Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming
Abstract
:1. Introduction
2. Operation Optimization Model of Cascade Reservoirs
2.1. Objective Function
2.2. Main Constraints
- (1)
- Water balance constraints
- (2)
- Reservoir volume limits
- (3)
- Comprehensive utilization limits of water resources required at downstream
- (4)
- Output limits
- (5)
- Boundary conditions limits
3. Multi-Dimensional Dynamic Programming
3.1. Basic Principle
3.2. Calculation Procedure of MDP
4. Case Study
4.1. Basic Data and Regularity of the Optimal Sample Data
- (1)
- Regularity of the operation of upstream reservoir
- (2)
- Regularity of the operation of middle reservoir
- (3)
- Regularity of the operation of downstream reservoir
4.2. Extraction of Operation Rules Based on the Optimal Results
4.3. Discussion and Analysis of Simulation Results
5. Conclusions
- (1)
- In this paper, the MDP model of cascade-reservoir operation optimization was proposed, and the MDP successfully realized its effective application in the optimization of cascade reservoirs. Based on the optimal sample data, the general regular information of each reservoir in each operation stage was summarized and extracted, and seven uncertain problems over the whole operation period of cascade systems were summarized.
- (2)
- In order to solve the uncertain problems of cascade system during the operation period, this paper proposed two sub-models, i.e., sub-model for the last three stages of non-flood season and sub-model for the first two stages of non-flood season. The two sub-models successfully solved the water storage operation problem of middle reservoir at the beginning of the non-flood season, and the water discharge problem of upstream and downstream reservoirs at the end of the non-flood season. The operation rules of each reservoir were finally extracted by dividing the whole operation period into four characteristic sections.
- (3)
- When comparing the simulation results of the extracted rules with those of conventional joint operation method, it was found that the power generation of the proposed rules had a certain degree of improvement both in inspection years and typical years, and the increase is 0.7%, 0.4%, 2.3%, and 1.7%, respectively. The guarantee rate of output was basically unchanged. So, on the whole, the operation rules extracted in this paper have the practical value, and they can be used to guide the actual operation of Li Xianjiang cascade reservoirs.
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Yüksel, I. Hydropower for sustainable water and energy development. Renew. Sustain. Energy Rev. 2010, 14, 462–469. [Google Scholar] [CrossRef]
- Li, F.; Qiu, J. Multi-objective optimization for integrated hydro-photovoltaic power system. Appl. Energy 2016, 167, 377–384. [Google Scholar] [CrossRef]
- Gebretsadik, Y.; Fant, C.; Strzepek, K.; Arndt, C. Optimized reservoir operation model of regional wind and hydro power integration case study: Zambezi basin and South Africa. Appl. Energy 2016, 161, 574–582. [Google Scholar] [CrossRef]
- George, C. Feasibility study of a hybrid wind/hydropower-system for low-cost electricity production. Appl. Energy 2002, 72, 599–608. [Google Scholar]
- Lu, D.; Wang, B.; Wang, Y.; Zhou, H.; Liang, Q.; Peng, Y.; Roskilly, T. Optimal operation of cascade hydropower stations using hydrogen as storage medium. Appl. Energy 2015, 137, 56–63. [Google Scholar] [CrossRef]
- Kangrang, A.; Chaleeraktrakoon, C. Genetic algorithms connected simulation with smoothing function for searching rule curves. Am. J. Appl. Sci. 2007, 4, 73–79. [Google Scholar] [CrossRef]
- Jiang, Z.Q.; Sun, P.; Ji, C.M.; Zhou, J.Z. Credibility theory based dynamic control bound optimization for reservoir flood limited water level. J. Hydrol. 2015, 529, 928–939. [Google Scholar] [CrossRef]
- Chang, F.; Chen, L.; Chang, L. Optimizing the reservoir operating rule curves by genetic algorithms. Hydrol. Process. 2005, 19, 2277–2289. [Google Scholar] [CrossRef]
- Taghian, M.; Rosbjerg, D.; Haghighi, A.; Madsen, H. Optimization of conventional rule curves coupled with hedging rules for reservoir operation. J. Water Resour. Plan. Manag. 2014, 140, 693–698. [Google Scholar] [CrossRef]
- Ding, Y.; Tang, D.; Meng, Z. A new functional approach for searching optimal reservoir rule curves. Adv. Mater. Res. 2014, 915–916, 1452–1455. [Google Scholar] [CrossRef]
