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On-Load Apparent Inductance Derivative of IPMSM: Assessment Method and Torque Estimation

This article presents a new method to evaluate the on-load apparent inductance derivative for interior permanent-magnet synchronous machine (IPMSM) and, consequently, to estimate the on-load reluctance torque. It is well known that the on-load inductances (self and mutual) are dependent of the machine’s electric load, and since the reluctance torque of the IPMSM is the interaction between the armature current and apparent inductance derivatives (self and mutual), the saturation effects in the on-load inductances have a high influence in the reluctance torque (waveform and value), increasing the torque ripple and affecting the machines’ self-sensing capability. If the on-load inductance derivative waveforms are calculated inaccurately or, at least, are affected by numerical errors inherent to the evaluating method, as found when they are assessed by means of differentiating the on-load inductances, which accounts for the high-order harmonic content introduced by the current waveform, the spatial harmonic contribution on the inductance harmonic content, and the non-linearities inherent to the stator and rotor materials, an incorrect on-load reluctance torque is estimated. This way, this article proposes a new numerical method, based on the concept presented in the on-load back electromotive force (EMF) Maxwell stress tensor (MST) method, to properly evaluate the on-load inductance derivatives (self and mutual) in order to avoid and to overcome the drawbacks presented in the differentiating method. The proposed method differs from the back EMF MST based on its own constraints and simulation conditions. On the other hand, it still needs the usage of the frozen permeability method and the Maxwell stress tensor method. The proposed technique is discussed and explained in small details, showing how it overcomes the drawbacks highlighted previously. Finally, the results for two different current waveforms (sinusoidal and non-sinusoidal) are presented in order to validate the proposed method’s accuracy.