Profitability and need of storages in the German electricity network

We study the profitable amount of additional storages in the German electricity network. The more storages there are the less profitable they become. To account for this effect, we construct a price model based on German data from 2015. This price model is based on the merit order theory and the explanatory variables are conventional generation and export. Then we build a cost model for different kinds of long-term storages and assume that they are perfectly scheduled. We combine both models and set up optimization problems to find the optimal additional capacity and power of the storage types for a monopolist as well as in complete competition. We show that the optimization problems are convex and solve them. Assuming a reasonable annual discount rate, we conclude that in the current situation, additional storages are not profitable. When assuming a discount rate of zero, only pumped hydroelectric storages are profitable. With a discount rate of zero and complete competition, it would have been profitable to double the storage capacity in Germany from 60 to 122.5 GWh, which would only have a minor effect on electricity prices.