# Design and finite element analysis of a high-performance surface-permanent magnet synchronous reluctance machine with optimised robustness towards demagnetisation

Hamidreza Ghorbani, Behrooz Majidi, Mohamed Benbouzid

► To cite this version:

Hamidreza Ghorbani, Behrooz Majidi, Mohamed Benbouzid. Design and finite element analysis of a high-performance surface-permanent magnet synchronous reluctance machine with optimised robustness towards demagnetisation. IET Electric Power Applications, 2024, 18 (12), pp.1965-1977. 10.1049/elp2.12521 . hal-05344722

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https://hal.univ-brest.fr/hal-05344722v1

Submitted on 3 Nov 2025

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# Design and finite element analysis of a high-performance surface-permanent magnet synchronous reluctance machine with optimised robustness towards demagnetisation

Hamidreza Ghorbani<fnref n="1" /> ID

Behrooz Majidi<fnref n="1" /> ID

Mohamed Benbouzid<fnref n="2" /> ID

### Correspondence

Behrooz Majidi and Mohamed Benbouzid.
Email: bmx@aut.ac.ir and mohamed.benbouzid@univ-brest.fr

### Abstract

The aim of this paper is to design and Finite Element Analysis (FEA) of a novel rotor topology for a permanent magnet synchronous reluctance machine. According to the advantages and drawbacks of the PMSyncRM and the SPMSM, a conventional PMSyncRM rotor design combined with surface-mounted magnets is introduced as the SPMSyncRM. The surface-PM arc size is investigated, so that it is considered as multiplication of an integer coefficient and the angle between two adjacent slots of the stator. The analysis involves simulation of the electromagnetic characteristics and the numerical model of each structure using finite element method. Each E-Magnetic character is calculated for a better understanding of the benefits of the SPMSyncRM. Applying 2D FEA, the optimised surface-PM arc size is calculated and the static and dynamic operational behaviour of the SPMSyncRM is simulated. Moreover, short circuit analysis is performed to study the demagnetisation of magnets. All results are reported comparatively considering a conventional PMSyncRM, so that the proposed SPM-SyncRM topology presents high torque-power density, lower values of cogging torque, higher values of power factor and efficiency, better static and dynamic performance, and robustness towards demagnetisation.

### KEYWORDS

demagnetisation, design, finite element analysis, synchronous machines

## 1 INTRODUCTION

In recent decades, a huge number of investigations has been dedicated to studying the electromagnetic characteristics of Permanent Magnet Synchronous machines (PMSM). Generally, the PMSM can be categorised as:

(i) Interior Mounted PMSM (IPMSM)

(ii) Surface-Mounted PMSM (SPMSM)

(iii) PMSync Reluctance Machine (PMSyncRM/PMSyncRM/PMSRM) [1, 2].

The reason behind this attraction is that the PMSM provides desirable electromagnetic performance [3] as the IPMSM

provides high torque/power density and high efficiency [2, 4, 5]; high values of torque and power factor (PF) are observed for the PMSyncRM [1] and low values of torque ripple along with the ease of manufacturing are achieved for the SPMSM [6]. However, the SPMSM operates at lower values of efficiency [7] and PMSRM suffers from higher values of torque ripple [8–11]. Thus, various analytical, experimental and numerical methods have been adopted to optimise and enhance the characteristics of the PMSM topologies; some studies are devoted to the performance calculation of different types of the PMSM [12–20]. While others are dedicated to comparatively study design configurations [3, 21–24] and investigating design optimisation procedures [25–34], In addition, some novel rotor/stator topologies are presented in ref. [35–43]. In

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2024 The Author(s). *IET Electric Power Applications* published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

<footnote n="1">¹Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran</footnote>

