## 4 Simulation Result and Comparison  
To confirm the effectiveness of introducing ATCTr (with a provision of \(\pm 10\%\) change in voltage at 1.25% additional voltage per tap), simulation results based on the physical structure of the current distribution system is shown in Figure 1.  
Proper range for voltage deviation as defined by standard is \(0.95\leq V_{i}\leq 1.05\) pu. The proposed distribution network parameters considering daily load profile and real-time voltage profile of the entire system are plotted in Figure 4a,b, respectively. This is followed by the distribution voltage magnitude using ATCTs in Figure 4c. The number of tap position changes in a 24-h period (\(g_{C}\)) is 15 times. Moreover, the Pareto optimum solution for minimizing the number of introduced ATCTs and minimizing of the voltage deviation considering tap position changes is shown in Figure 4d. \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} \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
**Installed position** & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Binary coding use for ATCTrs placement in nodes. Figure 3: Flowchart of the multiobjective optimization of ATCTs. Figure 2: An example of auto-tap-changer pole transformer (ATCTr) installation placement coding. Genetic algorithm (GA) as a multiobjective optimization technique is used to obtain study objectives. Since the number of tap position changes is representative of a rough equipment lifetime, multiobjective optimization was solved for tap position using the number of tap position changes as a parameter (\(g_{A}\)-\(g_{C}\)). Tables 3-6 show the location of ATCTs for the solutions A-D. Pareto optimal solutions are shown in Figure 4d. \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 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 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ \hline \(g_{C}\) & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimum placement of ATCTs (solution B). Figure 4: Real distribution network model: (**a**) Daily load profile; (**b**) hourly voltage profile (uncontrolled); (**c**) voltage profile using ATCTs (controlled); (**d**) Pareto optimal solutions. \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} \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 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Equality constraint & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimum placement of ATCTs (solution A).