Acoustic Based Localization of Partial Discharge inside Oil-Filled Transformers

This paper addresses the localization of Partial Discharge through a 3D Finite Element Method analysis of acoustic wave propagation inside a 3-phase 35kV transformer with the help of COMSOL Multiphysics software. Due to the complexity inside transformers, acoustic waves generated by PDs cannot simply be detected with typical acoustic sensors, especially when PDs happen inside inner windings. These waves are distorted and attenuated along with their propagation. The type, number, and position of sensors are essential factors in PD localization inside a transformer. A new installation arrangement of fiber-optic acoustic sensors inside the transformers is proposed with this information. This array of acoustic sensors has significant effects on PD localization accuracy and has immunity from on-site noise and interference; more importantly, they can be installed after transformer manufacturing. They are reachable if needed to be repaired or replaced. Several numerical studies have been carried out considering different PD source positions, and the Levenberge-Marquardt algorithm is employed for solving localization equations.


I. INTRODUCTION
Power transformers are one of the most important and costly equipment in power systems. Based on transformer failure statistics in [1], the most common reason for failure in the power transformers is assigned to winding and insulation faults. Therefore, online monitoring of insulation systems of power transformers could avoid failures and catastrophic chain of events that lead to more destructions. One of the best ways to monitor transformers is PD measurement. PD in high voltage equipment is an electrical discharge in points with poor insulation or high electrical field. PD phenomenon has some electrical, electromagnetic, chemical, acoustic, and optical effects that can be detected with an appropriate type of sensor. In some studies, HFCTs, HVCCs, UHF Antennas, and acoustic sensors have been used for PD detection and measurement [2][3][4][5][6][7][8].
Due to the size of power transformers, PD measurement is not merely enough, and localization is needed to speed up fault detection and troubleshooting process. There are some challenges in PD localization in power transformers, such as choosing the type of sensors and their installation's position. Notably, the position of sensors is essential for achieving better accuracy. In some cases, UHF antennas and PZT sensors have been used for PD detection. These sensors could easily be influenced by the transformer's EMI and environment noises and interferences [9][10][11]. Commercial UHF sensors are costly, and the transformer's tank should be modified to install them [12][13]. Typical acoustic methods could make localization of PDs inside LV-winding or between winding and core difficult with typical acoustic methods [14]. The Fiber-Optic acoustic sensor array can be used to overcome the related problems of the conventional methods, such as on-site electromagnetic interference and noises, low sensitivity, faulty localization, and installation limitation.
These sensors should be closed to or even embedded inside the transformer's windings in order to receive less distorted PD signals. In [15], a new array has been introduced for sensor installation inside a single-phase transformer. However, this array cannot be used in transformers currently in service. It can only be installed during the manufacturing process of the transformer due to its installation position. The study of the acoustic pressure wave propagation path inside the transformer is crucial for the measurements and localization of the acoustic PD waves. [16][17] analyzed the acoustic wave propagation within the transient state using numerical calculation. [18][19] investigated the PD acoustic pressure wave distribution inside a transformer model. [20][21] studied the PD acoustic pressure wave distribution inside a transformer using a simulation model and experimental results. Most of the previous papers that studied acoustic PD wave propagation inside transformers with FEM analysis did not present a comprehensive model of a real transformer. Recently, the authors have considered the transformer winding as an integrated cylinder, and in some of them, they modeled only the high voltage winding without the low voltage [18][19]. Lack of recording the response of acoustic waves using the probe point feature at different points within the simulated model and lack of post-processing of collected data from FE software are other disadvantages of previous works [18][19][22][23]. These papers solely focused on acoustic pressure wave distribution inside transformers and showed the acoustic pressure at different simulation times. In past years, fiber-optic acoustic sensors have been used in the laboratory, and real-world applications such as measurement and localization of PDs inside oil impressed transformers [15,[23][24][25][26][27][28][29]. The placement of these sensors greatly affects the accuracy of localization.
