Eddy Current Loss Model Research Articles

Analytical Modeling of Eddy Current Losses and Thermal Analysis of Non-Uniform-Air-Gap Combined-Pole Permanent Magnet Motors for Electric Vehicles

Analytical Modeling of Eddy Current Losses and Thermal Analysis of Non-Uniform-Air-Gap Combined-Pole Permanent Magnet Motors for Electric Vehicles

Improved 2-D Analytical Model for Rotor Eddy Current Loss of HS PMSMs With Rotor Retaining Sleeve Based on Accurate Subdomain Method

Improved 2-D Analytical Model for Rotor Eddy Current Loss of HS PMSMs With Rotor Retaining Sleeve Based on Accurate Subdomain Method

Numerical Model for Eddy-Current Loss of Wound Core in Single-Phase Transformer

Taking the wound core transformer widely used in the field of traction energy saving as the research object, considering its unique geometric structure, combined with the magnetic circuit theory and finite element calculation of Ansys Maxwell software, the phenomenon of the magnetic flux distortion of the wound core is revealed, and the influence degree of various factors is analyzed; based on the Maxwell equation system of the magnetic quasi-static field, the calculation model of the magnetic flux distortion considering joints is deduced, and then the numerical calculation model of the eddy-current loss of the wound core considering the magnetic flux distortion is presented, which is verified by no-load tests and can reflect the change of the eddy-current loss caused by the geometry of the core with different frequencies and magnetic flux densities, and it can be applied to large-capacity traction transformer with calculation error less than 3%. The numerical model can quickly calculate the eddy-current loss by core structure parameters and material properties without sample preparation and simulation in design stage, which greatly saves engineering cost and can be used for structural design and optimization of the wound core.

Hybrid Network Model for PM Eddy Current Losses Considering Eddy Current Reaction Field and PWM Effects of PM Machine

Hybrid Network Model for PM Eddy Current Losses Considering Eddy Current Reaction Field and PWM Effects of PM Machine

Improved Iron Loss Prediction Models for Interior PMSMs Considering Coupling Effects of Multiphysics Factors

This article presents improved iron loss analytical prediction models for interior permanent magnet synchronous motors (IPMSMs) used in electric vehicles. The effects of slotting harmonics, pulsewidth modulation (PWM) carrier harmonics, temperature rise, and mechanical stress are considered in the proposed models. Specifically, by investigating the stator flux density as piecewise linear with trapezoidal waveform, the iron losses in the teeth and yoke regions are calculated separately, considering the different magnetic field distributions and waveforms. To deliberate the PWM harmonic influence, a correction coefficient is added to the hysteresis loss models, while the eddy current loss models are updated by summing all the eddy current losses caused by the power supplying current harmonics. Moreover, the coupling interaction effects of magnetic, thermal, and stress fields on the empirical coefficients of hysteresis and eddy current losses are analyzed in detail and also implemented in the iron loss prediction process. The feasibility and superiority of the proposed models are verified by numerical and experimental case studies on an IPMSM prototype.

Investigation of Bessel Functions in Analytical Modeling of Rotor Eddy Current Losses in PM Machine Rotor With Copper Shield

In high-speed surface-mounted permanent magnet (SPM) brushless machines, time- and space-harmonic excitations can induce significant eddy currents flowing in the rotor conductive parts. An effective measure to suppress the eddy currents is to employ a copper shield between the magnets and the retaining sleeve. In this article, a Fourier-based analytical model is proposed to evaluate the rotor eddy current losses. The model is set up in the cylindrical coordinate system and is able to compute the eddy current fields and losses in all rotor domains, that is, the sleeve, shield, magnets, and shaft. Although it is generally believed that both ordinary Bessel functions (OBFs) and modified Bessel functions (MBFs) are workable for solving the magnetic vector potential, it is argued in this article that only the MBF-based models are numerically stable when the high-conductivity domain (e.g., the copper shield) exists, while the OBF-based models may result in irrational results. Both the OBF- and MBF-based analytical models for a prototype motor are established and comparatively studied, with verification of the finite-element (FE) method. Moreover, the cause of losing analysis accuracy in the OBF-based models is revealed.

