# Numerical Study of Estimating the Arrival Time of UHF Signals for Partial Discharge Localization in a Power Transformer

## Article information

## Abstract

Partial discharges (PDs) are electrical sparks that occur inside insulation between two conducting electrodes and can lead to the disastrous failure of insulation systems. To determine the location of a PD, a distributed array of UHF PD sensors is used to detect the electromagnetic (EM) signals emitted from the PD source, and the localization of the PD source can be estimated using the time difference of arrival (TDOA) between EM signals captured by the UHF PD sensor array. There are four popular methods to estimate the TDOA—the first peak method, the cross-correlation method, the energy criterion method, and the average time window threshold method. In this work, we numerically investigate the influence of noise on estimating the TDOA for the four different methods. Numerical results show that the energy criterion method is more robust against noise than other methods.

## I. Introduction

Partial discharges (PDs) are electrical sparks that occur inside insulation between two conducting electrodes. This phenomenon causes physical damage to the insulator inside a power transformer and seriously degrades the performance of the transformer. Therefore, the localization of PD signals is critical to maintain the insulation condition of high-voltage insulation systems. The ultra-high frequency (UHF) technique is a useful method to detect PD signals [1–3]. One advantage of this technique is that it is less susceptible to external environments and is less affected by external noise compared to the ultrasonic method. A distributed array of UHF PD sensors is used to detect PD signals simultaneously, and the localization of PD signals can be estimated using the time difference of arrival (TDOA) between electromagnetic (EM) signals captured by the sensor array.

EM propagation from a PD source is very complicated due to multiple reflections inside a power transformer. Therefore, an accurate estimation of the TDOA is essential for precise localization of the PD source. Four methods are commonly used to estimate the TDOA—the first peak method [4], the cross-correlation method [5], the energy criterion method [6], and the average time window threshold method [7, 8]. In practice, PD signals received by UHF sensors are usually contaminated by unwanted signals, such as digital radio signals, thermal noise in detection systems, and telecommunication signals. These noise degrades the accuracy of estimating the TDOA and therefore may result in a false PD location.

The purpose of this work is to determine a robust method of accurately ascertaining the TDOA of PD signals in the presence of noise. As stated, UHF signals captured by PD sensors have complex waveforms due to non-line-of-sight (NLOS) propagation. Therefore, a full-wave EM analysis method is required to accurately obtain UHF signals emitted from PD sources. Of the many EM analysis methods, this study employs the finite difference time domain (FDTD) method because of its versatility, robustness, and accuracy [9–13]. In contrast to the method of moment [14] and the finite element method [15], in the FDTD method it is not necessary to perform the inverse Fourier transformation to obtain time-domain EM signals to estimate the TDOA.

## II. Numerical Simulaion

Numerical simulation of UHF signal propagation from a PD signal in an actual oil-immersed power transformer that is 7,000 × 4,000 × 5,000 mm^{3} in volume is performed using the CST Microwave Studio time-domain solver, which is based on FDTD. The transformer configuration is shown in Fig. 1. The transformer mainly consists of an iron core, a coil, and a tank. The iron core and coil are colored yellow and grey, respectively, in Fig. 1. The tank is used to hold oil and to isolate components from the external environment. The dimension of the tank is the same as the simulation area. The diameter of the coil is 2,774 mm, and the width and length of the core are 1,320 mm and 6,520 mm, respectively. All components are set as perfect electric conductor in the FDTD simulation. The PD signal is modelled with an exponential function [1]. Note that the dielectric constant of oil was measured using an Agilent 85070E dielectric probe kit and an 8719ES network analyzer and was determined to be 1.7. In this work, we simulate many scenarios by changing the location of a PD source. To this end, the transformer structure is divided into 140 (7 × 4 × 5) subdomains, as shown in Fig. 2. The dimension of each subdomain is 1,000 × 1,000 × 1,000 mm^{3}. The PD source is placed at the center of each subdomain, and then 80 scenario simulations are performed by changing the PD source position. The last 60 scenarios are excluded because each center of the 60 subdomains is enclosed or located in windings and iron core.

