Purpose The prompt measurements of variation in phase, amplitude and frequency of a sinusoidal signal are crucial in a complex electrical network system. A Phasor measurement unit (PMU) uses a phasor estimation technique to estimate the phasor of the voltage and current signals, frequency and rate-of-change of frequency. The phasor estimation technique must adhere to the compliance requirements mentioned in the IEC/IEEE 60255-118-1 Standard. It is observed that fulfilling the IEEE compliance is a challenging task with a low sampling rate. This paper aims to develop a phasor estimation technique fulfilling the performance criteria at low sampling frequency. Design/methodology/approach To provide high accuracy during off-nominal frequency estimation, this work attempts to enrich the attenuation level at the side-lobe using a five-term cosine function, namely, an enriched side-lobe suppressor (ESS). It enhances the phasor estimation in the interpolation discrete Fourier transform (IpDFT) technique to achieve the performance requirements at a low sampling rate. Findings The performance of the proposed ESS-IpDFT technique is evaluated under the static and dynamic compliance specified in the IEC/IEEE 60255-118-1 Standard. The ESSIpDFT complies with the M-class performance requirements by maintaining the performance indices within the limits specified in the Standard. In addition, the performance of the ESSIpDFT approach is compared with the recently reported studies and found to offer better performance in most of the test indices. Originality/value A five-term cosine function-based ESS is designed to enrich the DFT interpolation for phasor estimation. The ESS-IpDFT based phasor estimation has been validated rigorously according to the IEC/IEEE 60255-118-1 Standard and compared with recently reported works.
Purpose This paper aims to investigate how to achieve a balance between high torque density and low vibration noise for the spoke-type permanent magnet (STPM) machine with a slotted rotor. Design/methodology/approach First, an analytical model (AM) of the radial electromagnetic force (REF) and electromagnetic torque for the STPM machine with a slotted rotor is proposed, and the influence of rotor slotting on the REF and electromagnetic torque is analyzed in combination with the finite element method. Then, the multi-physics model is established to analyze the electromagnetic torque and vibration noise with different rotor slotting structures to identify the optimal slotting configuration. Finally, the vibration noise is further optimized to achieve a balance between electromagnetic torque and vibration noise. Findings An appropriate rotor slotting structure can effectively enhance torque density and optimize electromagnetic noise. The optimized machine has higher torque density and lower vibration noise. Finally, two STPM prototypes with initial and optimized machines are manufactured and tested to verify the accuracy of the simulation results. Originality/value In this paper, the spatial order generation principle for REF density in the STPM machine with different rotor structures is revealed and analyzed. In addition, the electromagnetic torque and vibration noise of the STPM machine with different key parameters are analyzed and optimized to improve torque and reduce vibration noise.
PurposeThe application of high voltage direct current (DC) gas insulated lines in the power grid is expected to increase in the near future, due to its advantages considering safety, compactness and high voltage capacity. However, there are challenges in the design of the system which need to be addressed, such as space charge accumulation and high electric field stress. Therefore, precise simulation models of the gas insulated line need to be developed for examination purposes. One important aspect is the accurate representation of the conduction behavior of the insulating gas. Factors influencing the electrical conductivity, such as electric field strength, temperature, gas pressure and gas humidity, must be considered. In addition, an accurate determination of the temperature is essential for precise simulation results, since practical applications show different temperature distributions in the gas, depending on a horizontally or vertically arrangement of the gas insulated line. This study aims to develop a simulation model, which incorporates such phenomena. Design/methodology/approachA three dimensional model of a high voltage DC gas insulated line is developed, with the application of a nonlinear electrical conductivity model for the insulation gas, sulphur hexalfluoride. The conductivity model is derived from experimental measurements. The electric field distribution is investigated with a focus on the humidity content of the gas. For the determination of the temperature distribution, heat conduction is considered in the solid domain of the system and heat convection and heat radiation is considered in the gaseous domain, where the dynamic gas flow is explicitly modeled. FindingsThe simulation results reveal distinct electric field distributions for dry (2% humidity) or humid gas (30% humidity), where the difference of the maximum electric field value is up to 35%. The inclusion of heat convection and thermal radiation in the gaseous domain allows to consider the effect of a vertical or horizontal arrangement of the gas insulated line, where higher temperature values are seen on the upper parts in a horizontal construction, compared to a vertical arrangement. However, the consideration of such physical phenomena increases the complexity of the model and results in up to 12 times longer computation times. Originality/valueIn most scientific studies, the electrical conductivity of the sulphur hexalfluoride gas is assumed to be constant, and heat conduction is considered the dominant heat transfer mechanism throughout the system. In contrast, the present work describes the conduction behaviour of the gas by a nonlinear electrical conductivity model, e.g. enabling a comparative analysis of dry and humid gas conditions. In addition, heat convection and thermal radiation is considered as a heat transfer mechanism in the gaseous domain, to account for the influence of the geometrical configuration of the system on the temperature and electric field distributions.
