## 3 Results and Discussion
### Modified Two-Area Four-Machine Power System (System 1)  
The benchmark two-area symmetric system consists of five buses and two machines in each area, thus representing each substation with a single bus. Two double-circuit tie lines connect the two areas through a tie-line bus. As shown in Figure 6, the modified two-area four-machine power system model consists of four conventional synchronous generator-based power plants and two additional solar power plants. The modified system contains seven loads at bus 5L, 6L, 7L, 9L, 10-1L, 10-2L, and 11L. The modified two-area four-machine power system model with all typically used substation arrangements has been considered [28]. All conventional generators were configured with turbine governors, automatic voltage regulators, and power system stabilizers. The simulation used the RSCAD FX 2.1 software on the Real-Time Digital Simulator (RTDS) [33]. RSCAD software PMUs were utilized as the measurement instruments for this study. Substation 9 was configured as a single bus arrangement (SBA). The SBA was the fundamental arrangement. The reliability of the SBA is low due to a lack of redundancy under breaker, isolator failure, or bus fault. Due to the lack of reliability, using the SBA is limited in practice. Substation 11L was configured as an MTBA. It is important to highlight that the MTBA acts as an SBA substation under normal operation (transfer bus on standby). Thus, the MTBA was not considered in the test cases. Substation 5 was configured as an RBA. Substation 11 was configured as a DBSBA. Substation 8 was configured as a DBDBA. Substation 7 was configured as a BHA. All other substations were configured as SBAs. Further information on each substation arrangement type can be found in [28]. PMUs were installed in each substation. Thus, the current phasor measurements of each branch connecting to any substation, node voltages, and breaker currents are available. The H-TNTP-PMU was implemented based on the node voltage and branch current phasor measurements from the PMUs. PMUs were collecting measurements at 30 Hz. Three areas were identified for the D-LSE area level in the modified two-area four-machine system, as shown in Figure 6. The selection was made since Substation 8 was not included in either Area 1 or Area 2. Thus, an additional area was designated to cover Substations 7, 8, and 9 as Area 1-2. Thus, D-LSE Area 1 included the 5G, 5, 5L, 6G, 6L, 12, 7, and 7L substations. Area 1-2 included Substations 7, 8, and 9. Area 2 encompassed Substations 9, 13, 9L, 10G, 10, 10-1L, 10-2L, 11G, 11, and 11L.  
The estimation's accuracy assessment was based on error reduction. An error reduction factor (\(ERF\)), calculated in (11), indicates the estimation accuracy as many-fold better than the measurement (noisy or bad) received. The \(ERF\) is calculated by taking the inverse of the ratio of the absolute deviation between the estimated state and \(True\ Value\) against the _Measurement_ and \(True\ Value\). The \(ERF\) is a unitless metric.  
\[ERF_{i}=\frac{|Measurement_{i}-True\ Value_{i}|}{|Estimated_{i}-True\ Value_{i}|} \tag{11}\]  
For accuracy, each test case voltage estimation was analyzed based on the \(ERF\). It is important to emphasize that the \(ERF\) for the voltage estimation in SBA type was neglected, since the SBA only considers the available single bus voltage measurement as the estimated value from the weighted average. Furthermore, the SBA is an unreliable arrangement with limited practical use in the transmission network.  
Table 14 presents the voltage estimates for all the substations under all three levels when independently operated. Furthermore, the \(ERF\) for the voltage estimation of all three levels is shown in Table 14. Based on these results, the overall best accuracy under GWN was determined at the substation level.