Time-stepping Finite Element Analysis Research Articles

A FEA-Based Fast AC Steady-State Algorithm for a Voltage-Driven PMSM by a Novel Voltage-Flux-Driven Model

Finite element analysis (FEA) has been used more frequently than ever before in electrical machine design covering different disciplines such as electromagnetics, rotor dynamics, thermodynamics etc. The accuracy and speed of FEA are in high demands, especially when the time-stepping FEA is employed in the electromagnetic design of the machine. In this paper, to accelerate numerical transient in FEA of a voltage-driven permanent magnet synchronous machine (PMSM), a fast AC steady-state algorithm has been proposed, in which the voltage supply is converted into the stator flux linkage and the machine can be regarded as driven by the flux linkage directly. The electromagnetic transient is eliminated by injecting additional voltage signals to compensate the oscillating stator flux linkage in transient and the time-stepping error caused by the backward Euler in FEA. And the additional voltage signals will finally disappear after the steady state is achieved within about a half electrical time period. In addition, the maximum torque per ampere (MTPA) control logic can also be realized by adjusting the initial phase angle of the voltage supply based on the vector diagram. The simulation speed of the proposed method in this paper was compared to other traditional models and the accuracy was verified by experimental results.

Influence of Rotor Pole Number on the Output of Double Stator Flux-Switching Machine

Influence of rotor pole numbers on the output performance of a double stator flux-switching permanent magnet machine is investigated and compared in this study. A description of the analyzed machine is first given. Maxwell-2D time-stepping finite element analysis is adopted in estimating the results. The no-load and load characteristics of the investigated machine is considered and quantitatively compared amongst four different rotor pole configurations. The compared machine categories are designated as: 6S/10P, 6S/11P, 6S/13P and 6S/14P, where P stands for rotor pole and S stands for stator slot. It is revealed that the compared 6S/11P machine topology has a lot of good qualities amongst all the compared machine types, since it exhibits the largest electromotive force (EMF), power, torque and greatest overload sustainability feature, etc. Though, the 6S/14P has excellent flux-weakening capability. Moreover, the 6S/13P machine configuration would produce the largest torque if all the compared machines are equipped with same amount of permanent magnet volume/material. The compared machine topologies have reasonably good anti-demagnetization potentials; particularly, the 6S/13P topology.

Hybrid-Excited Variable Reluctance Resolver With Wide Speed Range

The accuracy of the variable reluctance resolver (VR-Resolver) highly depends on the rotational speed and its rotational speed range is limited by the frequency of the excitation signal. To eliminate the mentioned performance dependency, this paper proposes a hybrid-excited VR-Resolver (HVR-Resolver) with two separate sets of excitation windings: a toroidal excitation winding for the AC excitation supply and an on-tooth one for the DC excitation supply. Similar to the conventional method, the HVR-Resolver is working with AC excitation ON and DC excitation OFF at the low-speed range. For high-speed operation, the excitation switched from AC excitation to DC. By using this technique, the proposed HVR-Resolver is able to accurately estimate the position at a wide speed range. This feature makes the HVR-Resolver an outstanding candidate for EV applications. The proposed design is simulated using time-stepping finite element analysis (TSFEA) in order to study the performance at both low-speed and high-speed ranges with different rotor pole numbers. In addition, an optimization process is conducted to find the best rotor shape factors. The experimental test on the proposed HVR-Resolver indicates a close agreement between simulation and experimental results.

Variable-Reluctance Permanent Magnet Resolver Design Guidelines

This article presents the design considerations and geometrical optimization of a variable-reluctance permanent magnet resolver (VRPM resolver). The above-mentioned resolver utilizes permanent magnets (PMs) and magnetic flux measurement units (MFMUs) instead of excitation windings and signal windings. The operating principle of the VRPM resolver is presented, and the geometric and magnetic properties of its various components that influence the accuracy are identified. To study the performance of the resolver, the magnetic equivalent circuit (MEC) model is utilized to ensure both calculation speed and accuracy, while taking saturation and nonlinear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}$ </tex-math></inline-formula> curve effects into account. The developed analytical model is coupled with a multiobjective optimization solver to conduct repetitive simulations and attain an optimal design for the studied VRPM resolver. The objective of the optimization process is to achieve the minimum position error, while simultaneously improving the computational time. Time-stepping finite-element analysis (TSFEA) is used to validate and measure the performance in detail. Finally, experimental tests on a prototyped VRPM resolver are employed to verify the simulation results.

