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A Bayesian Stochastic Optimization Model for a Multi-Reservoir Hydropower System

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  • P. Mujumdar
  • B. Nirmala

Abstract

This paper presents the development of an operating policy model for a multi-reservoir system for hydropower generation by addressing forecast uncertainty along with inflow uncertainty. The stochastic optimization tool adopted is the Bayesian Stochastic Dynamic Programming (BSDP), which incorporates a Bayesian approach within the classical Stochastic Dynamic Programming (SDP) formulation. The BSDP model developed in this study considers, the storages of individual reservoirs at the beginning of period t, aggregate inflow to the system during period t and forecast for aggregate inflow to the system for the next time period t + 1, as state variables. The randomness of the inflow is addressed through a posterior flow transition probability, and the uncertainty in flow forecasts is addressed through both the posterior flow transition probability and the predictive probability of forecasts. The system performance measure used in the BSDP model is the square of the deviation of the total power generated from the total firm power committed and the objective function is to minimize the expected value of the system performance measure. The model application is demonstrated through a case study of the Kalinadi Hydroelectric Project (KHEP) Stage I, in Karnataka state, India. Copyright Springer Science+Business Media, Inc. 2007

Suggested Citation

  • P. Mujumdar & B. Nirmala, 2007. "A Bayesian Stochastic Optimization Model for a Multi-Reservoir Hydropower System," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(9), pages 1465-1485, September.
    • Handle: RePEc:spr:waterr:v:21:y:2007:i:9:p:1465-1485
    DOI: 10.1007/s11269-006-9094-3
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    Citations

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    Cited by:

    1. Qiao-feng Tan & Guo-hua Fang & Xin Wen & Xiao-hui Lei & Xu Wang & Chao Wang & Yi Ji, 2020. "Bayesian Stochastic Dynamic Programming for Hydropower Generation Operation Based on Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(5), pages 1589-1607, March.
    2. Alcigeimes Celeste & Max Billib, 2010. "The Role of Spill and Evaporation in Reservoir Optimization Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(4), pages 617-628, March.
    3. Wei Xu & Xiaoli Zhang & Anbang Peng & Yue Liang, 2020. "Deep Reinforcement Learning for Cascaded Hydropower Reservoirs Considering Inflow Forecasts," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(9), pages 3003-3018, July.
    4. Mengfei Xie & Suzhen Feng & Jinwen Wang & Maolin Zhang & Cheng Chen, 2022. "Impacts of Yield and Seasonal Prices on the Operation of Lancang Cascaded Reservoirs," Energies, MDPI, vol. 15(9), pages 1-11, April.
    5. H. Lu & G. Huang & G. Zeng & I. Maqsood & L. He, 2008. "An Inexact Two-stage Fuzzy-stochastic Programming Model for Water Resources Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(8), pages 991-1016, August.
    6. Tan, Qiao-feng & Lei, Xiao-hui & Wen, Xin & Fang, Guo-hua & Wang, Xu & Wang, Chao & Ji, Yi & Huang, Xian-feng, 2019. "Two-stage stochastic optimal operation model for hydropower station based on the approximate utility function of the carryover stage," Energy, Elsevier, vol. 183(C), pages 670-682.
    7. Katerina Spanoudaki & Panayiotis Dimitriadis & Emmanouil A. Varouchakis & Gerald A. Corzo Perez, 2022. "Estimation of Hydropower Potential Using Bayesian and Stochastic Approaches for Streamflow Simulation and Accounting for the Intermediate Storage Retention," Energies, MDPI, vol. 15(4), pages 1-20, February.
    8. Xiaoli Zhang & Yong Peng & Wei Xu & Bende Wang, 2019. "An Optimal Operation Model for Hydropower Stations Considering Inflow Forecasts with Different Lead-Times," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(1), pages 173-188, January.
    9. A. Lust & K.-H. Waldmann, 2019. "A general storage model with applications to energy systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 71-97, March.
    10. Liu, Yuan & Ji, Changming & Wang, Yi & Zhang, Yanke & Jiang, Zhiqiang & Ma, Qiumei & Hou, Xiaoning, 2023. "Effect of the quality of streamflow forecasts on the operation of cascade hydropower stations using stochastic optimization models," Energy, Elsevier, vol. 273(C).
    11. Lisicki, Michal & Lubitz, William & Taylor, Graham W., 2016. "Optimal design and operation of Archimedes screw turbines using Bayesian optimization," Applied Energy, Elsevier, vol. 183(C), pages 1404-1417.
    12. Qiuxiang Jiang & Tian Wang & Zilong Wang & Qiang Fu & Zhimei Zhou & Youzhu Zhao & Yujie Dong, 2018. "HHM- and RFRM-Based Water Resource System Risk Identification," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(12), pages 4045-4061, September.
    13. Li, W. & Li, Y.P. & Li, C.H. & Huang, G.H., 2010. "An inexact two-stage water management model for planning agricultural irrigation under uncertainty," Agricultural Water Management, Elsevier, vol. 97(11), pages 1905-1914, November.
    14. Shu, Xingsheng & Ding, Wei & Peng, Yong & Wang, Ziru, 2024. "Value of long-term inflow forecast for hydropower operation: A case study in a low forecast precision region," Energy, Elsevier, vol. 298(C).

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