PurposeThis paper aims to develop and experimentally validate a three-dimensional (3D) multiphysics model for predicting the transient magneto-thermal behavior of an axial-flux permanent-magnet (PM) braking system. Design/methodology/approachA coupled 3D finite element model is proposed, combining electromagnetic and transient thermal analyses to account for eddy-current losses, temperature rise and torque reduction. The model includes full geometry and armature reaction effects. A prototype is designed and experimentally tested to validate the approach. FindingsThe proposed coupled 3D magneto-thermal FEM model shows very good agreement with experimental results, accurately predicting both the transient magnetic field distribution and the temperature-dependent reduction in braking torque. The results confirm the capability of the model to reliably reproduce the real operating behavior of axial-flux PM braking systems. Practical implicationsThe proposed approach provides an efficient tool for the design and optimization of PM braking systems, reducing development time while improving performance prediction. Originality/valueThe contribution lies in a coupled 3D magneto-thermal framework experimentally validated on a dedicated prototype and integrating full 3D geometry, armature reaction and temperature-dependent effects within a unified multiphysics model.
Purpose Distortion of the magnetotelluric response is an obstacle that prevents the full use of numerous advantages of the method. Current approaches to removing distortion from measured data depend largely on favourable circumstances and the subjective assessment of their processor. The purpose of this study is to present a correction method that only requires a more precise approach to measurement and data storage. Design/methodology/approach The method is based on the physical interpretation of response distortion, according to which the disturbances that cause it are generically associated with the primary electromagnetic field. It assumes a simple source of disturbances. In the first step, the resistivity of the near-surface layer is determined using the response for the highest frequencies and equations valid only for the impedance of the first layer. This knowledge is also associated with determining the position of the distortion source. The obtained values are then used to identify and numerically remove the disturbance effect from the response for the entire measured spectrum. Findings Testing on synthetic data has shown that with a reasonable initial estimate, the method is able to remove not only the static shift in apparent resistivity caused by charge induction on the surface of the inhomogeneity, but also the spurious layers resulting from induction processes within it. Thus, it can almost accurately restore the intact response and provide reliable information about the subsurface structure. Originality/value Consistent elimination of the impact of disturbances from the response based on understanding the mechanism of their occurrence represents an original approach to the problem.
Purpose The paper aims to provide a numerical exploration of the effect of fractional spatial derivatives and a non-sinusoidal current-phase relation for systems modelled using sine-Gordon equations and, in particular, Josephson junction parallel arrays. Design/methodology/approach The effect of fractional derivatives is examined for single, double and triple sine-Gordon equations. This is then extended to the Josephson junction array model. In addition, the effect of a non-sinusoidal current-phase model is examined. The effect on an initial spatial distribution with no input is considered and subsequently analysis with an input current is examined. Findings The findings indicate that higher-order harmonics can result in non-monotonic behaviour or an oscillation for the case of an initial spatial distribution. Similarly, fractional spatial derivatives introduce an oscillation and result in non-monotonic behaviour. The incorporation of additional harmonics affects the response of the Josephson array system, which can have consequences in relation to signal detection. Fractional derivatives affect the damping of the response of the system. Originality/value The paper is original in investigating the combination of fractional spatial derivatives and a non-sinusoidal current-phase relation for a Josephson junction parallel array.
