*3.4. Mathematical Representation and Specifications of the Hybrid System Components* 3.4.1. Wind Turbine System

The detailed technical information of the considered wind turbine (WT) is given in Table 8, while its cost data are presented in Table 9 [44]. The Weibull k parameter is a measure of the long-period distribution of wind speed (WS) for a year, taken herein as 2. The diurnal pattern strength, specified as 0.25, is a measure of how strong WS depends on the daytime, while the 1 h autocorrelation factor in the HOMER Pro® software is a measure of the hour–hour randomness of WS, considered as 0.85. The hour of peak WS is taken as 15. The quantities of WTs needed to reliably satisfy the EV charging requirement at a low cost are optimized. The relationship between the output power and the WS is illustrated via the WT power curve in Figure 5. The mechanical power *Pm* of the WT with regard to the air density *ρ* (1.22 kg/m3), surface area *A* swept by the rotor (m2), and velocity *V* are evaluated as:

$$P\_m = \frac{1}{2} \times \rho \times A \times V^3 \tag{1}$$

**Table 8.** Technical specification of the WT.



**Table 9.** Economic data of the hybrid energy system components.

**Figure 5.** The WT power curve.

The electrical power *Pe* in terms of the power coefficient *Cp* is given as:

$$P\_t = \frac{1}{2} \times \rho \times \mathbb{C}\_p \times A \times V^3 \times 10^{-3} \,\text{,}\tag{2}$$

#### 3.4.2. Solar Photovoltaic System

In this study, the SunPower X21-335-BLK PV panel was selected due to its high efficiency. The details of the cost variables associated with the PV panel are given in Table 9. The mean efficiency of the solar panel is 21%. The technical specification of the solar photovoltaic is presented in Table 10 [41]. The panel has 96 monocrystalline cells at nominal power and operating cell temperature of 0.335 kW and 43 ◦C, respectively. The sizes of PV panels needed to efficiently meet the EV charge demand are optimized. The output power *PPV* of the PV module is analyzed in terms of the solar irradiation, de-rating factor, and temperature influence as follows [65]:

$$P\_{PV} = \chi\_{PVPV} (\frac{G\_T}{G\_{T,STC}}) [1 + \alpha\_P (T\_C - T\_{C,STC})] \tag{3}$$

where *YPV* refers to the PV power output under standard test conditions (STC) in kW, *PV* represents the PV de-rating factor (%), *GT* is the solar radiation incident on the PV panel in the current time step (kW/m2), *GT*,*STC* refers to the incident radiation under standard test conditions (1 kW/m2), *α<sup>P</sup>* is the temperature coefficient of power (%/degree Celsius), *TC* is the temperature of the PV cell (\_C), and *TC*,*STC* is the PV cell temperature at STC (25 degree Celsius) [42].


**Table 10.** Technical data of the PV panel.

#### 3.4.3. Battery System

The economic data and technical specifications, including the storage properties of the selected battery bank, are presented in Tables 9 and 11 respectively. The string of the battery storage consists of 20 batteries per string. The maximum capacity of the battery is 408 Ah at a capacity ratio of 0.0699. The peak charge and discharge current are 74 A and 300 A at a maximum charge rate of 1 A/Ah. The *SOC*minimum value of 20% was considered in the study. The battery capacity *CBat* is calculated by utilizing the daily load energy *EL* and autonomy days (*AD*) as stated in Equation (4) below [49,66]. The battery state of charge (*SOC*) *SOCB*(%) is determined as a percentage of the ratio of its charge *qb* to its maximum charge *qbm* using Equation (5) [67].

$$\mathcal{C}\_{\text{Bat}} = \frac{E\_L A D}{\eta\_{\text{inv}} D \mathcal{D} D \eta\_{\text{bat}}} \tag{4}$$

where *ηinv* denotes inverter efficiency, *DOD* is the battery's depth of discharge and *ηbat* refer to the battery efficiency.

$$\text{SOC}\_{B}(\%) = \frac{q\_b}{q\_{bm}} \times 100\tag{5}$$

**Table 11.** Technical details of the selected battery.

