Preventive-Corrective Control for Static Voltage Stability Under Multiple $N-1$ Contingencies Considering Wind Power Uncertainty

An optimal preventive-corrective control model for static voltage stability under multiple <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-1$</tex> contingencies considering the wind power uncertainty is established in this paper. The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency. The chance constraints of the static voltage stability margins (SVSMs) in the normal operation state and after each <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-1$</tex> contingency are included. The approximate functions between the probability density functions (PDFs) of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SVSM chance constraints into deterministic expressions. An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model. In each iteration, the approximate expressions and range are determined by the generated data samples. Moreover, a fast approximation calculation method of second-order matrices is proposed. By the naive Bayes classifier, the most severe <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-1$</tex> contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency. Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.