In-Depth Exploration of Design and Analysis for PM-Assisted Synchronous Reluctance Machines: Implications for Light Electric Vehicles

Abstract

In electric or hybrid vehicles’ propulsion systems, Permanent Magnet-Assisted Synchronous Reluctance Machines represent a viable alternative to Permanent Magnet Synchronous Machines. Based on previous research work, the present paper proposes, designs, and optimizes two ferrite PMaSynRM topologies, analyzed against a reference machine (also PMaSynRM) with improved torque ripple content, based on similar specifications and dimensional constraints. Considering the trend of increasing the DC voltage level in electric and hybrid vehicles, the optimal topology is included in an analysis of the DC voltage level impact on the design and performances of PMSynRM.

1. Introduction

Electric machines have found extensive applications across various automotive sectors, with the current focus primarily directed towards enhancing their capabilities for powering fully electric vehicles. The undeniable energy efficiency of electric vehicles lies in their electric motors, which convert approximately 75% of chemical energy, a stark contrast to internal combustion engines that manage a mere 20% conversion rate.

Numerous configurations of electric machines have been specifically engineered for electric vehicle propulsion. Predominantly, permanent magnets (PM) or induction machines are utilized in the majority of electric or hybrid vehicles available [1,2,3]. While the permanent magnet synchronous machine (PMSM) is recognized for its remarkable power density and efficiency, its reliance on rare earth elements presents challenges in terms of cost, future availability, and environmental impact. Consequently, there is a growing inclination towards exploring electric machinery options that either eliminate or reduce reliance on heavy rare earth materials. Alternative topologies such as switched reluctance, synchronous reluctance, or PM-assisted machines have garnered attention and undergone significant research and development for application in this domain. Their applicability and potential for the use of traction machines are discussed in [4,5,6,7,8].

Moreover, the basic machine configurations utilized in traction are examined in [9,10], while in [11,12], propulsion systems, both with and without permanent magnets, and various alternatives to address this increasing demand are explored.

The Permanent Magnet-Assisted Synchronous Reluctance Machine (PMaSynRM) is an innovative electric motor that merges the high efficiency and power density of PMSMs with the durability and straightforwardness of synchronous reluctance machines (SynRM). Similar to PMSMs, PMaSynRM motors integrate permanent magnets into the rotor, ensuring a consistent magnetic flux to amplify torque generation and enhance overall efficiency. The rotor’s saliency structure minimizes losses and enables the precise regulation of magnetic flux, thereby boosting efficiency and dynamic performance. Additionally, the synergy between permanent magnets and reluctance torque in PMaSynRM leads to a heightened torque density, smoother torque distribution, and enhanced performance across a broad speed spectrum. In essence, PMaSynRM represents a promising electric motor technology aimed at optimizing performance, efficiency, and environmental sustainability across diverse applications, providing an attractive alternative to conventional motor designs. Continuous research and development endeavors are underway to refine and advance PMaSynRM motor design and implementation, aligning with the evolving demands of the transport electrification [13,14,15,16].

Electric vehicles can be categorized based on various factors such as their powertrain configuration, vehicle size, driving range, and intended use. The voltage levels in these vehicles can vary significantly depending on their category and technological specifications [17,18]. Light electric vehicles (LEVs) operate at lower voltage levels compared to larger electric vehicles (EV) like cars. Common voltages range for LEVs typically fall between 24 V and 48 V. Some high-performance LEVs may operate at higher voltage levels, up to 96 or even 120 V (for increased power and speed). Larger EVs typically operate at voltage levels ranging from around 200 V to 800 V. However, it is essential to note that this range can vary depending on the specific design and model of the EV. Higher-voltage systems offer several advantages, including improved efficiency, faster charging capabilities, and better performance.

