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.

中文翻译：

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IPMSM 的负载视在电感导数：评估方法和扭矩估计

本文提出了一种新方法来评估内部永磁同步电机 (IPMSM) 的负载视在电感导数，从而估算负载磁阻转矩。众所周知，负载电感（自电感和互电感）取决于电机的电气负载，并且由于 IPMSM 的磁阻转矩是电枢电流和视在电感导数（自电感和互电感）之间的相互作用，饱和负载电感的影响对磁阻转矩（波形和值）有很大影响，增加转矩脉动并影响机器的自感能力。如果负载电感导数波形计算不准确，或者至少受到评估方法固有的数值误差的影响，通过区分负载电感来评估它们时发现的，这说明了电流波形引入的高次谐波含量、电感谐波含量的空间谐波贡献以及定子固有的非线性和转子材料，估计不正确的负载磁阻转矩。这样，本文基于负载反电动势 (EMF) 麦克斯韦应力张量 (MST) 方法中提出的概念，提出了一种新的数值方法，以正确评估负载电感导数（自和互感）为了避免和克服微分方法中存在的缺点。所提出的方法不同于基于其自身约束和模拟条件的反电动势 MST。另一方面，它仍然需要使用冻结渗透率方法和麦克斯韦应力张量方法。对所提出的技术进行了详细的讨论和解释，展示了它如何克服之前强调的缺点。最后，给出了两种不同电流波形（正弦和非正弦）的结果，以验证所提出方法的准确性。