Partial Discharge Pulse Segmentation Approach of Converter Transformers Based on Higher Order Cumulant

Abstract

As one of the most effective methods to detect the partial discharge (PD) of transformers, high frequency PD detection has been widely used. However, this method also has a bottleneck problem; the biggest problem is the mixed pulse interference under the fixed length sampling. Therefore, this paper focuses on the study of a new pulse segmentation technology, which can separate the partial discharge pulse from the sampling signal containing impulse noise so as to suppress the interference of pulse noise. Based on the characteristics of the high-order-cumulant variation at the rising edge of the pulse signal, a method for judging the starting and ending time of the pulse based on the high-order-cumulant is designed, which can accurately extract the partial discharge pulse from the original data. Simulation results show that the location accuracy of the proposed method can reach 94.67% without stationary noise. The field test shows that the extraction rate of the PD analog signal can reach 79% after applying the segmentation method, which has a great improvement compared with a very low location accuracy rate of 1.65% before using the proposed method.

1. Introduction

The safe and stable operation of UHV converter transformers is the key to ensure the stability and reliability of cross regional energy interconnection. However, due to the long-term bearing of various extreme loads such as electrical stress, thermal stress and mechanical stress, the insulation performance of insulating components will deteriorate over time. One of the most effective methods to monitor this degradation process is partial discharge detection [1,2]. Among them, high frequency partial discharge detection systems have been widely used in electrical equipment health management by electrical equipment maintenance enterprises, mainly including daily maintenance online monitoring and periodic diagnostic live detection [3,4]. Because of its high sampling rate and high sensitivity, it can obtain rich defect information so as to improve the accuracy and reliability of subsequent diagnosis results.

Despite these advantages, high frequency partial discharge detection also has significant disadvantages, such as a large amount of data and large interference noise. In terms of sampling signal preprocessing, the whole sampling sequence is mainly used. In reference [5], the independent principal component analysis method is used to design a filter to filter the stationary noise in field detection, which has a large amount of calculation; on this basis, document [6] introduces the singular spectrum front end to further filter out white noise and periodic narrowband interference and solves the problem of the difficult extraction of principal component analysis under a low signal-to-noise ratio. In terms of feature extraction, the literature [7,8] still adopts complete sampling sequence. Because of the large amount of data, it adopts the calculation methods of a large amount of data such as fuzzy clustering and knowledge reasoning.

In fact, except for the data segment containing partial discharge (PD) pulses, most of the other real-time data are useless for diagnostic analysis. On the one hand, these redundant data parts will not only occupy a lot of storage space and computing resources but will also have pulse characteristics similar to partial discharge signals, which will lead to the deviation of diagnosis results from reality. A suitable method to solve this problem is pulse truncation, which aims to detect and intercept partial discharge pulses from measured data [9,10,11].

At present, the most mature field of pulse truncation is biomedical engineering, especially heart sound separation [12,13,14,15]. For example, the authors decompose heart sounds into intrinsic mode functions (IMF) using ensemble empirical mode decomposition (EEMD), and then calculate kurtosis statistics to separate the first and second heart sounds (S1, S2) [16]. In addition to biomedical applications, pulse segmentation method is also a promising signal processing tool in power quality disturbance detection [17] and seismic longitudinal wave detection [18].

According to the existing knowledge, there are few reports on the application of pulse truncation in partial discharge analysis. Reference [19] first applied mathematical morphological gradient (MMG) to reflect the time-domain changes caused by PD. The author developed an adaptive extraction system, which divides the original discrete PD sequence into several time frames and continuously performs discrete wavelet transform (DWT) on each frame until the segment containing partial discharge pulse is identified [20,21,22]. The Kurtosis method is also used to detect mutation in PD identification [23,24,25].

