Improved dynamic programming for parallel reservoir system operation optimization

Optimizing a multi-reservoir system is challenging due to the problem of the curse of dimensionality. In this paper, rule-based improved dynamic programming (RIDP) and stochastic dynamic programming (RISDP) algorithms for the optimal operation of a system with a number of parallel reservoirs are proposed to alleviate the dimensionality problem. The improvement is based on a key property: the monotonic dependence relationship between individual reservoir carryover storage and system water availability, which is derived with the assumption of the non-decreasing storage distribution characteristic of a parallel reservoir system. Furthermore, a diagnosis procedure is employed to remove infeasible state transitions, which enables the application of the monotonic relationship within the feasible solution space. In general, the computational complexity of (NS)ⁿ² from DP can be reduced to (NS)ⁿ from RIDP (NS is the number of storage discretization for individual reservoirs, n is the number of reservoirs in a parallel system), with controlled solution accuracy. The improved algorithms are applied to a real-world parallel reservoir system in northeastern China. The results demonstrate the computational efficiency and effectiveness of RIDP and RISDP.