## 4 Simulation Result and Comparison
Simulation findings manifest a decisive improvement of voltage profile with stability indicator. Comparison of Figure 4b, c shows an entire system of stable operation and voltage profile transition from lower than 0.85 pu to more than 0.98 pu. Previous studies relied on optimal placement of control devices; while, this study in addition to optimal placement of control devices (Tables 3-6), focused on optimum number of control devices to ensure technical and economic dimensions within a single solution. Figure 4d shows the Pareto optimum solution, which indicates the relationship between the number of ATCTs and voltage deviation. Besides, number of tap position changes have also been considered as an important factor in a rough equipment life time of an ATCTr depreciation. Increasing changing tap position can significantly reduce a contact lifespan, and accelerates deterioration of \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Node Number** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **21** & **22** \\ \hline Equality constraint & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline Equality constraint & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline Equality constraint & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline Equality constraint & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimum placement of ATCTs (solution D). Figure 5: Node voltages of solution A for all tap position constraints (\(g_{A}\)–\(g_{C}\)). (**a**) Node voltages (equality constraint of \(g_{A}\)); (**b**) node voltages (equality constraint of \(g_{B}\)); (**c**) node voltages (equality constraint of \(g_{C}\)). transformer oil in switching process. Therefore, the control of changing tap potions is a known exigence. As shown in Figures 5-8, depending on the equality constraints (\(g_{A}\)-\(g_{C}\)), reducing voltage deviation for constants (\(g_{B}\) and \(g_{C}\)) is very close (almost equal). With automatic control and using \(g_{B}\) instead of \(g_{C}\) (in addition to setting voltage) enhances the lifespan of ATCTr. Figure 6: Node voltages of solution B for all tap position constraints (\(g_{A}\)–\(g_{C}\)). (**a**) Node voltages (equality constraint of \(g_{A}\)); (**b**) node voltages (equality constraint of \(g_{B}\)); (**c**) node voltages (equality constraint of \(g_{C}\)). Figure 7: Node voltages of solution C for all tap position constraints (\(g_{A}\)–\(g_{C}\)). (**a**) Node voltages (equality constraint of \(g_{A}\)); (**b**) node voltages (equality constraint of \(g_{B}\)); (**c**) node voltages (equality constraint of \(g_{C}\)). The results are visualized in Figures 5-8, and simulation findings are summarized in Table 7.  
The first column of Table 7 shows voltage magnitudes for solution A, which shows an increase in accordance with equality constraints (\(g_{A}\)-\(g_{C}\)), respectively. In the second column, by adding the number of ATCTs in solution B, voltage magnitudes are maintained at statutory limits (\(0.95\leq V_{i}\leq 1.05\) pu). For constant \(g_{C}\), voltage is at an acceptable range. In the third column of Table 7, in addition to maintaining voltage in an appropriate range, a comparison of \(g_{B}\) and \(g_{C}\) indicate that voltage values are very close and almost equal (Figure 7). Furthermore, the fourth column shows the similarity of the voltage magnitudes for constants \(g_{B}\) and \(g_{C}\) as well (Figure 8). Hence, using \(g_{B}\) is preferred compared to \(g_{C}\) for ATCTr's better performances. For the entire system, the proposed method can improve reinstates busses voltage to rated level and maintain unity behavior among all buses in term of voltage profile.