Furthermore, F. Selimefendigil et al. [26] studied the forced convection of pulsating nanofluid flow over corrugated parallel plates in the presence of an inclined magnetic field by using the Galerkin weighted residual finite element method. The authors also investigated the effects of pulsating frequency and other factors on the fluid flow and heat transfer characteristics, which provide a theoretical basis for the research of this paper [27].

According to the above literature, these pulse segmentation methods can be reasonably divided into two categories: (1) signal analysis and pulse detection; (2) feature extraction and pulse recognition.

The effectiveness of the methods in the first category is realized by a successful denoising process, which is not easy for PD electromagnetic signals. In addition, due to the non-stationary characteristics of pulse detection, the determination of the threshold is also a challenging topic. For the second kind of methods, it is of great significance to find out the distinguishable features and design a recognition algorithm. Although this method can achieve satisfactory results in some applications, it will also increase complexity. Based on the distortion characteristics of a high-order cumulant of a time series, an algorithm based on the threshold of variation of a high-order cumulant is proposed to determine the boundary of PD induced electromagnetic waves. The advantages of the proposed method are that it is: (1) simple and clear and (2) can avoid complex denoising and intelligent recognition processes.

To verify its effectiveness, the high-frequency signal of the transformer core clamp of the condenser is actually measured in a UHV converter station. The signal includes an analog PD signal and a commutation pulse interference signal. Then, the method in this paper is used to truncate and process these recorded high-frequency signals. The results show that this method can accurately detect the local PD pulse and determine its boundary. The signal before truncation is a multiple pulse signal, which cannot effectively separate the local PD analog signal. After truncation, the signal is a single pure pulse signal, which can realize the separation of the commutation pulse and the analog signal.

2. Fundamental Theory

2.1. Higher Order Cumulant of Time Series

The higher-order cumulant of the signal sequence is a numerical statistic reflecting the singularity of the time series. For the discrete signal x with sequence length N, m₁, m₂, m₃ and m₄ are the 1st to 4th order origin moments of the sequence array, respectively, and its expression is shown in formula (1). Based on the known origin moment, the expression of the higher-order cumulant of the time series is shown in Equation (2).

$$\{\begin{array}{l}{m}_1=E\left(x\right)\\ m_2=E\left(x^2\right)\\ m_3=E\left(x^3\right)\\ m_4=E\left(x^4\right)\end{array}$$

(1)

$$\{\begin{array}{l}{c}_1=m_1\\ c_1=m_2-m_1^2\\ c_1=m_3-3m_2{m}_1+2m_1^3\\ c_1=m_4-3m_2^2-4m_1{m}_3+12m_1^2{m}_2-6m_1^4\end{array}$$

(2)

In formula (1), x², x³ and x⁴ represent the sequence composed of the square, cubic and quartic of the elements in sequence x, respectively. Therefore, (x²), E(x³) and E(x⁴) represent the second-order moment, third-order moment and fourth-order moment of sequence x, respectively. On the premise that the time series is a Gaussian signal, taking the Gaussian random signal x~N(0,1) as an example, its mean value is E(x) = 0, the central moment is the origin moment, and D(x) = 1. Therefore, the result of each order origin moment can be expressed by Equation (3). In this case, the cumulant of each order of the sequence is always zero, as shown in Equation (4).

$$\{\begin{array}{l}{m}_1=0\\ m_2=E\left(x^2\right)=1\\ m_3=E\left(x^3\right)=0\\ m_4=E\left(x^4\right)=3\end{array}$$

(3)

$$\{\begin{array}{l}{c}_1=m_1=0\\ c_2=m_2-m_1^2=1\\ c_3=m_3-3m_1{m}_2+2m_1^3=0\\ c_4=m_4-3m_2^2-4m_1{m}_3+12m_1^2{m}_2-6m_1^4=0\end{array}$$

(4)

$$\{\begin{array}{l}{c}_1=m_1=0\\ c_2=m_2-m_1^2={\sigma }^2\\ c_3=m_3-3m_1{m}_2+2m_1^3=0\\ c_4=m_4-3m_2^2-4m_1{m}_3+12m_1^2{m}_2-6m_1^4=3-3{\sigma }^4\end{array}$$

