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

An interior permanent-magnet (PM) 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 delta-connected stator winding.