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. The problem is modeled 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 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. 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 experiences indicate that when an adequate sample size is used, the solution obtained is close to the optimal one.

Citation
Lima, R. M., Conejo, A. J., Giraldi, L., Le Maître, O., Hoteit, I., & Knio, O. M. (2021). Sample average approximation for risk-averse problems: A virtual power plant scheduling application. EURO Journal on Computational Optimization, 9, 100005. doi:10.1016/j.ejco.2021.100005

Acknowledgements
Research reported in this publication was supported by research funding from King Abdullah University of Science and Technology (KAUST). Antonio J. Conejo's contribution is partly supported by NSF project 1808169. We would like to thank two referees for their comments and contributions that helped to improve the presentation of this work.

Publisher
Elsevier B.V.

Journal
EURO Journal on Computational Optimization

DOI
10.1016/j.ejco.2021.100005

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2021-04-13 09:29:24
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