Modelling of anisotropic synchronous machine in stator-reference frame including torque calculation

Interior permanent magnet-synchronous machines (IPMSM) feature many favourable properties for e-mobility application as high power density and good efficiency. However, they require careful modelling because of strong anisotropies of the rotor, as they are also known from salient-pole synchronous machines. These anisotropies are often accounted for by different values for the d-axis and q-axis inductances in a rotor-flux-oriented coordinate system. With regard to asynchronous machine control, stator-flux-oriented control could provide improved dynamic behaviour - especially in the field-weakening range. The representation of fault conditions inside the machine, leading to asymmetrical machine parameters, suggests a phase-wise description instead of the usual two-component (d-q or space-vector) analysis. In order to allow comprehensive studies of the overall vehicle behaviour, the torque has to be calculated in time domain, taking into account the influences of any occurring symmetric and asymmetric faults. In this paper, the torque is derived for arbitrary combinations of L_d and L_q in the stator-reference frame in phase-wise description. The calculation is based on space-vector theory (commen approach) and on the co-energy approach, which provides a basis for stator-flux-oriented control and for the simulation of fault conditions inside the machine. A comparison of the phase-wise representation to the common approach - using rotor-flux-oriented d-axis and q-axis inductances - is performed, in order to verify the results. Different operational scenarios are simulated to outline the capability of the chosen approach.