This paper presents a method to determine the optimal location, energy capacity, and power rating of distributed battery energy storage systems at multiple voltage levels to accomplish grid control and reserve provision. We model operational scenarios at a one-hour resolution, where deviations of stochastic loads and renewable generation (modeled through scenarios) from a day-ahead unit commitment and violations of grid constraints are compensated by either dispatchable power plants (conventional reserves) or injections from battery energy storage systems. By plugging-in costs of conventional reserves and capital costs of converter power ratings and energy storage capacity, the model is able to derive requirements for storage deployment that achieve the technical-economical optimum of the problem. The method leverages an efficient linearized formulation of the grid constraints of both the HV (High Voltage) and MV (Medium Voltage) grids while still retaining fundamental modeling aspects of the power system (such as transmission losses, effect of reactive power, OLTC at the MV/HV interface, unideal efficiency of battery energy storage systems) and models of conventional generator. A proof-of-concept by simulations is provided with the IEEE 9-bus system coupled with the CIGRE benchmark system for MV grids, realistic costs of power reserves, active power rating and energy capacity of batteries, and load and renewable generation profile from real measurements.
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