Stochastic Security Constrained AC Optimal Power Flow Using General Polynomial Chaos Expansion

Abstract

Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper presents a stochastic security constrained optimal power flow model with chance constraints supporting nonlinear AC power flow equations and non Gaussian uncertainties. We use general polynomial chaos expansion to model arbitrary uncertainties of finite variance, enabling accurate moment computations and robust prediction of system states across diverse operating scenarios. The chance constraints probabilistically limit inequality violations, providing a more flexible representation of controllable variables and the consequent power system operation. Case studies validate the proposed models effectiveness in satisfying operational constraints and capturing uncertainty with high fidelity. Compared to the deterministic formulation, it also uncovers a wider set of unsecure contingencies, highlighting improved uncertainty capture and operational insight.