*3.3. Net Savings and Charge and Discharge Times*

The savings for the owner is largely dependent on the cost of the battery for the EV as a costly battery may lead to a lower net profit. The savings can be calculated through this section. A new Tesla Model S has a battery warranty of 8 years, which can last 20 years or more [12]. Three EV models are used to calculate the rate of battery degradation. The models are classified as type A, B and C. EV type A, and type B have a battery warranty of 8 years. The cost of type C's battery is replaced roughly \$5000 to \$7000 according to 'Interesting Engineering' [11], whereas type A's battery will cost \$5500 [13] with a lifespan of 20 years also. On average, the cost for an EV car battery then is \$6000 or £4666.20 on 20 February 2020. The lifespan of an EV battery during this method must include faster battery degradation, so using the data taken from References [11,12,36,37], it would have a rough lifespan of 4.81 years until it has 80% of its full battery capacity left, which has been shown below.

If the average UK mileage is 12,231 km per annum and type A's battery lasts 20 years, this equates to 244,620 km. The term '*NFc*' is the number of full charges, '*DL*' is the distance travelled before 20% battery capacity loss, and '*DFc*' is the distance from a full charge in miles.

$$\text{NFc} = \frac{DL}{DFc} = \frac{152,000}{73} = 2082\tag{12}$$

Assuming the EV is plugged in at 80% at 08:00 and is un-plugged at 100% at 17:00, the battery discharges by 25.3 kW/day, and charges 33.3 kW/day. The battery is discharged 63.25% per day. The standard capacity '*SC*' over 20 years is:

$$\text{SC} = \text{NFc} \times \text{Fc} = \text{2082} \times 40 \text{ kW} = 83,280 \text{ kW} \tag{13}$$

The EV must charge by 69,330.6 kW over the 20 years instead of 16,656 kW if it were not using the V2G method. If 16,626 kW reduces the battery to 80% in 20 years, then at 208.2 kW, there is a 1% loss per year. If the EV is being charged by 69,330.6 kW, there is a 4.16% loss per year. The lifespan calculation of the battery has been shown in Equation (14).

$$\frac{20\text{ Y}}{4.16\text{\textdegree\textdegree}} = 4.81\text{ Y} \tag{14}$$

The EV's battery will have deteriorated to 80% after 4.81 years of the maximum capacity where Tesla recommends that the battery is replaced. If EV type A's battery costs £4265 and needs to be replaced every 4.81 years instead of every 20, the incentives must be great. As shown above, the EV owners will make £268.52 /year or £1291.64 before purchasing another battery. For the consumer to break even, the campus must pay £3.30

1

per day or £0.825 per hour to the EV owner, assuming the simulation parameters. The campus will save £1749.45 per year using these parameters.

The outcome will be greatly affected by the energy demand of the building as for this example, if the battery storage were for only peak times, it would only need to have a capacity of 1916 kW over 4 h, which is equivalent to 72 charging stations. A 10-year simulation on the cost analysis and ROI of installing EV chargers on campus with storage equivalent of all times of the day showing V2G storage is significantly less costly in Figure 8. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 13 of 25 *Sustainability* **2021**, *13*, x FOR PEER REVIEW 13 of 25 Purchase from grid Battery Equivalent EV V2G Storage

**Figure 8.** 10-year energy price for all times of the day. **Figure 8.** 10-year energy price for all times of the day.

The battery equivalent is only the price for the battery capacity, as the battery will also need to be charged, so the energy still needs to be bought. The EV V2G storage is the cost of the charging stations. After 2 years, the campus Li-ion battery should be replaced, whereas the EV battery should be replaced every 4.81 years. A 10-year simulation on the cost analysis and ROI of installing EV chargers on campus with storage equivalent of only peak-times of the day leading to a smaller cost for V2G storage than any other system, which is presented in Figure 9. The battery equivalent is only the price for the battery capacity, as the battery will also need to be charged, so the energy still needs to be bought. The EV V2G storage is the cost of the charging stations. After 2 years, the campus Li-ion battery should be replaced, whereas the EV battery should be replaced every 4.81 years. A 10-year simulation on the cost analysis and ROI of installing EV chargers on campus with storage equivalent of only peak-times of the day leading to a smaller cost for V2G storage than any other system, which is presented in Figure 9. The battery equivalent is only the price for the battery capacity, as the battery will also need to be charged, so the energy still needs to be bought. The EV V2G storage is the cost of the charging stations. After 2 years, the campus Li-ion battery should be replaced, whereas the EV battery should be replaced every 4.81 years. A 10-year simulation on the cost analysis and ROI of installing EV chargers on campus with storage equivalent of only peak-times of the day leading to a smaller cost for V2G storage than any other system, which is presented in Figure 9.

**Figure 8.** 10-year energy price for all times of the day.

**Type of use Figure 9.** A 10-year simulation on the cost analysis during peak time.

**Figure 9.** A 10-year simulation on the cost analysis during peak time.

A 10-year simulation of cost analysis and ROI of installing EV chargers on campus with storage equivalent of peak and off-peak times shows the significant price difference between off-peak and peak-time, which is presented in Figure 10. between off-peak and peak-time, which is presented in Figure 10.

A 10-year simulation of cost analysis and ROI of installing EV chargers on campus with storage equivalent of peak and off-peak times shows the significant price difference

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 14 of 25

**Figure 10.** A 10-year simulation on the cost analysis on campus during off-peak time.

**Figure 10.** A 10-year simulation on the cost analysis on campus during off-peak time.

After one year, it is cheaper to purchase the peak-time energy from the grid, rather than using the V2G method at peak-times. This is because the EV chargers must be bought and installed for the first year. The year 5 and 10 year plans show that the V2G method is cheaper than purchasing from the grid. Off-peak prices from the grid are higher overall than peak-time as more off-peak hours are available than peak-hours. After one year, it is cheaper to purchase the peak-time energy from the grid, rather than using the V2G method at peak-times. This is because the EV chargers must be bought and installed for the first year. The year 5 and 10 year plans show that the V2G method is cheaper than purchasing from the grid. Off-peak prices from the grid are higher overall than peak-time as more off-peak hours are available than peak-hours.
