Optimization and Performance Evaluation of PM Motor and Induction Motor for Marine Propulsion Systems

Abstract

The electrification of ships and the use of electric propulsion systems are projects which have attracted increased research and industrial interest in recent years. Efforts are particularly focused on reducing pollutants for better environmental conditions and increasing efficiency. The main source of propulsion for such a ship’s shafts is related to the operation of electrical machines. In this case, several advantages are offered, related to both reduced fuel consumption and system functionality. Nowadays, two types of electric motors are used in propulsion applications: traditional induction motors (IMs) and permanent magnet synchronous motors (PMSMs). The evolution of magnetic materials and increased interest in high efficiency and power density have established PMSMs as the dominant technology in various industrial and maritime applications. This paper presents a comprehensive comparative analysis of PMSMs and both Squirrel-Cage and Wound-Rotor IMs for ship propulsion applications, focusing on design optimization. The study shows that PMSMs can be up to 3.11% more efficient than IMs. Additionally, the paper discusses critical operational and economic aspects of adopting PMSMs in large-scale ship propulsion systems, such as various load conditions, torque ripple, thermal behavior, material constraints, control complexity, and lifetime costs, contributing to decision making in the marine industry.

1. Introduction

Nowadays, much effort is being focused on increasing efficiency and reducing harmful emissions. Modern propulsion systems are an emerging technology being applied to electrify transportation [1,2]; similar efforts have been applied to other industries, such as elevators, aerospace, ships [3], and electric vehicles [4]. Electric motor manufacturers have focused on producing suitable subsystems such as batteries, power electronics, and electrical machines.

Traditional propulsion systems suffer from several limitations, e.g., low efficiency, high fuel consumption, and elevated emissions. Additionally, they require large installation spaces and offer limited maneuverability [5]. In contrast, the use of electric motors provides advantages such as reduced fuel consumption, reduced maintenance requirements, smaller volume for propulsion systems, and flexibility in space utilization, thereby increasing a ship’s payload, improving ship handling during low-speed movements in shallow waters and during embarkation/disembarkation phases, and reduced noise and vibrations, resulting in a significantly improved experience for the crew and passengers of the ship [6].

These features have led to the integration of electric motors contributing to the generation of electricity, as parts of auxiliary systems, and as the main propulsion engines of ships’ propeller [7]. In the case of electric generators, significant research has been devoted to their design and control. Advanced algorithms have been developed to manage ship power more efficiently, taking into account electric machine behavior, operational constraints, and environmental conditions. These strategies aim to reduce both fuel consumption and costs [8].

Electrical machines are the main propulsion units in hundreds of ships of different types, such as cruise ships, ferries, pleasure boats, warships, fishing vessels, icebreakers, and research vessels [9]. At the same time, research is being carried out on the use of electric propulsion in new vessel designs. Nowadays, integrated electric ships have become increasingly attractive for commercial fleets. This shift is driven by advances in power electronics, improvements in electric motor design, and the emergence of new propulsion architectures. These systems provide notable advantages compared to conventional axial propulsion [10].

Research has shown that the use of electric propulsion is limited to high-volume vessels such as cargo and box ships, tankers, LNG carriers, and chemical carriers, due to their high investment costs [6] and environmental impact [11]. Effective propulsion systems should demonstrate high efficiency and a suitable power factor. They must also exhibit low losses, acceptable thermal behavior, and minimal cogging torque and torque ripple [12]. Also, they must have a high power and torque density, as the installation space for motors is limited [13].

Different topologies of electric motors have been investigated in order to determine their suitability for specific applications. Among these categories are induction motors (IMs) [14], permanent magnet synchronous motors (PMSMs) [15], high temperature superconducting motors (HTSMs) [16], high efficiency super drive systems (HESDSs) [17], and acyclic coaxial motors [18].

The first two categories are the most widely used technology. Their specific characteristics and advantages are well known and have been documented in numerous published scientific papers [19]. At this point, it should however be pointed out that modern motors carrying either internally or surface mounted magnets can be used just as effectively. As highlighted [20], the power and torque transmitted to a ship’s propeller reach their maximum values when the rotational speed achieves its peak level. Achieving this condition depends on the optimal operation of the propulsion system, efficient energy management, and the minimization of losses in both mechanical and electrical subsystems [21]. The integration of energy storage systems with lithium-ion batteries (Li-ion ESS) as backup energy sources further enhances the resilience and fault tolerance of these systems [22]. Hybrid electric propulsion systems, which combine traditional diesel generators with advanced energy storage systems such as lithium-ion batteries, offer promising solutions for reducing greenhouse gas emissions by using hardware-in-the-loop (HIL) simulations to analyze the interaction between diesel generators, battery storage systems, and propulsion components [23].

In order to achieve the best possible PMSM design, several models based on both traditional genetic algorithms and modern machine learning techniques have been proposed [24]. Utilizing the Symbiotic Organisms Search Algorithm (SOS), PMSM optimization in azimuth thruster type propulsion systems was achieved. The algorithm is judged to be an efficient solution, achieving reductions in core losses and oscillation torque of 12.5% and 60%, respectively [25].

Thus, the torque–speed profile in electric ship propulsion differs significantly from that in a typical electric vehicle. Therefore, the operation of the motor in the region of magnetic field attenuation, which is the great advantage of topologies with internally mounted magnets, is no longer necessary [26].

Another category includes superconducting motors that show particular advantages over induction motors and modern permanent magnet motors. Their main advantages are related to their high power density and torque and their overloading capabilities. They are mainly observed in military applications, as their costs are considered particularly high for conventional merchant ships [27]. One exception to this which has been used in small vessels is BLDC motors made from standard conventional materials with 3D printed technology, as presented in [28]. In addition, Vernier-type motors [29] have been investigated and tested, focusing on their optimization [30]; however, for reasons of manufacturing complexity, they are not preferred.

The construction of electric motors for large volume ship propulsion systems is of great research interest. With the evolution of exhaust systems, LNG carriers have replaced steam and given rise to the creation of dual-fuel systems with electric propulsion [31]. Such systems include dual-fuel generators, which use both boil off gas (BOG) and heavy fuel oil (HFO). Propulsion engines are typically high-power induction motors of the order of 10–15 MW each, driven by variable speed drives with pulse-width modulation. Such an electric propulsion system was studied in [32]. Multiphase induction motors in marine applications show increased efficiency, reduced harmonic distortion, and minimized torque ripple. Their design requires adjustments to achieve the optimal winding arrangement [33]. In this study, the specifications that a motor should satisfy are determined. Then, through sensitivity analyses and the application of an optimization algorithm, an optimal geometry for an induction motor is obtained.

In the context of ship electrification, the selection of electric propulsion systems must consider various operational constraints such as the installation space, continuous operation under varying loads, and the need for high efficiency to optimize fuel consumption. PMSMs offer distinct advantages in terms of power density and operational efficiency, while IMs remain a cost-effective and well-established alternative. Wound Rotor Induction Motors (WRIMs) offer significant advantages over Squirrel Cage Induction Motors (SCIMs) for high-power marine applications, primarily due to their ability to regulate rotor resistance via slip rings, enabling superior starting torque and controlled acceleration—critical for large vessels which need to overcome high inertia loads [34]. Unlike SCIMs, WRIMs allow for precise speed control without complex external converters, thereby enhancing adaptability to varying operational conditions [35]. Although WRIMs require more maintenance due to slip rings, advancements in materials have improved their durability, making them viable for long-term ship propulsion applications [36]. Their capacity to adjust torque and efficiency dynamically makes them well-suited for marine environments where load demands fluctuate [37]. Despite the growing interest in electric propulsion, there is a lack of comprehensive studies comparing PMSMs and IMs in terms of efficiency under variable load profiles, thermal limitations, control strategies, lifetime costs, and overall optimization strategies. This study aims to bridge this gap by providing a comprehensive design and optimization analysis of both PMSMs and IMs under marine operating conditions, offering insights into their respective strengths and limitations in ship propulsion applications, thereby informing more effective motor selection and design processes.

The main objective of this paper is the design and analysis of a PMSM with a surface magnet topology in order to characterize its integration in propulsion systems. Section 2 will describe the geometric characteristics of the SCIM design in order to apply finite element analysis to simulate the operating characteristics of the machine. In addition, a wound rotor is included instead of a SC to show the differences and improvements which seek to meet the specific operational needs of electric propulsion of ships with an induction motor. In Section 3, the design methodology of the PMSM will be analyzed in order to minimize losses and reduce torque ripple during nominal operation by sensitivity analysis. In Section 4, the appropriate final PMSM manufacturing configuration topology will be derived, while Section 5 gives the comparative selection criteria derived from the design and includes the initial and operational costs, maintenance costs, cooling and control systems, and the life cycle for the aforementioned application. Finally, Section 6 discusses the challenges and possible future implications that could be presented in other work, while Section 7 summarizes the key findings of the present research.

2. Optimized Geometric and Operational Design of an Induction Motor

The first key element for the comparative investigation in our study was the appropriate design configuration based on the specific selection data. A numerical approach using finite element analysis (FEA) approximation was used to visualize the magnetic field of the motor and its operational characteristics under specific loading conditions such as the torque, nominal current, and power factor. For the purpose of design and simulation, Ansys Maxwell 2023R1 software was used, while modeling was performed in Matlab 2023a environment.

The electric propulsion system studied included two identical induction motors with a short-circuited cage rotor with an output power equal to 10 MW. The motors were powered through an AC/DC/AC inverter with pulse width modulation (PWM) and polar voltage equal to 6600 Volt at a frequency of 60 Hz. Their nominal mechanical rotational speed was equal to 504 rpm, giving an output torque of 189,512 Nm. The efficiency of the final topology developed was 95.20%.

High-power electric propulsion motors for ships, particularly those rated at 10 MW, must meet strict requirements to ensure efficiency, reliability, and performance. These motors need to exhibit high efficiency across various load conditions to minimize operational costs and energy consumption. Compact design and high power density are essential to save space and reduce weight in a ship’s propulsion system. Durability and resistance to harsh marine environments, including humidity, vibrations, and temperature variations, are critical for reliable long-term operation. Smooth torque delivery, fast response, and low acoustic noise are necessary for precise maneuvering and passenger comfort. Additionally, motors must support advanced control systems for optimal performance, while maintenance should be straightforward to minimize downtime. As such, the design and optimization process for an induction motor for marine electric propulsion contains several key steps [38].

