# Transmission Line Fault-Cause Identification Based on Hierarchical Multiview Feature Selection
## 3 Material and Characterization
### Waveform Characteristics  
It is believed that the disturbance variation of electrical quantity after faults occurring contains important transient information for fault diagnosis [33]. The original waveform data are recorded in COMTRADE files with the sampling frequency of 5 kHz. The first step is to acquire fault segments and extract valid waveform segments without disturbance caused by tripping. In this paper, the beginning of valid segments is determined by inspection thresholds based on root mean squared (rms) current magnitude. \(dI\) is the difference between consecutive values. \[dI\geq 0.15\;\text{pu or}\;I\geq 1.2\;\text{pu}. \tag{22}\]  
The start thresholds are determined by inspection to make sure that fault measurements in this study are correctly captured. Since COMTRADE stores not only electrical  
Figure 1: Distribution of transmission line fault cause after cleansing. signals in analog channels but also tripping information in digital channels, one and a half cycles after tripping enabling signal is regarded as the end of the segment. In characterization, we extend previous research work on waveform characterization. The following waveform features are considered and extracted. 1. Maximum Change of Sequence Components: Instantaneous magnitude is calculated relative to prefault amplitude in order to be compatible with measurements from different voltage levels and operation conditions. Karenbauer transformation is used to obtain zero, positive and negative components of three-phase signals, denoted by \(s\), \(s=0\), 1, 2. \[V_{s(\text{max})}=\frac{\text{max}\Big{(}V_{s(fault)}\Big{)}}{V_{s(pre-fault)}},s =0,2.\] (23) \[\text{I}_{s(\text{max})}=\frac{\text{max}\Big{(}I_{s(fault)}\Big{)}}{I_{s( pre-fault)}},s =0,1,2.\] (24)
2. Maximum Rate of Change of Sequence Components: \[\Delta V_{s(\text{max})}=\frac{\text{max}(|\Delta V_{s}|)}{V_{s(pre-fault)}},s =0,1,2.\] (25) \[\Delta\text{I}_{s(\text{max})}=\frac{\text{max}(|\Delta I_{s}|)}{I_{s(pre-fault)}},s =0,1,2.\] (26)
3. Sequence Component Values at \(t\)-cycle: \(t\) is set to be 0, 0.5, 1 and 1.5. For instance, \(t=0.5\) means the measuring point is 1/2 cycle from the start. \[V_{s(t)}=\frac{V_{s(t)}}{V_{s(pre-fault)}},s=0,1,2.\] (27) \[\text{I}_{s(t)}=\frac{\text{I}_{s(t)}}{I_{s(pre-fault)}},s=0,1,2.\] (28)
4. Custom Time Constant of Sequence Current: Inspired by a linear time-invariant system, time content is introduced to reflect the dynamic response of the network [23]. Time content is the time required to rise from the zero point to \(1/e\) of the maximum current. In this study, \(1/e\) is replaced with a custom value, \(m\). These features are denoted as \(TC\_I_{s(m)}\), \(m=0.1,0.2,\dots,0.9,1\)
5. DC and Harmonic Content: Hilbert-Huang transform is used to conduct spectrum analysis [17]. The harmonic content and DC content are calculated from the ratio of the specific component to the fundamental component. DC and harmonic content are denoted as \(Har\_k,k=0,3,5,7,9,11\)
6. Wavelet Energy and Energy Entropy: Discrete wavelet transform is applied to decompose fault-phase current signals into three wavelet scales. Wavelet energy \(E\) and energy entropy \(S\) are calculated for each scale. \[p_{j}=\frac{E_{j}}{\sum\limits_{j}E_{j}}=\frac{\sum\abs{C_{j}}^{2}}{\sum \limits_{j}\sum\abs{C_{j}}^{2}},S_{j}=-p_{j}\log_{2}(p_{j}).\] (29) where \(C_{j},E_{j},p_{j}\) denote wavelet coefficient, wavelet energy and relative energy in scale \(j,j=1,2,3\). Maximum DC Current: Equation (30) is used to calculate the maximum DC current on three-phase signals. \(N_{s}\) is the number of data points in one cycle, and \(n=0\) means the triggering point. \[I_{dc(\max)}=\max(I_{dc,a},I_{dc,b},I_{dc,c}),I_{dc}=\frac{\sum\limits_{n=1}^{ N_{s}}i_{n}-\sum\limits_{n\leq-N_{s}}^{N_{s}}i_{n}}{\max(I_{pre-fault})}. \tag{30}\]  
* Time Domain Factors: Form factor, crest factor, skewness and kurtosis, denoted as \(t_{1}\)-\(t_{4}\), respectively, are introduced to reflect characteristics of waveform shape and the shock for fault-phase current signals.