EP4097493A1

EP4097493A1 - Partial discharge localization using time reversal: application to power transformers and gas-insulated substations

Info

Publication number: EP4097493A1
Application number: EP20828310.1A
Authority: EP
Inventors: Hamidreza KARAMI; Amirhossein MOSTAJABI; Farhad Rachidi-Haeri; Mohammad AZADIFAR; Marcos RUBINSTEIN
Original assignee: Ecole Polytechnique Federale de Lausanne EPFL
Current assignee: Ecole Polytechnique Federale de Lausanne EPFL
Priority date: 2020-01-29
Filing date: 2020-11-30
Publication date: 2022-12-07
Also published as: WO2021152377A1

Abstract

A method for locating one or multiple partial discharge sources in a power transformer or a Gas-Insulated Substation, whereby the partial discharges emit electromagnetic and acoustic waves, the method comprising recording a signal corresponding to the waves from the partial discharge sources by means of at least one sensor; time-reversing the recorded waves, thereafter back propagating the recorded signals into the power transformer or Gas-Insulated Substation by means of numerical simulations; and localizing the focal spots of the partial discharge sources.

Description

Partial Discharge Localization Using Time Reversal: Application to Power Transformers and Gas-Insulated Substations

Technical field

The invention is in the field of monitoring of power apparatus, and more specifically in the localization of partial discharge sources in a power transformer or a Gas-Insulated Substation (GIS).

Background

Nowadays, power transformers play a key role in electrical power system grids. Any failure in power transformer functionality would decrease the reliability of electrical power networks. Partial Discharges (PDs) are partial electrical breakdowns taking place in the transformer insulation. PDs may result, in the long term, in the breakdown of the insulation system and in severe damage to the transformer. Therefore, the detection and localization of PD sources are important diagnostic tools to monitor the insulation condition in power transformers.

PD measurement techniques [1] can be divided into four categories, 1) electrical, 2) chemical, 3) acoustic and 4) electromagnetic.

In the electrical detection category [1], [2], the current or voltage waveforms are measured at the HV and LV terminals of the power transformer. The high frequency content of the signals is used to estimate the existence of PDs. The methods belonging to the electrical detection category are sensitive to weak PD activity and they are mainly useful only for the detection of PDs inside the transformer, even though some of the methods in this category can predict the turn number in which a PD occurred and thus perform a 1-D localization [3]

In chemical detection methods [1], [4], the composition of dissolved gases in power transformer oil is analyzed to detect PDs. These methods cannot be applied to localize PDs in power transformers.

Acoustic detection methods [1], [5]— [8] are based on the detection of the sound waves emitted from the PD sources. Using these methods, 3-D localization of PD sources is possible. However, the acoustic method has generally low sensitivity to weak PDs and to those that occur inside the winding [5], [9] Acoustic sensors can be mounted on the outside walls of the power transformer, thereby making acoustic detection a non-invasive technique. In the acoustic-based methods, the acquired signals are not affected by electromagnetic interference in the measurement environment.

Electromagnetic detection methods [1], [5], [7], [9]— [11 ] are applied to detect PD sources from the electromagnetic waves radiated from them. Using these methods, 3-D localization of PD sources is possible. The PD detection methods using UHF radiation (UHF-PD) are sensitive to weak PDs and to those that are inside the winding. In addition, UHF-PD measurements are usually electromagnetically shielded by the grounded transformer tank against external disturbances like corona and environmental noise.

Acoustic and electromagnetic 3D-localization methods are based on the time difference of arrival (TDoA) of signals. These methods are highly sensitive to noise as TDoA requires a precise determination of the onset time of the arriving signals. They also need 4 or more time- synchronized sensors to operate. The TDoA-based techniques in the acoustics methods can provide reasonable accuracy by performing proper signal processing and having suitable propagation paths from the PD sources to the multiple sensors. However, TDoA-based electromagnetic methods suffer from inaccuracies because of inhomogeneities and scattering inside transformers.

The present invention aims at proposing a new method based on time reversal to locate PD sources in power transformers using either acoustic and/or electromagnetic sensors. The method can also be used to locate PD sources in other power apparatus such as Gas-Insulated Substations.

Summary of invention

The invention provides a method for locating at least one partial discharge source in a power transformer or Gas-Insulated Substation, whereby the at least one partial discharge(s) emit(s) electromagnetic and acoustic waves, the method comprising recording a signal corresponding to the waves from the at least one partial discharge source(s) by means of at least one sensor; time-reversing the recorded waves, thereafter back propagating the recorded signals into the power transformer or Gas-Insulated Substation by means of numerical simulations; and localizing respective focal spot(s) of the at least one partial discharge source(s) in the power transformer or Gas-Insulated Substation. In a preferred embodiment, the step of recording involves mounting at least one acoustic sensor either on an inside or on an outside of walls of the power transformer or Gas-Insulated Substation; and measurement of acoustic radiation using the at least one acoustic sensor.

In a further preferred embodiment, the step of recording involves installing at least one electromagnetic sensor inside a tank of the power transformer or on an outside of transformer walls in case the transformer is equipped with an active dielectric window; and measurement of electromagnetic radiation using the at least one electromagnetic sensor.

In a further preferred embodiment, the at least one electromagnetic sensor is a UHF sensor.

