Detection of Power Transformer Winding Deformation ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 4, APRIL 2018

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Detection of Power Transformer Winding Deformation Using Improved FRA Based on Binary Morphology and Extreme Point Variation Zhongyong Zhao

, Chenguo Yao, Member, IEEE, Chengxiang Li, and Syed Islam, Senior Member, IEEE

Abstract—Frequency response analysis (FRA) has recently been developed as a widely accepted tool for power transformer winding mechanical deformation diagnosis, and has proven to be effective and powerful in many cases. However, there still exist problems regarding the application of FRA. FRA is a comparative method in which the measured FRA signature should be compared with its fingerprint. Small differences of FRA signatures in certain frequency bands might be produced by external disturbance, which hinders fault diagnosis. Additionally, the existing correlation coefficient indicator recommended by power industry standards cannot reflect key information of signatures, namely the extreme points. This paper proposes an improved FRA based on binary morphology and extreme point variation. Binary morphology is first introduced to extract the certain frequency bands of signatures with significant difference. A composite indicator of extreme point variation is adopted to realize the diagnosis of fault level. A ternary diagram is constructed by the area proportions of the binary image to identify winding faults, which has a potential to realize cluster analysis of fault types. Index Terms—Binary morphology, extreme point, frequency response analysis (FRA), ternary diagram, transformer, winding deformation.

I. INTRODUCTION HE power transformer is one of the most valuable and expensive pieces of equipment in a power substation; it is of significance to ensure its stable, reliable, and safe operation [1]. Core failure, overvoltage, aging of insulation, insulation

T

Manuscript received March 5, 2017; revised May 29, 2017 and July 6, 2017; accepted July 30, 2017. Date of publication September 13, 2017; date of current version January 5, 2018. This work was supported in part by the National Natural Science Foundation of China (No. 51377175). (Corresponding author: Chenguo Yao.) Z. Zhao is with the State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, and also with the College of Engineering and Technology, Southwest University, Chongqing 400716, China (e-mail: [email protected]). C. Yao and C. Li are with the State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044, China (e-mail: [email protected]; [email protected]). S. Islam is with the School of Electrical Engineering and Computing, Curtin University, Perth, W.A. 6102, Australia (e-mail: s.islam@curtin. edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2017.2752135

