Pseudospectral method for hydropower optimal control problem

Optimal control is a mathematical optimization problem and optimal control problems seek optimal control design subjective to a system of differential equations. Because of the nonlinearity of problems, it is hard to derive the analytic solutions for optimal control problem. Hence, the research uses an efficient numerical method, pseudospectral method, to solve complex optimal control problem. The design of the algorithm is based on using the pseudo-spectral differentiation matrix to reduce a high-dimensional function to low-dimensional functions, and the low-dimensional functions are more possible to solve difficult optimization problems. The reservoirs generate electricity constantly is built on the basis of steady inflow, but Taiwan's reservoirs unable to provide a stable amount of water. So designing a mathematical model of optimal control is used to deploy water distribution ratio for hydropower of wet and dry seasons. Because of the hydrological and geographical conditions in water resources systems in Taiwan, unstable water flow is hard to provide steady hydropower generation. An optimal control problem of hydropower generation is formulated for water resources system. A case study of Taiwanese water resources system is conducted. This study use monthly rainfall and output hydropower data to analysis the maximum hydropower with steady outflow. The results show the optimal control of water management and hydropower generation.