- Chang, F.; Lai, J.; Kao, L. Optimization of operation rule curves and flushing schedule in a reservoir. Hydrol. Process. 2003, 17, 1623–1640. [Google Scholar] [CrossRef]
- Afshar, A.; Emami Skardi, M.; Masoumi, F. Optimizing water supply and hydropower reservoir operation rule curves: An imperialist competitive algorithm approach. Eng. Optim. 2015, 47, 1208–1225. [Google Scholar] [CrossRef]
- Ak, M.; Kentel, E.; Savasaneril, S. Operating policies for energy generation and revenue management in single-reservoir hydropower systems. Renew. Sustain. Energy Rev. 2017, 78, 1253–1261. [Google Scholar] [CrossRef]
- Chang, J.; Li, Y.; Yuan, M.; Wang, Y. Efficiency evaluation of hydropower station operation: A case study of Longyangxia Station in the Yellow River, China. Energy 2017, 135, 23–31. [Google Scholar] [CrossRef]
- Eum, H.; Kim, Y.; Palmer, R.N. Optimal drought management using sampling stochastic dynamic programming with a hedging rule. J. Water Resour. Plan. Manag. 2010, 137, 113–122. [Google Scholar] [CrossRef]
- Shokri, A.; Haddad, O.B.; Marino, M.A. Reservoir operation for simultaneously meeting water demand and sediment flushing: Stochastic dynamic programming approach with two uncertainties. J. Water Resour. Plan. Manag. 2013, 139, 277–289. [Google Scholar] [CrossRef]
- Kangrang, A.; Lokham, C. Optimal reservoir rule curves considering conditional ant colony optimization with simulation model. J. Appl. Sci. 2013, 13, 154–160. [Google Scholar] [CrossRef]
- Chu, W.; Yang, T.; Gao, X. Comment on “High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing” by Eric Laloy and Jasper A. Vrugt. Water Resour. Res. 2014, 50, 2775–2780. [Google Scholar] [CrossRef]
- Yang, C.; Chang, L.; Yeh, C.; Chen, C. Multi-objective planning of surface water resources by multi-objective genetic algorithm with constrained differential dynamic programming. J. Water Resour. Plan. Manag. 2007, 133, 499–508. [Google Scholar] [CrossRef]
- Zhu-Ge, Y.; Xie, P. The application of DDDP method to optimal operation for cascade reservoirs based on state transformation matrix. In Proceedings of the 2010 International Conference on Computational and Information Sciences ICCIS, Chengdu, China, 17–19 December 2010; pp. 76–80. [Google Scholar]
- Lu, B.; Li, K.; Zhang, H.; Wang, W.; Gu, H. Study on the optimal hydropower generation of Zhelin reservoir. J. Hydro-Environ. Res. 2013, 7, 270–278. [Google Scholar] [CrossRef]
- Mathlouthi, M.; Lebdi, F. Use of generated time series of dry events for the optimization of small reservoir operation. Hydrol. Sci. J. 2009, 54, 841–851. [Google Scholar] [CrossRef]
- Pereira, M.V.F.; Pinto, L.M.V.G. Multi-stage stochastic optimization applied to energy planning. Math. Program. 1991, 52, 359–375. [Google Scholar] [CrossRef]
- Zhang, R.; Zhou, J.; Zhang, H.; Liao, X.; Wang, X. Optimal operation of large-scale cascaded hydropower systems in the upper reaches of the Yangtze River, China. J. Water Resour. Plan. Manag. 2014, 140, 480–495. [Google Scholar] [CrossRef]
- Momtahen, S.; Dariane, A.B. Direct search approaches using genetic algorithms for optimization of water reservoir operating policies. J. Water Resour. Plan. Manag. 2007, 133, 202–209. [Google Scholar] [CrossRef]
- Arnel, G.; Aleš, Z. Short-term combined economic and emission hydrothermal optimization by surrogate differential evolution. Appl. Energy 2015, 141, 42–56. [Google Scholar]
- Ji, C.; Yu, S.; Zhou, T.; Yang, Z.; Liu, F. Application of ant colony algorithm for hydropower dispatching function optimization. Autom. Electr. Power Syst. 2011, 35, 103–107. [Google Scholar]
- Hormwichian, R.; Kangrang, A.; Lamom, A. A conditional genetic algorithm model for searching optimal reservoir rule curves. J. Appl. Sci. 2009, 9, 3575–3580. [Google Scholar] [CrossRef]
- Mensik, P.; Starý, M.; Marton, D. Water management software for controlling the water supply function of many reservoirs in a watershed. Water Resour. 2015, 42, 133–145. [Google Scholar] [CrossRef]
- Helseth, A.; Fodstad, M.; Askeland, M.; Mo, B.; Nilsen, O.B.; Pérez-Díaz, J.I.; Chazarra, M.; Guisández, I. Assessing hydropower operational profitability considering energy and reserve markets. IET Renew. Power Gener. 2017, 11. [Google Scholar] [CrossRef]
- Ma, C.; Lian, J.; Wang, J. Short-term optimal operation of Three-gorge and Gezhouba cascade hydropower stations in non-flood season with operation rules from data mining. Energy Convers. Manag. 2013, 65, 616–627. [Google Scholar] [CrossRef]