<footnote n="2">²Institut de Recherche Dupuy de Lôme (UMR CNRS 6027 IRDL), University of Brest, Brest, France</footnote>
which, Li et al. [37] investigate a novel magnet-axis shifted PM machine (MAS-HPM) to achieve higher torque and efficiency ranges for electric vehicle application. The characteristics comparison between the proposed MAS-HPM and the BMWi3 interior mounted permanent magnet machine (IPM) is done applying finite element method. Based on the reported results, the total torque and the back electromotive force (Back-EMF) are improved and better flux-weakening higher peak efficiency, and lower mechanical stress are observed for the proposed MAS-HPM in comparison with the conventional BMW i3 IPM. Chai et al. [42] present the design of a novel Consequent-Pole PMSM providing lower cost. The proposed structure exhibits satisfying average torque with lower manufacturing costs due to the use of a combination of iron and soft ferrite. However, the proposed machine suffers from high values of torque ripple. An optimal selection of slot-pole combinations for a PMSM is studied in ref. [23]. According to the presented results, the machine with higher pole pairs provides a larger maximum winding factor and torque compared with lower pole one, particularly for outer rotor topology. Maroufian and Pillay [40] investigate a novel topology of PMSRM with AlNiCo PMs. By aiming for low manufacturing costs and based on experimental results, the proposed PMSRM demonstrated improved torque and PF. A new ribless rotor structure for SyncRM is studied in ref. [39], investigating the impact of each geometry parameter on torque production. By the absence of the iron ribs and according to the mechanical Finite Element Analysis (FEA) and experimental results, the novel SyncRM showed enhanced torque capabilities for any current loading. The loss-es of a Concentrated Winding (CW) are investigated for a high-speed PMSRM for washing machine application in ref. [44]. The torque performance of the proposed machine is simulated using FEA and examined under no-load and on-load conditions, calculating iron, skin, and proximity losses. The results show that the proposed PMSRM operates at a wide range of speeds and provides desirable performance for washing machine applications. In order to decline the high torque pulsations in PMSRM plus achieving higher values of PF and efficiency in SPMSM, a novel Surface-Mounted Permanent Magnet Synchronous Reluctance Machine (SPMSyncRM/SPMSRM) is studied in this paper. The proposed model is a combination of SPMSM and PMSRM, considering three layers of flux barrier that two of which are filled with rare-earth PMs and an extra PM is attached to the surface-notch of the rotor structure. The arc size of the surface-PM is studied so that it is considered as $n\alpha_{ez}$, the multiplication of an integer coefficient (n) and the angle between two adjacent slots ($\alpha_{ez}$) of the stator. Moreover, in order to comparatively show the advent of the proposed SPMSRM, a conventional PMSRM is included in the study. By applying 2D FEA, one can get that the proposed optimised design structure of the SPMSRM gains advantages over the conventional PMSRM as higher torque and power density, constant torque region for speeds more than two times of the rated speed, lower values of torque ripple and cogging torque, the higher amplitude of Back-Electromotive Force (Back-EMF), desirable values of air-gap flux density, operating more

efficiently and bring about higher values of PF. In addition, a short circuit analysis is performed for the candidate models, high robustness towards demagnetisation observed for the SPMSRM during a short circuit fault (SCF) condition. This paper is organised as following: machine topologies and specifications are presented in Section 2, the optimisation criteria are proposed in Section 3, FEA results for steady-state, dynamic performance, and SCF condition are submitted in Section 4 and some conclusions are given in Section 5.

## 2 | MACHINE TOPOLOGIES AND SPECIFICATION

A new rotor design is introduced in this study in which an extra PM is placed into the rotor surface-notch of a conventional PMSRM for each of the rotor poles. In addition, in order to study the enhancements of the proposed SPMSRM precisely, a conventional rotor configuration is included to comparatively investigate the electromagnetic performance of the machines. The arc size of the added surface-PM is investigated based on some mathematical winding design equations, presented in Section 3. A double-layer Distributed Winding (DW) pattern supplied by a three-phase drive system is applied to the proposed models. Figure 1 demonstrates the general view of a conventional PMSRM rotor-stator design configuration: flux barriers, PMs, and winding pattern, in which PMs are inserted into rotor flux barriers and a rotor notch considered based on an analytical design in refs. [19, 20, 34]. The proposed models of this study are shown in Figure 2a and b. According to Figure 2, the rotor notch in PMSRM (Figure 2a) is replaced with a surface-mounted PM, introducing the SPMSRM (Figure 2b) which the Magnetic Equivalent Circuit diagram is shown in Figure 2c. The design parameter values are listed in Table 1. The models are designed and studied under the same condition using 2D FEA for 50°C of ambient temperature.

