The paper presents a centralized real-time adaptive and model-based voltage control algorithm for Active Distribution Networks (ADNs). Differently from the available literature, the proposed algorithm merely relies on the control of Battery Energy Storage Systems (BESSs). In this respect, an experimentally model-fitted two-time constant dynamic model of BESS is used. In particular, this model is used to compute the constraints of the BESSs in terms of DC active power at each controller iteration. These constraints are subsequently used in the central controller for the solution of the optimal voltage control problem. The performances of the proposed method are compared with those obtained for the case where BESSs are modeled as ideal energy reservoirs. Such an assessment is carried out using a numerical example referring to IEEE 13 buses distribution test feeder suitably adapted to include stochastic generation and BESSs.