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

A control model of the operating head dynamics of Jebba hydropower system

Electricity availability in Nigeria has been very poor over the years, underscoring the need for a better approach for managing generating resources. This paper presents the development of a dynamical model of the operating head of Jebba hydroelectric power plants for system studies and control system design. The mathematical model of the plant was developed from flow continuity conditions, some model parameters were obtained from the source while others were estimated from observations and analysis of the measured data. The developed dynamical equation was validated by comparing the response produced with values obtained by measurement. Upon integrating the model equation in Microsoft EXCEL VBA® environment, a deviation of 2% from measured values was observed. Operators can therefore use the model as a decision support system, while control engineers can find the model directly applicable for optimal and robust control system design for the station.Keywords: Control, Dynamical model, Hydropower, Inflow, Operating head