Modeling and control of unbalanced three-phase systems containing PWM converters

This paper proposes two complex vector models to characterize three-phase unbalanced systems with four wires and containing PWM converters. In the first case, the three-phase system is decomposed in orthogonal odq components. A complex vector model is then built from the dq components and o component. In the second case a complex vector model is introduced by decomposing the system in three single-phase systems. In both cases, a second orthogonal simulated model is introduced to handle a single-phase system, such as the homopolar system or each of the three single-phase systems that compose a three-phase four wires system. From the vector models, a vector controller that employs two different reference frames is proposed and emulated on the stationary reference frame. A digital version for such a controller is also presented. As an example, a current control in a PWM-VSI system is presented.