Time-harmonic Finite Element Analysis Research Articles

Fast Calculation of Electromagnetic Forces in IPMSMs Under PWM VSI Supply Based on Small-Signal Time-Harmonic Finite Element Method

This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines (IPMSMs) under pulse width modulation (PWM) voltage source inverter (VSI) supply based on the small-signal time-harmonic finite element analysis (THFEA), which has been successfully utilized for fast calculating the PWM-induced losses in silicon steel sheets and permanent magnets. Based on the small-signal THFEA, the functional relationships between high-frequency harmonic voltages (HFHVs) and corresponding airgap flux densities are established, which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra. Then, the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs, which are converted to the electromagnetic force spectra at last. The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis (TSFEA) using PWM voltages as input are within 3.1%, while the proposed method is 24 times faster than the traditional TSFEA.

Fast Computation Method for Stator Winding Skin-Effect Additional Losses in Synchronous Machines With Open Slots and Arbitrary Rotor Geometry

Large medium-voltage electric machine stators are usually equipped with form wound coils made of flat conductors (strands) and embedded in open (rectangular) slots. Air-gap magnetic flux lines can enter the slot and, sweeping the strands placed nearest the slot opening, induce eddy currents in them. Such eddy currents cause additional losses which can be much higher than usual skin-effect and proximity losses. In order to avoid dangerous overheating and hot spots, the additional losses in question need to be carefully predicted in the design stage. Time-stepping finite-element analysis (TSFEA) can be used for the purpose, which however implies a large computational burden and requires the machine geometry to be modeled in detail. This article proposes alternative methods based on time-harmonic finite-element analysis (THFEA) simulations performed on highly simplified machine models and with no need to take rotor motion into account. The proposed methods are shown to produce very accurate results, compared to TSFEA, but with very significant time and computational savings.

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.

Fast calculation of carrier harmonic iron losses caused by pulse width modulation in interior permanent magnet synchronous motors

Normal calculation of the carrier harmonic iron losses (CHILs) brought by the pulse width modulated (PWM) voltage source inverter in interior permanent magnet synchronous motors by the time-stepping finite-element analysis (TSFEA) with short time steps is very time-consuming. In this study, a novel method for fast calculation is proposed, where a combination of the frozen differential reluctivity tensor method and the time-harmonic finite-element analysis is proposed to investigate the relationship between PWM voltage harmonics and the corresponding CHILs, with which the CHILs in stator and rotor are fast-calculated with the voltage harmonics in stator and rotor reference frames, respectively. Besides, the eddy current reaction effect in electrical steel sheets on the CHILs at high frequency is considered by an analytical method and validated with the TSFEA. The results reveal that eight parameters are recommended to calculate the CHILs at different operating conditions, which vary with the fundamental current. Consequently, the CHIL map over the entire operating conditions can be fast-calculated using the analytical spectra of the PWM voltages. Experiment on a specimen is conducted to validate the accuracy of the proposed method, which shows it depends on whether the equivalent differential permeability of the silicon steel can be accurately modelled.

A Hybrid Methodology for Analyzing the Performance of Induction Motors with Efficiency Improvement by Specific Commercial Measures

This paper presents a hybrid methodology to analyze the commercial measures of changing stator windings and adjusting air gap length to upgrade efficiency of typical three-phase direct-on-line induction motors with die-cast copper rotor (DCR). The calculation is carried out through combining the time-stepping and time-harmonic finite element analysis (FEA) and the circuit equivalent circuit model. Typical full-load performance of stator windings with different air gap lengths are computed by MATLAB invoking the 2D transient and eddy current field analysis in ANSYS/MAXWELL. Then, MATLAB scripts about post-processing of the FEA results are used to obtain the full-load running performance including the loss distribution and circulating current. The MATLAB scripts of circuit model built based on the FEA results is used to compare the overload and starting performance. After that, four stators with the four windings and three DCRs with different air gap of an 11 kW motor are fabricated and tested to validate the calculations. By comparing results from both calculations and measurements, it is shown that the factors of stator windings and air gap length can effectively improve the efficiency of the 11 kW DCR induction motor without the addition of extra materials. The motor with the 11/12 pitch Y-Δ series winding and 0.6 mm air gap has the best performance, in terms of efficiency, overloading capability and starting performance. Its efficiency can increase from 90% to the highest 92.35% by sole adjustment of stator winding and air gap length.

