PurposeThis paper aims to present an adapted DC power supply for a high-current regulation system based on an iron-core inductance with local saturations. The present work highlights a magnetic coupling between the power circuit and its command which creates a 100 Hz current component because of the non-linearity of the iron-core. With the simple structure well adapted to high current applications, it is not possible to remove this AC component superimposed on the DC current. A dedicated DC supply is proposed to maintain a stable average current in the command coils despite the 100 Hz current component.Design/methodology/approachThe magnetic coupling between the power circuit and command coils is investigated and highlighted using finite element simulations and measurements. Based on these results, a dedicated DC power supply is designed and experimentally validated on the high-current regulation system.FindingsExperimental observations confirm the good performance of the proposed control strategy. The DC supply provides a stable average command current despite the 100 Hz component impossible to remove.Originality/valueBecause of the 100 Hz current component superimposed on the DC command current, a standard DC power supply cannot be used. The main contribution of this work is designing of a power supply able to tune the average current in the command coils despite the 100 Hz current component inherent in the non-linearity which is the principle of local saturation inductance.
Purpose According to the international standard IEC 60404-2:1996 + A1:2008, the magnetic characterization is only considered compliant if the magnetic polarization applied to the magnetic sheets under test has a sinusoidal waveform. The purpose of this study is therefore to propose a new approach to generate a sinusoidal magnetic polarization at the standard mains frequency of 50 Hz.Design/methodology/approach The method proposed in this paper is very simple. It is based solely on the use of a sinusoidal power supply and a negative resistor. The latter consists of an operational amplifier, two identical precision resistors and one power resistor. The negative resistor's role is to compensate for the voltage drop in the Epstein frame.Findings This paper also presents an experimental validation carried out on an Epstein frame with grain-oriented silicon steel sheets. The obtained results confirm the effectiveness of the proposed method for generating a sinusoidal magnetic flux density, thus guaranteeing an accurate characterization of the sheets.Practical implications Given the advantages mentioned above, the proposed method can be easily implemented in the laboratories for a magnetic pre-characterization of the magnetic materials.Originality/value Compared to existing methods in the literature, the proposed method is distinguished by the absence of the feedback loop. In terms of performance, it has several advantages: it is very simple to implement, less expensive, requires less equipment and offers remarkable efficiency.
Purpose The purpose of this paper is to propose a hybrid calculation method to efficiently estimate flux density harmonics caused by Pulse Width Modulation (PWM), which is suitable for conventional and unconventional Permanent Magnet Synchronous Machines (PMSMs).Design/methodology/approach First, the principle and modeling of PMSM are recalled. Secondly, realizing hybrid calculation is divided into two main steps: calculating the harmonic currents from PWM voltage sources in the analytical model based on electrical circuits; and importing the harmonic currents into the static and linear magnetic model with frozen permeability to calculate flux density harmonics. Finally, a validation by comparison to a transient finite element approach simulation shows the reliability and accuracy of the proposed hybrid method.Findings This hybrid calculation can provide accurate results and significantly reduce computation time from several hours to minutes when estimating high-frequency harmonic flux densities in conventional or unconventional PMSMs.Originality/value This paper presents a universal hybrid computational method for the rapid calculation of magnetic flux harmonics because of PWM, applicable to both conventional and unconventional PMSMs.
Purpose This paper aims to evaluate the thermal feasibility and reliability implications of maintaining full nominal torque in a five-phase permanent-magnet synchronous motor (PMSM) under a single open-phase fault. It examines how post-fault current redistribution strategies affect copper losses, thermal behavior and insulation aging to assess whether high-performance fault-tolerant control can be achieved without compromising the machine’s operational lifespan. Design/methodology/approach A coupled electromagnetic–thermal workflow is adopted. Electromagnetic finite-element simulations compute spatial copper and iron losses for two post-fault strategies: Equal-Current redistribution and Copper-Loss-Minimization. These losses are then imported into a detailed 2D transient thermal finite-element model to calculate winding temperature rise, hotspot location and steady-state thermal gradients. The analysis focuses on the effect of asymmetric current loading and interphase thermal coupling when full torque must be preserved. Findings Both strategies restore full torque, increasing the winding hotspot from 105°C in healthy operation to approximately 130°C–131°C. The Copper-Loss-Minimization strategy reduces total copper losses but introduces thermal imbalance. Nevertheless, strong lateral thermal coupling within the stator redistributes heat effectively, leading both strategies to converge to nearly identical peak temperatures. Since insulation aging is governed by hotspot temperature, both approaches impose comparable insulation stress. However, the significant temperature rise accelerates aging, drastically reducing the machine’s lifetime. Consequently, full-torque fault tolerance is viable only as a short-term emergency state for mission completion rather than continuous long-term service. Research limitations/implications The adopted 2D model inherently neglects axial heat transfer and end-winding effects, but it fully captures the radial and orthoradial thermal coupling that drives spatial heat redistribution across the stator. While the machine proves thermally robust, the findings suggest that the inverter, lacking such internal coupling, constitutes the true system bottleneck. Future research should therefore prioritize coupled machine–inverter thermal dynamics. Originality/value The study shows that a five-phase PMSM can sustain full-torque operation under an open-phase fault without immediate overheating, challenging the assumption that immediate post-fault derating is required. However, it demonstrates that such operation significantly accelerates aging, classifying it as an emergency state rather than a continuous mode. It further confirms that Copper-Loss Minimization control can be applied safely for short durations, as intrinsic thermal coupling limits hotspot escalation. The results indicate that inverter thermal limits, rather than motor heating, are more likely to constrain ultimate post-fault performance.
