Evaluating the Marginal Utility of Two-Stage Hydropower Scheduling
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 6
Abstract
Understanding the trade-offs associated with the two operation stages of hydropower generation is critical for guiding efficient reservoir operations. Previous studies showed that the marginal return in Stage 2 is always higher than the marginal cost in Stage 1 if variations in tailwater levels are ignored. However, the tailwater level often raises faster than the reservoir water level, and thus reduces the net hydraulic head of the reservoirs with reaction turbines, especially in large-scale and low-head reservoirs. Therefore, this study considers the variations in tailwater levels and theoretically evaluates the marginal utility of the total power generation (TPG) in the two stages. It is found that the variation of TPG presents diminishing marginal utility and is closely related to the topography characteristics of the reservoir and downstream channels, as well as the relationship between releases in the two stages. The marginal return in Stage 2 might be lower than the marginal cost in Stage 1 when the release in Stage 2 exceeds that in Stage 1 for the reservoirs in which the tailwater level is sensitive to discharge and hydraulic head. This suggests that the carryover storage equalizing the marginal utility in the two stages is optimal, i.e., satisfying the marginal utility principle. Otherwise, the marginal return is always higher than the marginal cost, which suggests that as much carryover storage as possible should be saved. Following these findings, the reservoir states, represented by the storage difference and the total inflow in the two stages, that satisfy the marginal utility principle are identified. Further, the optimal carryover storage under different levels of inflow and storage difference is derived. The theoretical findings are verified with four hydropower plants in China. Results confirm the theoretical findings and show that two-stage hydropower generation coupled with operating rules can greatly improve the performance of hydropower generation.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request, including the characteristic parameters and the Java codes for the two-stage optimal hydropower scheduling model.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant Nos. 51925902, 52079015, and 51709036).
References
Azamathulla, H. M., A. A. Ghani, C. S. Leow, C. K. Chang, and N. A. Zakaria. 2011. “Gene-expression programming for the development of a stage-discharge curve of the Pahang River.” Water Resour. Manage. 25 (11): 2901–2916. https://doi.org/10.1007/s11269-011-9845-7.
Baños, R., F. Manzano-Agugliaro, F. G. Montoya, C. Gil, A. Alcayde, and J. Gómez. 2011. “Optimization methods applied to renewable and sustainable energy: A review.” Renewable Sustainable Energy Rev. 15 (4): 1753–1766. https://doi.org/10.1016/j.rser.2010.12.008.
Berga, L. 2016. “The role of hydropower in climate change mitigation and adaptation: A review.” Engineering 2 (3): 313–318. https://doi.org/10.1016/J.ENG.2016.03.004.
DHV Consultants, and Delft Hydraulics. 1999. How to establish stage discharge rating curve. Washington, DC: Word Bank.
Dincer, I. 2000. “Renewable energy and sustainable development: A crucial review.” Renewable Sustainable Energy Rev. 4 (2): 157–175. https://doi.org/10.1016/S1364-0321(99)00011-8.
Ding, W., C. Zhang, Y. Peng, R. Zeng, H. Zhou, and X. Cai. 2015. “An analytical framework for flood water conservation considering forecast uncertainty and acceptable risk.” Water Resour. Res. 51 (6): 4702–4726. https://doi.org/10.1002/2015WR017127.
Draper, A. J., and J. R. Lund. 2004. “Optimal hedging and carryover storage value.” J. Water Resour. Plann. Manage. 130 (1): 83–87. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(83).
Eum, H.-I., Y.-O. Kim, and R. N. Palmer. 2011. “Optimal drought management using sampling stochastic dynamic programming with a hedging rule.” J. Water Resour. Plann. Manage. 137 (1): 113–122. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000095.
Hashimoto, T., J. R. Stedinger, and D. P. Loucks. 1982. “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.” Water Resour. Res. 18 (1): 14–20. https://doi.org/10.1029/WR018i001p00014.
International Hydropower Association. 2021. Hydropower status report 2021: Sector trends and insights. London: International Hydropower Association.
Kratzert, F., D. Klotz, C. Brenner, K. Schulz, and M. Herrnegger. 2018. “Rainfall–runoff modelling using long short-term memory (LSTM) networks.” Hydrol. Earth Syst. Sci. 22 (11): 6005–6022. https://doi.org/10.5194/hess-22-6005-2018.
Labadie, J. 2004. “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage. 130 (2): 93–111. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:2(93).
Liu, P., S. Guo, X. Xu, and J. Chen. 2011. “Derivation of aggregation-based joint operating rule curves for cascade hydropower reservoirs.” Water Resour. Manage. 25 (13): 3177–3200. https://doi.org/10.1007/s11269-011-9851-9.
Lu, D., B. Wang, Y. Wang, H. Zhou, Q. Liang, Y. Peng, and T. Roskilly. 2015. “Optimal operation of cascade hydropower stations using hydrogen as storage medium.” Appl. Energy 137 (Jan): 56–63. https://doi.org/10.1016/j.apenergy.2014.09.092.
Pérez-Díaz, J. I., and J. R. Wilhelmi. 2010. “Assessment of the economic impact of environmental constraints on short-term hydropower plant operation.” Energy Policy 38 (12): 7960–7970. https://doi.org/10.1016/j.enpol.2010.09.020.
