H. L. Li

Inclusion of interbar currents in a network-field coupled time-stepping finite-element model of skewed-rotor induction motors

In order to include the interbar currents of skewed-rotor inductor motors in finite-element analysis, a three-dimensional (3-D) model is usually necessary. In this paper a two-dimensional multislice time-stepping finite element method of skewed-rotor induction motors is presented to solve such complicated 3-D problems. It is shown that the network of the rotor cage is coupled to finite-element equations so that the interbar currents in the rotor can be taken into account. By arranging the unknowns and mesh-current equations ingeniously, the resultant coefficient matrix of the global system equations are made symmetrical. Compared with 3-D finite-element methods, the computation time for solving field equations with the proposed method is significantly shorter. The model can be used to estimate the high-order harmonic stray losses in induction motors. A comparison between computed and tested results is also given.

A novel approach to circuit-field-torque coupled time stepping finite element modeling of electric machines

This paper presents a sub-block algorithm for the time stepping finite element solution of problems in which sets of electromagnetic field equations, circuit equations and mechanical equation are coupled together. The proposed method ensures that identical solutions are obtained for the sub-blocks by controlling the step size of the time stepping process. This new method simplifies the process of dealing with coupled-system problems and it also greatly reduces the computation time. A time stepping finite element model of an induction motor is used to demonstrate the proposed method in details.

An effective method to reduce the computing time of nonlinear time-stepping finite-element magnetic field computation

Time-stepping finite-element methods have been widely used to compute the magnetic field of electrical machines. Because the reluctivities of magnetic materials are nonlinear, the finite-element equations have to be solved iteratively. In this paper, an effective method for reducing the computing time of the Newton-Raphson method coupled with the incomplete Cholesky-conjugate gradient algorithm for solving time-stepping finite-element problems is presented. The proposed method is based on a proper prediction of some predefined error tolerances in the iteration processes at each time-stepping finite-element computation. The computational analysis on an induction motor shows that the proposed strategy can reduce the nominal computing time by as much as 50%.

A multislice coupled finite-element method with uneven slice length division for the simulation study of electric machines

To consider the changes of the magnetic field along the axial direction when simulating the operations of electric machines, a multislice circuit-field coupled finite element method is presented. The formulations reported allow unequal division of the axial length of the motor in the multislice model. The proposed circuit-field coupled technique provides a simple, general, and yet systematic way to couple arbitrary circuits with the magnetic field.

A Post-Assembly Magnetization Method of Direct-Start Interior Permanent Magnet Synchronous Motors and Its Finite-Element Analysis of Transient Magnetic Field

A novel post-assembly magnetization method of direct-start interior permanent magnet synchronous motor is presented. The squirrel cages in the rotor are ingeniously used as exciting coils for the realization of magnetization. The advantage is that no special magnetizing fixtures are required. A finite-element method, which addresses dynamic material properties of the magnets and yet can be implemented readily in the software, is presented for finding the parameters of the magnetization circuit. A numerical computation is reported to validate the proposed method.

An Improved Nodal Method for Circuit and Multi-Slice Magnetic Field Coupled Finite Element Analysis

A general and simple method to couple arbitrarily connected circuits and multi-slice magnetic fields in the time stepping finite element analysis of electromechanical devices and electrical machines is presented in detail. The merits of the proposed method are that the sparsity of the finite element equations is improved, the formulations to be described will allow unequal division of the axial length of the motor in the multi-slice model, the stranded windings (with negligible eddy current) and solid conductors (with eddy current) in the field domain can be connected arbitrarily with the external circuits, and the coefficient matrix of the system is symmetrical and the nonlinear power electronic elements can be easily maneuvered in the formulations. As illustrating examples, the proposed approach is used to simulate the operations of a brushless d.c. motor and a hard disk drive spindle motor.

Application of Multi-Stage Diagonally-Implicit Runge-Kutta Algorithm to Transient Magnetic Field Computation Using Finite Element Method

A multi-stage diagonally-implicit Runge-Kutta (DIRK) algorithm is applied to discretize the time variable in transient magnetic field computation using finite element method (FEM). A formulation, which has the same format as the backward Euler (BE) algorithm for both linear and nonlinear problems, is deduced for simple and ready numerical implementation. The DIRK algorithm is compared with the BE algorithm which is an effective and popular algorithm in FEM. The merits and disadvantages of these two algorithms are highlighted. An ingeniously combined algorithm exploiting the merits of both BE and DIRK is presented and a numerical experiment shows that it can significantly improve the accuracy with no additional computing burden. For nonlinear problems, a DIRK nonlinear iteration strategy is presented and it can be shown that the total computing time of one integration time step can be shortened by about 36% without any accuracy loss in the solutions.

A Versatile Finite Element Model of Electric Machines

A versatile numerical model for the simulation of dynamic operations of electric machines and drives is presented, and the formulations of the model are described in detail. To consider the field changes along the axial direction, the magnetic field equations are derived using the multislice finite element method. A systematic and simple method to couple the arbitrarily connected external circuits with the multislice magnetic fields using the nodal method is also presented. Because the system equations are derived directly from the fundamental formula describing the machine construction, the model can be applied to simulate the operations of an induction motor, synchronous motor, and brushless d.c. motor. The examples reported include a critical study of a synchronous motor with its windings connected in star and delta, the calculation of the interbar current losses in the rotor cage of an induction motor, and the computation and comparison of the stator phase current waveforms of a brushless d.c. motor with its corresponding experimental results. Moreover, the study also includes the estimation and comparison of the output torque profiles of a five-phase synchronous reluctance motor with its two different rotor structures, the computation of the stator current with or without third harmonics, as well as when the rotor has nonskewed or skewed magnetic poles. In other words, a wealth of examples are reported in this paper to illustrate the versatility and superiority of the proposed algorithm when compared to conventional techniques.

A Multi-Slice Finite Element Model Including Distributive Capacitances for Wireless Magnetic Resonant Energy Transfer Systems With Circular Coils

A multi-slice finite element model for wireless magnetic resonant energy transfer systems with circular spiral tape coils is presented. As the system is constructed using distributive capacitance, it is difficult to determine the parameters in the equivalent circuits analytically. To address the aforementioned problem, a multi-slice axisymmetric finite element method (FEM) is applied to analyze this wireless power transfer system. The merits of the proposed method are that three-dimensional FEM is not required and yet the distributive capacitances among the coils can be fully included in the proposed two-dimensional model. Compared with normal axisymmetric FEM without multi-slices, the proposed method can include the effect of distributive capacitance to produce more precise solutions. The proposed method is validated against experimental data.

Precise Magnetic Field Modeling Techniques of Rotary Machines Using Transient Finite-Element Method

A general and precise method to model rotary machines based on transient magnetic field computation using finite-element method (FEM) is presented. The merits of the proposed method are that the nonlinear iteration on the rotor position can be avoided. Formulas to predict the rotor position and speed of the machine are deduced based on Taylors expansion. A curvilinear element is used on the two sides of the sliding surface to reduce the numerical noises arising from mesh rotation. The proposed methods for dealing with matching boundary conditions and periodic boundary conditions are very general, accurate and flexible. Typical numerical experiment shows that the numerical error of the local magnetic potentials on the motion sliding surface is only one twentieth of that of traditional interpolation method.