Performance Comparison of Permanent Magnet and Electrically Excited Motors for Electric Vehicles

This research presents two types of electric motors, an electrically excited synchronous motor (EESM) and an interior permanent magnet (IPM) motor, for an electric vehicle (EV) application based on a Volkswagen ID.3 2020 reference model. The IPM motor is well known for its high efficiency, high torque density, and extended speed range due to magnets placed inside the rotor, but the performance of this motor was affected by the rotor topologies as proposed in the study [1]. This paper presented a way to reduce the torque ripple and electromagnetic vibration via a change of the new rotor configuration for V-shaped rotor of the IPM. In the studies [2, 3], an enhanced skewing technique and a novel dual-rotor axial-gap flux-switching permanent-magnet machine were presented to effectively reduce both cogging torque and electromagnetic torque ripple. In the study [4], a paper introduced a topology utilizing a homopolar machine configuration. The design incorporated consequent-pole permanent magnet (PM) poles positioned on the stator surface, while the DC field winding was wound around the mover yoke. The paper [5] presented a novel design for a hybrid excitation synchronous machine in which a magnetic shunting rotor to enhance torque density and flux regulation capability, particularly in the EV traction applications.

In the study [6], the authors redesigned and improved each topology to meet new design requirements based on the same constraints, and evaluate the motors for motor performance, torque segregation, demagnetization, mechanical stress, and radial forces. A new approach for designing permanent magnet synchronous motors (PMSMs) by optimizing the PM structure to achieve better performance and lower manufacturing costs [7]. The studies [8, 9] provided a valuable contribution to the fields of IPM machine via the finite element analysis. The results could have significant practical implications for the development of high-performance traction systems. The authors [10] proposed a new approach based on the detection method for sensorless control of the IPMSM to improve initial rotor position. The irreversible demagnetization level of the line-start PM assistance synchronous reluctance motors (PMA-SynRMs) was investigated to evaluate the efficiency, torque and output power [11].

In this paper, a comparative analysis of the EESM and IPM motors for an EV application is presented via the analytic model and finite element method to examine and simulate the torque, power, efficiency map and current with a step-skewed magnet rotor. It will be intriguing to observe the impact of the hybrid rotor shape and step-skewed magnet segment on the motor performance, as well as to determine if the EESM can rival the IPM motor in terms of efficiency and torque density.

The structure of this study can be outlined as follows: In Section 2, it provides an overview of the analytical program of IPM and EESM designs, focusing on their main context. In Section 3, it delves into the theoretical background concerning the electromagnetic performance analysis of the proposed machine, providing a comprehensive analysis. In Section 4, it presents an analysis of various electromagnetic performance aspects, including flux density, cogging torque, output power, power loss, and efficiency. Finally, the conclusion section summarizes the main findings and contributions of the study.

In order to satisfy the performance specifications given in Table 1 and Figure 2 for the electric vehicle (EV), the motors used in the design must exhibit exceptional capabilities in flux-weakening and peak torque output while operating within the limits of current and voltage imposed by the inverter. Consequently, the primary restriction involves the maximum current and voltage for the IPM motor and EESM, which can be derived from reference [12, 13].

Basic parameters are defined by an analytical model. Indeed, if the rotor diameter (D) is equal to rotor length (L), the electromagnetic torque (T) of the IPM motor can be defined [12, 13]:

$T=\frac{\pi}{4} . D^2 . L_s . T R V$               (1)

where, the torque volume density (TVR) is then defiened as:

$T R V=\frac{\pi}{\sqrt{2}} k_{W 1} A . B \mathrm{Nm} / \mathrm{m}^3$               (2)

At a synchronous speed, the electromagnetic torque and power can be computed via the phasor diagram as pointed out in Figure 6.

