Flux Saturation Model Including Cross Saturation for Synchronous Reluctance Machines and Its Identification Method at Standstill

This article proposes a magnetic flux saturation model that well represents the cross saturation of synchronous reluctance machines (SynRMs) and a parameter estimation method of the proposed saturation model. Existing magnetic flux models do not satisfy the reciprocity condition or express cross saturation well. The proposed flux saturation model consists of terms for self-saturation and cross saturation, and it expresses well the nonlinear relationship between current and flux of SynRMs, as well as satisfies the reciprocity condition. The data of flux saturation are obtained at standstill using the hysteresis voltage injection method. Using the flux saturation data, the parameters of the flux saturation model are estimated. Because the proposed magnetic flux saturation model includes an arctangent function, it is not possible to estimate parameters directly using the linear least-squares method (LSM). However, the proposed parameter estimation method integrates the self-saturation model and transforms it into a polynomial to which linear LSM can be applied. In addition, parameters related to cross saturation are also estimated using linear LSM. Therefore, the proposed parameter estimation method is easy to implement and can be applied to general-purposed inverter products. The effectiveness of the proposed model and its identification method are experimentally evaluated with a 1.5-kW SynRM. Additionally, the identified model is verified with the accuracy of the maximum torque per ampere table and the performance of sensorless control of the tested motor.