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Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Author

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  • Li Dai

    (State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, China)

  • Dahai You

    (State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, China)

  • Xianggen Yin

    (State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan 430074, China)

Abstract

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

Suggested Citation

  • Li Dai & Dahai You & Xianggen Yin, 2020. "Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model," Energies, MDPI, vol. 13(18), pages 1-18, September.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:18:p:4642-:d:409997
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    References listed on IDEAS

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    1. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    2. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    3. Chen, Yue & Wei, Wei & Liu, Feng & Mei, Shengwei, 2016. "Distributionally robust hydro-thermal-wind economic dispatch," Applied Energy, Elsevier, vol. 173(C), pages 511-519.
    4. Li, Zhigang & Qiu, Feng & Wang, Jianhui, 2016. "Data-driven real-time power dispatch for maximizing variable renewable generation," Applied Energy, Elsevier, vol. 170(C), pages 304-313.
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