Linking Nelder–Mead Simplex Direct Search Method into Two-Stage Progressive Optimality Algorithm for Optimal Operation of Cascade Hydropower Reservoirs
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 5
Abstract
To satisfy growing energy demand, the hydropower industry of China is experiencing unprecedented development, and the total power generation and installed capacity of hydropower in China rank first in the world. The system scale and rate of development have posed computational modeling challenges, because the computational burden in hydropower optimization modeling using classical dynamic programming methods grows exponentially as the number of reservoirs increases. One method designed to reduce this burden, the progressive optimality algorithm (POA), still suffers from the dimensionality problem and the need for iterative computations to address large-scale hydropower systems. To enhance the performance of POA, this work develops a new method referred to as the simplex progressive optimality algorithm (SPOA). In SPOA, the complex multistage problem is divided into several easy-to-solve two-stage subproblems, and then the Nelder–Mead simplex direct search method is adopted to search for the improved solution to each subproblem, enhancing the solution’s quality via iterative computation. Experimental results indicate that the proposed SPOA method can significantly reduce execution time and memory usage under different cases, demonstrating its applicability for large-scale hydropower system operation problems.
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Data Availability Statement
Due to the strict security requirements from the departments, some or all data, models, or code generated or used in the study are proprietary or confidential in nature and may only be provided with restrictions (e.g., anonymized data).
Acknowledgments
This paper is supported by the National Natural Science Foundation of China (51709119), Natural Science Foundation of Hubei Province (2018CFB573) and the Fundamental Research Funds for the Central Universities (HUST: 2017KFYXJJ193). The writers thank editors and reviewers for their valuable comments and suggestions.
References
Bai, T., Y. B. Kan, J. X. Chang, Q. Huang, and F. J. Chang. 2017. “Fusing feasible search space into PSO for multi-objective cascade reservoir optimization.” Appl. Soft Comput. 51 (Feb): 328–340. https://doi.org/10.1016/j.asoc.2016.12.005.
Cao, Y., Y. Cao, S. Wen, T. Huang, and Z. Zeng. 2019. “Passivity analysis of delayed reaction–diffusion memristor-based neural networks.” Neural Networks 109 (Jan): 159–167. https://doi.org/10.1016/j.neunet.2018.10.004.
Catalão, J. P. S., H. M. I. Pousinho, and V. M. F. Mendes. 2010. “Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain.” Electr. Pow. Syst. Res. 80 (8): 935–942. https://doi.org/10.1016/j.epsr.2009.12.015.
Chang, J., Y. Li, M. Yuan, and Y. Wang. 2017. “Efficiency evaluation of hydropower station operation: A case study of Longyangxia station in the Yellow River, China.” Energy 135 (Sep): 23–31. https://doi.org/10.1016/j.energy.2017.06.049.
Fan, S. K. S., and E. Zahara. 2007. “A hybrid simplex search and particle swarm optimization for unconstrained optimization.” Eur. J. Oper. Res. 181 (2): 527–548. https://doi.org/10.1016/j.ejor.2006.06.034.
Feng, Z., W. Niu, S. Wang, C. Cheng, and Z. Song. 2019a. “Mixed integer linear programming model for peak operation of gas-fired generating units with disjoint-prohibited operating zones.” Energies 12 (11): 2179. https://doi.org/10.3390/en12112179.
Feng, Z., W. Niu, W. Wang, J. Zhou, and C. Cheng. 2019b. “A mixed integer linear programming model for unit commitment of thermal plants with peak shaving operation aspect in regional power grid lack of flexible hydropower energy.” Energy 175 (May): 618–629. https://doi.org/10.1016/j.energy.2019.03.117.
Feng, Z. K., W. J. Niu, and C. T. Cheng. 2017a. “Multi-objective quantum-behaved particle swarm optimization for economic environmental hydrothermal energy system scheduling.” Energy 131 (Jul): 165–178. https://doi.org/10.1016/j.energy.2017.05.013.
Feng, Z. K., W. J. Niu, and C. T. Cheng. 2018a. “Optimization of hydropower reservoirs operation balancing generation benefit and ecological requirement with parallel multi-objective genetic algorithm.” Energy 153 (Jun): 706–718. https://doi.org/10.1016/j.energy.2018.04.075.