(5)

$$\{\begin{array}{l}{y}_0=\frac{y-\mu }{{\sigma }^2}\\ m_1=E(y_0)=0\\ m_2=E(y_0^2)=1\\ y_0\sim N(0,1)\end{array}$$

(6)

when the time series does not obey the standard normal distribution N(0,1), it will become a zero mean random time series y~N(0,σ²). Obviously, the fourth-order cumulant may not be zero. At this time, the noise signal is normalized or standardized. Thus, a random signal sequence y₀ is constructed to meet the conditions listed in Equation (6).

$$\{\begin{array}{l}{c}_1=m_1=0\\ c_2=m_2-m_1^2=1\\ c_3=m_3-3m_1{m}_2+2m_1^3=0\\ c_4=m_4-3m_2^2-4m_1{m}_3+12m_1^2{m}_2-6m_1^4=0\end{array}$$

(7)

Therefore, the fourth-order cumulant of the random sequence y₀ is always zero. After normalization, the fourth-order cumulant of the noise is as shown in Equation (7), and its impact on the fourth-order cumulant of the original signal can be minimized through normalization.

2.2. Characteristic Analysis of Noisy Local Radio Signals

The measurement signal of the converter transformer contains not only PD pulse but also a large number of noise signals. The noise signals include pulse interference and smooth interference. In this case, the analysis of the PD signal shall include the characteristic analysis of all of the components in the signal.

Generally, the stationary background noise in the field can be regarded as a normal random time series, which follows a normal random distribution with mean μ₀ and variance δ². For the noise sequence N with sequence number N, its variance δ² can be expressed as Equation (8).

$${\delta }^2=\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(n-\mu \right)}^2}$$

(8)

In general, the more elements in the sequence, the more accurate the calculation result of the variance δ² will be. When N is large enough, the variance δ² can be regarded as fixed.

2.3. Characteristic Analysis of Time Series Cumulant

The simulation definition of the PD signal of the noisy converter transformer with sampling point B is a₀. The signal is composed of a₀₁, a₀₂, a₀₃ and a₀₄, of which a₀₁ is the pre trigger segment, while a₀₂ to a₀₄ are the trigger segments. The trigger time is included in a₀₂. x_iq is defined as the nth order origin moment of segment i. The four segments a₀₁, a₀₂, a₀₃ and a₀₄ are assigned according to the conditions listed in Equations (9) and (10), respectively.

$$\{\begin{array}{l}{a}_{01}=\left[x_1,x_2,\cdots ,x_{q-1},x_q\right]\hfill \\ a_{02}=\left[x_{q+1},x_{q+2},\cdots ,x_{2q-1},x_{2q}\right]\hfill \\ a_{02}=\left[x_{2q+1},x_{2q+2},\cdots ,x_{3q-1},x_{3q}\right]\hfill \\ a_{04}=\left[x_{3q+1},x_{3q+2},\cdots ,x_{4q-1},x_{4q}\right]\hfill \\ L=size\left(a_0\right),q=L/4\hfill \end{array}$$

(9)

$$\{\begin{array}{l}{a}_{01}=\left[0,0,\cdots ,0,0\right]\hfill \\ a_{02}=\left[\sin \left(\frac{\pi }{q}\right),\cdots ,\sin \left(\frac{\left(q-1\right)\pi }{q}\right),\sin \left(\frac{q\pi }{q}\right)\right]\hfill \\ a_{03}=a_{04}=a_{01}\hfill \end{array}$$

(10)

The derivation of each order origin moment and higher-order cumulant of the sampled signal can be divided into four segments. a₀₁₂, a₀₁₃ and a₀₁₄ in Equation (11) represent the sequence composed of the square, cubic and quartic of the elements in sequence a₀₁. Therefore, E(a₀₁²), E(a₀₁³) and E(a₀₁⁴) represent the second-order moment, third-order moment and fourth-order moment of sequence a₀₁, respectively. The fourth-order advanced cumulant in the signal interval is constant to zero.

