Modeling and Control of AC Machines using Complex State Variables

It showed that the conventional state matrix consists of an arrangement of all parameters of the machine. These do not allow understanding the physics of the machine dynamics. Insight is obtained when modeling the machine using complex state variables. The method demonstrates that the dynamics are deteriorated by cross-coupling effects between the real and imaginary parts of the respective state variables. The effects are compensated when operating at high switching frequency. They show only at high-power drive systems where increased switching losses call for operating at lower switching frequencies. The degree of cross-coupling is represented by a cross-frequency transfer function. Conventional feedforward compensation even increases cross-coupling, and leads to temporary de-magnization at transients. The problem is cured when using a current controller having complex coefficients.