1 Introduction

The power transformer is an important and expensive component of the power grid [1]. Any failure in a transformer can affect the supply network and inflict serious damage on the operators of the grid [2, 3]. The lifetime of a transformer generally depends on the insulation system [4]. All over the world and for more than a century, insulating liquid and liquid-impregnated cellulose products such as wood, pressboard and Kraft paper have been largely used to ensure the internal electrical insulation of the power transformers [5]. This is due to their low price and desirable features. However, unavoidable defects in the transformer insulation during the construction, assembly, transport or operation may cause degradation or failure in the insulation system [5, 6].

Creeping discharges on pressboard insulation constitute one of the failures faced in high-voltage apparatus such as power transformers. These creeping discharges may result in flashover and/or breakdown of the solid insulation that could cause permanent damage even under normal working conditions [7]. The investigations on the insulation failure commonly report signs of creeping discharge in a tree-like pattern with carbonized tracks on the pressboard surface. Discharge energy produces high temperatures in a local area close to the electrical discharge channels. Then, the overheating will carbonize the cellulose fibers, leaving irreversible paths on the surface of the cellulosic insulation. These carbonic paths are electrically conductive which could promote the development of creeping discharges up to flashover causing the deterioration of the insulation system [8, 9]. In the case of transformer in service, it is fundamental to follow the evolution of some specific parameters, associated with those discharges, in real time to make a diagnosis and take a decision to disconnect it at the right time to avoid its destruction, even its explosion and therefore a blackout. To do this, the current is one of the most accessible parameters; the real-time analysis of the current signal thus constitutes a useful tool for diagnosis.

Numerous researchers have focused their efforts on the understanding of the initiation and development of creeping discharges at the liquid/pressboard interface. Most of those studies deal with the aging of constituents (liquids and solids) of insulating systems, the different failure mechanisms related to these phenomena, such as pressboard tracking and treeing, fault progression and models of these discharges [10,11,12].

Various signal processing techniques have been used to analyze the electrical, luminous and acoustic signals associated with discharges in dielectric fluids. FFT analysis of current signals from low-energy discharges was used to differentiate between two classes of oil (new and aged) [3]. The use of wavelet technique gave good results in the analysis of acoustic emission pulses [13]. And for robust partial discharge classification in oil–paper insulation systems, machine learning techniques were employed [14]. To follow this trend for the characterization of creeping discharges from the recorded currents using artificial intelligence techniques, it is necessary to understand the features of these currents.

In previous studies, we analyzed the evolution of the shape and stopping length (maximum extension) of creeping discharges as well as the associated currents versus the liquid type and pressboard thickness, under AC, DC and standard lightning impulse voltages [15, 16]. In this works, the study of the creeping discharge currents was limited to the comparison of the shape of the current signals according to the type of interfaces.

The present work is aimed at the analysis of the shape of typical discharge current shapes accompanying the creeping discharges propagating over solid/liquid interfaces, through two techniques of signal analysis, namely the traditional FFT and the DWT (discrete wavelet transform) and to evidence the specific spectral signature on the currents for each liquid/pressboard interface. This would be a valuable tool to differentiate between each type of interface and to be able to use this data for diagnosis on immersed power transformers.

2 Experimental setup

The experimental setup consists of a high-voltage supply, test cells, a current probe and an oscilloscope enabling to record the discharge currents (Fig. 1). Two different test cells were used as presented in Fig. 2. The first one is constituted of a point-to-plane electrodes system in which the tip is perpendicular to the solid insulator (pressboard placed perpendicular to the direction of the electric field). This test cell consists of a cylindrical core with 11 cm inner diameter and 9 cm height, and two flat and circular covers; the lower cover constituting the electrode plane was made of brass, and the upper one supporting the point electrode was made of Plexiglas enabling to visualize/record the discharges and to check the contact/distance between the point electrode and the solid insulator. The second test cell contains a point-bar electrode system where the point is parallel to the pressboard (pressboard placed in the parallel direction to the electric field). It contains a cylindrical Teflon core with an inner diameter of 11.2 cm and a height of 8 cm, and two flat, circular covers in methyl methacrylate (PMMA known as Plexiglas).