Purpose This study aims to enhance the performance of sensorless vector control for permanent magnet synchronous motor (PMSM) drives by developing an improved sliding-mode observer (SMO) with current disturbance compensation (CDC). This observer is designed to achieve chattering attenuation induced by sliding-mode dynamics while improving the estimation accuracy of both current and rotor position parameters. Design/methodology/approach To address the chattering and disturbance rejection shortcomings of conventional first-order SMOs, this paper proposes a higher-order SMO based on a hyperbolic tangent sliding surface (HTSMO) and then deeply integrates it with CDC, forming the CDC-HTSMO. First, a hyperbolic tangent sliding-mode surface is designed to achieve chattering suppression. Then, considering external current disturbances, CDC is added to the observed current to reduce current errors. Findings Comparative experiments are conducted to verify the effectiveness of CDC-HTSMO in current disturbance and rotor position compensation. The final results demonstrate that the proposed method exhibits excellent performance in reducing chattering, suppressing current ripple and improving rotor position estimation accuracy. Originality/value The improved observer proposed in this study is co-developed and experimentally validated with SMO based on a first-order sliding-mode framework and an extended-model-based full-order sliding-mode observer. Systematic comparative analyses are conducted under diverse operating conditions, including speed variations, no-load/load disturbances and parameter variations.
Purpose This paper aims to investigate the influence of geometric dimensions on the macroscopic magnetic properties of nanocrystalline laminates through experimental measurement and analytical interpretation. Design/methodology/approach This paper develops a new system for testing the magnetic properties of nanocrystalline laminates with different dimensions and examines seven laminates of two types under various flux densities and excitation frequencies. The effects of geometric parameters, such as length-width ratio and thickness-width ratio, on typical magnetic parameters, including loss density, permeability and coercivity, are investigated through comparative analysis of the experimental data. Furthermore, the established analytical model is used to investigate the nonuniform internal magnetic field intensity distribution in nanocrystalline laminates with different dimensions. Findings The results demonstrate that wider laminates exhibit higher loss density, reduced permeability and increased coercivity, with the dimensional influence becoming more pronounced at higher frequencies. Furthermore, the analytical results provide a qualitative explanation for the nonuniform internal magnetic field intensity distribution caused by dimensional variations. Overall, within the investigated dimensional range and excitation conditions of this work, the influence of geometric parameters on the magnetic performance of nanocrystalline laminates tends to increase in the order of thickness, length and width and the effect is frequency-dependent. Originality/value This work not only proposes an effective testing method for nanocrystalline laminates of variable dimensions but also provides theoretical and experimental insights for optimizing the design of high-frequency magnetic components.
Purpose This study aims to extract a reduced order model based on the Cauer ladder network (CLN) method from a partial element equivalent circuit (PEEC) formulation of the eddy current problem in parallel conductors. The obtained equivalent circuit can then be effectively used for time domain simulations.Design/methodology/approach The PEEC formulation has been written as a first-order linear dynamic system, and the CLN algorithm has been applied to extract the reduced-order model. The numerical results of the reduced order model have been then compared with the reference results obtained both with the finite element method (FEM) and the PEEC method for a canonical test case of two rectangular conductors.Findings The Cauer ladder network representation of the eddy current fields is proved to be accurate enough in frequency and in time domains, provided that a sufficient number of the equivalent circuit stages is considered.Originality/value The CLN method has already been applied in the past to FEM for eddy current problems. In this work, the CLN has been applied to the PEEC method for the first time.
