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Bayesian Stochastic Dynamic Programming for Hydropower Generation Operation Based on Copula Functions

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Abstract

Bayesian stochastic dynamic programming (BSDP) has been widely used in hydropower generation operation, as natural inflow and forecast uncertainties can be easily determined by transition probabilities. In this study, we propose a theoretical estimation method (TEM) based on copula functions to calculate the transition probability under conditions of limited historical inflow samples. The explicit expression of the conditional probability is derived using copula functions and then used to calculate prior and likelihood probabilities, and the prior probability can be revised to the posterior probability once new forecast information is available by Bayesian formulation. The performance of BSDP models in seven forecast scenarios and two extreme conditions considering no or perfect forecast information is evaluated and compared. The case study in the Ertan hydropower station in China shows that (1) TEM can avoid the shortcomings of empirical estimation method (EMM) in calculating the transition probability, so that the prior and likelihood probability matrices can be distributed more uniformly with less zeros, and the problem that the posterior probability cannot be calculated can be avoided; (2) there is a positive correlation between operating benefit and forecast accuracy; and (3) the operating policy considering reliable forecast information can improve hydropower generation. However, an incorrect decision may be made in the case of low forecast accuracy.

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Notes

  1. In China, a month can be divided into three periods of approximately 10 days each: the first 10 days (early), the middle 10 days (mid) and the rest days (late) of the month.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (U51909063, U1765201), the China Postdoctoral Science Foundation (2019 M651681), the Fundamental Research Funds for the Central Universities of China (2019B11514), the National Key Research and Development Project of China (2018YFC1508200). The authors also thank the support from international Clean Energy Talent Program (iCET) from China Scholarship Council.

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Authors and Affiliations

  1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China

    Qiao-feng Tan, Guo-hua Fang & Xin Wen

  2. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    Qiao-feng Tan

  3. Sate Key Laboratory of Stimulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China

    Xiao-hui Lei, Xu Wang & Chao Wang

  4. School of Water Conservancy & Civil Engineering, Northeast Agricultural University, Harbin, 150030, China

    Yi Ji

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  1. Qiao-feng Tan
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  2. Guo-hua Fang
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  3. Xin Wen
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  4. Xiao-hui Lei
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  5. Xu Wang
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  6. Chao Wang
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  7. Yi Ji
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Correspondence to Xin Wen.

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Tan, Qf., Fang, Gh., Wen, X. et al. Bayesian Stochastic Dynamic Programming for Hydropower Generation Operation Based on Copula Functions. Water Resour Manage 34, 1589–1607 (2020). https://doi.org/10.1007/s11269-019-02449-8

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  • DOI: https://doi.org/10.1007/s11269-019-02449-8

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