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Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system

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Abstract

In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system.

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Acknowledgments

We would like to thank the anonymous referee for many insightful comments and constructive suggestions, which led to significant improvements in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Hunan First Normal University, Changsha, 410205, China

    X. J. Tong

  2. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    H. Xu

  3. Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong

    F. F. Wu

  4. Hunan Province Key Laboratory of Smart Grids Operation, 410114, Changsha, China

    Z. Zhao

Authors
  1. X. J. Tong
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  2. H. Xu
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  3. F. F. Wu
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  4. Z. Zhao
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Corresponding author

Correspondence to X. J. Tong.

Additional information

This work is supported by Natural Science Foundation of China (11171095, 71371065).

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Tong, X.J., Xu, H., Wu, F.F. et al. Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system. Comput Manag Sci 13, 393–422 (2016). https://doi.org/10.1007/s10287-016-0251-8

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  • DOI: https://doi.org/10.1007/s10287-016-0251-8

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