Purpose The main objective of this purpose is to provide a general and systematic method for obtaining the inductance matrices of induction machines under rotor asymmetry faults without requiring a full redefinition of the winding model for each case.Design/methodology/approach This paper combines the winding tensor formalism with the use of connection tensors to automatically generate the inductances corresponding to any configuration of broken bars.Findings Firstly, it introduces a unified mathematical framework capable of modelling arbitrary rotor asymmetries using only the inductances of the healthy machine. Secondly, it demonstrates how connection tensors can encode the structural effects of faults in a compact and algebraically tractable manner. Thirdly, it provides a scalable and computationally efficient procedure that avoids the cumbersome derivation of fault-specific inductance expressions, thereby facilitating both numerical simulation and the development of diagnostic tools.Originality/value The methodology presented in this paper offers a significant simplification of the modelling process while preserving the accuracy required for the analysis of fault-induced harmonic phenomena.
Purpose The purpose of this work is to develop an improved equivalent circuit model for air-core transformers operating at higher frequencies. By refining the classical Cauer-based representation, this study aims to achieve more accurate impedance and current behavior over a wide frequency range, with particular emphasis on improving low-frequency performance. Design/methodology/approach This research uses a full field-circuit modeling approach. Initially, a finite element method (FEM) of coupled coils is formulated to capture electromagnetic interactions. These complex matrix equations are then reduced using the Padé via Lanczos (PvL) method, which accurately approximates the frequency response while significantly lowering the computational order. Based on the reduced model, impedance characteristics are determined for both magnetizing and horizontal branches. A modified circuit structure is then proposed and rigorously validated by comparing its performance − specifically impedance characteristics and current waveforms − against field-model simulations under various load conditions. Findings The analysis demonstrates that the classical equivalent circuit fails to accurately reproduce the impedance behavior of the magnetizing branch at lower frequencies. The proposed modified structure rectifies this, achieving significantly better agreement with results of field-model. Simulation results confirm that the proposed equivalent circuit in the more accurately replicates both the amplitude and phase of load currents, eliminating the discrepancies found in the classical model. Originality/value This study identifies a limitation of the classical Cauer-based representation of the magnetizing branch in air-core transformers, related to its improper low-frequency behavior. It is shown that the traditional structure does not satisfy the zero-pulsation boundary condition, leading to a non-zero remainder in the PvL approximation and reduced modeling accuracy at low frequencies. To overcome this issue, a physically consistent modification is proposed by introducing an additional resistance R0 into the magnetizing branch. By combining field-based parameter extraction with PvL reduction, the method preserves computational efficiency while significantly improving low-frequency accuracy, providing a reliable tool for wide-frequency analysis of higher-frequency coupled systems.
PurposeThe multiscale magnetic domain energy model (MMDEM) is widely used for analyzing the magnetic properties of grain-oriented electrical steel sheets; however, its high computational cost significantly limits its efficiency under fine discretization. This study aims to propose a parallel computing-based acceleration method to improve computational efficiency while maintaining simulation accuracy.Design/methodology/approachA parallel acceleration framework is developed and applied to the magnetic characterization of grain-oriented electrical steel sheets. The sample is discretized into independent computational elements suitable for parallel execution. The demagnetization coefficient tensor of each element is computed in parallel and incorporated into the energy formulation. In addition, a parallel global optimization algorithm is used to minimize the total magnetic domain energy. The computational performance and accuracy are evaluated under different discretization levels.FindingsThe proposed method significantly reduces computation time compared with the conventional serial MMDEM, particularly at higher discretization levels. Meanwhile, the simulation accuracy is well preserved, and the results show good agreement with experimental data.Originality/valueThis work presents a parallel computing-based acceleration strategy for MMDEM, providing an efficient and scalable framework for magnetic domain modeling. The proposed method improves computational efficiency while maintaining accuracy, enhancing the applicability of MMDEM in large-scale and practical engineering problems.