Volumic Eddy-Current Losses in Conductive Massive Parts with Experimental Validations

In this paper, the analytical determination of volumic eddy-current losses in rectangular-shaped conductive massive parts is presented with experimental validations. Eddy currents, as well as the resulting volumic losses, are generated by a sinusoidal spatially uniform applied magnetic field. A U-shaped electromagnetic device with a flat mobile armature (or adjustable air gap) is used to measure the eddy-current losses. The experimental device, its instrumentation, and the conductive massive parts are presented in detail in the paper. Thereafter, the magnetic field distribution applied on the conductive massive parts, which is the mean input data for the eddy-current loss model, is studied. A two-dimensional (2D) numerical model, under the FEMM software, for the magnetic field calculation was also developed. A comparative analysis between the experimental measurements and the numerical results allowed the distribution of the applied magnetic field to be accurately validated. In the final phase, the objective was to estimate the volumic eddy-current losses in rectangular-shaped aluminium conductive massive parts generated by the variation of this applied magnetic field. An analytical model, based on the Maxwell–Fourier method, for the accurate prediction of eddy-current losses has also been developed. An electromagnet with and without the conductive massive parts is characterized in terms of power consumption. By using the power conservation method (i.e., Boucherot’s theorem), the eddy-current losses could be quantified experimentally. The influence of segmentation is also studied. The analytical results are compared to the experimental test results.

Kinematic model of bulk acoustic wave antenna considering magnetic damping

The bulk acoustic wave (BAW) antenna suffers from eddy current loss as well as magnetic damping loss, which are important factors affecting the performance of the antenna. The Lorentz force generated from piezomagnetic layer during the radiation process of BAW antenna is solved based on the eddy current loss model constructed previously. Then a kinematic model of BAW antenna considering magnetic damping is constructed by introducing the acoustic resonance model. A finite element analysis (FEA) model for magnetic damping behavior of BAW antenna is developed to verify the analytical model. The results from the numerical simulation and the theoretical calculation are in good agreement, which verifies both the analytical model and FEA modeling method. Finally, the resonant displacement of BAW antenna with different thickness ratios of piezoelectric and piezomagnetic layers is studied by the verified kinematic model. It is found that the antenna has the maximum resonant displacement when the thickness ratio is 1:1.

Analytical Model and Experimental Verification of Permanent Magnet Eddy Current Loss in Permanent Magnet Machines With Nonconcentric Magnetic Poles

Permanent magnet synchronous motors (PMSMs) with nonconcentric magnetic poles (NCMP) structure are widely used as high-precision servo motors. The current subdomain method mainly equates the NCMP to a rectangular magnet to make each subdomain boundaries of magnet parallel when calculating the magnet eddy current loss (ECL), which results in a lower accuracy of the calculation. This article divides the NCMP into nonconcentric region and concentric region along the radial direction. The nonconcentric region is further divided along the circumferential direction, and each divided region has a single thickness. Based on the subdomain method, a novel analytical method of magnet ECL in PMSMs with NCMPs is proposed. Moreover, the three-dimensional distribution coefficient of ECL in the NCMP is derived by the equivalent impedance method. The effects of eddy current reaction and stator slotting are taken into account to improve the calculation accuracy. Then, through theoretical derivation, the relationship between the minimum magnet loss and the pole parameters is obtained, which provides a reference for the design of NCMPs. Finally, the loss separation experiment is performed on four prototypes with NCMPs. The experimental results, finite element method results and analytical results are compared to verify the correctness of the model.

An improved eddy current loss model over broadband frequency range

To accurately predict the eddy current loss of silicon steel laminations over broadband frequency range, an improved parametric magneto dynamic model (IPMD) is proposed in this paper. According to the nonuniform distribution of magnetic field in the cross-section of the silicon steel lamination under high-frequency magnetization, the analysis area of the lamination is divided into several slices by nonlinear segmentation, wherein each slice the magnetic field distribution is regarded as uniform. Meanwhile, to accelerate the calculation speed of the IPMD model, the relationship between skin depth and slice number is deduced and verified. Furthermore, the Tellinen (TLN) hysteresis model is used when implementing the IPMD model to further increase the accuracy of eddy current loss calculation.

