Disturbance-rejection control for unbalanced operation of microgrids: Invariant-set approach

In microgrids, voltage imbalance control is crucial to preserving the required level of power quality. The article presents a tracker design that mitigates the unbalance in the microgrids. The proposed microgrid model includes positive and negative sequences, whereby the positive sequences are controlled, and the negative sequence is treated as an external disturbance (whose effect must be attenuated). The uncertainty in the external disturbance is modelled in the norm-bounded form. The suggested control is based on attracting (driving) the state trajectory into a small region, including the origin (attracting ellipsoid-set). The effect of the negative sequence components is attenuated by minimizing the ellipsoid volume. When the state trajectory enters that region, it will never leave it for the future time (termed invariant-set). Two theorems were formulated for tracker synthesis that follows the desired reference and reduces the negative sequence impact. These theorems are the invariant-set method and the H_∞ approach. The validity of the suggested control is demonstrated via testing the system under various operational unbalanced scenarios, such as unbalances or faults at the load side or in the transmission lines. The simulations show the superiority of the suggested method in terms of accuracy and dynamic response when compared with the H∞ . Additionally, a comparison is made between the suggested tracker and Active Disturbance Rejection Control (ADRC).