**2. Problem Formulation and Methodology**

### *2.1. Mathematical Modeling of Solar Panels*

Figure 1 depicts the PV panel's comparable circuit model. At the output terminal, the correlation between voltage (*V<sup>l</sup>* ) and current (*I<sup>l</sup>* ) is expressed as: = − ௦ௗ ቈ ቆ൫/<sup>௦</sup> + <sup>௦</sup> /൯ ቇ − 1 − /<sup>௦</sup> + <sup>௦</sup> / ௦

$$I\_l = I\_p - I\_{sd} \left[ \exp\left(\frac{q\left(V\_l/N\_s + R\_s I\_l/N\_p\right)}{a\,\,k\_B T}\right) - 1\right] - \frac{V\_l/N\_s + R\_s I\_l/N\_p}{R\_{sh}}\tag{1}$$

where *N<sup>p</sup>* and *N<sup>s</sup>* denote the count of solar cells interconnected in parallel and series combinations. The *<sup>k</sup><sup>B</sup>* is the Boltzmann constant (1.3806 <sup>×</sup> <sup>10</sup>−<sup>23</sup> <sup>m</sup>2kgK−<sup>1</sup> s −2 ), *T* is the cell/module temperature, *q* is elementary charge, *I<sup>p</sup>* is photovoltaic current, *Isd* is diode saturation current, *R<sup>s</sup>* series resistance, *Rsh* shunt resistance, and *a* is the module quality factor. Only five parameters (*Ip*, *Isd*, *a*, *R<sup>s</sup>* , *Rsh*) are required to calculate the minimum value of root mean square error (RMSE). ௦ௗ <sup>௦</sup> ௦ ௦ௗ <sup>௦</sup> ௦

**Figure 1.** PV panel module equivalent circuit.
