## Case Study
### Simulation Results
As shown in Figure 14, the load active power of the buses where the ELS stations are located decrease rapidly after the load-shedding action, while the load active power of the buses connected with VPP decrease in a ramp style. The power changes of the rest of the busbars are mainly caused by fluctuations of the system frequency and bus voltage. Figure 15 shows the response proportion of each ELS station and VPP in the EFC strategy. ELS can act quickly, but its control cost is high, while VEPR has a lower control cost but has an obvious response process. It is impossible, therefore, to qualitatively determine their response proportion, and the EFC optimization model must be built to solve the optimal control amounts. Two strategies are selected to verify the effectiveness of the proposed EFC strategy in reducing the total control cost. Strategy 1 is a traditional EFC, which only considers HVDC emergency power support and ELS, and the control amount of ELS is based on the principle of average allocation. Strategy 2 considers VEPR, but the control amounts of ELS and VPP are also based on the principle of average allocation. The control amounts of HVDC emergency power support are the same as the proposed EFC strategy. In strategy 1, the total control amount of ELS is at least 1925 MW; that is, the control amount of each ELS is 120.31 MW, and the total control cost is 111.123. In strategy 2, the total control amount  
Figure 14: Active power curves of load buses with EFC strategy. Figure 13: Rotor angle curves with EFC strategy. of ELS and VPP is at least 2030 MW; that is, the control amount of each ELS and VEPR is 56.39 MW, and the total control cost is 87.033. Figure 16 shows the frequency curves under the three strategies. As shown in Figure 16, because ELS acts faster than VPP, strategy 1 has the lowest rate of change of frequency at the beginning time, and it requires the least total control amount. Although the total control amounts of strategy 2 and the proposed EFC strategy are greater than that of strategy 1, the lower control cost of the VEPR makes up for the shortage of its slow response speed compared with that of ELS. All three strategies can avoid the transient frequency deviation triggering the under-frequency load shedding, but the participation of VEPR can significantly reduce the total control cost, and the proposed EFC strategy can further reduce the total control cost. The EFC scheme shows that all of the VPP response proportions are less than 70%, which reduces the influence of a VEPR evaluation error on control instruction following. Table 4 shows the DERs response priority based on absolute time margin and dynamic priority sequence. The regulation duration \(T\) is 5 min. As Table 4 shows, the time between arrival and departure of EV is usually on the hourly scale, while the on-time (i.e., cooling duration for AC and heating duration for WH) for household AC or WH is usually on the minute scale. In the test scenario, if only the absolute time margin is used to construct response priority, it will result in high priority for EV and low priority for AC and WH. When the dynamic priority of DERs is constructed by considering both the improved time margin and state margin, the difference in absolute  
Figure 16: Grid frequency curves with different control strategies. (**a**) Grid frequency curves; (**b**) Grid frequency curves at the beginning time. Figure 15: Response proportion of load-shedding stations and VPPs. time margin between EV and TCL is weakened, which improves the priority of AC and WH and improves the fairness between different device types.