France



I. INTRODUCTION&lt;br/&gt;In order to achieve reliable and high-performance control of permanent magnet synchronous machines (PMSMs), the accurate model of electromagnetic characteristics of PMSMs under different load conditions is critical [1]. The conventional method is to use the finite element analysis (FEA) to derive the magnetic model of PMSM [2]. However, this method requires accurate geometric parameters and material information of the machine and the results must be validated by experiments. Therefore, it is desirable to obtain accurate machine model from measurable terminal signals.&lt;br/&gt;To date, considerable research work has been conducted to deal with the flux linkage identification problem for PMSMs [3]-[5]. However, either magnetic saturation or spatial harmonics effects have been ignored during the flux linkage identification in the existing methods. Therefore, this paper proposes a novel two-step flux linkage identification method for PMSMs considering both magnetic saturation and spatial harmonics. Step one is an offline estimation of the flux linkages considering magnetic saturation based on genetic algorithm (GA) , while the spatial harmonics effect has been mitigated compared with the existing method. In the second step, a state-space observer is employed to estimate the spatial harmonics online with the estimated offline data in step one. In addition, Kalman filter is applied in dq-axis inductances harmonics estimation to reduce the influence of noise and high order harmonics in the motor drive system. Therefore, the proposed method achieves to consider both magnetic saturation and spatial harmonics for PMSM flux linkage identification. The proposed approach is validated on both the surface-mounted and interior PMSMs.&lt;br/&gt;II. Magnetic Saturation Modeling and Parameter Estimation using GA&lt;br/&gt;To consider magnetic saturation in the machine model, the dq-axis flux linkages are modeled using the quadratic equation as in (1).&lt;br/&gt;Ψ&lt;sub&gt;d&lt;/sub&gt;(i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;)= α&lt;sub&gt;0&lt;/sub&gt;+α&lt;sub&gt;1&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;+α&lt;sub&gt;2&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;+α&lt;sub&gt;3&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;+α&lt;sub&gt;4&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;+α&lt;sub&gt;5&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;;&lt;br/&gt;Ψq(i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;)= β&lt;sub&gt;0&lt;/sub&gt;+β&lt;sub&gt;1&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;+β&lt;sub&gt;2&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;+β&lt;sub&gt;3&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;+β&lt;sub&gt;4&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;+β&lt;sub&gt;5&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;. (1)&lt;br/&gt;Where i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;, Ψ&lt;sub&gt;d&lt;/sub&gt;, Ψ&lt;sub&gt;q&lt;/sub&gt; are dq-axis currents and flux linkages; α&lt;sub&gt;0&lt;/sub&gt; denotes the fundamental PM flux linkage; β&lt;sub&gt;0&lt;/sub&gt; is adopted to generalize the quadratic form of the model and compensate the offset for Ψ&lt;sub&gt;q&lt;/sub&gt;; α&lt;sub&gt;1&lt;/sub&gt; and β&lt;sub&gt;1&lt;/sub&gt; denote self-inductances in the dq-axis; α&lt;sub&gt;2&lt;/sub&gt;,…, α5 and β&lt;sub&gt;2,…,&lt;/sub&gt; β&lt;sub&gt;5 &lt;/sub&gt;denote the cross-coupling effect and the influence of magnetic saturation. There are 12 parameters to be estimated, while the rank number is two. Therefore, the coefficients of flux linkages equations cannot be solved directly as it is rank-deficient. To solve this issue, a GA based estimation approach is proposed.&lt;br/&gt;Suppose that, for a given pair of (i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;), the (u&lt;sub&gt;d&lt;/sub&gt;, u&lt;sub&gt;q&lt;/sub&gt;) under a certain speed ω&lt;sub&gt;m&lt;/sub&gt; during the period T seconds (T=2πn/ω&lt;sub&gt;m&lt;/sub&gt;, where n=1,2, …,N represents the number of rotations) are recorded in order to mitigate the influence of spatial harmonics. To estimate the coefficients of flux linkages, two fitness functions are designed as follows:&lt;br/&gt;F&lt;sub&gt;d&lt;/sub&gt; = ∑&lt;sub&gt;i=1..I&lt;/sub&gt;∑&lt;sub&gt;j=1..J&lt;/sub&gt;[α&lt;sub&gt;0&lt;/sub&gt; + α&lt;sub&gt;1&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;(i) + α&lt;sub&gt;2&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;(j) + α&lt;sub&gt;3&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(i) +α&lt;sub&gt;4&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(j) + α&lt;sub&gt;5&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;(i)i&lt;sub&gt;q&lt;/sub&gt;(j)-Ψ&lt;sub&gt;d&lt;/sub&gt;(i&lt;sub&gt;d&lt;/sub&gt;(i), i&lt;sub&gt;q&lt;/sub&gt;(j))];&lt;br/&gt;F&lt;sub&gt;q&lt;/sub&gt; = ∑&lt;sub&gt;i=1..I&lt;/sub&gt;∑&lt;sub&gt;j=1..J&lt;/sub&gt;[β&lt;sub&gt;0&lt;/sub&gt; + β&lt;sub&gt;1&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;(i) + β&lt;sub&gt;2&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;(j) + β&lt;sub&gt;3&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(i) +β&lt;sub&gt;4&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;(j) + β&lt;sub&gt;5&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;(i)i&lt;sub&gt;q&lt;/sub&gt;(j)-Ψ&lt;sub&gt;q&lt;/sub&gt;(i&lt;sub&gt;d&lt;/sub&gt;(i), i&lt;sub&gt;q&lt;/sub&gt;(j))], (2)&lt;br/&gt;where i=1,…, I and j=1,…, J are directories of (i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;). Based on (2), the coefficients of dq-axis flux linkages at each pair of (i&lt;sub&gt;d&lt;/sub&gt;, i&lt;sub&gt;q&lt;/sub&gt;) can be obtained by using GA to achieve the minimization of F&lt;sub&gt;d&lt;/sub&gt; and F&lt;sub&gt;q&lt;/sub&gt;.&lt;br/&gt;III. Online Parameter Estimation Considering Spatial Harmonics&lt;br/&gt;Considering spatial harmonics, dq-axis voltage equations of a PMSM can be written as (3) under the steady state.&lt;br/&gt;u&lt;sub&gt;d&lt;/sub&gt; = Ri&lt;sub&gt;d&lt;/sub&gt;-ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;qq,0&lt;/sub&gt;i&lt;sub&gt;q+&lt;/sub&gt;ω&lt;sub&gt;e&lt;/sub&gt;Ψ&lt;sub&gt;d6&lt;/sub&gt;sin(6pθ)+sin(6pθ)(-6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dd,6&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;-ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dq,6&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;)+cos(6pθ)(6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dq,6&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;-ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;qq,6&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;)+ε&lt;sub&gt;d&lt;/sub&gt; ; u&lt;sub&gt;q&lt;/sub&gt; = Ri&lt;sub&gt;q&lt;/sub&gt;+ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dd,0&lt;/sub&gt;i&lt;sub&gt;d+&lt;/sub&gt;ω&lt;sub&gt;e&lt;/sub&gt;Ψ&lt;sub&gt;d1&lt;/sub&gt;+ω&lt;sub&gt;e&lt;/sub&gt;Ψ&lt;sub&gt;q6&lt;/sub&gt;cos(6pθ)+sin(6pθ)(-6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;qq,6&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;-ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dq,6&lt;/sub&gt;i&lt;sub&gt;q&lt;/sub&gt;)+cos(6pθ)(6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dq,6&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;-ω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;dd,6&lt;/sub&gt;i&lt;sub&gt;d&lt;/sub&gt;)+ε&lt;sub&gt;q&lt;/sub&gt;, (3)&lt;br/&gt;where u&lt;sub&gt;d&lt;/sub&gt;, u&lt;sub&gt;q&lt;/sub&gt; are dq-axis voltages; θ is the electrical rotor position; p is the number of pole pairs; R is the resistance; ω&lt;sub&gt;e&lt;/sub&gt; is the rotor speed; Ψ&lt;sub&gt;d6&lt;/sub&gt; and Ψ&lt;sub&gt;q6&lt;/sub&gt; are the magnitudes of the 6th permanent magnet (PM) flux-linkage harmonics in dq-axis. L&lt;sub&gt;dd,0&lt;/sub&gt;,L&lt;sub&gt;qq,0&lt;/sub&gt;,L&lt;sub&gt;dd,6,&lt;/sub&gt;L&lt;sub&gt;qq,6 &lt;/sub&gt;are the magnitudes of fundamental and the 6th harmonic of self-inductances in the dq-axis; L&lt;sub&gt;dq,6&lt;/sub&gt; is the magnitude of the 6th harmonic of mutual-inductance; ε&lt;sub&gt;d&lt;/sub&gt; and ε&lt;sub&gt;q &lt;/sub&gt;are high order harmonics and high frequency noise components in the dq-axis. The harmonic magnitudes of the PM flux linkage can be easily obtained by using FFT analysis of the back-electromotive force. To achieve an online identification of the dq-axis inductances harmonics, a state observer is employed.&lt;br/&gt;The state observer model is firstly built based on (3) to get the magnitude of the 6th harmonic of the self-inductance and mutual-inductance in the dq-axis. The state vector is built as:&lt;br/&gt;x=[ L&lt;sub&gt;s6&lt;/sub&gt;cos(6pθ); L&lt;sub&gt;m6&lt;/sub&gt;sin(6pθ); -6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;s6&lt;/sub&gt;sin(6pθ); 6pω&lt;sub&gt;e&lt;/sub&gt;L&lt;sub&gt;m6&lt;/sub&gt;cos(6pθ)], (4)&lt;br/&gt;with L&lt;sub&gt;s6&lt;/sub&gt;=L&lt;sub&gt;dd,6&lt;/sub&gt; and L&lt;sub&gt;m6&lt;/sub&gt;=L&lt;sub&gt;dq,6. &lt;/sub&gt;The estimated dq-axis flux linkage maps are shown in Fig.1 and Fig.2. Detail analysis and experimental results will be given in the full paper.&lt;br/&gt;IV.CONCLUSION&lt;br/&gt;This paper proposes a novel two-step method to identify flux linkages in PMSMs considering both the effects of magnetic saturation and spatial harmonics during the estimation process. In step one, GA is used to estimate the magnetic saturation coefficients of flux linkage. With the results obtained from GA, the Kalman filter based online method is proposed to estimate the spatial harmonics to achieve an accurate estimation of the flux linkage map. The co-simulation results show that the proposed approach is effective for flux linkage estimation.