2.1. Preliminary Design Stage

The goal in the first step was to establish the motor’s basic geometrical and electrical characteristics. Total mechanical output power P_out delivered by the motor is related to its torque T_out and rotation speed n by T_out = P_out/ω, where ω is the angular velocity (rad/s) and n is the rotational speed (rpm). Air gap length L_g is crucial for determining a motor’s efficiency and performance and can be estimated based on the mechanical power derived from Equations (1) and (2), where k_g is an empirical coefficient typically between 0.001 to 0.005, D is the stator inner diameter, C_d is the design constant (typically 11–13 for large machines), and L’_g is the effective length of the stator.

$${\mathrm{L}}_{\mathrm{g}}=k_g\times \mathrm{D}$$

(1)

$$\mathrm{D} =\sqrt{{\displaystyle \frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{C_d {\mathrm{L}}_{\mathrm{g}}^{\prime }\mathrm{n}}}}$$

(2)

The number of stator slots Q_s was calculated based on the winding configuration and pole pairs from Equation (3).

$${\mathrm{Q}}_{\mathrm{s}}=m \times p\times q$$

(3)

where m is the number of phases, p the number of pole pairs, and q the number of slots per pole per phase.

The electromotive force (EMF) induced in each phase winding is given from Equations (4) and (5) as

$$E=4.44 f\times N\times A\times B$$

(4)

$$A={\displaystyle \frac{\pi {\mathrm{D}}^2}{4}}$$

(5)

where f is the supply frequency (Hz), N is the number of turns per phase, A is the cross-sectional area of the winding, and B is the flux density in the stator core.

• Rotor Design

Building upon the preliminary design, a rotor configuration was developed, emphasizing factors influencing magnetic flux and mechanical stability. The rotor’s diameter and the number of rotor bars were determined similarly to the stator, ensuring the machine operated at the desired efficiency and speed range. The rotor slot shape and material choice, i.e., typically copper for high efficiency, significantly affect a motor’s performance. Additionally, the rotor slot geometry directly affects the torque production. For a squirrel-cage rotor, the number of rotor bars should be slightly different from the number of stator slots to reduce harmonic effects. The depth and width of the slots were chosen to balance mechanical strength with electrical performance and were optimized using Finite Element Method (FEM) analysis, covered later in the section on optimization. Rotor slot pitch τ_r was determined from Equation (6), where Q_r is the number of rotor slots.

$${\tau }_r={\displaystyle \frac{{360}^{\mathrm{o}}}{{\mathrm{Q}}_{\mathrm{r}}}}$$

(6)

• Equivalent Circuit Model

The next step included the construction of the equivalent circuit, enabling the simulation of electrical behavior under various operating conditions. The equivalent circuit of an induction motor models its electrical performance. The parameters include stator resistance R_s, rotor resistance R_r, stator reactance X_s, and rotor reactance X_r. To determine the values of the equivalent circuit parameters, standard tests were employed. The no-load test was used to evaluate the core losses of the motor, e.g., hysteresis and eddy current losses under unloaded conditions. The locked rotor test, on the other hand, provided insights into the rotor resistance and leakage reactance, both critical for understanding motor starting behavior and torque production.

Figure 1 shows the parameters for the equivalent circuit of the three-phase induction motor.

The parameters inside the box were acquired through the 2D FE simulations of the indirect tests of the induction motor; they were not constant. The magnetizing inductance L_M was a function of the stator flux linkage Λ_s and the total leakage inductance L_2D and the rotor resistance R_r,2D were functions of the rotor frequency, which was a function of slip s. The stator winding resistance Rs, the end-winding leakage inductance Ls, 3D, and the rotor parameters Rr, 3D, Lr, 3D, which take into account the rotor rings and the bar skewing, were considered constant and were computed analytically according to the method described in [39]. Once all the parameters had been found, it was possible to predict the motor performance under different operating conditions.

• Loss Calculation and Efficiency

In the last step, an assessment of different loss components was conducted to evaluate their impact on overall efficiency, providing insights into performance optimization. Losses in the motor consisted of copper losses in the windings of the stator and rotor, iron losses in the core due to hysteresis and eddy currents, and mechanical and stray losses.

Stator and rotor copper losses P_scu and P_rcu, were calculated using Equations (7)–(9), respectively, where I_ph is the nominal phase current, R_s is the stator resistance, P_m is the air-gap power, and s is the slip.

$${\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}=3{ I}_{ph}^2\times {\mathrm{R}}_s$$

(7)

$${\mathrm{P}}_{\mathrm{r}\mathrm{c}\mathrm{u}}=\mathrm{s}\times {\mathrm{P}}_{\mathrm{m}}$$

(8)

$${\mathrm{P}}_{\mathrm{m}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{1-s}}$$

(9)

Iron losses in the stator core depended on the core material and operating frequency and were calculated using Steinmetz’s Equation (10).

$${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}=k_h{B}_m^{2}fV+k_e{B}_m^2{f}^{2}V$$

(10)

where k_h and k_e are material-specific constants, B_m is the maximum flux density, V is the core volume, and f is the frequency.

The efficiency rate is given by Equation (11):

$$\eta ={\displaystyle \frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{i}\mathrm{n}}}} ={\displaystyle \frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}+{\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}+{\mathrm{P}}_{\mathrm{r}\mathrm{c}\mathrm{u}}+{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}+{\mathrm{P}}_{\mathrm{m}\mathrm{s}}}}$$

(11)

Equation (11) can be written as a function of slip s; thus, the efficiency of the induction motor depends on the value of the slip, as shown in Equation (12).

$$\eta \left(s\right) ={\displaystyle \frac{{(1-s)\mathrm{P}}_{\mathrm{m}}}{{(1-s)\mathrm{P}}_{\mathrm{m}} +{\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}+{s\mathrm{P}}_{\mathrm{m}}+{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}+{\mathrm{P}}_{\mathrm{m}\mathrm{s}}}}$$

(12)

Figure 2 shows the efficiency vs. slip curve for the induction motor under nominal and off-nominal operating conditions. As expected, the efficiency decreased as slip increased, with the motor operating most efficiently at lower slips. The curve highlights the peak efficiency zone near the rated slip (0.02–0.05) with a notable decline in performance at higher slip values due to increased rotor copper losses. This behavior is critical in marine applications where partial-load operation is frequent.

2.2. Finite Element Method (FEM) Simulation

After establishing the preliminary design, FEM analysis was used to simulate the motor’s electromagnetic performance. This involved solving Maxwell’s equations to understand the flux distribution, torque, losses, and thermal effects.

The analysis refined the rotor and stator slot geometry to minimize losses, particularly core and copper losses, ensuring the motor operated efficiently under nominal conditions.

This study’s methodology considered the unique operational characteristics of ship propulsion systems, including load variations, extended operational hours, and harsh environmental conditions such as humidity and temperature fluctuations. The design of the motors was tailored to meet these specific requirements, with a focus on optimizing efficiency and reliability under dynamic operating conditions. In particular, the finite element analysis (FEA) and sensitivity analysis conducted in this study considered marine-specific constraints to ensure that a realistic and practical design approach was devised. The simulation utilized a mesh convergence study to ensure result accuracy, with three levels of mesh density progressively being refined until variations in key performance indicators, such as torque and flux density, were below 2%. Boundary conditions were meticulously defined, applying fixed constraints to the stator and appropriate current excitations to the windings, reflecting realistic operational scenarios. A constant temperature of 75 °C was imposed on the stator housing, reflecting cooling performance for marine-grade propulsion drives. The outer stator was assumed to be mechanically fixed with zero radial and axial displacement. Rotor movement was modeled with rotational periodicity and ideal airgap preservation. Rated supply conditions were used, and appropriate winding configurations were applied based on manufacturer data. To validate the FEA models, our results were compared with established benchmarks from the recent literature, demonstrating a high degree of correlation and thus confirming the model’s reliability [40,41,42].

• Optimization

After the initial design and the FEM simulation, the geometry was optimized by performing a sensitivity analysis on the key dimensions (e.g., stator slot width, rotor bar height). The objective was to minimize losses, including both core and copper losses, and ensure smooth torque with minimal ripple for smooth sailing.

Using optimization techniques, the motor’s final geometry was selected, which minimized the objective function of losses while maintaining high performance.

As is known, an advanced induction motor is powered by a converter and not directly from the network. This fact offers the possibility, during the optimization of the initially designed motor, to vary the current density supplied to the stator windings, within the limits of the thermal resistance of the windings as well as the slip, in order to find an optimal operating point of the motor that will deliver the rated torque and at the same time increase its efficiency. To achieve maximum motor efficiency, it is sufficient to achieve a balance between electric and magnetic charging. The methodology for the 10 MW induction motor design combined preliminary analytical modeling with Finite Element Method (FEM) simulations for optimization. The initial design featured a 14-pole (7 pole pairs) squirrel-cage induction motor with 42 stator slots and 54 rotor bars. Geometrical dimensions included a stator outer diameter of 3100 mm, inner diameter of 2300 mm, and axial length of 720 mm. The air gap length was set to 5.8 mm to balance efficiency and thermal management. Distributed double-layer winding was used to minimize harmonic distortions and torque ripple. The nominal performance metrics before optimization included an efficiency of 92.74% and significant copper losses (241.54 kW in the stator and 372.60 kW in the rotor). The total losses amounted to 782.14 kW.

The optimization focused on minimizing losses and improving thermal and electromagnetic performance. FEM simulations iteratively adjusted rotor bar height, stator slot width, and air gap length. Constraints included limiting the stator winding current density to 6 A/mm², ensuring thermal stability, and adhering to material and manufacturing specifications using NEMA Class A copper bars. The implementation of this algorithm resulted from an investigation into the initial geometry of the motor. Specifically, a first algorithm was implemented to change the current density of the stator windings from 5 A/mm² to 6 A/mm² with a step of 0.1 A/mm². In this way, the operating slip and the new nominal operating points were found. Regarding the range of the current density of the stator windings, an increase up to 6 A/mm² was applied, although this was the upper limit before forced cooling would have been required; this was nonetheless acceptable due to the fact that the motor was immersed in seawater, so there was sufficient cooling of the stator windings. A sensitivity analysis revealed critical relationships between key parameters and performance metrics. The optimization of the motor began with the selection of the two parameters that were to be optimized. Initially, a sensitivity analysis was carried out for the height and width of the stator teeth. Then, the two variables that were optimized through sensitivity analysis concerned the stator tooth shoe and its height. The last pair in the analysis consisted of the height and width of the rotor teeth. The initial and final values of the parameters, as well as the change step, were selected based on construction constraints and the existing design. Increasing the air gap length reduced torque ripple by 15% but required larger stator slots, while increasing the rotor bar height by 5% reduced core losses by 8% due to improved magnetic flux paths. The final optimized design achieved 95.2% efficiency, reduced copper losses, and minimized torque ripple.

Table 1. Main Optimized Characteristics of the Induction Motor.

