Data-driven convex optimal power flow approximation for uncertainty-aware static voltage stability margin calculation

When taking the uncertainty of the renewable energy source (RES) output in a power system into account, the uncertain fluctuation of RES will lead to the deviation of the power system responses' evolution. This evolution further affects the static voltage stability (SVS) margin value determined by the maximum load growth parameter. The SVS margin (SVSM) can be calculated based on the optimal power flow (OPF) method. The uncertain injected bus power and non-convex extended power flow equation constraints make the OPF model of SVSM calculation difficult to solve. To address these problems, an uncertainty-aware model (UaM) is established to identify the convex relationship represented by the uncertain non-convex extended power flow equations when the load growth parameter reaches SVSM. Based on historical data samples of the system, the UaM model establishes a training model to obtain a new convex relationship. By proposing an improved relaxed least absolute shrinkage and selection operator (LASSO) regression, the calculation efficiency and accuracy of the UaM based training model are improved. Case studies on IEEE 14, 39 and 118-bus systems indicate that the UaM based training model can capture the uncertainties of injected bus power to reduce the influence of RES power's predicted errors on the calculation results. And the proposed improved relaxed LASSO regression can increase the calculation efficiency of the SVSM result compared with the regular regressions.