**References:**

[1] E. Armando, R. I. Bojoi, P. Guglielmi, G. Pellegrino and M. Pastorelli, in IEEE Transactions on Industry Applications, vol. 49, no. 5, pp. 2116-2125, Sept.-Oct. 2013.&lt;br/&gt;[2] N. Bianchi and S. Bolognani, in Proc. Int. Conf. IEEE Ind. Appl., Oct. 1998, pp. 27–34.&lt;br/&gt;[3] Z. Li, G. Feng, C. Lai, W. Li and N. C. Kar, in IEEE Transactions on Transportation Electrification, vol. 5, no. 4, pp. 1430-1440, Dec. 2019.&lt;br/&gt;[4] Q. Chen, W. Zhao, G. Liu, Z. Lin, in IEEE Transactions on Industrial Electronics., vol. 66, no. 2, pp. 944-955, Feb. 2019.&lt;br/&gt;[5] K. Liu, J. Feng, S. Guo, L. Xiao and Z. Zhu, in IEEE Transactions on Industrial Informatics, vol. 14, no. 2, pp. 556-568, Feb. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cdb1bbe318f847c1cdda6bffcdd7b846.jpg)
Fig. 1. SPMSM q-axis flux linkages estimation results.

![](https://assets.underline.io/uploads/markdown_image/1/image/a4a335ed2eb49867f6497eb0dde4319d.jpg)
Fig. 2. IPMSM q-axis flux linkages estimation results.

INTERMAG 2021

 A Novel Two-Step Flux Linkage Identification for PMSMs Considering Magnetic Saturation and Spatial Harmonics

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I. INTRODUCTION In order to achieve reliable and high-performance control of permanent magnet synchronous machines (PMSMs), the accurate model of electromagnetic characteristics of PMSMs under different load conditions is critical [1]. The conventional method is to use the finite element analysis (FEA) to derive the magnetic model of PMSM [2]. However, this method requires accurate geometric parameters and material information of the machine and the results must be validated by experiments. Therefore, it is desirable to obtain accurate machine model from measurable terminal signals. To date, considerable research work has been conducted to deal with the flux linkage identification problem for PMSMs [3]-[5]. However, either magnetic saturation or spatial harmonics effects have been ignored during the flux linkage identification in the existing methods. Therefore, this paper proposes a novel two-step flux linkage identification method for PMSMs considering both magnetic saturation and spatial harmonics. Step one is an offline estimation of the flux linkages considering magnetic saturation based on genetic algorithm (GA) , while the spatial harmonics effect has been mitigated compared with the existing method. In the second step, a state-space observer is employed to estimate the spatial harmonics online with the estimated offline data in step one. In addition, Kalman filter is applied in dq-axis inductances harmonics estimation to reduce the influence of noise and high order harmonics in the motor drive system. Therefore, the proposed method achieves to consider both magnetic saturation and spatial harmonics for PMSM flux linkage identification. The proposed approach is validated on both the surface-mounted and interior PMSMs. II. Magnetic Saturation Modeling and Parameter Estimation using GA To consider magnetic saturation in the machine model, the dq-axis flux linkages are modeled using the quadratic equation as in (1). Ψd(id, iq)= α0+α1id+α2iq+α3id2+α4iq2+α5idiq; Ψq(id, iq)= β0+β1id+β2iq+β3id2+β4iq2+β5idiq. (1) Where id, iq, Ψd, Ψq are dq-axis currents and flux linkages; α0 denotes the fundamental PM flux linkage; β0 is adopted to generalize the quadratic form of the model and compensate the offset for Ψq; α1 and β1 denote self-inductances in the dq-axis; α2,…, α5 and β2,…, β5 denote the cross-coupling effect and the influence of magnetic saturation. There are 12 parameters to be estimated, while the rank number is two. Therefore, the coefficients of flux linkages equations cannot be solved directly as it is rank-deficient. To solve this issue, a GA based estimation approach is proposed. Suppose that, for a given pair of (id, iq), the (ud, uq) under a certain speed ωm during the period T seconds (T=2πn/ωm, where n=1,2, …,N represents the number of rotations) are recorded in order to mitigate the influence of spatial harmonics. To estimate the coefficients of flux linkages, two fitness functions are designed as follows: Fd = ∑i=1..I∑j=1..J[α0 + α1id(i) + α2iq(j) + α3id2(i) +α4iq2(j) + α5id(i)iq(j)-Ψd(id(i), iq(j))]; Fq = ∑i=1..I∑j=1..J[β0 + β1id(i) + β2iq(j) + β3id2(i) +β4iq2(j) + β5id(i)iq(j)-Ψq(id(i), iq(j))], (2) where i=1,…, I and j=1,…, J are directories of (id, iq). Based on (2), the coefficients of dq-axis flux linkages at each pair of (id, iq) can be obtained by using GA to achieve the minimization of Fd and Fq. III. Online Parameter Estimation Considering Spatial Harmonics Considering spatial harmonics, dq-axis voltage equations of a PMSM can be written as (3) under the steady state. ud = Rid-ωeLqq,0iq+ωeΨd6sin(6pθ)+sin(6pθ)(-6pωeLdd,6id-ωeLdq,6id)+cos(6pθ)(6pωeLdq,6iq-ωeLqq,6iq)+εd ; uq = Riq+ωeLdd,0id+ωeΨd1+ωeΨq6cos(6pθ)+sin(6pθ)(-6pωeLqq,6iq-ωeLdq,6iq)+cos(6pθ)(6pωeLdq,6id-ωeLdd,6id)+εq, (3) where ud, uq are dq-axis voltages; θ is the electrical rotor position; p is the number of pole pairs; R is the resistance; ωe is the rotor speed; Ψd6 and Ψq6 are the magnitudes of the 6th permanent magnet (PM) flux-linkage harmonics in dq-axis. Ldd,0,Lqq,0,Ldd,6,Lqq,6 are the magnitudes of fundamental and the 6th harmonic of self-inductances in the dq-axis; Ldq,6 is the magnitude of the 6th harmonic of mutual-inductance; εd and εq are high order harmonics and high frequency noise components in the dq-axis. The harmonic magnitudes of the PM flux linkage can be easily obtained by using FFT analysis of the back-electromotive force. To achieve an online identification of the dq-axis inductances harmonics, a state observer is employed. The state observer model is firstly built based on (3) to get the magnitude of the 6th harmonic of the self-inductance and mutual-inductance in the dq-axis. The state vector is built as: x=[ Ls6cos(6pθ); Lm6sin(6pθ); -6pωeLs6sin(6pθ); 6pωeLm6cos(6pθ)], (4) with Ls6=Ldd,6 and Lm6=Ldq,6. The estimated dq-axis flux linkage maps are shown in Fig.1 and Fig.2. Detail analysis and experimental results will be given in the full paper. IV.CONCLUSION This paper proposes a novel two-step method to identify flux linkages in PMSMs considering both the effects of magnetic saturation and spatial harmonics during the estimation process. In step one, GA is used to estimate the magnetic saturation coefficients of flux linkage. With the results obtained from GA, the Kalman filter based online method is proposed to estimate the spatial harmonics to achieve an accurate estimation of the flux linkage map. The co-simulation results show that the proposed approach is effective for flux linkage estimation.