The voltage level significantly impacts the design of electrical machines, influencing various aspects of their performance, efficiency, size, and complexity. Here are some key impacts of the voltage level on the electrical machine design [19,20,21]:

• Power Density and Efficiency: Higher voltage levels typically allow for higher power densities in electrical machines. This means that, for a given power output, a machine operating at a higher voltage can be physically smaller and lighter than a machine operating at a lower voltage. Additionally, higher-voltage systems often result in lower current levels, reducing resistive losses and improving overall efficiency.
• Insulation Requirements: Higher voltage levels require more robust insulation materials and design considerations to withstand the increased electrical stress. This includes insulation between windings, within the insulation system, and at the interfaces between different components of the machine. Ensuring adequate insulation is critical to prevent electrical breakdown and ensure safe operation.
• Cooling Requirements: Higher-voltage machines tend to generate more heat due to increased power levels. This necessitates more effective cooling systems to maintain the optimal operating temperatures and prevent overheating. Cooling methods such as forced air, liquid cooling, or a combination of both may be employed, depending on the specific requirements of the machine and its application.
• Materials Selection: The choice of materials for various components of the machine, such as conductors, magnets, and core materials, may be influenced by the voltage level. For example, higher-voltage machines may require materials with higher electrical conductivity, superior magnetic properties, and increased thermal stability to ensure reliable performance and longevity.
• Control and Protection: Higher-voltage machines often require more sophisticated control and protection systems to ensure their safe and reliable operation. This includes voltage regulation, current limiting, fault detection, and rapid shutdown mechanisms to protect against overvoltage, overcurrent, and other electrical faults.
• Manufacturing and Assembly: The manufacturing and assembly processes for higher-voltage machines may be more complex and require tighter tolerances to maintain their electrical integrity and performance. Specialized equipment and techniques may be necessary for winding, insulation, and assembly operations.
• Electromagnetic Design: The electromagnetic design of the machine, including the selection of winding configurations, magnetic circuit geometry, and flux distribution, is influenced by the voltage level. Higher voltages may necessitate different design approaches to optimize magnetic flux paths, minimize losses, and maximize performance.

Increasing the voltage needs to take into account the drive limitations as well. For example, a consequence of increasing the voltage can be the need for more DC-link capacitors. DC-link capacitors are components in the drive system that store and release electrical energy as needed. When the voltage is increased, the number or size of these capacitors may also need to be increased. This, in turn, can lead to a larger overall size of the driving system.

In addition to active components, it is crucial to evaluate the reliability of capacitors while conducting a reliability study for the entire system [22]. It is necessary to have knowledge about batteries, their state of charge, and their remaining useful life. However, this article does not explain the battery technology itself, including power electronics for balancing.

Figure 1 illustrates the role of power electronics at several levels of an electric vehicle power system. It presents a block diagram of the standard electrical power system architecture in an electric car, highlighting the main power electronic systems commonly found in such vehicles [23,24]. The high-voltage (HV) direct current (dc) bus is usually between 250 and 450 Vdc, depending on the battery voltage used. The low-voltage (LV) dc bus is rated at 12/48 Vdc. Various power train structures for electric vehicles (EVs) can be found in the automotive market, as documented in references [25,26,27] and more information about power electronics for electric vehicles can be found in reference [28].

This study combines the iterative process of designing and analyzing a PMaSynRM for light electric vehicle (LEV) propulsion, with an examination of how different voltage levels affect the machine’s electromagnetic behavior and performance. Two different topologies are suggested, designed, optimized, and then compared to a reference machine—a Ferrite-assisted SynRM—using the same specifications. Following that, a comprehensive investigation is conducted to examine the influences of various levels of direct current (DC) voltage on the performance of the topology that exhibits the lowest amount of torque ripple content.

Section 2 provides an elaborate description of the reference machine, including its performance in the stated configuration. It also contains important information regarding the optimization process of the suggested machine topologies and the key dimensions that were obtained after their optimization. The third section of the study presents the results of the Finite Element Analysis (FEA) for both suggested topologies. This analysis includes an assessment of the electromagnetic torque, phase voltage waveform characteristics, and torque ripple content.

Section 4 describes the methodology underpinning the design approach for the voltage levels adopted in this study. Section 5 presents the empirical data obtained from the PM synchronous reluctance machine operating at different voltage levels. These findings provide detailed insights into the machine’s performance under varied operational settings. In addition, this part thoroughly examines the impact of voltage level variations on important performance parameters such as torque, phase voltage waveform, and torque ripple content, therefore enhancing our understanding of the operational dynamics of the machine.

Section 6 presents a comprehensive analysis of the performance evaluation carried out on the selected topology, utilizing Finite Element Analysis (FEA) simulations at a fixed voltage of 560 V.

Section 7 concisely summarizes the findings and methodological foundations of this research project, effectively condensing the overall conclusions derived from the examination.

