Maximum income resulting from energy arbitrage by battery systems subject to cycle aging and price uncertainty from a dynamic programming perspective

To obtain that optimal value, this paper describes a dynamic program approach, with the particularity that the switching decisions are optimized considering an uncertain price evolution and a dynamic calculation of the aging cost. A practical implementation of this approach is proposed, in which the problem is conveniently sliced into matrices corresponding to single decisions. It is shown that such an arrangement, combined with shift and re-indexing operators, provides a fast solution to the optimization problem consisting of a huge number of decision evaluations. The algorithm is then applied to a number of European electricity markets, with a particular focus on arbitrage. The particularities of the algorithm solutions are analyzed, and it is shown that not considering the imperfect foresight and the aging impacts leads to considerable errors in valuing an ESS.