<figure><img src="image_2.png" /><figcaption>FIGURE 1 Cross-section view of a conventional PMSRM.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>FIGURE 2 Proposed rotor configurations: (a) PMSRM, (b) Surface-Mounted Permanent Magnet Synchro-nous Reluctance Machine (SPMSRM) and (c) Magnetic Equivalent Circuit (MEC) Diagram for PMSRM and SPMSRM.</figcaption></figure>

3 | DESIGN OPTIMISATION CRITERIA

Generally, two types of winding are used in electric motors which are categorised based on the value of the *q*, the number of the stator slots (*N*<sub>s</sub>) per phase (*m*) per number of rotor poles (*N*<sub>p</sub>) ratio as Eq. (1) [45, 47–50]:

$$q = \frac{N_s}{mN_p} \qquad (1)$$

In general, if the value of the *q* is an integer, the winding is called *DW* type, otherwise the winding type is *CW* type (In order to recognise *CW* type, winding steps shall be considered along with the value of *q*). Overall, in the *DW* type, the greater values of the *q* result in more sinusoidal Back-EMF

wave. The winding can be single- or double-layered, which the double layer comes with advantages such as: (i) lower fundamental winding factor, (ii) shorter end-winding, lower values of (iii) torque fluctuations, (iv) eddy current losses, (v) over-load torque capabilities and (vi) EMF harmonic contents [45–51].

According to Figure 3, the arc size value of the surface-PM is considered as an optimisation variable of the SPMSRM model. Thus, it is assumed equal to the multiplication of the angle between two adjacent stator slots ($\alpha_{ez}$) and an integer coefficient (*n*) as Eq. (2):

$$PM_{Arc} = n \times \alpha_{ez} \quad (E Deg.) \quad ; \quad n = (1, ..., 8) \quad (2)$$

where the $\alpha_{ez}$ can be expressed as follows [45]:
<table><caption>TABLE 1 Machine specifications.</caption><thead><tr><td>Design parameter</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Stator slots Num., N<sub>S</sub></td><td>36</td><td>---</td></tr><tr><td>Rotor poles Num., N<sub>P</sub></td><td>4</td><td>---</td></tr><tr><td>Rated speed, n<sub>r</sub></td><td>1.5</td><td>kRPM</td></tr><tr><td>Peak current, I<sub>n</sub></td><td>15</td><td>A</td></tr><tr><td>Phase voltage, V<sub>ph</sub></td><td>230</td><td>v</td></tr><tr><td>Stator outer Dia., D<sub>SO</sub></td><td>160</td><td>mm</td></tr><tr><td>Stator inner Dia., D<sub>SI</sub></td><td>90</td><td>mm</td></tr><tr><td>Rotor outer Dia., D<sub>RO</sub></td><td>89.15</td><td>mm</td></tr><tr><td>Stack length, L<sub>m</sub></td><td>100</td><td>mm</td></tr><tr><td>Notch depth, D<sub>N</sub></td><td>4</td><td>mm</td></tr><tr><td>PM thickness, W<sub>PM</sub></td><td>4</td><td>mm</td></tr><tr><td>Air-gap length, L<sub>g</sub></td><td>0.85</td><td>mm</td></tr><tr><td>Steel material</td><td>M400-50A</td><td>---</td></tr><tr><td>PM material</td><td>N42SH</td><td>---</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>FIGURE 3 The mechanical view of the surface-PM arc size and the $\alpha_{ez}$.</figcaption></figure>

$$ \alpha_{ez} = \frac{180 \times N_p}{N_s} \quad (E Deg.) \quad (3) $$

According to Figure 3 and Eq. (3), for the proposed PMSRM and SPMSRM with 36 stator slots and 4 rotor poles, the $\alpha_{ez}$ equation gives $20^{\circ}$. Hence, the corresponding arc size value of the surface-PM varies from $20^{\circ}$. to $160^{\circ}$.

## 4 | FINITE ELEMENT ELECTROMAGNETIC RESULTS

This section is dedicated to the presentation of the electromagnetic (E-Magnetic) analysis results. A 2D FE analysis is applied to the proposed models of this study. Primarily, the arc

size of the surface-PM is analysed considering the variation of 20–160 electrical degrees (According to Section 3. for $n = 1$ to $n = 8$) to determine the best-performed $n$ value which the corresponding model operates desirably in terms of higher amounts of torque and power density and lower values of torque fluctuations. Afterwards, the best-performed SPMSRM designed by the candidate $n$ value and the PMSRM are comparatively studied to examine the benefits of the SPMSRM structure. The results are comparatively illustrated and reported in the following subsections.

