Dynamic analysis and design of static series compensators for unbalanced AC voltage supplies

The implementation of high-performance VAr compensators for unbalanced AC sources or loads requires the control of the static power converter under unbalance conditions. This paper is a contribution to this topic and presents a complete description of the dynamic behaviour and design of a static series VAr compensator for unbalanced AC voltage sources. The technique consists in separating the system into two independent balanced networks by using an instantaneous symmetrical components transformation, and then eliminating the time dependency by a d-q transformation of both the positive and the negative sequence components. It is shown that the control of the unbalanced system is reduced to a set of four DC loops, the d and q components of the positive and negative sequences. A detailed description is given of all the steps of the method, including the transformations, the positioning of the d-q frame for further simplification of the control loops and the graphical modeling of the compensator. A design example with simulated results confirms the validity of the proposed method