梯级水电站群中长期优化调度的离散梯度逐步优化算法
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摘要
充分利用现有水电资源,进行库群中长期优化调度是构建清洁低碳、安全高效的现代能源体系的重要措施。逐步优化算法(POA)将多阶段问题转化为多个两阶段子优化问题,是求解中长期库群优化调度较为广泛且有效的一种方法。但随着水库数目的增加,POA仍会面临严重的"维数灾"问题。本文以梯度下降法为基础,提出离散梯度的概念及离散梯度逐步优化算法(DGPOA),该方法在不直接求导的情况下充分利用局部离散梯度信息确定最优搜索方向,可以快速获得优化结果。最后将该算法应用到澜沧江流域五水库梯级系统中,在不同离散精度和来水条件下,利用POA、POA-DPSA和DGPOA算法对梯级水库进行优化计算。结果表明,在不显著降低全局搜索能力的情况下,DGPOA的计算速度分别达到了POA-DPSA算法的8~12倍,POA算法的50~250倍,是一种解决梯级水库站群中长期优化调度中"维数灾"问题的有效方法。
Making full use of existing hydropower resources and carrying out mid-long-term optimal dispatch of reservoirs is important for building a clean,low-carbon,safe,and efficient modern energy sys-tem. The progressive optimality algorithm(POA) converts multi-stage problems into multiple two-stage sub-optimization problems. It is an effective and widely used algorithm for solving mid-long-term optimal opera-tion of multi-reservoir system. However,with the increase in the number of reservoirs,POA will still faceserious "curse of dimensionality". Based on the gradient descent method,the concept of discrete gradientand the discrete gradient progressive optimality algorithm(DGPOA) are proposed. This algorithm makes fulluse of local discrete gradient information to determine the optimal search direction without derivation andcan quickly obtain optimal results. Finally,the algorithm was applied to the cascade system of the 5 reser-voirs of the Lancang River Basin. The results of POA,POA-DPSA,and DGPOA with different discrete pre-cisions and inflow scenarios were obtained. The results show that the DGPOA computing performance canreach 8 to 12 times the POA-DPSA algorithm and 50 to 250 times the POA algorithm without significantlyreducing the global search capability. The conclusion can be drawn that DGPOA is an effective algorithmto solve the "curse of dimensionality" problem in the mid-long-term optimal operation of multi-reservoir system.
Making full use of existing hydropower resources and carrying out mid-long-term optimal dispatch of reservoirs is important for building a clean,low-carbon,safe,and efficient modern energy sys-tem. The progressive optimality algorithm(POA) converts multi-stage problems into multiple two-stage sub-optimization problems. It is an effective and widely used algorithm for solving mid-long-term optimal opera-tion of multi-reservoir system. However,with the increase in the number of reservoirs,POA will still faceserious "curse of dimensionality". Based on the gradient descent method,the concept of discrete gradientand the discrete gradient progressive optimality algorithm(DGPOA) are proposed. This algorithm makes fulluse of local discrete gradient information to determine the optimal search direction without derivation andcan quickly obtain optimal results. Finally,the algorithm was applied to the cascade system of the 5 reser-voirs of the Lancang River Basin. The results of POA,POA-DPSA,and DGPOA with different discrete pre-cisions and inflow scenarios were obtained. The results show that the DGPOA computing performance canreach 8 to 12 times the POA-DPSA algorithm and 50 to 250 times the POA algorithm without significantlyreducing the global search capability. The conclusion can be drawn that DGPOA is an effective algorithmto solve the "curse of dimensionality" problem in the mid-long-term optimal operation of multi-reservoir system.
引文
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[14]钟平安,张卫国,张玉兰,等.水电站发电优化调度的综合改进差分进化算法[J].水利学报,2014,45(10):1147-1155.
[15] HOWSON H R,SANCHO N G F. A new algorithm for the solution of multi-state dynamic programming problems[J]. Math. Programming,1975(8):104-116.
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[18] FENG Z,NIU W,PH D,et al. Optimizing hydropower reservoirs operation via an orthogonal progressive optimality algorithm[J]. 2018,144(3):1-12.
[19] JIANG Z,QIN H,JI C,et al. Two dimension reduction methods for multi-dimensional dynamic programming and its application in cascade reservoirs operation optimization[J]. Water(Switzerland),2017,9(9):634.
[20]李义,李承军,周建中. POA-DPSA混合算法在短期优化调度中的应用[J].水电能源科学,2004,22(1):37-39.
[21] BAI T,CHANG J X,CHANG F J,et al. Synergistic gains from the multi-objective optimal operation of cascade reservoirs in the Upper Yellow River basin[J]. Journal of Hydrology,2015,523:758-767.