**References:**

[1] E. Armando, R. I. Bojoi, P. Guglielmi, G. Pellegrino and M. Pastorelli, in IEEE Transactions on Industry Applications, vol. 49, no. 5, pp. 2116-2125, Sept.-Oct. 2013. [2] N. Bianchi and S. Bolognani, in Proc. Int. Conf. IEEE Ind. Appl., Oct. 1998, pp. 27–34. [3] Z. Li, G. Feng, C. Lai, W. Li and N. C. Kar, in IEEE Transactions on Transportation Electrification, vol. 5, no. 4, pp. 1430-1440, Dec. 2019. [4] Q. Chen, W. Zhao, G. Liu, Z. Lin, in IEEE Transactions on Industrial Electronics., vol. 66, no. 2, pp. 944-955, Feb. 2019. [5] K. Liu, J. Feng, S. Guo, L. Xiao and Z. Zhu, in IEEE Transactions on Industrial Informatics, vol. 14, no. 2, pp. 556-568, Feb. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cdb1bbe318f847c1cdda6bffcdd7b846.jpg)
Fig. 1. SPMSM q-axis flux linkages estimation results.

![](https://assets.underline.io/uploads/markdown_image/1/image/a4a335ed2eb49867f6497eb0dde4319d.jpg)
Fig. 2. IPMSM q-axis flux linkages estimation results.

technical paper

I.Introduction With the development of more electric aircraft (MEA), higher demand for electrical energy is put forward in generation systems. In order to reduce the weight of the aircraft generation system, the requirement on the power density of generator becomes higher [1]. Wound rotor synchronous machines (WRSMs) are most widely used in aircraft applications. However, the reliability of rotating rectifier is low. In addition, the starting processing is complex. Hybrid excitation synchronous machines (HESMs) are recently proposed as the potential candidates for EV drive systems, wind power generation and more electric aircraft, for the air-gap flux can be regulated by field current efficiently. This paper proposes a new hybrid excited starter-generator (HESG) with magnetic field decoupling topology for MEA applications. The predicted electromagnetic performance is validated by the 3-D finite-element analysis (FEA) model. Finally, the results of FEA are confirmed by the experiments on a 60kVA HESG. The contribution of this paper is to propose a promising HESG to replace WRSMs in aircraft starter-generator applications. II.Operation Principle and Machine Specification Table I presents the design requirements of a starter-generator for aircraft generation system. The structure of the HESG with decoupling magnetic field is shown in Fig. 1, it can be seen that the PM side air-gap is larger than EE side air-gap. In order to implement high air-gap flux density, the Halbach-array PM rotor is preferred for the flux concentrating characteristic, low harmonic components and low inductance characteristic. Fig. 2 shows the HESG topology. It can be seen that the PM rotor and the two EE rotors can be installed on the shaft together seamlessly, which can greatly improve the compactness, torque density and power density. As shown in Fig. 3, the magnetic flux path can be divided into axial part and radial part. There is no axial flux in the stator core so that the stator can keep the same with that in WRSM and brings sinusoidal back EMF, which makes it suitable for starter-generator system. Table II provides the main parameters of the designed HESG with decoupling magnetic field. III.Electromagnetic Performance Analysis In order to verify the applicability of the new HESG magnetic field decoupling topology for AC starter-generator system, the electromagnetic performance analysis mainly focus on the power characteristics and flux regulation capability. Fig. 4 shows the distribution of magnetic field with different field currents. As shown in Fig. 5, the back-EMF magnitude increases with field current. Fig. 6 shows the output voltage versus output current at 8000r/min for different field currents. It can be seen that the output characteristics can be regulated by field current. The output power versus speed for different field currents is shown in Fig. 7. A 60kVA prototype is manufactured and measured for the verification of previous analysis. The photos of the motor are shown in Fig. 8. The experimental results will be supplemented in the later formal paper. IV.CONCLUSION In this paper, a new HESG is proposed for aircraft generation system. The topology and operating principle are described in detail. In addition, the electromagnetic performance of HESG is investigated to verify the applicability of the HESM to a starter-generator system for aircraft applications.

**References:**

[1] Y. Liu, Z. Zhang and X. Zhang, "Design and Optimization of Hybrid Excitation Synchronous Machines With Magnetic Shunting Rotor for Electric Vehicle Traction Applications," in IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5252-5261, Nov.-Dec. 2017.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/d1a01027692aa59030478c3a38de0002.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/112fdd56d19723570dd66e8465c54e37.jpg)

 Electromagnetic Performance Analysis of a New Hybrid Excitation Synchronous Generator with Decoupling Magnetic Field

I. Permanent magnet (PM) motors have become great alternatives to traditional motors. Overhang, either on the rotor or the stator, is commonly used is these motors. In this study, various alternatives of stator or rotor overhang in PM synchronous motors are investigated in detail. Both asymmetric and symmetric overhang cases are considered in the paper. Impact of overhang on the torque quality and torque densities are investigated using 3D Finite Element Analysis (3D-FEA). Axial magnetic forces during assembly with and without overhang are also simulated and variation of axial forces for different cases of overhangs are explored. A prototype PM motor with rotor overhang is used to validate the analyses experimentally. II. INTRODUCTION Rotor overhang is commonly used in different types of permanent magnet motors for numerous reasons. There are various studies in literature covering rotor overhang including magnetic modelling, 2D and 3D-FEA mostly for linear permanent magnet and induction motors, axial flux motors and brushless DC motors. Very limited studies exists on radial flux PM synchronous motors. Most studies are focused on analytical modelling of overhang and 2D/3D simulations [1-4]. However, no detailed investigation on both symmetric and asymmetric overhangs on the motor performance are conducted. Influence of torque quality, cogging and back-EMF harmonics are not covered especially for asymmetric overhang cases since some applications do require asymmetric placement of the rotor. In this paper, both asymmetric and symmetric overhang cases will be investigated in detail. Impact of such cases on the motor performance and torque quality are covered. Axial magnetic forces are also be explored for PM motors since it is a crucial issue in assembly of framed and frameless PM motors. III. INVESTIGATED PM MOTOR CASES AND FEA SIMULATIONS AND IV. EXPERIMENTAL VERIFICATION Detailed 3D-FEA is performed for different cases of overhang. The motor is selected as a low speed surface mounted permanent magnet synchronous motor as shown in Fig. 1. The prototype motor in a test system is also shown in Fig. 2. Various cases of overhang is investigated in great detail using 3D-FEA. Cases-1 does not have any overhang. Case-2 has rotor overhang and Case-3 has stator overhang. In each case, rotor stack is kept the same and torque quality as well as motor performance is explored. Axial magnetic forces acting on the rotor are also covered in 3D-FEA as seen in Fig3, 4 and 5. A prototype motor with rotor overhang is also manufactured and tested for different cases and some of the 3D-FEA simulations including axial magnetic forces are verified. The test results and comparison with the FEA simulations will also be given in the final version of the paper.