Eddy Current Loss Model for Ferrite Ring Cores Based on a Meta-Material Model of the Core Properties

A model for estimating the total eddy current losses in ring ferrite cores is proposed, which is based on a microstructure model of the electrical parameters of the material (conductivity and permittivity) and on the solution of the wave equations in the core. The presented model, combined with state-of-the-art estimation of the hysteresis losses, gives good agreement with the core loss measurements, over a wide range of frequencies (10–700 kHz).

Modeling and Suppression of Eddy Current Loss for BAW Magnetoelectric Devices

The conductive magnetic film will produce eddy current loss when it works in a high-frequency band, which will reduce the performance of bulk acoustic wave magnetoelectric (BAW ME) devices. If the eddy current loss is not taken into account in the devices modeling, the models will be seriously distorted. Therefore, combining the Maxwell's equations with constitutive relations of ME material, we define the eddy current loss angle as a figure of merit to evaluate the eddy current loss. Then the models of eddy current loss rate of the potential energy and average radiated power are constructed, respectively. The finite element analysis is used to further validate the analytic model. In addition, the effect of isolation layers on eddy current suppression is studied by using the analytical model. The results show that the analytical solutions match with the numerical simulation results perfectly.

An Improved Core Loss Model of Ferromagnetic Materials Considering High-Frequency and Nonsinusoidal Supply

With the emerging power electronic technologies, numerous electrical devices use high-frequency and nonsinusoidal supplies. Such sources generate complex harmonic fields that overburden the accurate prediction of core losses using the conventional finite element method (FEM). Thereby, to predict core losses under those high-frequency and nonsinusoidal supplies accurately, this study first built a test system for core losses measurement of ferromagnetic materials (e.g., soft ferrite, laminated steels, and nanocrystalline alloy) fed by the square and pulsewidth modulated (PWM) supplies. Then, the loss prediction problems of the classical core loss model under high-frequency and nonsinusoidal supplies are revealed. Afterward, an improved FEM-based core loss model is proposed, which includes a piecewise variable parameters based hysteresis loss model, an eddy current loss model considering different cross sections of magnetic circuit and supply waveforms, and improved excess loss coefficients. Experimental validations on different materials, the nanocrystalline alloy in an 11-kVA intermediate frequency transformer, the ultrathin silicon sheets in a 10-kW high-speed permanent magnet motor, and the nanocrystalline alloy in a 3-kW wireless power transfer system, are conducted systematically. The effectiveness and generality of the improved core loss model were verified.

A Model for Stator Eddy Current Losses Due to Axial Flux in Synchronous Generators at Steady State and under Load Angle Oscillations

The load angle of a synchronous generator connected to a power grid has an eigenfrequency that depends on the operating conditions. The existence of an eigenfrequency can make the generator sensitive to electrical and mechanical disturbances and motivates the use of damper windings and power stabilizing systems. Another reason for keeping load angle oscillations small is that they increase the eddy current losses in the stator core and clamping structure due to axial leakage flux. This is shown with transient finite element analyses and can be explained by a loss model derived from a phasor model of the eddy current loss density.

Eddy Current Loss Model Unifying the Effects of Reaction Field and Non-Homogeneous 3-D Magnetic Field

In this article, a new analytical method is proposed to estimate eddy currents inside linear conductive materials. The novel closed-form formulation takes into account the effects of both conductor reaction field that dominates at high frequencies as well as the spatially non-homogeneous nature of the magnetic field penetrating the material. Although the model is suitable for most kinds of permanent magnet machines, it is particularly useful for Surface-mounted Permanent Magnet (SPM) machines where both of these phenomena are prominent. The numerical implementation of the proposed model, which consists of a combination of the method of images and 4-D Fourier transform, is presented. The model is then validated against 2-D and 3-D finite element models (FEMs) for a simple magnetic circuit, showing good agreement. Finally, the eddy current magnet loss in an SPM synchronous machine is evaluated and results are discussed.