In this paper, the acoustic localization of PD has been studied with finite element simulation of acoustic partial discharge wave propagation inside a transformer. A new array for sensor installation's position has been proposed. The advantage of this array is that sensors can be installed after transformer manufacturing, and they are reachable if needed to be replaced or repaired. A real 3-phase oil-filled transformer has been simulated in the COMSOL Multiphysics software environment.
Acoustic wave propagation inside the transformer has been analyzed with numerical methods. This paper simulates PDs as acoustic pressure sources in four positions, Case A and D inside LV-winding and Case B and C inside HVwinding. Eight sensors have been installed in one phase winding of the transformer as an observation point. Using FEM simulations, acoustic wave propagation has been solved numerically. PD signals originated from transformer winding are shielded, distorted, attenuated, and reverberated along with their propagation before reaching the sensors. Sensors closer to PD sources or direct paths to them receive signals with less distortion and attenuation and more SNR. With this array, at least four sensors can detect direct signals with acceptable SNR that can be used for localization. Arriving time of acoustic signals, also known as the TOA, has been used in some cases. Sufficient accuracy, immunity from onsite noise and interference, and accessibility are advantages of this array of acoustic sensors. This method's localization of PDs requires a PD propagation time reference measured by electrical or UHF methods [30][31][32]. TDOA between received signals among all the sensors in the array, initiated from the same PD acoustic source, can be used for localization instead, and it can be carried out independently with acoustic sensors [33][34][35]. Localization equations have been formed and solved with the Levenberge-Marquardt algorithm Using FEM simulation results and the TDOA method [36]. The main contributions of this work are: • Conducting a comprehensive 3D model of a real-size 3phase oil-filed 35kV transformer. • Proposing a new array of fiber-optic acoustic sensors for installation inside existing oil-filled power transformers that enables high accuracy PD localization. • Studying the full in-depth study of acoustic PD phenomenon using finite element analysis. This paper is organized as follows: Section II describes the analysis of acoustic wave propagation inside a 3D model of a 3-phase transformer using FEM simulations. The proposed sensor array and localization results are presented and discussed in Section III. In section IV, a new case study is presented to verify localization results, and section V reports the conclusions of this paper.

II. FINITE ELEMENT-BASED ANALYSIS OF ACOUSTIC WAVE PROPAGATION
The first step for finite element simulations is building a 3D model of the transformer. This 3D model is based on a realsize 3-phase oil-filed 35kV transformer. The geometry of the model is shown in Fig. 1. Moreover, the dimensions are shown in Table I [15]. The transformer tank has been filled with oil, the fluid model is linearly elastic, and the oil temperature is 20℃. Three iron cores have been surrounded by the low voltage and the high voltage windings. The transformer core, transformer yoke, and tank material are steel for structural and copper for windings. The materials inside the transformer tank have been assigned to insulation oil, the transformer core, and windings. By adding the material from the software library, these materials' properties will be automatically added to the transient pressure acoustic module. The software predefined the relative permeability of the structural steel, the relative permittivity of the copper, the thermal conductivity of the oil, and other properties of the materials. Some properties of the material, such as material density and the speed of the sound inside them, need to be defined, shown in Table II [15]. Some of the predefined properties of the material in the software are shown in Table  III. A transient pressure acoustic module has been chosen for modeling the acoustic wave propagation caused by the PD source inside the transformer. With the help of COMSOL Multiphysics, acoustic pressure physic law could easily be applied to the model. For acoustic pressure analysis, materials have been assumed to be isentropic, which means they are lossless and adiabatic. Also, the material density and the sound speed can be assumed constant and isotropic. The momentum equation and the continuity equation for isotropic fluid flow are extracted from [15]: where v is the velocity field. is the total density, and P is the total pressure. The compressibility of liquids can be stated: where B is the bulk modulus, and C is the speed of sound inside the liquid. For acoustic propagation study driven by PD events, all the variables can be treated as just small perturbations around their stationary quiescent values [15]: After inserting these extensions into the governing equations, with Taylor expansion, if necessary, reshuffling and dropping the minor variations can yield the wave equation for sound waves [15]: where ρc 2 (N/m 2 ) is recognized as bulk modulus, the dependent variable in the wave equation is the sound pressure, P. The sound pressure is propagating in a medium with density at the speed of sound, C. The qd and Qm represent the dipole and monopole domain sources. A monopole domain source can be described as a small pulsating sphere, contracting and expanding with time. In other words, the monopole source radiates sound equally in all directions.
