Solving optimal power flow with non-Gaussian uncertainties via polynomial chaos expansion

The increasing penetration of renewable energy sources to power grids necessitates a structured consideration of uncertainties for optimal power flow problems. Modeling uncertainties via continuous random variables of finite variance we propose a tractable convex formulation of the uncertain optimal power flow problem. The uncertainties can be (non-)Gaussian, multivariate and/or correlated. We employ polynomial chaos expansion to rewrite the infinite-dimensional random-variable optimization problem as a finite-dimensional convex second-order cone program. This problem can be solved efficiently in a single numerical run for all realizations of the uncertainty. The solution provides a feedback policy in terms of the fluctuations. No Monte Carlo sampling is required to obtain either the solution or its statistics. The reduced computational effort and yet consistent results stemming from polynomial chaos are demonstrated in comparison to a Monte-Carlo-based solution for the ieee 300-bus test system.