Overall, when compared with the PMSRM, the newly introduced model provides about 19% higher average torque (24.5 Nm) with approximately 34% lower cogging torque (1.2 Nm) while the torque ripple remains almost the same (30.6%). The SPMSRM also demonstrated a higher torque-efficiency region and peak phase Back-EMF. It achieved higher torque density with lower stator current angles compared to the PMSRM, while maintaining similar total losses. Additionally, transient short circuit analysis showed that the SPMSRM performed well under fault conditions, exhibiting greater robustness against demagnetisation (23% in SPMSRM vs. 63.5% in PMSRM). Hence, the SPMSRM not only offers higher torque and power density and efficient operation under steady-state and dynamic conditions, but also shows improved reliability during short circuit faults and high-temperature operation.

### 4.1 | Surface-PM arc sizing

Figure 4 and Figure 5 exhibit the steady-state E-magnetic performance results for the SPMSRM with the proposed $n$ values and PMSRM at the rated speed of 1.5kRPM. As shown in Figure 3 and description of Eq. (2), for $n$ values of 1–8, the torque performance of the SPMSRM and PMSRM are presented in Figure 4. Accordingly, the average torque ($T_{avg}$) produced by the SPMSRM increased with the increasing value of PM arc. However, for $n = 7$ and $n = 8$, the $T_{avg}$ remained almost the same. In comparison with the PMSRM, for $n > 2$, the value of average torque in the SPMSRM (19.9 Nm in $n = 2$ to above 26 Nm in $n = 8$) took over that of the PMSRM (20.5 Nm).

Based on the cogging torque ($T_{Cog}$) results illustrated in Figure 4, the conventional PMSRM produces high values of $T_{Cog}$ (1.75 Nm). For the SPMSRM models, for $n \le 5$, $T_{Cog}$ increased to the highest value (1.9 Nm), and then it dropped to 1.2 Nm for $n = 6$ and then increased to 1.35 Nm and 1.65 Nm for $n = 7$ and $n = 8$ respectively.

According to the torque ripple ($T_{Ripple}$) results in Figure 4, similar to $T_{Cog}$, Ripple is also increased for $n \le 5$, from 19.5% in $n = 1\%$ to 45.1% in $n = 5$. Then decreased to 30.6% in $n = 6$ which is almost equal to that of the PMSRM (30.54%), where the $n = 7$ gained the highest $T_{Ripple}$ value (49.4%).

The efficiency ($\eta$) results are shown in Figure 5. Based on the displayed results, the $\eta$ increases along with the increasing value of $n$, so that the PMSRM and the SPMSRM with $n \le 5$ provide efficiency below 85%, while for the SPMSRM with $6 \ge n \ge 8$, $\eta \ge 85\%$ is calculated.
Demonstrating the PF results in Figure 5 for the SPMSRM and the PMSRM, the PF ≥ 0.9 is provided by all the proposed models in this study, in which the SPMSRM with 4 ≥ *n* ≥ 6 present PF close to 1.

Figure 6 illustrates the dynamic performance results of the electromagnetic torque (EMT) (Figure 6a), the electromagnetic power (EMP) (Figure 6b), the efficiency (Figure 6c), and the

PF (Figure 6d) for the proposed machines of this study. Based on Figure 6a, the value of EMT increases along with the increasing value of *n*. In comparison with the PMSRM, the EMT reaches from 20.6 Nm in *n* = 1 and 21 Nm in the PMSRM to the 30 Nm in *n* = 8 for the SPMSRM. However, it can be seen that the speed value corresponding to the knee point of the operating region decreased along with the

<figure><img src="image_5.png" /><figcaption>**FIGURE 4** Torque performance of the proposed models at rated speed.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**FIGURE 5** Efficiency and power factor (PF) of the proposed models at rated speed.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 6** Dynamic performance:</figcaption></figure>

(a) electromagnetic torque (EMT),

(b) electromagnetic power (EMP), (c) efficiency, and

(d) power factor (PF).
increasing value of $n$, resulting in a more restriction of the constant torque region to below 3kRPM of speed. This is because adding extra PM to the rotor surface of conventional PMSRM increases the probability of demagnetisation for high-speed operations. Thus, in comparison with $n = 8$ which operates at most with 2kRPM of speed, the SPMSRM with $n = 6$ providing high constant EMT (28 Nm) with a wider speed region up to 2.5kRPM, presents desirable performance.

