Comparison of Finite-Element-Based State-Space Models for PM Synchronous Machines

Abstract

An interior-permanent-magnet motor is modeled by a combined analytical-numerical approach, in which the relationships between the stator currents and flux linkages are identified with static finite-element (FE) analysis. In addition to the previous approaches using the current space vector as the state variable, new models are also developed using the flux linkage space vector, which leads to more convenient time integration of the voltage equations. In order to account for the zero-sequence effects in delta connection, the models also include either the zero-sequence flux or current as an additional state variable. Finally, the possibilities of deriving the required quantities as partial derivatives of the magnetic field energy are discussed. The energy-based approaches avoid inaccuracies related to torque computation and thus allow better satisfying the power balance in the state-space model. We show the ability of the developed state-space models to predict the currents and torque equally to a nonlinear time-stepping FE model with much less computational burden. The results are validated by means of measurements for a prototype machine in both star and delta connections. In addition, we also demonstrate the effect of the zero-sequence current on the torque ripple in case of a deltaconnected stator winding.