2. PMaSynRM: A Viable Alternative to PMSM in EV Propulsion Systems

PMaSynRM motors are being increasingly favored in electric vehicles (EVs) due to their array of advantages. Compared to induction motors, they boast superior efficiency, resulting in an enhanced performance. Their design enables compact and lightweight construction, which proves advantageous in EVs, where reducing weight is pivotal for maximizing efficiency and range. With a higher power density, they can deliver substantial power outputs relative to their size and weight, thereby improving acceleration and the overall EV performance [29,30].

In contrast to PMSMs, PMaSynRM motors offer several benefits. They exhibit a greater resilience to thermal variations and demagnetization, enhancing reliability and extending lifespan, critical factors in EV applications, where minimizing downtime and maintenance costs is essential. Additionally, they demonstrate superior torque characteristics at low speeds, ideal for urban driving conditions characterized by frequent stops and low-speed maneuvering.

Furthermore, PMaSynRM motors eliminate the need for rare earth permanent magnets, which are utilized in PMSM motors. This reduces reliance on rare earth materials, streamlines the manufacturing process, and potentially mitigates the environmental impact associated with magnet production [31].

The torque production in PMaSynRM is characterized by two components: reluctance torque via saliency and PM torque resulting from the interaction between PMs and the magnetic field generated by the current flowing through the stator coils:

$$T=\frac{3}{2}p[(L_d-L_q)I_d{I}_q+{\psi }_{PM}{I}_q]=T_{rel}+T_{PM},L_d>L_q$$

(1)

where $p$ is the number of pole pairs, ${\psi }_{PM}$ is the magnitude of the flux that comes from magnets, $L_d,L_q$ and $I_d,I_q$ are the axis inductances and currents, respectively, and $T_{rel}$ and $T_{PM}$ are the reluctance and PM torque components, respectively.

However, due to the predominant reluctance torque, PMaSynRM machines often experience considerable torque ripples. These ripples stem from the interaction between the spatial harmonics of the stator magnetomotive force and airgap permeance. They may induce unwanted mechanical vibrations, leading to premature bearing aging and potentially affecting motor control stability, particularly at high speeds. Minimizing torque ripples in PMaSynRM machines emerges as a key priority in their development. To overcome this limitation, different solutions have been investigated in the literature [32,33,34,35]. The selection of the appropriate combination of number of stator slots and number of poles, as well as of the number and shape of the flux barriers, can lead to minimizing torque ripples. The rotor skewing technique classically used in PMSM can be also implemented, but with the cost of reducing the torque capability of the machine.

2.1. Reference Machine

A PMaSynRM with Ferrite PMs was designed, analyzed, and built as a propulsion machine for a micro-EV, based on the specifications presented in

Table 1. PM-assisted SynRM specifications.

Parameter	Unit	Value
Rated Output Power	W	7000
Rated Speed	rpm	2100
Maximum Speed	rpm	7000
DC Power Supply Voltage	$V_{dc}$	120 V
Rated Torque	Nm	31.5
Maximum Torque	Nm	70
Exterior Diameter	mm	170
Stack length	mm	110
Airgap Length	mm	0.5

.

To meet the specified requirements, following the preliminary sizing of the machine, numerous sensitivity analyses and optimization procedures were conducted. Various combinations of stator slots and rotor poles were scrutinized to pinpoint the configuration that yielded the highest electromagnetic torque while minimizing the torque ripple. Both concentrated and distributed winding arrangements were evaluated. Special emphasis was placed on the rotor topology to determine the ideal number and configuration of flux barriers for optimizing the saliency ratio, while also monitoring mechanical stress to prevent rotor damage at high speeds.

The reference topology corresponds to a machine with 36 stator slots and 6 rotor poles in a single-layer distributed winding configuration. In order to meet the demands of manufacturing cost reduction, the stator geometry and winding arrangement are similar to those of an induction machine. Each rotor pole is built with three flux barriers accommodating ferrite PMs (Figure 2).

The operating range of the machine (torque and output power versus speed) is presented in Figure 3. The designed machine offers constant torque operation (blue line) up to 2100 rpm. Above this speed, the torque gradually decreases, while the output power (orange line) is kept constant up to 6000 rpm. Above 6000 rpm, the output power decreases, especially due to the increase in electromagnetic losses.

