## 4 Experimental Results and Discussion
### PQD Signal Decomposition and Detection  
An artificial signal that represents an interruption with harmonics will be discussed, as follows, in order to verify the effectiveness of VMD. Figure 6 shows the PQD type of the interruption with third and fifth harmonics in the time series. As seen, the electric power is interrupted from 0.035 s to 0.117 s. Meanwhile, the obtained signal is contaminated with the third and fifth harmonics. Additionally, white noise is added with 25 dB SNR to represent the real signal.  
Figure 4: Experimental setup for power quality disturbances.  
Figure 5: The architecture diagram of the experimental setup.  
Figure 7 presents the different decomposition result of VMD, and Figure 7a-d represent the decomposed number K = 3, 4, 5 and 6, respectively. When K = 3 in Figure 7a, it appears that the PQD signal is under-decomposed. Although the fundamental component is obtained in the first IMF, the third and fifth harmonics mix in the second IMF. Figure 7b shows the same result. When K = 5 in Figure 7c, the first three IMFs are decomposed as fundamental components, the third and fifth harmonics, effectively. Interestingly, the fourth IMF presents two mutation pulses for detecting the start and the end of the PQD. By setting an appropriate threshold, the start and the end of the PQD can be easily detected and implemented on the hardware with less computational cost. Meanwhile, Figure 7d also shows a similar result when K = 6, which reveals that the PQD signal is over-decomposed, because the other two IMFs share the noise component. Nevertheless, this situation is less harmful than the under-decomposed situation, since feature selection in the next step will help to filter redundant IMFs. Moreover, from Figure 7c, it is apparent that the first four IMFs carry valid information and the remaining IMFs are invalid. Therefore, it is obligatory to consider these four IMFs for feature extraction. Meanwhile, the permutation entropy of each IMF is 0.231, 0.357, 0.442, 0.553, and 0.689, which verifies the observation results.  
Additionally, as referred to in Ref. [24], the wavelet packet decomposition (WPD) is imported for comparison. Figure 8a,b present the decomposition result by WPD when the decomposition level is 2 and 3, respectively. In Figure 8a, since the decomposition level is 2, the corresponding wavelet node is 4, which reveals that WPD can only filter noise, but the first node still retains the main component of the original signal. Though the number of the wavelet nodes increases to 8, it still reveals a similar result in Figure 8b. By contrast, VMD performs better, even if the decomposed number K is not suitable for decomposition. The reason for this phenomenon is that each node of the wavelet packet can be approximately treated as a band-pass filter at the specific frequency range. As mentioned in Section 3.1, the sampling frequency is selected as 10 kHz. For the two levels of WPD that are shown in Figure 8a, the band width of each node is approximately 1.25 kHz. Meanwhile, for the three levels of WPD that are shown in Figure 8b, the band width of each node is approximately 0.625 kHz. However, the PQD signal is defined as the interruption of the third and fifth harmonics, where sinusoidal components with frequencies of 50 Hz, 150 Hz, and 250 Hz exist. Hence, all of these components are retained and mixed in the first node, so the WPD does not seem to work effectively. Based on the decomposition result, VMD is adaptive and robust for PQD signal decomposition, especially for recursive calculation and mode mixing problems.  
Figure 6: Original signal of interruption with harmonics.