Recent attention to industrial peak shaving applications sparked an increased interest in battery energy storage. Batteries provide a fast and high power capability, making them an ideal solution for this task. This work proposes a general framework for sizing of battery energy storage system (BESS) in peak shaving applications. A cost-optimal sizing of the battery and power electronics is derived using linear programming based on local demand and billing scheme. A case study conducted with real-world industrial profiles shows the applicability of the approach as well as the return on investment dependence on the load profile. At the same time, the power flow optimization reveals the best storage operation patterns considering a trade-off between energy purchase, peak-power tariff, and battery aging. This underlines the need for a general mathematical optimization approach to efficiently tackle the challenge of peak shaving using an energy storage system. The case study also compares the applicability of yearly and monthly billing schemes, where the highest load of the year/month is the base for the price per kW. The results demonstrate that batteries in peak shaving applications can shorten the payback period when used for large industrial loads. They also show the impacts of peak shaving variation on the return of investment and battery aging of the system.