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This paper presents a method for the dimensioning of a battery energy storage system (BESS) to provide a primary frequency reserve. Numerical simulations based on historic frequency measurements are used to determine the minimum possible capacity, i.e., the lowest possible cost, which fulfills the technical requirements of the grid code. We implement a novel control algorithm with adjustable state of charge limits and the application of emergency resistors. At current European market prices, an optimized lead-acid BESS can be a profitable utility solution for the primary frequency control.