Solving Chance Constrained Optimal AC Power Flow Problems with Smooth Approximation

With the wide application of renewable electricity generation, uncertainties in power systems increase and may compromise the safe operation of power systems. In this article, the AC optimal power flow problem considering the influence of renewable electricity generators as chance constraints is addressed. To convert this problem to a numerically tractable form, an idea is to approximate the chance constraints with analytical ones. Although the feasibility of existing methods has been shown in certain cases, the approximate error of existing methods is not limited. To overcome this issue, a smooth approximate function is designed in this article. We showed that solutions of the approximate optimization problem with different parameters are feasible and converge to the original chance constrained optimization problem. Case studies and comparative studies are conducted to show the feasibility and reduced conservatism of the proposed method.