failure, and winding deformation are the key factors affecting the occurrence of a transformer fault, even resulting in the outage of the transformer and power network. The statistics obtained by CIGRE working groups have revealed that the winding deformation fault causes one third of all transformer failures. Winding deformation is typically induced by winding electromagnetic force, where the force is the outcome of an external short-circuit (SC) current and internal magnetic field [2]–[4]. Besides, earthquake, careless transportation, aging of insulation material, and explosion of combustible gas in the transformer oil could also be reasons for giving rise to winding mechanical faults [5]–[7]. The ability of the transformer to guard against SC current will decrease considerably after the occurrence of a minor winding deformation fault; winding mechanical deformation faults and interturn SC faults are easily produced and develop simultaneously. Minor winding faults eventually develop into catastrophic failure if no steps are taken, which will result in the outage of the transformer and decrease the economic benefits. Thus, timely detection and diagnoses of winding deformation fault are required. Various methods have been recommended as effective and promising diagnosis tools for past few decades and are still continuing today. Dissolved gas analysis was first introduced as an auxiliary method to detect winding deformation [8]; however, it turns out this method is not sensitive to winding mechanical faults. Other diagnosis methods have been successively introduced and studied. Offline diagnosis methods, including the SC impedance method [9], [10], the ultrasonic method [11], the lowvoltage impulse technique [12], and frequency response analysis (FRA) [13]–[15], have been developed for years. Recently, some researchers have also established publications regarding online diagnosis methods, the online FRA [16], [17], the vibration method [18], and the ultrawideband antenna detective method [19], [20] show great potential in this field. However, offline methods are used more frequently than online techniques. Among the various methods available, FRA is known as an accurate, economical, reliable, fast, and nondestructive method, and is widely accepted in the power industry [21]. The China Power Industry and International Electrotechnical Commission (IEC) have even proposed standards for use of FRA [22], [23]. The basic theory of FRA is to apply a sinusoidal sweep voltage with an amplitude of 1 kHz) [26], [27]. The occurrence of winding distortion, buckling, displacement, and interturn SC faults induces a variation in the configuration and parameter values of the equivalent circuit, resulting in variations of the frequency response signature. Variations in the signature have been typically present in the shift of resonance and antiresonance (extreme point) [28]. Thus, transformer winding deformation can be detected and analyzed by comparing the measured signature and reference signature (fingerprint). However, problems still exist when FRA is adopted in the field. 1) The measured FRA signature is occasionally disturbed due to the interaction of noise, measuring cable and other factors [29]. Two FRA signatures measured on the same transformer at different periods may exhibit minor deviations in certain frequency ranges even though transformer winding deformation is not actually present, which would result in an inaccurate diagnosis. External disturbances typically induce minor variations in the FRA signatures. Fault diagnosis would be improved if the effect of a measuring disturbance could be reduced and only the frequency response data with a significant difference in a certain frequency range could be analyzed. To solve this problem, this paper introduces binary morphology mathematics to eliminate the frequency bands with minor differences in two FRA signatures. 2) In addition, the correlation coefficient (CC) recommended by China’s power industry standards is typically used as an indicator to analyze the FRA signatures at the moment [22], [30]; the CC is a mathematical statistics indicator and cannot effectively represent the key information of FRA signatures, namely the variations in the frequency and amplitude of extreme points. Detection performance using the CC is typically not satisfactory in practice. In this paper, a composite indicator of extreme point variation is adopted to represent the characteristic of variations in the FRA signatures and diagnose the fault level. A ternary diagram is also introduced to identify fault types. The remainder of this paper is organized as follows. First, the basic principle of binary morphology is introduced in Section II. Then, Section III proposes the composite indicator of extreme point variation, followed by a representation of the diagnosis process in Section IV. Section V presents the experimental results and analysis. The conclusions of this study and avenues for future work are introduced in Section VI.

Fig. 1. FRA signature of a power transformer before and after the occurrence of winding deformation fault.

II. BASIC PRINCIPLE OF BINARY MORPHOLOGY In the FRA test, the frequency response signature of the power transformer is constructed by an excitation signal and response signal, as expressed in (1) [31], [32]: H ( f ) = 20 log10

|Rout ( f )| |Rin ( f )|

(1)

where Rin represents the excitation voltage or current signal, Rout represents the response voltage or current signal, and H(f) is the frequency response signature (amplitude versus frequency). Fig. 1 shows the typical FRA signature of a power transformer before and after the occurrence of a winding deformation fault. There is a minor difference between the deformed signature and healthy signature in the frequency range of 350–500 kHz, which might be caused by external factors, such as measurement disturbances, and hinders the fault diagnosis. Binary morphology is used to eliminate the frequency bands with minor difference between two FRA signatures, and preserve the frequency bands with significant difference; only the FRA signatures within these frequency bands are analyzed to diagnose the winding fault. Binary morphology is the basis of mathematical morphology, and is a process used to treat an image set [33]. The inspected binary image is called the targeted image, generally represented by set A. The probe used for collecting information is called the structural element, generally represented by set B. Binary image is an important component of the digital image technique, in which the gray scale has only two values. Generally, in order to clearly distinguish the object and background of an image, the number “1” and the color gray are used to indicate the foreground pixels in the binary image and the number “0” and the color white are used to indicate the background pixels. The binary morphology calculation process involves the following steps: The structural element is moved within the targeted image; then, the structural element and overlapping image are calculated by intersection and union; and finally, the information of the targeted image is successfully collected [34].