$$\{\begin{array}{l}{m}_{41}=m_{31}=m_{11}=E\left(a_{01}\right)=0\hfill \\ m_{42}=m_{32}=m_{12}=E\left(a_{01}^2\right)=0\hfill \\ m_{43}=m_{33}=m_{13}=E\left(a_{01}^3\right)=0\hfill \\ m_{44}=m_{34}=m_{14}=E\left(a_{01}^4\right)=0\hfill \end{array}$$

(11)

$$\{\begin{array}{l}{c}_{31}=c_{41}=c_{11}=0\hfill \\ c_{32}=c_{42}=c_{12}=0\hfill \\ c_{33}=c_{43}=c_{13}=0\hfill \\ c_{34}=c_{44}=c_{14}=0\hfill \end{array}$$

(12)

For segment a₀₂, the higher-order origin moment and each order cumulant are shown in Equations (13) and (14), and the fourth-order cumulant of the signal is non-zero.

$$\{\begin{array}{l}{m}_{21}=E\left(a_{02}\right)=\frac{2}{\pi }\hfill \\ m_{22}=E\left(a_{02}^2\right)=\frac{1}{2}\hfill \\ m_{23}=E\left(a_{02}^3\right)=\frac{4}{3\pi }\hfill \\ m_{24}=E\left(a_{02}^4\right)=\frac{3}{8}\hfill \end{array}$$

(13)

$$\{\begin{array}{l}{c}_{21}=m_{21}=\frac{2}{\pi }\\ c_{22}=m_{22}-m_{21}^2\approx \frac{1}{10}\\ c_{23}=m_{23}-3m_{21}{m}_{22}+2m_{21}^3=\frac{16-5{\pi }^2}{3{\pi }^3}\\ c_{24}=m_{24}-3m_{22}^2-4m_{21}{m}_{23}+12m_{21}^2{m}_{22}-6m_{21}^4=\frac{40}{3{\pi }^2}-\frac{3}{4}\approx \frac{7}{12}\end{array}$$

(14)

Therefore, the mathematical relationship between the higher-order cumulant and the change of the higher-order cumulant of each segment is the equal relationship shown in Equation (15). For the pure noiseless signal, the calculation results show that, for the trigger segment, the higher-order cumulant itself has the same significant feature as the change of the higher-order cumulant, which is not available in other segments. This shows that this feature can be used to identify the rising edge of the signal, that is, the starting time of the signal.

$$\{\begin{array}{l}{c}_{24}-c_{14}=\frac{7}{12}=c_{24}\hfill \\ c_{34}-c_{24}=-\frac{7}{12}=-c_{24}\hfill \\ c_{44}-c_{34}=0\hfill \end{array}$$

(15)

3. Steps of Pulse Truncation Method

Based on the fundamental feature that the fourth-order cumulant in the time domain is equal to the change of the fourth-order cumulant in the time domain, the final pulse truncation method based on high-order cumulant is formed by integrating various influencing factors and optimization measures, as shown in Figure 1.

The method includes the following main processes:

(1)

Signal preprocessing. Filter, segment and normalize the sampled signal.

(2)

The rising edge of the pulse is determined. According to the characteristics of the time-domain cumulant and the time-domain RMS, judge whether it is the rising edge of the independent signal according to the principle that the change of the fourth-order cumulant is equal to the fourth-order cumulant.

(3)

The pulse initiation time is determined. At the beginning time, the fourth order cumulant in the time domain and the change of the fourth order cumulant in the time domain are calculated for all of the segments, the three condition signal segments of CUM(i) = ΔCUM(i), CUM(i) > CUM₀ and RMS(i) > RMS₀ are judged simultaneously and the time is determined to be the beginning time. CUM₀ is the threshold value of the fourth-order cumulant, which is set as 3.0 in this paper, and RMS₀ is the threshold value of the effective value.