At the rated operation point of 2100 rpm, the developed electromagnetic torque is depicted in Figure 4, with a mean value of 31.5 Nm, indicating the average torque output. Additionally, the torque ripple content is 28%, signifying the percentage variation in torque values around the mean, providing insights into the system’s stability and smoothness of operation.

A maximal current density of 4.5 A/mm² is necessary due to the machine being naturally cooled. The magnetic flux density map depicted in Figure 5 reveals a peak value of around 1.8 T in both the stator back iron and the stator teeth. This value is considered to be acceptable, as it does not exceed the saturation limit of the lamination material. There are certain places in the machine that surpass this value, typically found near the edges of the magnetic flux barriers. However, these areas do not affect the main path of the flux and do not have a substantial impact on the machine’s performance.

2.2. Newly Proposed Configurations of the PMaSynRM

The torque ripple of the reference machine exceeds the acceptable limits set for LEV propulsion systems. Consequently, an exhaustive examination of various topologies was conducted to enhance the torque capabilities and minimize the torque fluctuations. When developing a new electrical machine, it is imperative to consider the thoroughly researched and analyzed aspects documented in the literature. In line with this design strategy, two topologies were considered, featuring 33 and 27 stator slots with coil pitches of 8 and 6, respectively. An extensive literature review guided the selection of an optimal number of rotor poles for the SynRM [36,37,38,39,40,41,42], resulting in the adoption of a four-pole configuration for the rotor section. Additionally, cost considerations played a significant role. Thus, Ferrite magnets (with the characteristic given in Figure 6) were chosen to ensure consistent thickness across all obstacles, maintaining an identical rotor topology for both machines.

The optimization procedure employed utilizes a multi-objective genetic algorithm to iteratively refine the design parameters of the machine (the main dimension restrictions used are the outer and inner diameter, stack length, and airgap, which are detailed in Table 1). Beginning with the parametrization of both the stator and rotor components, the optimization process proceeds iteratively, tailoring the machine design to meet the specified performance criteria.

For the 33-slot machine, optimization was conducted to determine the final rotor shape. In contrast, for the 27-slot machine, the rotor shape obtained from the initial step was retained, and only the stator's geometrical dimensions were modified.

To achieve the optimal operating point and satisfy the requirements listed in Table 1 (rated power, rated speed, and rated torque etc.), several key factors were considered. The primary objective functions were maximizing torque (Figure 7a) and minimizing torque ripples, which are typically the focus in design and optimization procedures. Additionally, the stator and rotor lamination materials had a saturation limit of approximately 1.8 T, located in the knee area of the saturation curve. Therefore, it was crucial to keep the magnetic flux below this limit in both the stator back iron and teeth to avoid oversaturation.

Given that the machines will employ natural cooling, it is essential to maintain the current density within the coils below 4.3 A/mm² to prevent overheating (Figure 7b). The final objective function aims to keep the induced RMS phase voltage (Figure 7c) within acceptable limits, as specified by Equation (2).

$$V_{phaseRMS}=0.4714V_{DC}$$

(2)

The variables considered in the optimization process for the 33-slot machine include:

• Barrier width.
• Magnet width and height.
• Distance between barriers.
• Stack length.
• Stator tooth width.
• Stator and rotor back iron dimensions.

Although most of the geometric dimensions remained unchanged, the stack length was increased by 10 mm during the optimization process. After 392 iterations, the optimization process concluded, resulting in the determination of the optimal machine geometry. The final specifications, which meet the desired performance criteria, are detailed in

Table 2. Key dimensions for the designed machines.

Parameter	Unit	33 Stator Slots	27 Stator Slots
Outer Diameter	mm	170	170
Stack Length	mm	120	120
Airgap	mm	0.5	0.5
Number of Slots	-	33	27
Number of Poles	-	4	4
Number of Turns	-	16	17
Coil Pitch	-	8	6
End Barrier Iron	mm	2	2
Mid Barrier Iron	mm	1	1
Distance Magnets 1 2	mm	3.8	3.8
Distance Magnets 2 3	mm	3.56	3.56
Distance Magnets 3 4	mm	3.61	3.61
Barrier Thickness	mm	3.4	3.4
Magnet Thickness	mm	3.87	3.87
Stack Length	mm	133	133
Stator Back Iron	mm	11.75	12.1
Stator Tooth Width	mm	4.56	6.72

[43]. The cross-sections of the two proposed topologies are displayed in Figure 8. As can be noticed, the number of rotor poles was reduced to four, and the number of flux barriers per pole was increased to four.

