Time-periodic Finite Element Method Research Articles

Performance of Krylov subspace method with SOR preconditioner supported by Eisenstat’s technique for linear system derived from time-periodic FEM

PurposeThis paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system derived from the time-periodic finite element method (TP-FEM). To solve the time domain electromagnetic field problem with long transient state, TP-FEM is very useful from the perspective of rapidly achieving a steady state. Because TP-FEM solves all of the state variables at once, the linear system derived from TP-FEM becomes the large scale and nonsymmetric, whereas the detailed performance of some preconditioned Krylov subspace method is not reported.Design/methodology/approachIn this paper, BiCGStab and BiCGStab2 are used as the linear solver for a large-sparse nonsymmetric linear system derived from TP-FEM. In addition, incomplete LU (ILU) factorization is applied as a preconditioner to compare SOR supported by Eisenstat’s technique. As examples, the pot-type reactor and three-phase transformer is analyzed.FindingsIn the problem of the pot-type reactor, when SOR preconditioner supported by Eisenstat’s technique is applied to BiCGStab and BiCGStab2, the elapsed time can be reduced dramatically. However, in the problem of the three-phase transformer, the iterative process of the linear solvers with SOR preconditioner is not terminated, whereas the iterative process of linear solvers with ILU preconditioner is terminated. The preconditioner that can be supported by Eisenstat’s technique is not necessarily appropriate for the problem to derive from TP-FEM.Originality/valueIn this paper, the affinity of preconditioned linear solver supported by Eisenstat’s technique for the nonsymmetric linear system derived from TP-FEM is demonstrated.

Enhancement of convergence characteristics of Newton-Raphson method with line search for nonlinear eddy current analysis based on time-periodic FEM

PurposeThe paper aims to improve convergence characteristics of the Newton–Raphson (NR) method applied to time-periodic finite element method using various line searches, as time-periodic finite element method causes deterioration of convergence characteristic of nonlinear analysis based on NR method. The study also aims to accelerate and improve accuracy of electromagnetic field analysis for improvement of the performance of electrical machine.Design/methodology/approachThe paper proposes new type line searches that set approximate step size for NR method. The line search evaluated step size using higher-order interpolation of functional derivative. In addition, two criteria for applying these line search were proposed. First method set one scalar value for every NR iteration that is named constant step size. Second method define different step size in each time step of time-periodic finite element method to update solution vector that is named different step size.FindingsThe paper provides efficient line searches to improve convergence characteristics for NR method. Nonlinear magnetic field analysis of two transformer models is demonstrated. The proposed methods achieve the following results: higher-order functional NR is efficient in improving convergence characteristics, and the proposed methods succeeded about twice faster in both models.Originality/valueThe paper fulfills improvement of convergence characteristics of the NR method applied to time-periodic finite element method using proposed line searches and accelerate electromagnetic field analysis.

Comparison of 2 methods for the finite element steady‐state analysis of nonlinear 3D periodic eddy‐current problems using the A,V− formulation

AbstractTwo different techniques for the analysis of nonlinear, periodic eddy‐current problems are compared using a three‐dimensional benchmark problem. The methods are the parallel time periodic finite element method and the time periodic fixed‐point technique.

Asymmetrical DC bias analysis of the no‐load series transformer by using the TPFEM

The time-periodic finite element method (TPFEM) is coupled with circuit equations to study the asymmetrical DC bias problems of series transformer in this study. The periodic characteristics of the current and the magnetic field are taken as the restraint conditions. Taking into account the external voltages and determining the equivalent thickness of the two-dimensional magnetic system by calculating the magnetic field energy, the field–circuit coupled time-periodic finite element equations are built. The locally convergent fixed-point method is used to solve the non-linear time-varying equations by updating the fixed reluctivity. The calculated results agree well with those measured on a no-load low-voltage series transformer prototype under asymmetrical DC bias, which verifies the effectiveness of TPFEM in the DC bias calculation. The characteristics of the no-load series transformer prototype under asymmetrical DC bias are analysed based on this method.

Steady-State Algorithms for Nonlinear Time-Periodic Magnetic Diffusion Problems Using Diagonally Implicit Runge–Kutta Methods

A general framework is presented for the formulation of steady-state simulation algorithms for magnetically nonlinear eddy-current problems using implicit Runge-Kutta (RK) methods. A close analogy is drawn between equations discretized using the backward-Euler method and fully implicit RK methods. Detailed formulations of the time-periodic finite-element method (TPFEM) and the shooting-Newton method (SNM) are derived using the popular family of diagonally implicit RK (DIRK) methods. Both algorithms employ the generalized minimum residual method to solve the linear equations arising at each Newton iteration. The benefits of higher-order DIRK methods are demonstrated by simulating a surface mount permanent magnet synchronous machine. The effects of using a solid versus a laminated rotor back iron on the simulation time are examined. Simulation results indicate that the performance of TPFEM and SNM is quite similar and much faster than transient analysis.

