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Batteries provide growing amounts of Frequency Containment Reserve (FCR) in the German electricity market. We examine the ideal battery capacity as well as the optimal state of charge (SoC) setpoint for provision of FCR following a profit maximization approach. While a lot of research neglects taxes, their huge influence on the results is considered. In addition to stand-alone battery systems, we also consider hybrid systems, combining a battery storage with a Powerto-Heat (PtH) module. The hybrid system has two variants: In one variant energy is sold when the battery is fully charged, while in the other one the PtH module is used. Based on historical frequency and market data for one year, the performance of the different system variants is evaluated via a simulation. 2048 different combinations of battery capacity and SoC setpoint are examined. The performance of each configuration is evaluated with the net present value (NPV) method, allowing an economic comparison. The results show a financial advantage for the hybrid systems which sell energy when the battery is fully charged. The system configuration with the best NPV is a hybrid system with a battery capacity of 480 kWh and an SoC setpoint of 98 %. The optimal battery capacity of all considered variants has a lower capacity to power ratio than the usual ratio of 1 MWh to 1 MW, assumed in most other studies. Nonoptimal battery capacities have a stronger negative effect on the economic efficiency of the systems than non-optimal SoC setpoints. The results emphasise that the battery capacity is a critical investment decision.

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