## Case Study
### Simulation Results  
The population size is set at 60 and the maximum number of iterations is 50. In the initial population of particles, the response proportion interval of HVDC emergency power support is [0.6,1], and the response proportion intervals of ELS and VEPR are all [0,0.6]. A \(\pm\)800 kV HVDC bipolar blocking is utilized to verify the effectiveness of the proposed EFC strategy. The power deficiency due to the disturbance is 8 GW, which makes up 13.59% of the total grid demand. The amount of all resource responses and their control costs of the EFC scheme obtained by improved PSO are shown in Table 3.  
The total control cost of EFC is 79.234. The frequency curves with and without the EFC are shown in Figure 10, and the frequency curves of generator buses are shown in Figure 11. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Resource Type**} & **Control** & \multirow{2}{*}{**Control Amount (MW)**} & \multirow{2}{*}{**Control Cost**} \\  & **Resources** & & \\ \hline \multirow{2}{*}{HVDC} & 1 & 400.00 & 2.000 \\  & 2 & 200.00 & 1.000 \\ \hline \multirow{6}{*}{Embedergency load shedding} & 1 & 36.05 & 1.836 \\  & 2 & 41.77 & 2.553 \\  & 3 & 31.15 & 1.581 \\  & 4 & 21.74 & 1.148 \\  & 5 & 41.79 & 2.550 \\  & 6 & 75.40 & 3.997 \\  & 7 & 12.46 & 0.651 \\  & 8 & 32.64 & 1.652 \\  & 9 & 17.09 & 0.913 \\  & 10 & 63.28 & 3.246 \\  & 11 & 27.46 & 1.385 \\  & 12 & 31.68 & 1.929 \\  & 13 & 12.76 & 0.769 \\  & 14 & 19.23 & 1.065 \\  & 15 & 36.21 & 1.857 \\  & 16 & 45.34 & 2.305 \\ \hline \multirow{6}{*}{VPP emergency power support} & 1 & 86.66 & 2.706 \\  & 2 & 65.96 & 2.023 \\ \cline{1-1}  & 3 & 82.64 & 2.586 \\ \cline{1-1}  & 4 & 55.31 & 1.706 \\ \cline{1-1}  & 5 & 60.59 & 1.890 \\ \cline{1-1}  & 6 & 21.75 & 0.658 \\ \cline{1-1}  & 7 & 91.61 & 2.853 \\ \cline{1-1}  & 8 & 41.20 & 1.284 \\ \cline{1-1}  & 9 & 205.35 & 6.406 \\ \cline{1-1}  & emergency power support & 10 & 64.05 & 1.978 \\ \cline{1-1}  & power power support & 11 & 170.61 & 5.300 \\ \cline{1-1}  & support support & 12 & 44.30 & 1.350 \\ \cline{1-1}  & 13 & 90.27 & 2.774 \\ \cline{1-1}  & 14 & 78.38 & 2.423 \\ \cline{1-1}  & 15 & 29.54 & 0.901 \\ \cline{1-1}  & 16 & 82.43 & 2.538 \\ \cline{1-1}  & 17 & 90.03 & 2.779 \\ \cline{1-1}  & 18 & 76.09 & 2.362 \\ \cline{1-1}  & 19 & 29.44 & 0.895 \\ \cline{1-1}  & 20 & 44.84 & 1.386 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The response amounts of resources in EFC strategy. As shown in Figures 10 and 11, the system frequency will rapidly drop to 49.25 Hz without the EFC strategy, resulting in under-frequency load-shedding action. The proposed EFC strategy can reduce the rate of change of frequency after resources act, and the transient frequency nadir for each bus is higher than the setting under the frequency load-shedding threshold, which is 49.25 Hz. Meanwhile, the quasi-steady frequency of the system with EFC strategy is 49.74 Hz, which is close to the rated frequency of the system, ensuring the frequency security of the receiving-end power grid. To further check voltage stability and rotor angle stability, bus voltage and rotor angle curves with EFC strategy are shown in Figures 12 and 13, respectively. Figure 11: Bus frequency curves with EFC strategy. Figure 10: Dynamic frequency curves of HVDC blocking event with and without EFC strategy. As can be seen from Figure 12, since the HVDC converter station absorbs a large amount of reactive power during steady-state operation, the system voltage increases rapidly after HVDC blocking due to excessive reactive power in the grid. With the adjustment of the generator excitation adjustment, the voltage gradually returned to a steady state. It is shown that the voltage deviation is very small during the transient state as well as during the steady state. Figure 13 shows that the receiving-end power grid has angular stability. Figure 14 shows the active power curves of load buses.