Fig.1
figure 1

General view of experimental setup

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Fig. 2
figure 2

Electrodes arrangement and used test cells: a point electrode perpendicular to the pressboard, and b parallel to the pressboard

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The investigated solid insulators are square samples of pressboard (PB) with a side of 7.5 cm, the dielectric constant of which is εPB = 4. Three different thicknesses (e) were considered, namely 4, 8 and 12 mm; the measured water content of PB is around 0.5%. The impregnation and drying of PB samples were performed according to IEC60641-2 standard.

The point electrode is made of tungsten whose radius of curvature is 10 ± 5 μm. This latter is regularly checked with a microscope; the tip is replaced each time its head is eroded.

The optical observation of the discharges is based on the integrated images taken with a CCD camera connected to a high performance video card (Meteor-II/Multi-Channel). The camera is a “SONY XC-HR58,” with high-resolution SVGA (767 × 580 pixels) and a speed of 50 frames per second. It is set to capture 900 frames before stopping.

Negative and positive surge voltages are supplied by a Marx generator (200 kV–2 kJ–1.2/50 μs). To minimize space charge accumulation resulting from repeated discharges on the pressboard, a minimum of 5 min was set as the time between two successive tests. The Pearson 6585 current monitor was used as a current probe to measure creeping discharge currents. It was connected in series to the test cell and the oscilloscope. The oscilloscope was from Agilent (MSO 6014A, 1 GHz, 4 Gsa/s).

The investigated insulating liquids are mineral oil (MO), a synthetic ester (SE) that is tetra-ester, a natural ester that are rape-seeds (NE) oil and an extra virgin olive oil (OO). SE and NE are two esters that are already used in some power transformers. OO is a virgin oil that needs a transesterification before its possible use. It has been investigated only for comparison and “curiosity” as it is a food and expensive product; it cannot be considered/used in industrial applications. Karl Fischer Coulometer Meter (Toledo type KF DL39) was used to measure the water content. Note that the water content was high in OO. Therefore, an absorption process was carried out to limit the water content to an acceptable level by adding a 3A molecular sieve. Table 1 gives the main characteristics of the tested liquids. The samples of the PB and the liquid were changed after each flashover or when the discharge traces are observed on PB.

Table 1 The characteristics of the tested fluids
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3 Methods of signal processing

The aim of this section is to provide a short background on the FFT and DWT methods used to analyze the resulting creeping discharge current signals. The DWT and FFT calculation programs have been developed in MATLAB® 2013.

3.1 FFT technique

Generally, the time domain is not appropriate for signal analysis in engineering [17]. Conventional techniques are used to transform signals from the time domain to the frequency domain in order to understand the inherent signal characteristics. Diverse characteristics can be extracted from the frequency spectrum [17]. For signals in the time domain, there are related frequency characteristics. The FFT is the most usually employed technique to convert signals due to its simplicity and computation rapidity in comparison with the other conventional techniques. FFT analysis of current signals provides full discharge current details such as amplitude and frequency responses. FFT analysis of creeping discharge currents enables to extract its characteristic frequencies and obtain a noticeable difference between similar current signals. The equation below illustrates the transformation method from one domain to the other (time/frequency) [17]:

$${L_s}(f) = \int\limits_{ - \infty }^{ + \infty } {{l_s}(t){e^{ - 2\pi ift}}} dt$$
(1)

where i is the imaginary unit, f is the signal frequency (in the frequency domain (\({L_s}(f)\))), and t is the signal time (in the time domain (\({l_s}(t)\))).