Purpose This paper aims to propose a novel global optimization algorithm for fast and precise parameter identification of the inverse Preisach hysteresis model. Design/methodology/approach An enhanced parallel Runge-Kutta (ERUN) algorithm is proposed to identify the nine-parameter inverse Preisach model. Integrates chaotic mapping, parallel processing and adaptive perturbation to strengthen global exploration and convergence robustness. The Preisach model used in this paper is established by analytically deriving the inverse Everett function from first-order reversal curves (FORCs) and validated against experimental hysteresis loops of 20SW1200 nonoriented (NO) silicon steel, B30P105 grain-oriented silicon steel and 50WW470 NO silicon steel. Findings The ERUN algorithm achieves a 1.83% error and a computation time of 40.6 s, outperforming the genetic algorithm, simulated annealing, particle swarm optimization and the original Runge-Kutta (RUN) optimization method. The average relative root mean square error analysis confirms that all simulated hysteresis loop errors remain below 10%, even at low magnetic flux densities. Originality/value The proposed ERUN algorithm extends the original RUN method by introducing chaotic mapping and parallel computing strategies, effectively alleviating the premature convergence problem. This work presents a progressive improvement to the global optimization algorithm for inverse Preisach hysteresis model parameter identification, extending the original RUN optimizer with chaotic mapping and parallel computing strategies to achieve faster convergence and higher accuracy, achieving the lowest parameter estimation error (1.83%) and the shortest computational time (40.6 s) among the benchmarked algorithms.
Purpose This study aims to address tedious filtering procedure and enhance manufacturability of the optimized structure for interior permanent magnet synchronous motor (IPMSM), this paper presents a multi-material topology optimization method based on the Laplace network and adaptive mesh sequence cleaning algorithm (LAMSC). Design/methodology/approach The multi-material topology optimization mentions four different materials including iron core, permanent magnet with two different magnetizing directions and air. In the proposed LAMSC method, the adaptive mesh sequence cleaning algorithm enhances rotor manufacturability by eliminating micro-regions within the given design domain. The weights of the Laplace function are selected as design variables, the torque performance of IPMSM and the volume of permanent magnet are optimized as objectives of optimization process. Findings Based on the proposed the multi-material topology optimization method LAMSC, it is evident that compared with traditional structures, the proportion of permanent magnet volume in the optimized rotor decreases by 0.50%, 2.44%, 4.61%, 4.80% and 5.58% when the mesh densities are 90, 900, 1,440, 1,500 and 1,728, respectively. Furthermore, the average torque increases by 9.06%, 9.22%, 12.81%, 11.88% and 10.78%, respectively. Originality/value A multi-material topology optimization method based on the LAMSC is proposed to enhance the manufacturability of IPMSM optimization results, which may provide more flexible technical support for the reshaping of motor structures.
Purpose The purpose of this study is to provide a formula for the homogenized reluctivity of an electrically insulated spherical conductive magnetic particle. The insulated particle is excited by azimuthally symmetric boundary conditions for the magnetic field in the polar direction. Otherwise, the boundary conditions are arbitrary. Design/methodology/approach A magnetodynamic formulation of Maxwell’s equations is considered inside the particle. An electrostatic formulation is considered inside the insulation. The homogenized reluctivity is derived using mathematical methods based on analytical solutions of the formulations. The leading principle in the derivation of the homogenized reluctivity is energy consistency. Findings The most important finding is the formula for the homogenized reluctivity. Furthermore, considering an orthogonal decomposition of the magnetic flux density in terms of spherical harmonics, it turns out that homogenization only distinguishes the first mode of the flux density, regardless of which modes are excited by the boundary conditions. This result is somewhat expected, but it forces us to lump the energy exchange of the higher modes into the homogenized magnetic field strength. The treatment also exposes some of the mathematical structures required for homogenization. Originality/value The formula for the homogenized reluctivity is novel. It admits arbitrary but rotationally symmetric boundary conditions for the magnetic field strength at the outer boundary of the insulation in the polar direction. Industrial applications of the developed methods include powder-like materials such as soft magnetic composites. New perspectives on homogenization are provided.
Purpose This paper aims to present a novel analytical search space-narrowing optimization algorithm for accurately estimating the enhanced lumped mutually coupled (ELMC) equivalent model parameters of transformer windings. The ELMC model is an extension to the lumped mutually coupled (LMC) model, whose performance has been improved by adding stray mutual capacitances. Design/methodology/approach The ELMC model has been developed using a new proposed analytical formula of the total equivalent capacitance. Using this formula, a novel search space narrowing of the series and stray mutual capacitances for the grey wolf optimization (GWO) algorithm has been proposed. Findings The proposed approach proved its effectiveness and robustness in estimating the ELMC model parameters using frequency response analysis data measurements on two different cases of transformer windings. Moreover, the parameters obtained using the ELMC model via the GWO algorithm with a physics-informed constrained search space (GWO-PICSS) showed more accurate results than the LMC model despite the complexities introduced due to the increased number of parameters. Research limitations/implications The true internal behavior of the transformer winding is displayed as accurately as possible through the ELMC model and the proposed analytical relationship that illustrates the overall capacitive coupling to overcome the parameters estimation task. Originality/value A new methodology to construct the ELMC equivalent circuit of transformer winding using an improved search space narrowing GWO algorithm is presented to obtain a more accurate model, which may contribute to power transformer faults diagnosis.
