An electric vehicle takes 8 hours to charge at 7 kW from the grid. Assume the battery SOC goes from 20 to 80 % during this time and the battery is 99% efficient during charging. The battery is made up of 10 modules in series, each with 30 strings of 22 cylindrical cells. The strings are in parallel. The cells have a voltage of 3.6 V. The electric vehicle has an electric motor with the following characteristics, a constant maximum torque of 500Nm from 0 to 2000 rev/min and then constant maximum power of 104.5kW above 2000 rev/min. The motor has an efficiency of 96%. The gear ratio from the motor to the wheels is 5.9 and the efficiency of the gear box is 94%. The vehicle parameters are: = 2050 kg = 0.28 = 2.3 m mass drag coefficient Frontal area Rolling resistant coefficients Tyre radius And assume the density of air is fo= 0.015, f1 = 0 = 0.33 m p = 1.2 (kg/m). Answer the following questions: i) Calculate the size of the battery in kWh and Joules. ii) Calculate the number of cells in the battery pack and pack voltage. [2 marks] [2 marks] iii) Calculate the overall internal resistance of the battery. [2 marks] iv) A new battery is being designed with pouch cells that have a voltage of 3.7V and a capacity of 56 Ah. If the battery is one string of cells in series, what is the minimum number of cells to achieve the same capacity? [3 marks] v) Calculate the range of the vehicle with the original battery at a constant speed of 100 kph on flat ground assuming that the battery is only used between 20 and 80% SOC. [3 marks] vi). Describe two approaches to calculate the battery SOC, include equations and a sketch of any characteristics that you may use to perform this calculation. [2 marks] vii) Calculate the maximum speed in km/h for the vehicle on flat ground. You can use a graph to estimate the solution. [6 marks]