In a further preferred embodiment, the step of recording further comprises continuously monitoring the signal for a determined partial discharge criterion corresponding to an occurrence of the at least one partial discharge.

In a further preferred embodiment, the step of localizing the respective focal spot(s) of the at least one partial discharge source(s) is achieved using the step of time-reversing, and the focal spot(s) are determined using a determined focal spot criterion such as any one from the list comprising a maximum electric / magnetic /acoustic field criterion, a maximum power criterion, a cross-correlation criterion, a minimum entropy criterion.

Brief description of the drawings

The invention will be better understood through the detailed description of preferred embodiments, and in reference to the drawings, wherein

Figure 1 contains a schematic view of a partial discharge localization approach based on a time-reversal method, according to an example embodiment of the invention;

Figure 2 shows a schematic representation of a transformer tank with sensors (Si and S2) according to an example embodiment of the invention;

Figure 3 presents the normalized distribution of the maximum electric field power in three cut planes within the transformer tank over the total back-propagation simulation time, 2 sensors are used;

Figure 4 shows a normalized distribution of the maximum electric field power over the whole simulation time inside the transformer tank (CS #2). The ground truth location of the PD source (PD1) is shown by the “+” marker. Only one sensor (SI) is used;

Figure 5 shows a normalized distribution of the maximum electric field power over the whole simulation time inside the transformer tank in the x-z cut plane at y = 250 mm (CS #3). The active parts of the transformer are included. The ground-truth location of the PD source (PD1) is shown by the “+” marker. Only one sensor (SI) was used a) full x-z cut plane, b) x-z cut plane removing the area around the sensor;

Figure 6 shows a normalized distribution of the maximum electric field power over the whole simulation time inside the transformer tank in the x-z cut plane (CS #4). The active parts of the transformer are included. The ground truth locations of the PD sources (PD1 and PD3) are shown by “+” markers. Only one sensor (SI) is used;

Figure 7 shows a normalized distribution of the maximum electric field power over the complete simulation time inside the transformer tank in the x-z cut plane (CS #5). The active parts of the transformer are included. The ground truth locations of the PD sources (PD1 and PD2) are shown by “+” markers. Only one sensor (SI) is used;

Figure 8 shows: (a) Signal recorded by sensor SI. (b) The time reversed signal with added noise (SNR=20 dB). (c) The time reversed signal with added noise (SNR=10 dB);

Figure 9 shows a normalized distribution of the maximum electric field power over the complete simulation time inside the transformer tank in the x-z cut plane (CS #5). (a) An SNR of 20 dB is considered and (b) an SNR of 10 dB is considered. The active parts of the transformer are included. The ground truth locations of the PD sources (PD1 and PD2) are shown by “x” markers. Only one sensor (SI) is used;

Figure 10 shows a test setup including the model for the transformer tank and the VNA. a) The monopole antenna used as a sensor, b) the monopole antenna used to emulate the PD source, and c) metallic object representing the transformer winding;

Figure 11 shows: a) Assumed PD locations on the floor of the tank (L1, ..., L 6) with the metallic object removed temporarily and replaced with a translucid parallelepiped for clarity b) On the left- wall of the transformer tank, Pi, ..., P9 are spaced 2.5 cm from each other;

Figure 12 shows normalized time reversed responses for two guessed locations L4 and L5. LA is the PD source location. In this scenario, the metallic object is removed;

F igure 13 shows normalized peak values of the time reversed response at the guessed locations L1 to L6. The maximum peak occurs at LA, which corresponds to the PD source location. In this scenario, the metallic object is removed;

Figure 14 shows normalized time reversed responses for two guessed locations L2 and L6. L6 is the PD source location. In this scenario the metallic object is included in the transformer tank model;

Figure 15 shows the normalized peak values of the time reversed response at the guessed locations L1 to L6. The maximum peak occurs at L6, which corresponds to the PD source location. In this scenario, the metallic object is included in the transformer tank model;

Figure 16 shows time reversed responses for two guessed locations of Ps and P9. In this scenario, the metallic object is removed. The location of Ps is considered as the ground truth PD source location;

Figure 17 shows the normalized peak values of the time reversed response at the guessed locations of Pi to P9. In this scenario, the metallic object is removed. The location of Ps is considered as the ground truth PD source location;

Figure 18 shows a 2D model or the top view of the 3D model for the power transformer;

Figure 19 shows an expanded view of the middle winding composed of two concentric rings;

Figure 20 shows a side view of the 3D power transformer model;

Figure 21 shows normalized pressure values over the whole solution space. A single sensor (S1 in Table 3 and Table 4 below) is used and represented by a magenta square outside the transformer tank (white border around the computational domain). A circle 2100 and a cross 2101 show the considered location and estimated location obtained by way of the proposed acoustic TR method, respectively. The PD1 (in Table 3 and Table 4 below) source (not illustrated in the figure) is located between the primary and secondary windings of the transformer (CS#1 in Table 4 below);

Figure 22 shows normalized pressure values over the whole solution space. A single sensor (51 in Table 3 and Table 4) is used and represented by a magenta square outside the transformer tank (white border around the computational domain). A circle 2200 and a cross 2201 show the considered location and estimated location obtained by way of the proposed acoustic TR method, respectively. The PD2 (in Table 3 and Table 4 below) source (not illustrated in the figure) is between two windings (CS#2 in Table 4 below);