Purpose This paper aims to address large torque ripple and high production costs in neodymium-iron-boron (NdFeB) permanent magnet-assisted synchronous reluctance motors (PMaSynRMs), which typically feature high torque density. To this end, a novel rotor structure integrated with segmented non-uniform air gaps and hybrid ferrite-NdFeB magnets is proposed. Design/methodology/approach The electromagnetic characteristics of four motors with different rotor structures are compared: NdFeB rotor, hybrid magnet rotor and non-uniform air-gap rotor. The reason for larger torque ripple in hybrid magnet motors is elucidated. A Gaussian process regression (GPR) surrogate model with average torque, torque ripple, efficiency and permanent magnet cost as objectives is established. The 15 geometric parameters are co-optimised using the adaptive non-dominated sorting genetic algorithm III (A-NSGA-III). Findings For the optimised motor, NdFeB consumption is reduced by 27.12%, torque ripple is decreased from 16.66% to 7.17% and efficiency remains at 89.39%. Average torque is maintained at 28.19 N·m, permanent magnet cost is reduced by 10.18%. Originality/value This paper proposes a novel rotor structure integrating segmented non-uniform air gaps with hybrid ferrite-NdFeB magnets. Through the multi-objective co-optimisation of the GPR surrogate model and the A-NSGA-III algorithm, the motor manufacturing cost is reduced, while its electromagnetic performance is significantly enhanced. This study provides an effective engineering solution for the development of low-cost, high-performance and low-torque-ripple PMaSynRMs.
Purpose As the new energy vehicle industry advances, the demands for motors’ speed regulation range and power density are steadily rising. This paper aims to design a motor that combines high efficiency with a wide high-speed range and high power density. To achieve this, a negative-salient permanent magnet synchronous motor is proposed (NSPMSM). Design/methodology/approach This paper presents a new NSPMSM topology for vehicles, which is based on the conventional interior permanent magnet synchronous motor. Firstly, the current trajectories in various operating regions of the NSPMSM are analyzed, along with the effect of the saliency ratio for the distribution of dq-axis current. Secondly, the field-circuit co-simulation framework is built based on the finite element method, using Maxwell-Simplorer-Simulink Real-time data exchange between different software tools allows for transient simulation of the model under varying operating conditions. Through simulations, the laws of distribution of dq-axis current, current variations under changing conditions, and transient data of the NSPMSM are verified. Additionally, the speed range of constant power and full-speed domain efficiency of the NSPMSM are analyzed. Findings The results indicate that compared to conventional motors, the NSPMSM increases the speed range from 4.5:1 to 6.5:1, effectively broadening speed range of the motor, while also improving efficiency under high-speed operating conditions. Originality/value The proposed NSPMSM can effectively increase power density and expand the motor’s speed regulation range.
Purpose This paper aims to propose a deterministic framework for the robust synthesis of microstrip filters and multiplexers under manufacturing-induced geometrical uncertainties, ensuring bounded passband ripple and steep out-of-band attenuation under worst-case deviations. Design/methodology/approach A distortion-aware extremal polynomial framework is developed by reformulating the Chebyshev optimality condition to include bounded root perturbations dictated by manufacturing-yield statistics. Probabilistic tolerances of critical geometrical parameters are mapped to electrical deviations and subsequently to admissible polynomial root variations through a yield-based statistical model. Constrained optimisation reshapes the polynomial response so that all passband extrema remain within prescribed ripple limits while preserving sharp out-of-band attenuation. The optimised polynomials are back-annotated to the physical structures and validated using full-wave finite-element simulations. Findings Validation on two microwave structures shows that the optimised designs maintain return-loss ripple within specifications under worst-case geometrical deviations while preserving steep out-of-band rejection. Among the proposed schemes, the recursive optimisation method provides the strictly minimax solution. Originality/value The proposed framework enables deterministic worst-case robustness under fabrication uncertainties. Unlike Monte Carlo or sensitivity-based approaches, robustness is enforced directly at the synthesis stage with minimal simulation cost, making the method well-suited for yield-driven industrial microwave and electromagnetic compatibility applications.
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.
