*2.2. Objective Function*

 ௦ௗ <sup>௦</sup> ௦ The main objective of the presented study is to lessen the variance among experimental and estimated data by optimizing unknown parameters for the single-diode model. Unknown parameters (*Ip*, *Isd*, *a*, *R<sup>s</sup>* , *Rsh*) are employed as decision variables during the optimization process. The accumulative squared variation between calculated and observed data is applied as an objective function. The error objective function is denoted as follows [37,38]:

$$\text{RMSE} = \sqrt{\frac{1}{k} \sum\_{N=1}^{k} f(V\_{l\prime} \mathbf{l}\_{l\prime} \mathbf{X})^2} \tag{2}$$

− 

⎟ ⎞

, ௦ ൯ ⎠

RMSE = ඩ 1 ሺ , , ሻ<sup>ଶ</sup> ேୀଵ where *V<sup>l</sup>* and *I<sup>l</sup>* denote the observed value of voltage and current of the PV module. The range of experimental datasets is specified by the parameter '*k*' and the algorithm's best answer is indicated by a vector *X*. In the case of the PV panel module:

$$\begin{pmatrix} f\_{\text{single}}(\mathbf{V}\_{\text{l}} \mid \mathbf{I}\_{\text{l}} \mid \mathbf{X}) = \mathbf{I}\_{p} - \mathbf{I}\_{\text{sd}} \begin{bmatrix} \exp\left(\frac{q\left(\frac{V\_{\text{l}}}{N\_{\text{s}}} + \frac{R\_{\text{s}}I\_{\text{l}}}{N\_{\text{p}}}\right)}{a\_{1}k\_{\text{B}}T}\right) - \mathbf{1} \end{bmatrix} - \frac{\frac{V\_{\text{l}}}{N\_{\text{s}}} + \frac{R\_{\text{s}}I\_{\text{l}}}{N\_{\text{p}}}}{R\_{\text{sh}}} - \frac{I\_{\text{l}}}{N\_{\text{p}}} \\ \mathbf{X} = \mathbf{I}\_{p\text{s}} \mid \mathbf{I}\_{\text{sd}} \mid a\_{\text{s}} \text{ R}\_{\text{s}} \text{ R}\_{\text{sh}} \end{bmatrix} \tag{3}$$

൫ = , ௦ௗ, , <sup>௦</sup>