Shiau, J.-T. 2011. “Analytical optimal hedging with explicit incorporation of reservoir release and carryover storage targets.” Water Resour. Res. 47 (1): W1515. https://doi.org/10.1029/2010WR009166.
Shih, J.-S., and C. ReVelle. 1994. “Water-supply operations during drought: Continuous hedging rule.” J. Water Resour. Plann. Manage. 120 (5): 613–629. https://doi.org/10.1061/(ASCE)0733-9496(1994)120:5(613).
Shih, J.-S., and C. ReVelle. 1995. “Water supply operations during drought: A discrete hedging rule.” Eur. J. Oper. Res. 82 (1): 163–175. https://doi.org/10.1016/0377-2217(93)E0237-R.
Singh, V. K., N. S. Chauhan, and D. Kushwaha. 2015. “An overview of hydro-electric power plant.” J. Mech. Eng. 1 (6): 59–62.
Soares, S., and C. T. Salmazo. 1997. “Minimum loss predispatch model for hydroelectric power systems.” IEEE Trans. Power Syst. 12 (3): 1220–1228. https://doi.org/10.1109/59.630464.
Stedinger, J. R., B. F. Sule, and D. P. Loucks. 1984. “Stochastic dynamic programming models for reservoir operation optimization.” Water Resour. Res. 20 (11): 1499–1505. https://doi.org/10.1029/WR020i011p01499.
Subramanya, K. 2013. Engineering hydrology. New York: Tata McGraw-Hill Education.
Tayebiyan, A., T. A. Mohammed Ali, A. H. Ghazali, and M. A. Malek. 2016. “Optimization of exclusive release policies for hydropower reservoir operation by using genetic algorithm.” Water Resour. Manage. 30 (3): 1203–1216. https://doi.org/10.1007/s11269-015-1221-6.
Tu, M.-Y., N.-S. Hsu, F. T.-C. Tsai, and W. W.-G. Yeh. 2008. “Optimization of hedging rules for reservoir operations.” J. Water Resour. Plann. Manage. 134 (1): 3–13. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:1(3).
Xu, W., Y. Peng, and B. Wang. 2013. “Evaluation of optimization operation models for cascaded hydropower reservoirs to utilize medium range forecasting inflow.” Sci. China Technol. Sci. 56 (10): 2540–2552. https://doi.org/10.1007/s11431-013-5346-7.
Xu, W., C. Zhang, Y. Peng, G. Fu, and H. Zhou. 2014. “A two stage Bayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts.” Water Resour. Res. 50 (12): 9267–9286. https://doi.org/10.1002/2013WR015181.
Yang, T., A. A. Asanjan, E. Welles, X. Gao, S. Sorooshian, and X. Liu. 2017. “Developing reservoir monthly inflow forecasts using artificial intelligence and climate phenomenon information.” Water Resour. Res. 53 (4): 2786–2812. https://doi.org/10.1002/2017WR020482.
You, J.-Y., and X. Cai. 2008a. “Hedging rule for reservoir operations: 1. A theoretical analysis.” Water Resour. Res. 44 (1): W01415. https://doi.org/10.1029/2006WR005481.
You, J.-Y., and X. Cai. 2008b. “Hedging rule for reservoir operations: 2. A numerical model.” Water Resour. Res. 44 (1): W01416. https://doi.org/10.1029/2006WR005482.
Zeng, Y., X. Wu, C. Cheng, and Y. Wang. 2014. “Chance-constrained optimal hedging rules for cascaded hydropower reservoirs.” J. Water Resour. Plann. Manage. 140 (7): 04014010. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000427.
Zhao, J., X. Cai, and Z. Wang. 2011a. “Optimality conditions for a two-stage reservoir operation problem.” Water Resour. Res. 47 (8): W08503. https://doi.org/10.1029/2010WR009971.
Zhao, T., X. Cai, and D. Yang. 2011b. “Effect of streamflow forecast uncertainty on real-time reservoir operation.” Adv. Water Resour. 34 (4): 495–504. https://doi.org/10.1016/j.advwatres.2011.01.004.
Zhao, T., J. Zhao, P. Liu, and X. Lei. 2015. “Evaluating the marginal utility principle for long-term hydropower scheduling.” Energy Convers. Manage. 106 (12): 213–223. https://doi.org/10.1016/j.enconman.2015.09.032.
Zhao, T., J. Zhao, J. R. Lund, and D. Yang. 2014a. “Optimal hedging rules for reservoir flood operation from forecast uncertainties.” J. Water Resour. Plann. Manage. 140 (12): 4014041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432.
Zhao, T., J. Zhao, and D. Yang. 2014b. “Improved dynamic programming for hydropower reservoir operation.” J. Water Resour. Plann. Manage. 140 (3): 365–374. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000343.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 148 • Issue 6 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Sep 22, 2020
Accepted: Jan 25, 2022
Published online: Mar 24, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 24, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Weisa Meng, Wenhua Wan, Zhongjing Wang, Jianshi Zhao, Physical and Economic Determinants on Forecast Horizon for Long-Term Reservoir Operation, Journal of Water Resources Planning and Management, 10.1061/JWRMD5.WRENG-5973, 149, 7, (2023).
- Jiechen Wang, Zhimei Gao, Yan Ma, Prediction Model of Hydropower Generation and Its Economic Benefits Based on EEMD-ADAM-GRU Fusion Model, Water, 10.3390/w14233896, 14, 23, (3896), (2022).