**References:**

V. References: 1. Yon-Do Chun;Ju Lee;S. Wakao,‘Overhang effect analysis of brushless DC motor by 3-D equivalent magnetic circuit network method’, IEEE Trans. Magn., vol. 39, pp. 1610–1613, May. 2003. 2. P. Upadhayay; K. R. Rajagopal, ‘Permanent magnet overhang effect in PM BLDC motor using 2D & 3D finite element analysis’, 2012 Nirma University International Conference on Engineering , India. 3. Jung-Moo Seo, In-Soung Jung, Hyun-Kyo Jung, and Jong-Suk Ro, ‘Analysis of Overhang Effect for a Surface-Mounted Permanent Magnet Machine Using a Lumped Magnetic Circuit Model’, IEEE Trans. Magn., vol. 50, Issue: 5, May. 2014. 4. Kyu-Yun Hwang;Hai Lin;Se-Hyun Rhyu;Byung-Il Kwon, ‘A Study on the Novel Coefficient Modeling for a Skewed Permanent Magnet and Overhang Structure for Optimal Design of Brushless DC Motor’, IEEE Trans. Magnetics., vol. 48, Issue: 5, May. 2012. 5. Han-Kyeol Yeo;Hyeon-Jeong Park;Jung-Moo Seo;Sang-Yong Jung;Jong-Suk Ro;Hyun-Kyo Jung, ‘Electromagnetic and Thermal Analysis of a Surface-Mounted Permanent-Magnet Motor with Overhang Structure’, IEEE Trans. Magnetics., vol. 53, Issue: 6, June 2017.

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 Impact of Asymmetric and Symmetric Overhangs on Torque Quality and Axial Magnetic Force Computations in Surface Mounted PM Synchronous Motors

1. Introduction The advantage of interior permanent magnet synchronous motor (IPMSM) is known for having high power density by utilizing not only magnetic torque but also reluctance torque. Accordingly, the IPMSM is used in various industrial components such as robots, electric vehicles (EVs), and home appliances to exert high-performance. The performances required for the industrial components are high power density and low torque ripple. The torque ripple is related to noise and vibration characteristics of the IPMSM. Thus, it is necessary to reduce the torque ripple when designing the IPMSM. Many design method has been reported for torque ripple reduction, such as rotor eccentricity, skew, notch, and chamfer. These methods are related to changing the length of the air-gap [1]. However, changing the air-gap length makes the average torque decrease because the effective air-gap length increases [2]. To reduce the torque ripple while maintaining the average torque, a design method of asymmetric rotor shape has been proposed [3]. The symmetric and asymmetric rotor shapes are illustrated in Fig. 1. The significant difference between the symmetric and asymmetric rotors is the effects of the rotating directions on the torque ripple. When applying the symmetric rotor, the torque ripple is constant regardless of the rotating directions. On the other hand, the torque ripple is different depending on the rotating directions when applying the asymmetric rotor. Since some applications such as an EV traction motor require rotating in the forward and reverse directions, it is necessary to consider the rotating directions in the design for the torque ripple reduction of an IPMSM. In this paper, the design of an IPMSM for an EV traction to reduce the torque ripple is performed considering the rotating directions of the asymmetric rotor. Unlike the conventional design method for torque ripple reduction, the average torque is maintained with an asymmetric rotor. In the EV traction motor, the driving time in the forward direction is longer than the driving time in the reverse direction. Therefore, the torque ripple of the forward direction is minimized, and the torque ripple of the reverse direction is designed at the same level as the base model. To verify the result of the design optimization, prototypes of the base and the optimum models are fabricated and the experimental results of the base and optimum models are compared. 2. Design Optimization Process By applying the asymmetric rotor, the air-gap magnetic field distribution at load conditions can be sinusoidal compared with the base model. Considering that the magnetic permeance of the rotor is determined by the shape of the rotor, the three design variables are selected as shown in Fig. 2. In the figure, the lx and ly represent the x-axis and y-axis directional displacements. la represents the positional angle of the permanent magnet (PMs) which implies the degree of the asymmetry of the rotor. For comparison, the same stator of the base model is used in the asymmetric rotor design. Moreover, the PM size, the pole angle, the rib thickness, and the rib angles are the same as those of the base model. The objective function and the constraints for the torque ripple minimization are defined considering the rotational directions: the forward and reverse directions. Since the targeted system mainly rotates in the forward direction, the torque ripple when rotating the forward direction is set as the objective function while the torque ripple when rotating in the reverse direction is considered in the constraint. Besides, the average torque is maintained with the value of the base model. In the optimization process, the objective and constraints values are predicted using kriging surrogate models based on the finite element analysis (FEA). As the design of experiment (DOE) technique for constructing the kriging surrogate models, a combination of optimal Latin hypercube (OLHD) and sequential maximin distance design (SMDD) are adopted [4]. Using the constructed kriging surrogate models, the design optimization is performed and the optimum model of the asymmetric rotor is determined. Using the constructed kriging surrogate models, the design optimization is performed and the optimum model of the asymmetric rotor is determined. 3. Design Result In Fig. 2, the FEA results are compared to the base model with the symmetric rotor and the optimum model with the asymmetric rotor. The average torque in the forward and reverse directions is the same. The torque ripple in the forward direction is reduced in the optimal model compared to the base model. The torque ripple in the reverse direction is similar between the base model and the optimum model. 4. Experiment Verification and Conclusion The test result is used to compare and verify the base model and the optimum model. The test of the base model and the optimum model will be performed under the same load conditions. In conclusion, a design for torque ripple reduction using the asymmetric rotor was performed considering the forward and reverse directions. The torque ripple in the reverse direction and the average torque are similar to that of the base model, while the torque ripple in the forward direction is reduced. Therefore, the design result can be applied to various applications having the forward and reverse rotations.

**References:**

[1] T. Ishikawa, M. Yamada, and N. Kurita, IEEE Trans.Magn., vol. 47, pp. 1290–1293, (2011) [2] Y.H. Jung, M.S. Lim, and J.-P. Hong, IEEE Trans. Energy Convers., vol. 33, pp. 333–340, (2018) [3] W. Ren, Q. Xu, Q. Li, and L. Zhou, IEEE Trans.Magn., vol. 52, Art. ID 8104105, (2016) [4] S.K. Kim, S.G. Lee, and M.S. Lim, IEEE Trans. Energy Convers., vol. 35, pp. 2056–2065, (2020)

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 Design Optimization for Torque Ripple Reduction using Asymmetric Rotor in IPMSM considering Forward and Reverse Directions

