## 4 Methodology Evaluation
### Analysis and Comparison of the Results  
This section presents the analysis and comparison of the results obtained from the two simulation professional tools. To present this comparison, it the voltages at the all buses of the power system, rotor speed at the generator G1, and the angle \(\theta\) of the voltage at bus 1 were used. Figure 4 shows the plots, in both software, of the results of the voltages in the buses of the system. The signals have almost the same behavior, but there are some differences in the values in the first oscillations, whereas in RTDS, the value is 1.95 in p.u. at B3 and in DIgSILENT PowerFactory is 1.05  
Figure 3: Hardware-in-the-loop implementation in RTDS. Figure 2: Implementation in RSCAD-RTDS. PSS, Power System Stabilizer. G, Generator; B, Bus. p.u. These differences are due to the models used in elements such as the AVR, governors, excitation systems, synchronous machines, and transmission lines between RTDS and DIgSILENT PowerFactory. In addition, the short-circuit produced some oscillations at the beginning and at the end of the event, but as the behavior of the voltages indicated, the system was stable. Figure 5 displays the rotor speed of the generator G1. It can be appreciated that both signals in RTDS and DIgSILENT PowerFactory were almost the same, but in \(t=\)1.14 s, the speed in RTDS was 374.1 rad/s, while in DIgSILENT PowerFactory, it was 374.9 rad/s. In addition, the results suggest that the power system would be able to reach a new steady state, without loss of stability after being subjected to a three-phase short-circuit. Figure 6a presents the voltage angle \(\theta\) at bus 1 obtained from the PMUs' SEL in radians. Figure 6b shows the same angle in degrees and referenced to the generator G1, obtained from RTDS and DIgSILENT PowerFactory, respectively. From Figure 6b, it can be observed that the signals presented the same behavior, but in detail, there were some differences; this was because the RTDS waveform was obtained directly from the industrial PMUs, while the DIgSILENT PowerFactory waveform was  
Figure 4: Voltages in the buses of the power system: (**a**) RTDS. (**b**) DIgSILENT PowerFactory. Figure 5: Rotor speed comparison between two professional tools. obtained from the RMS simulation. These signals were used to estimate the inertia for the generation unit G1. On the other hand, the derivative of the voltage angle \(\theta\) on the bus followed closely the angular speed of the rotor \(\omega_{r}\), as shown in Figure 7. This signal was used to estimate the inertia value. Table 2 presents the results of the inertia estimation for this case study. The results obtained demonstrate that there was concordance and that the results were better in comparison with the results reported in [24; 25; 37], where the error in the estimation was between 0.22% and 41.11%. On the other hand, [11] reported an estimation error of 16%. It is important to mention that it is not possible to establish a perfect comparison between the results obtained in this research with the results reported in the literature because the test systems were different; however, the models used and perturbations applied were similar. It is worth mentioning that the estimation errors obtained both in the literature and in this research were compared with previously-reported values, and this makes the comparison valid and fair and demonstrates that using the methodology presented in this contribution, better results were obtained. Figure 6: Voltage synchrophasors: (**a**) phase angles of the voltages provided by the PMUs. (**b**) angular difference between Buses B1 and B5 from RTDS and DIgSILENT PowerFactory. Figure 7: Rotor speed and derivative of the angle bus in RTDS. In order to evaluate the accuracy and robustness of the methodology used in this paper, another case study was carried out.