3. SynRM Performance Evaluation: Comparative FEA Analysis of the Two Topologies

During this phase of study, the performances of the two machines are compared, considering the optimized shape that meets the requirements. The main performances of both analyzed topologies, such as the torque, torque ripple, and voltage levels, are presented and analyzed. Furthermore, the efficiency maps for both machines are presented. The simulation was conducted considering a DC power supply with a voltage value of 110 V.

A torque comparison is shown in Figure 9, where a significant difference in torque ripple can be noticed between the two machine topologies. Although torque ripple affects the waveform, the overall value remains excellent at 31.5 Nm. Other measures like stator skewing could be used to reduce the torque ripple content in future analyses.

In

Table 3. Torque comparison between two machines configurations.

Parameter	Unit	33 Slots	27 Slots
Average Torque	Nm	31.5	31.5
Torque Ripple	%	11	7.5

can be seen the average torque and torque ripple content for the two topologies under the study.

The phase voltage level achieves an RMS value of 48.5 V. However, a phase difference between the two machines can be noticed due to a difference in the winding configurations. Based on the waveform illustrated in Figure 10, it is noticeable that the harmonics content in 33/4 SynRM is higher than that in the 27/4 topology and the numerical values of the harmonics are mentioned in

Table 4. Magnitude of EMF harmonics for the two topologies studied [V].

Harmonic Order	1	3	5	7	9	11
27 stator slots	68.2	5.6	0.85	0.49	0.17	0.64
33 stator slots	71	8.15	1.07	0.98	2.13	0.95

.

Efficiency maps are available for both machines (Figure 11), with no significant differences, and the values in the rated operating point (2100 rpm speed and 31.5 Nm torque) are 93.6% for the 33-slot topology and 94.2% for the 27-slot topology.

4. Voltage Level Impact Approach and Work Methodology

The trend of increasing the voltage levels of the power sources in order to reduce the current required for machine operation presents the question of how the proposed topology can be efficiently adapted to produce beneficial outcomes when powered at levels greater than the nominal value. Figure 12 depicts the processes performed to investigate the effect of voltage supply levels on machines’ performance.

The inputs of the design process for an electrical machine are often determined by the requirements of the application.

4.1. Voltage Level Design Approach

For a DC power supply, the phase voltage, $V_{phase}$, for a star-connected three-phase machine is:

$$V_{phase}=\frac{V_{DC}}{\sqrt{6}}=R_{phase}{I}_{phase}+\frac{d\psi }{dt}$$

(3)

The voltage pulsation, $\omega$, equation is:

$$\omega =2\pi f$$

(4)

The frequency, $f$, depends on number of pole pairs, $p$, and the operation speed of the machine, $n$:

$$f=p\frac{n}{60}$$

(5)

The maximum phase-induced electromotive force can be written as:

$$E_{phase\max }=\omega {\psi }_{phase\max }=\omega N_{phase}{\Phi }_{\max }$$

(6)

The number of turns per phase is represented by $N_{phase}$, and ${\Phi }_{\max }$ is the maximum flux crossing the airgap, given by the follow equation:

$${\Phi }_{\max }=B_{\delta \max }{\tau }_{p}L=B_{\delta \max }\frac{D_{is}\pi }{2p}L$$

(7)

In Equation (7), the magnetic flux density in the airgap is represented by $B_{\delta \max }$, and the interior stator diameter is noted with $D_{is}$. The stack length of the machine is noted with L.

By substituting Equations (4), (5), and (7) into Equation (6), the maximum phase-induced electromotive force equation becomes:

$$E_{phase\max }=\frac{{\pi }^{2}n}{60}{B}_{\delta \max }{D}_{is}{N}_{phase}L$$

(8)

If the winding factor is taken into consideration, then Equation (8) becomes:

$$E_{phase\max }=k_w\frac{{\pi }^{2}n}{60}{B}_{\delta \max }{N}_{phase}L$$

(9)

To evaluate the influence of phase voltage, and consequently, power supply voltage, on the design of a synchronous machine, it is essential to first establish an analysis and design framework.

