1. Introduction
Power transformers provide indispensable services for the transmission and distribution of electrical power. Failures of in-service power transformers not only impair the system’s performance, but also have a serious social impact because of unscheduled outages of the electricity supply [
1,
2]. Consequently, advanced diagnostic methods for detecting transformer faults are becoming vitally important for maintenance work.
Many monitoring and diagnostic technologies have been developed to address the problems in transformers. Online monitoring technologies can provide real-time information of the power equipment’s state [
3]. Nowadays, the key operation parameters of power transformers such as terminal voltage, current, ampere turns, and temperature are usually monitored continuously. These monitoring data are used in the transformer protection zone for real-time state estimation [
4,
5]. Besides, there is a growing trend to develop the dissolved gas analysis (DGA) as an online monitoring measurement for detecting the incipient fault of power transformers [
6,
7]. Several intelligent machine learning approaches, such as genetic algorithm, the neuro-fuzzy inference system, and vector support machine have been used to analyze the DGA results [
6,
7]. However, some types of internal faults of power transformers are undetectable by these online monitoring and diagnostic methods. According to a statement in [
8], statistics show that 70% to 80% of failure regarding power transformers are caused by undetected winding faults. Commonly used approaches for detecting incipient winding faults are usually offline tests, such as the short-circuit impedance measurement (SCI) [
9], low-voltage impulse tests (LVI) [
10], and frequency response analysis (FRA) [
11,
12,
13,
14,
15].
Among the existing test approaches, FRA is a well-recognized technique for diagnosing incipient winding faults in power transformers [
11,
12,
13,
14,
15]. Depending on the types of injected signals, there are two major types of FRA, which are the sweep frequency response analysis (SFRA) and impulse frequency response analysis (IFRA) [
8]. The injected signal of SFRA is a sinuous wave, and the response signal is measured in the frequency domain. For IFRA, an impulse wave with a wideband frequency spectrum is injected as the input, and the output is measured in the time domain. Then, the frequency response (FR) is derived by converting the results to a frequency domain [
16]. Based on the comparing the studies in [
8,
15], the results and sensitivities of SFRA and IFRA are similar for detecting faults in the short circuit. However, in some literature [
17], it states that IFRA could encounter drawbacks of low resolution in low frequencies. In recent years, online FRA has been studied by some researchers [
18,
19], and online FRA measurements in the low-frequency range has been found to be easily affected by external disturbances. This online technology has not been applied in real in-service power transformers and is also not widely accepted by the industry. Because the analysis in this paper is based on offline SFRA, for convenience of description, the FRA mentioned below represents SFRA.
The faults (or ‘failure modes’) of windings are typically caused by a mechanical change or electrical change inside the transformer. Mechanical changes, including radial bulking, axial displacement, tilting, and hoop tension arise for many reasons, such as electromagnetic force induced by a short-circuit current, improper transportation, and damage from a natural outside force [
20,
21,
22,
23]. This type of fault in transformer winding is difficult to perceive because of the imperceptible impact on the normal operation of power transformers. Electrical changes, such as short-circuited turns (SCT) and open-circuited turns (OCT), are typically caused by aging of the insulation layer and the explosion of combustible gas in oil [
24]. SCT and OCT lead to different deteriorative consequences, and the FRA results of these two types of faults can be used to confirm the results of other diagnostic tests, such as direct-current winding resistance. These failure modes are not necessarily a real failure, but they degrade the ability to withstand short-circuit current and overvoltage, thereby eventually leading to solid failure. Thus, as an outstanding technique for the diagnosis of windings, academic institutions have recommended that the offline FRA test is performed on new transformers and as a standard procedure of subsequent routine tests [
12,
24].
However, FR diagnosis requires engineers to have experiential knowledge of the FRA test [
12,
24]. With regard to this, most recent FRA measurement instruments typically contain computer-aided software to automatically diagnose the transformer conditions [
10]. The software uses a certain index to quantitatively analyze the FRA results. A variety of indices have been proposed for quantitative FRA interpretation, such as the correlation coefficient (CC), spectrum deviation (σ or SD), and absolute sum of logarithmic error (ASLE) [
23,
24,
25,
26,
27,
28,
29]. However, the sensitivity of each index differs with respect to different morphological characteristics of the deviation between two FR curves over the entire spectrum. For instance, CC is insensitive to the vertical displacement of curves. Because of a lack of effective methods to automatically identify types of transformer winding faults, the quantitative interpretation methods adopted in modern FRA measurement instruments only provide information on the severity of deformation at the current stage [
30]. Despite this, identifying different faults that result in different consequences does not only provide information on preventive actions, but also supports a united diagnosis with other diagnostic tests. Therefore, the purpose of this paper is to propose a new automatic approach to identify three types of typical incipient winding faults (i.e., mechanical deformation (MD), SCT, and OCT) that require different further preventive and inspective actions.
