International Journal of Applied Electromagnetics and Mechanics 33 (2010) 343–350 343

DOI 10.3233/JAE-2010-1132

IOS Press

A study on the performance simulation of interior permanent magnet synchronous motor for electric vehicle considering nonlinear parameters

Ki-Chan Kim^lowast;

Department of Electrical Engineering, Hanbat National University, Dukmyung, Yuseong, Daejeon, 305-719, South Korea

Abstract. In this paper, we propose a simulation algorithm for driving characteristics of interior permanent magnet synchronous motor (IPMSM) for electric vehicle considering nonlinear parameters like d-axis and q-axis inductances as well as core loss. D-axis and q-axis inductances as well as core loss parameter are changed according to both current magnitude and current angle between q-axis and current axis because of nonlinearity of magnetic flux density in stator and rotor core. Therefore, the calculation of d-axis and q-axis inductances with nonlinearity of magnetic flux density and core loss is performed by using FEM. We can get precise driving performance of traction motor for electric vehicle adopting nonlinear d-axis and q-axis inductance table and core loss table.

Keywords: Electric vehicle, IPMSM, driving characteristics, nonlinear inductance and core loss

Introduction

It is important to calculate exact values of d-axis and q-axis inductances at the design stage of interior permanent magnet synchronous motor (IPMSM) because these parameters are related to torque and speed characteristics of IPMSM closely if it is controlled by field weakening control mode [1,2]. The d-axis inductance and the q-axis inductance mean the ratio of linkage flux to input current of d-axis and q-axis, respectivelywhich are perpendiculareach other. D-axis means the direction-axis of magnetic flux of permanent magnet rotor and q-axis means the direction-axis which is displaced 90 degree in electrical angle from the d-axis. However, it is very difficult to calculate the exact d-axis and q-axis parameters in an application area which is needed for compact and high power density design owing to magnetic flux saturation phenomenon in its steel core. Analytical method by using equivalent magnetic circuit makes the error of d-axis and q-axis inductance values maximize under the extreme magnetic saturation region [3]. Therefore, d-axis and q-axis inductances considering nonlinear characteristics according to current angle between q-axis and current axis as well as magnitude of armature current should be analyzed by FEM. Moreover, in order to calculate an efficiency map for traction motor precisely, core

^lowast;Corresponding author: Ki-Chan Kim, Tel.: 82 42 821 1090; Fax: 82 42 821 1088; E-mail: kckim@hanbat.ac.kr.

1383-5416/10/$27.50  2010 – IOS Press and the authors. All rights reserved

Table 1

Brief specifications of IPMSM

Fig. 1. Analysis model and proto type of IPMSM for electric vehicle.

loss should be analyzed according to its rotation speed and its operation current by using FEM in which core loss can be solved by distributed potentials at each element node.

In the paper, a simulation algorithm for driving performance of IPMSM considering nonlinearity of d-axis and q-axis inductances as well as core loss according to current angle and current magnitude is studied. Moreover, the algorithm is very effective for performance analysis of traction motor for electric vehicle with field weakening control which needs the information on the d-axis and q-axis inductances according to current angle. The driving performance only considering constantvalue of d-axis and q-axis inductances is compared with proposed one.

Nonlinearity of inductance and core loss

Figure 1 shows analysis model of IPMSM for the paper. It is a 4 kW traction motor which application is NEV (neighborhood electric vehicle) whose power source is 48 V battery. Table 1 shows brief specifications of IPMSM.

There are several methods for the calculation of d-axis and q-axis inductances [4]. In the paper, we adopted the inductance calculation method derived from two-axis vector diagram of IPMSM as shown in Fig. 2. In the figure, we can calculate d-axis and q-axis inductances by using following equations based

Fig. 2. 2-axis Vector Diagram of IPMSM for the calculation of inductances.

Fig. 3. The magnetic flux density distribution by FEM analysis.

on amarteur reaction field theory, respectively.