Torque Capability Comparison of Induction and Interior Permanent Magnet Machines for Traction Applications

This paper investigates the torque generating capabilities and performance comparison of induction machines (IM) and interior-permanent magnet (IPM) machines for electric vehicle (EV) traction applications. Electromagnetic performance characteristics, such as torque, torque ripple, air-gap flux density, etc. are quantitatively compared by changing the level of electric loading. Other performance metrics such as saturation factor, power losses, efficiency, and so on, as well as the flux-weakening capability and efficiency map have also been compared. For calculations of the electromagnetic performance characteristics, 2D time-stepping finite element analysis (FEA) has been employed. It has been revealed that due to the reduction in torque components of IPM machine as a consequence of magnet demagnetization, it cannot generate toque as high as IM under overloading operating conditions. A thorough review of the literature on comparative studies on the electrical machines used in EV or Hybrid EV (HEV) applications is also included.

Design of Limited-Angle Wound Rotor Resolvers for High Accuracy and Easy Manufacturability

The limited-angle resolver is commonly employed instead of an optical encoder as a position sensor in medical, special industrial, custom robotics, transportation and military applications owing to their reliability, low cost, and ability to work steadily in harsh and contaminated environments. In the design and optimization of resolvers, achieving high precision while maintaining a simple manufacturing process for mass production is a big challenge. This study proposes a systematic method for the determination of slot and pole number combinations of limited-angle wound rotor resolvers (LAWRRs) for high accuracy and easy manufacturability. A set of stator and rotor slot numbers ranging from 8–64 for 2 and 4 poles, which are suitable for concentric winding (CW) topology, have been considered. For high accuracy, number of turns distribution waveforms and their total harmonic distortion (THD) percentages are investigated. In addition, for easy manufacturability, low slot number combinations providing high accuracy are determined and the feasibility of employing solid core instead of laminated core is examined. Analytical calculation results of the proposed configurations are validated utilizing a two-dimensional time-stepping finite-element analysis (2D-FEA). Finally, in order to experimentally validate the methodology and analyses, two prototypes with low and high slot numbers are manufactured and tested.

Quantitative Analysis of Hybrid-Excited Doubly Salient Machine With Subslot Bottom PMs and Its Comparative Study

This paper proposes a doubly salient machine (DSM) with sub-slot bottom PMs to enhance the torque production. The key is that with auxiliary slot-PM excitation, the stator yoke DC saturation can be mitigated to enhance the torque production capability of DC field excitation, meanwhile additional slot-PM flux can be pushed into the airgap, which can build a parallel excitation and generate additional effective torque. Comparing DC-excited DSM and sub-slot bottom PM DSM (SBPM-DSM), the steady torque can be enhanced by 12.8&#x0025; with the use of sub-slot bottom PMs. In this paper, torque separation effects due to DC field excitation and slot-bottom PMs are quantitatively analyzed with frozen permeability method. By using time-stepping finite-element analysis, the electromagnetic performances of two machines are evaluated. Experimental results verify validity of the proposed design.

Comparative Study of Linear Variable Flux Reluctance Machine with Linear Wound Field Flux Reversal Machine

As members of doubly salient magnetless linear machines, linear variable flux reluctance (LVFR) and wound field flux reversal (LWFFR) machines inherit the merits of conventional magnetless linear machines such as low cost, high flux adjustment capability and high reliability. Furthermore, like linear switched reluctance machine, they have a very simple and compact long secondary, which are very attractive for long stroke applications. However, low force capability is their major defect. To solve this issue, new LVFR and LWFFR machine topologies were proposed in recent work, while lacking studies on their force improvement mechanism and further force evaluation. In this paper, LVFR and LWFFR machines with improved force performance are comparatively studied with the emphasis on their force capabilities. The operation principle of the two machines is analyzed based on magnetic field harmonics produced by flux modulation. Contributions of air-gap flux density harmonic components to no-load back electromagnetic forces of the two machines are analyzed and the average force equation is derived. Moreover, force capabilities of the both machines are investigated by means of the time-stepping finite-element analysis to verify the theoretical analysis.