Flux Switching Machines (FSMs) are competent applicant for high speed brushless AC applications due to double-salient robust rotor structure, high torque, efficiency, and power density. Hybrid excited FSM (HEFSM) are widely applicable to many industrial applications, Electric Vehicles (EVs), Hybrid Electric Vehicles, electric propulsion, electric craft, electric power-assisted steering, renewable and automotive application due to high power and torque density and flux controllability [1]. However, the compact stator structure of conventional HEFSM (as shown in Fig. 1(a)) [2] suffer from parasitic effects of iron loss, demagnetization due to spatial harmonics in non-overlapped winding. This effect greatly effects electromagnetic performance i.e. average torque (Tavg), torque density (Tden), average power (Pavg), power density (Pden), efficiency (η), flux controllability, flux focusing effects and fault tolerant capability. To overcome the aforesaid demerits, in this research a novel H-type stator core (as shown in Fig. 1(b)) is proposed to improve electromagnetic performance and flux controllability. Furthermore, the proposed model is converted to modular stator by introducing flux gaps in all and alternate stator teeth as shown in Fig 1(c, d), because considering steel lamination in modular topologies with segmented stator, manufacturing process i.e. winding process is made at ease. Moreover, modular structure offers thermal, mechanical, and physically magnetic separation between armatures winding hence, on-site maintenance is reduced, and fault tolerant capability is improved [3]. In mechanical aspect, it is noteworthy that combination of consequent pole rotor with modular stator structure effectively results higher PM utilization and ease manufacturing process, transportation, assembly and on-site maintenance when design in large-dimension for wind power application whereas in electromagnetic analysis, modular structure shows dominant influence on electromagnetic performance. In order to show effectiveness of the proposed modular H-type HEFSM, a comprehensive electromagnetic performance analysis is investigated (as shown in Fig. 2(a-d)) at armature current density (Js) of 15 at constant magnetic loading in both conventional and proposed design. Analysis concludes that in proposed design, Tavg is improved by 42.35% whereas Pavg is enhanced by 48.48%. Moreover, Tden is increased by 42.04% and Pden by 48.68% in comparison with conventional design. In additional, the proposed design offers highest efficiency of 98.68% whereas conventional design has efficiency of 87.20%. thus, improving the efficiency by 13.07%. Despite of electromagnetic performance proposed modular structure improve flux focusing effects by decoupling mutual phase coupled flux linkage which greatly enhanced fault tolerant capability and improve flux weakening capability and overload capability. This analysis is comprehensively investigated under varying flux gap at all stator teeth and alternate stator teeth. Analysis concludes that flux gap (FG) increases self-inductance and reduces mutual inductance thus, mitigating short circuit current and separate healthy and faulty phases during fault and hence improve fault tolerant capability.

**References:**

[1] W. Ullah, F. Khan, E. Sulaiman, M. Umair, N. Ullah and B. Khan, "Analytical validation of novel consequent pole E-core stator permanent magnet flux switching machine," in IET Electric Power Applications, vol. 14, no. 5, pp. 789-796, 5 2020 [2] S. Cai, Z. -Q. Zhu, C. Wang, J. -C. Mipo and S. Personnaz, "A Novel Fractional Slot Non-Overlapping Winding Hybrid Excited Machine With Consequent-Pole PM Rotor," in IEEE Transactions on Energy Conversion, vol. 35, no. 3, pp. 1628-1637, Sept. 2020 [3] R. Zhou, G. -J. Li, K. Zhang, Z. Q. Zhu, M. Foster and D. Stone, "Performance Investigation of Consequent-Pole PM Machines with E-core and C-core Modular Stators," in IEEE Transactions on Energy Conversion, doi: 10.1109/TEC.2020.3027366.

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Fig. 1: Cross sectional view (a) conventional design (b) proposed non-modular (c) proposed modular with alternate stator teeth FGs and (d) proposed modular with all stator teeth FGs

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Fig. 2: Electromagnetic performance analysis (a) Tavg and Tden (b) Pavg and Pden (c) η and (d) Torque speed curve

 A Novel Hybrid Excited Machine with H-type Modular Stator and Consequent Pole PM Rotor

I. In this paper, a new two-stage harmonic current injection (TSHCI) technique is proposed for permanent magnet synchronous machines to reduce the cogging torque and torque ripple components at low speeds. The developed algorithm is validated for different AFPM motors experimentally. It has been shown that the proposed technique help reduce the cogging components significantly especially at very low speeds. II. INTRODUCTION The use of permanent magnet (PM) synchronous motors is increasing in industrial applications compared to conventional AC and DC motors due to their high torque density and efficiency. Axial flux permanent magnet (AFPM) motors move forward in many applications due to their geometric benefits, high efficiency and high power density. Such motors may suffer from high torque ripple in some slot-pole combinations. At high speeds, torque ripple can be filtered by the system inertia. However, it would be imperative to reduce the cogging torque components at low speeds in some applications. Harmonic current injection is used to reduce the torque ripple in some PM motors [1-5]. However, it has been observed that such studies are generally carried out at high speeds [6-7]. In this paper, a harmonic current injection algorithm is proposed to reduce both torque ripple and cogging torque at very low speeds. Two AFPM prototype motors is used so as to validate the developed proposed algorithm. The proposed algorithm is validated with and without harmonic current injection for such PM motors at different speed levels. III. EXPERIMENTAL VERIFICATION OF PROPOSED TWO-STAGE HARMONIC CURRENT INJECTION The proposed two-stage harmonic current injection method is used for two different AFPM synchronous motors. In order to adapt the algorithm, shown in Fig. 1, the cogging torque and its harmonics are determined first as shown in Fig. 2. After the harmonic current injection, the variation of cogging component and its harmonics are shown in Fig. 3. It has been observed that the effect of the cogging torque can be reduced from 55.91% to 36.2% with the proposed method. The reduction of the impact of the cogging torque by the harmonic current addition method applied to the q-axis current when the AFPM motor is running at 4.5Nm at 10rpm speed. It has been observed that the impact of the cogging torque can be reduced from 55.91% to 30.9% with the proposed method. IV. CONCLUSIONS In this paper, two-stage harmonic current injection is proposed and the algorithm is validated for AFPM motors at very low speeds. Torque ripple at low speeds are reduced by more than 51% with the developed method. The validity of the proposed technique is shown in 2 different AFPM motor.

**References:**

[1] Hongyun Jia, M. Cheng, W. Hua, Zhengzhuan Yang and Yunqian Zhang, "Compensation of cogging torque for flux-switching permanent magnet motor based on current harmonics injection," 2009 IEEE IEMDC, Miami, FL, 2009, pp. 286-291. [2] A. Ebrahimi, "A Novel Harmonic Current Control Algorithm for Torque Ripple Reduction of Permanent Magnet Synchronous Motors for Traction Application," 2018 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Nottingham, 2018, pp. 1-5. [3] H. Le-Huy, R. Perret and R. Feuillet, "Minimization of Torque Ripple in Brushless DC Motor Drives," in IEEE Transactions on Industry Applications, vol. IA-22, no. 4, pp. 748-755, July 1986. [4] Ma, Y.; Li, Y. Active Disturbance Compensation Based Robust Control for Speed Regulation System of Permanent Magnet Synchronous Motor. Appl. Sci. 2020, 10, 709. [5] Y. A. I. Mohamed and E. F. El-Saadany, "A Current Control Scheme With an Adaptive Internal Model for Torque Ripple Minimization and Robust Current Regulation in PMSM Drive Systems," in IEEE Transactions on Energy Conversion, vol. 23, no. 1, pp. 92-100, March 2008. [6] M. Lukaniszyn, M. JagieLa and R. Wrobel, "Optimization of permanent magnet shape for minimum cogging torque using a genetic algorithm," in IEEE Transactions on Magnetics, vol. 40, no. 2, pp. 1228-1231, March 2004. [7] P. Mattavelli, L. Tubiana and M. Zigliotto, "Torque-ripple reduction in PM synchronous motor drives using repetitive current control," in IEEE Transactions on Power Electronics, vol. 20, no. 6, pp. 1423-1431, Nov. 2005.

