3.3.2. Area Calculation Model

In actual cases, the PV power plant installation area is limited in surface and does not have a uniform shape. However, this proposed methodology can be applied to all actual area shapes to determine the optimal size and configuration of large-scale PV power plants. This methodology supports actual area shapes by using the coordinates of the location under study. Additionally, the universal transverse Mercator coordinate (UTM, X: east, Y: north) system is used to model the PV power plant area. Furthermore, the PV plant occupying the surface, length, and width of each row, junction boxes, and cable length are computed on the basis of the coordinates. As mentioned in the previous section, PV nodules are oriented towards the south in the installation field, as illustrated in Figure 7.

**Figure 7.** Arrangement of PV modules according to PV plant shape.

The Y-axis was used to calculate the total number of rows supported by the PV plant area and the width (*WT*). of each row. The space between two adjacent rows *Fy* , which is a design variable, and its optimum value were calculated by the algorithm process. The following equation expresses the total number of rows:

$$N\_{\text{row}} = flow\left(\frac{\max(Y) - \min(Y)}{W\_T + F\_y}\right) \tag{22}$$

After calculating the total number of rows (*Nrow*), it can be used to calculate the north coordinates of each row (*YNi*) in the PV plant, as expressed in the following equation:

$$\mathcal{Y}\_{Ni} = \min(\mathcal{Y}) + \left(\mathcal{W}\_T + F\_y\right)\mathcal{N}\_i \tag{23}$$

The parameters (*Ni*) and (*YNi*) are subject to a constraint in this methodology, as provided in Equations (24) and (25):

$$1 \le N\_{\bar{l}} \le N\_{row} \tag{24}$$

$$
\min(\mathbf{Y}) < \mathbf{Y}\_{Ni} < \max(\mathbf{Y}) \tag{25}
$$

The X-axis presents the east coordinates and is used for calculating the length of each row in the PV plant *XNi*, as expressed in the following straight-line equation:

$$X\_{Ni} = \frac{(X\_2 - X\_1)(Y\_{Ni} - Y\_1)}{Y\_2 - Y\_1} + X\_2 \tag{26}$$

where (*X*<sup>1</sup> ,*Y*1). and (*X*<sup>2</sup> ,*Y*2) correspond to the coordinates of two consecutive points. The parameter *XNi* is a constraint in this methodology, as provided in the following expression:

$$
\min(X) \le \mathcal{X}\_{N\_l} \le \max(X) \tag{27}
$$

The row length (*Mrowi* ) is obtained after the calculation of the east coordinates (*XNi*) of each row, considering the difference between these coordinates, and is expressed by using Equation (28):

$$M\_{\text{row}\mathbf{w}\_i} = X\_{\text{Ni1}} + X\_{\text{Ni2}} \tag{28}$$

The PV power plant area calculation process considers other important parameters, such as row height (*HT*), row width (*WT*) and the space between two adjacent rows *Fy* . These parameters can be calculated on the basis of the following equations:

$$\mathcal{W}\_T = N\_r L\_{pv,2} \cos \beta \tag{29}$$

$$H\_T = N\_r I\_{pv,2} \sin \beta$$

$$F\_{\mathcal{Y}} = dH\_T \tag{31}$$

where (*Nr*) and (*Fy*) are considered as design variables, and their optimal values are calculated via optimisation. Notably, (*Nr*) is the number of PV module lines in each row, and (*Fy*) is the distance between two adjacent rows. In this methodology, all rows in the installation area have the same lines of PV modules. The arrangement of rows and PV modules in a row within the installation area is shown in Figure 7.

#### 3.3.3. Components Arrangement

The arrangement of the components within the installation area is an essential part of the PV plant design process in the presence of several parameters, such as the location characteristics and the device's specifications. In addition, component arrangement depends on the optimal topology selected by the optimisation algorithm. Furthermore, the distribution of a large amount of the components among the PV power plant is computed in terms of several constraints.

However, PV modules and inverters are the two main devices considered in the PV power plant arrangements. Additionally, in case of the optimisation algorithm select central topology, the junction box arrangement is considered, and its distribution among the PV modules and the inverters is calculated on the basis of its rating power.

Finally, the PV power plant device arrangement is influenced by the amount of solar irradiance, ambient temperature, wind speed, and the geographic location. These parameters affect the tilt angle of PV modules and increase or decrease the PV module energy output, leading to the installation of varying numbers of inverters in the PV plant. Moreover, in this methodology, the aforementioned parameters are considered to control the total cost.

