 # Fast Charging

## Fast Charginguse case

We have randomly generated the time of arrival, stay duration, and energy demand:

• The time of arrivals follow a normal distribution with mean equals to 8.00 and standard deviation equals to 1.5 hours
• The stay durations follow a normal distribution with mean equals to 8 hours and standard deviation equals to 1 hour
• The energy demands follow a normal distribution with mean equals to 30 kWh and standard deviation equals to 5 kWh
 Time of Arrivals Stay Durations (h) Time of Departures Energy Demands (kWh) 9.93 8.20 18.13 31.60 10.17 8.13 18.30 41.95 8.10 8.55 16.65 31.01 6.85 7.09 13.94 29.28 6.36 8.01 14.37 36.16 8.05 7.94 15.99 30.99 6.47 6.49 12.96 34.55 5.84 8.54 14.38 28.17

The time of departures are the sum of time of arrivals and the stay durations.

Assume that the supply cable has been limited to 64 A and there are 8 charging stations, and the maximum charging current is 32 A for each charging station or electric vehicle.

We have the following 3 scenarios for setting the charging limit at each charging station:

With this setting, the charging stations will all be fixedly allocated 8 A. Provided the above information, we can calculate and illustrate the charging schedule: And the total charging time for this scenario is 48.17 hours.

With this setting, the charging stations are aware of which charging station(s) is not connected to electric vehicle and thus reallocate the supply capability to others. Provided the above information, we can calculate and illustrate the charging schedule: And the total charging time for this scenario is 33.58 hours.

With this setting, the charging stations are aware of which charging station(s) is not charging electric vehicle and thus reallocate the supply capability to others. Provided the above information, we can calculate and illustrate the charging schedule: And the total charging time for this scenario is 21.17 hours.

#### Comparison and Conclusion

When static averaging is applied, the time needed to charge the randomly generated sessions is 33.58 hours, compared with 48.17 hours in brute force scenario, it has saved 30.29% charging time. If the done charging feature is enabled, compare with brute force scenario, it will save 56.05% charging time.

NOTE: In reality, the charging profile for EV follows a nonlinear curve, and for simplicity, we assumed that the EV can always take up to 32 A until it is fully charged.