Feng, Z. K., W. J. Niu, and C. T. Cheng. 2018b. “Optimizing electrical power production of hydropower system by uniform progressive optimality algorithm based on two-stage search mechanism and uniform design.” J. Cleaner Prod. 190 (Jul): 432–442. https://doi.org/10.1016/j.jclepro.2018.04.134.
Feng, Z. K., W. J. Niu, and C. T. Cheng. 2019c. “China’s large-scale hydropower system: Operation characteristics, modeling challenge and dimensionality reduction possibilities.” Renewable Energy 136 (Jun): 805–818. https://doi.org/10.1016/j.renene.2019.01.059.
Feng, Z. K., W. J. Niu, C. T. Cheng, and X. Y. Wu. 2017b. “Optimization of hydropower system operation by uniform dynamic programming for dimensionality reduction.” Energy 134 (Sep): 718–730. https://doi.org/10.1016/j.energy.2017.06.062.
Feng, Z. K., W. J. Niu, C. T. Cheng, and J. Z. Zhou. 2017c. “Peak shaving operation of hydro-thermal-nuclear plants serving multiple power grids by linear programming.” Energy 135 (Sep): 210–219. https://doi.org/10.1016/j.energy.2017.06.097.
Ji, C., Z. Jiang, P. Sun, Y. Zhang, and L. Wang. 2015. “Research and application of multidimensional dynamic programming in cascade reservoirs based on multilayer nested structure.” J. Water Resour. Plann. Manage. 141 (7): 04014090. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000489.
Jiang, Z., C. Ji, H. Qin, and Z. Feng. 2018. “Multi-stage progressive optimality algorithm and its application in energy storage operation chart optimization of cascade reservoirs.” Energy 148 (Apr): 309–323. https://doi.org/10.1016/j.energy.2018.01.176.
Jiang, Z., H. Qin, C. Ji, Z. Feng, and J. Zhou. 2017. “Two dimension reduction methods for multi-dimensional dynamic programming and its application in cascade reservoirs operation optimization.” Water 9 (9): 634. https://doi.org/10.3390/w9090634.
Kang, F., J. Li, and Q. Xu. 2009. “Structural inverse analysis by hybrid simplex artificial bee colony algorithms.” Comput. Struct. 87 (13–14): 861–870. https://doi.org/10.1016/j.compstruc.2009.03.001.
Lei, X., J. Zhang, H. Wang, M. Wang, S. T. Khu, Z. Li, and Q. Tan. 2018. “Deriving mixed reservoir operating rules for flood control based on weighted non-dominated sorting genetic algorithm II.” J. Hydrol. 564 (Sep): 967–983. https://doi.org/10.1016/j.jhydrol.2018.07.075.
Li, C., J. Zhou, S. Ouyang, X. Ding, and L. Chen. 2014. “Improved decomposition-coordination and discrete differential dynamic programming for optimization of large-scale hydropower system.” Energy Convers. Manage. 84 (Aug): 363–373. https://doi.org/10.1016/j.enconman.2014.04.065.
Li, Y., T. Zhao, P. Wang, H. B. Gooi, L. Wu, Y. Liu, and J. Ye. 2018. “Optimal operation of multimicrogrids via cooperative energy and reserve scheduling.” IEEE Trans. Ind. Informat. 14 (8): 3459–3468. https://doi.org/10.1109/TII.2018.2792441.
Li, Y. P., G. H. Huang, and X. Chen. 2011. “Planning regional energy system in association with greenhouse gas mitigation under uncertainty.” Appl. Energy 88 (3): 599–611. https://doi.org/10.1016/j.apenergy.2010.07.037.
Liu, Y., Y. Li, H. B. Gooi, Y. Jian, H. Xin, X. Jiang, and J. Pan. 2019. “Distributed robust energy management of a multimicrogrid system in the real-time energy market.” IEEE Trans. Sustain. Energy 10 (1): 396–406. https://doi.org/10.1109/TSTE.2017.2779827.
Ma, C., J. Lian, and J. Wang. 2013. “Short-term optimal operation of Three-gorge and Gezhouba cascade hydropower stations in non-flood season with operation rules from data mining.” Energy Convers. Manage. 65 (Jan): 616–627. https://doi.org/10.1016/j.enconman.2012.08.024.