Dependent on PV inverter size, the number of series PV modules in each string (*Ns*) and parallel PV modules (*Np*) should be computed by the algorithm to meet a specific voltage and current requirement of inverters. On the one hand, to avoid the inverter damage that can be caused by overvoltage in case of low temperature in some locations, in every string, the number of PV modules connected in series has to be optimally computed. On the other hand, the number of parallel-connected PV modules (*Np*) multiplied by its current is equal to the input current of the inverter. To avoid the inverter damage created by the overcurrent locations with high solar irradiance, a limited number of PV modules connected in parallel (*Np*) should be addressed.

The first part handles PV modules distribution among the inverters and their arrangement within the PV plant area. The number of series (*Ns*) and parallel (*Np*) PV modules are computed in accordance with the optimum selected inverter by the optimisation process. In this proposed methodology, the number of PV modules connected in series (*Ns*) and parallel (*Np*) were considered as the design variables, and their optimum values were calculated using the optimisation algorithm. The (*Ns*) design variable involves a number of minimum (*Ns*,*min*) and maximum (*Ns*,*max*) PV modules, and these limitations can be calculated on the basis of the inverter input voltage range in [11,22], as expressed in the following equations:

$$N\_{s, \text{min}} = \frac{V\_{i, \text{min}}}{V\_{\text{upper}, \text{min}}} \tag{32}$$

$$N\_{s, \text{min}} = \frac{V\_{i, \text{max}}}{V\_{\text{oc,max}}} \tag{33}$$

$$N\_{sm,2} = \frac{V\_{i,mpp\,tmax}}{V\_{mpp,max}}\tag{34}$$

$$N\_{s,max} = \begin{cases} N\_{sm,1\prime} N\_{sm,1} \le N\_{sm,2} \\ N\_{sm,2\prime} N\_{sm,2} < N\_{sm,1} \end{cases} \tag{35}$$

The maximum number of PV modules connected in parallel (*Np*) was calculated according to the selected inverter by using the nominal power (*Pi*), and the PV module maximum output power (*Pmpp*,*max*) was selected with respect to the optimum number of PV modules connected in series (*Ns*) [22], as provided in the following expression:

$$N\_{p, \text{max}} = \frac{P\_i}{N\_s P\_{mpp, \text{max}}} \tag{36}$$

As mentioned in the previous section, the arrangement of PV modules in the PV plant area requires the use of the length of each row in the PV plant to determine the optimum number of PV modules installed in each line (*Nci* ) and the total number in each row (*Nrowi*, *pv* ). The total number of PV modules installed in each line (*Nci* ) of rows, which are described as the function ratio between the length of each row *Mrowi* and the length of the optimum PV modules *Lpv*,1 , is given in the following equation:

$$N\_{\mathbb{C}\_i} = \frac{M\_{\text{revw}\_i}}{L\_{\text{pv},1}} \tag{37}$$

The total number of PV modules installed in each row *Nrow*,*pv* depends on the number of PV module lines (*Nr*), which is a design variable in this methodology, and its optimum value is computed by the optimisation algorithm.

$$N\_{nwv\_{i\rho w}} = N\_r N\_{c\_i} \tag{38}$$

The sum of PV modules in each row of the PV plant results in their total number in the installation area as expressed in the following equation:

$$N\_{\rm I} = \sum\_{1}^{i} N\_{\rm row\_{i,pv}} \tag{39}$$

The number of series (*Np*) and parallel (*Np*) PV modules are the main parameters in the inverter calculation process. These design variables determine the number of blocks, and *xinv* represents the pieces of inverters in blocks, and each piece is composed of *Nblock* [22], as given in the following equations:

$$N\_{black} = N\_s N\_p \tag{40}$$

$$y = (N\_{i\ \prime} N\_{\text{block}}) \tag{41}$$

$$\mathbf{x}\_{\text{inv}} = \frac{\mathbf{N}\_i - \mathbf{y}}{\mathbf{N}\_{\text{block}}} \tag{42}$$

Finally, the total number of inverters is calculated on the basis of the following expression:

$$N\_{i} = \begin{cases} \begin{array}{c} \chi\_{inv} \left( \frac{y}{x\_{ipv}} \right) P\_{pv, stc} \le 0.1 P\_{i} \\\ x\_{inv} + 1 \left( \frac{y}{x\_{ipv}} \right) P\_{pv, stc} > 0.1 P\_{i} \end{array} \tag{43}$$

#### 3.3.4. PV Plant Total Energy

The proposed methodology offers many alternatives for PV modules with different specifications. Additionally, the optimisation algorithm was applied to determine the best candidate for the design of the PV plant and the optimum configuration of the PV plant as a global solution. However, the PV module output power depends on the amount of solar radiation, ambient temperature, wind speed, and electrical characteristics. Moreover, a recent review [71] has covered approximately 70 important papers on PV cell modelling, and the equations used in this proposed methodology have been applied in several papers, as shown in this review. The equations have been used in a recent paper [72], and the obtained results by the proposed procedure are more accurate than the [73] model, which involves the use of the same equations. Accordingly, these equations are suitable for calculating the performance of PV modules in our proposed design procedure.