The EMP results are shown in Figure 6b. Similarly, the EMP line gradient in constant torque region increased with the value of $n$, so that the maximum EMP value of about 7 kW achieved at 3kRPM of speed for the PMSRM and the SPMSRM with $1 \ge n \ge 5$ and for greater values of $n$, the same peak EMP happens at lower speeds.

According to Figure 6c and d, the models present efficiency and PF value above 80% and 0.8 respectively, for 1 to 3kRPM of speed where the maximum $\eta = 92\%$ and PF = 0.99 are achieved at speed of above 2kRPM for $n \ge 5$.

According to (Baek et al., 2016), for an m-phase PMSM, the torque ($T$) equation can be expressed as follows:

$$T = \frac{m}{2} \frac{N_p}{2} [\lambda_{PM} I_d + (L_d - L_q) I_d I_q] \quad (4)$$

where $\lambda_{PM}$ is the PM flux linkage, $I_d$, $I_q$, $L_d$ and $L_q$ are the d-q axes currents and inductances respectively. As shown in Eq. (4), the greater the difference between $L_d$ and $L_q$, the higher values $T$ reaches. Hence, based on the results demonstrated for d-q axes inductances in Figure 7, the value of the $L_d$ and $L_q$ for the proposed machines in this study increased along with the increasing values of stator d-q axes currents and $n$, so that for the SPMSRM models operating at rated current, the highest inductances difference occurs when $n$ equals to 6.

Figure 8 illustrates the air-gap flux density ($B_g$) comparison for the proposed models. It can be seen that adding the surface-PM to the PMSRM highly influences the $B_g$ waveform. So that lower values of $B_g$ in the PMSRM at 30$^{\circ}$C, to 60$^{\circ}$C, turned to a peak value of 1T in the SPMSRM models.

Overall, according to the presented results at rated speed in Figure 4 and 5, and dynamic performance results in Figures 6–8, the proposed SPMSRM structures show higher torque and

<figure><img src="image_8.png" /><figcaption>FIGURE 7 Inductance: (a) d-axis, and (b) q-axis.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 8 Air-gap flux density.</figcaption></figure>
power capabilities, high efficiency, and high values of PF, in which the model designed with $n = 6$ ($n\alpha_{ez} = 120^{\circ} \text{E. Deg}$) value of surface-PM arc size, not only exhibits the higher values of EMT and EMP (kW), it also presents about 30% less $T_{cog}$, almost equal value of $T_{Ripple}$, performs more efficiently and higher PF, compared with the conventional PMSRM.

The full FEA results are reported in Appendix A (Table A1) and the flux density distribution map of the proposed models in this study is illustrated in Appendix B (Figure B1). It can be seen that all models operate with a flux density of no more than 2.5 T even in critical regions which provides acceptable electromagnetic performance.

## 4.2 | Dynamic performance comparison of the Surface-Mounted Permanent Magnet Synchro-nous Reluctance Machine

Figure 9 demonstrates the torque performance ($T_{avg}$, $T_{Ripple}$, $T_{Cog}$, and Torque per Rotor Volume ($T|_{R.V}$)) for both the

proposed SPMSRM and the PMSRM against current phase angle variations. As shown in Figure 9a and b, the highest torque density is achievable as the current phase angle equals $\alpha_{ez}$ and about $2\alpha_{ez}$ for the SPMSRM and the PMSRM respectively. Lower cogging torque is observed in the SPMSRM, while the value of torque ripple remains almost constant as the current phase angles vary. However, higher values of $T_{Cog}$ are calculated for the PMSRM, while the produced $T_{Ripple}$ is reduced for current phase angles above $2\alpha_{ez}$ (Figure 9b).