Performance Improvement of Axial Flux Permanent Magnet Machine with Phase Group Concentrated Coil Winding

This paper suggests a method to improve the performances of the Dual Stator Axial Flux Spoke-type Permanent Magnet (DSAFSPM) machines with phase group concentrated coil (PGCC) windings, by incorporating continuous and discrete step-skewing along with a special winding connection. The purpose of the study is to mitigate the cogging torque and torque ripples while increasing the output torque so it ameliorates the machine performance at minimum cost for various applications such as wind power plants and electric vehicles (EVs). Cogging torque produces noise and vibrations which degrade the machine’s performance and reduces its life span. The proposed winding sequence enhances the output torque by improving its distribution factor along with the use of continuous skew and step-skew magnets. This research work improved the cogging torque and torque ripples with the help of skew techniques while output torque is increased by the proposed winding sequence. Further harmonics and ripples are also mitigated by the proposed winding sequence. The overall machine volume is kept constant along with the magnet size and the design parameters for fair performance analysis. Comparative analysis of these machines is performed using three-dimensional (3-D) time-stepped finite element analysis (FEA). Proposed model I and proposed model II reduce the harmonics by 42% and 23%, respectively. By using continuous skew and discrete step-skew magnets, cogging torque is reduced up to 81.5% and 75%, respectively. This reduction in cogging torque reduces the noise and vibration in machines which assists the machines to perform a smooth operation. The reduction in output torque ripples in proposed model I is 60.8% while that of proposed model II is 59.3%.

High-Fidelity Induction Motor Simulation Model Based on Finite Element Analysis

This article proposes a new high-fidelity simulation model of an induction motor (IM) based on finite-element analysis (FEA). The proposed model enables fast and accurate IM simulation with the inverter circuit model and control algorithm. That is, the proposed model can represent non-ideal features of IM, such as magnetic saturation, spatial harmonics, skew, and saturation-induced saliency in high accuracy. To construct the proposed model, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> equivalent circuit of the squirrel cage rotor is introduced. Based on this, the static FEA is conducted which can accelerate the model construction compared to the conventional time-stepping FEA technique. Then, a flux-based IM model is established, which has advantages on speed, accuracy, and memory size in the simulation. To verify the effectiveness of the proposed model, the models are constructed for two commercial IMs used for the industrial drive. IM control algorithms are tested in various operating conditions on the proposed model. The results are compared with the time-stepping FEA and the experiment for the verification of the proposed model.

Estimation of losses and efficiency of double-stator switched flux permanent magnet machines

Losses such as rotor iron and stator iron losses, magnet eddy current loss, as well as efficiency of a double stator permanent magnet machine having varying rotor pole numbers is estimated and presented in this study. This current investigation would be vital for electrical machine designers in quantifying the amount of losses in the various sections of a given double stator electric machine and as well provide better insight on resulting output efficiency of the machine. Time-stepping finite element analysis (TS-FEA) procedure is adopted in the calculations using ANSYS-MAXWELL simulation software. The compared machines having the same stator teeth/pole number (Ps) and different rotor pole (Pr) numbers are designated as: 6Ps/10Pr, 6Ps/11Pr, 6Ps/13Pr and 6Ps/14Pr. The predicted total loss values at rated current and operating base speed is 13.02 Watts, 13.13 Watts, 13.539 Watts, 13.537 Watts, from the 6Ps/10Pr, 6Ps/11Pr, 6Ps/13Pr and 6Ps/14Pr machine types, respectively. The corresponding efficiency of the machine types at rated working conditions is: 81.76%, 88.17%, 86.95% and 78.61%, respectively. The results show that magnitude of losses in a given machine would largely depend upon factors such as number of rotor poles and hence, the machine’s operating speed, electric loading and angular rotor position of the machine, etc. It is also found that the number of loss waveform cycles (Nc) in an electric revolution of the investigated machine would depend upon its stator and rotor arrangements. The most performing compared machine types are the ones that have 11- and 13-rotor pole numbers, while the least amount of efficiency is obtained from the machine type that has 14-rotor pole number. Above all, the 6Ps/10Pr and 6Ps/14Pr are characterized with high amount of pulsations or ripples and this is detrimental to the overall performance of the machines.

