Inductance Evaluation and Average Torque Separation of Externally Excited Synchronous Machines Using Frozen Permeability

This paper investigates an externally excited synchronous machine (EESM), designed for traction application, regarding the calculation of its absolute inductances and the determination of its average torque constituents. In order to compute the torque components precisely, the magnetic field density produced in the EESM is resolved into individual components corresponding to the different sources of excitation, namely the d-axis, the q-axis and the rotor field current. The frozen permeability (FP) method is employed to compute these magnetic field density components enabling the computation of the flux linkage produced by each source of excitation individually. Subsequently, self, mutual and cross-coupling inductances of the EESM are calculated in the dq-frame as a function of stator and rotor currents. Finally, using the absolute inductance values the different torque components, namely the Lorentz (excitation) torque, the reluctance torque and the cross-coupling torque, are also evaluated as a function of stator and rotor currents. The torque maps are presented at discrete rotor excitation levels to understand the movement of the maximum torque per ampere (MTPA) line with respect to the d-axis and q-axis currents, for different field current values. The results discussed in this paper also provide an insight into the difference between the impact of the reluctance torque on the total torque of salient pole permanent magnet synchronous machines (PMSMs) and EESMs.