Optimal impoundment operation for cascade reservoirs coupling parallel dynamic programming with importance sampling and successive approximation

Abstract The optimal impoundment operation of cascade reservoirs can dramatically improve the utilization of water resources. However, their complex non-convexity and computational costs pose challenges to optimal hydroelectricity output and limit further development of joint operation within larger-scale cascade reservoirs. In recent decades, parallel dynamic programming (PDP) has emerged as a means of alleviating the ‘curse of dimensionality’ in the mid-long term reservoir operation with more involved computing processors. But it still can't effectively solve the daily impoundment operation of more than three reservoirs. Here, we propose a novel method called importance sampling-PDP (IS-PDP) algorithm in which the merits of PDP are integrated with importance sampling and successive approximation strategy. Importance sampling is first used to construct the state vectors of each period by introducing ‘Manhattan distance’ in the discrete state space. Then the PDP recursive equation is used to find an improved solution during the iteration. The IS-PDP method is tested to optimize hydropower output for the joint operation of an 11-reservoir system located in the upper Yangtze River basin of China after establishing impoundment operation by advancing impoundment timings and rising water levels. We find that our methodology could effectively deal with the ‘curse of dimensionality’ for such mega reservoir systems and make better use of water resources in comparison to the Standard Operation Policy (SOP). Given its computational efficiency and robust convergence, the methodology is an attractive alternative for non-convex operation of large-scale cascade reservoirs.