## 4 Simulation and Results  
The proposed optimization method is tested on a 33-bus IEEE-standard network to solve the multiyear network expansion planning problem. The single-line diagram of this network is shown in Figure 3. The network consists of 32 load buses, a reference bus, and 32 lines. The data of this network is visible in Table 1. The active and reactive load of the network are 3715 kW and 2300 kVAR, respectively. Figure 2: Flowchart of the dragonfly algorithm. In addition, the annual growth of the network 0.05 is assumed. Table 2 reports the required data for simulation, which are used from [26]. For this network, the three-level load is assumed based on which size of the load, the duration of load level, and the price of electricity at each level are shown in Table 3. The problem is solved by the proposed method and the details of the best solution are given in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Number of Buses**} & \multicolumn{1}{c}{\(R\) **(ohm)**} & \multicolumn{1}{c}{**X (ohm)**} & \multicolumn{1}{c}{\(P\) **(kw)**} & \multicolumn{1}{c}{\(Q\) **(kVAR)**} \\ \hline
**From Bus \(i\)** & **  
presented in Table 4. In this scenario, four DGs in the first and second years, two DGs in the third year, and one DG in the fourth year are installed. \begin{table}
\begin{tabular}{c c c} \hline \hline Objective function value (M5) & 4.7403 \\ Feeders’ reinforcement cost & 0.006584 \\ DG investment cost & 0.300479 \\ Purchased power cost & 2.308 \\ DG operation cost & 1.8586 \\ Reliability cost (M5) & 0.04806 \\ \hline \multirow{4}{*}{Optimal DG capacity and location for every year of the planning period} & \multirow{4}{*}{Second year} & 100 kW at bus 16 \\  & & 200 kW at bus 17 \\  & & 400 kW at bus 31 \\  & & 100 kW at bus 32 \\ \cline{2-3}  & & 100 kW at bus 6 \\ \cline{2-3}  & & 400 kW at bus 11 \\  & & 200 kW at bus 15 \\  & & 100 kW at bus 20 \\ \cline{2-3}  & & 100 kW at bus 20 \\ \cline{2-3}  & & 100 kW at bus 3 \\  & & 100 kW at bus 26 \\ \hline \multirow{4}{*}{Feeders’ reinforcement pattern for every year of the planning period} & \multirow{4}{*}{Second year} & \multirow{4}{*}{Feeders 1, 3, 29} \\ \cline{2-3}  & & 1 Third year \\ \cline{2-3}  & & 100 kW at bus 26 \\ \cline{2-3}  & & 1 Fourth year \\ \cline{2-3}  & & 100 kW at bus 22 \\ \cline{2-3}  & & 1 First year \\ \cline{2-3}  & & 1 Second year \\ \cline{2-3}  & & 100 kW at bus 11 \\ \cline{2-3}  & & 100 kW at bus 15 \\  & & 100 kW at bus 20 \\ \cline{2-3}  & & 100 kW at bus 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of the best solution based on the proposed method. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Unit** \\ \hline \(Inv^{DG}\) & 318 & \$/kW \\ \(Ope^{DG}\) & 0.036 & \$/kWh \\ \(FR_{j}\) & 6000 & \$/km \\ \(IL\) & 0.4 & - \\ \(IR\) & 10 & \% \\ \(Dr\) & 12 & \% \\ \(N_{y}\) & 4 & Years \\ \(Population\) size & 200 & - \\ \(Max\_iter\) & 100 & - \\ \(Power\) factor & 0.9 & - \\ \(\sigma i\) & 0.2 & fr/yr/km \\ \(Vmin\) & 0.95 & p.u. \\ \(Vmax\) & 1.05 & p.u. \\ \(Trs\) & 1 & hr \\ \(Trp\) & 4 & hrs \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The simulation data [26]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Level** & **Percentage of Annual** & **Time Duration** & \(P_{0,ls}\) \\  & **Peak Load (\%)** & **(hrs)** & **(\$/MWh)** \\ \hline Heavy (\(ls=1\)) & 100 & 1500 & 70 \\ Medium (\(ls=2\)) & 70 & 5000 & 50 \\ Light (\(ls=3\)) & 50 & 2260 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The details of the load duration curve [26]. Figure 4 represents the average network voltage before (without DG) and after (with DG) simulation. According to Figure 4, the voltage improvement rate could be clearly seen. As shown in the diagram, the base year of the program is also below the rated voltage (0.95) and, in order to improve the network voltage in the first year, it is necessary to add the DGs to the network.