Optimization of the short term operation of a cascade of hydro power stations

摘要

We study the operation of a cascade of hydropower stations for given time varying prices and given inflows. The objective is to maximize the value of the power output, under constraints on final dam contents. The flow of the river is modelled through nonlinear PDE:s, the St. Venant equations, which has to be solved iteratively. For the stations empirical but smooth efficiency curves are used. Using the structure of the problem, a descent method of reduced gradient type is developed. The problem has also been successfully convexified temporarily to avoid getting trapped in local minima. Further, scaling of the problem has been used with a rather dramatic success. MATLAB computations on a small but realistic problem are presented