## 3 Results and Discussion
### Modified Two-Area Four-Machine Power System (System 1)
#### 3.1.1 Steady State with Gaussian White Noise for Topology Change  
The D-LSE was tested for the topology changes detected by H-TNTP-PMU [28]. The topology changes from Topology S1A (fully connected network) considered for the modified two-area four-machine power system are Topology S1B and Topology S1C. The topology changes were selected in accordance with the test cases presented in [28], which elaborates the topology processing with H-TNTP-PMU. The topology was changed from Topology S1A to Topology S1B by removing TL1111L (single line outage). In the next experiment, the topology was changed from Topology S1A to Topology S1C by removing the double circuit tie lines, TL78-1, TL78-2, TL89-1, and TL89-2 (area separation), as shown in Figure 6. The H-TNTP-PMU outputs are shown in Figure 7. The pretopology change (from Topology S1A to Topology S1B or Topology S1C) matrix values are shown in orange, and the post-topology change values are shown in black. Table 14 presents the steady state voltage estimation for all three levels of the D-LSE in Topology S1A. Table 1 presents the steady state voltage estimation for all three levels in Topology S1B and Topology S1C. Due to the change in topology from Topology S1A to Topology S1B, substation 11L was isolated. Due to the change in topology from Topology S1A to Topology S1C, substation 8 was isolated. The performance of the three levels was tested during the transition from Topology S1A to Topology S1B and Topology S1A to Topology S1C. Furthermore, both topology transitions were conducted under SOTA TNTP, which typically updates the topology in 2 s to 5 s [15] and H-TNTP-PMU, which typically updates the topology in every PMU data frame [28]. The topology change experiment followed the setup shown in  
Figure 6: Modified two-area four-machine power system model indicating substation level, area level, and network level. Topology was changed from Topology S1A (fully connected network) to Topology S1B by removing TL1111L (single line outage), which is indicated in blue. Topology was changed from Topology S1A to Topology S1C by removing two double circuit tie lines, TL78-1, TL78-2, TL89-1, and TL89-2 (area separation), which is shown in red. Breakers in each substation are identified with lowercase letters. Figure 8. The substation-level, area-level, and network-level estimations for Substation 11, which were directly affected by Topology S1A to Topology S1B (TL1111L single line outage) transition, are shown in Figures 9 and 10 under both H-TNTP-PMU and SOTA TNTP. The substation-level and area-level estimations for Substation 7, which were directly affected by Topology S1A to Topology S1C (area separation) transition, are shown in Figure 11 under both H-TNTP-PMU and SOTA TNTP. The start of the transition is indicated using \"P\", and the SOTA TNTP detection of the topology change is indicated using \"Q\" in the Figures 9-11. It can be seen that H-TNTP-PMU-based D-LSE and enhanced network-level LSE had an accurate estimation compared to the inefficient SOTA TNTP-based D-LSE and enhanced network-level LSE. Figure 9: Voltage phasor magnitude estimation of the Substation 11 during the Topology S1A to Topology S1B change. (**a**) Substation level. (**b**) Area level. (**c**) Network level. Figure 10: Voltage phasor angle estimation of the Substation 11 during the Topology S1A to Topology S1B change. (**a**) Substation level. (**b**) Area level. (**c**) Network level. 1.3 Steady State with Gaussian White Noise, Circuit Breaker Current Bad Data, and Injection Current Bad Data  
The substation level of the D-LSE was tested for the inclusion of multiple bad data. A circuit breaker current with bad data and a single injection current with bad data were included at the substation.