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

Li Dai, Dahai You and Xianggen Yin
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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

Energies, 2020, vol. 13, issue 18, 1-18

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.

Keywords: energy and reserve dispatch; data driven robust optimization; polyhedral uncertainty set; nonparametric Dirichlet process Gaussian mixture model (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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