## 2 Materials and Methods
### Different Possible Connections Computation Approach  
Adaptive parts in PV array consist of panels that can connect to different fixed-part to adapt to varying shading scenarios. These connections are optimized to enhance the overall energy efficiency of the system. The adaptivity count and the number of rows in the PV array are utilized to calculate the possible connections. The proposed method employs a dual-adaptive structure. The number of rows in the PV array further expands the solution space in a dual-adaptive structure, increasing the likelihood of achieving a more optimized configuration. For instance, a PV array with dual adaptivity and 3 rows, or a PV array with dual-adaptivity and 4 rows, defines the PV panel structure at this stage. The number of rows in the PV array is denoted as \(m\), with adaptive and fixed parts, respectively, defined as \(A\in\{A_{1},A_{2},\ldots,A_{2m}\}\) and \(F\in\{F_{1},F_{2},\ldots,F_{m}\}\). In the developed method, the number of rows  
Figure 4: Block diagram illustrating the operation of the system designed for the reconfiguration process of a PV array with a three-row and dual-adaptive structure. in the PV array is detected vectorially. Figure 4 illustrates the process of obtaining \(I\)sc(\(A\)) and \(I\)sc(\(F\)) values, which include this information, and transferring them into the algorithm. In a single-adaptive structure, there are \(m\) fixed panels denoted as \(F\in\{F_{1},F_{2},\ldots,F_{m}\}\), where \(m\) represents the number of rows. Similarly, there are adaptive panels denoted as \(A\in\{A_{1},\,A_{2},\,\ldots,\,A_{m}\}\). The total number of all possible connections between fixed and adaptive panels in a single-adaptive structure with \(m\) rows is calculated using the permutation \(P(\binom{2^{m}}{m})\). For instance, in a structure with \(m=3\) rows, there are \(P(\binom{8}{3})=336\) different fixed-adaptive panel matching possibilities. In a dual-adaptive structure, the configuration of fixed panels is the same as in the single-adaptive structure and is represented as \(F\in\{F_{1},\,F_{2},\,\ldots,\,F_{m}\}\). However, the adaptive panels are arranged in two identical rows, making the total number of adaptive panels twice that of the single-adaptive structure. Therefore, the set of panels in the dual-adaptive structure is expressed as \(A\in\{A_{1},\,A_{2},\,\ldots,\,A_{2m}\}\). The total number of all possible unique connections between fixed panels and adaptive panels in this structure is calculated using \(P(\binom{2^{m}}{m})\). For example, in a structure with \(m=3\) rows, the total number of different fixed-adaptive panel connection possibilities is \(P(\binom{2^{23}}{3})=P(\binom{2^{6}}{3})=P(\binom{64}{3})=249,984\). Similarly, in a structure with \(m=4\) rows, the total number of fixed-adaptive panel matching possibilities is \(\binom{2^{24}}{4}=P(\binom{2^{8}}{4})=P(\binom{256}{4})=4,195,023,360\). When all different connection possibilities are calculated with permutation, the number of different connections increases exponentially as the number of rows increases. Since this means evaluating the connections in the entire probability space, there may be situations where the calculation of the appropriate connection can take days. Table 1 demonstrates all different fixed-adaptive connection possibilities according to the number of rows in single and dual-adaptive structures. As seen in the table, as the number of rows increases, especially in dual-adaptive structures, the number of all possible connections increases up to twenty-two digits in the 6-row structure. Evaluating all possibilities one by one in such a space creates very unrealistic time costs. Even if the 6-digit number in the single-adaptive structure is handled by checking the entire space one by one, the processing and time costs are not acceptable in real terms.