- Yuan, W.; Wu, Z. Discussion on application of cooperative coevolution of differential evolution algorithm to optimal operation of cascaded reservoirs. J. Hydroelectr. Eng. 2012, 31, 39–43. [Google Scholar]
- Raso, L.; Schwanenberg, D.; van de Giesen, N.C.; van Overloop, P.J. Short-term optimal operation of water systems using ensemble forecasts. Adv. Water Resour. 2014, 71, 200–208. [Google Scholar] [CrossRef]
- Zhang, Y.; Jiang, Z.; Ji, C.; Sun, P. Contrastive analysis of three parallel modes in multi-dimensional dynamic programming and its application in cascade reservoirs operation. J. Hydrol. 2015, 529, 22–34. [Google Scholar] [CrossRef]
- Jiang, Z.; Qin, H.; Ji, C.; Feng, Z.; Zhou, J. Two dimension reduction methods for multi-dimensional dynamic programming and its application in cascade reservoirs operation optimization. Water 2017, 9, 634. [Google Scholar] [CrossRef]
- Ji, C.M.; Jiang, Z.Q.; Sun, P.; Zhang, Y.K.; Wang, L.P. Research of multi-dimensional dynamic programming based on multi-layer nested structure and its application in cascade reservoirs. J. Water Resour. Plan. Manag. 2015, 141, 1–13. [Google Scholar] [CrossRef]
- Nandalal, K.D.W.; Bogardi, J.J. Dynamic Programming Based Operation of Reservoirs: Applicability and Limits; Cambridge University Press: Cambridge, UK, 2007. [Google Scholar]
- Jiang, Z.; Li, A.; Ji, C.; Qin, H.; Yu, S.; Li, Y. Research and application of key technologies in drawing energy storage operation chart by discriminant coefficient method. Energy 2016, 114, 774–786. [Google Scholar] [CrossRef]
- Yang, G.; Guo, S.; Liu, P.; Xu, C. Multiobjective reservoir operating rules based on cascade reservoir input variable selection method. Water Resour. Res. 2017, 53, 3446–3463. [Google Scholar] [CrossRef]
Items | Unit | Ya Yangshan | Shi Menkan | Long Ma |
---|---|---|---|---|
Normal water level | m | 835 | 756 | 639 |
Dead water level | m | 818 | 740 | 605 |
Total storage volume | 108 m3 | 3.08 | 1.75 | 5.1 |
Regulation volume | 108 m3 | 1.34 | 0.82 | 3.34 |
Storage factor | -- | 0.035 | 0.02 | 0.056 |
Regulation performance | -- | season | season | season |
Design assurance rate | % | 95 | none | 95 |
Guaranteed output | MW | 23.2 | 33.5 | 61.2 |
Annual power generation | GWh | 499 | 573 | 1284 |
Water head loss coefficient | 10−5 | 8.658 | 5.28 | 2.642 |
Maximum head loss | m | 5.59 | 2.33 | 3 |
Integrated efficiency coefficient | -- | 8.3 | 8.3 | 8.3 |
Flood control level | m | 818 | 740 | none |
Flood season | month | 6~10 | 6~10 | none |
Reservoir | Upstream Reservoir | Middle Reservoir | Downstream Reservoir |
---|---|---|---|
Segmentation diagram | | | |
Section A | Operating at the flood control level in flood season | Operating at the flood control level in flood season | Operating with output ceiling when water level is below normal level, and trying to keep high water level and not to abandon water when water level is equal to normal level |
Section B | Operating with the sub-model for the first two stages of the non-flood season | Operating with the sub-model for the first two stages of the non-flood season | Maintain the normal water level operation |
Section C | Maintain the normal water level operation | Maintain the normal water level operation | Maintain the normal water level operation |
Section D | Operating with the sub-model for the last three stages of the non-flood season | Operating with the sub-model for the last three stages of the non-flood season | Maintain the normal water level operation |
Year | Simulation Results by Rules (1) | MDP (2) | Decrement [(2) − (1)]/(1) |
---|---|---|---|
Multi-year average | 2323 | 2392 | 3.0% |
Wet year | 2710 | 2816 | 3.9% |
Normal year | 2214 | 2263 | 2.2% |
Dry year | 1822 | 1888 | 3.6% |
Year | Simulation Results by Rules (1) | Conventional Joint Operation (2) | Increment [(1) − (2)]/(1) |
---|---|---|---|
Multi-year average | 2323 | 2307 | 0.7% |
Wet year | 2710 | 2699 | 0.4% |
Normal year | 2214 | 2164 | 2.3% |
Dry year | 1822 | 1792 | 1.7% |
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Jiang, Z.; Qin, H.; Wu, W.; Qiao, Y. Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming. Water 2018, 10, 20. https://doi.org/10.3390/w10010020
Jiang Z, Qin H, Wu W, Qiao Y. Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming. Water. 2018; 10(1):20. https://doi.org/10.3390/w10010020
Chicago/Turabian StyleJiang, Zhiqiang, Hui Qin, Wenjie Wu, and Yaqi Qiao. 2018. "Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming" Water 10, no. 1: 20. https://doi.org/10.3390/w10010020