3.2 DWT technique

The discrete wavelet transform is a new mathematical technique, which is used to improve the analysis of signals in transient and steady state. It is the object of particular attention by many scientists [18]. It is appreciated for its quality in information and signal processing. There are two types: discrete wavelet transform (DWT) and continuous wavelet transform (CWT). However, it is the first technique (DWT) that is most used for processing a given signal. Two successive filters are used for the DWT computation of the discrete signal in the time domain, together with variations in sampling rates. The obtained signal is passed through the two filters that have dissimilar cutting frequencies where low-pass filters allow analyzing of the low frequencies and high-pass filters to analyze the high frequencies. These filters are employed to decompose the signal in multi-resolution, facilitating the analysis and the study of the signal at diverse scales. Each signal decomposition step is associated with a particular resolution. The process of signal decomposition can be repeated, with the successive approximations being in turn decomposed in the same way.

Several studies have demonstrated the effectiveness of DWT in the monitoring and diagnosis of the HV systems. Table 2 gives some of the works that have used DWT.

Table 2 Examples of work reported in the literature that used DWT
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This method is very useful for the analysis of non-stationary signals, which is the case of creeping discharge currents [19]. It makes it possible to analyze the signal of the discharge currents and to make the distinction between the various signatures. The comparison of the decomposed frequency bands of the discharge current signals is the basis of the analysis. Before requesting the DWT, one must first choose the mother wavelet and select the estimate of the number of decomposition levels.

3.2.1 Mother wavelet

The first essential phase for carrying out the analysis operation is the discrimination of the mother wavelet. As reported in the literature, many wavelets families of mother wavelets (Symlet, Daubechies, etc.) with numerous properties have been used to extract the most useful information. The efficiency of these wavelets is highly dependent on the application. A wavelet could be perfect for specific applications and inappropriate for others [20].

Daubechies families showed acceptable performance in signal filtering. However, their non-ideal frequency responses would create some problems like overlap in different frequency bands. It has been shown that the use of high-order Daubechies wavelets gives satisfactory results with the improvement of the filter behavior reducing the overlapping effect. Daubechies 8 and Daubechies 10 have shown an excellent analyzing behavior against long-time perturbation. On the other side, Daubechies 4 and Daubechies 6 have shown an appropriate performance to identify a high frequency in a perturbation of a short time, which is the case of creeping discharge currents [21]. Using the DWT technique, the Daubechies 4 is employed as the mother wavelet for the current signals analysis.

3.2.2 Calculation of the decomposition levels

The number of decomposition levels is a fundamental parameter that can affect the performance of DWT analysis. The results of the DWT analysis are very sensitive to the chosen number of decomposition levels. At higher levels of decomposition, detailed data and additional larger scale sub-bands will appear, decreasing thus computational efficiency while reducing system stability. On the other hand, a poor analytical process and key information relating to the current signal could be missed with a few decomposition levels. An appropriate number of levels must be chosen to avoid losing information and to obtain a correct analysis process. Usually, two additional levels are required to be added to the obtained decomposition levels to enhance the analysis. The decomposition levels can be calculated using the following equation [18]:

$$ {N_L} > \frac{{\log ({f_e}/{f_s})}}{\log (2)} + 2$$
(2)

where fe and fs represent the supply frequency and the sampling frequency, respectively.

4 Experimental results

Current waveforms accompanying the creeping discharges are generally used with other characteristics such as their morphology and stopping length (Ls) to describe their propagation; the stopping length represents the resulting discharge image in its maximum extension. These two last characteristics show a dependency on the thickness of the pressboard, on the polarity and the amplitude of the voltage, in addition to the nature of the insulating liquids. However, it is difficult to differentiate the currents obtained with time-based approaches under lightning impulse stresses. Irrespective of voltage polarity, type of liquid and thickness of the pressboard, the shapes of the discharge currents were very similar as shown in Fig. 3 and Fig. 4. Those consist of intense and discrete pulses comparable to those obtained in liquids alone. The repetition and amplitude of these discharge currents increase with applied voltage under both polarities.

