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

泛函分析具有高度抽象性和概括性,因此可用来对某些复杂的问题进行建模,进而采用更加简便的数学方法进行求解。本文针对动态规划算法在水库优化调度中计算规模大和时间长的问题,引入泛函分析思想,构建了时段平均出力的泛函计算模型,并基于此提出了一种改进的动态规划算法,该算法省去了传统动态规划算法中大量重复的计算过程,减小了计算规模,从而提高求解效率。分别以我国某流域中M水电站和M、N组成的梯级水电站为例进行实例研究,从多年平均发电量和计算用时等方面将改进动态规划算法与传统动态规划算法以及逐步优化算法进行了详细的对比分析。结果表明,该算法能在保证全局收敛的基础上减少动态规划计算量,缩短计算时间。

Research and application of dynamic programming algorithm in reservoir operation based on functional analysis

The functional analysis can be used to model for complex problems due to its high abstraction and generality, then the problems can be solved using simple mathematical method. For the large calculation scale and long calculation time of the traditional dynamic programming algorithm in reservoir optimal operation, an average output model has been built and a new modified dynamic programming algorithm based on functional analysis is introduced in this paper. The new algorithm eliminates a large number of repeated calculation procedures in the traditional DP, and reduces the computational scale, which can improve the efficiency of the algorithm. A hydropower station is taken as the study instance. The paper compares the annual average generating capacity and the cost time using the traditional DP, DPSA and the modified DP. The result shows that on the basis of ensuring the global convergence, the modified DP can reduce the calculation scale and shorten the calculation time compared to the traditional DP.