A new dual-ferrite–assisted hybrid reluctance machine with two-stage excitation for starter generator application

Reluctance machines with DC field coil in stator are a competitive candidate for starter generation application, due to the elimination of rare-earth permanent magnet (PM), robust structures, and controllable excitation. However, due to the poor excitation ability of DC field coils, the torque density is disadvantageous. Moreover, with the increase in the DC field current, it is exposed to the risk of extra DC saturation in stator teeth. As a consequence, the torque density and efficiency are both constrained. To solve the aforementioned problems, based on the comprehensive consideration of production cost and torque performance, this study proposed a novel type of hybrid reluctance machine with dual-ferrite–assisted in stator slots. The inner-layer ferrite PM is magnetized tangentially, which can effectively achieve the DC-saturation–relieving effect, while the outer-layer ferrite PM is magnetized radially to increase the machine torque density through the flux modulation effect. Based on finite element analysis, the machine torque density and efficiency can be improved by 20 and 5%, respectively. Furthermore, to simplify the excitation system of the DC terminal, a two-stage excitation method is proposed by splitting some turns of armature winding to feed DC field winding with passive rectifier. No power switching devices are needed for the excitation system in this way, making the system highly robust. The effectiveness of the proposed design is verified by time-stepping finite element analysis.

Fast and Accurate Traction Induction Machine Performance Calculation Method for Integrated Onboard Charging in Vehicle to Grid Application

Reusing traction electric machine windings in electric vehicles as an integrated filtering inductor is a promising solution to reduce the size of the vehicle to grid (V2G) charging/discharging system. Obviously, the integrated inductors need to meet the requirements of traction and charging/discharging, which brings challenge for the design of traction machines. As one of the most popular traction electric machine types, the high-speed induction machine usually has large electrical time constant and consequently unacceptably long transient time in the design stage when finite element analysis is adopted. In this article, a method is proposed to quickly and accurately calculate the steady state performance of the induction machine by time-stepping transient magnetic finite element analysis. First, the stator current magnitude is ramped up from zero to full magnitude gradually to control the DC component in rotor flux and torque. Second, a multistep equivalent resistance method is adopted to decrease rotor time constant and suppress slot-tooth harmonic transient response. The proposed method can predict the FEA computation load before running the calculation, and it does not rely on the machine parameter and feedback signal. Its performance is tested by an example induction machine. The result shows that the proposed method can reduce the finite element calculation time of a high-speed operating point by 99%.

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.

Dynamic Phasor Finite Element Modeling of Grid-Connected DFIG Considering Winding Space Harmonics

This paper presents a new technique for quantifying the winding MMF space harmonics of wind-driven Doubly-Fed Induction Generator (DFIG) for power quality assessments. Instead of following the commercial electromagnetic transient programs in modeling electric machines using lumped-parameters models, the paper uses a combined Dynamic Phase modeling and Finite Element Method (FEM) to model the generator accurately while reducing the computational burden and simulation time associated with the conventional time-stepped finite element analysis. The technique has the ability to efficiently model core nonlinearity and stator/rotor MMF space harmonics. The results of a C++ code written by the authors of the new dynamic phasors FEM technique are compared to the conventional time-stepping FEM to show the capability of the method to produce comparable results in shorter simulation time.

