The growing global electricity demand and the upcoming integration of charging options for electric vehicles is creating challenges for power grids, such as line over loading. With continuously falling costs for lithium-ion batteries, storage systems represent an alternative to conventional grid reinforcement. This paper proposes an operation strategy for battery energy storage systems, targeted at industrial consumers to achieve both an improvement in the distribution grid and electricity bill savings for the industrial consumer. The objective is to reduce the peak power at the point of common coupling in existing distribution grids by adapting the control of the battery energy storage system at individual industrial consumer sites. An open-source simulation tool, which enables a realistic simulation of the effects of storage systems in different operating modes on the distribution grid, has been adapted as part of this work. Further information on the additional stress on the storage system is derived from a detailed analysis based on six key characteristics. The results show that, with the combined approach, both the local peak load and the global peak load can be reduced, while the stress on the energy storage is not significantly increased. The peak load at the point of common coupling is reduced by 5.6 kVA to 56.7 kVA and the additional stress for the storage system is, on average, for a six month simulation, period only 1.2 full equivalent cycles higher.