Technical Papers
Jan 21, 2021

Performance Comparison of Equivalent Reservoir and Multireservoir Models in Forecasting Hydropower Potential for Linking Water and Power Systems

Publication: Journal of Water Resources Planning and Management
Volume 147, Issue 4

Abstract

To link water and power systems on a regional scale, equivalent reservoir models—an aggregated representation of a multireservoir system—are commonly used because conventional river-basin scale optimization models become computationally expensive with increasing dimensionality. Although equivalent reservoir models are widely applied in power system operation, analyses comparing the performance of equivalent reservoir models with multireservoir cascade models are limited. To this end, this study systematically compares two equivalent reservoir models, an aggregated water balance and an energy balance representation, with a multireservoir cascade representation for a system of three reservoirs in series in Savannah, South Carolina, in terms of the total end-of-period release, hydropower and storage based on simulation, simulation optimization, and analytically over a 30-year period. Findings from the pilot basin are generalized by altering the storage-to-demand ratio (SDR) to understand the effect of different system characteristics on the equivalent reservoir representation under observed and predicted inflows of different skills. Equivalent reservoir models perform similarly to the cascade model for systems with large SDRs, but for systems with smaller SDRs, equivalent reservoir models perform poorly because spill and other losses from individual reservoirs cannot be effectively represented in the aggregated approach.

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Data Availability Statement

All data used in this analysis are available from the authors upon request.

Acknowledgments

This research work was partially funded by the project Cybersees Type 2: Cyber-Enabled Water and Energy Systems Sustainability Utilizing Climate Information (https://www.nsf.gov/awardsearch/showAward?AWD_ID=1442909).

