基于灰色离散微分动态规划的梯级水库优化调度

Optimal operation model of cascade reservoirs based on grey discrete differential dynamic programming

针对梯级水库群优化调度中离散微分动态规划(DDDP)方法全局收敛性差及计算效率低的问题,本文提出了一种基于灰色系统预测方法的离散微分动态规划方法(GDDDP)。该方法以DDDP为基础,每次迭代前把历史迭代中得到的最优轨迹和历史预测轨迹组成的数据序列作为灰色系统预测方法的输入进行预测;然后在各个水库预测轨迹的基础上进行离散迭代求解,以此来提高算法的求解精度及计算效率;同时针对灰色系统预测方法对于振荡序列有较大误差的缺点,采用等差数列递推式改进了灰色系统预测方法。最后白山-丰满梯级水电站的调度结果也表明了GDDDP的有效性。

In this paper, a grey discrete differential dynamic programming （GDDDP） algorithm based on the grey system prediction is presented for solving the problems of poor global convergence and low calculation efficiency in application of the discrete differential dynamic programming （DDDP） to optimal operation of cascade reservoirs. As an improved DDDP method for better accuracy and efficiency, this new algorithm adopts the grey system prediction and makes forecasting before each iteration, and then starts the iteration using the forecasted trajectories of all the reservoirs and taking the data sequences of optimal trajectories and forecasted trajectories obtained in previous iterations as an input of the ongoing iteration. It also adopts a recursive arithmetic progression formula to eliminate the low accuracy defect of the grey system prediction method in its forecasts of oscillatory sequences. A case study of the operation of Baishan-Fengman cascade reservoirs is given to verify the effectiveness of GDDDP.