Network Methods for Head-dependent Hydro Power Scheduling

Abstract

We study short-term planning of hydro power with a nonlinear objective function. Given prices on the power one seeks to maximize the value of the production over a time-horizon. By assuming a bilinear dependency on head and discharged water we prove that the objective varies concavely when one sends flow along cycles. It follows that in each set of points of equal value containing a local optimum, there is an extreme point of the feasible set. This suggests computing stationary points by using a modified minimum cost network flow code. The model also allows us to derive explicit convex lower bounding functions of the objective. We present computational results for a real-sized hydro-power system.