1238 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 Dynamic Modeling, Experimental Characterization, and Veriﬁcation for SRM Operation With Simultaneous Two-Phase Excitation Amit Kumar Jain, Member, IEEE, and Ned Mohan, Fellow, IEEE Abstract—Dynamic modeling of switched reluctance motors (SRMs) is usually done on a per-phase basis. However, in most applications, SRMs are used with simultaneous excitation of more than one phase. Thus, a model accounting for mutual coupling in the presence of magnetic saturation is needed to predict and optimize their performance in terms of efﬁciency and torque ripple. This paper presents a dynamic two-phase excitation model of the SRM. Motor symmetry is used to reduce the amount of ﬂux linkage data needed for the model. An experimental procedure to obtain the ﬂux linkage data is described. Measured ﬂux linkage data for the 8/6 SRM are also included. Details of the simulation model and comparison with experimental waveforms along with their implications for performance prediction are presented. Index Terms—Dynamic modeling, experimental characteriza- tion, switched reluctance motor (SRM), two-phase excitation. I. I NTRODUCTION F OR dynamic simulation purposes, switched reluctance motors (SRMs) are usually modeled on a per-phase basis [1]. The ﬂux linkage data utilized for the electrical equation are obtained with current ﬂowing in only one phase winding. The torque generated by each phase is computed as the derivative of the coenergy associated with that phase. The total torque is then computed as the sum of the individual phase torques. However, in most applications, SRMs are used with simultaneous excita- tion of two or more phases. Thus, it is necessary to account for mutual couplings between different phases. In addition, since SRMs are designed to operate under magnetic saturation, modeling of mutual effects needs to account for saturation due to more than one phase current. A dynamic model that is circuit oriented in nature will be useful for improved prediction of both steady state and transient performance while allowing easy integration with power electronic converter models and controls. In addition, it will provide information for position estimation using mutually induced voltages or ﬂux linkages. SRM models that account for the effects of multiphase exci- tation in the presence of magnetic saturation can be classiﬁed into models based on: 1) the magnetic circuit of the entire Manuscript received November 18, 2004; revised June 13, 2005. Abstract published on the Internet May 18, 2006. This work was supported by the Ofﬁce of Naval Research under Grant N00014-03-1-0153. A. K. Jain is with Peregrine Power LLC, Wilsonville, OR 97070 USA (e- mail: amit_k_jain@ieee.org). N. Mohan is with the Department of Electrical and Computer Engineer- ing, University of Minnesota, Minneapolis, MN 55455-0170 USA (e-mail: mohan@ece.umn.edu). Digital Object Identiﬁer 10.1109/TIE.2006.878310 motor and 2) the terminal quantities of ﬂux linkage and current associated with each phase. The magnetic circuit approach was ﬁrst presented by Moreira and Lipo [2], followed by a more detailed model by Davis and Al-Bahadly [3] to explain experimentally observed mutually induced voltages, and further reﬁnements by Preston and Lyons [4] and Sawata et al. [5]. In this approach, the motor is divided into several reluctance elements; some may be assumed constant, e.g., elements in the stator back iron, some may have position dependence, while some others, especially the rotor and stator pole tips, may have both position and ﬂux dependence. For simulation, the magnetic circuit is modeled as an equivalent electric circuit ideally suited to simulators like SPICE [6] and Saber [7], which are optimized for the solution of network equations. This model requires data to represent all the reluctance elements at different rotor positions and ﬂux levels. Some of these can be approx- imately computed using analytical formulas [4], while others have to be determined either using ﬁnite element analysis ﬁnite- element analysis (FEA) or by experimental measurements. The accuracy of this model depends to a great extent on the number of reluctance elements chosen and the accuracy in modeling each reluctance element. Using the second approach, Panda et al. [8], [9] implemented a model where the total ﬂux linkage of one phase winding (λ a for phase a) is calculated using the single-phase voltage equation. Then, the self-ﬂux linkage of that winding is calculated by subtracting mutual ﬂux linkages due to currents in all the other phases. However, it was assumed that the mutual ﬂux λ a,j (i j ) depends only on the current ﬂowing in phase j , an assumption not true under magnetic saturation. In [10], Michaelides and Pollock considered the case of two-phase excitations with constant phase current for the purpose of machine design. In [11], Pillay et al. discussed sim- ilar effects and presented differences between torque predicted by superimposition in the single-phase model and that predicted by simultaneous excitation. In [11], FEA was used to compute static characteristics for particular current levels at various rotor positions. A dynamic model was not presented. This paper presents a dynamic modeling strategy that ac- counts for the simultaneous two-phase excitation of SRMs. Motor symmetry is used to reduce the amount of ﬂux linkage data needed for the model. The experimental procedure used to measure the required ﬂux linkage data is described. Exper- imentally measured mutual ﬂux linkage data for the 8/6 SRM are presented along with implications. Simulation model imple- mentation and comparison with experimental waveforms along 0278-0046/$20.00 © 2006 IEEE