Linking Nelder–Mead Simplex Direct Search Method into Two-Stage Progressive Optimality Algorithm for Optimal Operation of Cascade Hydropower Reservoirs

Abstract

To satisfy growing energy demand, the hydropower industry of China is experiencing unprecedented development, and the total power generation and installed capacity of hydropower in China rank first in the world. The system scale and rate of development have posed computational modeling challenges, because the computational burden in hydropower optimization modeling using classical dynamic programming methods grows exponentially as the number of reservoirs increases. One method designed to reduce this burden, the progressive optimality algorithm (POA), still suffers from the dimensionality problem and the need for iterative computations to address large-scale hydropower systems. To enhance the performance of POA, this work develops a new method referred to as the simplex progressive optimality algorithm (SPOA). In SPOA, the complex multistage problem is divided into several easy-to-solve two-stage subproblems, and then the Nelder–Mead simplex direct search method is adopted to search for the improved solution to each subproblem, enhancing the solution’s quality via iterative computation. Experimental results indicate that the proposed SPOA method can significantly reduce execution time and memory usage under different cases, demonstrating its applicability for large-scale hydropower system operation problems.