*5.1. Test System 1*

The topology of test system 1 is shown in Figure 5. There are 64 equivalent loads, 39 equivalent generators, 101,000 kV buses, 80,500 kV buses, and 3 HVDC lines: ±660 HVDC 1, ±800 HVDC 2, and ±800 HVDC 3. The total capacity of equivalent loads is 59.6 GW, and the transmission power of the HVDC lines are 4, 8, and 8 GW, respectively. That is, the capacity proportion of HVDCs is 33.56% of the equivalent loads.

**Figure 5.** Topology of test system 1.

#### 5.1.1. Construction of the Hybrid Simulation

As discussed in Section 3.2.1, the accuracy of the hybrid simulation is related to the interface buses, so the frequency-domain characteristics analysis is conducted to determine the interface buses.

For the convenience of description, the number of branches in the shortest path between two buses is defined as the electrical distance. For example, the electrical distance between bus 38 and bus 66 is 3. Since the commutation buses are modeled as the internal nodes of the HVDC model in PSS/E, the buses with an electrical distance of 2, 3, 4, and 5 from the commutation buses are taken as the interfaces to construct the hybrid simulation models, respectively. According to Section 3.2.1, the impedance-frequency characteristics at the commutation buses of HVDCs are obtained based on the frequency-domain characteristics analysis. Take HVDC 2 as an example, the positive-sequence impedance-frequency characteristics of the rectifier-side bus 301 and inverter-side bus 55 are shown in Figure 6.

**Figure 6.** (**a**) Impedance-frequency characteristic of the rectifier-side bus 301; (**b**) Impedance-frequency characteristic of the inverter-side bus 55.

As can be seen in the figures, the differences of the impedance-frequency characteristics at bus 301 under different interface locations are negligible, which may result from the direct connection with generator 302. Additionally, the four waveforms at bus 55 match well when the frequency is lower than 110 Hz and higher than 400 Hz. Although some di fferences exist under other frequencies, the characteristics under 2 buses away and 3 buses away are very close. Buses with an electrical distance of 2 from the commutation buses are taken as the interface location.

5.1.2. Implementation of Security Assessment and Emergency Control Strategy Decision-Making

As discussed in Section 2, operation failure of protection and reclosing failure caused by a permanent fault are two issues of interest to researchers in recent years. Therefore, they are studied as two scenarios in the study. To verify the accuracy of the proposed EMT-TS hybrid simulation, the PSS/ E simulator is adopted as the pure TS simulation tool for comparison.

In the EMT-TS simulation, the limit of the extinction angle for commutation failures determination is 7.2◦. In PSS/E, the actual AC voltage criteria of commutation failures for HVDC 1, HVDC 2, and HVDC 3 are 528, 628, and 628 kV while the criteria of blocking events are 0.6 p.u.

• Scenario 1: Operation Failure of Protection

a. Implementation of Security Assessment.

In this case, a three-phase short-circuit fault occurs at line from bus 29 to bus 46 at 1.1 s, and the opening of the circuit breaker fails due to its malfunction. Therefore, the faulted line is finally isolated by tripping circuit breakers of adjacent lines at 1.4 s, which is called failure protection.

Figure 7 shows the corresponding responses of typical interface buses and HVDC 2 in the hybrid simulation and PSS/E. As can be seen from Figure 7a, the waveforms of interface buses match well before the fault occurs. Although there is a slight deviation in the transient process before the fault removal, a similar trend is obtained, which can verify the correctness of the hybrid simulation results. Meanwhile, continuous commutation failures of HVDC 2 are observed in both PSS/E and hybrid simulations during the fault. It should be noted that due to the di fferent modeling methods of HVDC converters, the extinction angle under commutation failures is di fferent in PSS/E and the hybrid simulation. In PSS/E, the extinction angle is set to 90◦ [45], while in the hybrid simulation, the extinction angle is lower than 7.2◦ [46]. Therefore, it can be seen from the waveforms of the extinction angle in Figure 7b, in both PSS/E and the hybrid simulation, the intervals between two commutation failures (extinction angle is lower than 7.2◦ in the hybrid simulation while equals to 90◦ in PSS/E) are longer than 200 ms, which indicates the occurrence of continuous commutation failures. Nevertheless, HVDC 2 is blocked at 1.4 s in the hybrid simulation while not in PSS/E, which can be seen from the slow restoration of the inverter-side active power in PSS/E. Therefore, it validates that the ETM-TS hybrid simulation proposed in this paper can detect the blocking event while there is a limitation in using pure TS simulation to detect blocking events.

Through traversing the simulation results of scenario 1, it can be found that the steady-state frequency deviation |Δ*f*| is 0.24956, which exceeds the threshold of 0.05, and the minimum transient frequency is 49.169, which is lower than the threshold of 49.25 Hz. Therefore, the emergency control strategy should be developed to maintain the security and stability of the receiving-end system.

b. Implementation of Emergency Control Strategy Decision-Making.

Since there is no pumped storage in the provincial power system, only HVDCs and interruptible loads are taken as the control resources. By applying the decision-making method proposed in Section 4.2, the emergency control strategy for the bipolar blocking event of HVDC 2 is to increase the transmission power of the rest HVDC systems by 1.2 GW at 1.5 s and shear a load of 6.16 GW at 1.7 s. The static security indices and dynamic security indices before and after adopting the emergency control strategy are shown in Figure 8. The steady-state and transient frequency indices will exceed the preset range without control, while all static and dynamic indices are within preset ranges with the control strategy obtained by the proposed method.