Time-Domain Parallel Finite-Element Method for Fast Magnetic Field Analysis of Induction Motors

This paper investigates the effectiveness of the time domain parallelization in magnetic field analyses of practical electric machines. We propose an efficient procedure to parallelize transient as well as steady-state analyses by generalizing the formulation of the parallel time-periodic finite element method. The proposed method is called the time domain parallel finite element method (TDPFEM) because it can be applied to both transient and steady-state analyses. Additionally, we derive a special condition of the slip to reduce computational costs for steady-state analyses of induction motors by using a half-cycle polyphase time-periodic condition.

Parallel Time-Periodic Finite-Element Method for Steady-State Analysis of Rotating Machines

This paper investigates the parallelization of the time-periodic finite-element method in nonlinear magnetic field analyses of rotating machines. The developed method, which can obtain the steady state solutions directly, provides large granularity even in the small-scale problems compared with the ordinary parallel FEM based on the domain decomposition approach. Furthermore, we apply the parallel TPFEM to analyses of induction motors which have different time periodicities in stator and rotor regions due to the slip. Numerical results verify the effectiveness of the developed method.

Convergence Acceleration of Time-Periodic Electromagnetic Field Analysis by the Singularity Decomposition-Explicit Error Correction Method

This paper proposes a novel method for the improvement of the convergence to a steady state in time-periodic transient nonlinear eddy-current analyses. The proposed method, which is based on the time-periodic finite element method and the singularity decomposition-explicit error correction method, can extract poorly converged error components corresponding to the large time constants of an analyzed system. The correction of the extracted error components efficiently accelerates the convergence to a steady state. Numerical results verify the effectiveness of the proposed method.

Analysis of Induction Motor Using Field-Circuit Coupled Time-Periodic Finite Element Method Taking Account of Hysteresis

A new method to simulate the steady-state magnetic fields of blocking up for induction motor is proposed. The field-circuit coupled model is combined with time-periodic finite element (FE) method to reduce the CPU time. The inductances and resistances of the stator end windings and the rotor end rings are considered in the loop circuit equations. In order to take account of the local magnetic saturation and hysteresis in the steel core, the Preisach model is incorporated in the time-periodic finite element method. An example for a two-pole three-phase induction motor is analyzed with this method. The calculation results of time-stepping method and time-periodic finite element method are compared.

Improvement of Convergence Characteristic in Nonlinear Transient Eddy-Current Analyses using the Error Correction of Time Integration based on the Time-Periodic FEM and the EEC Method

This paper proposes novel techniques for the improvement of the convergence characteristic of step-by-step time integrations in nonlinear transient eddy-current analyses. The proposed methods, which are based on the time-periodic finite-element method and the explicit error correction method, can extract poorly-converged error components corresponding to large time constants of an analyzed system. The correction of the extracted error components accelerates the convergence of transient calculation efficiently. Furthermore, we extend the performance of the proposed methods in nonlinear problems. Some numerical results that verify the effectiveness of the proposed methods are also presented.

Time-periodic finite-element method for hysteretic eddy-current analysis

The time-periodic finite-element method is applied to hysteretic eddy-current analysis. A new method for determining the relaxation factor of Newton iteration is proposed for fast convergence to periodic solutions. The influence of hysteretic terms in the Jacobian matrix on the Newton iteration is discussed. Application examples show that the proposed method efficiently yields periodic solutions for both hysteretic and nonhysteretic eddy-current fields.

Practical analysis of 3-D dynamic nonlinear magnetic field using time-periodic finite element method

A practical 3-D finite element method using edge elements for analyzing stationary nonlinear magnetic fields with eddy currents in electric apparatus, in which the flux interlinking the voltage winding is given, has been proposed. The method is applied to the analysis of magnetic fields in the Epstein frame. >

Time-periodic finite element method for nonlinear diffusion equations

A new numerical calculation method, the time-periodic finite element method, for the nonlinear diffusion equation is proposed. In the method, the equation is closed by the periodic-time of electrical characteristics and is solved by the numerical procedure which is used not for the initial value problem but for the boundary value one. The method is applied to the calculations of the voltage across the nonlinear corona shield region of a rotating machine. The results demonstrate that the method extensively reduces the computing time without losing the accuracy compared to the conventionally used methods.

Analysis of characteristics of electromagnet with shading coil by time periodic finite element method

Analysis of characteristics of electromagnet with shading coil by time periodic finite element method

時間周期有限要素法によるくま取りコイル付電磁石の特性解析

時間周期有限要素法によるくま取りコイル付電磁石の特性解析