A steepest descent algorithm for the optimal control of a cascaded hydropower system

Abstract

Optimal power generation along the cascaded Kainji-Jebba hydroelectric power system had been very difficult to achieve. The reservoirs operating heads are being affected by possible variation in impoundments upstream, stochastic factors that are weather-related, availability of the turbo-alternators and power generated at any time. Proposed in this paper, is an algorithm for solving the optimal release of water on the cascaded hydropower system based on steepest descent method. The uniqueness of this work is the conversion of the infinite dimensional control problem to a finite one, the introduction of clever techniques for choosing the steepest descent step size in each iteration and the nonlinear penalty embedded in the procedure. The control algorithm was implemented in an Excel VBA® environment to solve the ormulated Lagrange problem within an accuracy of 0.03%. It is recommended for use in system studies and control design for the optimal power generation in the cascaded hydropower system.

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

“…67 Moreover, this method requires a proper selection for the step size parameter. This method has been implemented, for example, in applications involving power generation, 68 heat transfer operations, 69 and crystallization processes. 70…”