6.png

Figure 6. Phasor diagram of IPM motor

The phasor diagram is divided into two parts: the electrical quantities on the left side and the corresponding magnetic flux linkages on the right side. The magnetic flux linkages are represented by space vectors, which are three-dimensional vectors that rotate in space at an angular velocity. These vectors are used to describe the physical orientation of the magnetic flux in the motor. The space vectors can also be projected onto a 2-D to create a phasor diagram that represents the magnitude and phase angle of the magnetic flux linkages. In general, the phasor diagram is a useful tool for analyzing the performance of electric machines, including IPM and EESM motors. It allows designers and engineers to visualize the relationship between electrical and magnetic quantities, and to make informed decisions about the design and operation of the motor.  

Based on the diagram in Figure 6, the armature current ( $I_{\text {arm }}$ ) is defined via the d- and q- axis component currents (I_d and I_q) [12, 13]:

$I_{\text {arm }}=\sqrt{I_d^2+I_q^2} \leq I_{\text {arm_max }}$               (3)

where, I_{arm_max} is the maximum current given by the inverter. The maximum phase (V_{arm_max}) is thus defined as:

$V_{\text {arm_max }}=p \sqrt{\left(L_d I_d+\lambda_m\right)^2+\left(L_q I_q\right)^2} \leq \frac{V_{D C}}{\sqrt{3} w_r}$               (4)

where, p is the number of pole pair, L_d is the d-axis inductance, L_q is the q-axis ductance, V_DC is the battery voltage and w_r is the speed of rotor. At the maximum speed (w_{r_max}), the back electromagnetic force (EMF) (E) is defined as:

$E=p \lambda_m w_{r_{-} \max } \leq \frac{V_{D C}}{\sqrt{3}}$               (5)

In order to obtain a maximum flux weakening capability and constant power speed range, it is required by the traction motor. For the IPM motor, the condition need to be satisfied [12]:

$\lambda_m=L_d I_{\text {arm }}$               (6)

and for the EESM motor [13]:

$\lambda_m=L_q I_{\text {arm }}$               (7)

It should be noted that the conditions in (8) and (9) are the ideal conditions. The linkage flux in stator is actually limited, thus the PM will not be demagnetized.

In order to obtain the high efficiency for a wide speed range, the maximum torque per ampere control at the low speed is maintained for the peak torque and the flux weakening control at the high speed. For the two types of motors, the electromgantic torque are then expressed as [14-16]:

$\begin{aligned} & T=\frac{3}{2} p\left[\lambda_d\left(I_d, I_q\right) I_q-\lambda_q\left(I_d, I_q\right) I_d\right] =\frac{3}{2} p[\lambda_d\left(I_d=0, I_q\right) I_q +\frac{\lambda_d\left(I_d, I_q\right)-\lambda_d\left(I_d=0, I_q\right)}{I_d} I_d I_q -\frac{\lambda_q\left(I_d, I_q\right)}{I_q} I_d I_q] =\frac{3}{2} p\left\{\lambda_m\left(I_q\right) I_q\right. \left.+\left[L_d\left(I_d, I_q\right)-L_q\left(I_d, I_q\right)\right] I_d I_q\right\} \\ & \end{aligned}$               (8)

where, λ_d and λ_q are d- and q-axis flux linkage, respectively. The flux linkages of PM are then expressed by [17, 18]:

$\lambda_m\left(I_q\right)=\lambda_d\left(I_d=0, I_q\right)$               (9)

$\lambda_d\left(I_d, I_q\right)=L_d\left(I_d, I_q\right) I_d+\lambda_m\left(I_q\right)$               (10)

$\lambda_q\left(I_d, I_q\right)=L_q\left(I_d, I_q\right) I_q$               (11)

It should be noted that from Eqs. (3)-(11), the value of pλ_m in Eqs. (10) and (11) is small for a low back EMF at a high speed. On the other hand, it is large for the high torque and a high efficiency.

The analysis and comparison of flux density torque, power and efficiency of the EESM and IPM motor for EV applications have been successfully obtained. The obtained results have shown that the EESM has some advantages over the IPM motor in terms of efficiency and output power, particularly in the lower-torque and higher-speed regions. This information could be valuable for researchers and engineers working in the field of electric vehicle motor design and development. Also, the development of the proposed method suggests that the EESM can be a promising solution for improving the performance of electromagnetic parameters in various applications.