Relevance of Including Saturation and Position Dependence in the Inductances for Accurate Dynamic Modeling and Control of SynRMs

Abstract

In synchronous reluctance motors (SynRMs), the d- and q -axis inductances ( $L_{d}$ and $L_{q}$ ) are nonlinear functions of d- and q -axis currents ( $i_{d}$ and $i_{q}$ ) and rotor position ( $\theta _{r}$ ). The main research question for dynamic studies of SynRMs in this paper is how accurate should the inductance model be to have a reliable computation of dynamic behavior and stability limits? The stability limits are important in the case of $V/ f$ control without position feedback. To answer the question, we consider three cases: 1) inductances are function of $i_{d}$ , $i_{q}$ , and $\theta _{r}$ ; 2) inductances are function of $i_{d}$ and $i_{q}$ , averaged over the position $\theta _{r}$ ; and 3) inductances are constant values, with properly chosen values. The cases 1 and 2 include saturation and cross saturation, while case 3 does not. It is found that averaging the rotor position $\theta _{r}$ is almost not jeopardizing accuracy of the SynRM model. However, including magnetic saturation is crucial: it is observed that using constants $L_{d}$ and $L_{q}$ to represent the SynRM modeling leads to a large deviation in the prediction of the torque capability compared to the practical motor. In addition, including the magnetic saturation effect in the closed-loop control of SynRMs is necessary. Then, maximum torque per ampere can be achieved. Finally, the proposed method of including the magnetic saturation and the rotor position effects in the SynRM modeling has been validated by experimental measurements.