*4.4. Dynamic Schedule of EVs with*/*without Appointments*

Three cases are considered in this investigation:


The arrival and departure times are randomly assigned within the eight timeslots. The users with prior booking need to provide the expected arrival time, departure time, and charging demand. For EVs without booking, the EVs' expected departure time and charging demand are provided when they reach the CS. To keep the same total demand in the three cases, only the arrival and departure times are randomly generated. In each case, the results are obtained using the SFLA and then compared with the PSO and FIFS scheduling algorithms. The dynamic system can determine a charging schedule at the beginning of each timeslot using all the EVs with and without booking, and then the PL can charge arrived vehicles with the use of the schedule for the immediate timeslot. At the beginning of each timeslot, the computational process has to be executed.

It can be seen that the electricity purchasing cost of the PL is reduced when the EVs arrived with reservation. Using FIFS, the charging price for cases 2 and 3 is increased by 3.26% and 3.11%, respectively, compared to the base case. Using SFLA, the charging price for cases 2 and 3 increased by 2.06% and 3.03%, respectively, compared to the base case (case 1). Also, using PSO, the charging price for cases 2 and 3 is increased by 2.70% and 2.89%, respectively, compared with case 1. The cost comparison with and without prior booking is given in Table 13, in which the MG case is not considered. Unexpected arrival and departure are considered for unappointed vehicles, as shown in Tables 14 and 15. Table 16 shows the scheduling when 5/20 vehicles have arrived without a booking, and Table 17 shows the scheduling of 10/20 vehicles have arrived without booking. These two cases are performed to minimize the electricity purchase cost, and the results show that the charging demands can be fulfilled in the three scenarios. Also, the needs are the same for the three cases; hence the cost can be compared.


**Table 13.** Cost comparison of the charging schedule of EVs arriving with/without prior booking.


**Table 14.** Unexpected arrival and departure considered for unappointed vehicles: when 5/20 EVs arrived without an appointment.

**Table 15.** Unexpected arrival and departure considered for unappointed vehicles: when 10/20 EVs arrived without an appointment.



**Table 16.** Unexpected arrival and departure considered for unappointed vehicles: schedule when 5/20 EVs have arrived without an appointment.

**Table 17.** Unexpected arrival and departure considered for unappointed vehicles: schedule when 10/20 EVs have arrived without an appointment.


In Table 13, the comparison shows that the electricity cost is less than that obtained using the FIFS scheme.

FIFS scheme.

Furthermore, when the MG supplies the PL, the charging costs are reduced, as presented in Table 18. A comparison of the three algorithms' values obtained in the three cases without and with MG consideration are shown in Figures 6 and 7, respectively. 20 12.37 - - - - 12.375 0 0 Total 61.50 61.50 37.96 53.23 55.71 44.89 21.12 0.00 In Table 13, the comparison shows that the electricity cost is less than that obtained using the

*Energies* **2020**, *13*, x FOR PEER REVIEW 20 of 25 16.74 - - - - - 16.74 0 0 9.6 - - 9.6 0 - - - - 11.79 - - - 11.792 0 - - - 16.1 - - - - - 16.1 0 0 12.04 - - - - - 12.045 0 0 25.20 23.438 1.762 - - - - - - 14.18 - - - - 14.186 0 0 0 21.12 - - - - - - 21.12 0


**Figure 6.** Charging costs without MG consideration: (1) 20/20 EVs arriving with booking; (2) 15/20 EVs arriving with booking; and (3) 10/20 EVs arriving with booking. **Figure 6.** Charging costs without MG consideration: (1) 20/20 EVs arriving with booking; (2) 15/20 EVs arriving with booking; and (3) 10 *Energies* **2020**, *13*, x FOR PEER REVIEW /20 EVs arriving with booking. 21 of 25

**Figure 7.** Charging costs with MG consideration: (1) 20/20 EVs arriving with booking; (2) 15/20 EVs arriving with booking; and (3) 10/20 EVs arriving with booking. **Figure 7.** Charging costs with MG consideration: (1) 20/20 EVs arriving with booking; (2) 15/20 EVs arriving with booking; and (3) 10/20 EVs arriving with booking.

#### **5. Conclusions 5. Conclusions**

reservation.

**6. Future Works**

version of the manuscript.

CC Constant current

CS Charging station CSP Charging service provider CV Constant voltage

**Abbreviations**

**Funding:** This research received no external funding.

CCCV Constant current constant voltage

**Conflicts of Interest:** The authors declare no conflict of interest.

A dynamic charging scheduling scheme for charging EVs in a PL is proposed for minimizing the charging costs. First, a conventional FIFS scheduling scheme is performed for the EV charging. Economic scheduling is found using PSO and SFLA. In this regard, the dynamic charging scheme allocates the optimal electric power in each slot for the vehicles that have arrived. Scheduling is undertaken for the vehicles that have arrived at the PL with and without prior booking. This scheme considers the electricity price at each hour and the charging limit of the PL every hour for all the three methods considered. When the electricity price is low, the entire timeslot is fully utilized to charge A dynamic charging scheduling scheme for charging EVs in a PL is proposed for minimizing the charging costs. First, a conventional FIFS scheduling scheme is performed for the EV charging. Economic scheduling is found using PSO and SFLA. In this regard, the dynamic charging scheme allocates the optimal electric power in each slot for the vehicles that have arrived. Scheduling is undertaken for the vehicles that have arrived at the PL with and without prior booking. This scheme

> the EVs effectively. Also, the PL operator provides 100% of the EV user's power within the available time. The results showed that more significant savings could be reached if the EV arrives with a prior

**Author Contributions:** Conceptualization, G.S.F. and V.K.; methodology, G.S.F.; software, S.K.; validation, J.S.A., Z.M.A. and S.H.E.A.A.; formal analysis, G.S.F.; investigation, V.K.; resources, S.K.; data curation, G.S.F..; writing—original draft preparation, S.H.E.A.A.; writing—review and editing, J.S.A. and Z.M.A.; visualization, V.K.; supervision, A.E.-S.; project administration, A.E.-S. All authors have read and agreed to the published

available at the CS may help floating customers who want quick charging.

In this work, the charging demand of each EV is considered as 100%, but this limit can vary, and random charging demand can be considered. Service delay can be regarded to benefit both the user and CS operator. Reserve charging points can be taken into account, and the charging can be undertaken for users with a special tariff based on the CS operator's decision. This kind of option considers the electricity price at each hour and the charging limit of the PL every hour for all the three methods considered. When the electricity price is low, the entire timeslot is fully utilized to charge the EVs effectively. Also, the PL operator provides 100% of the EV user's power within the available time. The results showed that more significant savings could be reached if the EV arrives with a prior reservation.
