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.