Electrical vehicles $($EVs$)$ are becoming more and more common on the roads. They

are usually powered by a battery. EV batteries undergo cycles of 'discharge' that

occur when driving and 'charge' when the car is plugged in$.$

The state of charge $(SOC)$ of a battery denotes the capacity that is currently available

as a function of the rated capacity. The value of the SOC varies between $0\%$ and

$100\%.$ Accurately estimating the SOC of the battery is important for estimating the

remaining travel range of a vehicle, deciding when to recharge the battery and

estimating how long it would take to charge it$.$

Coulomb Counting method is a popular method for estimating the SOC of the battery.

It is based on the calculation of electric quantity during charging and discharging. A

simplified equation for calculating the SOC using this method is below.

SOC$=\frac{Q_0+{\displaystyle \underset{0}{\overset{}{}}}{i}_{c}dt-{\displaystyle \underset{0}{\overset{}{}}}{i}_{d}dt}{Q}*100\%$

where $Q$ is the rated capacity of the battery, unit: $A*h$;$Q_0$ is the initial charge of the

battery, unit: $A*h$;$$ is the charging or discharging time, unit: $h$;$$ is the charging

efficiency; $i_c$ is the charging current, unit: $A$;$i_d$ is the discharging current, unit: $A.$ In

a$)$ Write a $C++$ function to calculate the SOC. The function should have the input

parameters for the values of $,Q,Q_0,S,i_c$ and $i_d.$ In this question, assume that

$i_c$ and $i_d$ are constants.

$[10$ marks$]$

b$)$ Write a $C++$ program to calculate the SOC values for a battery when $$ is

changing between $0$ and $5$ with a step of $0\mathrm{.}1$ and output all calculated SOC

values into a file. Use the function written in part $($a$)$ of this question for these

calculations.

The battery has the rated capacity of $80kWh.$ Assume that the initial charge of

the battery is $20kWh$ and that $i_d$ is equal to $0.$

Assume that a standard charger with the current of $13A$ is used. The standard

charger has the charging efficiency of $87\%.$