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Distributionally robust chance constrained optimization for economic dispatch in renewable energy integrated systems

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Abstract

Distributionally robust optimization (DRO) has become a popular research topic since it can solve stochastic programs with ambiguous distribution information. In this paper, as the background of economic dispatch (ED) in renewable integration systems, we present a new DRO-based ED optimization framework (DRED). The new DRED is addressed with a coupled format of distribution uncertainty for objective and chance constraints, which is different from most existing DRO frameworks. Some approximation strategies are adopted to handle the complicated DRED: the data-driven approach, the approximation of chance constraints by conditional value-at-risk, and the discrete scheme. The approximate reformulations are solvable nonconvex nonlinear programming problems. The approximation error analysis and convergence analysis are also established. Numerical results using an IEEE-30 buses system are presented to demonstrate the approach proposed in this paper.

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Notes

  1. Note that the Matlab solver “fminimax” is often used to solve smooth problem. In numerical tests, we applied the smoothing method in [36, Formulation (1.6)] and [37, Formulation (4.2)] to nonsmooth objective function in (3.15) and (3.26). Note also that the smoothing method is well known and it is not our main focus, we omit the details. For more details about the smoothing method, see [36,37,38].

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Acknowledgements

The authors thank Professor Huifu Xu and Dr Yun Shi for valuable discussion on technique details and the presentation of the paper. The authors are also grateful to the three anonymous referees for careful reading and constructive comments that improved the quality of this paper significantly.

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Authors and Affiliations

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

    Xiaojiao Tong

  2. School of Economics and Management, Nanjing University of Science and Technology, Nanjing, 210049, China

    Hailin Sun

  3. Hunan Electric Power Research Institute, Changsha, 410007, China

    Xiao Luo

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

    Quanguo Zheng

Authors
  1. Xiaojiao Tong
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  2. Hailin Sun
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  3. Xiao Luo
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  4. Quanguo Zheng
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Corresponding author

Correspondence to Hailin Sun.

Additional information

This work is supported by National Natural Science Foundation of China (11671125, 71371065, 51707013, 11401308) and Natural Science Foundation of Jiangsu Province, China (BK20140768).

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Tong, X., Sun, H., Luo, X. et al. Distributionally robust chance constrained optimization for economic dispatch in renewable energy integrated systems. J Glob Optim 70, 131–158 (2018). https://doi.org/10.1007/s10898-017-0572-3

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  • DOI: https://doi.org/10.1007/s10898-017-0572-3

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