Purpose - This work aims to propose a novel post-fault direct torque control (DTC) scheme for induction motor drives supplied by an eight-switch three-phase inverter (ESTPI), implemented through the design of three new look-up tables. Design/methodology/approach - A comprehensive analysis is performed to evaluate the effect of each voltage vector generated by the ESTPI on the stator flux, electromagnetic torque, DC-link capacitor voltages and common-mode voltage (CMV). To mitigate the capacitor voltage imbalance, a dedicated hysteresis comparator is incorporated to regulate the voltage difference between the DC-link capacitors. Torque ripple is reduced by eliminating vectors responsible for excessive torque pulsations, while CMV variations are minimized through the creation of two virtual vectors that replace those generating high CMV levels, effectively confining CMV within +/- Vdc/6. Findings - The validity and effectiveness of the proposed DTC strategy are confirmed through extensive simulation studies. By introducing three redesigned look-up tables and incorporating dedicated control mechanisms, namely, a hysteresis comparator for neutral point voltage (NPV) balance, the removal of torque-inducing vectors and the use of virtual vectors to constrain CMV, the proposed approach significantly enhances the drive's post-fault performance. Originality/value - The ESTPI, obtained by reconfiguring a faulty three-level NPC inverter, enables robust post-fault operation by maintaining balanced power delivery, reducing circuit complexity and preserving acceptable output voltage levels. However, when feeding induction motor drives, the performance of the ESTPI can be hindered by several critical challenges, including DC-link capacitor voltage imbalance, elevated torque ripple and fluctuations in CMV. Simultaneously addressing these issues is crucial to ensure stable, efficient and reliable motor-drive operation under fault conditions.
PurposeThis study aims to develop an efficient level-set (LS)-based multi-objective topology optimization framework capable of handling strongly nonlinear electromagnetic design problems, and to demonstrate its applicability through the design of synchronous reluctance motors.Design/methodology/approachThe proposed level-set adaptive switching method (LASM) combines an LS-based topology optimization scheme with an adaptive switching mechanism of weighting coefficients. The weights are automatically determined by solving a mixed-integer linear programming problem that maximizes the expected shape variation, and switching is triggered when objective improvement stagnates, deteriorates or oscillates. This dynamic framework enables continuous exploration of Pareto fronts in multi-objective design spaces.FindingsNumerical experiments demonstrate that LASM achieves broader and more uniformly distributed Pareto fronts and improved design performance compared with conventional weighted-sum optimization. The obtained geometries maintain smooth and manufacturable boundaries, confirming the practicality of the proposed framework.Originality/value LASM builds upon the LS-based switching concept of Shigematsu et al. (2022) and extends it by introducing a shape-variation-driven automatic weight computation scheme and enabling a scalable application to three or more objectives. Through these extensions, LASM eliminates designer dependency in weight setting, enhances robustness against local minima and provides a practical and fully automated framework for multi-objective electromagnetic design.
PurposeThis study aims to propose a permanent magnet (PM) magnetization estimation method that utilizes the induced voltage measured by a pickup coil.Design/methodology/approachTo efficiently minimize the objective function, a gradient-based optimization method supported by the adjoint variable method is applied.FindingsThe estimation of PMs magnetization was successfully carried out. Furthermore, the reconstructed induced voltages were quite similar to the target distribution.Originality/valueThe estimation method for PM magnetization using induced voltage at pickup coil located on the airgap of surface permanent magnet synchronous motors derived from rotor rotation.
PurposeThis paper aims to present an efficient analytical model based on the mirror-image method with frequency-dependent current density correction, designed to address the trade-off between accuracy and efficiency in calculating harmonic losses in transformer windings.Design/methodology/approachA 2D analytical model incorporating the mirror-image method was developed to account for core effects, augmented by a frequency-dependent current density correction for skin and proximity effects. The model was validated against both 3D finite element method (FEM) simulations and experimental measurements, conducted on a three-phase and a single-phase transformer, respectively.FindingsThe proposed method achieves a maximum relative error of less than 10% in the calculation of winding eddy current losses compared to 3D-FEM, while reducing computation time by over 70 times. Experimental results confirm its accuracy across frequencies, with an average error below 7%.Originality/valueThis study presents a computationally efficient 2D analytical model that accurately captures complex frequency-dependent losses, which serves as a key component for fast physical field evaluation in transformer digital twins.