Time-harmonic finite element analysis of guided waves generated by magnetostrictive patch transducers

Transducers made of thin magnetostrictive patches and magnetic circuits have been recently developed as an effective means for non-destructive guided wave inspection of elastic structures. However, important characteristics of transducers, such as their wave radiation patterns, have been tested only by experiments or a first-order theoretical analysis. There have been some finite element analyses related to magnetostrictive actuators, but no numerical analysis has been performed to predict the wave radiation patterns of various magnetostrictive patch transducers. In this paper, we formulate a finite element procedure and implement it to predict the wave radiation pattern of a magnetostrictive patch transducer installed on a plate. In particular, a linearized model determining coupling matrix appearing in the magnetostrictive constitutive equation of a magnetostrictive patch in a transducer is developed. The developed model is then used to deal with the arbitrarily polarized static magnetic field induced in the transducers. For numerical efficiency, time-harmonic analysis is carried out and a technique to extract data corresponding to target guided wave modes is used. The validity of the developed finite element analysis is checked by comparing the simulated wave radiation patterns from the present analysis with experimental results. The reasons why certain radiation patterns are obtained for selected magnetic circuits are explained by physical reasoning and simulation results.

Use of Time-Harmonic Finite-Element Analysis to Compute Stator Winding Eddy-Current Losses Due to Rotor Motion in Surface Permanent-Magnet Machines

It is known from the literature that in electric machines with open stator slots, the air-gap flux partly enters the slot openings and induces eddy currents in the conductors placed closest to the air gap, possibly causing local overheating issues. For the study of such phenomenon, time-stepping finite-element analysis (TSFEA) is employed by many authors. This paper presents an alternative approach based on a set of time-harmonic finite-element analysis (THFEA) simulations. The proposed method can be applied to surface permanent-magnet machines and offers the advantage of a shorter computation time with respect to THFEA. It is also more suitable for being integrated into automatic design optimization programs. The accuracy of the approach is assessed by comparing stator eddy-current losses independently computed by THFEA and TSFEA for different machine geometries and operating conditions. Results obtained in the two ways are shown to be in good accordance.

Absorbing boundary conditions for solid waveguides

Abstract We present two simple and effective schemes to formulate absorbing boundary conditions for time harmonic finite element analyses of waveguide structures. An impedance matching condition, applicable to single mode waveguides, is derived as well as an enhanced method for multi-modal wave propagation, making use of guided wave mode orthogonality. Both types are implemented in models generated with standard finite element software. Two examples of ultrasonic transducers attached to cylindrical waveguides are presented.

Axial Flux and Eddy-Current Loss in Active Region of a Large-Sized Squirrel-Cage Induction Motor

This paper analyzes the axial flux and the corresponding eddy currents inside the laminated cores of a large-sized squirrel-cage induction motor running under the steady-state operation in order for possible optimum design of large-sized induction motors used in industry. The analysis was based on a complete 3-D numerical model. In the model, the laminated cores were replaced by anisotropic solid bodies, and the eddy currents inside the end portion of the stator frame were modeled with the standard impedance boundary condition. A time-harmonic finite-element analysis based on the magnetic vector potential-electric scalar potential formulation was performed. According to the results, under steady-state no-load, the axial flux, caused mainly by the air-gap fringing flux and the end-winding leakage flux, appears in the end portion of the cores, and decays rapidly toward the middle of the cores. The corresponding planar eddy currents inside the laminations of the stator core are mainly concentrated near the edges of the stator teeth. The eddy-current loss is small, but the distribution of the loss over the laminations is definitely non-uniform.

Nonlinear time-harmonic finite-element analysis of coupled circuits and fields in low frequency electromagnetic devices

Many electromagnetic devices operate under sinusoidal excitation, in which case a time-harmonic (TH) analysis may be applied; in particular, a TH field solution is much more economic than a time-transient field solution. Although the material nonlinearity cannot be strictly taken into account in the TH case, it determines the true operating condition of the device, together with the external circuit connections. In this paper, an efficient finite-element (FE) formulation to solve the 2D TH circuit-field (CF) problem posed by low-frequency (LF) electromagnetic devices is presented, approximately taking into account the effect of the material nonlinearity. Consideration is given to theoretical aspects that had not been previously studied: the resulting nonlinear complex equation does not possess an exact Jacobian, because one of its terms involves a nonanalytic function. This is circumvented by using pseudo-Jacobians derived from the Cauchy–Riemann expressions. Solid and filamentary conductors may be connected to external circuits of arbitrary topology using a novel Modified Nodal Analysis (MNA) approach. Methods for correcting magnetization curves and calculating the electromagnetic force are proposed. An induction motor test case is used to illustrate the capabilities of the formulation, and the numerical results are compared with those of a validated commercial package.