A comparative illustration for torque and power of the SPMSRM and the PMSRM is shown in Figure 10. As shown in Figure 10a and b, for increasing values of peak stator current the total torque and power are increased, which higher values of average torque and out-put power are determined for the SPMSRM with $n = 6$. Figure 10c and d illustrate the Copper loss ($L_C$), Rotor back iron loss ($L_R$), Stator iron loss ($L_S$), and total losses ($L_t$) as the summation of the losses, for the SPMSRM and the PMSRM respectively. While $L_S$ and $L_R$ remain almost the same value, the $L_C$ and consequently $L_t$ increased along with the increasing value of the stator peak

<figure><img src="image_10.png" /><figcaption>FIGURE 10 Torque and power performance: (a) Average torque, (b) Out-put power, (c) Losses (Surface-Mounted Permanent Magnet Synchro-nous Reluctance Machine (SPMSRM)), and (d) Losses (PMSRM).</figcaption></figure>
current. It can be determined from Figure 10c and d, the total losses remained almost the same value, when replacing SPMSRM with the conventional PMSRM.

Based on the FEA results discussed in Section 4. A., the proposed SPMSRM with $n\alpha_{ez} = 120^{\circ} \text{ Deg}$ performed desirably in terms of low torque fluctuations, high torque capabilities, power density, efficiency, and PF, compared with other n values and the PMSRM. Hence, this candidate SPMSRM and the PMSRM are also studied under dynamic performance status in this subsection. Figure 11 demonstrates the dynamic performance of these machines, where Figure 11a and c show the η map and Figure 11b and d exhibit the PF map for the SPMSRM and the PMSRM respectively. It can be got from this figure that in comparison with the PMSRM, the candidate SPMSRM presents a higher torque-η region. So that, the 7.5Nm ≥ EMT ≥ 26 Nm with η ≥ 90% is available for 1.5kRPM ≥ $n_r$ ≥ 3.5kRPM of speed. Whereas, based on Figure 11c, η ≥ 90% is available for speed ≥1.8kRPM with a max value of EMT of below 21 Nm. Therefore, as the candidate SPMSRM performed desirably by providing satisfying value torque/power density with low torque pulsations, it can be adopted as a vital alternative for high-torque applications.

The one-phase Back-EMF and the corresponding Fast Fourier Transform of the Back-EMF related to the candidate SPMSRM and the PMSRM are shown in Figure 12, in which in comparison with the PMSRM, below 125v of the one-phase Back-EMF, the candidate SPMSRM presents a higher peak value of one-phase Back-EMF above to 200v.

## 4.3 | Short circuit analysis of the Surface-Mounted Permanent Magnet Synchro-nous Reluctance Machine

The phenomenon of demagnetisation in permanent magnet machines has largely been overlooked. When a PM machine with a constant torque load experiences partial demagnetisation, it will draw more current to maintain the required torque. This increased current can lead to further demagnetisation, creating a cycle of rising current and demagnetisation. The higher current also results in greater copper losses, which increase temperatures and reduce the intrinsic coercivity of the magnets, making them more susceptible to demagnetisation [52]. It is crucial to examine whether this cycle continues until

<figure><img src="image_11.png" /><figcaption>FIGURE 11 Dynamic performance results for SPMSRM: (a) efficiency map, (b) power factor (PF) map, and PMSRM: (c) efficiency map, (d) PF map.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>FIGURE 12 Back electromotive force (Back-EMF) comparison: (a) 1-P Back-EMF, and (b) Fast Fourier Transform (FFT).</figcaption></figure>
the machine stalls and to determine the point at which demagnetisation ceases.

While alternating current permanent magnet synchronous motors offer stator fault tolerance and can function with one or more faulty phases, they are still susceptible to rotor magnet demagnetisation. Demagnetisation results from a combination of mechanical, electrical, and primarily thermal stresses. Rotor magnet demagnetisation is a reversible process that can progressively become irreversible under overload or fault conditions. The magnetic properties of permanent materials, such as neodymium, iron, boron, and samarium-cobalt, change with temperature, with remanence and coercivity decreasing as temperature rises [4, 52, 53]. Figure 13 illustrates the demagnetisation B-H- curve for the N42SH magnet material used in this study. Considering a transient SCF condition for the candidate SPMSRM and the PMSRM, for NdFeB magnetic material the probability of the demagnetisation is more likely to occur at high temperatures. In addition, the highest SCF is mostly happening when the SCF arises at peak torque (25 Nm for the SPMSRM and 20 Nm for the PMSRM at 3kRPM of speed). In other words, two