On the other hand, a dipole source is made up of two identical monopole sources in opposite phases and separated by a minimal distance compared to the wavelength of sound.  The continuity boundary condition is applied to all the transformer model's inner boundaries, and the transformer tank's outer boundaries have been defined as impedance. PDs inside the transformer have the main frequency between 20 kHz to 500 kHz [14]. The acoustic PD source is like a damped sine wave. The monopole acoustic source behavior is close to a PD event, so the PD source has been defined as a monopole domain source, and it can be described with: where f is the acoustic wave frequency produced by PD, 20 kHz; in this study, Aq is the flow of energy and is set as a constant (Aq = 1). The decay of the acoustic wave, τ, is equal to 50 s and the acoustic wave dies after 200 s. The suggested iterative solver by the software is the GMRES solver. The GMRES method is an iterative method for the numerical solution of an indefinite nonsymmetrical system of linear equations. The GMRES solver with the Geometric multigrid preconditioner ensures low memory consumption at a high mesh resolution. In the simulation, the GMRES linear system solver with a geometric multigrid preconditioner is applied for transient analysis with a time step of 1 s. The study has been carried out 1000 s time duration after PD happens. The divided mesh grid consisted of 175054 tetrahedral elements, and the minimum element quality is 0.05583 m, as shown in Fig. 2 and Table IV.
Simulations have been carried out for different PD source positions, Case A and D inside LV-winding and Case B and C inside HV-winding, and it is shown in Fig. 3.

FIGURE 2. Mesh grid of the 3D model
From Fig. 3, it is obvious that the center of the cylindrical iron core is selected as the origin point of the X and Y axis, while the origin point of the Z-axis is set in the plane, which is defined by the circular bottom surface of the cylindrical iron core. The acoustic wave propagates outward from the PD source through spherical waves inside the transformer as the lossless propagation process gets further attenuated toward receivers. This can be demonstrated in Fig. 4; total acoustic pressure originating from the PD source in point A has been shown in 200, 500, and 1000 s after propagation. In Fig. 4, the intensity of the acoustic pressure field is demonstrated by the color map. It can be seen that the acoustic pressure amplitude has decreased over time as the acoustic wave travels away from the PD source. When a PD happens inside a transformer, the acoustic wave spreads through the medium, and with the total energy of the acoustic wave being constant, an increase in diffusion distance results in decreasing of energy per unit area with the square of the distance from the acoustic source (i.e., diffusive attenuation). Refraction and reflection will occur during the propagation of the acoustic waves through the windings and the iron core, and the acoustic signals will reverberate. The speed of sound in the iron core and the windings is faster than in the oil. So, the signals propagate faster in the windings, core, and other mediums than in the oil. But the attenuation in the windings and core is greater, which is consistent with the theory of acoustic wave propagation.