Quantity	Symbol	Value
Output Power	${\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	10,000.00 kW
Input Power	${\mathrm{P}}_{\mathrm{i}\mathrm{n}}$	10,504.38 kW
Electromagnetic Torque	${\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	189.51 kNm
Poles (Pair of Poles)	2p (p)	14 (7)
Frequency	f	60 Hz
Nominal Speed	nm	504 rpm
Slip	s	2%
Nominal Phase Current	${\mathrm{I}}_{\mathrm{p}\mathrm{h}}$	1150 A
Nominal Voltage	${\mathrm{V}}_{\mathrm{n}}$	6.6 kV
Power Factor	PF	0.80
Copper Losses Stator	${\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}$	132.30 kW
Copper Losses Rotor	${\mathrm{P}}_{\mathrm{r}\mathrm{c}\mathrm{u}}$	204.08 kW
Core Losses	${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}$	50.00 kW
Mechanical and Stray Losses	${\mathrm{P}}_{\mathrm{m}\mathrm{s}}$	118.00 kW
Total Losses	${\mathrm{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$	504.38 kW
Efficiency Rate	η%	95.20%

shows the basic final optimized characteristics (electrical and mechanical) of the machine, taking into account the sum of the individual losses of the motor. Similarly, the geometric characteristics of the induction motor are highlighted in

Table 2. Initial and Optimized Geometrical Variables of the Induction Motor.

Quantity	Symbol	Initial Value	Optimized Value
Outer diameter stator	${\mathrm{D}}_{\mathrm{o}}$	3100 mm	3050 mm
Inner diameter stator	D	2300 mm	2250 mm
Outer diameter rotor	${\mathrm{D}}_{\mathrm{r}}$	2285 mm	2235 mm
Shaft diameter	${\mathrm{D}}_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}}$	1020 mm	1020 mm
Motor axial length	L	720 mm	710 mm
Stator slots	${\mathrm{Q}}_{\mathrm{s}}$	42	48
Rotor slots	${\mathrm{Q}}_{\mathrm{r}}$	54	60
Airgap length	${\mathrm{L}}_{\mathrm{g}}$	6 mm	6.2 mm
Stator opening width	${\mathrm{H}}_{\mathrm{s}0}$	8.2 mm	8.0 mm
Stator base width	${\mathrm{H}}_{\mathrm{s}1}$	8.2 mm	7.8 mm
Stator top width	${\mathrm{H}}_{\mathrm{s}2}$	145.0 mm	140.0 mm
Stator slot opening heigh	${\mathrm{B}}_{\mathrm{s}0}$	37.5 mm	38.0 mm
Stator tip heigh	${\mathrm{B}}_{\mathrm{s}1}$	56.0 mm	55.0 mm
Stator body heigh	${\mathrm{B}}_{\mathrm{s}2}$	290.0 mm	290.0 mm
Tooth width	${\mathrm{w}}_{\mathrm{s}\mathrm{t}}$	118.5 mm	120.0 mm
Stator yoke length	${\mathrm{T}}_{\mathrm{b}\mathrm{i}}$	240 mm	245 mm
Rotor bar body height	${\mathrm{H}}_{\mathrm{r}}$	290 mm	295 mm
Rotor bar opening width	${\mathrm{B}}_{\mathrm{r}0}$	57.8 mm	60.0 mm
Rotor bar base width	${\mathrm{B}}_{\mathrm{r}1}$	29.0 mm	30.0 mm

, including both the initial and final optimized values. Our design comprised a multi-pole motor with 14 poles (7 pair), 48 slots in the stator, and 60 rods in the rotor. The choice of the number of slots for both the stator and the rods was based on the criterion of reducing vibrations, noise, and the occurrence of extended alignment torque and other parasitic phenomena that can occur during motor operation. The number of stator windings was chosen to achieve a distributed winding double layer. In addition, it was considered appropriate to increase the length of the air gap in order to significantly increase the current required to create a magnetic field which induced currents in the rotor.

The stator’s outer and inner diameters were slightly adjusted for better magnetic flux management. The dimensions of the stator and rotor slots increased slightly to improve efficiency and reduce torque ripple. The airgap length was slightly increased for improved cooling and magnetic performance. The yoke and tooth dimensions were optimized to balance mechanical strength and core losses. These adjustments ensured the motor achieved higher efficiency, better cooling, and reduced losses, aligning with the constraints and objectives of the optimization process.

The double layer winding compared to single layer brought about lower core losses due to the lower harmonic content of the magnetic force caused by the drum reaction. At the same time, the torque ripple was also reduced by using such a winding [43]. The maximum acceptable value for the current density of stator winding J_s was set to 6 A/${\mathrm{m}\mathrm{m}}^2$. The rotor bars were made of copper and their design was based on NEMA specifications for the construction class A bars. Finally, silicon-doped steel was used for the stator core and rotor. Due to the varying frequency of the magnetic materials, a specific process of pre-processing, analysis, and post-processing of the data had to be completed [44].

A view of the motor (1/2 part) under study is shown in Figure 3. A detailed illustration of its basic dimensions and the geometric characteristics of the stator and rotor are given in Figure 4, including the stator inner diameter, slot pitch, and air gap length. These parameters correspond directly to the variables listed in Table 2, offering a clear visual reference.

Figure 5 shows the distribution of the magnetic field. We observed a high magnetic flux density with a strong concentration of the field around the slots, which is normal, as this is where the excitation currents that create the main magnetic field are located. In the rotor, the bars show areas of lower field density, as the field is induced in the bars by the changing stator field.

In addition, in the air gap, the field appeared relatively uniform, indicating that the machine was well designed to reduce asymmetries and maintain a constant flow between stator and rotor. The rotor bars appeared to have different field densities. This was due to the varying magnetic flux induced as the rotor rotated, while the areas of high field density (near the bars) showed active current induction. As for saturation, the red area near the stator and in the slots may indicate areas reaching magnetic saturation levels. In this case, control was required as saturation can reduce efficiency and increase losses.

Based on an analysis of the methodology, optimization, sensitivity analysis, and final geometric characteristics of the SCIM for high-power (10 MW) ship propulsion, it is essential to discuss the distinctive aspects of designing and manufacturing a Wound-Rotor Induction Motor (WRIM) for similar applications. The WRIM is distinguished by its rotor construction, where externally accessible slip rings and brushes enable variable rotor resistance control. This design feature offers distinct advantages over SCIMs in demanding environments. The ability to adjust the rotor resistance dynamically allows for better control of slip, making WRIMs particularly suitable for variable-load applications such as ship propulsion. Compared to SCIMs, WRIMs can provide a higher starting torque with lower inrush current, thereby reducing mechanical and electrical stress on ship power systems. Copper losses in the rotor are typically higher in WRIMs due to external resistance insertion. However, this can be mitigated by optimizing the resistance value to balance efficiency and performance.

The general equation for the induced torque in a WRIM is derived from the equivalent circuit (Figure 1) and is given by Equation (13).

$${\mathrm{T}}_{\mathrm{i}\mathrm{n}\mathrm{d}}={\displaystyle \frac{3{\mathrm{V}}_{\mathrm{t}\mathrm{h}}^2 }{{\omega }_{\mathrm{s}}s}} ·{\displaystyle \frac{{\mathrm{R}}_{\mathrm{r} \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{{\left({\mathrm{R}}_{\mathrm{t}\mathrm{h}}+{\mathrm{R}}_{\mathrm{r}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}/s\right)}^2+{\left({\mathrm{X}}_{\mathrm{t}\mathrm{h}}+{\mathrm{X}}_{\mathrm{r}}\right)}^2}}$$

(13)

where ${\mathrm{V}}_{\mathrm{t}\mathrm{h}} ={\mathrm{V}}_{\mathrm{s}}{\displaystyle \frac{{\mathrm{X}}_{\mathrm{M}}}{\sqrt{{{\mathrm{R}}_{\mathrm{s}}^2+\left({\mathrm{X}}_s+{\mathrm{X}}_{\mathrm{M}}\right)}^2}}}$, ${\mathrm{R}}_{\mathrm{t}\mathrm{h}}+{j\mathrm{X}}_{\mathrm{t}\mathrm{h}}={\displaystyle \frac{j{\mathrm{X}}_{\mathrm{M}} \left({\mathrm{R}}_{\mathrm{s}}+j{\mathrm{X}}_{\mathrm{s}}\right)}{{\mathrm{R}}_{\mathrm{s}}+j\left({\mathrm{X}}_{\mathrm{s}}+j{\mathrm{X}}_{\mathrm{M}}\right)}}$, ${\mathrm{R}}_{\mathrm{r}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\mathrm{R}}_{\mathrm{r}}+{\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$, R_s is the stator resistance, R_r the rotor resistance, X_s the stator reactance, X_r the rotor reactance, ${\mathrm{X}}_{\mathrm{M}}$ the magnetizing reactance, and ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ the external resistance.

To ensure optimal torque performance in a WRIM, the external rotor resistance must be carefully adjusted. While an increase in ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ can improve starting torque by increasing rotor slip and reducing inrush currents, excessive values can lead to a reduction in both starting torque and steady-state performance. According to the Maximum Power Transfer Theorem, the maximum torque at startup is achieved when the total rotor resistance is equal to the rotor reactance at the slip corresponding to peak torque.

For starting conditions (i.e., s = 1), the external resistance should be chosen such that ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}={\mathrm{X}}_{\mathrm{r}}-{\mathrm{R}}_{\mathrm{r}}$. This ensures that the motor develops maximum starting torque without excessive energy dissipation in the rotor circuit. If ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ is too high, the denominator in the torque equation increases disproportionately, leading to a decrease in torque. Conversely, if ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ is too low, the starting torque remains suboptimal due to an imbalance between resistance and reactance.

Thus, the ideal tuning of ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ depends on the motor’s design parameters, particularly the rotor resistance and reactance. In practical applications, a stepped resistance control or external resistor bank is often used to dynamically adjust ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ during startup and operation, ensuring that the motor achieves high torque during acceleration while minimizing power losses under steady-state conditions.

Rotor copper losses P_rcu were calculated using Equation (14):

$${\mathrm{P}}_{\mathrm{r}\mathrm{c}\mathrm{u}}=3{ I}_r^2\times {(\mathrm{R}}_r+{\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}})$$

(14)

This means that if a high ${\mathrm{R}}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ was maintained for an extended period, thermal losses increased, reducing the efficiency of the WRIM.

Unlike SCIMs, where rotor heat dissipation is passive, WRIMs require active cooling mechanisms for the rotor windings and external resistors. Liquid cooling may be necessary for high-power marine applications to maintain thermal stability and prevent excessive heating. An FEM analysis for SCIM revealed that reducing the rotor bar height by 5% and adjusting the stator slot width decreased core losses by approximately 8%, leading to a final efficiency of 95.2%. The WRIM FEM incorporated an external resistance which affected torque and efficiency at different slip values. This external resistance was varied between 0.15 Ω to 0.45 Ω to analyze its impact on torque-speed characteristics. WRIM simulations included rotor winding loss analysis due to higher resistive losses in the copper windings compared to SCIM bars. FEA-based thermal modeling was performed to ensure adequate cooling performance, especially under high-load conditions. Sensitivity analysis further indicated that fine-tuning the rotor slot shape and air gap length enhanced the machine’s overall performance, leading to improved torque characteristics and reduced thermal stress. Increasing the rotor slot depth by 4% and optimizing the winding distribution resulted in a 10–12% reduction in rotor copper losses, improving efficiency by up to 94.5%, i.e., slightly lower than SCIM, due to additional slip ring losses. Additionally, optimizing the external rotor resistance within the identified optimal range ensured maximum starting torque while minimizing steady-state losses, achieving an optimal balance between efficiency and controllability in marine propulsion applications.