References

Ahmed, I., and K. E. Lansey. 2001. “Optimal operation of multi-reservoir systems under uncertainty.” In Proc., World Water and Environmental Resources Congress, edited by D. Phelps. Reston, VA: Environmental and Water Resources Institute of ASCE.
Archibald, T., K. McKinnon, and L. Thomas. 2006. “Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming.” Nav. Res. Logist. 53 (3): 217–225. https://doi.org/10.1002/nav.20134.
Arvanitidis, N. V., and J. Rosing. 1970a. “Composite representation of a multireservoir hydroelectric power system.” IEEE Trans. Power Appartus Syst. 2 (PAS-89): 319–326.
Arvanitidis, N. V., and J. Rosing. 1970b. “Optimal operation of multireservoir systems using a composite representation.” IEEE Trans. Power Apparatus Syst. PAS-89 (2): 327–335. https://doi.org/10.1109/TPAS.1970.292596.
Barros, M. T., F. T. Tsai, S. L. Yang, J. E. Lopes, and W. W. Yeh. 2003. “Optimization of large-scale hydropower system operations.” J. Water Resour. Plann. Manage. 129 (3): 178–188. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(178).
Brandão, J. L. B. 2010. “Performance of the equivalent reservoir modelling technique for multi-reservoir hydropower systems.” Water Resour. Manage. 24 (12): 3101–3114. https://doi.org/10.1007/s11269-010-9597-9.
Brandi, R. B. S., T. P. Ramos, B. H. Dias, A. L. M. Marcato, and I. C. da Silva Junior. 2015. “Improving stochastic dynamic programming on hydrothermal systems through an iterative process.” Electr. Power Syst. Res. 123 (Jun): 147–153. https://doi.org/10.1016/j.epsr.2015.02.011.
Cain, M. B., R. P. O’neill, and A. Castillo. 2012. History of optimal power flow and formulations. Washington, DC: Federal Energy Regulatory Commission.
Crawley, P. D., and G. C. Dandy. 1993. “Optimal operation of multiple-reservoir system.” J. Water Resour. Plann. Manage. 119 (1): 1–17. https://doi.org/10.1061/(ASCE)0733-9496(1993)119:1(1).
Dahe, P. D., and D. K. Srivastava. 2002. “Multireservoir multiyield model with allowable deficit in annual yield.” J. Water Resour. Plann. Manage. 128 (6): 406–414. https://doi.org/10.1061/(ASCE)0733-9496(2002)128:6(406).
Das, P., J. Patskoski, and A. Sankarasubramanian. 2018. “Modeling the irrigation withdrawals over the coterminous US using a hierarchical modeling approach.” Water Resour. Res. 54 (6): 3769–3787. https://doi.org/10.1029/2017WR021723.
de Matos, V. L., and E. C. Finardi. 2012. “A computational study of a stochastic optimization model for long term hydrothermal scheduling.” Int. J. Electr. Power Energy Syst. 43 (1): 1443–1452. https://doi.org/10.1016/j.ijepes.2012.06.021.
de Matos, V. L., E. C. Finardi, and E. L. da Silva. 2008. “Comparison between the energy equivalent reservoir per subsystem and per cascade in the long-term operation planning in Brazil.” In Proc., Int. Conf. on Engineering Optimization EngOpt 2008. Rio de Janeiro, Brazil: International Conference on Engineering Optimization.
de Queiroz, A. R. 2011. “A sampling-based decomposition algorithm with application to hydrothermal scheduling: Cut formation and solution quality.” Ph.D. dissertation, Dept. of Industrial Engineering and Management Sciences, Univ. of Texas at Austin.
de Queiroz, A. R. 2016. “Stochastic hydro-thermal scheduling optimization: An overview.” Renewable Sustainable Energy Rev. 62 (Sep): 382–395. https://doi.org/10.1016/j.rser.2016.04.065.
de Queiroz, A. R., D. Mulcahy, A. Sankarasubramanian, J. P. Deane, G. Mahinthakumar, N. Lu, and J. F. DeCarolis. 2019. “Repurposing an energy system optimization model for seasonal power generation planning.” Energy 181 (May): 1321–1330. https://doi.org/10.1016/j.energy.2019.05.126.
Dias, B. H., M. A. Tomim, A. L. M. Marcato, T. P. Ramos, R. B. S. Brandi, I. C. da Silva Junior, and J. A. Passos Filho. 2013. “Parallel computing applied to the stochastic dynamic programming for long term operation planning of hydrothermal power systems.” Eur. J. Oper. Res. 229 (1): 212–222. https://doi.org/10.1016/j.ejor.2013.02.024.
Ehsani, N., B. M. Fekete, C. J. Vörösmarty, and Z. D. Tessler. 2016. “A neural network based general reservoir operation scheme.” Stochastic Environ. Res. Risk Assess. 30: 1151–1166. https://doi.org/10.1007/s00477-015-1147-9.
Fang, H. B., T. S. Hu, X. Zeng, and F. Y. Wu. 2014. “Simulation-optimization model of reservoir operation based on target storage curves.” Water Sci. Eng. 7 (4): 433–445. https://doi.org/10.3882/j.issn.1674-2370.2014.04.008.
Fredo, G. L. M., E. C. Finardi, and V. L. de Matos. 2019. “Assessing solution quality and computational performance in the long-term generation scheduling problem considering different hydro production function approaches.” Renew. Energy 131 (Jul): 45–54. https://doi.org/10.1016/j.renene.2018.07.026.