Fig. 3
figure 3

Negative creeping discharges and corresponding currents under 78 kV. The tip being perpendicular to PB, e = 4 mm

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Fig. 4
figure 4

Positive current and corresponding creeping discharge under 62 kV. The tip being perpendicular to PB, e = 4 mm

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Therefore, it is important to evaluate the creeping discharge currents by signal processing techniques. In the following, the current signals recorded for different experimental conditions (different liquids, various pressboard thicknesses, positive and negative polarities) will be analyzed using two techniques (FFT and DWT) under various test conditions for the two arrangements of electrodes.

4.1 FFT results

For each thickness of pressboard and for both polarities, the creeping discharge currents were measured. A series of five measurements were performed for each constraint and the signals recorded and transformed into the frequency spectrum domain using the FFT method. The number of recorded signals differs from one oil to another. For each polarity and for each oil, the number of signals is between 60 and 80. Figure 5 and Fig. 6 depict examples of creeping discharge spectrum of discharge currents under positive and negative polarity, respectively.

Fig. 5
figure 5

The measured currents and its respective FFT results under 74 kV negative polarity. The tip being perpendicular to PB, e = 4 mm

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Fig. 6
figure 6

The measured currents and its respective FFT results under 58 kV positive polarity. The tip being perpendicular to PB, e = 4 mm

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For the measurements under atmospheric pressure, the comparison of the signal spectrum of creeping discharge currents in the investigated pressboard/liquid interfaces shows a spectral signature that differs from one liquid/pressboard interface to another.

In negative polarity and for each liquid/pressboard interface, a higher-frequency component is observed in a given frequency range which changes from one interface to another. The same observations were made in positive polarity. Each interface has a unique spectral signature, which facilitates the identification of discharge currents and their characterization. The frequency range of the dominant peak is different to the frequency range observed under negative polarity. It emerges from the statistics analysis that the dominating peak is observed with an average of 26%. In 30% of cases, while the dominating peak is always at a specific frequency, numerous other peaks may be observed at various frequencies. For the remainder, the dominating peak is not found. The average value for all the tested fluids is indicated in these stats. Table 3 presents the frequency range of the dominating peak for each interface under positive and negative polarity.

Table 3 The frequency range of the dominating peak in every pressboard/fluid interface
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4.1.1 Influence of hydrostatic pressure and pressboard thickness

The measurement of the creeping discharge currents was also performed under different hydrostatic pressures, namely 0.5, 1 and 1.5 bar. The effect of hydrostatic pressure has been clearly evidenced in other studies [27, 28]. It was shown that the stopping length of the branches of creeping discharges is reduced when increasing the hydrostatic pressure for both negative and positive polarities. In this study, we did not notice any effect of hydrostatic pressure on the characteristics of currents. The range of frequencies of the dominating peak under different pressures is very similar to the range of frequencies under atmospheric pressure. However, for the same pressboard/liquid interface and for the same stress, the current amplitude decreases with the increase in pressure as indicated in Fig. 7. This is related to the difference in the stopping length with pressure variation. The comparison between the current amplitudes in the different liquid/pressboard interfaces must be for the same final length and not for the same stress.

Fig. 7
figure 7

Creeping discharges and corresponding measured currents in SE with different pressures: a 0.5 bar, b 1 bar and c 1.5 bar, under 52 kV positive polarity and FFT results. The tip being perpendicular to PB, e = 4 mm

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Regarding the influence of the thickness, a decrease in the amplitude of the current is observed with increasing thickness, in the time domain (Fig. 8). It has been shown that the thickness of the pressboard strongly influences the final length of creeping discharges; the final length decreases as the thickness of the pressboard increases [16]. However, this decrease in the current amplitude with the increase in the pressboard thickness could be related to the capacitive effect and electric field in the propagating process; the capacitive effect reduces when increasing the thickness. As a result, with the initiation of the creeping discharge, the field at the top will also be improved.

