## 3 Numerical Results and Discussion
### IEEE 6-Bus Test System
In this paper, the term _FC_ is considered 2000 $ to obtain high flexibility in a 6-bus network. The results of three cases are presented in Table 7, and accordingly, it is seen that the proposed CNEP strategy has the following results:  
* Reduce the operation cost: The operation cost in case II is 3,045,670 $, a reduction of 9.57% with respect to the TEP model. This term is 13.13% for the coordinated renewable sources and transmission expansion planning method. * Reduce the investment cost: In the proposed CNEP method (case III), there is one constructed line that is between busses 2 and 6, while the TEP model includes two constructed lines. * Improve the voltage profile: In case III, the maximum voltage drop is 0.053 p.u., while it is 0.065 and 0.059 p.u. in cases I and II, respectively. Therefore, the CNEP strategy can improve the voltage profile by about 18.46%. * Obtain high flexibility: Based on Table 7, the CNEP method includes system flexibility of 10.93 as well as 0.2186 million $ flexibility benefit, where it is high concerning cases I and II.  
lines for construction are shown in Table 8. Moreover, the wind farms with a capacity of 150 MW and ESSs with the maximum capacity of 400 MWh, 100 MW charging/discharging rate, and 88% efficiency can be connected to busses 13, 17, 21, and 23. The other data such as load factor, energy price, maximum RES power, etc., are the same as 6-bus test network data. The base power and base voltage of this network are 100 MVA and 230 kV, respectively.  
The results for the proposed CNEP method are shown in Figures 7 and 8. Figure 7 shows the energy profile of ESSs, in which the charging/discharging operation mode is represented by increasing/decreasing ESS energy. Accordingly, it is charged at the period of 1:00 to 8:00 due to the low energy price, and it is discharged at the period of 17:00 to 22:00 due to the high energy price as shown in Figure 4b. In other words, ESSs are charged during the low energy price period and are discharged at the high energy price time to have a low operation cost, based on objective function (1). Moreover, Figure 8 expresses the expected flexibility benefit and expected operation cost for the IEEE 24-bus network. According to Figure 8a, the expected flexibility benefit is increased by increasing the flexibility price (_FC_) to \(10^{5}\)\(\$\), and it is constant to \(2.5\times 10^{5}\) if _FC_ changes between \(10^{5}\) and \(10^{6}\)\(\$\). Also, the expected operation cost will be increased if _FC_ increases between 0 and \(10^{5}\)\(\$\), and it is constant to 60 M\(\$\) if _FC_ changes between \(10^{5}\) and \(10^{6}\)\(\$\). It is noted that the increase in _FC_ causes the number of flexible sources or ESSs to be increased in the power system to obtain the high flexibility benefit; hence, the operation cost will be increased because a high number of ESSs is used in the power system in this condition. As a result, the CNEP can provide a transmission network with a lot of flexibility by setting a high flexibility incentive price. A suitable cost of operation value is also required. Finally, Table 9 presents the values of maximum voltage drop, system flexibility, and problem convergence. Accordingly, the maximum voltage drop from 1.05 p.u. is 0.064 p.u., which is less than the allowed value, i.e., 0.1 (1.05-0.95) p.u. Also, system flexibility is 19.4. In the end, these capabilities are calculated in 21 s, where the solution situation is optimal. Thus, the proposed method can obtain a reliable optimal solution in a low calculation time. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Line** & **1** & **2** & **3** & **4** & **5** \\ \hline Initial-Final bus & 15-21 & 15–24 & 16–17 & 16–19 & 17–18 \\ \hline Construction cost (M\(\$\)) & 100 & 100 & 100 & 90 & 90 \\ \hline Line & 6 & 7 & 8 & 9 & 10 \\ \hline Initial-Final bus & 17–22 & 18–21 & 19–20 & 20–23 & 21–22 \\ \hline Construction cost (M\(\$\)) & 100 & 100 & 110 & 100 & 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The proposed line characteristics for construction.