Figure 23 shows normalized pressure values over the whole solution space at the last time step in the TR process. The three panels show the normalized pressure values in three cut planes. Only one sensor (not illustrated in the figure) (SI in Table 3 and Table 4 below) is used and the PD source (PD 1 in Table 4 below) (not illustrated in the figure) is located inside the winding between its two rings, CS#1 in Table 4. Circles 2300 / 2302 / 2304 and crosses 2301 / 2303 / 2305 show the considered location and the estimated PD location, respectively. Dashed lines show the boundary of the windings (a) xoy cut-plane, (b) yoz cut-plane, and (c) xoz cut-plane;

Figure 24 shows normalized pressure values over the whole solution space at the last time step in the TR process. The three panels show the normalized pressure values in three cut planes. Only one sensor (SI in Table 3 and Table 4 below) (not illustrated in the figure) is used and the PD source ( PD2 in Table 4 below) (not illustrated in the figure is located inside the winding between its two rings, CS#2 in Table 4. Circles 2400 / 2402 / 2404 and crosses 2401 / 2403 / 2405 show the considered location and the estimated location, respectively. Dashed lines show the boundary of the windings (a) xoy cut-plane, (b) yoz cut-plane, and (c) xoz cut-plane;

Figure 25 shows normalized pressure values over the whole solution space at the last time step in the TR process. The three panels show the normalized pressure values in four cut planes. Only one sensor (SI in Table 3 and Table 4 below) (not illustrated in the figure) is used and the PD sources (PD3 and 77)4 in Table 4 below) (not illustrated in the figure) are located behind the winding, CS#3 in Table 4 below. Circles 2500 / 2502 / 2504 / 2506 and crosses 2501 / 2503 / 2505 / 2507 show the considered location and the maximum value of the pressure inside the computational domain, respectively. Dashed lines show the windings (a) xoz cut-plane, (b )yoz cut-plane, (c) xoy cut-plane (z = 0), and (d) xoy cut-plane (z = 0.250 m); and

Figure 26. (a) 3D representation of simple GIS part including the locations of sensor (p2) and PD source (pi) (b) The normalized distribution of the maximum electric field power over the whole simulation time inside the GIS part in the x-z cut plane (c) The normalized distribution of the maximum electric field power over the whole simulation time inside the GIS part in the y-z cut plane (d) The normalized distribution of the maximum electric field power over the whole simulation time inside the GIS part in the x-y cut plane.

Detailed description of preferred embodiments

The present invention aims at proposing a new method for locating a partial discharge source, based on time reversal to locate PD sources in power transformers using either acoustic or electromagnetic sensors. The proposed method is able to locate PD sources in a 3D volume with less than 4 sensors. The proposed procedure is shown schematically in Figure 1. One or more acoustic/UHF/combined sensors are installed inside the power transformer tank, or one or more acoustic sensors (in the case of an active dielectric window, the electromagnetic sensor can also be installed outside) are installed on the exterior wall of the tank. The signal(s) are continuously monitored and processed as needed (e.g., filtered, denoised, amplified, etc.), digitized, and relayed to an industrial computer or some other processing unit. The occurrence of PD signal(s) is identified by a suitable criterion such as, for example, the acquired signals crossing of a threshold value.

The obtained signal(s) from the previous stage are time reversed and back propagated into the acoustic/electromagnetic model of the transformer tank. This step is performed in a simulation environment. In order to obtain the location of the PD source(s) in the transformer tank, the maximum electric/acoustic field criterion is employed.

The invention is tested in the present description using a computer simulation of a power transformer, but it is fully realizable in a real-world power transformer as well. The transformer is modelled representing the tank as a cavity. Three cylindrical tubes are used to represent the windings. Multiple PD sources are generated using dipole antennas in this model and the UHF signal from them is captured using a single dipole antenna in the tank. The effect of environmental noise is investigated by mixing the acquired signal with Gaussian white noise. The received signal is time reversed and back propagated into the medium and the maximum electric field criterion is used to locate the 3D position of each individual PD source.

I. METHODOLOGY

Since PDs produce acoustic and electromagnetic radiation, the problem of localizing PDs within the tank of a transformer can be considered equivalent to that of the localization of acoustic or electromagnetic sources. In this section, we first present the concept and application of time reversal for electromagnetic waves. Similar principles can be derived for acoustic waves.

A. Principle of electromagnetic time reversal

We use here the time reversal invariance property of Maxwell’s equations in the soft sense [12] By setting in Maxwell’s equations, one can write:

It can be seen that if we reverse time, Maxwell’s equations still hold under the condition of changing the sign of the magnetic field and current density . These sign changes can be explained by the fact that, when the direction of time is reversed, the velocity of the charges changes sign and, as a consequence, so does the sign of the electrical current and of the associated magnetic field.

Now, let us assume a lossless medium in which there is at least one source emitting waves. If we record the emitted waves using a sufficient number of sensors, the time reversal nature of the governing wave equation guarantees that the time-reversed waves will refocus back to the primary source location or locations. In practical situations, the quality of the far-field focusing that can be obtained depends on the number of recording sensors and on the losses in the propagating medium. Moreover, it has been experimentally proven that the efficiency of the time reversal process improves in highly scattering media, in which the focusing property of time reversal can be better exploited via multipath propagation between sources and sensors.

