This paper proposes a control method for battery energy storage systems (BESSs) to provide concurrent primary frequency and local voltage regulation services. The actual variable active and reactive power capability of the converter, along with the state-of-charge of the BESS, are jointly considered by the optimal operating point calculation process within the real-time operation. The controller optimizes the provision of grid services, considering the measured grid and battery statuses and predicting the battery DC voltage as a function of the current trajectory using a three-time-constant model (TTC). A computationally-efficient algorithm is proposed to solve the formulated optimal control problem. Experimental tests validate the proposed concepts and show the effectiveness of the employed control framework on a commercial utility-scale 720 kVA/560 kWh BESS.