Disc-type UHF PD sensors [16] are located on the inner surface of the power transformer to receive the propagated EM waves from the PD emitting source. The positions of the UHF PD sensors are given in Table 1.

## III. Numerical Results

In the power transformer tank, the localization of the PD source can be estimated using the TDOA between EM signals captured by the UHF PD sensor array. Usually, four methods—the first peak method, the cross- correlation method, the energy criterion method, and the average time window threshold method—are used to estimate the TDOA. In an actual power transformer environment, the main cause of TDOA errors is noise. Therefore, we investigate the influence of noise on the arrival time of UHF signals. In this work, white Gaussian noise (WGN) with three different intensities is used. In this work, signals with a signal-to-noise ratio (SNR) of −5 dB, −10 dB, and −20 dB are used. Fig. 3 shows the time-domain PD signals received at UHF sensor 1 with and without noise when the PD source is located at P1. The power of the PD signal in Fig. 3 was −38.95 dBm, and power of the noise was set to −43.95 dBm, −48.95 dBm, and −58.95 dBm for the SNRs of −5 dB, −10 dB, and −20 dB, respectively. To evaluate the robustness of each method, the noise-added PD signals are compared with the original PD signal.

### 1. First Peak Method

In the first peak method, the arrival time of UHF signals is defined as the first occurrence of a peak whose signal amplitude exceeds a specific threshold. The threshold value chosen is arbitrary and depends on visual inspection to determine the first peak. In this work, 10% of the normalized PD signal was chosen as the threshold value. Fig. 4 illustrates how the first peak method determines arrival time from the received signal. The time difference of the PD signals was calculated using the first peak method for 80 scenarios. Fig. 5 shows the results of the first peak method between the signal captured by reference sensor 4 and that captured by sensor 1 (i.e., TD14). When the stronger noise (SNR = −10 dB and −5 dB) are added, the time lags show nearly 0 seconds in Fig. 5, as the level of the first peaks is smaller than the noise level (refer to Fig. 3). Table 2 shows the average error of arrival time difference versus the SNR for the first peak method. Note that the first peak method is not at all robust against noise.

### 2. Cross-Correlation Method

The cross-correlation method is used to find the similarity of two received UHF signals. This method gradually shifts the reference signal over the others to find a matching signal. The cross-correlation value is maximum when signals are most comparable to each other. The cross-correlation is defined as [5]:

where *N* is the total number of data points. The maxima will not be located at the center of the similarity graph when the signals are not identical. Fig. 6 shows how much the maxima far from the center line represents the TDOA between two sensors. Fig. 7 shows the result of the cross-correlation between the signal captured by reference sensor 4 and that captured by sensor 1 for 80 scenarios. Table 3 shows the average error of arrival time difference for the cross-correlation method. The cross-correlation method is not particularly robust against noise.

### 3. Energy Criterion Method

The energy criterion method is based on the energy content of the signal, and the energy criterion signal is defined as [6]:

where *N* is the total number of data points and

### 4. Average Time Window Threshold Method

The average time window threshold method is used to generate an average signal over a shifting window on the time axis. Note that this method more robust against noise than the first peak method because it eliminates some oscillations. This method is defined as [7, 8]:

where *w** _{t}* is the width of the time window. Eqs. (4) and (5) are used to determine the value of

*w*

*using the frequency spectrum of the UHF signal.*

_{t}where, *f** _{a}* is the average frequency of the UHF signal calculated using its frequency spectrum

*V*(

*f*). In this work, the threshold value chosen is 10% of the time window averaged signal, as shown in Fig. 10. Fig. 11 shows an example of the average time window threshold between the signal captured by reference sensor 4 and that captured by sensor 1 for 80 scenarios. Table 5 shows the average error of arrival time difference for the average time window threshold method. We confirmed that the average time window threshold method is not robust to noise.

## IV. Conclusion

We have studied estimating the arrival time of UHF signals for PD localization in a power transformer. Four methods—the first peak method, the cross-correlation method, the energy criterion method, and the average time window threshold method—are used to estimate the accuracy of arrival time difference. We have investigated the influence of noise with three different intensities on the arrival time of UHF signals and have confirmed that the energy criterion method is the most robust to noise.