main factors which highly impact demagnetisation are high temperature and high values of the demagnetisation field [4, 17, 52]. Thus, assuming F class insulation (the max temperature of 155°C at the hottest spot), the temperature of 150°C and the corresponding B-H curve knee point of 0.5 T (Figure 13) are applied to the analysis, to calculate the d-axis short circuit (SC) current ($I_{d-SC}$). The resultant $I_{d-SC}$, torque, and speed results during the SCF condition are illustrated in Figure 14a,b and c respectively. The results of applying the peak value of the $I_{d-SC}$ (−52A for the SPMSRM and −41A for PMSRM) and the phase advance value of 90° (to put the stator current in the d-axis) are shown in Figure 14d. Consequently, the demagnetisation ratio of 23% and 63.5% was achieved for the SPMSRM and the PMSRM respectively. This means, the 63.5% of PMs in the PMSRM are permanently demagnetised during the SCF, while only 23% of the SPMSRM PMs are demagnetised considering the same fault situation (Figure 15). Thus, based on the transient SC analysis, in comparison with the PMSRM, and hence the proposed SPMSRM presents robust performance towards demagnetisation and more reliability.

<figure><img src="image_13.png" /><figcaption>FIGURE 14 Transient short circuit analysis:
(a) current, (b) torque, (c) speed, and
(d) demagnetisation ratio.</figcaption></figure>

<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /><figcaption>**FIGURE 15** Demagnetisation flux density distribution map: (a) Surface-Mounted Permanent Magnet Synchro-nous Reluctance Machine (SPMSRM) ($n\alpha_{ez} = 120^{\circ}\text{E. Deg}$), and (b) PMSRM.</figcaption></figure>

## 5 | CONCLUSION

This paper aims to present a novel SPMSRM. The SPMSRM structure is a combination of a PMSRM and an SPMSM. The proposed SPMSRM is comparatively investigated considering a conventional PMSRM using 2D (FEA). An arc sizing optimization analysis is conducted to the surface-PM. According to the presented results, the SPMSRM was designed with a surface-PM arc size equal to 120E. Deg. provides low amounts of torque fluctuations ($T_{Ripple} = 30.6\%$ and $T_{Cog} = 1.2$ Nm), high values of torque density ($T_{avg} = 25.4$ Nm), efficiency ($\eta = 85.3\%$) and power factor (PF = 0.99), in comparison with the PMSRM ($T_{Ripple} = 30\%$, $T_{Cog} = 1.75$ Nm, $T_{avg} = 20.5$ Nm, $\eta = 83\%$, PF = 0.97). Based on the resultant efficiency and PF map for the proposed candidates, the SPMSRM presents a higher torque-$\eta$ region and peak value of phase Back-EMF.

In addition, for the SPMSRM higher value of torque density is achievable with lower values of stator current angles in comparison with the PMSRM, and total losses remained almost the same value when transforming the PMSRM to the SPMSRM. Moreover, transient short circuit analysis is done for the PMSRM and the candidate SPMSRM. Accordingly, the SPMSRM performed well during the SC fault condition and provides robustness towards demagnetisation compared with the PMSRM with high values of demagnetisation ratio in the same fault condition (23% in the SPMSRM compared with 63.5% in the PMSRM). Overall, not only does the SPMSRM presents higher values of torque and power density and operates efficiently under steady-state and dynamic performance, but it also performed robustly towards demagnetisation during SCF and high-temperature operation providing more reliability.

## AUTHOR CONTRIBUTIONS

**Hamidreza Ghorbani:** Conceptualisation; formal analysis; investigation; methodology; software; visualisation; writing - original draft. **Behrooz Majidi:** Formal analysis; investigation; methodology; software; supervision; validation; visualisation; writing - review & editing. **Mohamed Benbouzid:** Methodology; supervision; validation; writing - review & editing.

## ACKNOWLEDGMENTS

The authors declare that they received no grants/funds from any institution upon preparing this paper.