Moreover, the indices involved in the typical quantitative methods are calculated either in the entire frequency range or by using fixed frequency sub-bands. In the mechanism research of FRA, the effects of different electrical parameters of power-transformer-equivalent circuits are perceptible in different frequency sub-bands [
21,
22,
31]. As stated in [
24], the described frequency regions are typical but not exact, and they vary slightly depending on the transformer’s design and arrangement. Hence, dynamically identifying the frequency sub-bands for every specific type of winding can provide a stronger connection between the quantitative results and the affected electrical parameters, thereby assisting the development of better interpretation tools for automatic diagnosis. Several methods that adapt frequency sub-bands for a specific winding have been proposed based on the zero crossing points in the phase plot of the FR [
32,
33]. However, according to a newly published discussion on the IEEE standard (C57.149-2012 [
24]), the theory of the relations between the resonance and phase zero points claimed in [
24] was misconstrued [
34]. It claimed that, at resonance, the input impedance is not purely resistive and the phase angle between the input voltage and current is not always zero. Inevitably, the dynamic methods of dividing frequency sub-bands according to the doubtful theoretical basis in [
32,
33,
35] are problematic. An improved approach, according to binary erosion and first anti-resonance, is adopted in this paper to divide the frequency sub-band dynamically. A similar method was proposed and validated in the authors’ previous research [
36].
The remainder of the paper is organized as follows: To normalize FR curves measured from different types of power transformers, image processing technologies, including image binarization and binary erosion, are introduced and used in
Section 2 as a preprocessing procedure. In
Section 3, an approach is presented for the dynamic division of frequency sub-bands on the basis of the five suggested sub-bands. In
Section 4, the experimental setup and data preparation are explained. In the following section, a new classifier, that is, the hierarchical dimension reduction (HDR) classifier, is proposed based on hybrid indices, including CC, SD, and two new types of indices. The purpose of this classifier is to identify three typical types of incipient winding faults that require different further preventive and inspective actions. Finally, in
Section 5, real case studies are investigated to demonstrate the performance of the HDR classifier, followed by a conclusions section.
3. Dynamic Division of Frequency Sub-Bands
Relevant international standards recommend that the frequency range of the FRA test shall be 20 Hz to 2 MHz, at the least [
33]. As mentioned previously, calculating indices in divided frequency regions can increase sensitivity to winding faults, because the effects of the equivalent electrical parameters are reflected in different frequency bands. A generalized sub-band structure of frequency boundaries is illustrated in
Figure 3. Another fact is that the patterns of FR to each specific transformer can vary according to its design and interconnections [
11]. The characterization of typical FR patterns was conducted in [
11], demonstrating that the boundaries of frequency sub-bands cannot be found explicitly. To adapt the frequency sub-bands to each specific FR, an improved and uncomplicated approach is adopted in this section. This approach is based on the sub-band structure and careful analysis of the FR patterns of multiform transformers. The algorithms illustrated in
Figure 4 provide the procedure that divides the frequency range into five sub-bands specifically for each case of FR curves. The explanation of the procedure is listed in detail as follows.
In LF1 shown as
Figure 3, the key feature of the FR curves is that they typically begin with an almost linearly decreasing magnitude of 20 dB/decade because of the magnetizing inductance (
Lm) of the core [
24]. For some connection configurations, they are typically smooth and dominated by the total inductance. This is then followed by a minimum, which is the key feature in sub-band LF2. This minimum resonance, marked as
Zm, occurs because of the series resonance between
Lm and shunt capacitance (
Cg). Hence, the boundaries B and C should satisfy the conditions that the potential linear part is located in LF1, and the minimum remains in LF2. Through the analysis of a variety of FR curves, the boundaries B and C can be determined using the left flowchart illustrated in
Figure 4. The essential strategy is to locate the minimum point
Zm. Typically,
Zm is the minimum point of the entire curve, but for some middle-voltage (MV) or low-voltage (LV) windings, drastic oscillations can occur at high frequencies. To eliminate the errors caused by these points, only the first three valleys are compared, without counting the valleys at comparatively higher frequencies according to the experience of FR patterns of power transformers. After locating
Zm, the peak next to point
Zm (marked as
Pm) can be located to define the upper boundary of LF2. Thus, following the algorithms in the left flowchart, the boundaries A, B, and C are defined.
