Traditionally, the safe operation of a battery energy storage system (BESS) is achieved by imposing conservative constraints on its DC bus current and voltage. By using a computationally efficient single particle model (SPM), we propose to replace these constraints with the battery internal ion concentrations and electrical potentials in order to avoid these quantities to exceed hazardous limits. Indeed, the in-depth knowledge of the BESS internal states provided by the SPM, enhances the awareness of a control action and allows for a better exploitation of the BESS energy and power capabilities, while maintaining safe operational conditions. The target application is composed by a model predictive control (MPC) applied to a MW-class grid-connected BESS responsible to dispatch the operation of a medium voltage (20 kV) feeder interfacing heterogeneous loads and distributed generation. The performance of the proposed MPC are assessed and compared with respect to a traditional approach constraining the BESS DC bus current and voltage.