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The modeling of permanent magnet synchronous motors (PMSM) through the use of a per-phase equivalent circuit presents difficulties due to permanent magnet excitation and the machine's magnetic parameter variations at high operating levels of saturation. This paper describes the development of a two-axis circuit model for PMSM by taking machine magnetic parameter variations and core loss into account. The circuit model can be applied to both surface mounted magnet and interior permanent magnet rotor configurations. A method for online parameter identification based on no-load parameters and saturation level, to improve the model, is discussed in detail. Test schemes to measure the equivalent circuit parameters and to calculate saturation constants which govern the parameter variations are also presented.
Wijenayake et al. (2002) studied this question.