*5.4. E*ff*ect of PV Inverter Power Factor on PV Optimum Size*

As the inverter power factor is reduced from unity, the optimum PV size kVA is affected. According to the results presented in Figures 13 and 14, it is observed that the maximum PV penetration into the power system varies with the inverter power factor. For non-unity power factor operation, the optimum size of PV is chosen according to the optimum inverter-to-PV ratio for each power factor. This section did not consider the available area when calculating the maximum PV penetration. The inverter-to-PV ratios considered were 1 for PF = 1, 1.11 for PF = 0.9, and 1.25 for PF = 0.8. As the power factor decreases, the power system's losses are lessened by reducing the reactive power load until the point where power losses start to increase, as for the case when PF = 0.8. The optimum inverter-to-PV ratio is 1.1 for this system. Changing the power factor setting of the inverter allows an increase in PV installation. Varying the inverter-to-PV ratio can affect the maximum connection that the system can allow. Therefore, the PV connection is more effective for systems with high line losses, as is the case when the PV is installed at the main buses (case in Figure 14).

**Figure 13.** Effect of PV inverter PF on PV optimum size—PV at EVCSs.

**Figure 14.** Effect of PV inverter PF on PV optimum size—PV at main buses.

According to the Ahmadi distribution, the rooftop area of the residence can allow an installation of no more than 5 kW per house, which refers to the case study in the next section.

### *5.5. Daily Assessment of the Power System for the Ahmadi Distribution Network with EVCSs and PV*

The daily load flow was obtained according to EVCSs' demand, PV power generation, and PV inverter reactive power. The case under study was conducted with the following (obtained from previous results and assumptions):


Figure 15 shows the load profile for the Ahmadi distribution network, which is the overall active power drawn by the network at bus 1.

Case 1: The base case with zero EVCSs connected. The load profile shows an increasing peak around noon. The daily load profile is generated by the network's maximum demand [32]. This case was studied according to the available data and the future development of the actual daily load demand required. The peak demand is approximately 1 MW and occurs between 11:00 and 15:00.

Case 2: This case studies the network at 100% EVCS penetration with no PV power. The EVCSs' demand is reflected in the overall power profile. The increase in the load occurs at night between 16:00 and 07:00, which refers to the time during the weekdays where people return to their homes after work.

**Figure 15.** Daily load profile at bus 1.

The noon peak increases by approximately 3.4%, and the new peak at 15:00 is 1.15 MW, which increases by 6.4%, with a higher peak at 22:00 of 1.27 MW (an increase of 17.4%). The load starts to reduce exponentially, which reflects the final behavior of the charging process of the electric vehicles' batteries. Adding an EVCS to the load demand affects daily power losses by an increase of 17% (see Table 10).


**Table 10.** Inverter power factor effect on system line losses.

Similar effect of EV charging on the load profile is found in the literature. The report in [41] shows two types of load factors (LFs) that of the load profiles. The system peak (SP) load factor and the non-coincident peak (NCP). The SP load factor is the ratio of the average EV demand to the EV peak demand, obtained here as 1.08. The NCP is the ratio between the average EV demand to the EV NCP demand, obtained here as 0.198.

Case 3: PV generation is the minimum where every house has an installation of only 4−5 kW, which operates around 2–3 kW per house. The total maximum PV generation occurs at noon, with approximately 130 kW, and load demand is reduced from 1.12 to 0.88 MW (a reduction of 21.4%). The power losses reduce by approximately 41% with PV generation (at 12:00 pm), as shown in Figure 16. At night, the PV inverter is used for reactive power compensation. The line losses are reduced by 16.6% during the night peak load (at 10 pm), and the daily power losses are reduced by 20% (see Table 10). This case considers the inverter-to-PV ratio to be 1; the available reactive power at the PV does not reach the installed capacity. Therefore, there is always available reactive power at the inverter to compensate for the system losses.

**Figure 16.** Daily losses.

Case 4: The non-unity power factor of the PV inverter is considered. The effect of reactive power compensation is reflected in the line losses. PV generation is not affected by the power factor because the inverter-to-PV ratio is 1.11 for this case (PF = 0.9). The daily power losses are reduced by 2.5% compared with the case involving unity power factor operation.

Case 5: The inverter-to-PV ratio of this case is 1.25. The effect of having the inverter compensate at PF = 0.8 causes a 5.67% reduction in daily line losses compared to the system at a unity power factor.

Furthermore, other cases were considered for PF = 0.6 and 0.5, with an inverter-to-PV ratio of 1.5 and 2, respectively, with further daily loss reductions of 7.26% and 12.73%, respectively.

### **6. Conclusions**

In this study, the impact of EV charging demand was analyzed for two case study power distribution networks with different characteristics. The power flow was validated by the standard IEEE 33 network. Different load flow scenarios were introduced to analyze the performance indices. Instead of varying the number of EVs, the number of EV charging stations was varied, and the maximum charging load capacity was obtained using the load flow analysis technique.

This paper suggests operating EVCS with PV power generation and reactive power compensation. The optimal PV size was considered by obtaining the optimum inverter-to-PV ratio for minimum power loss. The inverter optimum size was obtained at 0.9 power factor for the Ahmadi network without considering rooftop area limitations. The maximum PV size is not always the optimal solution when PVs are located at the same EVCS buses. Other cases show that reactive power increases the PV maximum penetration when the PV is located at the main feeder buses. The limitation factor refers to both cable ampacity and line losses at PV locations.

It was observed that PV integration with EV charging stations can decrease 21% of the load profile at noon in Kuwait. A high penetration of EV chargers among the houses in the Ahmadi case study causes a 17% increase in power demand at night. The increase does not exceed the network power system limitations for the worst-case scenario, which is the summer peak load. The capability for fast charging at residential areas is limited to the physical characteristics of the network. The maximum demand of an EVCS that can be provided for all customers is 4 kW, which limits the DC fast charging to be centralized at the network's main buses only. Deciding whether or not to have central or distributed charging stations depends on both network characteristics and customer needs. Varying the Inverter to PV ratio from 1.1 to 2 can decrease the system losses by 34% to 41%, which shall be considered based

on an economic assessment. Considering reactive power compensation with PVDG when integrating EVCS into the power system has triggered improvements in system efficiency and power delivery.

**Author Contributions:** Conceptualization, H.M.A.; formal analysis, H.M.A.; investigation, H.M.A. and R.M.K.; methodology, H.M.A.; project administration, A.G.; software, H.M.A. and A.T.; supervision, A.S. and A.G.; validation, R.M.K.; visualization, H.M.A. and A.T.; writing—original draft, H.M.A.; writing—review and editing, R.M.K and A.G. All authors have read and agreed to the published version of the manuscript.

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

**Acknowledgments:** The technical support given by the Housing team of Kuwait Oil Company, which provided all of the necessary data required for modeling Ahmadi Residential Network in this study.

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