Conventional dq-model is based on the assumption of having the sinusoidal flux and back emf waveforms. It also assumes that the mutual inductances and balanced, symmetric and vary sinusoidally. When these assumptions fail, the dq-model becomes mathematically incorrect. The terminology, physical motor model refers to the model whose working flux as well as the back emf contains all the possible harmonic components due to saturation and slotting effects. Two types of physical motor model and their coupling with external circuits are studied in this paper. One is the FE model while the other is the phase variable model. Its circuit parameters are calculated based on FE analysis. As an example, the FE model and physical phase variable model of a PM synchronous machine are established. The Coupling of the external circuits directly with the FE motor model is carried out. The physical phase variable model of PM synchronous motor is proposed and implemented in Simulink. The rotor position dependence of inductances is obtained through nonlinear transient FE analysis and energy perturbation method. The rotor position dependence of flux linkage contributed by the permanent magnet only is obtained from transient FE analysis. In addition to the electromagnetic torque component produced by the interaction between the armature field and the permanent magnetic field, the cogging torque due to the permanent magnet field and slotting is taken into account in the physical model. It is evaluated through FE analysis. The established physical motor models are applied in integrated motor drive systems.