PurposeThis paper aims to address the challenges of solving complex nonlinear optimization problems that simultaneously involve sizing and control of energy systems. The objective is to obtain realistic and computationally efficient solutions suitable for real-world applications. The study focuses on demonstrating the advantages of a bilevel approach compared to conventional single-level formulations, particularly in systems characterized by strong nonlinear interactions between design and operational variables. Design/methodology/approachA bilevel optimization framework is proposed, in which the lower level solves the control problem through a combination of nonlinear programming (NLP) and dynamic programming (DP). The upper level handles the sizing variables and coordinates the results from multiple control subproblems. The decomposition allows for a significant reduction in computational complexity while maintaining high accuracy. The methodology is validated and benchmarked against a classical linear programming (LP) approach. FindingsThe results show that the proposed bilevel NLP–DP methodology achieves performance close to that of linear programming in terms of energy cost while effectively handling nonlinearities inherent to real systems. It demonstrates strong robustness and stability over long-term optimization horizons, with deviations below 0.3% compared to LP. Moreover, the approach ensures physically realistic control trajectories and operational feasibility under nonlinear constraints. Originality/valueThis work introduces a unified bilevel optimization framework combining nonlinear and dynamic programming to jointly address sizing and control problems in complex energy systems. The originality lies in the decomposition strategy, which makes it possible to preserve nonlinear behavior while ensuring computational tractability. The proposed approach provides a practical and reliable tool for the optimal design and control of hybrid infrastructures, such as railway substations or microgrids.
PurposeThe purpose of this paper is to present an application-specific optimization methodology for the design of coupled inductors used in multilevel interleaved power converters. This study focuses on minimizing core losses to meet power density requirements, reducing component volume to address cost constraints and maximizing longitudinal inductance to enhance electromagnetic interference (EMI) performance.Design/methodology/approachA multiobjective optimization (MOO) approach based on the NSGA-II algorithm is used to determine the Pareto-optimal design of the coupled inductor that satisfies the target power rating of 120 kW while minimizing volume for improved cost-effectiveness. The optimization incorporates key functional parameters, including main inductance, core losses and coil leakage inductance, the latter serving as an element for EMI filtering. To efficiently address the MOO problem, analytical models of the main inductance and core losses are integrated with a surrogate model of the device under test leakage inductance, derived from 2.5D finite element simulations.FindingsThree Pareto-optimal designs are evaluated against a commercial reference in terms of core losses, inductance and cost. The low-loss design minimizes losses but requires a core twice as large as the reference, increasing cost by 60%. The compact design cuts material use by an order of magnitude but leads to substantially higher losses. The high-inductance design more than doubles inductance yet demands the largest core, raising cost by 70%. These results highlight a clear trade-off between magnetic efficiency, inductive performance and cost-effectiveness.Research limitations/implicationsThis study is limited by practical factors affecting manufacturability and performance. The proposed designs require complex multilayer windings that increase leakage inductance, parasitics and fabrication difficulty. Winding capacitance and thermal effects are not modeled, though both significantly impact high-frequency and high-loss operation. Assumed filling factors may not reflect real winding technologies, affecting packing density and losses. Moreover, the smallest-volume designs may demand extra cooling, reducing practical benefits. Future work should include detailed winding models, parasitic capacitance and coupled thermal-electromagnetic analysis to better capture real-world performance and reliability.Practical implicationsThe proposed methodology provides a quantitative framework to support informed trade-off decisions between key functional parameters - such as loss efficiency, inductance and space utilization - while also addressing EMI-related aspects and ensuring economic competitiveness.Originality/valueThe novelty of this work lies in its integrated optimization workflow for coupled inductor design, which simultaneously accounts for key functional parameters - such as efficiency, inductance and space utilization - while incorporating EMI-related factors and cost considerations within a unified framework.
Purpose - Engineering education, particularly in complex fields like electromagnetism, faces a significant challenge in conveying multiphysics systems. Traditional methods fall short in building deep, intuitive understanding. The purpose of this paper is to address this "cognitive interface challenge" by presenting a novel conceptual framework for creating human-centric, interactive learning environments to bridge this gap. Design/methodology/approach - This paper details a methodology of interdisciplinary knowledge transfer. The proposed conceptual framework is derived from a multi-year analysis of best practices in the Architecture, Engineering, Construction and Operations sector, which has already developed mature solutions for navigating complex three-dimensional digital twins. Findings - The primary contribution is a formal four-stage methodological framework for developing human-centric virtual environments. This model moves beyond traditional tools to create interactive systems based on defined cognitive goals and proven interactive design paradigms, providing a new, robust method for the computation and mathematics community. Research limitations/implications - As a conceptual paper, the primary implication is the need for empirical validation of the proposed four-stage framework. Future research should focus on implementing and testing the framework's effectiveness against traditional methods in controlled educational and professional settings. Practical implications - The framework provides a practical method for educators and engineers to design immersive virtual environments. This allows students and professionals to interact directly with complex simulations (e.g. electromagnetic fields), fostering a deeper, more intuitive understanding than traditional methods. Social implications - By fostering deeper understanding and more active student participation, this approach can help democratize complex scientific knowledge. This study makes invisible phenomena more accessible, leading to a more technically literate and engaged generation of engineers and scientists. Originality/value - This paper's originality lies in its interdisciplinary transfer of a proven methodology from the Architecture, Engineering, Construction and Operations sector to computational electromagnetism. This paper provides a novel, structured framework that enables users to "touch the invisible," offering a new paradigm for interacting with complex data.
