## 3 Results  
### Analysis of PV Features and Voltage Reference Estimator  
The characteristics curves shown in Figure 7 were obtained by a considerable value of resistance linked to the PV system; this value was decreased gradually while the data were being recorded. Simultaneously, the environment temperature and irradiation were gathered, which varied, respectively, between 14.6 \({}^{\circ}\)C and 36.6 \({}^{\circ}\)C and from 64 W/m\({}^{2}\) to 808 W/m\({}^{2}\). Figure 7a indicates the relation between the voltage and the current where three sections are distinguished and were labeled in the research conducted by the authors of [46]. The first is called the _current source part_, where this feature tends to stay constant; the second one, known as _the knee_ of the I-V curve, is the section where the MPP is achieved; and finally, the _voltage source part_ is where the current-voltage is linearly related. Along the current source section, this tends to stay almost constant between 0 V and 35 V.  
Figure 6: Flowchart of P&O algorithm. However, this section is highly dependent on the irradiation, which, ideally, lean these curves upwards, whereas the temperature shifts in a horizontal movement [47]. The knee and the voltage source part are mostly conditioned by the temperature, which moves the curves to the right hand side of the graph [48]. Figure 7b shows the voltage-power curve where, in this case, the irradiation leans the curves upwards and the slope of the initial linear behaviour ascends. Nevertheless, the temperature influences a diagonal drive of the curves. Therefore, this means that the irradiation moves the MPP on a vertical axis, whereas the temperature moves the curves on an slanted axis. Formerly, the authors have been working with a current reference estimator in power sources such as proton exchange membrane fuel cells (PEMFC), where the output reference was dependent on the temperature [23,49]. In this case, a VRE was developed by highlighting the MPP points from 790 curves like those in Figure 7b, which varied with the radiation, and then a surface \(V_{ref\_MPP}=f(P,T)\) was constructed. This function was attained with the Matlab Curve Fitting Toolbox since it employs an optimized solver to achieve suitable parameters that could reach the best fit quality for curves and surfaces. The framework provided a polynomial surface represented by Equation (13); these parameters were obtained through an optimization of performance metrics to acquire a suitable goodness of fitting (GOF); these are the sum of squared errors (SSE), R-square, adjusted R-square and root mean square of the errors (RMSE). Table 6 provides the obtained metric values, which are appropriate because the SSE and the RMSE should be minimum whereas the R-square and its adjusted version should be near the unit [50, 51, 52]. Furthermore, the coefficients of Equation (13) are also exhibited with 95% confidence bounds. The representation of the surface is shown in Figure 8 based on voltage, power and temperature. \[f(x,y)=p_{00}+p_{10}\cdot x+p_{01}\cdot y+p_{20}\cdot x^{2}+p_{11}\cdot x\cdot y +p_{30}\cdot x^{3}+p_{21}\cdot x^{2}\cdot y. \tag{13}\]  
Figure 7: PV panel characteristic curves, where: (**a**) voltage-current; (**b**) voltage–power. To verify the performance of the designed and explained VRE, two experiments were conducted in different conditions, the outcomes of which are shown in Figures 9 and 10. For each figure, (c) is the output of the VRE, whereas the data of (b) and (e) are the inputs. Based on both figures, the values of temperature and the irradiation match with each curve where the MPP voltage is around 36 V and 32 V, respectively, for each condition; this is verified with the obtained results where the voltages are around the mentioned values. Surely, these are inconstant as the power fluctuates as well as being mainly affected by the irradiation and temperature; this effect is seen as a correlation between sub-figures (a) and (e).