A Multiobjective Stochastic Programming Model for Hydropower Hedging Operations under Inexact Information
Tóm tắt
This study develops a multiobjective stochastic programming model for informing hedging decisions for hydropower operations under an electricity market environment considering the benefit from selling energy production and the cost of penalizing energy shortfall. Aiming to determine the optimal strategy that hedges the risk of energy shortfall while keeping a high level of direct revenue from energy production under uncertain streamflows and inexact penalizing price conditions, competing objectives of minimizing energy shortfall percentage and maximizing direct revenue from energy production are analyzed. The conflict is resolved by determining the optimal level of energy shortfall percentage such that the net benefit of the hydropower system is maximized. The first-order optimality condition of maximized system net revenue is derived, which states that the marginal benefit of hedging equals the marginal cost of hedging at optimality. The tradeoff ratio between the competing objectives serves as the marginal cost of hedging and the penalizing price of energy shortfall represents the marginal benefit of hedging. Using the optimality condition, sensitivity tests are conducted for investigating the influence of different ranges of penalizing prices and reservoir initial storages on hedging decisions. The proposed method is evaluated on the operations of the Three Gorges cascade hydropower system during the drawdown season. Results show that: (1) minimizing the energy shortfall percentage adversely affects the maximization in system direct revenue from energy production, and the conflicting results are related to the depletion strategies of reservoir storage; (2) to reduce the energy shortfall percentage to the lowest level could result in significant reduction in total energy production and the direct revenue, especially when reservoir initial storages are low; and (3) the optimal level of energy shortfall percentage would decrease as penalizing price increases, when the influence of penalizing cost from energy shortfall gradually dominates the influence of energy production on the net revenue. The model framework and the implications could be applied to rationalize hedging decisions for hydropower operations under inexact information upon streamflow and penalizing prices.
Tài liệu tham khảo
Abdelaziz FB (2012) Solution approaches for the multiobjective stochastic programming. Eur J Oper Res 216(1):1–16. doi:10.1016/j.ejor.2011.03.033
Ahmadianfar I, Adib A, Taghian M (2016) Optimization of fuzzified hedging rules for multipurpose and multireservoir systems. J Hydrol Eng 21(050160034). doi:10.1061/(ASCE)HE.1943-5584.0001329
Draper AJ, Lund JR (2004) Optimal hedging and carryover storage value. J Water Resour Plan Manag-ASCE 130(1):83–87
Dupacova J, Consigli G, Wallace SW (2000) Scenarios for multistage stochastic programs. Ann Oper Res 100(1):25–53. doi:10.1023/A:1019206915174
Housh M, Ostfeld A, Shamir U. (2013) Limited multi-stage stochastic programming for managing water supply systems. Environ Model Softw 41:53–64. doi:10.1016/j.envsoft.2012.11.006
Howard CT, D'Antonio LJ (1994) The cost of hedging and the optimal hedge ratio. J Futur Mark 14(2):237–258
Hui R, Lund J, Zhao J, Zhao T (2016) Optimal pre-storm flood hedging releases for a single reservoir. Water Resour Manag. doi:10.1007/s11269-016-1472-x
Li JQ, Marino MA, Ji CM, Zhang YS (2009a) Mathematical models of inter-plant economical operation of a Cascade hydropower system in electricity market. Water Resour Manag 23(10):2003–2013. doi:10.1007/s11269-008-9365-2
Li YP, Huang GH, Nie SL (2009b) Water resources management and planning under uncertainty: an inexact multistage joint-probabilistic programming method. Water Resour Manag 23(12):2515–2538. doi:10.1007/s11269-008-9394-x
Liu H, Jiang C, Zhang Y (2008) A review on risk-constrained hydropower scheduling in deregulated power market. Renew Sust Energ Rev 12(5):1465–1475. doi:10.1016/j.rser.2007.01.018
Lu G, Wu H, Xiao H, He H, Wu Z (2016) Impact of climate change on drought in the upstream Yangtze River region. Water-Sui 8(12):576. doi:10.3390/w8120576
Neelakantan TR, Sasireka K (2015) Review of hedging rules applied to reservoir operation. Int J Eng Technol 7(5):1571–1580
Rangel LF (2008) Competition policy and regulation in hydro-dominated electricity markets. Energ Policy 36(4):1292–1302. doi:10.1016/j.enpo1.2007.12.005
Reed PM, Hadka D, Herman JD, Kasprzyk JR, Kollat JB (2013) Evolutionary multiobjective optimization in water resources: the past, present, and future. Adv Water Resour 51:438–456. doi:10.1016/j.advwatres.2012.01.005
Shao LG, Qin XS, Xu Y (2011) A conditional value-at-risk based inexact water allocation model. Water Resour Manag 25(9):2125–2145. doi:10.1007/s11269-011-9799-9
Tilmant A, Marques G, Mohamed Y (2015) A dynamic water accounting framework based on marginal resource opportunity cost. Hydrol Earth Syst Sci 19:1457–1467
Xu B, Zhong P, Stanko Z, Zhao Y, Yeh WWG (2015a) A multiobjective short-term optimal operation model for a cascade system of reservoirs considering the impact on long-term energy production. Water Resour Res 51(5):3353–3369. doi:10.1002/2014WR015964
Xu B, Zhong P, Zambon RC, Zhao Y, Yeh WWG (2015b) Scenario tree reduction in stochastic programming with recourse for hydropower operations. Water Resour Res 51(8):6359–6380. doi:10.1002/2014WR016828
You J, Cai X (2008) Hedging rule for reservoir operations: 1. A theoretical analysis. Water Resour Res 44(1):1–9. doi:10.1029/2006WR005481
Yu Z, Pollard D, Cheng L (2006) On continental-scale hydrologic simulations with a coupled hydrologic model. J Hydrol 331(1–2):110–124. doi:10.1016/j.jhydrol.2006.05.021
Zeng Y, Wu X, Cheng C, Wang Y (2014) Chance-constrained optimal hedging rules for cascaded hydropower reservoirs. J Water Res Plan Man, 140(7)
Zeng X, Hu T, Xiong L, Cao Z, Xu C (2015) Derivation of operation rules for reservoirs in parallel with joint water demand. Water Resour Res 51(12):9539–9563. doi:10.1002/2015WR017250
Zhang JS, Zhang YQ, Zhang H (2011) Studies on the anti-drought operations of Three Gorges project. Paper presented at the China Hydropower Engineering Society Committee Proceeding of 2011 conference on cascade reservoir operations, Chengdu, China
Zhao T, Zhao J, Lund JR, Yang D (2014) Optimal hedging rules for reservoir flood operation from forecast uncertainties. J Water Res Plan Manag 140(12):4014041. doi:10.1061/(ASCE)WR.1943-5452.0000432
Zhao T, Zhao J, Liu P, Lei X (2015) Evaluating the marginal utility principle for long-term hydropower scheduling. Energy Convers Manag 106:213–223. doi:10.1016/j.enconman.2015.09.032
Zhong PA, Zhang W, Xu B (2013) A risk decision model of the contract generation for hydropower generation companies in electricity markets. Electr Power Syst Res 95:90–98. doi:10.1016/j.epsr.2012.06.016