A progressive domain expansion method for solving optimal control problem

Abstract

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.