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1、IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 20158100504 A New Decoupled Analytical Modeling Method for Switched Reluctance Machine Shoujun Song, Man Zhang, and Lefei Ge School of Automation, Northwestern Polytechnical University, Xian 710072, China This paper proposes a new decoupled analy
2、tical modeling method for switched reluctance machine (SRM). The fl ux linkage is represented by a second-order Fourier series, and the coeffi cients of the series are position dependent, which can be further expressed by another second-order Fourier series. The proposed method only needs 21 data po
3、ints from fi ve rotor positions. Then, the static torque characteristics are analytically obtained based on the expression of the fl ux linkage. The accuracy of the method is verifi ed by comparing the calculated fl ux-linkage and static torque characteristics with those from measurements. With the
4、calculated fl ux-linkage and static torque data, the dynamic performance of SRM is simulated under both motoring and generating mode. The simulation results, such as phase current and mechanical characteristics, agree well with those from the experiment, which further proves the effectiveness of the
5、 proposed method. IndexTermsDecoupledanalyticalmodel,dynamicperformance, fl uxlinkage,Fourierseries,switchedreluctance machine (SRM). I. INTRODUCTION S WITCHED reluctance machine (SRM) has simple and rugged structure, high effi ciency and reliability, wide speed range, fl exible control, and low cos
6、t, and it is suitable for working in harsh environment, such as high speed and high temperature. Due to these outstanding advantages, SRM has attracted increasing attention 1, and is competitive in many fi elds, including aviation industry, electric vehicle, wind power generation, household applianc
7、es, and so on 24. It is relatively diffi cult to derive an accurate mathematical model for SRM due to its doubly salient structure and saturated magnetic fi eld, which result in strong nonlinearities in fl ux-linkage and static torque characteristics 5. However, for performance prediction and advanc
8、ed control of SRM, an accurate model is critical. There are several approaches to build the model of SRM, such as lookup table techniques 6, magnetic equivalent circuit analysis 7, neural network (NN) 8, and fi nite- element method (FEM) 9. Magnetic equivalent circuit analysis and FEM are complex an
9、d time consuming and intensive computation is needed. The NN and lookup table techniques require numerous sample data from experiments or FEM, which inevitably takes much time. In some literature, analytical modeling methods for SRM have been presented. In 10, an accurate modeling method for SRM is
10、proposed based on exponential function. However, the least square method is adopted to obtain the coeffi cients, which is time consuming. In 11, the Fourier series in expression of current-dependent arctangent function is utilized to build the model of the SRM. However, the coeffi cients in arctange
11、nt function cannot be directly calculated and the accuracy of the model depends on the method used for curve fi tting. Effective modeling methods for SRM based on Fourier series are also proposed in 12 and 13, but the process to determine the coeffi cients of the series is relatively complex and/or
12、needs numerous sample data. Manuscript received May 19, 2014; revised August 23, 2014; accepted October 8, 2014. Date of current version April 22, 2015. Corresponding author: S. Song (e-mail: ). Color versions of one or more of the fi gures in this paper are available online at http:/ieeexplore.ieee
13、.org. Digital Object Identifi er 10.1109/TMAG.2014.2363214 In this paper, a new method to calculate the fl ux-linkage and static torque characteristics of SRM is proposed based on Fourier series expansion. The complicated and nonlinear infl uences of phase current and rotor position on fl ux linkage
14、 are decoupled and a limited amount of sample data is required to determine the coeffi cients of the Fourier series. By the proposed formula, the fl ux linkage and static torque with any phase current and rotor position can be calculated easily. The validity of the proposed method is verifi ed by co
15、mpari- son between calculated and measured characteristics. Finally, based on the characteristics obtained by the proposed method, the dynamic simulation model of SRM is built in MATLAB. The simulation results under different operation conditions are compared with those from experiments, and errors
16、between them are fairly small, which further demonstrates that the proposed method is effective and accurate. II. DECOUPLEDANALYTICALMODELINGMETHOD To improve the utilization ratio of material, SRM always operates with certain saturation, which results in nonlinear electromagnetic characteristics. The fl ux linkage (,i) is a function of phase current and rotor position, which can be analytically presented by the following Fourier series: (,i)=a