In the case of PD sources in a transformer, the transformer tank can be considered as an enclosed cavity. The focusing property of time reversal in cavities has been mathematically and experimentally established by [13], [14] Neglecting losses on the walls of the transformer tank and other materials within the tank, one can expect that the strong focusing property of time reversal in cavities can be exploited to localize PD sources.

Three steps must be taken in order to locate sources via the Time Reversal process:

(i) The electromagnetic or acoustic waves from the source or sources are measured (forward-time) at one or multiple locations.

(ii) The acquired waveforms are time- reversed and back- injected into the solution medium using numerical simulations (backward-time).

(iii) A criterion to detect and locate the source(s) is applied within the backward-time phase, such as the maximum amplitude of the total wave, its maximum energy, entropy, etc. to obtain the focal spot.

B. Mathematical Derivation in the Electromagnetic Regime

Herein, we assume the transformer tank as a rectangular box. The dyadic Green’s function in Cartesian coordinates of the magnetic vector potential for a rectangular cavity with dimensions of axbxc can be written as:

Let us assume the PD source as an infinitesimal dipole source along the y-axis at point (x,y,z) and derive as presented in Equation 3 using the concept of image theory. Other components of can be written accordingly. where in which, is the location of the image source and Si depends on the orientation of the image source and the sign of the current, mo is the permeability of free space, and k is the wavenumber.

The electric field at the observation point can be found by the electric field integral equation (EFIE) as:

Equation (4) can be used to obtain the electric field in the forward time step at the sensor location. The time reversed electric field can be found as:

In (5), the raised asterisk denotes the complex conjugate.

C. Mathematical Derivation in the Acoustic Regime

The linear acoustic equations [15] composed of the appropriate equation of motion, equation of continuity, and equation of state can be written as follows, where, u, p, p0, c, t, V, V -, and d are the acoustic particle velocity, the acoustic pressure, the ambient density, the thermodynamic sound speed, the time, and the gradient, divergence, and partial derivative operators [15], respectively.

The wave equation in lossless, isotropic, and source-free media, which results from (1) after some mathematical manipulations, can be written as follows [15], where the operator V² is the Laplacian.

D. Numerical Model

The Transient Solver of the CST Microwave Studio software [16] is used to simulate the electromagnetic wave propagation inside the transformer tank. This solver uses the Finite Integration Technique (FIT) to solve the Maxwell’s equations in their integral form. The computational model has been validated using an experimental setup presented in Section III- F.

An open source MATLAB toolbox called k-Wave [17] is used to solve the acoustic wave equation in (7). This toolbox has been designed to model linear and nonlinear acoustic wave propagation with an arbitrary distribution of heterogeneous materials with power-law acoustic absorption [17] This numerical code uses pseudo-spectral and k-space approaches to reduce, respectively, the number of mesh cells per wavelength and numerical dispersion due to increasing time steps.

II. PROOF OF CONCEPT: SIMULATIONS AND RESULTS A. Application of Electromagnetic Time Reversal in Power Transformers

To prove the feasibility and the performance of the method in the electromagnetic regime, we have designed and performed several case studies listed in Table 1 herein below. Figure 2 shows a transformer tank 200, including three windings 201 modelled by metallic cylinders. The materials of the transformer tank 200 and the windings 201 are steel ( s = 7.69e6 S/m) and copper ( s = 5.8e6 S/m), respectively. The thickness of the transformer tank 200 is 10 mm. The distance between the cylinders 201 is 50 mm and between the cylinders 201 and the wall of the transformer tank 200, it is 150 mm. Figure 2 illustrates the geometry of the problem used in case studies CS #1-5 (see Table 1). Thickness and distance values are indicated by way of example.

Four PD sources PD1, PD2, DP3, DP4 are modeled as dipole antennas as shown in Figure 2, excited with a Gaussian pulse with a frequency content of 300-3000 MHz [18] These sources are located in such a way that they represent specific conditions when the PD occurs outside, inside, and between the windings 201. Two UHF sensors (SI and S2 in Figure 2) are placed inside the transformer tank 200. In this example, we used the location recommended by standards (e.g., CIGRE [1]): at the bottom as they are assumed to be inserted through the standard drain valve. In all case studies, the length of the UHF sensors is 20 mm. The details of the location of the considered sensors and PD sources can be seen in

Table 2 herein below.

CS #1 aims to prove the feasibility of the TR method in localizing a PD source inside an empty transformer tank using two sensors. The study then continues with CS #2 to prove that the TR method requires only one sensor to accurately localize a PD source inside the transformer tank. We further included three active parts and applied the proposed approach (CS #3). Finally, CS #4-5 prove that the excellent performance of the TR method remains intact when multiple PD sources occur simultaneously inside the test object. What follows explains the simulation results of each of the aforementioned case studies.

Table 1. List of the performed case studies and the resulting location error.

Table 2. Location of the considered UHF sensors and PD sources inside the transformer tank.

All distances are in mm.