WRIMs facilitate improved speed control through external rotor resistance adjustment, eliminating the need for complex frequency inverters. However, for high-power propulsion, integrating a sophisticated inverter system with Field-Oriented Control (FOC) or Direct Torque Control (DTC) enhances performance. WRIMs generate a more controlled and stable magnetic field, improving torque smoothness and reducing oscillations. The ability to regulate the magnetic field dynamically can enhance performance under varying ship load conditions. WRIM rotors typically use copper windings instead of aluminum or copper bars in SCIMs, increasing material costs but offering performance advantages. Additional costs arise from the slip ring and brush maintenance, but the overall cost-effectiveness depends on long-term operational requirements. One major drawback of WRIMs compared to SCIMs is the higher maintenance requirement due to wear on slip rings and brushes. Regular inspection and replacement of brushes are necessary to ensure reliability in continuous ship operation environments. Due to its solid rotor construction, SCIMs generally have a 6–8% lower mass compared to WRIMs for the same power rating. However, they require larger stator dimensions to accommodate higher currents, increasing volume by 3–5%. For WRIMs, the inclusion of rotor windings and slip rings increases the mass by 10–12% but allows for a more compact stator design, optimizing the overall machine volume to fit within ship engine rooms.

Table 3. Comparison between SCIMs and WRIMs for 10 MW Ship Propulsion.

Feature	SCIM	WRIM
Slip Control	Fixed, determined by load	Adjustable via external resistance
Starting Torque	Moderate	High, tunable via external resistance
Efficiency	Higher at nominal load	Lower due to rotor resistance losses
Cooling Requirements	Passive (air/liquid)	Higher due to rotor windings
Inverter Complexity	High (FOC or DTC)	Lower (simple speed control via resistance)
Magnetic Field Stability	Moderate	High, tunable via rotor resistance
Maintenance	Low (no brushes/slip rings)	Higher (requires brush/slip ring maintenance)
Rotor Material	Aluminum or copper bars	Copper windings
Initial Cost	Lower due to simpler rotor construction	15–20% higher due to slip rings and external resistors
Operational Cost	Lower maintenance, but requires advanced inverter	Higher due to brush/slip ring wear and cooling needs
Maintenance Cost	Minimal (only stator windings)	Higher (slip rings and brushes require periodic replacement)
Lifecycle Cost	Longer lifespan (15–20 years) with minimal intervention	10–15% higher lifecycle cost due to frequent maintenance
Overall Cost	Lower initial cost, higher inverter cost	Higher maintenance cost but lower inverter cost

provides a detailed comparison of the features between the two motor options for high-power (10 MW) electric ship propulsion.

In the selection of an induction motor for ship propulsion, SCIMs are generally preferred when efficiency and low maintenance are the primary concerns, particularly in applications requiring constant speed operation without frequent torque variations. Their long lifecycle and minimal intervention needs make them a cost-effective solution for continuous-duty marine propulsion systems. On the other hand, WRIMs are advantageous in scenarios where high starting torque is essential, such as ship propulsion maneuvers, and when precise slip and speed control are required without the complexity of advanced inverters. They are particularly suited for vessels operating under variable load conditions, such as icebreakers or dynamic positioning ships. For large-scale ship propulsion systems, i.e., 10 MW or more, SCIMs remain the preferred choice due to their superior efficiency, lower operational costs, and reduced maintenance requirements. However, WRIMs can provide better performance in applications that demand frequent load adjustments and enhanced speed regulation, making them a viable alternative despite their higher costs and maintenance demands.

3. PMSM Design Process

The design process of an electrical machine usually starts from the constitutive equation given in (15), where S is the apparent motor power in VA, B_m is the magnetic charge, a_c is the specific electric charge in A/m, D is the inner diameter of the stator, L is the active length of the motor, k_w is the fundamental winding factor, and n is the rated speed in rpm. By initializing the above quantities, except those related to the motor dimensions, product D²L is calculated.

Then, following common practices, the designer accepts a specific value for the ratio of these two quantities and finally calculates the values of D and L. The problem with this approach is that on the one hand, the directions provided in the various scientific literature are empirical and, on the other hand, they relate to classic modern machines. As there are no guidelines relating to permanent magnet machines and, in particular, those with high-power motors, it was decided to take a different approach in this case.

S = 11k_wB_ma_cD²Ln

(15)

In the case under study, the design process started by calculating the DL product again, but this time using (16):

$$\mathrm{E}={\displaystyle \frac{4\mathsf{\pi }}{\sqrt{2}}}{\displaystyle \frac{\mathrm{f}{\mathrm{N}}_{\mathrm{s}}{\mathrm{K}}_{\mathrm{w}}{\mathrm{B}}_{\mathrm{g}}\left(\mathrm{D}-{\mathrm{L}}_{\mathrm{g}}\right)\mathrm{L}}{2\mathrm{p}}}$$

(16)

where E is the induced voltage, f is the motor supply frequency, N_s is the number of winding coils per phase, B_g is the desired average value of the magnetic flux density in the gap, L_g is the gap length, and p is the number of poles of the motor.

The number of coils per phase was calculated as a function of the number of stator slots Q_s and the number of conductors per slot n_s using Equation (17).

Value B_g requires initialization. In the considered case, this value was set to 0.8 T. At the same time, the induced voltage should be set to equal the phase supply voltage so that during its operation, the motor would absorb the minimum possible current. Therefore, $\mathrm{E}=U_{ph}=U_L/\sqrt{3}$, where $U_{ph}$ and $U_L$ are the phase and pole voltage, respectively. Having chosen the number of poles, slots of the stator, and the supply frequency and having determined the fundamental winding factor, it was easily understood that there were a large number of possible products N_s(D–Lg)L that could lead to the desired value for induced voltage. Then, taking into account the physical limitations imposed based on the specifications of the engine installation site, it was possible to calculate the values D and L.

$${\mathrm{N}}_{\mathrm{s}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{s}}{\mathrm{n}}_{\mathrm{s}}}{6}}$$

(17)

Then, the radial B_mr and tangential B_mθ component of the magnetic field in the gap produced by the surface-mounted magnets were calculated. The specific quantities were given as Fourier series in Equations (18) and (19), respectively, where r is the radius at the center of the gap, θ is the angular position with reference to the magnet-pole center, and p is the number of pole pairs.

$$B_{mr}\left(r,\theta \right)=\sum _{n=1,3,5}^{\infty }{K}_B\left(n\right)f_{Br}\left(r\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(np\theta \right)$$

(18)

$$B_{m\theta }\left(r,\theta \right)=\sum _{n=1,3,5}^{\infty }{K}_B\left(n\right)f_{B\theta }\left(r\right)\mathrm{c}\mathrm{o}\mathrm{s}\left(np\theta \right)$$

(19)

Radius r was calculated using the Equations (20)–(26), where L’_g is the effective length of the gap, γ is a factor necessary in determining the Carter coefficient k_c, B_s0 is the width of the groove at the opening (as defined in Figure 4), R_s is the inner radius of the stator, R_m is the radius up to the outer surface of the magnets, R_r is the outer radius of the rotor core, h_m is the height of the magnets, and μ_r is their magnetic permeability. The above geometric quantities are illustrated in Figure 6, which identifies the core design dimensions for the PMSM rotor and stator assembly, including the magnet arc angle and rotor outer diameter. These parameters were used in the analytical derivation of values in later equations.

$${\mathrm{L}}_g^{\prime }={\mathrm{L}}_g+h_m/{\mu }_r$$

(20)

$$\gamma ={\displaystyle \frac{4}{\pi }}\left[{\displaystyle \frac{{{\rm B}}_{s0}}{2{\mathrm{L}\prime }_g}} {\tan }^{-1}\left({\displaystyle \frac{{{\rm B}}_{s0}}{2{\mathrm{L}\prime }_g}}\right)-\log \left(\sqrt{1+{\left({\displaystyle \frac{{{\rm B}}_{s0}}{2{\mathrm{L}\prime }_g}}\right)}^2}\right)\right]$$

(21)

$$k_c={\displaystyle \frac{\pi \left(\mathrm{D}-{\mathrm{L}}_g\right)/Q_s}{\left(\frac{\pi \left(\mathrm{D}-{\mathrm{L}}_g\right)}{Q_s}-\gamma {\mathrm{L}\prime }_g\right)}}$$

(22)

$$R_s={\displaystyle \frac{\mathrm{D}}{2}}+\left(k_c-1\right){\mathrm{L}\prime }_g$$

(23)

$$R_m={\displaystyle \frac{\mathrm{D}}{2}}-{\mathrm{L}}_g$$

(24)

$$R_r=R_m-h_m$$

(25)

$$r=\left(R_m+R_s\right)/2$$

(26)

The calculation of quantities K_Β(n), f_Br(r), and f_Bθ(r) was carried out with the help of (27)–(29) when np ≠ 1 and (30)–(32) when np = 1, where μ₀ is the magnetic permeability of the vacuum, and Μ_n is the radial component of the magnetization vector for the case of radially magnetized magnets, which was determined through Equation (33); B’_r is the remanent magnetization of the magnets, and a_p is the ratio of the arc that the magnet to the pole step.

$$K_B\left(n\right)={\displaystyle \frac{{\mu }_0{M}_n}{{\mu }_r}}·{\displaystyle \frac{np}{{\left(np\right)}^2-1}}·{\displaystyle \frac{\left(np -1\right){+2\left(\frac{R_r}{R_m}\right)}^{np+1}-\left(np +1\right){\left(\frac{R_r}{R_m}\right)}^{2np}}{\frac{{\mu }_r+1}{{\mu }_r}\left[{\left(1-\frac{R_r}{R_s}\right)}^{2np}\right]-\frac{{\mu }_r-1}{{\mu }_r}\left[{\left(\frac{R_m}{R_s}\right)}^{2np}-{\left(\frac{R_r}{R_m}\right)}^{2np}\right]}}$$

(27)

$$f_{Br}\left(r\right)={\left({\displaystyle \frac{r}{R_s}}\right)}^{np-1}·{\left({\displaystyle \frac{R_m}{R_s}}\right)}^{np+1}+{\left({\displaystyle \frac{R_m}{r}}\right)}^{np+1}$$

(28)

$$f_{B\theta }\left(r\right)=-{\left({\displaystyle \frac{r}{R_s}}\right)}^{np-1}·{\left({\displaystyle \frac{R_m}{R_s}}\right)}^{np+1}+{\left({\displaystyle \frac{R_m}{r}}\right)}^{np+1}$$

