*2.2. Objective Function*

The key purpose of this work is to optimize the unknown parameters for both the models (SDM and DDM) and to reduce the error between experimental and estimated data. The objective function for error used here is same as the authors have used previously in as:

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

where *V<sup>l</sup>* and *I<sup>l</sup>* are the measured voltage and current of PV module. The parameter '*k*' stands for the number of experimental data set. The best solution found by WOAPSO is represented by a vector *X*. For the single-diode model:

$$\begin{cases} \begin{array}{c} f\_{\text{single}}(V\_{l\prime} \text{ } I\_{l\prime} \text{ } X) = I\_p - I\_{SD} \left[ \exp\left(\frac{q(V\_l + I\_l R\_s)}{a\_1 k\_B T}\right) - 1\right] - \frac{V\_l + I\_l R\_s}{R\_{sh}} - I\_l\\ \text{(X = } I\_{p\prime} \text{ } I\_{SD\prime} \text{ } a\_{1\prime} \text{ } R\_{s\prime} \text{ } R\_{sh} \end{array} \end{cases} \tag{3}$$

For the double-diode model:

$$\begin{cases} \begin{aligned} f\_{\text{double}}(\text{V}\_{l\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{I}}}}}}}}}}}}}}}}}\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{I}}}}}}}}}}}}}}}}\text{\text{\text{\text{\text{\text{I}}}}}}}}}\text{\text{I}}}} \mathbf{1}}} \mathbf{1} \mathbf{1} &= I\_{\text{SD2}} \left[ \exp\left(\frac{q(V\_{l} + I\_{l}\mathbf{R}\_{\text{\text{\text{I}}}})}{a\_{2}k\_{\text{B}}\mathbf{T}}\right)} - 1 \right] - \frac{V\_{l} + I\_{l}\mathbf{R}\_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{I}}}}}}}}}}}}}}}}}}}}\mathbf}}} \mathbf}} \mathbf{\text{\text{\text{\text{I}}}}}} \mathbf{1} \mathbf{1} \mathbf{1} \end{aligned}} \end{cases}$$

For the PV panel module model:

$$\begin{cases} \begin{aligned} f\_{\text{single}}(V\_{l\prime}, I\_{l\prime} \text{ X}) &= \ I\_{p} - I\_{SD} \left[ \exp\left(\frac{q\left(\frac{V\_{l}}{N\_{\text{s}}} + \frac{R\_{\text{s}}I\_{l}}{N\_{\text{p}}}\right)}{a\_{1}k\_{\text{B}}T}\right) - 1 \right] \\ &- \frac{V\_{l}/N\_{\text{s}} + R\_{\text{s}}I\_{l}/N\_{\text{p}}}{R\_{\text{sh}}} - I\_{l}/N\_{\text{p}} \\ \text{(X} &= \ I\_{p\prime} \ I\_{\text{SD}\prime} \ a\_{1\prime} \text{ R}\_{\text{s}\prime} \text{ R}\_{\text{sh}} \end{aligned} \end{cases} \tag{5}$$