ZHAO et al.: DETECTION OF POWER TRANSFORMER WINDING DEFORMATION USING IMPROVED FRA BASED ON BINARY MORPHOLOGY

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There also exist two critical morphological operations on the basis of erosion and dilation, namely the opening operation and closing operation. The opening operation involves first using the same structural element to erode the targeted image and then conducting a dilation operation, shown as Fig. 2. Process of erosion operation. Targeted image A is eroded by structural element B.

A ◦ B = (AB) ⊕ B.

The closing operation involves using the same structural element to dilate the targeted image and then conducting the erosion operation, shown as A • B = (A ⊕ B)B.

Fig. 3. Process of dilation operation. Targeted image A is dilated by structural element B.

Binary morphology is a nonlinear method for processing an image with the characteristic of irreversibility, which reflects the logical relationship between pixels. Erosion and dilation operations can be defined. The erosion operation is the most essential morphological operation; the targeted image A eroded by structural element B can be defined as follows: AB = {x : B + x ⊂ A}

(2)

where x is an image set that satisfies the condition and is a symbol denoting the erosion operation. The process of erosion operation is illustrated in Fig. 2. The erosion operation has a function of zooming out of the image and eliminating the components of the targeted image that are smaller than the structural element. The erosion operation is commonly used to remove the adhesion between objects and filter the small particle noise in the image. Correspondingly, the targeted image A dilated by structural element B can be defined as follows: A ⊕ B = ∪ {B + m : m ∈ A}

(3)

where the set m is contained in A, ⊕ is the symbol denoting the dilation operation, and ∪ represents the union operation. The process of dilation operation is illustrated in Fig. 3. The dilation operation has a function of zooming in of the image and padding the components of the targeted image that are smaller than the structural element. In practice, the dilation operation is commonly used to connect adjacent objects and fill in the small holes and narrow gaps in the image. Erosion and dilation are dual operations; performing the dilation (erosion) operation on the targeted image is equivalent of performing the erosion (dilation) operation on the background image, as shown in (4), where c represents the complement operation and ∧ represents the reflection set of B about the origin (A ⊕ B)c = Ac Bˆ (4) ˆ (AB)c = Ac ⊕ B.

(5)

(6)

According to the above operation rules of binary morphology, the difference between two FRA signatures can be translated into a binary image, and then, the erosion operation is performed to eliminate the components of the image that are smaller than the structural elements, thus eliminating the minor noise components. The frequency bands with significant differences will be selected and obtained, which is helpful for diagnosing winding faults. III. COMPOSITE INDICATOR OF EXTREME POINT VARIATION Currently, the CCs of faulty transformer and healthy transformer in the frequency bands of 1–100, 100–600, and 600–1000 kHz are calculated to diagnose transformer winding mechanical faults. However, detection performance is not satisfactory, in practice, because the CC indicator is a data similarity measure based on statistics; experienced personnel are required to observe the shape of the FRA signature and determine the status of windings in the field. In fact, the FRA signature of a power transformer is a signature with multi resonance and antiresonance. When an equivalent electrical model of a winding produces series resonance, its impedance is approximately zero and a peak will be generated in the FRA signature; when an equivalent electrical model produces parallel resonance, its impedance reaches infinite and a valley will be generated in the FRA signature [35]. Both peaks and valleys are extreme points. The parameters of the equivalent electrical model change after the winding is deformed; thus, the status of winding can be reflected by the variations in extreme points [36]–[38]. A composite indicator of extreme point variation on the FRA signature is proposed as the characteristic parameter to quantitatively analyze winding mechanical faults. A. Effective Extreme Point It is easy to obtain all extreme points on an FRA signature. Frequency response data can be scanned from low to high frequencies, and each data point is judged as to whether it is an extreme point. If both X k−1 and X k+1 are smaller than X k , then X k is a local maximum extreme point (peak); if both X k−1 and X k+1 are larger than X k , then X k is a local minimum extreme point (valley). However, not all extreme points are reliable and effective because there are uncontrollable factors, such as the complexity of field test and external disturbance. If all extreme points of the FRA signature are analyzed, there might be false

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Fig. 4.


