Vector modeling and control of unbalanced electrical systems

In this paper a vector modeling approach is employed to represent the transient and steady-state behavior of unbalanced three-phase (three wires), unbalanced two-phase and single-phase systems containing PWM converters. In the case of the three-phase system, it is decomposed on dq components, by using an appropriate coordinate transformation, and then the vector model is obtained. While in the case of the single-phase system, a fictitious second single-phase system is introduced to obtain the vector model. From the vector model, two vector controllers in the direct and indirect synchronous reference frames are defined. The digital version of this controller in the stationary reference frame is also presented. Simulations and experimental results are presented for a VSI power converter system