Risk-Averse Stochastic Programming vs. Adaptive Robust Optimization: A Virtual Power Plant Application

Ricardo M. Lima (), Antonio J. Conejo (), Loïc Giraldi (), Olivier Le Maître (), Ibrahim Hoteit () and Omar M. Knio ()
Additional contact information
Ricardo M. Lima: Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Antonio J. Conejo: Department of Integrated Systems Engineering, and Department of Electrical and Computer Engineering, The Ohio State University, Ohio 43210
Loïc Giraldi: Commissariat à l’Énergie Atomique et aux Énergies Alternatives (French Alternative Energies and Atomic Energy Commission), Direction des Énergies (Energy division), Institut de REcherche sur les Systèmes Nucléaires pour la production d’Énergie bas carbone (Research Institute for Nuclear Systems for Low Carbon Energy Production), Département d’Études des Combustibles (Fuel department), Cadarache F-13108 Saint-Paul-Lez-Durance, France
Olivier Le Maître: Centre de Mathématiques Appliquées, Centre National de la Recherche Scientifique, Inria, Ecole Polytechnique, Palaiseau 91128, France
Ibrahim Hoteit: Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Omar M. Knio: Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

INFORMS Journal on Computing, 2022, vol. 34, issue 3, 1795-1818

Abstract: This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done . A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization.

Keywords: stochastic programming; robust optimization; risk management; virtual power plant (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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