## Acknowledgments

This research was partly supported by the Hyundai Electric & Energy System Co., Ltd. and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1D1A1B03034537). We thank colleagues from the Transformer R&D Center who provided partial discharge information about the power transformer.

## References

_{2}nanoring plasmon waveguides at optical communications band. Journal of Lightwave Technology 25(9):2757–2765. 2007;

## Biography

**Sang-Gyu Ha** received a B.S. degree in Electrical and Computer Engineering from Ajou University, Suwon, South Korea and a Ph.D. degree in Electronics and Computer Engineering from Hanyang University, Seoul, Korea in 2011 and 2017, respectively. Since July 2017, he has been with LG Electronics. His current research areas are finite-difference time-domain (FDTD), non-Foster antennas, and 5G millimeter waves.

**Jeahoon Cho** received a B.S. degree in Communication Engineering from Daejin University, Pocheon, Korea and M.S. and Ph.D. degrees in Electronics and Computer Engineering from Hanyang University, Seoul, Korea in 2004, 2006, and 2015, respectively. From 2015 to August 2016, he was a Postdoctoral Researcher at Hanyang University. Since September 2016, he has worked at Hanyang University, Seoul, Korea, where he is currently a Research Professor. His current research interests include computational electromagnetics and electromagnetic pulse/electromagnetic interference/electromagnetic compatibility analysis.

**Juneseok Lee** received a B.S. in Electrical Engineering from Chungnam National University, Daejeon, Korea in 2010. He also received an M.S. degree from the Department of Electronics and Computer Engineering at The University of Queensland, Brisbane, Australia in 2011. He has also conducted research for a Ph.D. at Hanyang University, Seoul, Korea. He is interested in RF components, including antenna design, wireless communication systems, wireless power transferring, and wireless body area networks. Currently, his research is focused on designing microwave components for wireless body area network applications and antennas for next-generation wireless communication systems.

**Jaehoon Choi** received a B.S. degree from Hanyang University, Korea and M.S. and Ph.D. degrees from Ohio State University, Columbus, Ohio in 1980, 1986, and 1989, respectively. From 1989–1991, he was a research analyst with the Telecommunication Research Center at Arizona State University, Tempe, Arizona. He worked for Korea Telecom as a team leader of the Satellite Communication Division from 1991–1995. Since 1995, he has been a professor in the Department of Electronic Engineering at Hanyang University, Korea. He has published more than 200 peer-reviewed journal articles and has contributed to numerous conference proceedings. He holds over 50 patents. His research interests include antennas, microwave circuit design, and EMC. His current research is mainly focused on the design of compact, multi-band antennas for mobile wireless communication and various biomedical applications.

**Byoung-Woon Min** received B.S., M.S., and Ph.D. degrees in Electrical Engineering from Myoungji University, Yongin, South Korea, in 1997, 1999, and 2004, respectively. Since April 2004, he has been with the Research & Development Dept., Hyundai Electric & Energy Systems Co., Ltd., Korea, where he is currently a senior researcher. His current research interests include the analysis and diagnosis of partial discharge in high-voltage equipment.

**Kyung-Young Jung** received B.S. and M.S. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 1996 and 1998, respectively and a Ph.D. degree in Electrical and Computer Engineering from Ohio State University, Columbus, Ohio in 2008. From 2008–2009, he was a postdoctoral researcher at The Ohio State University, and from 2009–2010 he was an Assistant Professor with the Department of Electrical and Computer Engineering, Ajou University, Korea. Since 2011 he has worked at Hanyang University, where he is now an Associate Professor in the Department of Electronic Engineering. Dr. Jung was a recipient of the Graduate Study Abroad Scholarship from the National Research Foundation of Korea, the Presidential Fellowship from The Ohio State University, the Best Teacher Award from Hanyang University, and the Outstanding Research Award from the Korean Institute of Electromagnetic Engineering Society. His current research interests include computational electromagnetics, bio electromagnetics, and plasmonics.