This is a post-peer-review, pre-copyedit version of an article published in Water Resources Management. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11269-017-1893-1
[en] Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become obsolete. The main difficulty with bounds computation is to correctly take into account the high uncertainty about the inflows to the reservoir. In this article, we propose a methodology to derive minimum bounds while providing formal guarantees about the quality of the obtained solutions. The uncertainty is embedded using either stochastic or robust programming in a model-predictive-control framework. We compare the two paradigms to the existing solution for a case study and find that the obtained solutions vary substantially. By combining the stochastic and the robust approaches, we also assign a confidence level to the solutions obtained by stochastic programming. The proposed methodology is found to be both efficient and easy to implement. It relies on sound mathematical principles, ensuring that a global optimum is reached in all cases.
Abrahart RJ, See L (1998) Neural network vs. ARMA modelling: constructing benchmark case studies of river flow prediction. In: Proceedings of the 3rd international conference on geoComputation, Bristol. http://www.geocomputation.org/1998/05/gc_05.htm
Adam N, Erpicum S, Archambeau P, Pirotton M, Dewals B (2014) Stochastic modelling of reservoir sedimentation in a Semi-Arid watershed. Water Resour Manag 29(3):785–800. https://doi.org/10.1007/s11269-014-0843-4https://doi.org/10.1007/s11269-014-0843-4
Ahmad A, El-Shafie A, Razali SFM, Mohamad ZS (2014) Reservoir optimization in water resources: a review. Water Resour Manag 28(11):3391–3405. https://doi.org/10.1007/s11269-014-0700-5
Ahmadi Najl A, Haghighi A, Vali Samani HM (2016) Simultaneous optimization of operating rules and rule curves for multireservoir systems using a self-adaptive simulation-GA model. J Water Resour Plan Manag 142(10):4016,041
Ahmadianfar I, Adib A, Taghian M (2017) Optimization of multi-reservoir operation with a new hedging rule: application of fuzzy set theory and NSGA-II. Appl Water Sci 7(6):3075–3086
Akbari-Alashti H, Haddad OB, Mariño MA (2015) Application of fixed length gene genetic programming (FLGGP) in hydropower reservoir operation. Water Resour Manag 29(9):3357–3370
Arunkumar R, Jothiprakash V (2012) Optimal reservoir operation for hydropower generation using non-linear programming model. Journal of The Institution of Engineers (India): Series A 93(2):111–120. https://doi.org/10.1007/s40030-012-0013-8
Bashiri-Atrabi H, Qaderi K, Rheinheimer DE, Sharifi E (2015) Application of harmony search algorithm to reservoir operation optimization. Water Resour Manag 29(15):5729–5748. https://doi.org/10.1007/s11269-015-1143-3https://doi.org/10.1007/s11269-015-1143-3
Becker BPJ, Schruff T, Schwanenberg D (2014) Modellierung von reaktiver Steuerung und model predictive control. In: 37. Dresdner Wasserbaukolloquium 2014. https://izw.baw.de/publikationen/dresdner-wasserbauliche-mitteilungen/0/18_Heft_50_Modellierung_reaktive_Steuerung.pdf
Ben-Tal A, Nemirovski A (2002) Robust optimization: methodology and applications. Math Program 92(3):453–480
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton
Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: a fresh approach to numerical computing. SIAM Review 59(1):65–98. https://doi.org/10.1137/141000671. http://julialang.org/publications/julia-fresh-approach-BEKS.pdf.
Bieri M, Schleiss AJ (2013) Analysis of flood-reduction capacity of hydropower schemes in an Alpine catchment area by semidistributed conceptual modelling. J Flood Risk Manage 6(3):169–185. https://doi.org/10.1111/j.1753-318X.2012.01171.x
Birge JR, Louveaux F (2011) Introduction to Stochastic Programming, 2nd edn. Springer, New York. http://www.springer.com/mathematics/applications/book/978-1-4614-0236-7. https://doi.org/10.1007/978-1-4614-0237-4
Camnasio E, Becciu G (2011) Evaluation of the feasibility of irrigation storage in a flood detention pond in an agricultural catchment in northern italy. Water Resour Manag 25(5):1489–1508. https://doi.org/10.1007/s11269-010-9756-z
Castelletti A, Pianosi F, Soncini-Sessa R (2008) Water reservoir control under economic, social and environmental constraints. Automatica 44 (6):1595–1607. https://doi.org/10.1016/j.automatica.2008.03.003. http://www.sciencedirect.com/science/article/pii/S0005109808001271
Celeste AB, Billib M (2009) Evaluation of stochastic reservoir operation optimization models. Adv Water Resour 32(9):1429–1443. https://doi.org/10.1016/j.advwatres.2009.06.008. http://www.sciencedirect.com/science/article/pii/S0309170809001006
Chang FJ, Chen L, Chang LC (2005) Optimizing the reservoir operating rule curves by genetic algorithms. Hydrol Process 19 (11):2277–2289. https://doi.org/10.1002/hyp.5674