(4)

The pulse cut-off time is determined. The fourth-order cumulant and effective value of the minimum calculated signal of each segment are calculated by forward search with each rising edge time as the starting point. According to the attenuation characteristics of the signal, including the segments of the pulse cut-off time, the cumulative modulus value is less than the set threshold, and the effective value is also less than the set threshold. In addition, the signal from the cut-off time to the rising edge of the next pulse is flat, and the cumulative modulus value and signal effective value of this interval are also less than the set threshold. Therefore, the signal segment that first meets the threshold conditions should be regarded as the pulse cut-off time.

(5)

Form a truncated signal. According to the pulse start time and truncation time, the pulse time-domain sequence is intercepted from the original sampling signal. In order to reduce the influence of time length on equivalent time, the intercepted signal is zeroed to the same length, that is, the time domain length of the original signal.

4. Verification of Pulse Truncation Method

4.1. Calculation and Verification

To verify the effectiveness of the proposed method, field measured data from a ±1100 kV converter transformer was adopted for the study. A group of signals containing 50 datasets were obtained. Each dataset is composed of three independent pulses. The signals were introduced into the flow chart of the pulse truncation method shown in Figure 1.

A_m is the signal amplitude in mV; τ₁ is the signal rise and decay time, unit: μs, τ₂ is the signal decline attenuation time and unit: μs. f_c is the oscillation frequency in MHz; T_o is the signal starting time in MHz μs. In the process of the signal time-domain change, only the starting time changes, and the delay changes of sigB and sigC are greater than sigA so as to ensure that there will be no signal overlap in the whole process. The time domain waveform of the signal is shown in Figure 2a. Figure 2b shows the positioning results at the beginning and end of the pulse. There are 150 pulse signals in the signal group, and the start time results and end time of the group of signals are counted. Among them, the start time and end time of eight signals are equal, and the start time and end time of these eight signals are 0 μs. As shown in Figure 2b, the positioning results of the remaining 142 signals are obtained through calculation.

After obtaining the start and end time of the PD pulse, the pulse is truncated and extracted using the start time and end time. By observing the integrity of the extraction results, the accuracy of the calculation results of the start and end time can be evaluated, that is, the accuracy of the algorithm for pulse signal positioning.

The time domain waveform of the truncated signal intercepted according to the pulse positioning results shown in Figure 3. It can be seen that the integrity of the truncated signal is satisfactory, which shows that the positioning results of 142 signals are accurate. Therefore, the positioning accuracy of the algorithm reaches 94.67%, indicating that the effectiveness of the truncation method is not less than 90%.

The time-frequency features of the time-domain signals before and after truncation are extracted. The scatter diagram of the equivalent time/equivalent frequency eigenvalues is shown in Figure 4. The partial discharge signals we need cannot be screened out from the mixed signals. After truncation, the clustering object becomes an independent pulse signal, and good separation can be achieved between independent pulses.

4.2. Actual Measurement and Verification of Converter Station

In this paper, the PD detection scene of electrical equipment under the variable frequency speed regulation of the converter station is selected to verify the method. In this scene, there is a commutation pulse interference signal and an analog PD signal; the corresponding time domain waveform is shown in Figure 5. A total of 2000 signals are collected in the field measurement, and the time domain length of a single pulse is 100 μs. From the time domain waveform, the duration of the commutation pulse is less than 10 μs. The duration of a single PD pulse is about 20 μs. It can be seen that the amplitude of the commutation pulse is higher and the duration is longer, which indicates that the time domain energy of the commutation pulse is greater. In contrast, the amplitude of the PD pulse is low, but the oscillation times are significantly higher than that of the commutation pulse. This is because the high-frequency component of the commutation pulse attenuates to a great extent after filtering through the capacitance between windings and winding to ground. The propagation path of the PD pulse is shorter, so the high-frequency components are richer and the rising edge steeper.

