IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 11, NOVEMBER 2008 4385 Determining Parameters of a Line-Start Interior Permanent Magnet Synchronous Motor Model by the Differential Evolution Tine Marˇ ciˇ c , Gorazd ˇ Stumberger , Bojan ˇ Stumberger , Miralem Hadˇ ziselimovic ´ , and Peter Virtiˇ c TECES, Research and Development Centre for Electric Machines, Maribor, SI-2000, Slovenia University of Maribor, Faculty of Electrical Engineering and Computer Science, Maribor, SI-2000, Slovenia The line-starting performance and synchronization capability of a line-start interior permanent magnet synchronous motor (LSIPMSM) has to be evaluated by considering different loads and different values of supply voltages, which requires the usage of a reliable dynamic model. In this work the parameters of a magnetically linear lumped parameter LSIPMSM dynamic model were determined by the differential evolution (DE). The optimization objective was the best possible agreement between the measured and by the model calculated time-behavior of model variables. Parameters determined by the DE are used in the LSIPMSM dynamic model, improving agreement between measured and calculated responses of currents and motor speed. Index Terms—Modeling, optimization methods, parameter estimation, permanent magnet motors, squirrel cage motors. I. INTRODUCTION T HE line-start interior permanent magnet synchronous motor (LSIPMSM) presents an interesting and en- ergy-high-efficient alternative for induction motors widely used in low-cost electric drives, where the usage of a current-con- trolled voltage-source inverter is too expensive. Even in these (simple) drives the dynamic behavior is important, because a successful LSIPMSM design has to be able to line-start and synchronize under load. The LSIPMSM has permanent magnets inserted in magnetic flux barriers, which are located in the rotor back-iron, below the squirrel-cage (Fig. 1). The LSIPMSM’s stator structure is the same as of an ordinary synchronous motor. In order to evaluate the LSIPMSM’s line-starting performance, when coupled to different loads and fed with different supply voltages, a reliable dynamic model of the motor is required because its line-starting capability and synchronization capability depends on various LSIPMSM de- sign parameters (e.g., squirrel-cage design and material, design of magnetic flux barriers, placement and dimensions and the value of energy product of permanent magnets). The presence of a squirrel-cage and rotor saliency because of magnetic flux barriers, which have to accommodate the magnetic segments of permanent magnets below the squirrel-cage, present serious obstacles for determining all the needed LSIPMSM model parameters by the finite element method [1] or experimental method [2]. Thus, determining LSIPMSM dynamic model parameters presents an engineering challenge, which is in this work effectively solved by applying a stochastic search algorithm [3], called differential evolution (DE) [4]. In relation to electromagnetic devices, the DE has been previously used in optimization of magnetic bearings [5], electric power system switchgear devices [6], [7] and for determining magnetically nonlinear characteristics of power transformers [8]. In this work a magnetically linear lumped parameter dynamic model of LSIPMSM is presented. Some of its parameters, Digital Object Identifier 10.1109/TMAG.2008.2001530 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Fig. 1. LSIPMSM rotor structure. which are constants, were determined experimentally; others which could not (or were difficult to) be determined using available experimental or numerical methods, were determined by the DE. The optimization objective was the best possible agreement between the measured and by the model calculated time-behavior of model variables. As far as the authors of this paper are aware, this paper for the first time proposes the usage of DE for determining parameters of a LSIPMSM dynamic model. II. LUMPED PARAMETER DYNAMIC MODEL OF THE LSIPMSM The used magnetically linear lumped parameter LSIPMSM model was derived by using the well established modeling pro- cedure for electric rotating machines [9]. The voltage balance in the stator and rotor windings of the two-axis LSIPMSM model (Fig. 2) is described by (1), (2) and (3), (4) respectively. They represent the electrical subsystem of the LSIPMSM and are written in the d-q reference frame, where the d-axis is aligned with the permanent magnet flux linkage vector. The mechan- ical subsystem is described by the torque equation (5) and the motion equation (6). The subscripts and denote variables in the d- and q-axis, respectively; denotes voltages, de- notes currents, is the stator resistance, are the cage re- sistances, are the stator self-inductances, are the mu- tual inductances and are the rotor self-inductances, is the rotor position, is the length of the permanent magnet flux linkage vector, is the moment of inertia, is the electromag- netic torque, is the number of pole pairs, is the load torque, is the coefficient of viscose friction and is the Coulomb 0018-9464/$25.00 © 2008 IEEE