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

This paper proposes two complex vector models to characterize unbalanced three-phase four-wire systems that contain pulsewidth-modulated voltage-source converters (PWM-VSCs). In the first case, the three-phase system is decomposed in orthogonal odq components. A complex vector model is then built from the dq and o components. In the second case, a complex vector model is introduced by decomposing the system in three single-phase systems. In both cases, an orthogonal, fictitious circuit is introduced to handle a single-phase system, such as the homopolar system or each one of the three single-phase systems that compose a three-phase four-wire system. From the vector models, two digital controllers, which employ two different reference frames, are proposed. Also, the use of the same gains for both controllers simplifies the equations of the controller in the stationary reference frame. As an example, current control in a PWM-VSC system is presented