Sample average approximation for risk-averse problems: A virtual power plant scheduling application

Abstract

In this paper, we address the decision-making problem of a virtual power plant (VPP) involving a self-scheduling and market involvement problem under uncertainty in the wind speed and electricity prices, a computationally challenging problem. We model this problem using a risk-neutral and two risk-averse two-stage stochastic programming formulations, where the conditional value at risk is used to represent risk. A sample average approximation (SAA) methodology is integrated with an adapted L-Shaped solution method, which can solve risk-neutral and specific risk-averse problems. This methodology provides a framework to understand and quantify the impact of the sample size on the variability of the results. We aim at computing high-quality solutions for the VPP problem and also infer statistics on the optimal values and solutions. The numerical results include an analysis of the computational performance of the methodology for two case studies, estimators for the bounds of the true optimal solutions of the problems, and an assessment of the quality of the solutions obtained. In particular, numerical experiments indicate that if an adequate sample size is used, the solution obtained is close to the optimal one.