, (1)

, (2)

Where, Psi;0 is linkage flux of phase winding at load operation, Psi;_a lt;

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外文翻译

中文题目：考虑非线性参数的电动车用永磁同步电机性能仿真研究

外文题目：A study on the performance simulation of interior permanent magnet synchronous motor for electric vehicle considering nonlinear parameters

International Journal of Applied Electromagnetics and Mechanics 33 (2010) 343–350 343

DOI 10.3233/JAE-2010-1132

IOS Press

考虑非线性参数的电动车用

永磁同步电机性能仿真研究

Ki-Chan Kim

韩国国立韩巴大学，电气工程系，Dukmyung, Yuseong, Daejeon，305-719，南韩

摘要：本文针对电动汽车内永磁同步电机（IPMSM）的驱动特性，提出了一种考虑D轴、Q轴电感等非线性参数以及铁心损耗的仿真算法。由于定子和转子铁心中磁通密度的非线性，根据电流大小和Q轴与电流轴之间的电流角，改变了D轴和Q轴电感以及铁心损耗参数。因此，采用有限元法计算了具有磁通密度和磁芯损耗非线性的D轴和Q轴电感。采用非线性D轴、Q轴电感表和磁芯损耗表，可以获得电动汽车牵引电机的精确驱动性能。

关键词：电动汽车；永磁同步电动机；驱动特性；非线性电感和磁芯损耗

1. 说明

在内部永磁同步电动机（IPMSM）设计阶段，计算其D轴和Q轴电感的精确值非常重要，因为如果采用弱磁控制方式[1,2]控制，这些参数与IPMSM的转矩和速度特性密切相关。d轴电感和q轴电感分别表示d轴和q轴的连接磁通与输入电流之比，它们彼此垂直。d轴是永磁转子磁通量的方向轴，q轴是从d轴电角度偏移90度的方向轴。然而，由于钢芯中存在磁通饱和现象，在紧凑高功率密度设计所需的应用领域中，很难精确计算出D轴和Q轴参数。利用等效磁路的分析方法，使极端磁饱和区的d轴和q轴电感值的误差最大化[3]。因此，根据Q轴与电流轴之间的电流角以及电枢电流的大小，考虑非线性特性的D轴和Q轴电感应采用有限元法进行分析。此外，为了精确计算牵引电机的效率图，应根据电机的转速和运行电流，采用有限元法对电机铁心损耗进行分析，其中铁心损耗可通过各单元节点的分布电位来求解。

表 1

IPMSM的简要概述

图1. 电动汽车用永磁同步电机的分析模型和原型

本文研究了一种考虑d轴和q轴电感非线性以及电流角和电流幅度对磁芯损耗的永磁同步电动机驱动性能的仿真算法。此外，该算法对于弱磁控制的电动汽车牵引电机的性能分析非常有效，需要根据电流角对电机的D轴和Q轴电感进行信息分析。比较了仅考虑d轴和q轴电感恒定值的驱动性能。

1. 电感和铁心损耗的非线性

图1显示了本文的IPMSM分析模型。它是一个4千瓦的牵引电机，应用于NEV（邻里电动汽车），其电源为48伏电池。表1显示了IPMSM的简要规格。

图2. 用于计算电感的IPMSM的二轴矢量图.

图3. 通过有限元分析得到了磁通密度分布.

计算d轴和q轴电感有几种方法[4]。本文采用了由IPMSM的两轴矢量图导出的电感计算方法，如图2所示。在图中，我们可以分别使用基于阿玛特厄反应场理论的下列方程

来计算d轴和q轴电感：

， (1)

， (2)

式中，Psi;0为相绕组在负载运行时的联动磁通，Psi;_a为相绕组在空载运行时的联动磁通，alpha;为Psi;0与Psi;_a的夹角。

图3表示空载运行时磁通密度的有限元结果。由于磁芯中的磁饱和，d轴和q轴的电感随输入电流大小和q轴和电流轴之间的电流角而变化。这是因为即使在空载运行时，由于高能永磁体，气隙附近的磁通密度也会饱和。用有限元法计算电感的结果分别如图4（a）和图4（b）所示。图4（a）的分析条件是固定负载角delta;产生最大扭矩和可变输入电流i_a。另一方面，图4（b）的分析条件是可变负载角delta;和固定输入电流i_a，后者是46.5 A连续模式下的额定电流。图中，由于IPMSM的核心存在锰饱和，d轴和q轴之间的电感间隙根据输入电流的大小而减小。此外，由于Armateur反应场的磁饱和，在超过150负载角时，它开始减小。

图4. D轴和Q轴电感的有限元分析结果.

