermal Network (LPTN) 29
• 2.2.2 Thermal analysis of PMSM based on electromagnetic losses 36
• 2.3 Basic Principle of PWM Inverter 39
• 2.3.1 Basic Principle of Inverter 39
• 2.3.2 Pulse-width modulation inverter 47
• 2.3.3 Space vector PWM 54
• 3. PWM Current Harmonic Modeling Considering Axial Leakage Effects 60
• 3.1 Properties of Rotor Harmonic Losses in PMSMs 60
• 3.2 Modeling of PWM Current Harmonics 64
• 3.2.1 Mathematical Model of PWM Current Harmonics 64
• 3.2.2 Circuit Model of PWM Harmonics 65
• 3.2.3 Comparison between Mathematical Model and Circuit Model 73
• 3.3 Variance of Inductance due to Axial Leakage Effects 75
• 3.3.1 Leakage Flux of PMSMs 75
• 3.3.2 Variation of d- and q- axes Inductances due to Step-Skews 77
• 3.3.3 Electromagnetic Performances due to the Change of Inductances 82
• 3.4 Modeling of Axial Leakage Effects of Step-Skews 86
• 3.4.1 Skew Factor in the Winding Factor 86
• 3.4.2 Coefficient for Axial Leakage Effect of Step-Skews 88
• 4. Estimation of PWM-induced Rotor Harmonic Losses in PMSM 93
• 4.1 Analysis of Rotor Harmonic Losses in IPMSMs 93
• 4.1.1 Limitation of 2-D FEA for estimation of PM eddy current loss 93
• 4.1.2 Computational cost of PMECL estimation applying PWM current and 3-D FEA 97
• 4.1.3 Development of Reduced-Order PMECL Computational Framework 100
• 4.2 Modeling of PMECL in IPMSM with Axial Segmented PM 101
• 4.2.1 Specification of Analysis Model 101
• 4.2.2 Components of PMECL 104
• 4.2.3 Application of T-Ω Method for Calculation of the XPM-axis loss 111
• 4.2.4 Calculation of Coefficient for PM Axial Segmentation 115
• 5. Verification of the Proposed Method 120
• 5.1 Comparison between the 3-D FEA and the Proposed Method 120
• 5.2 Experimental Validation 126
• 6. Optimization using the Proposed Method 134
• 6.1 Energy Efficiency of EV Powertrain 134
• 6.1.1 Limitation of Motor's Efficiency Map in Design Stage 134
• 6.1.2 Definition of Energy Efficiency 137
• 6.2 Surrogate Model of IPMSM for Optimization 138
• 6.2.1 Specifications of EV 138
• 6.2.2 Driving Cycle and Operating Points 139
• 6.2.3 Feedforward Neural Network 145
• 6.2.4 Construction of Surrogate Model 146
• 6.3 Energy Efficiency Optimization of IPMSM 152
• 7. Conclusion 158
• References 160
• Korean Abstract 167