*2.2. PV Power with EVCSs*

Overloading the power system with EVCSs impacts power system voltage profiles, line currents, and total losses, according to the system topology and physical characteristics. Through the paper; *PT* and *QT* refer to the power system's total loading, while *PT,i* and *QT,i* refer to the power loading of a specific bus. Adding PV-distributed generation (PVDG) with EVCSs affects the overall loading of the power system. The main objectives of adding PVDG are:


The total system power is therefore sum of the load (*PL* and *QL*), EV load (*PEVCS* and *QEVCS*), line losses (*PLoss* and *QLoss*), and PV inverter output power (−*Pinv* and ± *Qinv*). Therefore, the total active and reactive powers can be calculated as follows:

$$P\_T = P\_L + P\_{EVCS} + P\_{Loss} - P\_{inv} \tag{4}$$

$$Q\_T = Q\_L \pm Q\_{EVCS} + Q\_{Loss} \pm Q\_{inv} \tag{5}$$

where, the negative sign at the inverter active power represents the direction of generated power (−) towards the grid. Also, the reactive power output of the inverter can either generate (−) or absorb (+) reactive power to or from the grid.

The maximum PV penetration is the capacity of the PV plant that can be added to the existing distribution network without the need for upgrading the infrastructure. The values of the maximum PV penetration are obtained by the optimum load flow, and the optimum solution is based on minimizing the line losses of the system without violating the physical constraints. The locations of the PV panels are predefined according to the available space.

### *2.3. Maximum PV Power Penetration*

The PVDG connected to the distribution network acts as a negative load, as given in Equation (4). Increasing PV generation reduces line currents until the power flow is reversed. As the PV continues to increase, line currents start to increase, contributing to power system line losses, as calculated by (6):

$$P\_{\text{limloss}} = I\_{\text{lim}}^2 R\_{\text{Linc}} \tag{6}$$

The maximum active power the inverter can deliver from the PV plant at unity power factor is limited by the inverter's size and efficiency. Otherwise, non-unity power factor operation allows the inverter the operation of reactive power injection or consumption.

This paper suggests obtaining the maximum PV penetration from the maximum apparent power of the inverter (*Sinv*) at the worst-case (lowest) power factor operation using Equations (7)–(9).

$$Q\_{\rm inv} = S\_{\rm inv} \sin(\theta) \tag{7}$$

$$P\_{\rm inv} = \sqrt{S\_{\rm inv}^2 - Q\_{\rm inv}^2} \tag{8}$$

$$P\_{\rm PV} = \frac{P\_{\rm inv}}{\eta\_{\rm inv}} + P\_{\rm Loss}^{\rm DC} + P\_{\rm Loss}^{\rm FV} \tag{9}$$

where *Qinv* is the reactive power injected bythe EV charging inverter; *Pinv* is the active power injected by the inverter; θ is the angle between them; *Sinv* is the complex (active and reactive) power injected by the EV charging inverter; *PF* is the inverter power factor; η*inv* is the inverter efficiency; *P*PV is the PV power; *P*DC *Loss* refers to the losses in the DC side (before inverter); and *<sup>P</sup>*PV *Loss* refers to the power losses in the PV.

DC system losses are taken into consideration when designing PV size, the calculation for which is as shown in Equation (9). Finally, the inverter-to-PV ratio is obtained according to this approach. The inverter size compared to the PV size is referred to as the inverter-to-PV ratio throughout this paper.

### *2.4. PV Inverter Reactive Power*

The available reactive power at the inverters of EVCSs and PV can be utilized for reactive power compensation in order to improve power loss reduction and voltage profile. Line losses are a function of line current, as in Equation (6). Reducing line losses can be achieved by the PV inverter's active and reactive power generation

Before adding the PV to the power system, the line current can be calculated as follow:

$$I\_{line} = \frac{R\_{line}P\_L + X\_{line}Q\_L}{V|Z\_{line}|} \tag{10}$$

After adding PV to the distribution system, the line current can be calculated by Equation (11) as follow:

$$I\_{line}^{new} = \frac{R\_{line}(P\_L - P\_{PV}) + X\_{line}(Q\_L + Q\_{PV})}{V|Z\_{line}|} \tag{11}$$

where *V* is the voltage between the two buses, and *Iline* is the cable line in between. The available reactive power at the inverter is calculated by:

$$Q\_{inv} = \sqrt{S\_{inv}^2 - P\_{inv}^2} \tag{12}$$

where *Pinv* can be the PV power at the PV inverter or the power consumed by the EV, which is considered an instantaneous value. Therefore, reactive power compensation application for voltage profile improvement can be realized when the EVCS is not receiving power [22].
