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Probabilistic constraints via SQP solver: application to a renewable energy management problem

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  • I. Bremer
  • R. Henrion
  • A. Möller

Abstract

This paper aims at illustrating the efficient solution of nonlinear optimization problems with joint probabilistic constraints under multivariate Gaussian distributions. The numerical solution approach is based on Sequential Quadratic Programming (SQP) and is applied to a renewable energy management problem. We consider a coupled system of hydro and wind power production used in order to satisfy some local demand of energy and to sell/buy excessive or missing energy on a day-ahead and intraday market, respectively. A short term planning horizon of 2 days is considered and only wind power is assumed to be random. In the first part of the paper, we develop an appropriate optimization problem involving a probabilistic constraint reflecting demand satisfaction. Major attention will be payed to formulate this probabilistic constraint not directly in terms of random wind energy produced but rather in terms of random wind speed, in order to benefit from a large data base for identifying an appropriate distribution of the random parameter. The second part presents some details on integrating Genz’ code for Gaussian probabilities of rectangles into the environment of the SQP solver SNOPT. The procedure is validated by means of a simplified optimization problem which by its convex structure allows to estimate the gap between the numerical and theoretical optimal values, respectively. In the last part, numerical results are presented and discussed for the original (nonconvex) optimization problem. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:3:p:435-459
    DOI: 10.1007/s10287-015-0228-z
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    Cited by:

    1. Jinxiang Wei & Zhaolin Hu & Jun Luo & Shushang Zhu, 2024. "Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models," Annals of Operations Research, Springer, vol. 338(2), pages 1283-1315, July.
    2. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.
    3. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    4. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    5. Martin Branda & Štěpán Hájek, 2017. "Flow-based formulations for operational fixed interval scheduling problems with random delays," Computational Management Science, Springer, vol. 14(1), pages 161-177, January.

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