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

TL;DR

This paper introduces a novel chance constrained optimization framework for microgrid stability that accounts for non-Gaussian uncertainties in renewable energy sources, improving solution efficiency and accuracy.

Contribution

It develops a bi-level optimization model with Gaussian mixture models and linear reformulations, enabling fast and precise stability-constrained power flow solutions in microgrids.

Findings

Model converges 30 times faster than benchmarks

Achieves more accurate solutions under non-Gaussian uncertainties

Effective handling of stability constraints in microgrid operation

Abstract

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.