Two-stage stochastic optimization for optimal power flow under renewable generation uncertainty

Abstract

We propose a two-stage stochastic version of the classical economic dispatch problem with alternating-current power flow constraints, a nonconvex optimization formulation that is central to power transmission and distribution over an electricity grid. Certain generation decisions made in the first stage cannot further be changed in the second stage, where the uncertainty due to various factors such as renewable generation is realized. Any supply-demand mismatch in the second stage must be alleviated using high marginal cost power sources that can be tapped in short order. We solve a Sample-Average Approximation (SAA) of this formulation by capturing the uncertainty using a finite number of scenario samples. We propose two outer approximation algorithms to solve this nonconvex program to global optimality. We use recently discovered structural properties for the classical deterministic problem to show that when these properties hold the sequence of approximate solutions obtained under both alternatives has a limit point that is a globally optimal solution to the two-stage nonconvex SAA program. We also present an alternate local optimization approach to solving the SAA problem based on the Alternating Direction Method of Multipliers (ADMM). Numerical experiments for a variety of parameter settings were carried out to demonstrate the efficiency and usability of our method over ADMM for large practical instances.