## CONFLICT OF INTEREST STATEMENT

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## ORCID

Hamidreza Ghorbani https://orcid.org/0000-0001-7117-3329

Behrooz Majidi https://orcid.org/0000-0001-5715-405X

Mohamed Benbouzid https://orcid.org/0000-0002-4844-508X

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**How to cite this article:** Ghorbani, H., Majidi, B., Benbouzid, M.: Design and finite element analysis of a high-performance surface-permanent magnet synchronous reluctance machine with optimised robustness towards demagnetisation. IET Electr. Power Appl. 18(12), 1965-1977 (2024). https://doi.org/10.1049/elp2.12521

## APPENDIX A

<table><caption>TABLE A1 Finite Element Analysis (FEA) results report at rated speed.</caption><thead><tr><th>Back-EMF</th><th>B<sub>g-avg.</sub></th><th>L<sub>q</sub></th><th>L<sub>d</sub></th><th>PF</th><th>η</th><th>P<sub>loss</sub></th><th>P<sub>out</sub></th><th>n<sub>r</sub> |<sub>T</sub><sup>ctea</sup></th><th>T<sub>Ripple</sub></th><th>T<sub>Cog.</sub></th><th>T<sub>avg.</sub></th><th>nα<sub>ez</sub></th><th></th></tr></thead><tbody><tr><td>125.6</td><td>0.51</td><td>41.2</td><td>18.4</td><td>0.94</td><td>82.7</td><td>0.62</td><td>2.99</td><td>3.07</td><td>19.5</td><td>0.35</td><td>19.3</td><td>n = 1</td><td>SPMSRM</td></tr><tr><td>152.9</td><td>0.58</td><td>40.1</td><td>18.3</td><td>0.95</td><td>82.7</td><td>0.64</td><td>3.07</td><td>3.07</td><td>27.5</td><td>0.6</td><td>19.9</td><td>n = 2</td><td></td></tr><tr><td>219.3</td><td>0.65</td><td>38.2</td><td>16.8</td><td>0.97</td><td>83.2</td><td>0.65</td><td>3.23</td><td>3.04</td><td>28.5</td><td>1.05</td><td>21</td><td>n = 3</td><td></td></tr><tr><td>218.5</td><td>0.72</td><td>37.5</td><td>15</td><td>0.99</td><td>83.7</td><td>0.65</td><td>3.39</td><td>3.04</td><td>42.4</td><td>1.06</td><td>22</td><td>n = 4</td><td></td></tr><tr><td>223.4</td><td>0.75</td><td>35.8</td><td>13.1</td><td>0.99</td><td>84.9</td><td>0.67</td><td>3.76</td><td>2.65</td><td>45.1</td><td>1.75</td><td>24.5</td><td>n = 5</td><td></td></tr><tr><td>209</td><td>0.8</td><td>31.4</td><td>8.9</td><td>0.99</td><td>85.3</td><td>0.67</td><td>3.87</td><td>1.2</td><td>30.6</td><td>2.5</td><td>25.4</td><td>n = 6</td><td></td></tr><tr><td>203.9</td><td>0.78</td><td>27.3</td><td>9.6</td><td>0.96</td><td>85.6</td><td>0.67</td><td>3.98</td><td>2.4</td><td>49.4</td><td>1.35</td><td>25.6</td><td>n = 7</td><td></td></tr><tr><td>192.6</td><td>0.71</td><td>24.5</td><td>8.3</td><td>0.95</td><td>86.3</td><td>0.64</td><td>4.03</td><td>2.36</td><td>26.6</td><td>1.65</td><td>26</td><td>n = 8</td><td></td></tr><tr><td>109.6</td><td>0.53</td><td>39.27</td><td>10.38</td><td>0.97</td><td>83.4</td><td>0.63</td><td>3.17</td><td>3.02</td><td>30.54</td><td>1.75</td><td>20.5</td><td>PMSRM</td><td></td></tr><tr><td>v</td><td>T</td><td>mH</td><td>mH</td><td>---</td><td>%</td><td>kW</td><td>kW</td><td>kRPM</td><td>%</td><td>Nm</td><td>Nm</td><td>Unit</td><td></td></tr></tbody></table>

<footnote>ªMaximum rotor speed operating with constant torque.</footnote>
APPENDIX B

Flux Density Distribution.

<figure><img src="image_16.png" /><figcaption>FIGURE B1 On-load flux density distribution map.</figcaption></figure>