The FR patterns in middle frequency (MF) sub-band typically present multiple oscillations in this range. The subsequent high-frequency (HF1) spectrum is often known to have a rising trend with damped oscillations typically because of high series capacitance (Cs) compared with Cg. However, for MV or LV windings, Cs is not required to be much higher than Cg in design. The FR patterns of these types of windings in HF1 do not demonstrate a capacitive rising trend. Consequently, boundaries D and E are difficult to determine. For this reason, a compromise between the representation of more general FR patterns and dynamic features for each specific case is reached to determine the boundaries D and E in this strategy.
The definition of boundaries D and E is based on the typical fixed values (illustrated in
Figure 3) and information in the retained segments after erosion. This procedure attempts to avoid the separation of a continuous white area near the fixed frequency boundaries D and E, because in most cases, deviations in the nearby areas in the FR patterns typically arise from a chain effect of the same electrical component. If the section with these deviations is separated into two sub-bands, then the sensitivity of the calculated statistical indices could be adversely affected. The strategic algorithms to identify D and E are shown by the flowchart on the right in
Figure 4, where
k is the abscissa of the pixel. The corresponding frequency value
f(k) can be derived using Equation (2). The basic idea is to search for a break column, where all the pixels in this column are black from right to left in a predefined range of frequencies around the fixed boundary.
To summarize, the algorithms illustrated in
Figure 4 provide a method that divides the frequency range into five sub-bands specifically for each case of FR. This method is based on the authors’ previous work in [
36], with a slight improvement. The performance of this approach was proven in [
36], so it will not be repeated in this article.
6. Validation and Discussion
To validate the HDR classifier, the proposed HDR classifier was further verified by five real FR cases. Two cases are discussed below.
Case 1: The FR curves of Case 1 were collected from the routine tests of a 240 MVA power transformer in a 220 kV substation in Guangzhou. According to the visual diagnosis conducted by experts, the result shows no fault in the tested windings. Because the two measurements were taken in different phases of the MV winding, the FR curves show deviation in the low-frequency range. In other words, the FRA result of this transformer winding deduces its healthy but different magnetism condition.
Figure 11a shows the FR curves with boundaries of frequency sub-bands, and
Figure 11b illustrates its eroded binary image.
From
Figure 11, it can be seen that the deviation is located in LF1 and LF2. The diagnosis result using the HDR classifier is shown is
Table 3. FLAG_MF, FLAG_HF1, and FLAG_HF2 all equal to 1, which means there is no noticeable deviation. FLAG_LF1 = 01 represents downward displacement in LF1, and FLAG_LF2 = 0 represents noticeable deviation in LF2. The diagnosed class of Case 1 is ‘A&B’, which means a healthy condition in a different magnetism. This result coincides with the visual diagnosis. Moreover, the relation coefficient (
Rxy) stated in the Chinese Standard [
25] was also applied to diagnose the FR curves, and its result is illustrated in
Table 3. This diagnosed result using
Rxy shows the tested winding is normal. The results are consistent, but a more detailed condition was given by using the HDR classifier.
Case 2: The FR curves used in this case are reprinted from [
11]. The data were collected from a 140 MVA, 220/69 kV autotransformer. According to [
11], the abnormality of the FR curves was caused by SCT.
Figure 12 shows parts of images obtained from the implementation of the HDR classifier, and
Table 4 illustrates the diagnosed results using the HDR and
Rxy, respectively. The final class of Case 2 is ‘C’, which represents SCT. It matches with the known condition. The diagnosed result using
Rxy also shows that a slight deformation of fault occurs in the tested winding, but the fault type cannot be revealed by using this common method.
The failure mode in this case mainly affects the Lm and winding resistance, so the most visible effect exists in LF1 and LF2. The effect of DMC is also located in these sub-bands. The identification between these two cases depends on the proposed indices, ARI and AD. Therefore, the result also verifies the performance of ARI and AD.
It can be summarized from the above cases that the HDR classifier has the ability to automatically identify the fault types in transformer windings. However, there are also drawbacks of this approach. (1) Due to lack of training data that covers all possible abnormalities in FRA, some abnormalities are not considered in the proposal of the HDR classifier, such as the abnormality caused by the reproducibility issue; (2) the training set is not particularly large. Despite this, the proposed approach is still serviceable. In future works, a larger number of training sets that cover more types of transformer winding faults are expected to be used to refine the threshold values for more classes of conditions. Moreover, the HDR classifier is applicable in potential commercial use. By embedding the HDR classifier into the FRA instruments, an automatic condition assessment of transformers could be realized during FRA measurement.