Calculation Of Eddy Current Losses Research Articles

Performance Analysis of High-Speed Electric Machines Supplied by PWM Inverters Based on the Harmonic Modeling Method

This paper presents a method for the performance analysis of high-speed electric machines supplied with pulse-width modulated voltage source inverters by utilizing a fast analytical model. By applying a strict mathematical procedure, effective expressions for the calculation of rotor eddy current losses and electromagnetic torque are derived. Results obtained by the approach suggested in this study are verified by the finite element model, and it is shown that the proposed method is superior in comparison to the finite element method in terms of computation time. The proposed method enables fast parameter variation analysis, which is demonstrated by changing the inverter switching frequency and electric conductivity of the rotor and analyzing the effects of these changes on rotor eddy current losses. The presented work separately models effects of the permanent magnet and pulse-width modulated stator currents, making it suitable for the analysis of both high-speed permanent magnet machines and high-speed induction machines.

Core loss analysis of soft magnetic composites considering the inter-particle eddy current loss

Soft magnetic composite (SMC) is composed of ferromagnetic particles surrounded by electrical insulation layer. During the manufacturing process, the electric insulation layer may be destroyed and thus the eddy current will be induced, which makes it difficult to calculate the accurate eddy current loss. In this paper, the inter-particle eddy current loss is calculated at the macro-scale by modeling the actual sample and using the measured conductivity of the sample, moreover intra-particle eddy current loss is calculated by modeling single particle of SMC base on the existing model. Then, under different particle sizes and frequencies, the influence of skin effect on the calculation of eddy current loss is analyzed. Finally, to verify the proposed model, the iron losses of two SMC materials are calculated and they are compared with measured results. It can be seen that when the inter-particle eddy current loss has been considered, then the core loss of SMC will be agreed very well with the measurement results, thus the proposed model can be used for the actual core loss calculation for the electrical machine or other electromagnetic device with SMC cores.

Numerical analysis of eddy current loss of high-speed axial magnetic drive spindle

Eddy currents will be generated in the spindle baseplate to cause energy loss when the axial magnetic force drives the spindle to rotate. Based on the magnetic field theory, the eddy current loss of the outer spindle baseplate of the axial magnetic drive spindle is analysed and calculated in the paper, and the mathematical model is established. The eddy current loss calculation method of axial magnetic drive spindle is proposed, and the factors affecting eddy current loss are analysed by finite element method. According to the analysis results, measures are presented to reduce the eddy current loss: under the condition of meeting the working strength, the outer spindle baseplate should be made of materials with small conductivity and permeability, and the thickness of the outer spindle baseplate should be as small as possible. The analysis results provide theoretical support for the optimisation design and energy consumption reduction of axial magnetic drive spindle.

Two-Step Method for the Calculation of Eddy Current Losses in an Open-Core Transformer

In order to minimize eddy current losses in an open-core type of transformer, a lower width-to-thickness ratio of lamination sheets and even varying lamination stacking direction than in the case of standard transformers are used. Consequently, narrow eddy current loops must be considered as a 2-D phenomenon, i.e., edge effects and irregular current density distributions cannot be neglected. A two-step method for the calculation of eddy currents and eddy current losses in an open-core transformer is presented. In the first step, using the anisotropic surrogate material, the magnetic flux density distribution within the bulk core model is calculated. In the second step, the magnetic flux density obtained in the first step is used as input to calculate eddy currents in a sufficient number of densely meshed 2-D slices of the laminated core. Numerical simulation of the method is carried out, and the results are compared with those obtained using a homogenization method and the brute force approach. The results show good agreement and indicate the importance of taking edge effects into account.

Comprehensive Investigation of Loss Calculation and Sequential Iterative Fluid-Solid Coupling Schemes for High-Speed Switched Reluctance Motors

This article proposes a comprehensive investigation method for loss calculation and temperature rise prediction in high-speed and high-power switched reluctance machines (SRMs). The losses are analyzed in details and the sequential iterative fluid-solid coupling (SIFSC) scheme is proposed for thermal analysis. In the iterative design stage of the SRM, it is important and urgent to figure out the power losses and temperature distribution in the motor, which affects the endurance of the motor operation, such as the maximum speed and highest operating temperature. A simplified finite element (FE) model of a turn and a proximity loss separation method are developed for the skin and proximity (SP) loss reduction. Then, an additional eddy current loss calculation method is developed with a simplified FE model of the winding. Additionally, the SIFSC scheme is further proposed and implemented by sequentially calculating the fluid and solid fields for airflow velocity and temperature distribution. Compared to conventional thermal calculation schemes, the proposed SIFSC scheme is faster than direct coupling methods and more accurate than thermal network methods. The accuracy and effectiveness of this scheme is verified by the simulation and experimental test for a 160 kW and 18000 r/min 6/2 SRM prototype.

