Large-scale battery energy storage systems (BESS) already play a major role in ancillary service markets worldwide. Batteries are especially suitable for fast response times and thus focus on applications with relatively short reaction times. While existing markets mostly require reaction times of a couple of seconds, this will most likely change in the future. During the energy transition, many conventional power plants will fade out of the energy system. Thereby, the amount of rotating masses connected to the power grid will decrease, which means removing a component with quasi-instantaneous power supply to balance out frequency deviations the millisecond they occur. In general, batteries are capable of providing power just as fast but the real-world overall system response time of current BESS for future grid services has only little been studied so far. Thus, the response time of individual components such as the inverter and the interaction of the inverter and control components in the context of a BESS are not yet known. We address this issue by measurements of a 6 MW BESS's inverters for mode changes, inverter power gradients and measurements of the runtime of signals of the control system. The measurements have shown that in the analyzed BESS response times of 175 ms to 325 ms without the measurement feedback loop and 450 ms to 715 ms for the round trip with feedback measurements are possible with hardware that is about five years old. The results prove that even this older components can exceed the requirements from current standards. For even faster future grid services like synthetic inertia, hardware upgrades at the measurement device and the inverters may be necessary.