(29)

$$K_B\left(n\right)={\displaystyle \frac{{\mu }_0{M}_n}{2{\mu }_r}}·{\displaystyle \frac{{\left(\frac{R_m}{R_s}\right)}^2-{\left(\frac{R_r}{R_s}\right)}^2+{\left(\frac{R_r}{R_s}\right)}^2\ln \left({\left(\frac{R_m}{R_r}\right)}^2\right)}{\frac{{\mu }_r+1}{{\mu }_r}\left[{\left(1-\frac{R_r}{R_s}\right)}^2\right]-\frac{{\mu }_r-1}{{\mu }_r}\left[{\left(\frac{R_m}{R_s}\right)}^2-{\left(\frac{R_r}{R_m}\right)}^2\right]}}$$

(30)

$$f_{Br}\left(r\right)=1+{\left({\displaystyle \frac{R_s}{r}}\right)}^2$$

(31)

$$f_{B\theta }\left(r\right)=-1+{\left({\displaystyle \frac{R_s}{r}}\right)}^2$$

(32)

$$M_n=2{\displaystyle \frac{{B\prime }_r}{{\mu }_0}}{a}_p{\displaystyle \frac{\sin \left(\frac{n\pi {\alpha }_p}{2}\right)}{\frac{n\pi {\alpha }_p}{2}}}$$

(33)

It should be noted that the magnet properties (B’r and H’c) were modified according to Equations (34) and (35) based on the engine operating temperature adopted during the design process. Considering the power of the engine and its operating environment, temperature T was set to 100 °C. The quantities k_Br and k_Hc are the temperature coefficients of the magnet. The specific coefficients take negative values.

$${B\prime }_r=B_r+\left[1+k_{B_r}\left(T-20\right)\right]$$

(34)

$${H\prime }_c=H_c+\left[1+k_{H_c}\left(T-20\right)\right]$$

(35)

Having now determined values D and L and the dimensions of the permanent magnets, the average value of the magnetic flux density in gap B_g and subsequently magnetic flux Φ_m produced by each pole of the motor could be calculated through Equation (36). As the generated magnetic flux was equally divided in stator and rotor, the magnetic flux in the stator core Φ_sy and in the rotor core Φ_ry were determined through (37). Length of the stator cheekbone T_bi, length of the rotor cheekbone h_ry, and width of the stator teeth W_st were calculated with the help of Equations (38)–(40), where k_fe is the compaction factor of the plates that was used to manufacture the motor cores, and B_sy, B_ry, and B_st are the maximum acceptable value for the magnetic flux density in the stator core, rotor core, and stator teeth respectively. For the cores, the corresponding value was set to 1.6 T, while for the stator teeth, it was set to 1.8 T. These values were determined taking into account the steel magnetization curve used for the design of the induction motor [32].

$${\mathsf{\Phi }}_m={\displaystyle \frac{\pi {{\rm B}}_g\mathrm{D}\mathrm{L}}{2p}}$$

(36)

$${\mathsf{\Phi }}_{sy}={\mathsf{\Phi }}_{ry}={\mathsf{\Phi }}_m/2$$

(37)

$$T_{bi}={\displaystyle \frac{{\mathsf{\Phi }}_{sy}}{B_{sy}{k}_{fe}\mathrm{L}}}$$

(38)

$$h_{ry}={\displaystyle \frac{{\mathsf{\Phi }}_{ry}}{B_{ry}{k}_{fe}\mathrm{L}}}$$

(39)

$$W_{st}={\displaystyle \frac{B_g\pi \left(\mathrm{D}-{\mathrm{L}}_g\right)}{Q_s{B}_{st}{k}_{fe}\mathrm{L}}}$$

(40)

The next step in the design process involved determining the other geometrical parameters of the stator and rotor. Although the number of turns per phase N_s and the number of conductors per groove n_s were known, the diameter of the conductors had not yet been determined. This element significantly affects the geometry of the stator groove. The groove had to be large enough to accommodate conduits of a suitable cross-section. At the same time, the current density J_s should not exceed the maximum acceptable value set by the designer, while at the same time, slot filling factor s_f should not be high. If the degree of fullness of the groove was too high, then the degree of manufacturing difficulty of the engine increased. In the case of concentrated winding, the degree of fullness of the groove usually did not exceed 60%.

The geometric quantities that shaped the final topology of the groove were the height of H_s2 and its width at the top B_s2. The width of the groove at opening B_s0 had to be initialized, while the width of the groove at the break B_s1 was determined through Equation (41), where H_s0 and H_s1 are the height of the tooth at the opening and the break, respectively. The above quantities are also illustrated in Figure 4. Based on what was mentioned earlier, it was necessary to create a repetition structure. In this iterative process, the quantity to be changed was H_s2; the following calculations were performed sequentially using Equations (42)–(57). With the help of the specific equations, the following factors, among others, were determined: width B_s2, diameter of the rotor D_r, diameter of the shaft D_shaft, outer diameter of the stator D_o, area of the groove of the stator A_s, mass of the rotor core M_Ryoke, mass of the magnets M_magnets, mass of the shaft M_shaft, friction losses P_f, Reynolds coefficient R_eg, coefficient C_f, windage losses P_wind, converted power P_conv, phase current I_ph, total area of copper conductors inside the groove A_Cu, and slot filling factor of the groove s_f. The iteration structure was completed when all constraints had been met and the stator geometric characteristics had been defined. The equations below include various quantities, such as density of the steel ρ_steel that was used to make the stator core and rotor and shaft, density of the magnet material ρ_magnets, and density of air ρ_air; k_ν is the kinematic viscosity of air. It is noted that for the case of the stator core and the rotor, electrical steel was used. Instead, non-magnetic steel was used for the shaft.

$$B_{s1}=\pi {\displaystyle \frac{\mathrm{D}+2\left(H_{s0}+H_{s1}\right)}{Q_s}}-W_{st}$$

(41)

$$B_{s2}=\pi {\displaystyle \frac{\mathrm{D}+2\left(H_{s0}+H_{s1}+H_{s2}\right)}{Q_s}}-W_{st}$$

(42)

$$D_r=\mathrm{D}-2{\mathrm{L}}_g$$

(43)

$$D_{shaft}=D_r-2h_m-2h_{ry}$$

(44)

$${\mathrm{D}}_0=\mathrm{D}+2\left(H_{s0}+H_{s1}+H_{s2}+T_{bi}\right)$$

(45)

$$A_s={B_{s0}H}_{s0}+{\displaystyle \frac{1}{2}}{H}_{s1}\left(B_{s1}-B_{s0}\right)+{B_{s0}H}_{s1}+{\displaystyle \frac{1}{2}}{H}_{s2}\left(B_{s1}+B_{s2}\right)$$

(46)

$${\mathrm{M}}_{Ryoke}=\pi {\displaystyle \frac{{\left(D_r-2h_m\right)}^2-D_{shaft}^2}{4}}\mathrm{L}{\rho }_{steel}{k}_{fe}$$

(47)

$${\mathrm{M}}_{magnets}=\pi {\displaystyle \frac{{D_r^2 -\left(D_r-2h_m\right)}^2}{4}}{\alpha }_p\mathrm{L}{\rho }_{magnet}$$

(48)

$${\mathrm{M}}_{shaft}=\pi {\displaystyle \frac{D_{shaft}^2}{4}}\mathrm{L}{\rho }_{steel}$$

(49)

$$P_f={\displaystyle \frac{3\left({\mathrm{M}}_{Ryoke}+{\mathrm{M}}_{magnets}+{\mathrm{M}}_{shaft}\right)120f}{2p·{10}^3}}$$

(50)

$${\mathrm{R}}_{eg}={\displaystyle \frac{120f{\rho }_{air}{\mathrm{L}}_g{D}_r}{0.5·2p{k}_{\nu }}}$$

(51)

$$C_f=\left\{\begin{array}{c} 1.03{\displaystyle \frac{{\left(2{\mathrm{L}}_g/D_r\right)}^{0.3}}{R_{eg}^{0.5}}}, \mathrm{for} R_{eg}\ge 500 \mathrm{and} R_{eg}\le {10}^4\\ 0.065{\displaystyle \frac{{\left(2{\mathrm{L}}_g/D_r\right)}^{0.3}}{R_{eg}^{0.2}}}, \mathrm{for} R_{eg}>{10}^4 \end{array}\right.$$

(52)

$${\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}={\left({\displaystyle \frac{D_r}{2}}\right)}^4\mathrm{L}{\left({\displaystyle \frac{120f}{2p}}\right)}^3\pi {\rho }_{air}{C}_f$$

(53)

$${{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}={\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}+{\mathrm{P}}_{\mathrm{f}}+\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}$$

(54)

$$I_{ph}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}}{3\mathrm{E}}}$$

(55)

$$A_{Cu}={\displaystyle \frac{I_{ph}}{J_s}}$$

(56)

$$s_f={\displaystyle \frac{A_{Cu}}{A_s}}$$

(57)

With the geometric characteristics of the engine now being known, we proceeded to calculate its electrical quantities. These included the resistance of stator winding R and its total inductance L. Resistance R was determined through Equation (58), where ρ_Cu is the density of the copper and k_ew is a coefficient related to the end-windings. The value of the specific resistance had to be corrected using to Equation (59), taking into account the temperature adopted during the design process.

$$R={\displaystyle \frac{{\rho }_{Cu}{n}_s^{2}q\left[2pL+k_{ew}\pi \left({D_s+H}_{s0}+H_{s1}+H_{s2}\right)\right]}{s_f{A}_s}}$$

(58)

$$R^{\prime }=R\left(1+0.004041\left(T-20\right)\right)$$

(59)

As far as the inductance of the winding is concerned, it included two components: (a) the synchronous magnetizing inductance L_m; and (b) the leakage inductance L_l. The first component was calculated using (60). The leakage inductance was a sum of the leakage inductance due to slots L_sl, the leakage inductance due to stator teeth L_tl, and leakage inductance due to the ends of the windings L_el. The specific values were calculated using Equations (61)–(65).

$$L_m={\displaystyle \frac{3}{\pi }}\left({\displaystyle \frac{2{\mathrm{{\rm N}}}_{\mathrm{s}}{k}_w}{2p}}\right)2{\displaystyle \frac{{\mu }_0}{{\mathrm{L}}_{\mathrm{g}}{k}_c}}\left(\mathrm{D}-{\mathrm{L}}_g\right)\mathrm{L}$$

(60)

$$L_l=L_{sl}+L_{tl}+L_{el}$$

(61)

$$L_{sl}={\displaystyle \frac{4{\mathrm{N}}_{\mathrm{s}}^2}{2pq}}\mathrm{L}{\mu }_0\lambda$$

(62)

$$\lambda ={\displaystyle \frac{9}{8}}\left[{\displaystyle \frac{H_{s0}}{B_{s1}{k}_{open}}}+{\displaystyle \frac{H_{s1}}{{B_{s1}-B}_{s1}{k}_{open}}}\log \left({\displaystyle \frac{B_{s1}}{B_{s1}{k}_{open}}}\right)+{\displaystyle \frac{H_{s2}}{{3B}_{s1}}}\right]$$