Fast calculation of eddy current losses caused by pulse‐width modulation in magnets of surface‐mounted PM machines based on small‐signal time‐harmonic finite element analysis

This study presents a novel method for fast calculating the eddy current losses (ECLs) caused by pulse-width modulation (PWM) harmonic voltages in the permanent magnets (PMs) of surface-mounted PM synchronous machines (SPMSMs) with distributed windings or concentrated windings. Based on the small-signal models of the SPMSMs, the functional relationships between the high-frequency harmonic voltages (HFHVs) in the rotor reference frame and the corresponding ECLs are investigated with the time-harmonic finite element analysis (THFEA). Instead of using complex analytical PM ECL models, the relationships are directly established with some numerical methods, such as the Gauss quadrature and the piecewise cubic Hermite interpolation method, based on the results from THFEA. With the functional relationships, the total PM ECL caused by all the HFHVs is simply calculated by summing the ECL generated by each harmonic component in the spectra of the PWM voltage in the rotor reference frame. Both two- and three-dimensional (2D and 3D) models of the SPMSMs are calculated. Besides, to further reduce the needed steps of 3D THFEA, an equivalent 2D THFEA method using modified PM conductivities under different-axis HFHV excitations is proposed. The merits of the proposed method are validated by comparing with the traditional time-stepping finite element method.

Microstructure Role in Permanent Magnet Eddy Current Losses

The impact of granular microstructure on permanent magnets on eddy current losses is investigated. A numerical homogenization procedure for electrical conductivity is defined. Then, an approximated simple analytical model for the homogenized conductivity able to capture the main features of the geometrical and material dependences is derived. Finally, analytic calculations of eddy current losses are given, and the two asymptotic expressions for losses in the stationary conduction limit and advanced skin effect limit are derived and discussed.

Two‐step method for calculation of eddy current losses in a laminated transformer core

A method for calculating eddy currents and corresponding losses in a laminated transformer core using finite element method is developed. The method is based on the transformation of the 3D model into the corresponding 2D model. The 2D laminated domain coincides with the slice of the 3D laminated domain. Eddy currents are therefore considered as 2D phenomena within lamination, instead of the 1D approximation, thus taking into account the edge effects. By using the 2D mesh, the number of finite elements is drastically reduced. The validity and precision of the method are verified by comparing the results of the simulation with the results obtained using the brute force approach and with the results obtained using the homogenisation method.

Increasing the required slip range of wound induction generator in wind power systems

Eddy currents losses in the rotor in high power generators do not allow operators, under high values of slip, to regulate voltage and control of reactive power flow. The paper presents a method that can accurately estimate the eddy current losses in electric machines with a less complicated procedure. The suggested method allows researchers to analyze and reduce the losses, and consequently, to improve the wind turbine induction generators efficiencies. The given approach, based on the conventional electric machine theory and the parameters supplied by the manufacturers, predicts the eddy current losses theoretically without the need of the measured material loss data or BH curve. Increasing the range of slip variation of induction motor can be achieved by using a rotor of two layers in the radial direction with different parameters. The first layer is a laminated layer of height (h), and the second is a solid (the rotor yoke). The computation of eddy current losses is useful to change the design of the machine to minimize the losses. This paper presents a detailed modeling of the effect parameters on the eddy current losses in wind turbine induction generator.