Analysis of Eddy-Current Loss in End Shield and Frame of a Large Induction Machine

This paper proposes an effective method of analyzing the eddy-current loss within the end shield and frame of an electric machine. The standard impedance boundary condition is applied to the conducting surfaces of complete 3-D models, and the models are solved by time-harmonic finite-element analyses. Measurement of the temperature rise is completed as a validation of the proposed method. The effect of the distances between the conducting surfaces and coil ends is studied by computing the eddy-current loss for a series of 3-D models having different distances. In addition, simplified 2-D models are used to study the influence of material nonlinearity. In brief, the proposed method is feasible in computing the eddy-current loss. The eddy-current loss within the regions close to the coil ends is larger than the other regions in the end shield and frame, but the total loss is quite small, compared, for instance, with the copper loss within the stator winding. Furthermore, the farther the end shield and frame are from the coil ends, the smaller the eddy-current loss is. Finally, it is found that the eddy-current loss is larger in the nonlinear case than in the linear case.

Calculation and Analysis of Stator End-Winding Leakage Inductance of an Induction Machine

This paper proposes an improved method for calculating the value of and for analyzing the frequency-dependence of the stator end-winding leakage inductance of an induction machine. The method was based on the stored magnetic energy, which was calculated by a 3-D time-harmonic finite element analysis. In this method, there were no rotary parts in the model of the simulated machine. The results of the analysis show that the stator end-winding is capable of influencing the end of the active region of the machine whereas the influence on the central part of the active region is small. In addition, the phenomenon that the stator end-winding leakage inductance, as well as the magnetic energy in the machine, relates to the frequency of the stator current is explored.

3-D Finite Element Analysis of Magnetic Forces on Stator End-Windings of an Induction Machine

This paper aims to analyze the magnetic forces on the stator end-windings of an induction machine at full load by a 3-D time-harmonic finite element analysis. Under the steady-state condition, the radial, circumferential, and axial forces all consist of a constant component and a sinusoidal component with a double-frequency. The analysis shows that the forces on the knuckle part of the upper part of a coil end are larger than on the other parts and that the constant components and the amplitudes of the sinusoidal components of the forces on the same positions of different coil ends in a phase belt are nearly different. Finally, the analysis of stresses indicates that the stresses in a coil end, corresponding to the constant components of the forces, are small.

Numerical impulse response test to identify parametric models for closed-slot deep-bar induction motors

An impulse response test for estimating the electrical parameters of a deep-bar induction motor is studied. The impulse response test is performed within the two-dimensional finite-element analysis (FEA). The impulse excitation is applied to the stator voltage. Since the test is suitable for modelling the perturbations about a certain operation point, a small-signal model for the double-cage induction machine is derived. The skin effect is taken into account by using two parallel rotor branches. In addition to the small-signal parameters, the steady-state parameters are also estimated using the time-harmonic FEA. The impulse response test is based on the assumption of linear behaviour about an operation point. Thus, the effects of nonlinearity are studied by several methods.

Time-harmonic finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor

A finite-element model for calculation of eddy-current and circulating current losses in a multi-conductor stator winding of a cage induction motor is presented. In this model, the eddy current formulation of the series and parallel connected stator bars is solved together with the circuit and field equations using a two-dimensional time-harmonic approximation. The Newton–Raphson method is applied to solve the total system of nonlinear equations. The finite-element mesh is discretised finely enough in order to take the phenomena correctly into account. The eddy-current loss distribution of the stator bars and the quantitative results of eddy-current and circulating current losses have been studied with two different conductor arrangements inside the stator slots. The results show that the eddy-current loss in the stator winding is one of the most significant loss components. They also show that the radial position of the stator bars has a remarkable effect on the losses. The radial flux that passes through the stator bars can be guided to stator teeth by using magnetic slot wedge material to reduce the eddy-current loss.

An effective reluctivity model for nonlinear and anisotropic materials in time-harmonic finite element computations

In time-harmonic finite element analysis, the nonlinear behavior of soft-magnetic materials is often modeled by effective reluctivity curves, to account for the time-dependence of the reluctivity during one cycle of the applied sinusoidal signal. In this paper, the effective reluctivity concept is generalized in such a way, that nonlinear and anisotropic materials can be modeled as well. The model is used to simulate the flux line distribution and the loss distribution in a three-phase transformer under no-load operation.