Complex Vector Modeling and Control of Interior Permanent Magnet Synchronous Machines

In applications where the ratio of switching frequency to fundamental frequency is low, time delays in the system lead to poor current regulation and cross-coupling between the d and q axes. The phase lag introduced by the PWM and sampling delays lead to poor transient characteristics and can even cause system system instability. This paper proposes a complex vector model of an interior permanent magnet synchronous machine (IPMSM) that requires only a single complex current controller and allows complex current controller design methods applied to non-salient pole machines to be easily adapted for salient pole machines. Simulation results using an IPMSM and experimental results using a 3-φ balanced RL load show that using the complex current controller reduces cross coupling in comparison to the conventional scalar approach at lower switching frequencies. With a sudden load torque change leading to a sudden change in i_q, the reduced deviation in i_d from its reference can help prevent the temporary demagnetization. Also, with a sudden change in i_d in the Maximum Torque per Ampere (MTPA) or Field-weakening (FW) mode, the reduced deviation in i_q from its reference can help avoid transient spike in electromagnetic torque.