Choice of the effective extreme point in FRA signatures.

positives and false negatives in the winding deformation diagnosis. It is necessary to extract the effective extreme points. According to the distribution characteristic of extreme points in the FRA signature, the effective extreme points can be selected by setting threshold values of two neighboring extreme points along the frequency axis and gain axis, respectively. Generally, in a noisy FRA signature, there are certain fake extreme points for which the resonant frequency is between those of the two neighboring real extreme points. These fake extreme points appear to be small oscillations in the signature, which are produced by uncontrollable external factors. For the sake of not overcomplicating the calculation, the neighboring extreme points with minor frequency variation or gain variation can be regarded as the noise or disturbance. The threshold value along the frequency axis can be fixed, whereas the threshold value along the gain axis should be self-adapting in pace with the span of the FRA gain. Consider Fig. 4 as an example, if the gain difference d between the local minimum extreme point a and the next neighboring local maximum extreme point b is larger than 0.005D (where D is the difference between the maximum and minimum gains of the FRA signature), then point a is an effective extreme point; otherwise, point a should not be counted [39]. The criteria 0.005D is obtained by a tentative analysis of the experimental data, which is generally applicable for most cases of experimental transformer. Extreme point b and its next neighboring extreme point are then assessed in accordance with the above rule, and so on. All effective extreme points can be extracted from low to high frequencies. B. Composite Indicator of Extreme Point Variation After extracting all effective extreme points of the FRA signature, the measured signature and reference signature should be compared. The effective extreme points of the reference signature are regarded as bases, and then, the corresponding extreme points of the measured signatures are compared on a case-bycase basis. Each composite indicator of extreme point variation in fingerprint is obtained. Fig. 5 shows three typical situations of extreme point variation, including an offset extreme point,

Fig. 5.

Three typical situations of extreme point variation.

missing extreme point, and extra extreme point. Here, the “frequency domain” is defined as the frequency range constructed by the neighboring extreme points of the analyzed extreme point in the reference signature. A local maximum extreme point to be analyzed is considered as an example in Fig. 5. “Offset extreme point” means that there is one maximum extreme point on the measured FRA signature within the “frequency domain;” “missing extreme point” indicates that there is no maximum extreme point in the measured signature within the “frequency domain;” and “extra extreme point” implies that there is more than one maximum extreme point within the “frequency domain.” For the situation of an offset extreme point, both the resonant frequency and the gain of the extreme point on the measured FRA signature will be generally altered compared to those of the reference signature after the occurrence of a winding mechanical deformation. In the “frequency domain” shown in Fig. 5, if the measured FRA signature is offset, then the composite indicator is calculated according to (7) Pk = (dk )2 + ( f k )2 where dk is the relative change rate of gain of the kth extreme point and f k is the relative change rate of frequency of the kth extreme point. d and f are the gain and frequency of the measured FRA signature, respectively, d and f are the gain and frequency of the reference FRA signature, respectively d − d × 100% (8) dk = d f − f × 100%. (9) fk = f


Fig. 7.

Fig. 6.

Process of fault diagnosis.

The composite indicator Pk of the offset extreme point is typically less than 1 in the analyzed “frequency domain” for most cases. If there exists serious winding deformation, the measured FRA signature is missing or extra within the “frequency domain,” and the recommended composite indicator is 1, shown as Pk = 1.

