This work simulates the performance of lithium batteries for electric vehicles under different charge and discharge rates. The simulation is based on similarity factors for power, voltage and current, reproducing the real operation conditions of an electric vehicle at the model scale. Most current driving modes have been analysed corresponding to discharge rates from 0.1C to 0.37C. The simulation has also been applied to determine charging time using charge power in real conditions, from 6.1 kW to 18.3 kW (0.1 C to 0.3C). Driving conditions are obtained using equations for vehicle motion including all forces. Tests have been run under two configurations, continuous and alternate current circuits, to reproduce the two types of engines that electric vehicles use. The simulation shows very good agreement in charge and discharge processes, average deviation of 3% related to real conditions, and 1.6% between them, which proves the validity of the simulation process.