## Case Study  
### Case Description  
In this section, a simplified model of a provincial power grid is used as the test system to verify the proposed EFC strategy. The studied provincial power grid consists of 132 buses, 32 generators, 200 transmission lines, three HVDC links, and 65 loads. The operation power of \(\pm\)660 kV HVDC link is 4 GW, and the other two \(\pm\)800 kV HVDC links are 8 GW for each one. The load capacity is 58.9 GW. The generation model for the generators in the HVDC sending-end units is the GENCLS model, and all the generation models for the generators in the provincial power grid are modeled with the GENROU model, SEXS exciter model, and TGOV turbine-governor model. All HVDC links models are the CDC4T model. The grid topology is shown in Figure 9.  
There are 16 ELS stations in the power grid. The bus number, shedding capacity, and cost factor are shown in Table 1. There are 20 VPPs, and the VPPs contain three device types: EV, AC, and WH. The number of VPP devices is shown in Table 2.  
Figure 9: The topology of the test power grid.  
The parameters are as follows: control resources weight coefficients \(\lambda_{\text{dc}}\), \(\lambda_{\text{tl}}\) and \(\lambda_{\text{vpp}}\) are all 1.0. The units of the cost factors of the control resources are all 100 MW\({}^{-1}\),\(c_{\text{dc}}\) is 0.5; \(b_{\text{vpp}}\), \(b_{\text{vpp}}\), \(K_{\text{vpp}}^{\text{c}}\), \(k_{\text{vpp}}^{\text{c}}\) and \(\theta\) are 3.0, 0.2, 70, 0.7 and 3, respectively. For the grid security and stability constraints, \(f_{\text{dn,min}}\) is 49.25 Hz, \(f_{\text{ss,min}}\) is 49.50 Hz, \(\Delta\delta_{\text{max}}\) is 180\({}^{\circ}\), \(\Sigma_{\text{sp,I}}^{\text{max}}\) is 0.1. \(K_{\text{dc}}\) is 1000 MW/s, \(t_{\text{st}}^{\text{dc}}\) is 100 ms, \(k_{\text{dc}}\) is 0.05. The sum of \(t_{\text{st}}^{\text{tl}}\) and \(t_{\text{br}}^{\text{tl}}\) is 200 ms. The sum of \(t_{\text{dc}}^{\text{Vpp}}\) and \(t_{\text{pr}}^{\text{vp}}\) is 250 ms, and \(t_{\text{pr}}^{\text{Vpp}}\) is 750 ms. PSO parameter setting: \(\omega_{\text{min}}\) and \(\omega_{\text{max}}\) are 0.4, 0.9, respectively; \(\alpha_{1}\) and \(\alpha_{2}\) are both 2. The penalty coefficients \(h_{1}-h_{5}\) are 10,000, 10,000, 100,000, and 10,000, respectively. The relevant parameters in the lower model are set as follows: \(h_{\text{la,TCL}}\) is 2; the weight coefficients \(\varphi_{1}\), \(\varphi_{2}\) are all 1.0.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**ELS Number** & **Bus** & \begin{tabular}{c} **Shedding** \\ **Capacity (MW)** \\ \end{tabular} & \
\begin{tabular}{c} **Cost Factor** \\ **Constant Term** \\ \end{tabular} &
\begin{tabular}{c} **Cost Factor** \\ **Growth Coefficient** \\ \end{tabular} \\ \hline
1 & 102 & 196.7 & 5 & 2 \\
2 & 110 & 221.6 & 6 & 2.4 \\
3 & 112 & 210.3 & 5 & 2 \\
4 & 117 & 141.3 & 5.2 & 2.1 \\
5 & 142 & 247.5 & 6 & 2.4 \\
6 & 143 & 190.8 & 5.1 & 2 \\
7 & 167 & 306.5 & 5.2 & 2.1 \\
8 & 169 & 266.3 & 5 & 2 \\
9 & 175 & 228.2 & 5.3 & 2.1 \\
10 & 184 & 244.2 & 5 & 2 \\
11 & 193 & 324.5 & 5 & 2 \\
12 & 195 & 211.6 & 6 & 2.4 \\
13 & 197 & 308.8 & 6 & 2.4 \\
14 & 201 & 280.5 & 5.5 & 2.2 \\
15 & 205 & 142.0 & 5 & 2 \\
16 & 208 & 273.8 & 5 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: ELS stations and their control test.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**VPP** & **Bus** & \begin{tabular}{c} **Device Amount (Thousand)** \\ **EV** \\ \end{tabular} & \
\begin{tabular}{c} **Operation** \\ **AC** \\ \end{tabular} &
\begin{tabular}{c} **Power Support** \\ **Power (MW)** \\ \end{tabular} \\ \hline
1 & 102 & 20 & 40 & 30 & 50.5 & 141.4 \\
2 & 110 & 30 & 50 & 50 & 78.2 & 195.7 \\
3 & 112 & 20 & 40 & 30 & 31.0 & 127.3 \\
4 & 117 & 20 & 50 & 25 & 52.1 & 131.7 \\
5 & 142 & 15 & 30 & 25 & 43.5 & 101.5 \\
6 & 143 & 20