The modelling of high power Lithium batteries may work as a powerful tool in the sizing of batteries pack in hybrid vehicles. Moreover, this tool can be used to evaluate accurately the battery characteristics at each level of its lifetime. Until now, the model structure differs according to its end-use due to simulation limitation. Indeed, impedance measurements obtained by electrochemical impedance spectroscopy needs non-integer order impedance in order to correctly model diffusive phenomenon. However, this impedance cannot be simulated easily in software dedicated to hybrid vehicles and needs approximations. Furthermore, impedance measurements are realised with low currents comparing to currents that are forecast in normal uses of high power batteries and can induce errors if the impedance is varying with the current. This paper deals with non linear dynamic models that use band-limited frequency impedance with non-integer order. The parameters are identified partly by impedance measurements for high frequencies and partly by chronopotentiometry measurements for low frequencies. Validation tests are made with staircase of high intensity and current profile simulated on a hybrid vehicle software. The hypothesis of non-linearity is verified.