Ming, B., P. Liu, J. Chang, Y. Wang, and Q. Huang. 2017. “Deriving operating rules of pumped water storage using multiobjective optimization: Case study of the Han to Wei Interbasin Water Transfer Project, China.” J. Water Resour. Plann. Manage. 143 (10): 05017012. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000828.
Niu, W. J., Z. K. Feng, C. T. Cheng, and X. Y. Wu. 2018. “A parallel multi-objective particle swarm optimization for cascade hydropower reservoir operation in southwest China.” Appl. Soft Comput. J. 70 (Sep): 562–575. https://doi.org/10.1016/j.asoc.2018.06.011.
Niu, W. J., Z. K. Feng, B. F. Feng, Y. W. Min, C. T. Cheng, and J. Z. Zhou. 2019a. “Comparison of multiple linear regression, artificial neural network, extreme learning machine, and support vector machine in deriving operation rule of hydropower reservoir.” Water 11 (1): 88. https://doi.org/10.3390/w11010088.
Niu, W. J., Z. K. Feng, M. Zeng, B. F. Feng, Y. W. Min, C. T. Cheng, and J. Z. Zhou. 2019b. “Forecasting reservoir monthly runoff via ensemble empirical mode decomposition and extreme learning machine optimized by an improved gravitational search algorithm.” Appl. Soft Comput. J. 82 (Sep): 105589. https://doi.org/10.1016/j.asoc.2019.105589.
Ren, G., Y. Cao, S. Wen, T. Huang, and Z. Zeng. 2018. “A modified Elman neural network with a new learning rate scheme.” Neurocomputing 286 (Apr): 11–18. https://doi.org/10.1016/j.neucom.2018.01.046.
Wang, S., Y. Cao, T. Huang, and S. Wen. 2019. “Passivity and passification of memristive neural networks with leakage term and time-varying delays.” Appl. Math. Comput. 361 (Nov): 294–310. https://doi.org/10.1016/j.amc.2019.05.040.
Wen, S., W. Liu, Y. Yang, T. Huang, and Z. Zeng. 2019. “Generating realistic videos from keyframes with concatenated GANs.” IEEE Trans. Circuits Syst. Video Technol. 29 (8): 2337–2348. https://doi.org/10.1109/TCSVT.2018.2867934.
Wen, S., X. Xie, Z. Yan, T. Huang, and Z. Zeng. 2018. “General memristor with applications in multilayer neural networks.” Neural Networks 103 (Jul): 142–149. https://doi.org/10.1016/j.neunet.2018.03.015.
Xie, X., S. Wen, Z. Zeng, and T. Huang. 2018. “Memristor-based circuit implementation of pulse-coupled neural network with dynamical threshold generators.” Neurocomputing 284 (Apr): 10–16. https://doi.org/10.1016/j.neucom.2018.01.024.
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.
Yuan, X., L. Wang, and Y. Yuan. 2008. “Application of enhanced PSO approach to optimal scheduling of hydro system.” Energy Convers. Manage. 49 (11): 2966–2972. https://doi.org/10.1016/j.enconman.2008.06.017.
Zahara, E., and Y. T. Kao. 2009. “Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems.” Expert Syst. Appl. 36 (2): 3880–3886. https://doi.org/10.1016/j.eswa.2008.02.039.
Zhang, C., B. Xu, Y. Li, and G. Fu. 2017. “Exploring the relationships among reliability, resilience, and vulnerability of water supply using many-objective analysis.” J. Water Resour. Plann. Manage. 143 (8): 04017044. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000787.
Zhang, W., P. Liu, X. Chen, L. Wang, X. Ai, M. Feng, D. Liu, and Y. Liu. 2016. “Optimal operation of multi-reservoir systems considering time-lags of flood routing.” Water Resour. Manage. 30 (2): 523–540. https://doi.org/10.1007/s11269-015-1175-8.
Zhao, T., J. Zhao, and D. Yang. 2014. “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.
Zheng, F., A. C. Zecchin, H. R. Maier, and A. R. Simpson. 2016. “Comparison of the searching behavior of NSGA-II, SAMODE, and borg MOEAs applied to water distribution system design problems.” J. Water Resour. Plann. Manage. 142 (7): 04016017. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000650.
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Published In
Journal of Water Resources Planning and Management
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Sep 28, 2018
Accepted: Oct 29, 2019
Published online: Feb 19, 2020
Published in print: May 1, 2020
Discussion open until: Jul 19, 2020
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