Research and Application of Multidimensional Dynamic Programming in Cascade Reservoirs Based on Multilayer Nested Structure.

The multidimensional dynamic programming (MDP) algorithm is a traditional method used to solve cascade reservoir operation optimization (CROO) problems, but the high dimensionality called the curse of dimensionalitycannot be ignored. In order to alleviate this problem, this paper proposes a new MDP algorithm named multilayer nested multidimensional dynamic programming (MNDP), which is based on a multilayered, nested structure. MNDP is mainly used to deal with computer memory space and computation complexity problems of MDP in CROO, and its recursive equation of reverse recursion calculation and specific calculation steps are presented in detail. This paper takes the cascade reservoirs of the Li Xianjiang River in China as an example to solve the CROO problem with the proposed MNDP. By comparing with the dynamic programming with successive approximations (DPSA) method, MNDP presents better performance in terms of power generation and the assurance rate in wet, normal, dry, and average years. The global optimality of MNDP is validated by MDP, and the parallel computing results of MNDP are shown in a case study. The MNDP proposed in this paper can reduce not only the programming complexity of MDP, but also the storage of intermediate variables during calculation, thus effectively solving the curse of dimensionality of MDP in CROO and keeping the global convergence feature of MDP. [ABSTRACT FROM AUTHOR]