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 A New Harmonic Current Injection Technique to Reduce Cogging Torque in Axial Flux Permanent Magnet Motors

Interior permanent magnet synchronous motor (IPMSM) are widely used for industrial and traction applications. IPMSM's are known for high efficiency, reliability, and power density. For certain applications, like traction in hybrid electric vehicles, a high torque and power density with wide range of speed is of high importance. The efficiency of the motors can be increased in two ways: (1) increasing the output torque of the motor or (2) reducing the losses of the motor. The torque of various motors has been improved by introducing dual rotor structure and dual excitation using the unused space in electrical machine [1, 2]. The authors in [3] compares number of electrical motors. A quantitative analysis of three types of dual stator flux modulation permanent magnet (PM) motors including magnetic geared motor, and vernier machine. High torque density has been achieved in [4] for double stator brushless PM motors. The design has also been optimized based on split ratio to achieve maximum torque density. Recently, a lot of research has been carried out on vernier permanent magnet motors (VPMMs). The authors proposed a dual stator VPMMs and performs a comparative analysis of proposed design with regular VPM [5]. The proposed design achieved high efficiency and torque density and lower cogging torque. Similarly, power factor based analytical and FEM analysis have been provided in [6] on dual stator VPMM. A high torque density VPMM with dual stator topology has been proposed in [7]. This draft proposes a drum type configuration of dual stator IPMSM with improvement in the torque density, rotor alignment and inner winding temperature compared to single stator IPMSM by utilizing the unused space in the motor. The new design of dual stator IPMSM with 16-poles and 72-slots in each stator are presented with the aim of improving the average torque and torque ripple for industrial and traction applications. The presented design is then compared with the commercial design of single stator IPMSM to show the direct and fair comparison. Fig. 1 (a) shows the proposed design (PD) and conventional design (CD). The CD uses tangential type rotor with rare-earth PMs mounted inside the surface of rotor. The conventional IPMSM offers a good torque capability, but this torque capability can be improved by utilizing the unused space of the rotor. For this purpose, another stator with the same number of stator slots has been added to replace the unused space of rotor resulting in a proposed dual stator IPMSM. To increase the torque of the proposed models, the inner stator is shifted by a half slot pitch to aid the flux lines of outer stator with the inner stator. As the slots of inner stator are aligned with the outer stator-teeth, hence the slot area of an inner stator is somewhat smaller compared to the outer stator-slots. The number of turns of the inner stator-slots are double compared to the outer stator-slots to reduce the current density and inner winding temperature. Due to the addition of an inner stator, the cup rotor is the suitable. However, the cup type rotor configuration decreases the rotor alignment because of only one bearing towards the rotor shaft. Hence, in this draft, the drum type rotor is introduced comprising of two bearing on both sides of stator to support the inner stator shaft and to improve the alignment of the rotor. Furthermore, to reduce the inner winding temperature, the curve-windows are introduced in the drum configuration for the air inlet to reduce the inner winding temperature as presented in Fig. 1 (b). The analysis is performed on the conventional and proposed designs to show the competency of the proposed model. The Fig. 2 (a), and (b) shows the back EMF of the inner and outer stator. Moreover, the back EMF of the conventional design is identical to the outer stator back EMF of the proposed model due to same geometry of outer stator. Moreover, the Fig. 2 (b) shows the substantial improvement in the average torque and torque ripple of the proposed model compared to the conventional design.

**References:**

[1] A. Toba and T. A. Lipo, "Generic torque-maximizing design methodology of surface permanent-magnet vernier machine," vol. 36, no. 6, pp. 1539-1546, 2000. [2] F. Zhao, T. A. Lipo, and B. Kwon, "Magnet flux focusing design of double stator permanent magnet vernier machine," in Proc. COMPUMAG, 2013. [3] C. Liu, K. Chau, J. Zhong, W. Li, and F. J. I. T. o. a. s. Li, "Quantitative comparison of double-stator permanent magnet vernier machines with and without HTS bulks," vol. 22, no. 3, pp. 5202405-5202405, 2011. [4] Y. Wang, M. Cheng, M. Chen, Y. Du, and K. J. I. E. p. a. Chau, "Design of high-torque-density double-stator permanent magnet brushless motors," vol. 5, no. 3, pp. 317-323, 2011. [5] Y. Gao, R. Qu, D. Li, H. Fang, J. Li, and W. J. I. T. o. M. Kong, "A novel dual-stator Vernier permanent magnet machine," vol. 53, no. 11, pp. 1-5, 2017. [6] Y. Shi and T. J. I. T. o. M. Ching, "Power Factor Analysis of Dual-Stator Permanent Magnet Vernier Motor with Consideration on Turn-Number Assignment of Inner and Outer Stator Windings," 2020. [7] N. Baloch, B.-i. Kwon, and Y. J. I. T. o. M. Gao, "Low-cost high-torque-density dual-stator consequent-pole permanent magnet Vernier machine," vol. 54, no. 11, pp. 1-5, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e08dd9b8ef2a303357bf995cb72dbe36.png)
Fig. 1. (a) Geometry of the proposed and conventional designs; (b) Proposed dual stator drum type rotor; (c) Configuration of the inner and outer stator with the inverter.

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Fig. 2. Back EMF of the (a) Inner Stator; (b) Outer Stator; and (c) torque comparison.

 Dual Stator Drum Rotor Interior Permanent Magnet Synchronous Motor with Improvement in Torque Density, and Rotor Alignment

I. Introduction Conventional radial flux permanent magnet machines (RFPMMs) and axial flux permanent magnet machines (AFPMMs) are always the research hotpot high performance drive systems. RFPMMs have simple structure and magnetic circuit, which makes them easy to design and analyze [1]. As for the AFPMMs, they are paid attention for their compactness [2]. The merit makes them more suitable for direct-drive system [3][4]. However, for some special applications such as industrial robotic arms, machines with higher torque density are required [5]. In this case, the axial-radial flux permanent magnet machines (ARFPMMs) may meet the requirements. Compared with the AFPMM and RFPMM, the proposed ARFPMM has the merits of compactness, high utilization of windings and high torque density. In this paper, The structures of ARFPMM, AFPMM and RFPMM are introduced. A detailed performance comparison between the three topologies is also conducted. 3D models of different topologies are built and 3D finite element method (FEM) is used to analyze them. The performances such as back electromotive force (EMF), torque density, and torque ripple are compared to specify the best topology for particular applications. II. Three Topologies In order to exclude factors which may affect the comparison results, some parameters of the machines are kept consistent. The inner/outer diameter and axial length of three machines are the same. As shown in Fig. 1, the pole/slot combinations of three topologies are all 20 poles 24 slots. In addition, toroidal windings are also adopted in the RFPMM to keep consistent with the AFPMM and ARFPMM. They are all placed in the opening slots. Permanent magnets which are mounted on the surface of rotors are arranged as Halbach array. It can suppress the harmonics of air-gap flux density [6]. Each pole pair contains six segments, so the angle of magnetization direction between permanent magnets is 60°. Fig. 1 shows that the numbers of rotors of three machines are different. The RFPMM and the AFPMM has a radial rotor and two axial rotors, respectively, while the ARFPMM has a radial rotor and two axial rotors. It makes the active part of windings of the ARFPMM the longest and that of the RFPMM the shortest. Those differences lead to different performances. III. Operation Principles of Three Topologies Due to the different configurations, the equivalent magnetic circuits of three machines are different. The magnetic flux of RFPMM goes from rotor to stator in radial direction. There are circumferential and radial components of magnetic flux in the stator core. The electromagnetic torque is generated by the reaction between the radial magnetic field and the outside components of windings. As for the AFPMM, the magnetic flux goes through air gap in axial direction. There are circumferential and axial components in the stator core. The electromagnetic torque is due to the reaction between the axial magnetic field and the radial components of windings. The magnetic flux of ARFPMM is the combination of that of RFPMM and AFPMM. It flows in the stator core in circumferential, radial, and axial direction. Similarly, the electromagnetic torque is also the combination of that of RFPMM and AFPMM. IV. Performance Comparison The three machines are analyzed through FEM. Considering the ending effect, a 3D model is also built for the RFPMM. Fig. 2(a) shows the back EMFs of three machines obtained through 3D finite element analysis. The amplitude of ARFPMM is the largest, while that of RFPMM is the smallest. The waveforms show that the distortion of back EMF in the ARFPMM is the most serious. However, as shown in Fig. 2(b), the largest harmonic of back EMF in the ARFPMM is the third harmonic, which can be neglected due to the star connection of three phase windings. V. Conclusion This paper has described the structures and operation principles of ARFPMM, AFPMM, and RFPMM. The results of 3D FEA show that the proposed ARFPMM has the highest torque density. Because the slots and PMs of RFPMM are all rectangular, while the PMs of AFPMM are fan-shaped and slots are rectangular, the percentage of torque ripple to average torque of the RFPMM is the largest. The ARFPMM is equipped with the characteristics of both AFPMM and RFPMM. Thus, the percentage of torque ripple of ARFPMM is in the middle. Acknowledge This work is supported in part by NSFC (52077186&51677159), in part by STIC of Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK.