There are different approach possibilities available, which depend on the limits set by the application. Every constraint, whether regarding geometry, dimensions, or technology, tends to restrict the range of possibilities of building or modifying the machine. Hence, when confronted with a diverse power supply voltage, modifications need to be implemented according to the rated speed of the application. If it is necessary to maintain the same rated speed, the winding must be redesigned, and the design for the power source voltage is limited by the stator slots’ ability to accommodate the changed number of turns per coil and per slot.

4.2. Work Methodology

As mentioned in the previous section, the design framework is established based on the limitations imposed by the application. This investigation aims to redesign the winding of the machine to accommodate different power supply voltage levels. The examination will concentrate on assessing aspects like the induced electromotive force, magnetic flux density across the airgap, electromagnetic torque, torque ripple content, efficiency map, and the range of constant torque operation.

An analysis will be conducted on a topology consisting of 27 slots and 4 poles to evaluate the effects of different power source levels on the previously specified parameters.

Table 5. PM-assisted SynRM voltage level.

Case Study	${\mathit{V}}_{\mathit{D}\mathit{C}}$ [V]	Base Speed [rpm]	Number of Turns
SynRM1	110	2100	3
SynRM2	200		6
SynRM3	310		9
SynRM4	400		13
SynRM5	560		17

displays the voltage levels used for the analysis. Taking into account the base speed, the number of turns per phase was determined for each voltage level.

5. PM-Assisted SynRM Results at Different Voltage Level Supplies

The analysis of the SynRM performance involved the consideration of five voltage levels. The power supply voltage served as a key input in the machine’s design process, influencing the re-dimensioning of windings. By adjusting the number of turns per slot per phase, the phase resistance, and the rated phase current (

Table 6. Rated current for each level of voltage supply.

Power Supply Voltage [V]	Rated Current [A]	Phase Resistance [Ω]
110	74	0.0265
200	37	0.112
310	24.5	0.23
400	17	0.574
560	13	1.244

), the performance and efficiency of the SynRM can be optimized for different voltage levels. This allows the machine to operate at its highest potential under varying power supply conditions. The analysis of these adjustments is crucial in determining the overall effectiveness and reliability of the machine in different operating scenarios.

The harmonic content of the voltage waveform produced by a machine is primarily determined by its electrical design, including its winding configuration, phase arrangement, and modulation techniques. While the number of winding turns may not directly dictate the harmonic content, variations in the winding design can indirectly influence the voltage harmonics by affecting the distribution of magnetic flux and the occurrence of magnetic saturation.

Figure 13 illustrates the phase voltage waveforms for the analyzed cases, and

Table 7. Magnitude of EMF harmonics [V].

Harmonic Order	1	3	5	7	9	11
SynRM1	68.2	5.6	0.85	0.49	0.17	0.64
SynRM2	136.68	12.27	1.71	0.98	0.35	1.28
SynRM3	204.13	18.47	2.58	1.46	0.54	0.6
SynRM4	291.05	26.6	3.72	2.11	1	2.78
SynRM5	381	34.85	4.87	2.77	1.01	3.64

provides the magnitudes of the harmonics associated with these waveforms. Notably, the electromotive force (emf) exhibits a significant third-order harmonic, constituting 9% of the fundamental component [44]. This harmonic distortion observed in the emf waveform can have negative effects on the performance and efficiency of electrical systems. Harmonics can lead to increased heating, voltage instability, and can interfere with the proper functioning of sensitive devices. Therefore, it is crucial to minimize the presence of harmonics in electrical systems using filters and other corrective measures.

Figure 14 depicts the electromagnetic torque created by the analyzed scenarios. Although torque ripple affects the waveform, the overall value remains satisfactory, averaging 31 Nm.

To lower the torque ripple content, further approaches such as stator skewing might be applied. For example, in electric vehicle motors, torque ripples can impact the smoothness of their acceleration and deceleration. By applying stator skewing, which involves intentionally tilting the stator slots, the electromagnetic torque variation can be reduced. This results in a more consistent torque output and a smoother driving experience for the vehicle’s occupants.

The analysis was extended to include the entire torque–speed range defined by the application, and the results in terms of efficiency maps are shown in the following figures (Figure 15, Figure 16 and Figure 17).

