## 2 Partial Discharge Detection Using the AE Method and Signal Processing Analysis
### Time-Domain Analysis  
AE is based on the detection of transient elastic waves generated by a rapid release of energy from localized sources inside a material. When applied to power transformers, these transient waves (acoustic emissions) are produced by faults inside the unit. These signals were detected by the piezoelectric sensors placed on the transformer's tank, and all data were collected and stored by an oscilloscope. Most articles that show the effectiveness of the proposed method is that the proposed method is able to detect the transient waves. Figure 4: AE sensors coupled with the transformer’s walls and PD signals captured by an oscilloscope. Figure 3: The copper electrode used to generate partial discharge (PD source). Figure 2: The three-phase distribution transformer under testing. of these low-cost piezoelectric sensors analyzed the signals only in the frequency-domain mode, which may hide useful information such as repetitive faults [16, 17]. Figure 5 shows the waveforms from acoustic sensors mounted on the outside of the transformer tank. Some of the features extracted were amplitude (volt), duration (nanoseconds), rise time (nanosecond), and counts, which are shown in detail for the PZT sensor in Figure 6 and for both sensors in Table 1. To understand whether an AE signal is a PD, factors such as burst length, movement of the AE signal relative to the excitation frequency, and rise time of the first oscillation that crosses the threshold are considered. The number of counts is usually higher when an AE signal is created by transient or environmental noises. The duration of the signal is another important factor that can help separate PD from on-site noises; for example, for a PD with the dominant frequency of 20 kHz, the duration of the acoustic PD signal is around 200 us [13]. PDs monitored by conventional electrical methods use a threshold to predict severe activity. This level is generally from about 300 pC to 500 pC [13]. There is no similar threshold for acoustic systems because of variations in the acoustic signal caused by distance and interfering materials. A strong signal buried deep within a winding may be very weak by the time it reaches the acoustic sensor. Differences in amplifier gain settings also cause differences in magnitude [13]. If these points are not taken into account, this method could lead to errors or false alarms. Another usage of the time-domain analysis is in the comparison of sensors' performance and characteristics. MFC has a higher amplitude because of its better sensitivity. Parameters such as rise time and duration can also help determine a sensor's characteristics. In Figure 5, by comparing these two sensors' responses for a fast edge pulse (PD), it is shown that the captured AE signal by MFC had a faster rise time and a lower duration. Therefore, it can be concluded that it follows a fast vibration better than the PZT sensor. The PD source was placed between these two sensors at equal distance, so the difference between the captured AE signals was due to their frequency response (Figure 5 and Table 1). Therefore, this analysis is crucial for differentiating PD signals from on-site noises and comparing sensors characteristics. These analyses were also confirmed by the results found in the frequency-domain and the statistical analysis presented in the next sections that show the complementary nature of these different types of analysis. The time of arrival of a PD signal to the sensors is another parameter that can be useful in AE analysis, especially for PD localization applications. A major error in PD localization is due to the time of arrival or the time delay calculation. Because of noise and initial oscillation, the exact time of arrival of an AE signal is difficult to obtain directly from the time-domain of the signal. The time of arrival (TOA) could be calculated based on the minimum point of a signal energy plot (Figure 7).