The paper discusses the model identification, validation and experimental testing of current-to-voltage dynamic circuit models for a grid-connected MW-class battery. The model refers to an utility-scale 720 kVA/560 kWh battery energy storage system (BESS) and is used in a model predictive control framework to forecast the evolution of the battery DC voltage as a function of the current trajectory. The model is identified using measurements from a dedicated experimental session where the BESS is controlled with a pseudo random binary signal (PRBS) to excite the system on a broad spectrum. The identified model relies on the assumption that the battery is a single cell. To test this assumption and assess the quality of predictions, we test the model performance by using a second data set coming from a real-life power system application, where the BESS is used to dispatch the operation of a group of stochastic prosumers (demand and PV generation). Experimental results show that the root mean square voltage prediction error of the best performing model (i.e. two time constant model, TTC) is less than 0.55% for look-ahead times in the range 10 seconds-10 minutes and better than persistence for all considered forecasting horizons.