Fig. 8
figure 8

Measured current and corresponding creeping discharge propagating radially in NE with different pressboards of 4 mm (a), 8 mm (b) and 12 mm thickness, under 56 kV in positive polarity and FFT results

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Thus, for a given stress, the thinner the PB, the higher the amplitude of the currents. However, after application of the FFT, it is noticed that the spectral signature of the various interfaces does not change with the variation of the thickness. For each interface, the frequency spectrum of the dominant peak is identical whatever the thickness. It should be noted that FFT results in the case of pressboard/MO interface were very bad for 12 mm thickness in both polarities, knowing that the current amplitude for MO in the time domain was very small for this thickness (12 mm) compared to other liquids. This could be due to the loss of certain time domain information when measuring discharge currents.

For the second electrode arrangement, when the point electrode is parallel to the pressboard, the FFT results are partially in accordance with the results obtained in the first arrangement. Note that in most cases, the discharges have been observed to propagate along the surface of pressboard. In certain cases, it is observed that there are branches that can go into the surrounding area as shown in Fig. 9. The FFT results for the last situations are different compared to the results obtained in the first arrangement suggesting that the area of the propagation influences the spectral signature.

Fig. 9
figure 9

Measured current and corresponding creeping discharge propagating in MO with a pressboard of 4 mm thickness, under 64 kV (a) and 62 kV (b), in negative lightning impulse voltage and FFT results. The point electrode being parallel to PB and the CCD camera in different positions

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Nevertheless, when analyzing the FFT results in the different pressboard/liquid interfaces, excepting the results in pressboard/MO for 12 mm thickness, the results obtained are acceptable for more than 60% of the cases for the first arrangement. For the other cases, the results are not satisfying; in some cases, the dominating peak is not detected in the processed signals and/or other peaks in a different frequency range can be observed. The frequency range and amplitude of these peaks change from one measure to the next, while the dominating peak is always present in the same range, resulting in potential perturbation of the analysis of the creeping discharge currents and their characterization. This is one of the drawbacks of this processing technique. The obtained signal after the transformation may lose some data from the time domain affecting the exactitude of the obtained creeping discharge current characteristics. Furthermore, the FFT technique gives only the frequency information and does not indicate the temporal one. In the next section, the focus will be on the time–frequency technique to overcome the limitations of FFT. Creeping discharge current signals will be analyzed and studied with the wavelet technique. This later has been successfully employed in several signal processing applications.

4.2 DWT results

In this study, the Daubechies 4 wavelet is used until 4 levels of decomposition. The sub-bands for each level are shown in Table 4. Figures 10 and 11 show examples of the real-time decomposition of radially propagating creeping discharge currents for both polarities in NE and MO, under negative and positive polarity, respectively. The first step to take after the decomposition is the comparison between the levels of signals in the different pressboard/liquid interfaces under various voltages. We observe that all results obtained with DWT evidence the existence of variation at various levels for the investigated interfaces.

Table 4 The sub-bands of frequency at each level
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Fig. 10
figure 10

Creeping discharge current in NE liquid under 64 kV (a), 68 (b) and 74 kV negative polarity and DWT results. The tip being perpendicular to PB, e = 4 mm

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Fig. 11
figure 11

Creeping discharge current in MO under 50 kV (a), 54 kV (b) and 60 kV positive polarity and DWT results. The tip being perpendicular to PB, e = 4 mm

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With increasing voltage, DWT analysis for pressboard/NE shows variation and oscillation in D2; the other levels vary slightly with the voltage. For the remaining pressboard/liquid interfaces, the difference is in D3 for the pressboard/NE, and in D1 for pressboard/MO.

One can be made the same observations in negative polarity. When the voltage varies, a variation of a particular level may be observed. For pressboard/MO, pressboard/NE and pressboard/OO, the difference is in D1. For pressboard/SE, the variation is in D2. For pressboard/NE and pressboard/SE interfaces, the varying levels are different in the positive and negative polarity results.