PurposeThis paper aims to propose an improved parameter identification method for the inverse play model to reduce the error in hysteresis simulation.Design/methodology/approachThis paper proposes an improved parameter identification method for the inverse play model, which selects a portion of the data from numerically generated first-order reversal curves to identify the shape function, thereby avoiding simulation errors caused by repeated hysteresis operators. The proposed method is then combined with an optimization algorithm to derive the optimal parameter solution for the model, enabling hysteresis simulation.FindingsBy using the proposed method to identify the parameters of the inverse play model and simulate hysteresis loops, it is demonstrated that the global error in hysteresis loss calculation is controlled within approximately 5%. This indicates a significant improvement in the accuracy of hysteresis simulation and also addresses the issue of non-smooth hysteresis loops.Originality/valueThe proposed method significantly improved the accuracy of hysteresis simulation with the inverse play model after parameter identification. Meanwhile, due to the reduced amount of data used for identifying the shape function, the efficiency of obtaining the optimal solution was increased, thereby shortening the computation time.
PurposeThis paper aims to propose a Physics Informed Neural Network (PINN) based method for the solution of inverse problems in magnetics, when the nonlinear characteristics of magnetic materials are included.Design/methodology/approachThe proposed method is designed to estimate the current sources from a set of magnetic field measurement, in presence of nonlinear magnetic materials. The PINN constructed to solve this problem is based on the physics laws of magnetism that are used to solve the direct problem of calculating the field in a set of points given magnetization and currents. A loss function (backpropagating the error in the NN) evaluates the discrepancies between estimation and measurements and imposes the magnetic characteristics of the material.FindingsThe method has proven to be characterized by accuracy and low computational time if compared to more classical approaches which include regularization: in particular, the PINN that penalizes both measurement discrepancy and constitutive relation error can substantially improve source reconstruction in magnetostatics with magnetic materials.Originality/valueTo the best of the authors' knowledge, the insertion of the constitutive error in the loss function proposed here is new and proves to be a step ahead in the utilization of PINN for the solution of nonlinear magnetic inverse problems. Furthermore, it paves the road for new applications in which inversion from data from complex systems can be a challenging task.
Purpose - This study aims to optimize the internal structure of an interior permanent magnet synchronous motor (IPMSM) with V-shaped magnets to maximize torque. Specifically, it addresses the issue of grayscale (intermediate density) regions that appear near material interfaces in conventional phase-field-based level set methods. The primary objective is to eliminate these intermediate regions to prevent inaccuracies in finite element analysis and to resolve ambiguities in practical manufacturing. Design/methodology/approach - The proposed method employs a phase-field-based level set framework combined with a dynamic remeshing technique. Unlike conventional approaches that rely on fixed meshes, the computational mesh is regenerated after each update of the level set function so that the mesh explicitly conforms to material boundaries. The optimization problem is formulated to maximize instantaneous torque, and sensitivity analysis is conducted using the adjoint variable method. In addition, the sensitivity of the optimization algorithm to different initial shapes and interface parameters is systematically investigated. Findings - The proposed remeshing strategy successfully suppresses the formation of grayscale regions, resulting in optimal structures that are completely free of intermediate density regions and exhibit improved structural clarity and manufacturability. The method also demonstrates low sensitivity to variations in the initial shape, yielding stable optimization results. However, the final geometry and torque performance depend strongly on the appropriate selection of the interface propagation speed and diffusion coefficient. Ultimately, the optimized design achieves a 146.2% increase in torque compared with the initial configuration. Originality/value - This research provides significant value by addressing the persistent issue of grayscale regions near material interfaces in phase-field-based topology optimization for electric machines. While prior studies typically relied on fixed meshes, this work integrates a dynamic remeshing strategy tailored for IPMSM design to achieve strictly grayscale-free optimal structures. Furthermore, the study contributes original insights by systematically investigating the sensitivity of the optimization algorithm to initial conditions, an aspect that has received limited attention in electromagnetic topology optimization literature.
