638 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 3, MAY/JUNE 2002 Evaluation of Third Harmonic Component Effects in Five-Phase Synchronous Reluctance Motor Drive Using Time-Stepping Finite-Element Method Longya Xu, Senior Member, IEEE, and Weinong N. Fu Abstract—Interaction of the third harmonic magnetic field with the third harmonic current in a five-phase synchronous reluctance motor (SynRM) can produce additional torque. However, it is still not clear about the SynRM power factor and its impact on the asso- ciated power converter because of the third harmonic components. Using time-stepping finite-element method, a mathematical model of the SynRM, which allows any desired harmonic component in computation, is presented. Performance of the five-phase SynRM with two rotor structures has been computed. The study finds that contribution of the third harmonic current to the output torque depends on the rotor structures. It is also shown that the required terminal voltage to regulate the desired current waveform is sub- stantially increased, a result not reported before. Index Terms—Finite-element methods, synchronous reluctance motor, third harmonic, time stepping. I. INTRODUCTION T HE synchronous reluctance motor (SynRM) has been favorably used because of the simple rotor structure, high reliability, and low cost. However, the SynRM’s poor power/torque density has always ben of great concern. Many types of reluctance rotor structures have been researched to improve the SynRM power/torque density. Another approach to the poor power/torque problem is to add a proper level of third harmonic current to interact with third harmonic magnetic field in the SynRM. The principle and method of adding third harmonic current by using a five-phase stator have been well discussed by the circuit approach [1]–[5]. However, accurate modeling of the SynRM still needs be done to address issues related to optimal electromagnetic design and complete evalu- ation of the overall system with harmonic excitation, including power converter and controller [1], [2]. As pointed out by recent publications, the SynRM, normally excited with sinusoidal current, now can be excited by a solid-state power converter with any desirable waveforms. It is found that adding proper third harmonic current to the funda- mental component to reshape the spatial magnetomotive force (MMF) for a peaked or flat-topped waveform could result in an increased torque-per-ampere ratio. Studies also indicated that, Paper IPCSD 02–002, presented at the 2000 Industry Applications Society Annual Meeting, Rome, Italy, October 8–12, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. Manuscript submitted for review May 1, 2000 and released for publication February 19, 2002. L. Xu is with the Department of Electrical Engineering, The Ohio State Uni- versity, Columbus, OH 43210-1272 USA (e-mail: xu.12@osu.edu). W. N. Fu is with Ansoft Corporation, Pittsburgh, PA 15219-1119 USA (e-mail: wfu@ansoft.com). Publisher Item Identifier S 0093-9994(02)04525-5. although a three-phase stator winding system cannot support such a desirable third harmonic current circulation, flow of the third harmonic current in a five-phase system is possible. On the other hand, it is still not clear whether injection of third harmonic magnetic field and current may seriously distort the back electromotive force (EMF). It is also not clear whether the required stator terminal voltages to control the current may have to be increased for the desired current shape and the power factor (PF) of the five-phase system may be noticeably reduced, which could lead to an oversized power converter. The literature so far has not addressed the impact of the third harmonic magnetic field and current on the motor and power converter sufficiently. In this paper, a time-stepping finite-element method (FEM) modeling and evaluation is presented to authentically study the performance of the five-phase SynRM with two typical rotor structures. With the rapidly increased computing power of com- puters in recent years, accurate modeling of electric machines using FEM has found favor and become a practical tool [6], [7]. With the time-stepping FEM, the desired current waveform can be taken in any shape and the required maintaining voltage be examined. The merits of this method are its straightforward con- cept and the detailed solution that directly includes the effects of lamination complexity, material saturation, eddy current, rotor movement, and high-order harmonic components of current and magnetic field. Compared to the circuit approach based on con- ventional – transformation and the concept of a matrix of inductance and resistance, the time-stepping field computation mimics the real-time physical operation of the SynRM. Natu- rally, the results from this method are comprehensive and in- structional, not only in terms of internal magnetic field but ter- minal characteristics. It will be shown in the paper that, indeed, the important effects of nonsine current and magnetic field to- ward the motor, the associated power converter, and controller are evaluated directly and effectively. II. SynRM SYSTEM DESCRIPTION A. Stator Structure The stator of the SynRM under investigation consists of a conventional cylindrical structure. It has five phases concen- trated, full-pitch windings with wye connection. The five-phase concentrated windings are placed in space in the sequence of from left to right hand. Here, the initial rotor position is as shown in Figs. 1 and 2 (only a quarter of the cross section is shown in both figures). The rotor rotates in 0093-9994/02$17.00 © 2002 IEEE