III. PROPOSED SENSOR ARRAY DESIGN AND LOCALIZATION OF DIFFERENT PD SOURCES
When PD occurs inside the transformer, the acoustic waves originating from the PD source can be detected and measured with acoustic sensors. Eight observation points have been defined as sensors on the top and bottom of one phase of transformer winding. These observation points/probe points are referred to as sensors in the text for ease. Four sensors have been placed at the bottom of the HV-Winding. Four sensors have been placed on the top of HV-Winding with a 45-degree clockwise shift, respectively, from the sensors placed below them. The coordinate for the position of the sensors is given in Table V. One of the important factors in PD localization is finding the arrival time of PD to each sensor. PDs that are closer to sensors or have a direct pass to them are less distorted and attenuated; as a result, they arrive faster at the sensors. TOA determines which sensor has more SNR and which received signal is closer to its original form. SNR is an essential factor in acoustic wave propagation analysis [14]. Due to placing sensors inside the transformer, white noise and other on-site noise and interference are shielded and blocked by the transformer tank. However, the impulse sound originating from the changing size and orientation of magnetic domains in the core material, the socalled Barkhausen noise, reaches well into several tens of kHz and can affect the measurement. It is possible to nullify many of these effects that are not associated with PDs by using a band-pass filter. These noises include vibrations caused by the magnetostrictive action of the core (Barkhausen noise), pumps, and fans. Most of these noises are below 30 kHz; however, the Barkhausen noise emanating from the core has sometimes been found to be in the 50 kHz range [14]. The distance between sensors causes a delay in time arrival of PD signals. By having the position of sensors and calculating the TDOA between sensors, PD localization is possible. For this purpose, four out of eight sensors that have acceptable SNR and are less distorted could be chosen for localization. For the PD source in position A, the acoustic signal arriving at sensors 7, 1, 5, and 8 have been shown in Fig. 5. The TOA for these sensors is less than others, so it could be concluded that these sensors receive signals with less vibration and distortion or are closer to the PD source to be used for localization. It is evident for the PD source in position A that the acoustic PD signals need to penetrate the core and the LV-Winding to reach the sensors 2, 3, 4. As a result, signals have a lower amplitude in the first cycles because of reflection and vibration, and they have low SNR. These acoustic signals contain information for all the distance the wave travels through different mediums after several unpredicted reflections, so these observation points cannot be used for localization. By choosing the sensor with the least TOA as a reference, the TDOA to sensors 1, 5, and 8 is 48 µs, 78 µs, and 190 µs. Absolut TOA for sensors 2, 3, 4, and 6 is 434 µs, 385 µs, 474 µs, and 379 µs, and it is shown in Fig. 6. The distance between each sensor to PD source is given by [37]: where Di is the distance between the sensor and PD source location, vs is the speed of sound in the oil, and Ti is the measured arrival time of the PD signal. The sound speed in the oil in the equations is 1400 m/s at 20 °C. The propagation speed goes down to about 1200 m/s for transformer mineral oil at 80 °C. In order to compare the result of our work with previous works, we assume that the oil temperature is 20°C [15]. If the PD coordinate is (x, y, z) and the sensors coordinate is defined as (xai, yai, zai), localization equations can be described as: In (8), Ti cannot be measured by acoustic sensors due to the time delay of these sensors in the range of micro or millisecond; for measuring the real PD propagation time, PD measurement with an electrical or UHF method is needed. Electrical or electromagnetic PD pulses (generated from PD source) arriving time to electric or UHF sensors is in the range of Nanoseconds. It is close to the signal's real-time propagation to be used as a time reference for acoustic signals. In this paper, localization has been carried out only with acoustic sensors, so TOA is unsuitable, and TDOA could be used instead. In the time-difference approach, assuming straight propagation, the acoustic wave reaches the nearest sensor first and triggers the recording process on all sensors simultaneously. So, for this purpose, sensor7 has been chosen as a time reference, and the TDOA has been calculated and respected by sensor7. Another form of the (8) has been written: where (xac, yac, zac) is calculated PD source position with localization algorithm. PD localization for four PD source positions has been calculated, and the results have been shown in Table VI. The proposed sensor array and the PD localization results for Case A are shown in Fig. 7. In Case B, sensors 7, 1, 5, and 8 have been chosen for localization, and the absolute TOA for these sensors is 174, 244, 275, and 345 µs. The localization method, in general, uses the time-offlight method for finding the source of acoustic signals. By assuming these captured acoustic signals have a straight pass from the acoustic source through the oil to the sensors, it is possible to form the equation and solve them using an optimization algorithm. However, this is feasible if the signal has high SNR and is clean (not distorted/reverberated) in the first cycles, as explained before. This shows the importance of the type of the sensor and the sensor installation position in capturing signals and the localization of PDs. For conventional acoustic emission sensors placed on the transformer's outside wall, this method suffers from significant uncertainties and potentially misleading results. This is because of the differences in wave propagation through the tank wall and the liquid. Furthermore, the wave may take other, longer paths to a remote sensor or perhaps not reach the sensor at all due to blockage. Second, in reality, the tank wall is a thick steel plate, which, by its nature, has faster sound transmission properties than the insulating liquid [14]. These issues can be avoided by using the proposed array of fiber-optic acoustic sensors used in this study that most likely capture direct, clean, and non-distorted acoustic signals. In this research, factors such as the placement of the sensor, the calculation of the signal arrival time, the localization equations, and the optimization algorithm can affect the localization error. Table VI shows that the proposed array of the acoustic sensor and the used localization equations alongside the optimization algorithm leads to acceptable localization accuracy. In real applications, in addition to the previous factors, localization accuracy depends on other factors such as the on-site noises and interference, the type of the sensor, the sensor sensitivity, the sensor bandwidth, and the complexity inside the transformer under test.