Modeling of Anomalous Eddy Current Losses Due to Movement of Domain Walls in Particles of a Soft Magnetic Composite

Soft magnetic composites (SMCs) are composed of ferromagnetic particles surrounded by electrical insulation. To establish a homogenization technique for the magnetic field analysis of an electrical machine with an SMC core, we have already proposed a method to evaluate the effective permeability and iron loss of the SMC core using a cell model of one particle taking into account the nonlinear magnetic characteristics and eddy currents. However, the measured eddy current loss cannot be represented by using the proposed method. In this article, a 3-D eddy current analysis method modeling the anomalous eddy current loss due to the movement of domain walls in the cell model is developed based on the Pry and Bean magnetic domain model. The effect of the non-uniformity of the domain structure on the anomalous eddy current loss is investigated. It is shown that the measured eddy current loss can be almost represented by adding the anomalous eddy current loss to the classical one.

Eddy Current Losses Analysis and Optimization Design of Litz-Wire Windings for Air-Core Compulsators

Compulsators are popular choices for high-end railgun power supplies. In order to increase the power density, air-core compulsators are proposed by using composite materials instead of ferromagnetic materials. Compared with the conventional iron-core machines, armature conductors of the air-core machines are not surrounded by the ferromagnetic teeth, resulting in the conductors been exposed to highly dense revolving magnetic field, which causes eddy current losses in the conductor strands. On the other hand, high-frequency currents flow through the armature winding during the self-excitation and discharge process, which also causes skin effect and proximity effect losses. Therefore, an effective winding design is essential to ensure proper current density distribution and eddy current losses of armature conductors to avoid local overheating. This paper deduced the calculation model of eddy current losses of a single conductor under alternating magnetic fields and then established the eddy losses calculation model of the air-core compulsator’s armature winding. The expression indicates that the eddy current losses of a conductor are determined by both the radial and tangential components of the flux density, which can be obtained by finite-element analysis. Based on the calculation model, the performance of two particular armature designs (a solid conductor and a compacted type-8 litz wire with the same area) are analyzed and discussed. The conductor eddy current losses are estimated and compared for both designs. Finally, an optimization study is carried out to find the best choice of strand diameter to minimize the total losses.

Development of a Hybrid Analytical Model for a Fast Computation of Magnetic Losses and Optimization of Coaxial Magnetic Gears

This paper focuses on a two-dimensional (2-D) analytical model for a fast computation of magnetic losses due to eddy currents in the permanent magnets as well as iron losses in the ferromagnetic parts within coaxial magnetic gears. The magnetic field distribution is computed in yokes and permanent magnets by solving both Maxwell's equations, whereas for pole pieces, the magnetic field is computed by coupling the previous analytical model with a reluctance network model. Both the eddy current losses and iron losses are determined from this hybrid analytical model. The iron loss model takes into account the temporal and spatial variations of flux density. The eddy current loss model takes into account the magnet splitting. Results of this magnetostatic eddy current loss model are then compared to the results obtained with a 2-D magnetodynamic finite element model. A verification of validity limits is also proposed. The final function of this analytical model is to ensure integration into a set of models in the aim of a global mechatronic optimization of magnetic gears, for their insertion into multimegawatt wind turbines. A preliminary bi-objective, mass-efficiency optimization protocol is subsequently proposed along with an analysis of the computation time reduction via the presented models.

Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers

This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.

Study on eddy current loss characteristics of precision giant magnetostrictive actuator considering magnetic field distribution

In order to accurately calculate eddy current loss of the rod-shaped giant magnetostrictive material, improve the giant magnetostrictive actuator control accuracy of displacement, an eddy current loss model of rod GMM that considering the skin effect was established. Firstly, the traditional eddy current loss of rod-shaped GMM was deduced, then discussed the influence of the skin effect for the inside magnetic field distribution of GMM rod, finally analysed the temperature characteristics of GMA through the comsolmultiphysics finite element numerical analysis method. Compared with traditional eddy current loss, under low frequency the two methods has same result, but under high frequency the new model can be more accurately calculate the eddy current loss of rod-shaped GMM. The research result has a great significance for improving the control precision and advancing the study of eddy current loss of GMA.