*3.7. Power Enhancement*

The power enhancement of game-puzzle-based configurations is evaluated with respect to the existing TCT scheme and expressed in Equation (13) [18] as

$$\%PE = \frac{P\_{\text{GMPP}}(SM/SDK/I\text{-SDK}) - P\_{\text{GMPP}}(TCT)}{P\_{\text{GMPP}}(SM/SDK/I\text{-SDK})} \times 100\tag{13}$$

### *3.8. Shading Patterns Analysis*

The obtained P-V and I-V curves during PSCs are described using MATLAB/Simulink modeling and experimentation studies.

#### (a) Shadowing pattern-I

Based on the different methodologies and placement of integer numbers, these are responsible for developing the game puzzle with shade dispersion capability as shown in Figure 11a–e. With the consideration of nonuniform shade profiles from a minimum to maximum irradiance range such as 200 W/m2, 400 W/m2, 600 W/m2, 800 W/m2 and 1000 W/m2, an inclusive study was carried out with conventional (SP, TCT) and game theory (SDK, I-SDK and SM) based configurations. The considered shading pattern showed a highly nonuniform nature in irradiance. Furthermore, the game-theory-based reconfigurable methodologies are beneficial in terms of performance improvement due to the higher shade dispersion factor.

**Figure 11.** *Cont*.


**Figure 11.** (**a**–**e**) Shade dispersion profiles for pattern-I.

To understand the feasibility of considered reconfiguration methodologies, a theoretical valuation of row-wise current was performed. The theoretical valuation of the produced row-wise current for the conventional SP configuration is expressed in Equations (14)–(16). Table 2 depicts the theoretical current assessment of other game-theory-based PV array systems.

$$I\_{r1} = I\_{r2} = I\_{r3} = \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} \\\ \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_{m} = 6I\_{m} \end{pmatrix} \tag{14}$$

$$I\_{r4} = \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_m + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_m + \begin{pmatrix} \frac{1000}{1000} \end{pmatrix} I\_m + \begin{pmatrix} \frac{600}{1000} \end{pmatrix} I\_m + \begin{pmatrix} \frac{200}{1000} \end{pmatrix} I\_m + \begin{pmatrix} \frac{200}{1000} \end{pmatrix} I\_m \\ \begin{pmatrix} \frac{200}{1000} \end{pmatrix} I\_m = 4I\_m \end{pmatrix} \tag{15}$$

$$I\_{r5} = I\_{r6} = \begin{pmatrix} \frac{800}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{800}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{800}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{600}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{400}{1000} \end{pmatrix} I\_{m} + \begin{pmatrix} \frac{400}{1000} \end{pmatrix} I\_{m} \\ \begin{pmatrix} \frac{400}{1000} \end{pmatrix} I\_{m} = 3.8 I\_{m} \end{pmatrix} \tag{16}$$

**Table 2.** Theoretical assessment: PV performance under shading pattern-I.

