*3.1. Parameter Estimation of Single-Diode Model Using WOAPSO*

Only five parameters (Ip, Isd, a, Rs, Rsh) are required to be estimated for a single-diode model. Table 2 signifies the values of parameters optimized by WOAPSO and RMSE for the comparison. The WOAPSO algorithm provides the lowest RMSE of 7.1700 <sup>×</sup> <sup>10</sup>−<sup>4</sup> than others (Table 2 and Table S2). Here RMSE values are acquired as the index for the evaluation of results with previously existing algorithms implemented by the researchers.

**Table 2.** Comparison of WOAPSO with different parameter estimation methods for SDM.


The characteristics curve of current-voltage and power-voltage for a single-diode model is redrawn based on the best optimized parameters obtained by implementing the WOAPSO algorithm and depicted in Figure 3. It is observed that the calculated data obtained by the WOAPSO is very effectively in keeping with the experimental data set, under S.T.C (i.e., 1000 w/m<sup>2</sup> and 33 ◦C), all over the voltage range. The error relating the measurement results for each of 20 pair points is determined by IAE and RE, which is calculated by using Equations (18) and (19), respectively.

$$IAE = |I\_{measured} - I\_{simulated}|\tag{18}$$

$$RE = (I\_{measured} - I\_{simulated}) / I\_{measured} \tag{19}$$

**Figure 3.** I-V and P-V characteristics curve for estimated and experimental values for single-diode model of R.T.C France solar cell.
