Quadratic approximate dynamic programming for scheduling water resources: a case study

We address the problem of scheduling water re-sources in a power system via approximate dynamic programming. To this goal, we model a finite horizon economic dispatch problem with convex stage cost and affine dynamics, and consider a quadratic approximation of the value functions. Evaluating the achieved policy entails solving a quadratic program at each time step, while value function fitting can be cast as a semidefinite program. We test our proposed algorithm on a simplified version of the Uruguayan power system, achieving a four percent cost reduction with respect to the myopic policy.