梯级水电站群中长期优化调度的离散梯度逐步优化算法

Discrete gradient progressive optimality algorithm for mid-long-term optimal operation of multi-reservoir system

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.