*3.3. Proposed Design Methodology*

The proposed methodology was applied to solve the PV power plant design and aimed to determine the optimal sizing and configuration of the PV plant, as shown in Figure 6. In the following section, the PV plant design parameters were calculated step by step by considering the measured meteorological data of the location, PV modules, inverter specifications, area coordinates, and cost units.

**Figure 6.** Flowchart of the proposed design methodology.

#### 3.3.1. Irradiance Model

Solar irradiance on tilted PV modules surface is a very important factor in the optimal design of PV power plants. Installation areas with PV modules facing south are suitable for PV power plants [35]. Additionally, a good agreement was shown by PV plants oriented towards the south by using the isotropic model [67].

Several models, which are classified as isotropic and anisotropic, can be used to estimate the solar irradiance on a tilted plane [67,68]. The treatment of diffuse radiation was the only difference between these two models, while the rest is treated the same. However, the isotropic model developed by Liu and Jordan [69] was applied to this methodology to estimate the solar irradiance on the tilted PV module surface [67].

The total radiation received on a horizontal surface (global radiation: I) can be divided into two components: beam and diffused radiation. The estimation of solar radiation on the tilted surface is calculated on the basis of these two components. The total radiation received on the horizontal surface is given by the following equation:

$$I(t) = I\_b(t) + I\_d(t) \tag{10}$$

The index of transparency of the atmosphere or the clearness index *kT* of the sky is an essential factor. The clearness index is the function of the ratio between the extraterrestrial and horizontal radiation, as expressed by the following equation:

$$k\_T(t) = \frac{I(t)}{I\_0(t)}\tag{11}$$

The diffuse fraction of total horizontal radiation depends on the clearness index of the sky [67] and is expressed by the following equation:

$$\frac{I\_d(t)}{I(t)} = \begin{cases} 1.0 - 0.09k\_T(\mathbf{t}), k\_T(\mathbf{t}) \le 0.22\\ 0.9511 - 0.1604k\_T(\mathbf{t}) + 4.388(\mathbf{t})k\_T^2 - 16.638k\_T^3(\mathbf{t}) + 12.336k\_T^4(\mathbf{t}), \ 0.22 \prec k\_T(\mathbf{t}) \le 0.8\\ 0.165, k\_T(\mathbf{t}) \le 0.80 \end{cases} \tag{12}$$

manipulating Equation (10), the beam radiation is given by the following expression:

$$I\_b(t) = I(t) - I\_d(t) \tag{13}$$

The total incident solar radiation on tilted surface is the sum of three components, namely, beam radiation from direct radiation of the inclined surface, diffuse radiation and reflected radiation.

$$I\_T(t, \boldsymbol{\beta}) = I\_B(t) + I\_D(t) + I\_R(t) \tag{14}$$

The beam irradiance on an inclined surface can be calculated on the basis of multiplication between beam horizontal irradiance and beam ratio factor *Rb*, as shown in the following expression:

$$I\_B(t) = I\_b(t) \mathcal{R}\_b(t, \boldsymbol{\beta}) \tag{15}$$

where the beam ratio factor *Rb* is a function of the ratio between beam irradiance on the inclined surface and horizontal irradiance, as expressed in the Equation (18).

The first component is the incidence angle cos(*t*, β), which can be derived as follows:

$$\begin{array}{l} \cos(t,\beta) &= \sin\delta(t)\sin\varphi\cos\beta - \sin\delta(t)\cos\varphi\sin\beta\cos\gamma\\ &+ \cos\delta(t)\cos\varphi\cos\beta\cos\omega(t) \\ &+ \cos\delta(t)\sin\varphi\sin\beta\cos\gamma\cos\omega(t) \\ &+ \cos\delta(t)\sin\beta\sin\gamma\sin\omega(t) \end{array} \tag{16}$$

where δ is the solar declination angle, ϕ is the location latitude, γ is the surface azimuth angle, and ω is the hour angle. The global radiation on the inclined surface calculation model's error was lower than 3% [70].

The second component deals with solar zenith angle cos θ*<sup>z</sup>* and can be calculated using the following equation:

$$\cos\theta\_5(t,\beta) = \cos\gamma\cos\delta(t)\cos\omega(t) + \sin\varrho\sin\delta(t) \tag{17}$$

$$R\_b(t, \beta) = \frac{\cos(t, \beta)}{\cos \theta\_z(t, \beta)}\tag{18}$$

Diffuse irradiance on an inclined surface is computed on the basis of the isotropic sky model. A well-known isotropic model was introduced by Liu and Jordan (1963). This model is simple, and the diffuse radiation has a uniform distribution over the skydome. The diffuse radiation on the inclined surface increases with an increasing amount of seen by the inclined surface, as expressed in Equation (19).

$$I\_D(t) = I\_d(t) \left(\frac{1 + \cos\beta}{2}\right) \tag{19}$$

where β is the surface tilt angle and considered as a design variable. Its optimal values are computed by the optimisation algorithm.

The reflected irradiance on an inclined surface is expressed by Equation (20) and depends on the transposition factor for ground reflection *Rr* given by Equation (21) and the reflectivity of the ground ρ that is equal to 0.2 [68].

$$I\_R(t) = I(t)\rho \mathcal{R}\_r \tag{20}$$

$$R\_r(t) = \frac{1 - \cos\beta}{2} \tag{21}$$
