Probabilistic sizing of battery energy storage when time-of-use pricing is applied

•A probabilistic battery sizing procedure is proposed for demand response applications.•The sizing procedure is based on a simple unconstrained minimization of a function.•The uncertainties of loads, prices and discount rate are taken into account in the total cost evaluation.•A simple formula is proposed to preliminary verify the profitability of the use of a battery technology.•Increase of the tariff values and load demand results in an increment of the optimal size of the battery.

Demand response (DR) is a useful tool for end users, since it allows noticeable reductions in the electricity bill. However, some customers have stringent constraints in terms of hourly active power, which makes DR attractive only when performed with the contemporaneous use of battery energy storage systems (BESSs). When this option is used, it is desirable to optimally size the BESSs, since their high investment costs could make their use impracticable for DR purposes. The uncertainties related to many of the inputs required by the BESS-sizing procedure make it necessary to use a probabilistic framework for sizing. In this paper, a probabilistic approach is proposed for the optimal sizing of BESSs when time-of-use (ToU) pricing is applied. The sizing procedure takes into account the uncertainties that unavoidably affect the evaluation of the total cost incurred by the customer such as load demand, energy prices, and economic factors.