*4.1. TSA for Parameter Extraction of Photowatt-PWP201 PV Module*

This section discusses the evaluation efficiency of the TSA algorithm. Parameters of the Photowatt-PWP201 PV module were estimated under standard temperature conditions by utilizing the SDM model. The optimal values of the five parameters (*Ip, Isd, a, R<sup>s</sup> , Rsh*) for SDM of the solar PV module are presented in Table 2. The characteristics curves of currentvoltage (I-V) and power-voltage (P-V) are redrawn by implementing the TSA algorithm

under optimized parameters. Figure 3 demonstrates the estimated and experimental I-V and P-V characteristics curves. It can be observed that the estimated parameters show good agreement with the measured ones, which proves the efficient performance of the TSA.

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**Table 2.** Comparison of TSA with other parameter estimation methods for Photowatt-PWP201 PV Module.


**Figure 3.** Current-Voltage (I-V) and Power-Voltage (P-V) characteristics curve for estimated and experimental values for single-diode model of Photowatt-PWP201 PV Module. Symbols represent measured data, and optimized data are represented by solid lines.

Table 3 represents the Internal absolute error (IAE) between the estimated and experimental data sets. Every determined value of IAE (at 1000 W/m<sup>2</sup> and 30 ◦C) is less than 0.0195, which indicates that the parameters optimized by the TSA are very precise. The error relating to the measurement results for each of the 23 pair points is determined by the IAE and Relative Error (RE). The IAE and RE values are calculated using Equations (11) and (12). The curve of IAE and RE between experimental and estimated values is shown in Figure 4.

$$\text{IAE} = |I\_{measured} - I\_{simulated}| \tag{11}$$

$$\text{RE} = \frac{(I\_{measured} - I\_{simulated})}{I\_{measured}} \tag{12}$$


**Table 3.** The calculated current and absolute error results of TSA (Tunicate swarm algorithm) for solar PV (Photovoltaic) module.

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**Figure 4.** (**a**) Internal absolute error and (**b**) relative error curve between measured and estimated current for Photowatt-PWP201 PV Module.