Ghimire, B. N. S., and M. J. Reddy. 2014. “Optimization and uncertainty analysis of operational policies for multipurpose reservoir system.” Stochastic Environ. Res. Risk Assess. 28 (7): 1815–1833. https://doi.org/10.1007/s00477-014-0846-y.
Golembesky, K., A. Sankarasubramanian, and N. Devineni. 2009. “Improved drought management of Falls Lake Reservoir: Role of multimodel streamflow forecasts in setting up restrictions.” J. Water Resour. Plann. Manage. 135 (3): 188–197. https://doi.org/10.1061/(ASCE)0733-9496(2009)135:3(188).
Goor, Q., R. Kelman, and A. Tilmant. 2011. “Optimal multipurpose-multireservoir operation model with variable productivity of hydropower plants.” J. Water Resour. Plann. Manage. 137 (3): 258–267. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000117.
Graf, W. L. 1999. “Dam nation: A geographic census of American dams and their large-scale hydrologic impacts.” Water Resour. Res. 35 (4): 1305–1311. https://doi.org/10.1029/1999WR900016.
Guo, X., T. Hu, C. Wu, T. Zhang, and Y. Lv. 2013. “Multi-Objective optimization of the proposed multi-reservoir operating policy using improved NSPSO.” Water Resour. Manage. 27 (7): 2137–2153. https://doi.org/10.1007/s11269-013-0280-9.
Hamlet, A. F., and D. P. Lettenmaier. 1999. “Effects of climate change on hydrology and water resources in the Columbia River basin.” J. Am. Water Works Assn. 35 (6): 1597–1623. https://doi.org/10.1111/j.1752-1688.1999.tb04240.x.
Kominoski, J. S., A. Ruhí, M. M. Hagler, K. Petersen, J. L. Sabo, T. Sinha, A. Sankarsubramanian, and J. D. Olden. 2018. “Patterns and drivers of fish extirpations in rivers of the American Southwest and Southeast.” Global Change Biol. 24 (3): 1175–1185. https://doi.org/10.1111/gcb.13940.
Koutsoyiannis, D., and A. Economou. 2003a. “Evaluation of the parameterization-simulation-optimization approach for the control of reservoir systems.” Water Resour. Res. 39 (6). https://doi.org/10.1029/2003WR002148.
Koutsoyiannis, D., and A. Economou. 2003b. Mathematical study of the concept of equivalent reservoir.. Athens, Greece: National Technical Univ. of Athens.
Labadie, J. W. 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).
Li, W., A. Sankarasubramanian, R. S. Ranjithan, and E. D. Brill. 2014. “Improved regional water management utilizing climate forecasts: An interbasin transfer model with a risk management framework.” Water Resour. Res. 50 (8): 6810–6827. https://doi.org/10.1002/2013WR015248.
Maceira, M. E. P., V. S. Duarte, D. D. J. Penna, L. A. M. Moraes, and A. C. G. Melo. 2008. “Ten years of application of stochastic dual dynamic programming in official and agent studies in Brazil-description of the newave program.” In Proc., 16th PSCC, 14–18. Zurich, Switzerland: Power Systems Computation Conference.
Maceira, M. E. P., V. S. Duarte, D. D. J. Penna, and M. P. Tcheou. 2011. “An approach to consider hydraulic coupled systems in the construction of equivalent reservoir model in hydrothermal operation planning.” In Proc., 17th Power Systems Computation Conf. (PSCC). Zurich, Switzerland: Power Systems Computation Conference.
Maurer, E. P., and D. P. Lettenmaier. 2003. “Predictability of seasonal runoff in the Mississippi River basin.” J. Geophys. Res.: Atmos. 108 (D16). https://doi.org/10.1029/2002JD002555.
Maurer, E. P., and D. P. Lettenmaier. 2004. “Potential effects of long-lead hydrologic predictability on Missouri River main-stem reservoirs.” J. Clim. 17 (1): 174–186. https://doi.org/10.1175/1520-0442(2004)017%3C0174:PEOLHP%3E2.0.CO;2.
Nandalal, K., and J. J. Bogardi. 2007. Dynamic programming based operation of reservoirs: Applicability and limits. Cambridge, UK: Cambridge University Press.
Oludhe, C., A. Sankarasubramanian, T. Sinha, N. Devineni, and U. Lall. 2013. “The role of multimodel climate forecasts in improving water and energy management over the Tana River Basin, Kenya.” J. Appl. Meteorol. Climatol. 52 (11): 2460–2475. https://doi.org/10.1175/JAMC-D-12-0300.1.
Pereira, M. V. F., and L. M. V. G. Pinto. 1985. “Stochastic optimization of a multireservoir hydroelectric system: A decomposition approach.” Water Resour. Res. 21 (6): 779–792. https://doi.org/10.1029/WR021i006p00779.
Pereira, M. V. F., and L. M. V. G. Pinto. 1991. “Multi-stage stochastic optimization applied to energy planning.” Math. Program. 52B (1–3): 359–375. https://doi.org/10.1007/BF01582895.
Petersen, T., N. Devineni, and A. Sankarasubramanian. 2012. “Seasonality of monthly runoff over the continental United States: Causality and relations to mean annual and mean monthly distributions of moisture and energy.” J. Hydrol. 468 (Oct): 139–150. https://doi.org/10.1016/j.jhydrol.2012.08.028.
Petersen, T., N. Devineni, and A. Sankarasubramanian. 2018. “Monthly hydroclimatology of the continental United States.” Adv. Water Resour. 114 (Feb): 180–195. https://doi.org/10.1016/j.advwatres.2018.02.010.