Chaves P, Kojiri T (2007) Stochastic fuzzy neural network: case study of optimal reservoir operation. J Water Resour Plan Manag 133(6):509–518
Chen HW, Chang NB (2010) Using fuzzy operators to address the complexity in decision making of water resources redistribution in two neighboring river basins. Adv Water Resour 33(6):652–666
Dunning I, Huchette J, Lubin M (2017) JuMP: a modeling language for mathematical optimization. SIAM Rev 59(2):295–320. https://doi.org/10.1137/15M1020575
Finch J, Calver A (2008) Methods for the quantification of evaporation from lakes. Tech. rep., http://nora.nerc.ac.uk/14359/1/wmoevap_271008.pdf
Jordan FM, Boillat JL, Schleiss AJ (2012) Optimization of the flood protection effect of a hydropower multi-reservoir system. International journal of river basin management 10(1):65–72
Klopstra D, van Eck NV (1999) Methodiek voor vaststelling van de vorm van de maatgevende afvoergolf van de Maas bij Borgharen. HKV Lijn in Water in opdracht van WL—Delft Hydraulics en Rijkswaterstaat RIZA
Kwon WH, Han SH (2005) Receding horizon control: model predictive control for state models, 1st edn. Springer, London. http://www.springer.com/us/book/9781846280245
Labadie JW (2004) Optimal operation of multireservoir systems: State-of-the-Art review. J Water Resour Plan Manag 130(2):93–111. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:2(93)
Maier HR, Kapelan Z, Kasprzyk J, Kollat J, Matott LS, Cunha MC, Dandy GC, Gibbs MS, Keedwell EC, Marchi A, Ostfeld A, Savic D, Solomatine DP, Vrugt JA, Zecchin AC, Minsker BS, Barbour EJ, Kuczera G, Pasha F, Castelletti A, Giuliani M, Reed PM (2014) Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions. Environ Model Softw 62:271–299. https://doi.org/10.1016/j.envsoft.2014.09.013. http://www.sciencedirect.com/science/article/pii/S1364815214002679
Nicklow JW, Mays LW (2000) Optimization of multiple reservoir networks for sedimentation control. J Hydraul Eng 126(4):232–242
Pan L, Housh M, Liu P, Cai X, Chen X (2015) Robust stochastic optimization for reservoir operation. Water Resour Res 51(1):409–429
Peng Y, Peng A, Zhang X, Zhou H, Zhang L, Wang W, Zhang Z (2017) Multi-core parallel particle swarm optimization for the operation of Inter-Basin water transfer-supply systems. Water Resour Manag 31(1):27–41
Sabzi HZ, Humberson D, Abudu S, King JP (2016) Optimization of adaptive fuzzy logic controller using novel combined evolutionary algorithms, and its application in Diez Lagos flood controlling system, Southern New Mexico. Expert Syst Appl 43:154–164
Schwanenberg D, Becker BPJ, Xu M (2015) The open real-time control (RTC)-Tools software framework for modeling RTC in water resources sytems. J Hydroinf 17(1):130 LP–148. http://jh.iwaponline.com/content/17/1/130.abstract
Shapiro A, Dentcheva D (2014) Lectures on stochastic programming: modeling and theory, vol 16, 2nd edn. SIAM, Philadelphia
Spierdijk L (2016) Confidence intervals for ARMA–GARCH value-at-risk: The case of heavy tails and skewness. Comput Stat Data Anal 100:545–559
Spiliotis M, Mediero L, Garrote L (2016) Optimization of hedging rules for reservoir operation during droughts based on particle swarm optimization. Water Resour Manag 30(15):5759–5778
Sulis A (2016) An optimisation model for reservoir operation. In: Proceedings of the institution of civil engineers-water management, Thomas Telford Ltd, pp 1–9
Taghian M, Rosbjerg D, Haghighi A, Madsen H (2014) Optimization of Conventional Rule Curves Coupled with Hedging Rules for Reservoir Operation. J Water Resour Plan Manag 140(5):693–698. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000355
Talsma J, Patzke S, Becker BPJ, Goorden N, Schwanenberg D, Prinsen G (2013) Application of model predictive control on water extractions in scarcity situations in the netherlands. Revista de Ingeniería Innova 6:1–10
Vanderbei RJ (2014) Linear programming, international series in operations research & management science, vol 196, 4th edn. Springer, Boston
Yeh WWG (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
Zhang Y, Jiang Z, Ji C, Sun P (2015) Contrastive analysis of three parallel modes in multi-dimensional dynamic programming and its application in cascade reservoirs operation. J Hydrol 529:Part:22–34. https://doi.org/10.1016/j.jhydrol.2015.07.017. http://www.sciencedirect.com/science/article/pii/S0022169415005144
Zhao T, Zhao J, Lund J, Yang D (2014) Optimal hedging rules for reservoir flood operation from forecast uncertainties. Journal of Water Resources Planning and Management Preview(2011). https://doi.org/10.1061/(ASCE)WR.1943-5452.0000432
Zhu X, Zhang C, Fu G, Li Y, Ding W (2017) Bi-Level optimization for determining operating strategies for Inter-Basin water Transfer-Supply reservoirs. Water Resour Manag 31(14):4415–4432. ISSN: 1573-1650. https://doi.org/10.1007/s11269-017-1756-9