(63)

$$L_{tl}={\displaystyle \frac{12{\mu }_0 }{Q_s}}\mathrm{L}{\mathrm{N}}_s^2{\displaystyle \frac{\frac{5{\mathrm{L}}_g}{B_{s0}}}{5+\frac{{4\mathrm{L}}_g}{B_{s0}}}}$$

(64)

$$L_{el}={\displaystyle \frac{1}{2}}2pq{\mu }_0 \left(W_{st}+{\displaystyle \frac{B_{s1}+B_{s2}}{2}}\right)\left({\displaystyle \frac{3{\mathrm{N}}_s}{Q_s}}\right)2\log \left({\displaystyle \frac{\left(W_{st}+\frac{B_{s1}+B_{s2}}{2}\right)\sqrt{\pi }}{\sqrt{2A_s}}}\right)$$

(65)

The last stage included the calculation of other forms of motor losses. Specifically, through Equations (66)–(68), copper losses P_Cu, magnet losses due to eddy currents P_pm, and core losses P_core were determined, where cond_magnet is the conductivity of the magnet material in S/m, f_u is the frequency of eddy currents, B is the value of the magnetic flux density in the stator and rotor cores, and k_c, k_h, and k_e are the steel coefficients related to eddy current, hysteresis, and anomalous eddy current losses. Finally, the engine efficiency was calculated through Equation (69).

$${\mathrm{P}}_{\mathrm{C}\mathrm{u}}=3 I_{ph}^2{R}^{\prime }$$

(66)

$${\mathrm{P}}_{\mathrm{p}\mathrm{m}}={\displaystyle \frac{M_{magnet}}{{\rho }_{magnet}}}·{\displaystyle \frac{{cond}_{magnet}}{24}}{h}_m\mathrm{L}{B}_m^2{\left({\displaystyle \frac{{\alpha }_p\pi \left(\mathrm{D}-2{\mathrm{L}}_g\right)}{2p}}\right)}^3{\left(2\pi f_u\right)}^2$$

(67)

$${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}=k_c{\left(f_{u}B\right)}^2+k_h{f}_u{B}^2+k_e{\left(f_{u}B\right)}^{1.5}$$

(68)

$$\eta ={\displaystyle \frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}+{\mathrm{P}}_{\mathrm{f}}+{\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}+{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}+{\mathrm{P}}_{\mathrm{C}\mathrm{u}}+{\mathrm{P}}_{\mathrm{p}\mathrm{m}}}}$$

(69)

4. Topology of the Permanent Magnet Synchronous Motor

The first step in implementing the design process described in the previous section required selecting number of poles 2p and number of slots Q_s. The number of slots then determined the relationship between the number of conductors per slot n_s and number of turns per phase Ns according to Equation (17). Having chosen the nominal speed to be equal to 500 rpm for the case of the permanent magnet synchronous motor, the supply frequency was related to the number of poles as follows: f = 500(2p)/120. The variation of frequency as a function of the number of poles is given in Figure 7.

The required speed could therefore be achieved using various combinations of frequency and number of poles. The small number of poles did not seem consistent with the case under study due to the high power of the motor and the increased requirements for the output torque. Therefore, cases with a number of poles less than 14 were rejected. Although a relatively small number of poles, and consequently, a low frequency would lead to lower core losses for the stator and rotor, in this case height of the magnets h_m had to be increased to achieve the desired value for the magnetic flux density in gap B_g. Despite the fact that the large height of the magnets contributed to preventing their possible demagnetization, it significantly increased the manufacturing difficulty. Additionally, the small number of magnets and poles would have led to a greater concentration of magnetic flux (saturation) in the stator teeth. Choosing too large a number of poles would have excessively increased core losses due to the increased frequency. Therefore, a compromise was made in choosing the appropriate combination, taking into account what was mentioned above. In addition, the value of fundamental winding factor k_w had to be considered when selecting the 2p-Q_s combination. A high value for this factor was desirable, as that would contribute to achieving an induced voltage close to that of the phase voltage, thus reducing the operating current of the motor and contributing to an increase in power density.

Taking into account the above, the selection process of the appropriate 2p-Q_s combination had to be done with the following criteria:

• A combination that allows the realization of the concentrated double-layer winding had a fundamental winding factor k_w > 0.93.
• We rejected cases where the number of 2p poles was less than 14 and Q_s was less than 42.
• Cases where Q_s was an odd number were discarded, because in the case where the number of grooves was even, a more uniform magnetic loading was achieved on the motor.
• We rejected combinations where 2p >> Q_s or the difference between these quantities was large.

Applying the above criteria to the sensitivity analysis resulted in few available combinations.

Table 4. Optimized Structural Variables for PMSM Design.

Quantity	Symbol	Value
Number of Poles	2p	38–60–100
Number of Slots	Qs	42–72–108
Fundamental Winding Factor	kw	0.925–0.933–0.954
Frequency	f	158.33–250–375

shows the extreme values of these combinations and the final optimal choice in bold. The supply frequency ranged from 158.33 Hz up to 375 Hz. It was understood that cases leading to a particularly high frequency should be rejected. At the same time, it was deemed necessary that the number of grooves be large enough so that the given number of coils per phase was divided into more grooves, thus reducing the electrical load on the motor. Therefore, it was decided to further study the combination 2p = 60 and Q_s = 72, which yielded a fundamental winding factor of 0.933 and a supply frequency of 250 Hz.

When the number of poles, the number of slots, and the fundamental factor of the winding had been determined, and assuming that gap length L_g was equal to 6mm, the product N_s (D − L_g) L was calculated using Equation (16). Then, the following four cases were considered in terms of the number of conductors per groove n_s. The specific size was successively set to 2, 3, 4, and 5, which resulted in the number of turns per phase being 24, 36, 48, and 60 respectively. Subsequently, applying the physical constraints governing sizes D and L, a large number of topologies emerged. In each case, the electrical and geometric characteristics of the motor were calculated with the help of the Matlab2023a software, the 2D representation of the topology was performed, and the operation of the motor was simulated with the help of the specialized Maxwell 2023R1 software of Ansys. For each topology, the dimensions of the inner diameter of stator D, the outer diameter of stator D_o, and the axial length of motor L were extracted, as well as efficiency η, as calculated and having previously determined the individual forms of losses. Figure 8 shows the variation of the engine performance as a function of the D/L ratio for each of the four considered cases. Based on the shape of the curves and the processing of the set of results, we concluded the following:

• As the D/L ratio increased, engine efficiency decreased. This reduction was more evident for cases where 24 and 36 turns per phase were used. For N_s = 60, the performance remained almost constant throughout the examined range of variation of the specific ratio.
• The decrease in efficiency with the increase of the diameter in relation to the effective length of the motor could be explained by the simultaneous increase of the mechanical losses and the losses in the magnets. Conversely, as the length of the motor became longer, the copper losses increased. As far as the core losses were concerned, they showed relatively little change. However, again, the greater axial length for the engine favored their reduction in the majority of cases.
• Topologies with N_s = 24 and N_s = 36 were rejected because they presented an obviously inferior performance compared to the other two considered cases (N_s = 48 and N_s = 60). The rejection of these topologies was justified by observing the curves in Figure 9, where the non-linear relationship between magnet mass and the diameter–to-length (D/L) ratio is illustrated. As D/L increased, the required magnet mass grew exponentially, highlighting a key design trade-off between torque production and material cost in PMSM design. A higher axial flux concentration could improve torque density but significantly increased material cost and thermal stress. Although the topologies showed a lower performance for N_s = 24 and N_s = 36, the mass of the magnets was considerably larger.
• Topologies with N_s = 60 seemed to be the most appropriate choice, as they combined the highest efficiency with the smallest mass of magnets. This characteristic also had a direct impact on the cost of the motor implementation due to the high cost of the magnets. So, the engines that belonged to this particular group of results were deemed to be the most economical option.

Among the topologies with Ns = 60, it was decided to study further the one presenting a value for the D/L ratio equal to 0.91. This particular choice was made considering the higher efficiency combined with the lower values in the eddy current loss density in the magnets presented by this configuration. The losses of the magnets had to remain within acceptable limits Otherwise, the intense circulation of eddy currents within their mass would have led to a significant increase in temperature during the operation of the motor and may have eventually caused their temporary or even permanent demagnetization.

Figure 10 shows 1/12 of the overall form of the specific topology. Its final optimized geometric characteristics are given in detail in

Table 5. Optimized Design Variables for PMSM.

Quantity	Symbol	Value
Outer diameter stator	${\mathrm{D}}_{\mathrm{o}}$	1795.5 mm
Inner diameter stator	D	1361.9 mm
Outer diameter rotor	${\mathrm{D}}_{\mathrm{r}}$	1361.8 mm
Shaft diameter	${\mathrm{D}}_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}}$	1140.2 mm
Motor axial length	L	1500 mm
Stator slots	${\mathrm{Q}}_{\mathrm{s}}$	72
Poles (Pair of Poles)	2p (p)	60 (30)
Airgap length	${\mathrm{L}}_{\mathrm{g}}$	6 mm
Stator opening width	${\mathrm{H}}_{\mathrm{s}0}$	8 mm
Stator base width	${\mathrm{H}}_{\mathrm{s}1}$	8 mm
Stator top width	${\mathrm{H}}_{\mathrm{s}2}$	116.54 mm
Stator slot opening heigh	${\mathrm{B}}_{\mathrm{s}0}$	20 mm
Stator tip heigh	${\mathrm{B}}_{\mathrm{s}1}$	33.33 mm
Stator body heigh	${\mathrm{B}}_{\mathrm{s}2}$	43.50 mm
Tooth width	${\mathrm{w}}_{\mathrm{s}\mathrm{t}}$	27.51 mm
Stator yoke length	${\mathrm{T}}_{\mathrm{b}\mathrm{i}}$	66.26 mm
Ratio of magnet arc length to pole pitch	αp	0.8533
Maximum magnet width	wm	59.32
Magnet height	hm	22.2

.

The axial length of the motor L was equal to 1.5 m, with the internal D and the external diameter Do of the stator taking values being equal to 1.36 m and 1.75 m, respectively. Therefore, the D/L and Do/L ratios were equal to 0.91 and 1.173, respectively. The gap length was set to 6 mm. The height of the magnets was chosen to be within acceptable limits in an effort to keep the manufacturing complexity low. The ratio of magnet arc length to pole pitch α_p was given by Equation (68), where LCM(Qs, 2p) is the least common multiple of the number of poles 2p and the number of stator slots Q_s, and k is an integer coefficient that takes values ranging from 1 to LCM(Qs, 2p)/2p − 1. The value of α_p was set at 0.8533 in order to minimize the cogging torque, following the directions provided in [45]. This torque was a result of the interaction of the stator teeth with the permanent magnets. It was affected by the dimensions of the stator teeth and the α_p size. It was one of the reasons why the motor showed ripple in the output torque.

$${\alpha }_p={\displaystyle \frac{\left(LCM\left(Q_s,2p\right) / 2p\right)-k}{LCM\left(Q_s,2p\right) / 2p}}$$

(70)

The operating characteristics of the motor at its rated load are summarized in

Table 6. Main Characteristics of PMSM.