It is obvious that the machine has a flux-weakening functioning range, allowing it to achieve a higher maximum speed. This is crucial for applications that require variable speed operation. Furthermore, the efficiency map demonstrates that the machine operates at its highest efficiency within a specific range of torque and speed. This information is valuable for optimizing the machine’s performance and ensuring energy savings during operation. Overall, the inclusion of the entire torque–speed range in the analysis provides comprehensive insights into the machine’s capabilities and performance characteristics.

The machine demonstrates an efficiency map exceeding 95% across a wide torque–speed range, with the power supply voltage level showing a minimal impact on its performance. This makes it highly reliable and adaptable for various applications.

6. Performance Evaluation of the Designed Machine

For the performance evaluation, the same topology was used (27 slots and 4 poles). The efficiency of the designed machine remained consistently high, showcasing the robustness and reliability of the design. Additionally, the performance metrics indicated no significant deviation or degradation in the machine performance at this voltage level. This analysis further solidifies the suitability and effectiveness of the selected topology for practical applications at 560 V.

The magnetic flux density map illustrated by Figure 18 , revealed a peak value of approximately 1.8 T within the stator and rotor back iron, as well as the teeth and flux barriers. These parts were unable to reach saturation in the lamination material of the rotor and stator.

Since the simulations employed an alternating current (AC) source, the resulting phase voltage had to be equal to that of a direct current (DC) power supply with a value of 560 V. Figure 19 illustrates the peak phase voltage (phase A-blue, phase B-yellow and phase C-red) exceeding 400 V, with a root mean square (RMS) value of 264 V.

Figure 20 illustrates electromagnetic torque, with an average value of 31.5 Nm and a torque ripple of approximately 7.5%. The machine is engineered to operate across a wide range while utilizing a field-weakening control method. This allows for the maximum torque to be achieved at the rated speed of 2100 rpm, gradually decreasing to 14 Nm at 7000 rpm, as depicted in Figure 17’s efficiency map.

The cogging torque can be a key contributor to noise generation, and decreasing the torque ripple content was one of the goals of optimizing the referenced architecture provided in Section 2 of this research. The large slot number and coil pitch allow for a reduction in torque ripples. This reduction in torque ripple is crucial for achieving a smoother operation of the motor, minimizing vibration and noise. By minimizing the cogging torque, the motor’s performance can be significantly improved, leading to a more efficient and quieter operation. The results shown in Figure 21 further validate the effectiveness of the optimized architecture in reducing torque fluctuations and its potential for noise reduction in various applications.

There are several critical categories of parameters influencing the performance of a machine, such as the machine geometry, electric parameters, and electromagnetic parameters, etc. Among these, the direct and quadrature inductances stand out as particularly crucial. These inductance values can be determined through calculations [45].

$$L_d=\frac{{\Phi }_d}{I_d}+L_0$$

(10)

$$L_q=\frac{{\Phi }_q}{I_q}+L_0$$

(11)

In Equations (10) and (11), ${\Phi }_d$ and ${\Phi }_q$ represent the flux linkages on the d and q axes, $I_d$ and $I_q$ are the currents on the d and q axes, and $L_0$ is the inductance contributed by the end winding connections and can be determined with Equation (12).

$$L_0=\frac{{\mu }_0{\mu }_{r}A}{2\pi \ln \left(\frac{r_{outer}}{r_{inner}}\right)}$$

(12)

The permeability of free space is represented by ${\mu }_0$, ${\mu }_r$ is the relative permeability of the winding material, A represents the cross-sectional area of the winding material, and $r_{outer}$ and $r_{inner}$ are the outer and inner radii of the winding, respectively.

The direct and quadrature inductances play significant roles in the functioning of a machine. They directly impact on its efficiency and overall performance. Calculating these inductance values is essential for accurately understanding and predicting the machine’s behavior. Several methods and formulas have been developed to determine these parameters, and they are often based on the machine’s geometry, electric parameters, and electromagnetic properties. These calculations provide valuable insights into the machine’s characteristics and enable engineers to optimize its design and operation.

Nevertheless, this method may be erroneous for interior PM machines; thus, an automated computation of the d- and q-axis inductances was carried out using FEA simulation in JMAG-Designer. Choosing the right current phase angle is an important factor in boosting the efficiency of the SynRM; thus, the correct phase current for the highest saliency ratio between the d- and q-axis inductances must be selected. Figure 22 shows the inductance variation vs. current phase angle, with a maximum saliency ratio of 4.33 at 81°. This is a key consideration when attempting to maximize power production and efficiency.

