## 5 Case Studies
### Performance Verification with Power-Quality Analyzer  
In this section, the measured current waveform of an EAF and the voltage waveform at a 161 kV bus connected with a 128 MW offshore wind farm by a commercialized power-quality meter (PQM) is applied. The results obtained from the proposed method are compared with the results analyzed by the PQM. Figure 10a illustrates the actual measured EAF current waveform by the PQM and the reconstructed one. Figure 10b depicts the time-frequency ridges. Figure 11 shows the reconstructed time-domain waveforms for selected frequency components up to 510 Hz using the inverse SSWT. For the offshore wind farm case, results are shown in Figure 12. Figure 13 illustrates the reconstructed time-domain waveforms for selected frequency components up to 690 Hz. Figure 14 also depicts the fundamental and major harmonic voltage magnitude variations of corresponding reconstructed time-domain waveforms in Figure 13.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Actual Frequency**} & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{4}\) & \(f_{5}\) \\  & **(Hz)** & **60.3** & **116** & **120.6** & **301.5** & **421.1** \\ \hline \multirow{2}{*}{DBSCAN} & Detected & 60.2465 & 116.0265 & 120.5671 & 301.7181 & 421.3898 \\  & Absolute Error & 0.0535 & 0.0265 & 0.0329 & 0.2181 & 0.2898 \\ \hline \multirow{2}{*}{FFT} & Detected & 60 & 115 & 120 & 300 & 420 \\  & Absolute Error & 0.3 & 1 & 0.6 & 1.5 & 1.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of frequency estimation of the proposed method.  
Figure 10: EAF case: (**a**) the actual measured current waveform and reconstructed one using the proposed method, (**b**) time–frequency ridges.  
Figure 11: EAF case: selected reconstructed time-domain waveforms up to 510 HZ corresponding to Figure 10b.  
Figure 12: Offshore wind farm case: (**a**) the actual measured current waveform and reconstructed one using the proposed method, (**b**) time–frequency ridges.  
In Figures 10-14, several harmonic or interharmonic components with low magnitudes are recognized as noise. Some mismatches between actual measured and reconstructed current waveforms are observed because the highest frequency components are considered up to 510 Hz and 690 Hz, respectively. By observing Figures 10a and 12a, the average errors between the reconstructed and actual measured waveforms are 2.1% and 14.7%, respectively. The average error is calculated by taking the sum of the absolute error between the difference of simulated and measured values at each point divided by the measured value for all points and then the sum of errors of all points is divided by the number of total measured points over one second. A larger average error is observed in Figure 12a, which is caused by neglecting the high-frequency terms in the waveform reconstruction and undetectable small-magnitude frequency components in the measured waveform. However, the reconstructed results obtained by the proposed method agree with the measured waveforms of PQM. Each time-varying frequency component of the  
Figure 13: Offshore wind farm case: selected reconstructed time-domain waveforms up to 690 Hz corresponding to Figure 12b.  
measured waveforms can be accurately detected and the time-domain waveform for each frequency is well reconstructed.