Analytic MTPA Solution for Synchronous Reluctance Machine

The maximum torque per ampere (MTPA) method offers a method of current minimizing solution. However due to the core saturation and cross-coupled inductance, the MTPA solutions do not appear on the 45° line in the current plane. In this paper, a method of finding analytic MTPA solution is proposed. With this solution, a control program can be developed without using a look-up table. First, the flux data resulted from finite element method (FEM) analysis are approximated as a polynomial of current variables. The coefficients are found using the least squares method(LSM). Then inductances are derived as functions of current variables. Finally, they are utilized in the torque equation and the MTPA solution is derived. The analytical solutions are compared with experimental results.