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