Preventive–corrective stability constrained OPF in microgrids for accommodating DG plug-and-play

To accommodate unpredictable plug-and-play (PnP) of distributed generators (DGs) in droop controlled microgrids, this paper proposes a preventive–corrective stability constrained optimal power flow (SC-OPF). Firstly, considering that DG droops are restricted by load sharing, we introduce the battery energy storage system (BESS) with adjustable droops, which acts as a new control resource. Secondly, we propose a bi-level optimization problem, where the upper level ensures minimizing the preventive–corrective coordinated cost and accommodating DG PnPs without violating stability constraints and the lower level focuses on the stability index given by semi-definite program (SDP) based on the Lyapunov equation. With the previously proposed analytical stability sensitivity, the lower level problem is reformulated by a series of linear constraints through the Benders decomposition method, and hence the entire bilevel problem can be solved efficiently and accurately. We apply the modified IEEE 33-bus system to validate the proposed SC-OPF model. From simulation results, the proposed model significantly improves the economic cost, stability, and computational efficiency compared to other SC-OPF models without considering BESS droop control or PnPs.