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To figure out the stability issues brought by renewable energy sources (RES)with non-Gaussian uncertainties in isolated microgrids, this paper proposes achance constrained stability constrained optimal power flow (CC-SC-OPF) model.Firstly, we propose a bi-level optimization problem, of which the upper levelaims to minimize the expected generation cost without violating the stabilitychance constraint; the lower level concerns about the stability index given bya semi-definite program (SDP). Secondly, we apply the Gaussian mixture model(GMM) to handle the non-Gaussian RES uncertainties and introduce analyticalsensitivity analysis to reformulate chance constraints with respect tostability index and operational variables into linear deter-ministic versions.By incorporating linearized constraints, the bi-level model can be efficientlysolved by Benders decomposition-based approach. Thirdly, we design asupplementary corrective countermeasure to compensate the possible controlerror caused by the linear approximation. Simulation results on the 33-busmicrogrid reveal that compared to benchmarking approaches, the proposed modelconverges 30 times faster with more accurate solutions.

Stability Constrained OPF in Microgrids: A Chance Constrained Optimization Framework with Non-Gaussian Uncertainty