(10)

The variation of each effective extreme point of the deformed signature compared to that of its fingerprint can be obtained and used for further analysis. IV. FAULT DIAGNOSIS PROCESS The proposed fault diagnosis process is shown in Fig. 6. Both the measured and reference FRA signatures are read in MATLAB software; a binary image regarding the difference between two signatures is constructed; the erosion operation is used to process the binary image; and the effective frequency bands with significant differences between FRA signatures are selected. In the meanwhile, a linear fitting moving average method is adopted to preprocess the initial FRA signatures; the larger burrs are smoothed to decrease the effect of external disturbance. The effective extreme points of two FRA signatures are extracted, and then, the composite indicators of extreme point variation within the effective frequency bands are calculated. The areas of the binary image after erosion are also calculated. Finally, the winding deformation fault analysis is conducted based on the value of the composite indicators and the area of the binary image. The binary image of the FRA signatures is created as follows. Step 1: Construct a matrix with proper rows and columns based on the shape of the FRA signature, where the

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Example of creating a reduced 0-1 matrix.

row represents the gain and the column represents the frequency. This matrix not only covers the deviations of two FRA traces, but also contains the regions of non-FRA data. Step 2: Scan the elements of the first column in the matrix, and analyze the two sets of FRA data for the corresponding frequency point. Set the corresponding positions of the analyzed elements, which are within the gains of the two FRA signatures, to be “1,” and the positions of the analyzed elements outside the gain to be “0.” Step 3: Repeat step 2. Scan the other columns of the matrix from low to high frequency and obtain a discrete binary 0-1 matrix after scanning all elements of the matrix. Fig. 7 introduces a simple example of creating a reduced 0-1 matrix according to the area of a chosen rectangle; the columns of the matrix correspond to the different frequency points, and the rows of the matrix, which contain 0 and 1, correspond to the gain of the chosen area. All “1” elements of the matrix represent the difference between the two FRA signatures. As the fact that the frequency interval of the FRA signature is fixed at 1 kHz, the resolution of the binary image is determined by the scanning interval along the gain axis, which can be adjusted by setting a proper parameter. The choice of the structural element is also significant; adopting different structural elements to explore the targeted image will yield different information from the image [40]. The features of the targeted image itself, including its shape and size, should be considered when a structural element is selected. With regard to the shape, the most frequently used structural elements are rectangular, circular, diamond, and triangle. With regard to the size, considering that the amplitude span of diverse FRA signatures is different, namely the difference between the maximum and minimum gains is different. The size of a structural element should have self-adaptability, namely the size should be large when the amplitude span is large, and vice versa. In this paper, we have assessed large amounts of data and selected the square as the structural element; the side length L is defined as L = 0.001 KM

(11)

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Fig. 8.


Tested model transformer with its tank uncovered.

where M is the difference between the maximum and minimum gains of the two FRA signatures, and K (100) is the enlargement factor of the gain when frequency response data are translated into a binary image. After the binary image is eroded, the frequency bands with small amplitude differences are filtered out. However, there are still some isolated segments with minor areas. These segments can be diminished by being compared to a threshold N; if the area of the segment is larger than N, it will be kept, and vice versa. After the erosion operation and processing of the image are performed, the effective frequency bands with significant amplitude differences are obtained, in which the composite indicator of extreme point variation can be calculated. V. EXPERIMENT AND ANALYSIS A. Introduction of the Experiment This paper also established a test bed for simulating winding deformation faults; the tested transformer is a specially manufactured model transformer with a voltage ratio of 10/0.4 kV, as shown in Fig. 8. The nameplate parameters are provided in the Appendix. The internal configuration of the model transformer is designed as that of a 110-kV power transformer. The HV winding is a disk-type winding with a total of 30 disks, where the upper and lower ten disks are interleaved twist and the middle ten disks are sequential twist. The LV winding is designed as a layer type with six layers. Variable windings were also manufactured, which can be used to replace the middle ten disks winding to emulate diverse winding radial deformation (RD) faults. Typical winding RD, interdisk SC fault, and disk space variation (DSV) fault were simulated, respectively. Fig. 9(a) shows a schematic of winding RD. In the simulated RD fault, d represents the amount of RD, which is variable; θ represents the angle that is fixed at 45°, and the ratio between d and winding radius r is set to 3%, 5%, 7%, and 10% to emulate different degrees of RD produced in one direction. Other RD fault windings are also simulated, where the faults are manufactured in different directions but the ratio of d to r is fixed at 5%, as