The PV power plant consists of a large number of PV modules. Additionally, the output power is assumed to be the same for all PV modules in the PV plant, except for the southernmost row, which is considered never shaded. More importantly, the degradation of PV modules is inevitable regardless of the size of a PV power plant [74,75]. However, this research considered the PV module output power derating factor (*df*) due to soiling effect on the PV module surface, which is equal to *df* = 0.069, and the annual reduction coefficient r of PV module [34], which is equal to 0.5%. Finally, PV modules output power can be calculated using the following expression:

$$P\_{\rm PV}(t,\beta) = (1-r)(1-\mathrm{d}\_f)P\_{\rm unpp}(t,\beta)\tag{44}$$

where *Pmpp* presents the produced power by each PV module in the PV plant.

The produced energy can be affected by the shadow area on PV modules and is related to the shade impact factor (SIF) [76], and its value is equal to 2 [35]. This parameter can be obtained using the following equation:

$$A\_{\mathbb{S}\_i}(t) = \mathbb{\xi}\_i(t) SIF \tag{45}$$

where (ξ*i*(*t*)) presents the ratio of the shadow area.

The total energy of the PV power plant can be calculated according to the optimum inverter topology selected by the optimisation algorithm. Furthermore, the PV power plant produced energy and the total cost can be influenced by the selected inverter topology. For string inverter topology, the following equation is applied to calculate the PV plant output power:

$$P\_{\rm planet}(t,\boldsymbol{\beta}) = n\_{\rm tr} (1 - \eta\_{\rm cac}) (1 - \eta\_{\rm cic}) P\_{o\_i}(t,\boldsymbol{\beta}) N\_i \tag{46}$$

where (*Poi* ) is the inverter output power, (*Ni*) represents the total number of inverters, (*ntr*) is the transformer efficiency, (η*cac*) presents the AC cable losses and (η*cic*) is the interconnection cable losses. *Energies* **2020**, *13*, 2776

In the case of central inverter topology, PV plant output power can be obtained using the following equation:

$$P\_{\rm plant}(t,\boldsymbol{\beta}) = (1 - \eta\_{\rm calc})n\_{\rm imppt}n\_{\rm inv}u\_{\rm tr}(1 - \eta\_{\rm circ})(1 - \eta\_{\rm circ})\sum\_{1}^{\rm row\_i}P\_{\rm row\_i}(t,\boldsymbol{\beta})\tag{47}$$

where *Prowi* (*t*, β) presents the PV row output power, *nmppt*, *ninv* and *ntr* are the efficiencies of the PV module, inverter and transformer, respectively, and η*cdc* and η*cac*, are the DC and AC cable losses, respectively.

However, in this methodology, the PV plant energy generation was directly injected to the electric network over its operational lifetime, and it was calculated using Equation (48):

$$E\_{\text{tot}} = P\_{\text{plant}}(t, \beta) n\_{\text{s}} EAF \tag{48}$$

where EAF is the energy availability factor, and (*ns*) is the PV plant operational lifetime.

3.3.5. PV Plant Total Cost

The PV power plant consists of two types of costs, as expressed by Equation (49):

$$\mathbb{C}\_{tot} = \mathbb{C}\_{\varepsilon} + \mathbb{C}\_{M} \tag{49}$$

The installation cost (*Cc*) deals with the cost of the device, such as *Cpv*, *Cinv* which represents the unit cost of the PV modules and inverters, respectively. In addition, *CB* is the PV module mounting structure cost. Moreover, *Ccb*, *Ctr*, *Cpd*, and *Ccm* represent the costs of the cable, transformer, protection devices and monitoring system, respectively. Finally, *CL* represents the cost of the plant area. The installation cost is expressed in Equation (50):

$$\mathbf{C}\_{\mathbf{c}} = N\_I \mathbf{C}\_{pv} + N\_i \mathbf{C}\_{inv} + \mathbf{C}\_L + \mathbf{C}\_B + \mathbf{C}\_{cb} + \mathbf{C}\_{tr} + \mathbf{C}\_{pd} + \mathbf{C}\_{cm} \tag{50}$$

The operation and maintenance costs of the PV plant during its lifetime depend on the annual inflation rate (*g*), the nominal annual interest rate (*ir*). and the operation and maintenance costs per watt *Mop* , as given in the following expression:

$$\mathbf{C}\_{\mathcal{M}} = N\_I P\_{pv, \text{stc}} \mathcal{M}\_{op} (1 + \mathcal{g}) \left[ \frac{1 - \left( \frac{1 + \mathcal{g}}{1 - i\_I} \right)^{n\_s}}{i\_r + \mathcal{g}} \right] \tag{51}$$