4.3 Comparative study between obtained results via the applied techniques DWT and FFT

From the obtained results, the frequency of the dominating peak obtained by the FFT technique corresponds to the frequency range level in which the difference appears using the DWT method for the same creeping discharge current. This shows a good agreement between the results provided by these two techniques and demonstrates their appropriateness. The comparison of the effectiveness of these methods shows some limited performance for the FFT technique in comparison with the DWT method. As mentioned above, information can sometimes be missed with the signal transformation by the FFT. There are indeed some difficulties in analyzing non-stationary signals. On the other hand, the DWT method appears as a very effective tool for the analysis of non-stationary signals.

This is related to the decomposition capacity of the recorded current signals in the into various frequency bands. Furthermore, it may determine the timing of the appearance of the bands, which the F.F.T technique is unable to do.

It should be noted that with DWT there is a similarity in the level of variation. This applies to pressboard/MO, pressboard/NE and pressboard/SE in negative polarity and pressboard/MO and pressboard/OO in positive polarity. Additionally, there is a similarity in the level of variation between positive and negative polarity in pressboard/MO and pressboard/OO. The calculation of the storage energy in the DWT variation level in the corresponding pressboard/liquid interface is required to overcome this obstacle. The storage energy for each frequency band is calculated as follows [18]:

$$ E{S_m} = \sum\limits_{k = 1}^{k = i} {{{\left| {{D_{m,k}}(n)} \right|}^2}}$$
(3)

where m is the decomposition level of the wavelet, n is decomposition time of the DWT, and D is the magnitude of the coefficient of the signal wavelet packet in the respective frequency band, at each discrete point.

Figure 12 illustrates the results for the energy stored at the same levels. A variance in energy of the D1 can be observed between the pressboard/MO, pressboard/NE and pressboard/OO interfaces with the negative polarity, and also between the pressboard/MO and pressboard/OO interfaces with the positive polarity. In addition, the energy is higher in the case of pressboard/OO than in the cases of pressboard/NE and pressboard/MO. Moreover, for detail D1, the energy is higher in positive polarity than in negative polarity for pressboard/OO and pressboard/MO interfaces. This allows us to differentiate the different discharge currents and helps in their characterization.

Fig. 12
figure 12

Energy values

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5 Conclusion

The characterization of the currents associated with creeping discharge propagating over different liquid/pressboard interfaces under lightning impulse voltages has been achieved using the fast Fourier transform and the discrete wavelet transform methods.

The fast Fourier transform results, when the tip is placed perpendicular to the solid insulator, show a specific spectral signature characteristic of each fluid/pressboard interface. In most situations, the dominating peak is observed in a particular frequency range at any voltage and differs from one interface to another. For pressboard thickness and pressure influence, the spectral signature of the different pressboard/liquid interfaces does not change with the variation of the pressure and pressboard thickness; the frequency range of the dominant peak is the same regardless of pressure or thickness. However, in certain situations, the FFT presents a limitation in the performance marked by the apparition of more peaks for different frequencies.

For the second electrode arrangement, when the point electrode is parallel to the pressboard, the FFT results are partially in accordance with the results obtained in the first arrangement. The analysis of creeping discharge currents by the discrete wavelet transform method clearly shows the existence of variation in various levels. The band of frequency of the level where the variation occurs agrees with the result found by the technique of fast Fourier transformation. There is an agreement between the frequency band of the level in which the change occurs and the result obtained by the FFT technique.

Comparatively to the DWT method, the FFT technique demonstrates a limited performance. This is related to each method’s performance in non-stationary signal analysis, which is the case for creeping discharge currents. In the future, it would be interesting to check the feasibility of these two techniques for the characterization of the creeping discharge currents under AC and DC voltages.

The use of both techniques (FFT and DWT) for analyzing the discharge current shapes accompanying the creeping discharges at solid/liquid interface is a novelty. The goal is to evidence the specific spectral signature on the currents for each liquid/pressboard interface what is of great interest to differentiate each type of interface and to be able to use such experimental data for diagnosis on immersed power transformers.