A progressive domain expansion method for solving optimal control problem

Electricity generation at the hydropower stations in Nigeria has been below the expected value. While the hydro stations have a capacity to generate up to 2,380 MW, the daily average energy generated in 2017 was estimated at around 846 MW. A factor responsible for this is the lack of a proper control system to manage the transfer of resources between the cascaded Kainji-Jebba Hydropower stations operating in tandem. This paper addressed the optimal regulation of the operating head of the Jebba hydropower reservoir in the presence of system constraints, flow requirement and environmental factors that are weather-related. The resulting two-point boundary value problem was solved using the progressive expansion of domain technique as against the shooting or multiple shooting techniques. The results provide the optimal inflow required to keep the operating head of the Jebba reservoir at a nominal level, hence ensuring that the maximum number of turbo-alternator units are operated

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

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