Figure 6 shows the time domain signal and equivalent time-frequency clustering results actually measured at an UHV converter station, with 10 selected μs. Under such a short sampling time, the collected signals are all single pulses. At this time, the clustering results of the sampling information divide the pulses into two categories, A and B, including 1700 in category A and 298 in category B. The category B signals belonging to the PD analog signals account for 19.9%. Once selecting a time series signal with 100 μs, the collected signal part is multiple pulses under such a long sampling time. According to the clustering results of multiple pulse sampling signals, the PD pulses are divided into three categories: A, B and C, including 1890 samples in category A, 33 samples in category B and 26 samples in category C. The signals of category B belonging to the PD analog signals account for 1.65%. It can be seen that there is a significant difference between the two samples.

The results show that the time-frequency characteristics of multiple pulse sampling signals cover the time-frequency characteristics of PD pulses. In the case of multiple pulse, the clustering algorithm cannot separate PD pulses and interference pulses, resulting in a significant reduction in the number of pulse extraction, and only 8% of PD pulses are separated. In order to reduce the impact of pulse interference on the clustering results, the pulse truncation algorithm proposed in this paper is used to separate multiple pulses in one sampling to ensure that the calculation object of the clustering separator is a single pulse signal.

A total of 2000 signal samples were collected under the sampling time of 100 μs for analysis with the flow shown in Figure 1 for truncation processing. After that, the time-frequency clustering was carried out after pulse truncation processing. The separation results are shown in Figure 7, including four types of pulses A, B, C and D. In the three-dimensional cluster diagram, the pulse clusters of A, B, C and D are significant and do not coincide. In the T_eq-F_eq two-dimensional projection surface, the four signals coincide on the T_eq-F_eq two-dimensional projection surface. In the separation results, there are 1930 class A signals, 1580 class B signals, 600 class C signals and 960 class D signals. After truncation, the extraction rate of class B signals of the partial discharge analog signal reaches 79%.

It can be seen from the clustering calculation results in Figure 7 that the equivalent time length of the class A pulse is between 0 and 10 μs. The equivalent bandwidth is between 7 and 11 MHz. The equivalent time length of the class B pulse is between 0 and 14 μs. The equivalent bandwidth is between 2 and 8 MHz; the equivalent time length of the class C pulse is between 0 and 10 μs. The equivalent bandwidth is between 1 and 4 MHz; the equivalent time length of the class D pulse is between 0 and 4 μs. The equivalent bandwidth is between 0 and 2 MHz. The separation results show that the number of multi pulses increases under long-time sampling, and the advantage of using the pulse truncation method appears. The pulse truncation method realizes the extraction of a single pulse. Compared with the clustering separation results without truncation, the calculation objects are single pulse after pulse truncation, and the clustering results are more precise. The time domain waveform shown in Figure 8 shows that the consistency and smooth of signal waveforms of each group are significantly improved after pulse truncation.

5. Conclusions

In this paper, a pulse truncation method for the VHF partial discharge detection of a converter transformer based on the high-order cumulant of a time series is proposed, based on which the fourth-order cumulant is equal to the change of the fourth-order cumulant. The main conclusions of this paper can be summarized as follows:

(1)

Comparing and analyzing the time-frequency clustering results of the multi pulse signal and the truncated signal, the accuracy of the separated pulse before truncation is 8%, and the accuracy of the separated pulse after truncation is more than 90%.

(2)

The pulse truncation method is verified and applied in the UHV converter station. This method realizes the separation of the commutation pulse and the PD pulse in the time domain waveform.

(3)

When there are many PWM commutation pulses, the sampling time length reaches 100 μs, the sampling signal contains a large amount of commutation pulse information and the accuracy of extracting the simulated PD signal is 1.65%. The method described in this paper extracts the PD signal separately so that the extraction rate of the PD signal is increased to 79%.