Application of Penalty Function Method and the Conjugate Gradient Method in Economic Scheduling of Cascade Hydropower Stations

Abstract

In this paper we use nonlinear programming of OR to build a mathematical model for optimal dispatch of active power of cascade hydro-power stations, and present a new optimality criterion for its short-term economic scheduling: the potential energy of reservoirs of the cascade be minimum. We have studied the mathematical expression of the constraints in detail. Using the mixed penalty function method SUMT we transform the constrained nonlinear programming problem into a sequence of unconstrained minimization problem. Then we use the conjugate gradient methodC CGM to find the search direction and find its optimal step-length by the proportional factor method PFM of linear search. The augmented objective function is defined and the formulas for computing the components of its gradient are derived. We have taken a test computation and analysing the results and compared them with the original design of an actual cascade hydropower stations, decreasing the water discharge and the incremental water rate of cascade, increasing the generated energy, we have provided several realizable designs for real-time control by computer.