Quantity	Symbol	Value
Output Power	${\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	10,235.00 kW
Input Power	${\mathrm{P}}_{\mathrm{i}\mathrm{n}}$	10,426.85 kW
Electromagnetic Torque	${\mathrm{T}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	198.4124 kNm
Torque Ripple	${\mathrm{T}}_{\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{e}}$	1.40%
Torque Angle	${\mathrm{T}}_{\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}}$	47.11 deg
Frequency	f	250 Hz
Nominal Speed	nm	500 rpm
Nominal Voltage	${\mathrm{V}}_{\mathrm{n}}$	6.6 kV
Power Factor	PF	0.83
Nominal Phase Current	${\mathrm{I}}_{\mathrm{p}\mathrm{h}}$	1101.94 A
Stator Winding Density	Js	2.75 A/mm2
Copper Losses Stator	${\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}$	38.083 kW
Magnet Losses	${\mathrm{P}}_{\mathrm{p}\mathrm{m}}$	35.616 kW
Core Losses	${\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}$	100.209 kW
Friction and Stray Losses	${\mathrm{P}}_{fs}$	17.576 kW
Wind Losses	${\mathrm{P}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}$	0.366
Total Losses	${\mathrm{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$	191.850 kW
Efficiency Rate	η%	98.16%

. The motor output torque T_avg was equal to 198.4124 kNm, absorbing a current equal to 1101.94 A. The stator winding density J_s was 2.75 A/mm². This value also guaranteed the satisfactory thermal behavior of the motor, ensuring that during its operation, a particularly high temperature would not develop near the gap, which would have negatively affected the permanent magnets. The output torque signal is given in Figure 11. Minimum T_min and maximum T_max of the torque were equal to 196.9841 and 199.7715 kNm, respectively. This implies that the torque ripple calculated from Equation (71) was equal to 1.40% of the output torque. This value was highly satisfactory and confirmed the effectiveness of the method followed in determining the α_p value with the aim of minimizing the alignment moment. Also, the small value for the torque ripple could also be explained by the use of a concentrated double-layer winding, which resulted in the appearance of a smaller harmonic content for the magnetomotive force compared to the single-layer winding counterpart. Regarding the various forms of losses, the motor showed low copper losses considering its rated output power. This feature was due to the small resistance of the stator winding due to the large diameter of the conductors.

$${\mathrm{T}}_{\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{e}}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{T}}_{\mathrm{a}\mathrm{v}\mathrm{g}}}}$$

(71)

At the same time, the slot filling factor of groove s_f was equal to 51%. It should be pointed out that when calculating the filling factor of the groove, the dimensions of the insulation carried by the conductors and the groove itself were taken into account. During the process, the insulation characteristics corresponding to class F were adopted. This value of s_f was acceptable and allowed the winding to be wound. The core loss density was approximately equal to 10 W/kg, which was an expected value for the silicon steel used for the stator and rotor core. This low value resulted in part from the fact that no strong saturation was observed in any part of the motor, based on Figure 12, which shows the distribution of the magnetic flux density in the motor under a nominal load. Even in the teeth of the stator, the magnetic flux density did not exceed 1.85 T. The losses in the magnets due to the eddy currents were equal to 35,616 W. The neodymium magnets used had a conductivity equal to 625,000 S/m. The frequency at which the eddy currents circulated in the magnet body was f_u = (500/60)Q_s, where 500/60 is the motor rotation speed in rps. With Q_s equal to 72, the eddy current circulation frequency was 600 Hz. The high frequency combined with the volume of magnets used justified the value of the losses. Finally, the sum of the mechanical losses of the motor was equal to 17,942.34 W, i.e., only 0.18% of the output power, since the motor had a low rotational speed and its diameter was approximately equal to its axial length.

Finally,

Table 7. Efficiency of the PMSM Under Various Loading Conditions.

Load per Nominal (%)	Efficiency η (%)
25	93.97
50	96.78
75	97.69
100	98.16
125	98.23
150	98.05

lists the performance of the PMSM for various loading conditions as a percentage of the nominal output load. The developed topology exhibited high performance over the entire considered operating range. Even in overload conditions, i.e., 125% and 150% of rated load, it remained at high levels.

5. Comparative Evaluation of the Two Motors for Electric Ship Propulsion

Regarding the functional characteristics of the two motors, a detailed comparison is made in

Table 8. Comparison of Operational Characteristics between Induction Motor and PMSM.

Quantity/Symbol	Induction Motor	PMSM	Percentage Difference
$\mathrm{Output} \mathrm{Power}/{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	10,000.00 kW	10,235.00 kW	+2.35%
$\mathrm{Electromagnetic} \mathrm{Torque}/{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	189.51 kNm	198.4124 kNm	+4.70%
Frequency/f	60 Hz	250 Hz	+316.67%
$\mathrm{Nominal} \mathrm{Phase} \mathrm{Current}/{\mathrm{I}}_{\mathrm{p}\mathrm{h}}$	1150.00 A	1101.94 A	−4.18%
Power Factor	0.80	0.83	+3.75
Nominal Speed/nm	504 rpm	500 rpm	−0.79%
Stator Winding Density/Js	5.85 A/mm2	2.75 A/mm2	−52.99%
Core Loss Density/Pdcore	2.57 W/kg	9.96 W/kg	+287.55%
$\mathrm{Copper} \mathrm{Losses} \mathrm{Stator}/{\mathrm{P}}_{\mathrm{s}\mathrm{c}\mathrm{u}}$	132.30 kW	38.083 kW	−71.21%
$\mathrm{Core} \mathrm{Losses}/{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}$	50.00 kW	100.209 kW	+100.42%
Total Mass of Motor/Mtotal	34,118 kg	13,088.7 kg	−61.64%
Total Magnet Mass/Mmag	---	882 kg	---
Efficiency/η (%)	95.20%	98.16%	+3.11%

, where the percentage of change (increase or decrease) is also noted, taking as a reference the elements of the induction motor.

From the data listed in this table, the following can be easily understood:

(i) The PMSM presented a significantly lower current during its nominal operation and therefore lower copper losses compared to the inductive one. This feature was particularly attractive in the case of electric propulsion where the energy available to power the motors was limited. In addition, lower copper losses would result in lower temperatures during engine operation. Therefore, the PMSM was expected to show better thermal behavior and, at the same time, the lifetime of the insulation of the windings would be enhanced. In addition, the lower current requirements were also beneficial for the inverter used to power the motor, as its cooling requirements were reduced and it was less stressed. It was noted that the requirements of this application were particularly high. Propulsion motors exhibit long continuous operation while being supplied with high currents.

(ii) The induction motor showed lower core losses compared to the PMSM counterparts. This was due to the fact that the supply frequency of the induction motor was equal to 60 Hz. In the case of PMSM, it was equal to 250 Hz. The higher supply frequency (almost 4.2 times that of the induction motor) may explain the higher core losses. This was also reflected in the density of core losses. For the induction motor, the specific magnitude was equal to 2.57 W/kg, while for the PMSM, it was equal to 9.96 W/kg.

(iii) The performance of the two engines showed a noticeable difference. The efficiency of the PMSM was higher by 3.11%, compared to the equivalent of the induction motor, and mainly quite stable in a large load range that did not depend on the operating conditions and the slip. In contrast, the induction motor performance was highly dependent on its loading conditions, which increased slip and reduced its efficiency (Figure 2).

(iv) The mass of the PMSM was 61.64% less than the mass of the induction motor. The masses of the stator core and the rotor for the PMSM were significantly smaller than the induction motor counterparts. This could also be explained by the fact that PMSM had a larger number of poles. The greater number of poles favored the reduction of the length of the zygoma in the stator as the magnetic flux that had to be produced was divided among a greater number of poles. Also, the rods used in the induction motor presented a significantly greater mass than that of the magnets carried in the PMSM.

(v) Based on the geometric parameters defined in Table 5 and the surface-mounted magnet topology illustrated in Figure 9, the total magnet mass was calculated for the 10.2 MW PMSM design. Using the average rotor diameter D_r = 1349.9 mm, magnet height h_m = 22.2 mm, pole coverage ratio α_p = 0.8533, and axial stack length L = 1.5 m, the resulting total volume of magnet material was approximately V = 0.119 m³. Assuming a standard NdFeB magnet density of 7400 kg/m³, the total magnet mass was estimated to be 882 kg. This quantification is critical for evaluating material costs and for understanding the thermal inertia introduced by high-density magnetic components. The result also validates the non-linear growth trend observed in Figure 9, where increasing the D/L ratio led to disproportionate increases in the required magnet volume due to elevated torque demands and flux density constraints.

A comprehensive analysis comparing PMSMs and IMs for 10 MW electric ship propulsion revealed significant differences in various aspects, including materials, operational efficiency, maintenance requirements, cooling systems, insurance costs, and control strategies. PMSMs utilize high-performance rare-earth permanent magnets, primarily Neodymium-Iron-Boron (NdFeB), which contribute substantially to their high costs due to the scarcity and geopolitical constraints surrounding these materials. Additionally, PMSMs require high-quality laminated silicon steel for stator cores to minimize core losses and advanced copper windings with superior insulation to achieve high efficiency. The estimated material cost share for PMSMs is approximately 60% of the total motor cost, reflecting the cost of rare-earth materials and complex manufacturing processes. In contrast, IMs employ more cost-effective materials such as copper or aluminum windings and squirrel-cage aluminum or copper bars for the rotor, which simplifies the manufacturing process and reduces initial costs. The estimated material cost share for IMs is around 40% of the total motor cost, benefiting from lower material costs and mass production advantages. The complex assembly and precision magnet placement in PMSMs lead to higher production expenses, whereas IMs benefit from simpler and more cost-efficient mass production methods.

In terms of operational efficiency, PMSMs achieve efficiencies of up to 97–98%, significantly reducing energy losses and offering lower copper losses since they do not require rotor current. This results in lower lifetime energy consumption and improved torque characteristics with minimal ripple, leading to smoother propulsion and reduced energy fluctuations. On the other hand, IMs exhibit slightly lower efficiency levels, typically around 93–95%, with higher power consumption over their operational lifespan due to slip losses and secondary current requirements. The operational cost savings provided by PMSMs can translate into a fuel consumption reduction of 5–8% over a period of 20–25 years, making them a more energy-efficient option despite the higher initial investment.

Maintenance requirements differ significantly between PMSMs and IMs. PMSMs have fewer mechanical components such as brushes and slip rings, leading to lower maintenance demands and higher reliability. However, they require periodic monitoring to prevent thermal demagnetization and insulation degradation due to high-speed operation. IMs, conversely, demand more frequent maintenance due to the presence of rotor windings and potential bearing failures. The squirrel-cage rotor design in IMs, while robust, may experience bar breakage over time, leading to increased maintenance interventions and higher downtime costs. Overall, PMSMs have approximately 30% lower maintenance costs compared to IMs, contributing to their long-term economic viability.