1. Capability of the TR method to localize a PD source using two sensors (CS #1)

In this case study, the windings are excluded from the presented transformer in Figure 2. The location of the PD source is that of PD1 according to Table 2. In this case, both sensors (SI and S2) are used with their location provided in Table 2. The proposed method as depicted in Figure 1 is applied. Figure 3 shows a normalized distribution of the maximum electric field power over the total simulation time inside the transformer tank (CS #1). Two sensors (SI and S2) are used. The distribution of the maximum electric field power in Figure 3 is shown in three cut planes within the transformer tank. The point corresponding to the maximum electric field power in Figure 3 is the estimated location of the PD source according to the proposed method. The ground truth location of the PD source (PD1) is shown by the “+” marker. The 3D location error is estimated to be 6 mm, which is smaller than l/10, where the wavelength l is equal to 100 mm at the maximum operation frequency. This result shows that the TR method can be effectively used to localize a PD source inside the transformer tank.

2. Single sensor PD localization (CS #2)

In this section, we investigate the performance of the proposed method when only one sensor is used (CS #2). The location of the PD source remained the same as in CS #1. In this case, sensor SI is kept operational and sensor S2 is removed. The windings are excluded from the presented transformer in Figure 2 and the proposed method as depicted in Figure 1 is applied. The obtained results are depicted in Figure 4. The 3D location error is estimated to be 5 mm, which is smaller than l/10 where the wavelength l is equal to 100 mm (corresponding to the maximum operation frequency). As it can be observed, the proposed method can successfully locate the PD source by using only one sensor and its accuracy did not degrade by reducing the number of sensors.

3. Single sensor PD localization in the presence of the active parts (CS #3)

So far, the transformer tank has been modelled as an empty cavity in the simulations. However, the presence of the active parts changes the wave propagations inside the tank, which may affect the localization results [19] We now include the three simple copper cylinders as depicted in Figure 2 representing windings of the transformer (active parts). The location of the PD source (PD1) and the sensor (SI) remained the same as in CS #2. It should be noted that the location of PD1 is behind the active part of the transformer and there is no line of sight path to the sensor, a scenario in which TDoA approaches fail. The proposed method, as depicted in Figure 1, is applied again in this case. The obtained results in the x-z cut plane are shown in Figure 5a, which shows the normalized distribution of the maximum electric field power over the whole time. According to Figure 5a, contrary to CS #1 and CS #2, the overall maximum over the whole time and space coincides with the location of the sensor. However, the primary knowledge of the location of the sensor is available and that location can therefore be disregarded. The second overall maximum corresponds to the location of the PD source (PD1). Figure 5b shows the x-z cut plane after removing the area of the known sensor. As shown in that figure, the locations of the winding cylinders are marked with close to zero field. The 3D location error is estimated to be 4 mm, which is smaller than l/10, where, as for the previous cases, the wavelength l is equal to 100 mm (corresponding to the maximum operational frequency). The proposed method can successfully locate the PD source even by including the active parts of the transformer. In other words, the presence of large scatterers such as windings does not degrade the performance of the proposed method.

4. Localization of multiple PD sources using the TR method (CS #4-5)

In practical cases, multiple sources might occur within the transformer tank. In this section, we demonstrate that the proposed method is able to locate multiple PD sources using only one sensor. To that end, we consider two case studies (CS#4-5). The location of the sensor (SI) is kept as that of CS#2-3. The locations of the PD sources are given in Table 2. In CS#4, PD1 and PD3 are considered, with PD1 located behind one of the active parts. In CS#5, we considered a more challenging scenario, in which PD1 and PD2 are considered, the latter being located at the center of the active part, inside the cylindrical winding of the transformer, and the cylindrical winding acts as a barrier for the wave. TDoA approaches are not applicable to such a scenario, even with four sensors. Figure 6 and Figure 7 show the normalized distribution of the maximum electric field power over the whole simulation time inside the transformer tank in the x-z cut plane for CS#4 and CS#5, respectively. In both of the figures, the locations of the cylindrical windings can be clearly identified (corresponding to the minimum field). The 3D location errors for CS#4 are estimated to be 5 mm and 6 mm for PD1 and PD3, respectively. The 3D location errors for CS#5 are estimated to be 4 mm and 3 mm for PD1 and PD2, respectively. It can be seen that the proposed method is capable of locating multiple simultaneous sources with high accuracy, considering the presence of the windings. It should be noted that in Figure 7, PD2 is located inside the winding and, as a result, its focal spot is less pronounced compared to PD1. 5. Further discussion on the performance of the method

In order to validate the applicability of the proposed method in the localization of PD sources for different source lengths and polarizations, we varied the length (5 mm, 10 mm, 20 mm, and 30 mm) and the polarization ([0 and 90) degrees) of the PD source. No degradation in the accuracy was observed. Furthermore, to investigate the effect of the presence of environmental noise on the performance of the system, we added white Gaussian noise to the signal recorded by the sensor (SI) in CS#5. Signal to Noise Ratios (SNR) of 20 and 10 dB were considered. Figure 8 shows the noiseless signal at the sensor along with the signal with added noise. Figure 9 shows the normalized distribution of the maximum electric field power over the complete simulation time inside the transformer tank in the x-z cut plane for CS#5 with added noise. Again, the cylindrical winding positions are clearly discernible. The 3D location errors for CS#5 with added noise are estimated to be 4 mm and 3 mm for PD1 and PD2, respectively.