Fig. 9. Diagrammatic sketch of winding RD. (a) Diagram and image of RD. (b) RD produced in one direction. (c) RD produced in two directions. (d) RD produced in three directions. (e) RD produced in four directions.

shown in Fig. 9(c)–(e). For the simulated DSV fault, a capacitor is connected to the connectors of two continuous disks [4]. The degree of fault is emulated by increasing and decreasing the capacitance value, and the fault location is emulated by changing the sequence numbers of the two connectors. The interdisk SC fault is simulated by shortening the connectors of the middle sequential twist windings; the more numbers of connectors are shorten, the more severity of interdisk SC fault is emulated. Experiments were performed with different fault statuses of the model transformer; in each status of the transformer, end-toend open-circuit measurement was carried out and a sample database for fault diagnosis was obtained. Various FRA signatures of variable simulated winding deformation are shown in Figs. 10–12. Cases of FRA signatures under simulated interdisk SC fault are presented in Fig. 10, in which “1-2 connector” means that the first and second connectors of the middle sequential twist windings, seen from top to bottom, are SC, and so on. Compared to a healthy signature, signatures of interdisk SC fault are entirely different throughout the entire frequency band. The FRA signatures of the 1-2 connector and 5-6 connector are similar because these two fault cases are artificially manufactured in the symmetrical position of the HV winding. Cases of experimental FRA signatures with simulated RD faults are shown in Fig. 11, in which the middle ten disks healthy


Fig. 10. Some cases of experimental FRA signatures under simulated interdisk SC fault.

Fig. 12. DSV.

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Some cases of experimental FRA signatures under simulated

B. Case Study of an Erosion Operation

Fig. 11. Some cases of experimental FRA signatures under simulated RD fault.

windings are replaced by RD fault winding with degrees of 5%, 7%, and 10%, all in one direction. This figure illustrates that the faulty FRA signature changes in the middle- and high-frequency bands compared to the healthy signature, and the difference of two signatures is particularly remarkable beyond 700 kHz; both the frequency and gain shift for certain extreme points. The overall variation of the faulty winding signature becomes more significant as the fault level increases. Cases of FRA signatures under simulated DSV faults are shown in Fig. 12, in which a capacitor with a different capacitance is paralleled with the third and fourth connectors of the middle windings. 10% indicates the percentage of the paralleled capacitance (200 pF) to the capacitance of the adjacent healthy disk (calculated to be approximately 2 nF based on the finite-element method), with similar meanings for 20%–40%. In Fig. 12, each faulty FRA signature changes notably in the middle- and high-frequency bands; the entire signature shifts toward the low-frequency band, which is significantly different from the effect of the interdisk SC fault. Furthermore, the variations in the faulty signature become more noticeable as the fault level increases.

Fig. 13 shows a case study of an erosion operation. The FRA signatures of healthy winding and simulated RD winding are presented in Fig. 13(a). The deformed signature differs from the healthy signature above 150 kHz, and several extreme points shift. However, the difference between the FRA signatures is highlighted between 250 and 1000 kHz, whereas the difference between 150 and 250 kHz is not significant and can be regarded as the disturbance induced by measurement. Minor differences between the FRA signatures in certain frequency bands can be easily affected and covered by external measurement disturbance. One cannot determine whether the difference is induced by the winding deformation or measurement disturbance; however, in engineering, such a difference is typically regarded as the result of external disturbance to avoid misjudgment of winding failure. The FRA signatures are converted into a binary image, as shown in Fig. 13(b); the area of the binary image below 250 kHz is extremely small. An erosion operation is conducted to process the binary image; the result is presented in Fig. 13(c), and the effective frequency bands (corresponding to significant gain differences between the two FRA signatures) are obtained, as 200–300, 350–500, 600–800, and 830–1000 kHz. The composite indicators of each effective extreme point variation within these frequency bands are then calculated, and the composite indicators outside these frequency bands are directly set to zero. Finally, a vector consisting of composite indicators is obtained for fault diagnosis.