Cooling systems are another critical factor to consider in such a comparison. PMSMs, due to their higher power density, require advanced cooling solutions such as liquid cooling systems using oil or water to prevent magnet demagnetization and maintain optimal performance. This complexity increases the overall system cost, with cooling expenses accounting for 15–20% of the total investment. In contrast, IMs can operate with simpler air or liquid cooling systems, which are more cost-effective and contribute only 5–10% to the total system cost. This makes IMs an attractive option in applications where cooling infrastructure is limited or cost-sensitive.

Insurance and lifecycle costs also play a significant role in motor selection. PMSMs, with their higher initial investment and advanced components, tend to have higher insurance costs due to the potential risks associated with magnet degradation and the need for specialized repair services. Estimated insurance costs for PMSMs range between 5–7% of the initial investment. On the other hand, IMs have lower insurance premiums, typically between 3–5%, owing to their well-established technology, availability of spare parts, and predictable failure modes, which make them easier to maintain and repair.

Control and drive systems differ significantly between the two motor types. PMSMs require advanced control techniques such as Field-Oriented Control (FOC) to achieve optimal efficiency and dynamic response, along with sensor-based position feedback for precise control. This results in higher drive system costs, which account for approximately 25–30% of the total cost. IMs, on the other hand, rely on simpler drive control methods such as vector control or field-oriented control without the need for complex rotor position sensors. Their drive systems are more cost-effective, representing around 15–20% of the total cost. Recent studies have also emphasized the energy-saving potential of PMSMs in maritime propulsion through system-level optimization techniques. In particular, Tarnapowicz et al. [46] demonstrated how PMSMs, when integrated with smart power management strategies, can significantly reduce overall energy consumption and improve propulsion system efficiency. Their findings confirm that, beyond machine-level design, system integration and operational profiles play a crucial role in achieving optimal performance. In addition to passive design improvements, active control strategies can significantly enhance the energy efficiency of PMSM-based propulsion systems. A recent study by Zwierzewicz et al. [47] proposed an adaptive control algorithm tailored to ship electric propulsion systems using PMSMs. Their method dynamically adjusted control parameters based on operational conditions, such as load variations and navigation modes, to minimize energy consumption without compromising propulsion performance. This approach demonstrated that beyond electromagnetic and thermal optimization, intelligent control systems represent a complementary pathway for further reducing operational costs and increasing propulsion flexibility in maritime environments.

Despite their superior performance characteristics, such as higher torque density, reduced maintenance, and greater efficiency, PMSMs face economic limitations due to the high cost of rare-earth permanent magnets. The dependence on rare-earth elements like neodymium and dysprosium not only increases initial investment but also introduces supply chain vulnerabilities, particularly in maritime applications where long-term maintenance is crucial. These economic constraints often lead designers or ship-owners to favor IMs due to the associated lower capital expenditure, especially in small-to-medium tonnage vessels or budget-constrained projects. Although PMSMs involve a higher initial cost due to magnets and complex control electronics, the reduction in ongoing maintenance (no brushes, reduced rotor losses) can lead to a lower total cost of ownership over a typical 20-year vessel lifespan. The break-even point is typically achieved in 5–7 years, depending on operational hours and energy tariffs.

While this study focused primarily on the electromagnetic and thermal performance of PMSMs and IMs, it is important to acknowledge that propulsion efficiency at the system level can be further enhanced through advanced energy management strategies. Recent developments in real-time, traffic-aware optimization frameworks for hybrid vehicles, such as the Internet-Distributed Energy Management Strategy (ID-EMS) proposed by Zhang et al. [48], have demonstrated how predictive algorithms based on external data (e.g., traffic flow or load demand) can significantly improve energy allocation decisions. The integration of similar global optimal control strategies in future marine propulsion systems, leveraging voyage planning data, load profiles, and environmental conditions, could offer substantial improvements in overall system-level energy efficiency. Such approaches present a promising direction for extending the present work beyond component-level optimization to holistic vessel-level control architectures.

Table 9. Comparison of Selection Criteria between Induction Motor and PMSM.

Parameter	Induction Motor	PMSM
Initial Cost	Lower	High (~30% higher than IM)
Efficiency	93–95%	97–98%
Maintenance Cost	Higher	Lower (~30% less)
Cooling System	Simpler and cost-effective	Complex and costly
Control System	Simpler, lower cost	Advanced, expensive
Lifespan	15–20 years	20–25 years
Total Lifecycle Cost	Higher due to energy losses	Lower long-term costs
Payback Period	__	~7 years (Based on fuel and maintenance savings)

summarizes the selection criteria and compares the operating characteristics between a high-power (10MW) IM and a corresponding PMSM both with an optimized design specific to applications in electric marine propulsion.

In conclusion, the choice between PMSMs and IMs for 10 MW electric ship propulsion systems involves a trade-off between initial cost, operational efficiency, maintenance, cooling requirements, and control system complexity. While PMSMs offer superior efficiency, reliability, and long-term operational savings, their high upfront costs and complex cooling and control requirements must be carefully considered. IMs provide a more economical and straightforward alternative with proven reliability, albeit at the cost of lower efficiency and higher long-term operational expenses. The ultimate choice depends on the specific application requirements, budget constraints, and the operational profile of the vessel.

6. Discussion

A comparative analysis between permanent magnet synchronous motors (PMSMs) and induction motors (IMs) revealed critical insights into their suitability for ship electrification applications. The study demonstrates that PMSMs offer significant advantages in terms of efficiency, power density, and reduced current requirements, which are crucial for applications with high-energy demands and constrained space, such as maritime propulsion. Specifically, PMSMs exhibit approximately 3.11% higher efficiency compared to IMs, largely due to lower copper losses, which translate to less heat generation and improved thermal performance. This not only supports better system reliability but also extends the lifespan of motor components, especially the insulation in windings, which is highly susceptible to thermal degradation.

On the other hand, IMs, while exhibiting lower efficiency and higher mass, operate at a lower frequency, which limits core losses in the stator and rotor. This characteristic is particularly beneficial in settings where efficiency is less of a concern and the initial cost and maintenance simplicity take priority. However, for advanced electric propulsion systems, PMSMs appear to be the superior choice, given their higher performance, especially when efficiency, weight reduction, and fuel savings are critical factors.

Our comparative analysis highlighted several key factors relevant to ship electrification. PMSMs, with their higher efficiency and power density, are particularly suited for applications where weight and space are critical constraints. However, their increased core losses at high frequencies necessitate advanced cooling strategies to ensure long-term reliability. On the other hand, IMs offer a proven and cost-effective solution with lower core losses and simpler cooling requirements, making them suitable for applications where initial investment costs are a primary concern. Additionally, WRIMs offer benefits in applications where high starting torque and precise slip control are essential. The external rotor resistance adjustment capability provides flexibility in regulating torque and speed, eliminating the need for complex inverter systems. However, this comes at the expense of increased maintenance due to the wear of slip rings and brushes, as well as higher rotor copper losses. Our FEM-based sensitivity analysis revealed that fine-tuning the rotor slot depth and stator design can improve WRIM efficiency by up to 94.5%, but this remains slightly lower than PMSMs due to additional slip ring losses. Moreover, WRIMs are heavier due to the presence of additional rotor components, increasing the mass by 10–12% compared to PMSMs, while SCIMs remain the lightest among the three configurations. PMSMs benefit from higher power density and reduced volume, which is advantageous in marine applications where spatial constraints are critical. However, the high-frequency operation of PMSMs leads to elevated core losses, necessitating advanced cooling solutions. Furthermore, the high-frequency operation of PMSMs introduces electromagnetic interference (EMI) challenges that require careful system integration within the ship’s electrical infrastructure.

This study highlights the importance of sensitivity analyses and optimization techniques, such as those using finite element methods, to optimize the motor topology and further reduce losses and torque ripple in PMSMs. These optimizations are essential in aligning motor characteristics with the demands of modern electric propulsion. The analysis also illustrates how PMSMs can be tailored through design iterations to meet specific operational and environmental constraints, underscoring the need for continued research into high-efficiency motor designs that minimize power losses.

Although experimental data on 10 MW motors for ship propulsion applications are scarce, the simulation results presented in this paper align with general trends reported in the literature [49]. Specifically, simulations confirmed that PMSMs achieve higher efficiency compared to IMs, and thermal analyses indicated that PMSMs exhibit lower temperature rise due to reduced rotor losses, reaffirming their superiority in applications where thermal management is crucial. Additionally, excellent acoustic performance makes them suitable for a wide range of ships. Overall, a comparison of our results with those in the literature [50] supports the validity of simulations and provides a reliable basis for evaluating the advantages and disadvantages of PMSMs and IMs in high-power ship propulsion applications. The lack of extensive experimental data for motors of this scale underscores the need for further research and experimental verification to confirm theoretical and simulation-based findings and guide the industry in making informed decisions regarding propulsion motor selection. While the presented results were derived from validated finite element models, it is acknowledged that simulation-based findings may deviate from real-world performance due to factors such as manufacturing tolerances, thermal aging, and marine environmental variability. A next step in this research includes experimental validation through lab-scale prototypes or full-system tests aboard electric vessels.

The fault-tolerant design of multi-phase PMSMs for ship propulsion is crucial to ensure operational reliability and safety in demanding maritime environments. Incorporating modular inverter systems and multi-phase stator coils enhances system resilience by allowing continued operation even in the event of partial inverter failures [51]. This approach minimizes downtime, reduces maintenance costs, and ensures uninterrupted propulsion, which is critical for mission-critical applications such as naval vessels and commercial shipping. The redundancy provided by a fault-tolerant design significantly enhances the overall robustness and lifecycle performance of ship propulsion systems.

Future research could explore further improvements in PMSM design by integrating advanced materials and exploring new topologies, potentially increasing efficiency and reducing weight further. Additionally, addressing the economic aspects, including the cost of materials like permanent magnets, could make PMSMs more accessible for a wider range of maritime applications.

7. Conclusions

In conclusion, the present research underscores that PMSMs are a viable alternative to traditional IMs for ship electrification, especially where enhanced efficiency, reduced emissions, and compact design are priorities. PMSMs offer reduced copper losses, enhanced thermal behavior, and superior efficiency across a wide load range, positioning them as ideal candidates for sustainable marine propulsion. However, the high-frequency operation of PMSMs introduces elevated core losses, which may necessitate advanced cooling solutions, optimized control strategies, and robust material selections to manage thermal performance effectively. Future research should explore the integration of next-generation magnetic materials and cooling technologies to further improve PMSM performance. Additionally, the economic viability of both motor types should be assessed in detail, considering lifecycle costs and operational efficiency in different maritime scenarios.