6. Experimental Validation of PD source Localization Using Electromagnetic Time Reversal

In this section, we provide detailed information on a test setup aimed at experimentally validating the proposed electromagnetic time reversal method to localize PD sources. In the experimental setup, an HP-8753D VNA in the frequency range of 30 kHz-3 GHz is used. The PD sources are represented using a Gaussian pulse with a significant frequency content within 300-3000 MHz, which is commonly used in PD studies [20]

To experimentally locate an arbitrary source using the TR algorithm (as shown in Figure 1), one should take the following three steps:

(i) The electromagnetic waves from the PD source are measured at one or more locations. The measured signal is denoted by r(t). This step is referred to as the forward propagation step.

To perform this step in the frequency domain, we measure the scattering parameter L'_5r using the VNA. Where, p is used for the PD source and s for the sensor. The response of the sensor can be evaluated as , where w is the angular frequency and the capital letters are reserved for the frequency domain parameters. G(co) denotes the PD source applied to the monopole antenna. The time domain response, if needed, can be obtained using the inverse fast Fourier transform,

(ii) The acquired waveform is time-reversed. In the frequency domain, this corresponds to the complex conjugate operation in which * denotes the conjugate operator. In the time domain, . The time reversed signal is injected back into the medium. To obtain the back-injected signal at an arbitrarily location in the medium, the S_Sp(ω ) parameter between the sensor and the guessed location for the PD source is measured using the VNA in the frequency domain. The indexes s and x denote, respectively, the sensor and the guessed location. Then, the time reversed response, XTR(t), can be found by applying the inverse Fourier transform to at the actual PD source location.

(iii) The peak value of XTR(t) over the whole time and for all of the considered guessed locations is used as a criterion to identify the location of the PD source.

It should be noted that the proposed experimental test does not require any information either on the size or on the material of the transformer tank model and its content, since the backpropagation step is carried out experimentally.

Figure 10 shows pictures of the transformer tank model, including one metallic object used to represent a scatterer inside the transformer, such as, for example, the transformer windings. The size of the transformer tank model is 101 x 73 x 73 cm³. The transformer tank and the winding are made of steel and aluminum, respectively. The thickness of the transformer tank model walls is 10 mm. The aluminum object is placed at the center of the transformer tank as shown in Figure 10-c. As mentioned previously, no knowledge of the material, dimensions or geometry is needed since the back-propagation step is carried out experimentally. A 10 mm monopole antenna, shown in Figure 10-b, is used as the PD source that is placed at different locations in the transformer tank model as shown in Figure 10-b. A monopole antenna is also used as the sensor, which was located on the right wall of the transformer tank model as shown in Figure 10-a. The monopole antenna used as the sensor was handmade while the one used to represent the PD source was a commercial monopole commonly used in wireless network communications. Ideally, we would measure the back-propagated, time-reversed signal at a large number of points in the tank and we would select the point with the maximum peak field. For practical reasons, we selected a limited number of locations and performed back-propagation measurement experiments for each one of them.

The assumed PD source locations, labeled L1 to L6 on the floor surface of the cavity, can be seen in Figure 11 -a. For each experiment, one of these points was chosen as the assumed PD source location and the field resulting from the back-injection of the time-reversed waveform was measured. In selecting points L1 to L6, we tried to choose challenging locations. For example, L2 and L6 are located close to the scattering object as seen in Figure 11 -a (L6 is located next to the object and L2 behind the object). Moreover, the line of sight between L6 and the sensor is blocked by the object.

Here, we first present an experimental validation of the electromagnetic time reversal localization technique for the case of an empty tank.

We considered our PD source to be located at point L4 (see Figure 11 -a). We applied the procedure described in Figure 1 and considered L1 to L6 as guessed locations. Figure 12 shows the time reversed response for the guessed locations 74 (dark lines) and L5 (grey lines). As it can be seen, the peak value of the time reversed response at 74 (the correct location) is 4 times higher than that at L5. Figure 13 shows the peak values of the time reversed responses at all of the guessed locations. It can be seen that the highest peak occurs at the real source location.

To demonstrate the method in the more realistic case in which a winding is present, we included the metallic object inside the transformer tank as shown in Figure 10-c. We considered a PD source located at 76 near the metallic object as shown in Figure 11-a and we applied again the procedure described in Figure 1. Figure 14 shows the time reversed response measured at the guessed locations L1 (grey lines) and L6 (dark lines). As can be seen, the peak value of the time reversed response at 76 is 1.8 times higher than that at L2. Figure 15 shows the peak values of the time reversed responses at all of the guessed locations, showing that the highest peak occurs at the position of the PD source.

To investigate the location accuracy of the proposed method, we considered nine equally spaced PD locations between Pi and P 9 on the front side wall of the cavity, as shown in Figure 11 -b. The distance between two adjacent PD locations is 2.5 cm, which is equal to l/4 at 3 GHz. In this scenario, the metallic object was removed from the transformer tank model.