IV. A NEW CASE STUDY FOR VERIFICATION OF LOCALIZATION RESULTS
A new case study has been investigated to better understand the sensor's installation position importance and localization accuracy factors, where a PD source is defined at point E, and acoustic signal propagating from this source is compared with the PD source placed in point A. A new sensor is placed in coordinate (0.045, 0.185, 0.6), and for a better look, a 2D cut-plane view of the transformer winding and the core is shown in Fig. 8. The total acoustic pressure originating from the PD source in points A and E has been shown in Fig. 9 at 50 µs and 100 µs after propagation time. The captured signals from points A and E by this sensor are shown in Fig.  10.
In Fig. 8, by comparing the pass of acoustic signal propagation to the sensor, the acoustic signal from Case E needs to penetrate layers of the winding disk to reach the sensor. However, in Case A, the pass of the signal to the sensor is much more direct. As a result, For Case A, the signal's amplitude is higher, the absolute arrival time of the signal is lower than in Case E, and the signal is much cleaner (less distorted and vibrated) in the first cycles. However, the PD source in point E is closer to the sensor than the PD source placed in position A, but the sensor position and the pass of signal to the sensor have much more effect on PD localization accuracy. So, for those PDs inside windings, the generated acoustic signals from them are more attenuated and reverberated along the way, the SNR is low, and localization error would be higher as the results of Table VI could conclude.

V. CONCLUSIONS
In this paper, a novel structure array of fiber-optic acoustic sensors has been proposed for installation inside oil-filled power transformers. By using the acoustic module of COMSOL Multiphysics software, the performance of this array has been investigated inside a 3D model of a real 3phase 35kV transformer. Using FEM simulation results and the TDOA method, localization equations have been formed and solved with the Levenberge-Marquardt algorithm. The analysis has been carried out for different PD source positions. The main conclusions and achievements of this work are: 1. When acoustic signals propagate inside an oil-impressed transformer, complex structures such as the transformer yoke, iron core, and windings affect the propagation path of the acoustic signals. A direct and non-distorted signal can be captured by placing the sensors close to or even embedded in windings. The direct acoustic signals most likely pass through the oil and reach the sensors with less attenuation or reverberation. 2. Using the proposed sensor's array, precise localization for a single PD event at any possible positions, including inside the low or high voltage windings or between the oil ducts, is achievable. The proposed array of acoustic sensors enables the localization of PDs inside transformers with less than 5 cm error. 3. Another advantage of the proposed array is that sensors can be installed inside existing oil-filled transformers, and they are reachable if needed to be repaired or replaced. Acceptable accuracy, immunity from on-site noise and interference, and accessibility are the main advantages of this array of acoustic sensors. Due to study limitations, confirming the results with an experimental study wasn't feasible. The results of this paper can be helpful in acoustic PD localization inside power transformers with Fiber-Optic sensors.

ACKNOWLEDGMENT
The publication of this article was funded by Qatar National Library.