The operating point (OP) of energy storage systems (ESS) may change drastically and with a certain frequency, depending on their dispatch. In order to use this technology to its full extent, such condition should not represent a limiting constraint in terms of performance and stability. However, linear controllers as the proportional-integral-derivative (PID) generally require the linearization of the system around a point to perform their tuning and do not necessarily guarantee correct operation over the wide range required by ESSs. In order to address this issue, this paper presents a study to select a consistent OP when tuning the PIDs for the active power control loop in an ESS. Two scenarios of simulated OPs were obtained from an optimal power flow (OPF) (critical setpoint shifts, and centroids of clusters for representative cases), with a third one to evaluate saturation. A genetic algorithm (GA) was used at each point to minimize reference tracking error and to ensure operating constraints. The simulation results were confirmed through a mathematical analysis which indicates that since the system's behavior depends heavily on the OP, tunings based on saturation points are the most consistent choice.