图5. 用有限元法对芯部损耗进行了分析

图5显示了使用FEM根据输入电流大小和负载角的非线性磁芯损耗特性。在频率域中，损耗分离法通常用于计算堆芯损耗[5]。

Pv = Ph Pc Pe = khfBmbeta; kc(fBm)2 ke(fBm)1.5 (3)

根据系数k_h, k_c, k_e和参数beta;，可以根据不同的峰值感应系数B_m和频率f计算单位体积P_v的总磁芯损耗，但用频域模型很难考虑谐波对小磁滞回线的影响。因此，我们决定采用D. Lin [6]提出的一种替代的动态滞回模型，用时间函数式（3）中的系数k_h(t), k_c(t), k_e(t)代替常值。

1. 电动汽车牵引电机驱动性能算法

一般来说，电动汽车的IPMSM采用最大功率控制模式控制，包括弱磁控制。然而，由于磁芯中的磁饱和，d轴和q轴电感具有非线性。因此，本文提出了一种考虑非线性daxis和q轴电感的IPMSM驱动性能算法。图6显示了驱动性能算法的流程图，该算法分为恒转矩和恒功率两种控制模式。为了考虑d轴和q轴电感的非线性，必须处理负载角和电流大小之间的电感表。该算法可以根据电机转速计算电压、电流、效率、功率因数、转矩、输出功率。图7显示了D轴和Q轴电流和电压、由磁阻转矩和磁转矩组成的总转矩、输出功率、功率因数和效率（根据电机转速）的模拟结果。特别是根据驱动速度计算了逆变器的电流矢量和电压矢量。从这些数据可以验证高速区的特性以及永磁同步电动机的起点。图8显示了利用所提出方法的整个驱动区域的效率结果得到的IPMSM的效率图。

图6.基于控制模式（恒转矩和恒功率模式）的永磁同步电动机驱动性能算法

图7.基于电机转速的永磁同步电动机转矩特性分析结果

图8.IPMSMS效率图分析结果

图9.用电感线性值和间歇模式下的非线性电感表计算转矩和功率参数的比较结果。

如果根据角度，我们有明显的误差，特别是在高速区域。考虑电感线性值和非线性值的驱动性能比较结果如图9所示。当输入电流为120A时，根据电机转速对应转矩和功率特性。

4.结论

本文提出了IPMSM非线性D轴和Q轴电感的有限元分析方法，提出了考虑非线性D轴和Q轴电感以及铁心损耗的最大功率控制模式驱动性能的算法，并通过仿真过程进行了验证。该算法可以方便地绘制出电动汽车牵引电机的效率图，是电动汽车牵引电机的主要设计目标。

致谢

这项研究得到了国家基础科学研究计划的支持。韩国基金会（NRF）由教育部、科技部资助（20100016727）。

参考文献

1. M.N. Uddin, T.S. Radwan and M.A. Rahman, Performance of Interior Permanent Magnet Motor Drive over Wide Speed Range, IEEE Transactions on Energy Conversion 17(1) (2002), 79–84.
2. J.S. Moghani and J.F. Eastham, Field Weakening Performance of a Linear Brushless AC Machine, IEEE Transactions on Magnetics 32(5) (1996), 5007–5009.
3. S.Y. Kwak, J.K. Kim and H.K. Jung, Characteristic Analysis of Multilayer-Buried Magnet Synchronous Motor using Fixed Permeablity Method, IEEE Transactions on Energy Conversion 20(3) (2005), 549–555.
4. K.C. Kim, J.S. Ahn, S.H. Won, J.P. Hong and J. Lee, A Study on the Optimal Design of SynRM for the High Torque and Power Factor, IEEE Transactions on Magnetics 43(6) (2007), 2543–2545.
5. G. Bertotti, General Properties of Power Losses in Soft Ferromagnetic Materials, IEEE Transactions on Magnetics <stron

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