Charge unbalance is one of the key issues for series-connected Lithium-ion cells. Within this context, model-based optimization strategies have proven to be the most effective. In the present paper, an ad-hoc electrochemical model, tailored to control purposes, is firstly presented. Relying on this latter, a general nonlinear MPC for balancing-aware optimal charging is then proposed. In view of the possibility of a practical implementation, the concepts are subsequently specialized for an easily implementable power supply scheme. Finally, the nonlinear MPC approach is validated on commercial cells using a detailed battery simulator, with sound evidence of its effectiveness., Comment: Submitted to the IEEE Transactions on Control Systems Technology