## 3 Numerical Results and Discussion
### IEEE 6-Bus Test System  
The diagram of the IEEE 6-bus test system is shown in Figure 3[47], where bold lines denote the existing lines, and dashed lines represent the proposed lines to be constructed in the network. The power demand at the peak load hour, line data, and generator characteristics are described in Tables 1-3. Also, a planning horizon of 5 years is considered for the transmission lines. Table 4 represents the load percentage for each year, and the _coincidence_ factor is considered to be 0.7 [21]. Moreover, it is forecasted that the wind farm with a capacity of 50 MW, and ESS with 200 MWh and charging/discharging rate of 50 MW and 88% efficiency can be installed in bus 4. Additionally, the forecasted daily load factor, the energy price, and the maximum RES (wind farm) power percentage are plotted in Figure 4[34; 48]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Bus** & **Active Load (MW)** & **Reactive Load (MVAr)** \\ \hline
1 & 80 & 16 \\ \hline
2 & 240 & 48 \\ \hline
3 & 40 & 8 \\ \hline
4 & 130 & 32 \\ \hline
5 & 240 & 48 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Load characteristics of 6-bus network [47]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Line** & **From-To Bus** & **Resistance (pu)** & **Reactance (pu)** & **Construction Cost (MS)** & **Capacity (MVA)** \\ \hline
1 & 1–2 & 0.04 & 0.4 & 0 & 100 \\ \hline
2 & 1–3 & 0.038 & 0.38 & 38 & 100 \\ \hline
3 & 1–4 & 0.06 & 0.6 & 0 & 80 \\ \hline
4 & 1–5 & 0.02 & 0.2 & 0 & 100 \\ \hline
5 & 2–3 & 0.01 & 0.1 & 0 & 200 \\ \hline
6 & 2–4 & 0.04 & 0.4 & 0 & 100 \\ \hline
7 & 2–6 & 0.01 & 0.1 & 60 & 300 \\ \hline
8 & 3–5 & 0.01 & 0.1 & 0 & 300 \\ \hline
9 & 3–6 & 0.048 & 0.48 & 48 & 100 \\ \hline
10 & 4–6 & 0.01 & 0.1 & 90 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Line characteristics of 6-bus network [47]. Figure 3: Structure of 6-bus network [47]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Bus** & **SG\({}^{max}\) (MVA)** & **Operation Price (\$/MWh)** \\ \hline
1 & 173 & 10 \\ \hline
3 & 390 & 8 \\ \hline
6 & 642 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Generator characteristics of 6-bus network [47]. The base power and base voltage are equal to 100 MW and 230 kV, and the minimum and maximum voltage is 0.95 and 1.05 pu. Moreover, the reference bus is bus 1 with a voltage of 1.05/0 pu. (A) TEP Analysis: To compare the results and to understand better, for each test system, three different models have been tested as follows:  
* Modeling of the TEP problem based on DC power flow equations (DCTEP) as an MILP problem. * Modeling of the TEP problem based on nonlinear AC power flow equations (NACTEP) as an MINLP problem. * Modeling of the TEP problem based on the linear approximation of AC power flow equations (LACTEP) as an MILP problem. In this section, the deterministic TEP model considers only peak load hours, and both ESS and RES are removed from the proposed problem. The corresponding results for the three models are presented in Figure 5 and Table 5.  
According to this figure, the results of modeling of the TEP problem based on the DC power flow, the nonlinear power flow, and the linear approximation of AC power flow are the same in selecting the transmission lines for construction. For each of the three models, a transmission line is constructed between busses 4 and 6 by considering the load increase. However, it is seen that in Figure 5, the active and reactive power of generators and bus voltages have different values for different TEP models. The difference in bus voltages is negligible where linear or nonlinear AC power flow is used, but the difference in generators' active and reactive power is about 3%. Also, it is observed that in the model based on DC power flow, bus voltages are always equal to 1 per unit and the reactive power is always zero. Figure 4: (**a**) Daily curve of power percentage for the load [21] and wind farm [48], (**b**) energy price [34].