Design and Analysis of Advanced Nonoverlapping Winding Induction Machines for EV/HEV Applications

This paper presents a detailed analysis and design guidelines for advanced nonoverlapping winding induction machines (AIMs) with coil-pitch of two slot-pitches by considering some vital empirical rules and flux-weakening characteristics. The aim of the study is to develop a type of new winding and stator topology for induction machines (IMs) that will lead to a decrease in total axial length without sacrificing torque, power, and efficiency. The key performance characteristics of the improved AIMs are investigated by 2D time-stepping finite element analysis (FEA) and compared with those of IMs having fractional and conventional overlapping and nonoverlapping windings. Compared with the conventional overlapping winding counterpart of the AIM, a ~25% shorter axial length without sacrificing torque, output power, and efficiency is achieved. In addition, the influences of major design parameters, such as stator slot, rotor slot and pole numbers, stack length, number of turns per phase, machine geometric parameters, etc., on the flux-weakening characteristics are investigated. It has been concluded that the major design parameters have a considerable effect on the electromagnetic performance. However, among those parameters, the influences of pole number and stack length together with the number of turns on flux-weakening characteristics are significant.

Coupled Finite Element and Extended-QD Circuit Induction Machine Model, Part I: Formulation

The design of squirrel-cage induction motors (IMs) entails the capability to predict the motor efficiency map with high accuracy over an operating range. In particular, modeling harmonic rotor bar currents becomes important for loss analysis. In theory, it is possible to analyze an induction motor using time-stepping finite element analysis (TS-FEA); however, this is not viable due to computational limitations. To bridge this gap, we set forth a computationally efficient method that couples magnetostatic FEA with a qd-circuit model of the cage. The proposed IM model includes the effects of saturation, winding and slot harmonics, as well as nonuniform current density distribution in the rotor bars. The model is presented in two parts. Part I focuses on the formulation of a qd cage circuit model with segmented bars. Part II is a companion paper that proposes an FEA-based parameter estimation and a solution method.

Analysis and Experimental Verification of the Demagnetization Vulnerability in Various PM Synchronous Machine Configurations for an EV Application

Safety is a critical feature for all passenger vehicles, making fail–safe operation of the traction drive system highly important. Increasing demands for traction drives that can operate in challenging environments over wide constant power speed ranges expose permanent magnet (PM) machines to conditions that can cause irreversible demagnetization of rotor magnets. In this paper, a comprehensive analysis of the demagnetization vulnerability in PM machines for an electric vehicle (EV) application is presented. The first half of the paper presents rotor demagnetization characteristics of several different PM machines to investigate the impact of different design configurations on demagnetization and to identify promising machine geometries that have higher demagnetization resistance. Experimental verification results of rotor demagnetization in an interior PM (IPM) machine are presented in the latter half of the paper. The experimental tests were carried out on a specially designed locked-rotor test setup combined with closed-loop magnet temperature control. Experimental results confirm that both local and global demagnetization damage can be accurately predicted by time-stepped finite element (FE) analysis.

Coupled Finite Element and Extended-QD Circuit Induction Machine Model, Part II: Implementation

This is Part II of a paper that sets forth a computationally efficient method to estimate harmonic rotor bar currents in induction motors for accurate loss analysis. The method couples magnetostatic finite element analysis (FEA) and an extended-qd cage circuit model. In Part I, we formulated two subproblems for determining separate components of the induced rotor currents. Part II begins with details regarding the subproblem solution methods. Second, we set forth an FEA-based parameter estimation for the subproblems. Finally, the proposed model is validated by comparing the estimated cage loss and computational effort against a 2-D nonlinear time-stepping FEA.

A novel doubly‐fed doubly‐salient machine with DC‐saturation‐relieving structure for wind power generation

This paper presents a novel doubly-fed doubly-salient machine (DF-DSM) with DC-saturation-relieving effect for wind power generation application, which possesses the advantages of enhanced torque density, reduced torque ripple and improved power density. The key is that PMs are introduced into the stator slot openings to mitigate the saturation effect in stator core caused by DC field excitation, and relatively large excitation current can be fed into stator field windings, which contributes to improved power density of machine. In addition, with the armature winding artificially connected, the reluctance of all magnetic paths is kept the same, and the variation of self-inductance is compensated, and the torque ripple is greatly suppressed. In this paper, the machine structure and DC-saturation-relieving working principle are introduced. The slot-pole combinations are analysed, and dimension parameters are optimized. By using time-stepping finite-element analysis, the electromagnetic performance of optimal machine is evaluated which verifies the validity of the proposed design.