**References:**

[1] H. Zhao, C. Liu, Z. Song and W. Wang, "Exact Modeling and Multi-Objective Optimization of Vernier Machines," in IEEE Transactions on Industrial Electronics, early access. [2] M. Aydin, Surong Huang and T. A. Lipo, "Torque quality and comparison of internal and external rotor axial flux surface-magnet disc machines," in IEEE Transactions on Industrial Electronics, vol. 53, no. 3, pp. 822-830, June 2006. [3] C. Liu, K. T. Chau, and C. H. T. Lee, "A Critical Review of Advanced Electric Machines and Control Strategies for Electric Vehicles," in Proceedings of the IEEE, early access. [4] M. Wang, C. Tong, Z. Song, J. Liu and P. Zheng, "Performance Analysis of an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine for Hybrid Electric Vehicles," in IEEE Transactions on Industrial Electronics, vol. 66, no. 1, pp. 806-817, Jan. 2019. [5] A. Dwivedi, S. k. Singh and R. K. Srivastava, "Analysis and Performance Evaluation of Axial Flux Permanent Magnet Motors," in IEEE Transactions on Industry Applications, vol. 54, no. 2, pp. 1765-1772, March-April 2018. [6] Z. Song, C. Liu, K. Feng, H. Zhao and J. Yu, "Field Prediction and Validation of a Slotless Segmented-Halbach Permanent Magnet Synchronous Machine for More Electric Aircraft," in IEEE Transactions on Transportation Electrification, vol. 6, no. 4, pp. 1577-1591, Dec. 2020.

**Images:**

Fig. 1 Topologies of three machines. (a) ARFPMM, (b) AFPMM, (c) RFPMM. 1-Stator, 2-Windings, 3-Radial PMs, 4-Radial back iron, 5-Axial PMs, 6-Axial back iron.

Fig. 2 Back EMF and torque analyzed through 3D FEM. (a) Back EMF, (b) Fast Fourier transform of back EMF, (c) Electromagnetic torque.

 Comparative Analysis of Axial-Radial, Axial, and Radial Flux Permanent Magnet Machines

I.Introduction The rare-earth permanent magnet (RE-PM) machines are ideally suited for electric vehicles (EVs) and hybrid electric vehicles (HEVs) due to high power density and efficiency. However, with the accelerated pace of industrialization, the RE-PMs resources are becoming less and less, and the price of RE-PMs are becoming higher and higher. Less resources and higher price have restricted the application of REPM machines. Therefore, the less-rare-earth PMSMs has become a research issue [1]. This paper proposes and designs a novel less-rare-earth spoke-type PM machine for EVs applications, where a parallel placement of the rare-earth PM (SmCo) and non-rare-earth PM (ferrite) is involved. The rotor key parameters of traditional spoke-type PM machine and novel spoke-type PM machine are optimized based on finite-element analysis (FEA) and genetic algorithm (GA). In addition, the electromagnetic performances are compared between two optimized spoke-type PM machines by the finite-element analysis (FEA) model. Finally, the results of FEA are confirmed by the experiments on a 50kW traditional spoke-type PM machine. The contribution of this paper is to propose a novel low cost spoke-type PM machine replacing PM machine in EVs applications. II.Spoke-type PM Machine with Different Rotors Fig. 1 (a) shows the 12-slot stator core and winding distribution. The traditional spoke-type PM rotor and novel low cost spoke-type PM rotor are shown in Fig. 1(b) and Fig. 1(c). In addition, the basic parameters are listed in Table I, which are the same for two machine stator diameter, axial length and air-gap length. In order to obtain better performance, the FEM coupled with multi-objective GA is adopted to optimize two machines, and the key parameters of the two machines rotor are listed in Fig. 3 and Table II. Fig. 4 shows the optimization results of average torque and torque ripple for two machines. It can be seen that the novel spoke-type PM rotor and traditional spoke-type PM rotor can obtain similar torque. However, the novel spoke-type PM rotor can obtain lower torque ripple. III.Electromagnetic Performance Comparison and Analysis Fig. 5 shows the two machines no-load distribution of air-gap flux density and its harmonic content. Furthermore, FE predicted average torque and torque ripple under rated current are shown in Fig. 6. Fig. 7 shows the variation of average torque with phase current for two machines. It can be seen that the novel spoke-type PM rotor has similar torque compared with the traditional spoke-type PM rotor, but it has the lower torque ripple. Considering the limit of dc voltage (540V), the efficiency contour maps and torque-speed curves of two machines under rated current are shown in Fig. 8. The measured back-EMF waveforms of traditional spoke-type PM machine at rated speed is shown in Fig. 9, and the measured average torque versus phase current is shown in Fig. 10. In addition, the tested current waveform is shown in Fig. 11. The novel spoke-type PM machine will be supplemented in the later formal paper. IV.CONCLUSION In this paper, a novel low cost spoke-type PM machine based on traditional spoke-type PM machine is proposed and designed for EVs. The rotor key parameters of two machines are optimized based on GA. In addition, the electromagnetic performance of two machines are compared, including flux density, torque, torque ripple, efficiency and cost. Both the simulation and experimental results demonstrate the effectiveness of the proposed machine and the design optimization method.

**References:**

X. Zhu, W. Zhu, L. Quan and W. Gu,. IEEE Trans. on Energy Convers., vol. 34, pp. 1178(2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2547d5d49efed1fb451a36711a17887.jpg)
Fig.1

 Design and Optimization of a Novel Low-Cost Hybrid-Pole Rotor for Spoke-type Permanent Magnet Machine

Fractional-slot concentrated-winding permanent magnet synchronous motors (FSCW-PMSMs) have been widely used in the field of electric vehicles (EVs) due to their high-power density, high efficiency, short end turns, low cogging toque, good flux weakening capability and so on [1]. However, these machines usually exhibit high amount of sub-harmonic spatial fields, which will lead to high rotor eddy current loss, particularly in NdFeB magnets. This part of loss will increase significantly as the speed goes up, causing the rising temperature and hence the potential irreversible demagnetization of NdFeB magnets [2]. Aiming at the reduction of magnet loss, a hybrid rotor structure FSCW-PMSM is proposed in the paper. The key is to introduce additional ferrite magnets in D and Q axis magnetic flux paths, respectively. Compared with traditional all-NdFeB structure, the proposed design can effectively curb the magnet loss due to the low conductivity of ferrite magnets. Fig.1 shows the comparison of existing all-NdFeB rotor structure and proposed hybrid rotor design for 12 slots/8 poles IPMSM with only the cross section of one pole illustrated, from which it can be seen that part of the tangentially magnetized NdFeB magnets are replaced with ferrite magnets and additional ferrite magnet is introduced to fill up the air at the bottom between the two tangentially magnetized magnets. Fig.2 shows the comparison of total magnet loss and the magnet loss in the tangentially magnetized magnets between existing and proposed FSCW-PMSM with respect to rotor speed. It can be seen that as the rotor speed goes beyond the rated value of 3700rpm with field-weakening operation, the total magnet loss of traditional all-NdFeB structure increases rapidly with the contribution mainly coming from tangentially magnetized NdFeB magnets. It can be well explained by the fact that as a result of increasing leading angle of current vector against Q-axis under field-weakening operation, more and more armature harmonic flux will cross-link with the tangentially magnetized NdFeB magnets and hence lead to high magnet loss in them. Despite of the significant loss reduction by partially replacing the tangentially magnetized NdFeB with ferrite magnets, the magnet loss in the radially magnetized NdFeB magnets still remain high. Therefore, additional ferrite magnets should also be introduced in the d-axis flux-path just as shown in Fig.1. As a result, the introduced ferrite magnets can not only effectively curb the magnet loss in the radial magnets but also contribute to the air-gap flux density and hence improve the output torque. Although the proposed design effectively diminishes the magnet loss, it inevitably leads to the decrease of output torque due to the reduced usage of NdFeB magnets as well as increased torque pulsation. Further optimization is still needed for the proposed structure to improve its competitive edge against the traditional design. Fortunately, the hybrid rotor structure leaves more scope for the improvement of saliency ratio so that it can be possible to enhance the reluctance torque. Furthermore, by adopting auxiliary slots design on the rotor surface, the torque pulsation is effectively curbed and the magnet loss in the radially magnetized NdFeB magnets is further reduced. As a result of the Finite Element analysis, compared with traditional NdFeB IPMSM with the maximum torque of 172N.m, the prototype with the proposed design can accomplish a maximum torque of 158N.m, nearly 92% of that of traditional one due to the contribution of enhanced reluctance torque through optimization, as well as reduced torque ripple from 10.6% to 6.9%, while the total cost of magnets is reduced by 39%. As a conclusion, the proposed hybrid rotor structure can not only solve the problem of excessive magnet loss of traditional NdFeB motor at high speed, but also present a cost-effective design approach for IPMSM for EV applications with less usage of expensive NdFeB magnets as well as enhanced reluctance torque capability.