[22]郑慧涛,梅亚东,杜亚平,等.大规模水电站群短期优化调度的并行求解[J].华中科技大学学报(自然科学版),2013,41(1):16-20.
[23]冯仲恺,廖胜利,程春田,等.库群长期优化调度的正交逐步优化算法[J].水利学报,2014,45(8):903-911.
[24]方红远,王浩,程吉林.初始轨迹对逐步优化算法收敛性的影响[J].水利学报,2002(11):27-30.
[2] CHENG C T,SHEN J J,WU X Y,et al. Operation challenges for fast-growing China’s hydropower systems and respondence to energy saving and emission reduction[J]. Renewable and Sustainable Energy Reviews,2012,16(5):2386-2393.
[3] LABADIE J W. Optimal operation of multireservoir systems:State-of-the-Art review[J]. Journal of Water Resources Planning and Management,2004,130(2):93-111.
[4]陈森林,黄宇昊,李丹,等.水库防洪补偿调节线性规划模型及应用[J].水科学进展,2017,28(4):507-514.
[5] BIRHANU K,ALAMIREW T,OLUMANA DINKA M,et al. Optimizing reservoir operation policy using chance constraint nonlinear programming for Koga Irrigation Dam,Ethiopia[J]. Water Resources Management,2014,28(14):4957-4970.
[6]梅亚东,冯尚友.网络流规划在水电站水库系统长期优化运行中应用[J].武汉大学学报(工学版),1989,5(2):8-17.
[7]陈西臻,刘攀,何素明,等.基于聚合-分解的并联水库群防洪优化调度研究[J].水资源研究,2015,4(1):23-31.
[8] BU?ONIU L,SCHUTTER B De,BABU?KA R. Approximate dynamic programming and reinforcement learning[J]. Collaborative Information Systems,2010,281:3-44.
[9]周佳,马光文,张志刚.基于改进POA算法的雅砻江梯级水电站群中长期优化调度研究[J].水力发电学报,2010,29(3):18-22.
[10]纪昌明,李传刚,刘晓勇,等.基于泛函分析思想的动态规划算法及其在水库调度中的应用研究[J].水利学报,2016,47(1):1-9.
[11] SHAW A R,SMITH S H,LEBOEUF E J,et al. Hydropower optimization using artificial neural network surrogate Models of a High-Fidelity Hydrodynamics and Water Quality Model[J]. Water Resources Research,2017,53(11):9444-9461.
[12]陈立华,梅亚东,董雅洁,等.改进遗传算法及其在水库群优化调度中的应用[J].水利学报,2007,38(5):550-556.
[13]纪昌明,刘方,彭杨,等.基于鲶鱼效应粒子群算法的水库水沙调度模型研究[J].水力发电学报,2013,32(1):70-76.
[14]钟平安,张卫国,张玉兰,等.水电站发电优化调度的综合改进差分进化算法[J].水利学报,2014,45(10):1147-1155.
[15] HOWSON H R,SANCHO N G F. A new algorithm for the solution of multi-state dynamic programming problems[J]. Math. Programming,1975(8):104-116.
[16] JIANG Z,JI C,QIN H,et al. Multi-stage progressive optimality algorithm and its application in energy storage operation chart optimization of cascade reservoirs[J]. Energy,Elsevier Ltd,2018,148:309-323.
[17] NANDA J,BIJWE P R. Optimal hydrothermal scheduling with cascaded plants using progressive optimality algorithm[J]. IEEE Transactions on Power Apparatus and Systems,1981,PAS-100(4):2093.
[18] FENG Z,NIU W,PH D,et al. Optimizing hydropower reservoirs operation via an orthogonal progressive optimality algorithm[J]. 2018,144(3):1-12.
[19] JIANG Z,QIN H,JI C,et al. Two dimension reduction methods for multi-dimensional dynamic programming and its application in cascade reservoirs operation optimization[J]. Water(Switzerland),2017,9(9):634.
[20]李义,李承军,周建中. POA-DPSA混合算法在短期优化调度中的应用[J].水电能源科学,2004,22(1):37-39.
[21] BAI T,CHANG J X,CHANG F J,et al. Synergistic gains from the multi-objective optimal operation of cascade reservoirs in the Upper Yellow River basin[J]. Journal of Hydrology,2015,523:758-767.
[22]郑慧涛,梅亚东,杜亚平,等.大规模水电站群短期优化调度的并行求解[J].华中科技大学学报(自然科学版),2013,41(1):16-20.
[23]冯仲恺,廖胜利,程春田,等.库群长期优化调度的正交逐步优化算法[J].水利学报,2014,45(8):903-911.
[24]方红远,王浩,程吉林.初始轨迹对逐步优化算法收敛性的影响[J].水利学报,2002(11):27-30.