Hydropower system operation optimization by discrete differential dynamic programming based on orthogonal experiment design

With the fast development of hydropower in China, a group of hydropower stations has been put into operation in the past few decades and the hydropower system scale is experiencing a booming period. Hence, the “curse of dimensionality” is posing a great challenge to the optimal operation of hydropower system (OOHS) because the computational cost grows exponentially with the increasing number of plants. Discrete differential dynamic programming (DDDP) is a classical method to alleviate the dimensionality problem of dynamic programming for the OOHS, but its memory requirement and computational time still grows exponentially with the increasing number of plants. In order to improve the DDDP performance, a novel method called orthogonal discrete differential dynamic programming (ODDDP) is introduced to solve the OOHS problem. In ODDDP, orthogonal experimental design is employed to select some small but representative state combinations when constructing the corridor around the current trajectory, and then dynamic programming recursion equation is used to find an improved trajectory for the next iteration. The proposed method is applied to the optimal operation of a large-scale hydropower system in China. The results indicate that compared to the standard DDDP, ODDDP only needs about 0.37% of computing time to obtain the results with about 99.75% of generation in the hydropower system with 7 plants and 3 states per plant, providing a new effective tool for large-scale OOHS problem.