The position P5 (the middle point between P1 to P9) was considered as the location of the PD source. Pi to P9 are considered as guessed locations. One more time, the procedure described in Figure 1 was applied. Figure 16 shows the time reversed response for guessed locations P5 (dark lines) and P9 (grey lines), showing that the peak value of the time reversed response for P5 is 1.5 times larger than that at P9. Figure 17 shows the peak values of the time reversed responses at all of the guessed locations, showing that the proposed method can distinguish the location of the PD source with an accuracy better than 2.5 cm (l/4). It should be noted that this value is less than the diffraction limit (l/2), a fact that has been previously reported in the literature as a feature of the TR technique.

B. Application of Acoustic Time Reversal in Power Transformers

To investigate the application of the time reversal algorithm to localize PD sources in a transformer tank in the acoustic regime, we consider a two-dimensional (2D) and a three- dimensional (3D) representation of a transformer model. In the 2D case, the power transformer including the winding is considered the same way it was modeled in [21] A representation of the model is shown in Figure 18. As we can see in that figure, the power transformer tank is modeled by an oil-filled rectangle. The thickness of each side of the tank is 5 mm. The length / and the width w are equal to 1000 mm and 500 mm, respectively. The material of the transformer tank is considered to be steel. The acoustic velocity and density of the steel are 5940 m/s and 7850 kg/m3, respectively. The tank is filled by the transformer oil. The acoustic velocity and density of the oil are, respectively, 1390 m/s and 920 kg/m3. Three equidistant transformer windings are placed in the tank, the center of the second winding being at the center of the tank. The center-to-center distance between two adjacent windings is e = 250 mm. The central winding of the power transformer is depicted in Figure 19. Each winding is composed of two concentric rings, each with 20 mm thickness. The gap between the two concentric rings is filled with transformer oil and its thickness is also 20 mm. The material of the windings is considered to be copper, characterized by an acoustic velocity of 4600 m/s and a density of 8930 kg/m³. The parameters a, b, d, and c in Figure 19 are 40 mm, 60 mm, 80 mm, and 100 mm, respectively. In the 3D case, the top and side views of the power transformer model, shown in Figure 18 (2D model and top view of 3D model) and Figure 20 (side view of 3D model), respectively, are the same as in the 2D case. The height of each winding is h = 300 mm. The structure of the winding inside the tank exhibits three symmetries: along the x-axis, y-axis, and z-axis.

In the 2D simulations, the time step and number of time steps are 0.25 ps and 4078, respectively. The computational domain is meshed using equally-spaced square cells with a length of 5 mm. The excitation source is considered to be a Gaussian waveform with a bandwidth of 139 kHz, which is in the range of acoustic waves emitted by the PD sources in our simulation. In the 3D simulations, the time step and the number of time steps are 0.25 ps and 4467, respectively. The computational domain is meshed using equally-spaced square cells with a length of 5 mm. The same excitation source used in the 2D simulations is used in the 3D simulations.

To evaluate the performance of the proposed method in the 2D model of the transformer, two case studies are considered. The locations of the assumed PD sources and sensors inside the transformer are given in Table 3. Table 4 shows the three considered case studies for the 2D and 3D simulations. In CS#1, the PD\ source is located inside the central winding of Figure 18. In this case, the propagation of the acoustic wave shows high attenuation. Localization of the PD source in this case study is difficult in the electromagnetic regime. In CS#2, the PD2 source is located between two windings. Again, the localization of the PD source in this situation is difficult in the electromagnetic regime. In CS#3, two simultaneous PD sources (77)3 and PDA) are considered. Both of the PD sources are hidden by the windings and the propagation of the acoustic waves shows high attenuation. In CS#l-3, only one sensor, SI, is considered. Except in Case CS#2, there is no direct path between the PD sources and sensors, a scenario in which the conventional PD localization methods cannot be used. In all the case studies, the sensors are installed on the outside boundary of the transformer tank. Therefore, the proposed method can be used to localize the PD sources for all the power transformers without any changes in the transformer.

Figure 21 and Figure 22 show the PD source localization results using the proposed method shown in Figure 1 for each one of the PD locations in CS#1 and CS#2, respectively. These figures show the normalized pressure value over the whole solution space. The red circle and the black cross show the actual considered location and the estimated location, respectively. Here, we used the maximum pressure value at the last time of the TR process. It can be seen that the proposed time reversal procedure provides a highly focused image of the assumed PD sources using only a single sensor. The localization error in Figure 21 and Figure 22 is 5 cm and zero, respectively.

Table 3. Location of the considered sensors and PD sources inside the 2D* and 3D model of transformer tank.

* For 2D case studies the y-coordinates should be discarded.

** This means that the sensor is located outside the transformer tank wall.

Table 4. The assumed case studies for the 2D and 3D simulations of the propose method.

In the 3D cases, only one sensor is used to record the acoustic waves and we consider all the case studies presented in Table 4. The sensor (S1 ) is placed outside the transformer wall. The location coordinates of the sensor are given in Table 3. To evaluate the performance of the proposed method shown in Figure 1, the locations of the PD source were selected to be especially challenging to be located using conventional methods, namely inside a winding (PD1 ), between the winding ( PD2 ), and two simultaneous PD sources (PD 3 and PD 4).