Figure 23 shows the iron losses across the whole operating range. At rated values, these iron losses are around 100 W, which is an appropriate value for this sort of machine; nevertheless, they grow with speed, reaching a maximum of 800 W at 9000 rpm. This increase in iron losses with speed is expected, as higher speeds result in an increased magnetic flux density and higher eddy currents within the iron core. It is important to consider these iron losses when designing the cooling system for the machine, as excessive heat generated by the losses can negatively impact the overall efficiency and performance of the system. Additionally, the proper insulation and material selection for the core laminations should be employed to minimize these losses and ensure the longevity of the machine.

7. Conclusions

This study primarily focused on the design aspects of the electrical machine, while recognizing the critical importance of the drive system for practical implementation. The article largely discusses the design aspects of the electrical machine, specifically exploring several factors such as adjusting the DC-link voltage to lower the current, minimize copper losses, and improve motor efficiency. It is evident that increasing the voltage necessitates a careful evaluation of drive limitations, such as the requirement for additional DC-link capacitors. These capacitors, which store and release electrical energy, may need to be increased in number or size with higher voltage levels, consequently leading to a larger overall drive system.

Moreover, although a phase voltage of 48.98 V RMS was selected, it is acknowledged that the actual voltage from the DC-link can vary due to factors such as IGBT voltage drop, deadtime effects, and the influence of long cables. These factors must be meticulously considered to ensure the machine's optimal performance and reliability.

Additionally, it is imperative to assess the reliability of capacitors and possess a thorough understanding of battery technology, including their state of charge, and remaining useful life, when conducting a comprehensive reliability study of the entire system. This article does not delve into the specifics of battery technology, or the power electronics required for balancing, as its focus remains on the machine design.

While this research provides valuable insights into the effects of voltage levels on the design and performance of electrical machines, further research is required to explore the comprehensive integration of the machine with the drive system. In future work, focus will be directed towards the overall system level, encompassing the phenomena related to the inverter alongside it. Such future research will be indispensable for the practical implementation of the proposed topology within real power systems.

The PM SynRM, despite its absence of rare earth element permanent magnets, demonstrates performance capabilities suitable for automotive applications. However, in contexts where spatial limitations are a concern, increasing the stack length becomes necessary to achieve performance parity with PMSM. This adjustment may render the PM SynRM unsuitable for certain applications where space constraints are critical.

Finally, the main conclusions can be encapsulated by

Table 8. Final conclusions of the study.

Conclusion	Reference Machine	33_4 Topology	27_4 Topology	Implication and Findings
Torque ripple content reduction	28%	11%	7.5%	Torque ripple content can be reduced by optimizing the topology using the technique that prioritizes a considerable number of slots with maximal coil pitch Improved operational smoothness Decreased level of noise and vibration Vital for applications like light electric vehicles
Efficient topology after optimization	-	-	The most efficient in reducing torque ripple	While the reduction in torque ripple content is substantial, additional analyses should incorporate strategies aimed at further minimizing it. This approach is essential to attain even better performance levels
DC power supply influence	-	-	Minimal effect The machine maintains a high effectiveness	The machine features a broad flux-weakening operational range, enabling it to achieve significantly higher maximum speeds. While the study indicates that the voltage level of the supply does not impact the machine’s performance, other aspects warrant consideration. For instance, reducing the current could mitigate losses in the windings and consequently lower the temperature in the stator core.
Suitability for higher voltage levels	-	-	Demonstrated the machines’ ability to work at higher voltage levels Indication of durability and dependability of the design Potential for practical applications at higher voltages	The motor’s performance at 560 V opens avenues for customization based on specific industrial needs. Tailoring the motor to different voltage requirements becomes feasible, offering flexibility in design Motors capable of handling higher voltage levels are often more compatible with advanced control systems and technologies. This compatibility enhances their integration into modern industrial setups
Further expansion possibilities	-	-	Can operate at elevated voltage levels with appropriate winding redesign Using ferrites instead of rare earth materials can significantly lower machine costs without sacrificing performance. Ferrites are more economical and readily available, offering a cost-effective solution for machine construction	The ability to expand without significant redesigning may result in cost-effective upgrades. This is advantageous for businesses seeking to enhance equipment performance without incurring substantial expenses

as follows: