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

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