Figure 23 and Figure 24 show the PD source localization results using the proposed method shown in Figure 1. These figures show the normalized pressure value over the whole solution space at the last time step in three possible cut planes. The red circle and the black cross show the considered location and the estimated location, respectively. The dashed lines show the location of the windings. As in the 2D case presented earlier, we used the maximum of the pressure value at the last time step of the TR procedure. It can be seen that the proposed time reversal procedure produces a highly focused image of the assumed PD sources using only one sensor. The localization error in both Figure 23 and Figure 24 is zero (lower than one mesh cell). Comparing the results of cases CS#1 and CS#2 obtained by the 2D and 3D simulations, we observe that, for the selected cases, the accuracy of the acoustic TR method to localize the PD source in 3D simulations is better than that for the 2D simulations. In 3D simulations the number of paths between the sensor and the PD source is higher than that for the 2D cases and this leads to the higher accuracy of the 3D simulations.

In the next example, we consider the CS#3 in 3D simulations. Note that, here, we have only one sensor. The results of the 3D simulation are shown in Figure 25, which shows the normalized pressure value obtained by the proposed method over the computational domain at the last time step in the TR process. The error in the location for both PD3 and PD4 is zero. Since we have two PD sources in different z-planes, the two cut-planes along the z-axis are depicted in Figure 25-c and Figure 25-(d), for z = 0 and z = 0.250 m, respectively.

C. Application of Electromagnetic Time Reversal in GIS

In the last example, we consider a part of a GIS as shown in Figure 26-a. The inner and outer radii of the GIS section are 0.12 m and 0.31 m, respectively. It is assumed that the GIS section is filled with SF6 gas. The location of the PD source (si) is assumed to be at z = -0.6 m and at a distance r = 0.145 m from the axis of the GIS according to Figure 26-a. In this case, one sensor (p2) is used, which is located at z = 0.7 m and r = 0.145 m. The method depicted in Figure 1 is applied. Figures 26b, 26c and 26d show the normalized distribution of the maximum electric field power over the simulation time inside the GIS section for three possible cut planes. The point corresponding to the maximum electric field power in Figure 26-(b-c) is estimated as the location of the PD source by the proposed method. The ground truth location of the PD source (pi) is indicated by the red “+” marker. The 3D location error is estimated to be lower than 7 mm, which is smaller than l/10 where the wavelength l is equal to 100 mm at the maximum operational frequency. This result shows that the TR method can be effectively used to localize a PD source inside the GIS. To the best of authors’ knowledge, this is the first proof of concept of the applicability of the TR method to locate PD sources inside the GISs.

III. SUMMARY

In this work, we proposed a novel method to localize PD sources based on the concept of time reversal using both electromagnetic and acoustic waves. As a proof of concept, we presented here results of both acoustic and electromagnetic time reversal source localization. To the best of our knowledge, this is the first time that the TR method is used to localize PD sources. Conventional methods such as TDoA require at least 4 sensors to locate PD sources. The proposed method is able to reduce the number of required sensors for the localization of PD sources to as few as a single sensor. The ability of the proposed method to locate multiple PD sources inside a transformer tank was demonstrated. Numerical simulations showed that multiple PD sources can be precisely localized with only one acoustic/electromagnetic/hybrid sensor. In the proposed method, the location accuracy is not affected by various factors such as the length and polarization of the PD sources. The maximum PD source localization error is less than 8 mm, which is lower than l/10. The proposed method is suitable for factory acceptance tests (FAT) and site acceptance tests (SAT), as well as on-line diagnostic tools for power equipment and apparatuses such as transformers and Gas Insulated Substations (GISs).

References

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Claims

1. A method for locating at least one partial discharge source in a power transformer or Gas-Insulated Substation, whereby the at least one partial discharge(s) emit(s) electromagnetic and acoustic waves, the method comprising recording a signal corresponding to the waves from the at least one partial discharge source(s) by means of at least one sensor; time-reversing the recorded waves, thereafter back propagating the recorded signals into the power transformer or Gas-Insulated Substation by means of numerical simulations; and localizing respective focal spot(s) of the at least one partial discharge source(s) in the power transformer or Gas-Insulated Substation.

2. The method of claim 1, whereby the step of recording involves mounting at least one acoustic sensor either on an inside or on an outside of walls of the power transformer or Gas-Insulated Substation; and measurement of acoustic radiation using the at least one acoustic sensor.

3. The method of claim 1, whereby the step of recording involves installing at least one electromagnetic sensor inside a tank of the power transformer or on an outside of transformer walls in case the transformer is equipped with an active dielectric window; measurement of electromagnetic radiation using the at least one electromagnetic sensor.

4. The method of claim 3, wherein the at least one electromagnetic sensor is a UHF sensor.

5. The method according to any one of claims 1 to 4, wherein the step of recording further comprises continuously monitoring the signal for a determined partial discharge criterion corresponding to an occurrence of the at least one partial discharge.

6. The method according to any one of claims 1 to 5, wherein the step of localizing the respective focal spot(s) of the at least one partial discharge source(s) is achieved using the step of time-reversing, and the focal spot(s) are determined using a determined focal spot criterion such as any one from the list comprising a maximum electric / magnetic /acoustic field criterion, a maximum power criterion, a cross-correlation criterion, a minimum entropy criterion.