## 5 Apparent Power Signature Processing
### Empirical Mode Decomposition (EMD)  
WPD, providing a multi-resolution analysis, can be regarded as a design of the band-pass filter. It is noteworthy that the filtering is not ideal which leads to a certain overlap between adjacent frequency bands [8]. Besides that, another noisy signal, which is irrelevant to the eccentricity fault, may have a bad influence on detecting the characteristic signature, especially in the case of low levels of DE. This process leads to distortion of fault severity and may cause erroneous detection. Therefore, EMD is introduced in order to eliminate or restrain noisy signals and extract the characteristic signature clearly. The EMD provides a time-frequency analysis method that decomposes the original signature into intrinsic mode functions (IMFs). The essence of this method is to identify the intrinsic oscillatory modes by their characteristic time scales in the data empirically [22]. For the original data \(X(t)\), the extrema including the local maxima and minima are identified. All the local maxima are connected via a cubic spline interpolation in order to produce the upper envelope \(\overline{X(t)}\); similarly, the lower envelope \(\underline{X(t)}\) can also be produced. All the data in \(X(t)\) should be covered by the upper and lower envelops. The distinction between the original data \(X(t)\) and \(m_{1}\) can be calculated by \(h_{1}=X(t)-m_{1}\). The purpose of this sifting process is to eliminate the riding waves and to make the wave-profiles more symmetric [23]. Hence, the aforementioned step has to be repeated more times until satisfying the stop criterion and the first IMF \(c_{1}\) can be obtained from the data. After that, the residue \(r_{1}\) between \(X(t)\) and \(c_{1}\) can be separated by Equation (15):  
\[r_{1}=X(t)-c_{1} \tag{15}\]  
In this step, the residue \(r_{1}\) is treated as the new data and repeated by the above sifting process. Finally, the \(X(t)\) can be decomposed into \(n\) IMFs and a residue \(r_{n}\) illustrated by Equation (16) [24; 25]:  
\[X(t)=\sum_{i=1}^{n}c_{i}+r_{n} \tag{16}\]  
Figure 6: Wavelet packet decomposition tree for decomposition of the original signal. In Figure 7, the corresponding frequency of the dominant components is \(f_{1}=48.34\) Hz. It is worth noting that there exist other frequency components decomposed in the 2 nd IMF. Moreover, the 2 nd IMF is mostly dominated by two components with periods of approximately 0.0393 s and 0.0226 s, and the corresponding frequencies are 25.39 Hz and 44.18 Hz, respectively. It implies that the characteristic harmonic component using WPD includes some noisy signals. These noisy signals may have a bad influence on detecting the fault severity under low levels of DE. Therefore, the combined use of WPD and EMD has the advantages of improving the SNR and also overcomes the drawbacks of simply use of WPD. However, the mode mixing is one of the problems when applying the EMD algorithm, and it can be reflected by the 2 nd IMF component shown in Figure 7. Two parts of noisy frequencies appear simultaneously in the 2 nd IMF. However, this problem has no effect on the filtering process. In this part, the 1 st IMF component has been extracted in order to identify the fault severity. The computation of the apparent power analysis scheme is shown in Figure 8. Firstly, the apparent power has been calculated after simulating the three-phase current signal and the corresponding voltage signal using FEM. Moreover, HT is used to eliminate the DC component. Secondly, in order to overcome the drawbacks under the simple usage of WPD, the combined use of WPD and EMD has been proposed to eliminate the noise component and extract the characteristic harmonic component related to DE fault. Finally, two factors including DE levels and rated loads are set to illustrate the relationship between the characteristic signal and factors. Figure 8: The computation of apparent power analysis scheme. Figure 7: The decomposed first four IMFs in the time domain with 2% DE under 33% rated load.