Rani, D., and M. M. Moreira. 2010. “Simulation–optimization modeling: A survey and potential application in reservoir systems operation.” Water Resour. Manage. 24 (6): 1107–1138. https://doi.org/10.1007/s11269-009-9488-0.
Saad, M., A. Turgeon, P. Bigras, and R. Duquette. 1994. “Learning disaggregation technique for the operation of long-term hydroelectric power systems.” Water Resour. Res. 30 (11): 3195–3202. https://doi.org/10.1029/94WR01731.
Sankarasubramanian, A., et al. 2017. “Synthesis of public water supply use in the United States: Spatio-temporal patterns and socio-economic controls.” Earth’s Future 5 (7): 771–788. https://doi.org/10.1002/2016EF000511.
Sankarasubramanian, A., U. Lall, and S. Espinueva. 2008. “Role of retrospective forecasts of GCMs forced with persisted SST anomalies in operational streamflow forecasts development.” J. Hydrometeorol. 9 (2): 212–227. https://doi.org/10.1175/2007JHM842.1.
Sankarasubramanian, A., U. Lall, F. A. Souza Filho, and A. Sharma. 2009. “Improved water allocation utilizing probabilistic climate forecasts: Short-term water contracts in a risk management framework.” Water Resour. Res. 45 (11): W11409. https://doi.org/10.1029/2009WR007821.
Santos, A. H. M., S. V. Bajay, and C. A. Coelho. 1989. “The use of both aggregate and disaggregate representations for the hydroelectric power plants, in the expansion planning of hydrothermal power systems.” In Vol. 4 of Proc., 24th Intersociety Energy Conversion Engineering Conf., 1827–1832. New York: IEEE.
Simonovic, S. P., and R. S. V. Teegavarapu. 2000. “Short-term operation model for coupled hydropower reservoirs.” J. Water Resour. Plann. Manage. 126 (2): 98–106. https://doi.org/10.1061/(ASCE)0733-9496(2000)126:2(98).
Soroush, M., and J. D. Fuller. 2013. “Accuracies of optimal transmission switching heuristics based on DCOPF and ACOPF.” IEEE Trans. Power Syst. 29 (2): 924–932. https://doi.org/10.1109/TPWRS.2013.2283542.
Tarroja, B., A. AghaKouchak, and S. Samuelsen. 2016. “Quantifying climate change impacts on hydropower generation and implications on electric grid greenhouse gas emissions and operation.” Energy 111: 295–305.
Turgeon, A. 1980. “Optimal operation of multireservoir power systems with stochastic inflows.” Water Resour. Res. 16 (2): 275–283. https://doi.org/10.1029/WR016i002p00275.
Turgeon, A. 1981. “A decomposition method for the long-term scheduling of reservoirs in series.” Water Resour. Res. 17 (6): 1565–1570. https://doi.org/10.1029/WR017i006p01565.
Turgeon, A. 1982. “Incremental dynamic programing may yield nonoptimal solutions.” Water Resour. Res. 18 (6): 1599–1604. https://doi.org/10.1029/WR018i006p01599.
Turner, S. W. D., N. Voisin, J. Fazio, D. Hua, and M. Jourabchi. 2019. “Compound climate events transform electrical power shortfall risk in the Pacific Northwest.” Nat. Commun. 10 (8). https://doi.org/10.1038/s41467-018-07894-4.
USACE. 2013 “Savannah district water management.” Accessed May 11, 2019. https://www.sas.usace.army.mil/.
Vogel, R. M., and J. R. Stedinger. 1987. “Generalized storage-reliability-yield relationships.” J. Hydrol. 89 (3–4): 303–327. https://doi.org/10.1016/0022-1694(87)90184-3.
Wang, H., E. D. Brill, R. S. Ranjithan, and A. Sankarasubramanian. 2015. “A framework for incorporating ecological releases in single reservoir operation.” Adv. Water Resour. 78 (Apr): 9–21. https://doi.org/10.1016/j.advwatres.2015.01.006.
Yeh, W. W. 1985. “Reservoir management and operations models: A state-of-the-art review.” Water Resour. Res. 21 (12): 1797–1818. https://doi.org/10.1029/WR021i012p01797.

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Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 147Issue 4April 2021

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Received: Jan 28, 2020
Accepted: Oct 2, 2020
Published online: Jan 21, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 21, 2021

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Former Graduate Student, Dept. of Civil, Construction, and Environmental Engineering, North Carolina State Univ., Raleigh, NC 27695-7908; presently, Postdoctoral Associate, Dept. of Biological and Environmental Engineering, Cornell Univ., Ithaca, NY 14853 (corresponding author). ORCID: https://orcid.org/0000-0002-3567-4801. Email: [email protected]
A. Sankarasubramanian, Ph.D., A.M.ASCE
Professor, Dept. of Civil, Construction, and Environmental Engineering, North Carolina State Univ., Raleigh, NC 27695-7908.
Anderson Rodrigo de Queiroz, Ph.D.
Assistant Professor, Dept. of Decision Sciences, School of Business, NC Central Univ., 1801 Fayetteville Rd., Durham, NC 27707.

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