C. Fault Diagnosis and Analysis A total of 42 experiments, including 15 groups of interdisk SC faults, 13 groups of RD faults, and 14 groups of DSV, were conducted. The erosion operation was used to process the faulty and healthy FRA signatures. The sum of vectors consisting of composite indicators within 1–1000 kHz was calculated to characterize the winding fault

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TABLE I THRESHOLD INTERVAL OF COMPOSITE INDICATORS FOR DIAGNOSING FAULT LEVEL Diagnosis Result (Fault Level)

Threshold Interval (P)

Healthy Minor Significant Catastrophic

P RLF ≥ 1.0 or 0.6 ≤ RMF < 1.0 1.0 > RLF ≥ 0.6 or RMF < 0.6 RLF < 0.6

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CC (R)

Composite Indicator (P)

LF

MF

HF

1–1000 kHz

1-2 SC

0.2076

0.1784

5% RD

2.2455

10% RD

2.8106

2.5% DSV

2.1599

30% DSV

2.4016

1.0327 obvious 3.1565 normal 2.1008 normal 1.6310 not estimated 0.0640 moderate

7.3032 significant 2.2747 minor 3.2786 minor 2.4957 minor 6.5619 significant

0.9923 0.7688 0.0458 −0.0831

the diagnostic result for 10% RD obtained with the proposed method is not considerably more accurate, it is more precise than the result obtained by the CC indicator. For 2.5% DSV, the diagnostic result cannot even be estimated by the CC according to the threshold interval of Table II, whereas the proposed method yields a reasonable result. E. Discussion

1 N

· Yi − X i i=1 Dx D y

N

1 N

N

and Dx and D y are defined as

N N 1 1 Dx = Xi 2 Xi − N i=1 N i=1

N N 1 1 Dy = Yi 2 . Yi − N i=1 N i=1

i=1 Yi

(16)

(17)

(18)

Table II provides the threshold intervals of the CC suggested by the Chinese standard for diagnosing fault levels. This section compares the diagnostic result of the proposed method with CC method for five cases of experimental tests. Considering that any form of interdisk SC fault must be significant or catastrophic failure, only one case of SC fault (1-2 connector) is incorporated. For RD fault, the middle ten disks radial deformed in one direction with degrees of 5% and 10% are analyzed. For the simulated DSV fault, two cases of 2.5% and 30% capacitance percentage (fault produced between the third and fourth connectors) are considered. The CC and composite indicator of the above experimental cases and diagnostic results using the suggested threshold interval are shown in Table III. Both 1-2 interdisk SC and 30% DSV present similar and correct diagnostic results. However, for 5% RD and 10% RD, two windings are diagnosed as normal status by the CC indicator, which are not reasonable. Correspondingly, the two composite indicators are 2.2747 and 3.2786, respectively. These indicators are estimated as minor status. Although

There are also drawbacks regarding the above experiment analysis and more experiments should be performed in the future. 1) The threshold P suggested by this paper is based on the statistical results of experimental tests on the model transformer; this threshold value may be dependent for other transformers of different types, structures, and voltage ratings. However, the proposed method is still serviceable. Further work must be performed to quantify the thresholds of other power transformers based on their failure history and statistical analysis to obtain a more general and universal threshold. 2) A ternary diagram of the frequency response image is constructed based on the experienced division standard of the frequency spectrum, in which the division is typically used to distinguish winding fault types in the field. Due to the limitations of the test condition, this paper did not present other experiments. Other typical winding deformation faults, such as axial displacement, interturn SC, could cause confusion in the ternary diagram because of overlapping areas. However, several primary winding failure types can be still distinguished because of their significant diversity in nature; more works are needed to obtain a detailed categorization. VI. CONCLUSION A developing procedure that facilitates the improvement in FRA based on binary morphology and extreme point variation has been presented. The erosion operation of binary morphology has been introduced to eliminate minor differences between the measured and reference FRA signatures and extract the effective frequency bands for further fault diagnosis. A composite indicator of extreme point variation in the effective frequency bands has