 **Figure 7.** (**a**) Voltage of typical interface buses; (**b**) Active power, dc voltage, and extinction angle at the inverter side of HVDC 2.

**Figure 8.** (**a**) Static indices; (**b**) Dynamic indices corresponding to the minimum transient frequency and voltage; (**c**) Dynamic indices corresponding to the maximum transient frequency and voltage.

In order to further verify the control effect of the emergency control strategy, the trajectory sensitivity-based LS scheme proposed in [55] is compared with the proposed scheme in the paper, and the results are shown in Figure 9. The LS ranges of the sensitivity-based scheme are set as (0, 10%) and (0, 14%), respectively. As can be seen from the results, the LS amount under the two ranges are

concentrated at the upper or lower limit, and there is significant non-uniformity. The control costs are 6.4763 and 6.4712 GW, respectively. In comparison, the LS amount obtained from the proposed scheme has higher consistency among the entire network, and the local LS is not uniform. Furthermore, the control cost of LS is reduced to 6.1646 GW.

**Figure 9.** Load shedding amount under di fferent schemes.

#### • Scenario 2: Reclosing at a Permanent Fault

#### a. Implementation of Security Assessment.

In this scenario, a three-phase short-circuit fault occurs at the line between bus 65 and 66 at 1.1 s, and the circuit breaker is opened at 1.2 s. In addition, the reclosing of the circuit breaker at 2.2 s fails due to a permanent fault. Therefore, the circuit breaker is reopened at 2.3 s.

The results of typical interface buses, HVDC 2 and HVDC 3, are shown in Figure 10. It can be seen in Figure 10a that the voltage waveforms of interface buses in hybrid simulation and PSS/E before reclosing are close. However, the HVDC systems show di fferent characteristics during the transient process. As can be seen in Figure 10b,c, in the hybrid simulation, continuous commutation failures are observed in HVDC 2 and HVDC 3 due to the unsuccessful reclosing of the breaker, so they are blocked at 2.3 s; while in PSS/E, the active power of the HVDC systems restores slowly after the reopening of the breaker. Obviously, reclosing to a permanent fault does not cause the second commutation failure in PSS/E, which shows the limitation of adopting the AC voltage at the inverter side as the criterion for detecting the commutation failure.

Di fferent from Scenario 1, in addition to the steady-state frequency deviation and the minimum transient frequency, the maximum transient frequency exceeds the threshold. Therefore, the emergency control strategy should be developed.

b. Implementation of Emergency Control Strategy Decision-Making.

As discussed in the above, the permanent fault will cause bipolar blocking events of HVDC 2 and HVDC 3, leading to a power loss of 16 GW. Through applying the decision-making method proposed in Section 4.2, the emergency control strategy is to increase the transmission power of the rest HVDC systems by 0.4 GW at 2.4 s and shear a load of 15.3 GW at 2.6 s. The static and dynamic indices before and after adopting the emergency control strategy are shown in Figure 11. The steady-state and transient frequency indices will exceed the preset ranges without control, while all static and dynamic indices are within preset ranges with the control strategy obtained by the proposed method.

**Figure 10.** (**a**) Voltage of interface buses; (**b**) Active power, dc voltage and extinction angle at the inverter side of HVDC 2; (**c**) Active power, dc voltage, and extinction angle at the inverter side of HVDC 3.

**Figure 11.** (**a**) Static indices; (**b**) Dynamic indices corresponding to the minimum transient frequency and voltage; (**c**) Dynamic indices corresponding to the maximum transient frequency and voltage.

#### *5.2. Test System 2*

Test system 2 is divided into three regional grids by 8 HVDC lines, as shown in Figure 12. There are 271 buses and 296 AC transmission lines. The total capacity of the generators and loads are 27,550 and 26,878 MW, respectively. For the HVDCs, the rated voltage is ±800 kV and the transmission power is 800 MW, respectively. The specific information of regions is shown in Table 3.

**Figure 12.** Topology of test system 2.



Due to the space limitations, only the results of the emergency control strategy are presented. Assume that HVDC 3 is blocked at 1.4 s under the scenario of operation failure of protection. The steady- state frequency and the transient frequency of region A and C exceed the threshold. Therefore, the emergency control strategy is developed based on the decision-making method proposed in Section 4.2.

The emergency control strategy for the bipolar blocking event of HVDC 3 is to increase the transmission power of the rest HVDC systems between region A and C by 160 MW (HVDC 2 and HVDC 6), HVDC systems between region B and C by 320 MW (HVDC 4, HVDC 5, HVDC 7, and HVDC 8), and decrease the transmission power of HVDC 1 by 320 MW at 1.5 s. Then, a generator of 600 MW in region A is sheared at 1.6 s and a load of 500 MW in region C at 1.7 s. The static and dynamic security indices of the three regions before and after adopting the emergency control strategy are shown in Figures 13–15, respectively. The steady-state and transient frequency indices of region A and C finally meet the preset ranges with the control strategy obtained by the proposed method.

**Figure 13.** Static and dynamic security indices of region A. (**a**) Static indices; (**b**) Dynamic indices corresponding to the maximum transient frequency and voltage.

**Figure 14.** Static and dynamic security indices of region B. (**a**) Static indices; (**b**) Dynamic indices corresponding to the maximum transient frequency and voltage.

**Figure 15.** Static and dynamic security indices of region C. (**a**) Static indices; (**b**) Dynamic indices corresponding to the minimum transient frequency and voltage.