Investigation of Volumic Permanent-Magnet Eddy-Current Losses in Multi-Phase Synchronous Machines from Hybrid Multi-Layer Model

This paper investigates the permanent-magnet (PM) eddy-current losses in multi-phase PM synchronous machines (PMSM) with concentric winding and surface-mounted PMs. A hybrid multi-layer model, combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series), performs the eddy-current loss calculations. First, the magnetic flux density was obtained from the 2-D generic MEC and then subjected to the Fast Fourier Transform (FFT). The semi-analytical model includes the automatic mesh of static/moving zones, the saturation effect and zones connection in accordance with rotor motion based on a new approach called “Air-gap sliding line technic”. The results of the hybrid multi-layer model were compared with those obtained by three-dimensional (3-D) nonlinear finite-element analysis (FEA). The PM eddy-current losses were estimated on different paths for different segmentations as follow: (i) one segment (no segmentation), (ii) five axial segments, and (iii) two circumferential segments, where the non-uniformity loss distribution is shown. The top of PMs presents a higher quantity of losses compared to the bottom.

Mathematical model and vector control of a six-phase linear induction motor with the dynamic end effect

This study investigates a short primary double-side six-phase linear induction motor (LIM) operating in non-periodic transient conditions. The main purpose is to solve the problems arising from the dynamic end effect. The equivalent circuit method is used for intensively studying the transient time-varying law of eddy current and excitation inductance, and the finite element method is adopted for verification. The calculation of eddy current loss leads to an expression of secondary equivalent resistance. Then, a mathematical model is established for the six-phase LIM involving the dynamic end effect. Furthermore, the matrix reconstruction method is adopted for the coupling of windings. Based on the time-varying characteristics of the model, an improved vector control method that can update the velocity-related correction coefficients through on-line calculation is proposed. During the transient process, the slip frequency and the torque current are modified in real-time to achieve the maximum output thrust of the motor. This approach can compensate for the thrust drop caused by the dynamic end effect, thereby improving the control precision. Simulations and experiments show that the related theory and the proposed control method are feasible and effective.

磁悬浮控制力矩陀螺高速电机绕组涡流损耗计算及热分析

磁悬浮控制力矩陀螺高速电机绕组涡流损耗计算及热分析

An Improved Loss-Separation Method for Transformer Core Loss Calculation and Its Experimental Verification

The separation of core loss plays an important role in the transformer loss calculation. To obtain more accurate core loss, based on the comparison and analysis on two traditional loss separation methods, an improved loss separation method was proposed for the core loss calculation of the transformer in a wide magnetic flux density range. Firstly, through analysis the eddy current loss was obtained by direct calculation, while the hysteresis loss was obtained by performing the quasi-static magnetization process. And the coefficient corrections for the hysteresis loss and eddy current loss calculation were conducted by using the experimental data. The result comparison between the proposed method and traditional ones were made. Secondly, by setting up the Epstein frame platform, the total loss and static hysteresis loss of 14 types of industrial silicon steel were measured. In addition, the suggestive values and the corresponding value range of the loss coefficients of 14 kinds of industrial silicon steel were given. The results obtained by the proposed method were in good agreement with the measured data in the wide magnetic flux density range, while the suggestive values and the corresponding value range of 14 kinds of industrial silicon steel can provides an effective data support for the accurate core loss calculation.

Unstructured–PEEC Method for Thin Electromagnetic Media

In this article, an unstructured–partial element equivalent circuit (PEEC) method for modeling electromagnetic thin regions is proposed. Two coupled circuits’ representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite-element surface mesh. Dynamic effects across the thickness of the sheet are modeled by equivalent complex conductivity and reluctivity. Nonsimply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation. The formulation enables the computation of eddy current losses and can be coupled with external circuits, PEEC cables or coils, thanks to the circuit representation.

Eddy Current Calculation of a High-Speed Slotted Machine With Halbach Magnetization at No-Load Condition

The eddy current and the eddy current loss in permanent magnets (PMs) are important factors in high-speed machine design and performance prediction. The eddy current loss is related to the magnetic field, the shape of magnets, and rotating speed. In this article, the eddy current is analytically calculated with a 2-D method in a high-speed machine with the Halbach magnetization. This analytical method calculates the eddy current with two parts: one part is induced by the instantaneous radial flux density and the other part is induced by instantaneous tangential flux density. The instantaneous radial and tangential flux densities are varying in the PM when the rotor rotates. The flux density in the PM is calculated by the 2-D complex relative permeance method with the SC-Toolbox aid. When the slotted machine operated at no-load condition, the eddy current is analytically calculated in this article based on the instantaneous flux density, and the eddy current distribution in the magnet is compared with the finite-element method (FEM) solutions, the comparison shows that the 2-D analytical method is an effective method for the eddy current and eddy current loss calculation. In the slotted machine with the Halbach magnetization, the eddy current loss increases with the arc angle of the main segment magnet increases, the eddy current loss increases fast at high speeds and cannot be ignored, but Halbach magnetization can reduce it in the high-speed machine as long as the magnetization parameters are chosen properly.