**References:**

[1] Ayman M. EL-Refaie, Fractional-Slot Concentrated-Windings Synchronous Permanent Magnet Machines: Opportunities and Challenges. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 1(2010) [2] Xinggang Fan, Bin Zhang, Ronghai Qu, Comparative Thermal Analysis of IPMSMs WithIntegral-Slot Distributed-Winding (ISDW) and Fractional-Slot Concentrated-Winding (FSCW) for Electric Vehicle Application. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 55, NO. 4(2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/555c3005c2af53d40b2f3bef59b8e5c8.jpg)
Fig.1 Comparison of the two rotor structures. Left. The traditional rotor structure. Right. The hybrid rotor structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc7fc0c12d1d9743419c8c6e2c07534a.jpg)
Fig.2 Comparison of magnet eddy current loss (MECL) between the traditional and hybrid rotor structure in full speed range

 A New IPMSM with Hybrid Rotor Structure for Electrical Vehicle with Reduced Magnet Loss

I. INTRODUCTION The permanent magnet (PM) machine has attracted wide attention in many application areas such as electric vehicles (EVs) for high output torque, high efficiency and high reliability. For the traditional PM machine, its maximum output torque is constricted by the current density supplied from the power source, which may lead to the insufficient output torque, especially at low speed [1-2]. Furthermore, in the direct-drive PM machines, the number of the pole-pair is usually relatively high to maintain the large output torque within the low speed range. However, due to the high pole-pair number, the PM dosage and the production cost are both increased accordingly. Therefore, the consequent-pole structure seems to be an appropriate choice to reduce the rare-earth materials and increase the pole-pair number in the limited space [3-4]. In this paper, a new consequent-pole segmented dual-stator permanent magnet (CPSDSPM) machine is proposed for some high-torque & low-speed applications. Compared with the traditional PM machines, this proposed CPSDSPM machine, which reasonably utilizes the internal space of the intermediate rotor, realizes the low-demagnetization, the low dosage of the rare earth, the flexible control strategy and the large output torque by a particular coupling effect between two stators. II. MACHINE TOPOLOGY As shown in Fig. 1(a), the topology of the proposed CPSDSPM machine mainly includes three parts: the external stator, the internal stator and the intermediate rotor. First, the external stator is divided into three sub-parts, in which the phase difference of two adjacent sub-parts of the external stator is a complete 360 electrical angle. Second, for convenient maintenance and low cost, the internal stator located inside the intermediate rotor is designed as an integrative structure. Third, the intermediate rotor, which adopts 12 V-type PMs and 6 iron cores, is sandwiched between the external stator and the internal stator. Forth, all the PMs and the iron cores located in the intermediate rotor are alternately distributed as the sequence of N-iron-N-S-iron-S. Fifth, two sets of windings, which are mounted in the external and the internal stator respectively, are adopted in this proposed topology. The five-phase winding is composed of three sub-windings connected in series. It's placed in the external stator and designed to produce the main output torque. The three-phase winding, which is housed in the internal stator, can not only be used as the field coil, but also offers an additional output torque directly when it's needed. III. WORKING PRINCIPLE According to the analysis result mentioned above, the flux paths in the proposed CPSDSPM machine are summarized in Fig. 1(b). These flux paths can be mainly divided into three types. First, the flux path 1 includes two PMs in different polarity. It can be seen that the flux path 1 exists in the external stator and the intermediate rotor. Second, the flux path 2 includes one PM and one iron core. Compared with the flux path 1, the ability of the PM excitation in the flux path 2 is weakened, but the total magnetic conductance is improved. Third, the flux path 3 needs to cross both the inner air gap and the outer air gap. It can be easily obtained that the flux density of both iron cores and PMs in the outer air gap can be adjusted by the three-phase winding. Therefore, the three-phase winding can also be regarded as the supplemental excitation source for the external stator. At last, the flux directions of these two iron cores marked in Fig. 1(b) are different. Because of the downward direction of the flux, the iron core on the left can be regard as S-pole. Similarly, the iron core on the right can be defined as N-pole. Therefore, these two iron cores can be regarded as one pole-pair equivalently in the intermediate rotor. IV. ELECTROMAGNETIC PERFORMANCE ANALYSIS First, the no-load phase back-EMF waveforms at rated speed of the five-phase winding presented in Fig. 2(a) are calculated by finite element method (FEM). It can be seen that the back-EMF of the proposed machine is extremely sinusoidal owing to the segmented structure, which can contribute to the electromagnetic performance of the external stator of the proposed CPSDSPM machine. Second, for the proposed machine, the cogging torque is mainly caused by the external stator. As shown in Fig. 2(b), it can be obviously found that the total cogging torque generated from the whole machine is decreased considerably, compared with the single part of the external stator. Third, due to the segmented structure, it can be obtained in Fig. 2(c) that the torque ripple generated by the external stator is quite low (around 0.4%). Furthermore, under the vector control strategy, the maximum total output torque waveform generated by both the external stator and the internal stator is shown in Fig. 2(c). V. CONCLUSION In this paper, a new CPSDSPM machine is proposed and analyzed. First, the configuration is introduced. Second, the working principle and the main flux paths of this machine are analyzed and classified. Third, the electromagnetic properties, such as the no-load phase back-EMF waveforms, the cogging torques and the output torques are all calculated by FEM, which can verify the correctness of the theoretical analysis and the superiority of the proposed CPSDSPM machine.

**References:**

[1] S. Niu, S. L. Ho and W. N. Fu, "A Novel Direct-Drive Dual-Structure Permanent Magnet Machine," IEEE Trans. Magn., vol. 46, no. 6, pp. 2036-2039, June 2010. [2] H. Yang et al., "Novel Dual-Stator Machines With Biased Permanent Magnet Excitation," IEEE Trans. Energy Convers., vol. 33, no. 4, pp. 2070-2080, Dec. 2018. [3] W. Li, T. W. Ching and K. T. Chau, "A New High-Temperature Superconducting Vernier Permanent-Magnet Machine for Wind Turbines," IEEE Trans. Appl. Supercond., vol. 27, no. 4, pp. 1-5, June 2017. [4] H. Hua, Z. Q. Zhu and H. Zhan, "Novel Consequent-Pole Hybrid Excited Machine With Separated Excitation Stator," IEEE Trans. Ind. Electron., vol. 63, no. 8, pp. 4718-4728, Aug. 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b99f8a29e0d766e89b9567b2626da29f.jpg)
Fig. 1. CPSDSPM machine. (a) Topology. (b) Magnetic paths.

![](https://assets.underline.io/uploads/markdown_image/1/image/fd107b6246fda9106441b1c62138c772.jpg)
Fig. 2. Electromagnetic field analysis of the proposed CPSDSPM machine. (a) No-load phase back-EMF waveforms. (b) Cogging torques. (c) Output torques.

A Novel Two-Step Flux Linkage Identification for PMSMs Considering Magnetic Saturation and Spatial Harmonics

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