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

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    Preprint_KAUST_SP_SAA.pdf
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    Type
    Preprint
    Authors
    Lima, Ricardo cc
    Conejo, Antonio J.
    Giraldi, Loic
    Le Maitre, Olivier
    Hoteit, Ibrahim cc
    Knio, Omar cc
    KAUST Department
    Academic Affairs
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Fluid Modeling and Prediction Group
    Earth Science and Engineering Program
    Office of the VP
    Physical Science and Engineering (PSE) Division
    Permanent link to this record
    http://hdl.handle.net/10754/662722
    
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    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.
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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