Calculation of Eddy Current Loss in a Tubular Oscillatory LPMSM Using Computationally Efficient FEA

In some special oscillatory applications, especially those operated at high speeds, the eddy current loss of a linear permanent-magnet (PM) synchronous machine (LPMSM) should be fully considered because the loss might be large and concentrated in PMs during the oscillation period. This paper presents a loss analysis method based on computationally efficient finite-element analysis (CE-FEA) for a 20-Hz oscillatory tubular LPMSM. Since the mover speed varies with time, an equally divided model in 1/4 period is introduced to calculate the average PM eddy current loss. The flux density curves in PMs are calculated at 18 intervals by the CE-FEA, through which the change rate of the magnetic flux density is analyzed, considering both the entering and leaving effects and coil end effects. The calculation results show that the eddy current loss is obviously concentrated in PMs near the two ends of coils. The calculation results at a speed of 3.6 m/s obtained by the CE-FEA and two-dimensional and three-dimensional time-stepping FEAs are compared to validate the accuracy. Finally, the proposed method is validated by the experimental test results on a prototype LPMSM.

Computationally Efficient Strand Eddy Current Loss Calculation in Electric Machines

A fast finite element (FE) based method for the calculation of eddy current losses in the stator windings of randomly wound electric machines is presented in this paper. The method is particularly suitable for implementation in large-scale design optimization algorithms where a qualitative characterization of such losses at higher speeds is most beneficial for identification of the design solutions that exhibit the lowest overall losses including the ac losses in the stator windings. Unlike the common practice of assuming a constant slot fill factor s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> for all the design variations, the maximum s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> in the developed method is determined based on the individual slot structure/dimensions and strand wire specifications. Furthermore, in lieu of detailed modeling of the conductor strands in the initial FE model, which significantly adds to the complexity of the problem, an alternative rectangular coil modeling subject to a subsequent flux mapping technique for determination of the impinging flux on each individual strand is pursued. Rather than pursuing the precise estimation of ac conductor losses, the research focus of this paper is placed on the development of a computationally efficient technique for the derivation of strand eddy current losses applicable in design optimization, especially where both the electromagnetic and thermal machine behavior are accounted for. A fractional-slot concentrated winding permanent magnet synchronous machine is used for the purpose of this study due to the higher slot leakage flux and slot opening fringing flux of such machines, which are the major contributors to strand eddy current losses in the windings. The analysis is supplemented with an investigation on the influence of the electrical loading on ac winding loss effects for this machine design, a subject that has received less attention in the literature. Experimental ac loss measurements on a 12-slot 10-pole stator assembly will be discussed to verify the existing trends in the simulation results.

Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation

In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA.

Calculation of Eddy Current Loss on Rotor Surface of Field-Winding type Claw-Pole Motor based on Reluctance Network Analysis

Calculation of Eddy Current Loss on Rotor Surface of Field-Winding type Claw-Pole Motor based on Reluctance Network Analysis

Rotor Eddy Current Loss Calculation of a 2DoF Direct-Drive Induction Motor

A two-degree-of-freedom direct-drive induction motor (2DoFDDIM), whose solid rotor is coated with a copper layer, is capable of linear, rotary, and helical motions and has widespread applications. For solid-rotor motors, the calculation and analysis of rotor total eddy current loss (TECL) are crucial in studying the factors causing such a loss and possible loss reduction methods. In this study, a new nonlinear analytical method considering the saturation of the rotor core is proposed to solve the fundamental magnetic field. The new method divides the time period into segments. The magnetic field distribution at any time is obtained using Maxwell equations. The eddy current losses in the copper layer and rotor core caused by the fundamental magnetic field are calculated. The surface eddy current losses in the copper layer and rotor core caused by harmonics are calculated using a 2D analytical method. TECL is determined by the sum of eddy current and surface eddy current losses. Coefficients are utilized to consider eddy, saturation, and end-region effects when calculating the rotor core TECL. The new method is verified using 3D FEM, and the results show the proposed method has higher accuracy than the original method. The errors of the rotor core and copper layer TECLs are less than 6% and 7.3%, respectively.