Mathematical modelling of the combined optimization of a pumped-storage hydro-plant and a wind park

The new Spanish regulations allow wind farms to go to the market to sell the energy generated by their facilities. In the case of over- or under-supply, other producers must reduce or increase their production to resolve the so-called deviation, thereby incurring financial losses. Faced with this situation, wind farms have several options. In this paper we consider one promising method: the combined optimization of a pumped-storage hydro-plant and a wind park. First, we are going to present the mathematical modelling of the resulting problem. Second, we shall solve the optimization problem using Optimal Control techniques and finally we shall present several examples of the combined optimization and analyse which strategy is the best one possible.