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been proposed and integrated to investigate the winding fault level. Forty-two groups of simulated fault experiments, including RD, interdisk SC, and DSV, have been analyzed to obtain the threshold interval of the composite indicator. Meanwhile, an area proportion vector of binary image has been proposed to construct a ternary diagram; faults of the same type exhibit similarity and clustering features. It has been demonstrated that the proposed method has reached the potential to characterize the extent of winding faults and classify the types of winding faults. Additionally, comparison of the proposed method with the Chinese standard indicates the potential of the proposed method. APPENDIX TABLE IV NAMEPLATE PARAMETERS OF THE MODEL TRANSFORMER Transformer template

Value

Transformer Power Phases Transformer ratio Vector group Working frequency Model series number

400 kVA 3 10000 V/400 V YNyn0 50 Hz M-400-2000/10

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Zhongyong Zhao was born in Guangyuan, Sichuan, China. He received the B.S. and Ph.D. degrees in electrical engineering from Chongqing University, Chongqing, China, in 2011 and 2017, respectively. He received a scholarship from China Scholarship Council to enable him to attend a joint-training Ph.D. program at Curtin University, Perth, W.A., Australia, in 2015–2016. He is currently a Lecturer with the College of Engineering and Technology, Southwest University, Chongqing. His research interests include condition monitoring and fault diagnosing for HV apparatus, and pulsed power technology.

Chenguo Yao (M’08) was born in Nanchong, Sichuan, China. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Chongqing University, Chongqing, China, in 1997, 2000, and 2003, respectively. He became a Professor with the School of Electrical Engineering, Chongqing University, in 2007. His current works include online monitoring of insulation condition and insulation fault diagnosis for HV apparatus, pulsed power technology and its application in biomedical engineering.

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Chengxiang Li was born in Shandong, China. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Chongqing University, Chongqing, China, in 2002, 2005, and 2011, respectively. He is currently an Associate Professor with the School of Electrical Engineering, Chongqing University. His research interests include pulse power technology and its application in biomedical engineering, and online monitoring of insulation condition for HV apparatus.

Syed Islam (M’83–SM’93) received the B.Sc. degree in electrical engineering from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 1979, and the M.Sc. and Ph.D. degrees in electrical power engineering from the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, in 1983, and 1988 respectively. He is currently the John Curtin Distinguished Professor in Electrical Power Engineering and the Director of the Centre for Smart Grid and Sustainable Power Systems, Curtin University, Perth, W.A., Australia. He is also the Dean International for the Faculty of Science and Engineering, Curtin University. He has been a Visiting Professor with Shanghai University of Electrical Power, Shanghai, China. He has published more than 300 technical papers in his area of expertize. He has been a keynote speaker and invited speaker at many international workshops and conferences. His research interests include condition monitoring of transformers, wind energy conversion, and smart power systems. Prof. Islam is a Member of the steering committee of the Australian Power Institute and a Member of the WA EESA board. He is a Fellow of the Engineers Australia, a Senior Member of the IEEE IAS, the PES, and the DEIS, a Fellow of the IET, and a Chartered Engineer in the United Kingdom. He is a Founding Editor of the IEEE TRANSACTION ON SUSTAINABLE ENERGY and an Associate Editor of the IET Renewable Power Generation. He was the Guest Editor in Chief for the IEEE TRANSACTION ON SUSTAINABLE ENERGY special issue on Variable Power Generation Integration into Grid. He received the Dean’s medallion for research at Curtin University in 1999. He received the IEEE T Burke Haye’s Faculty Recognition award in 2000. He received the Curtin University inaugural award for Research Development in 2012. He received the Sir John Madsen medal for best electrical engineering paper in Australia in 2011 and 2014, respectively.