Interpretation of Frequency Response Analysis for Fault Detection in Power Transformers

Frequency response analysis (FRA) is a method of monitoring a power transformer’s mechanical integrity. However, identifying the type of fault and its severity by comparing measured responses is still challenging and mostly relies on personnel expertise. This paper is taking one step forward to standardize the FRA interpretation process by proposing guidelines based on various international standards and FRA case studies. In this study, the FRA signature is divided into three regions: low-, midand high-frequency regions. The deviation from the fingerprint signature for various faults is classified into small, large, and no variations, based on the calculation of the correlation coefficient. The proposed guidelines are developed based on the frequency regions, and the level of variation is represented using a simple arrow method to simplify the interpretation process. A case study is conducted on a three-phase 11/0.433 kV, 500 kVA distribution transformer with a short circuit winding fault to validate the proposed guidelines.


Introduction
Frequency response analysis (FRA) is the most reliable diagnostic tool for detecting winding and core deformation in power transformers [1]. Such deformations affect the equivalent, inductive, and capacitive components of the transformer, thereby altering its frequency response. Currently, an expert is required to analyze the obtained results, which makes the interpretation process inconsistent and reliant more on personnel expertise than standardized guidelines. Essentially, FRA is a comparative technique that requires a reference signature (fingerprint) with which future signatures are compared, to identify any changes due to various internal faults. In case the reference signature is not available, a comparison with the response of other phases of the same transformer or with the response of an identical transformer (sister unit) is conducted. Although international standards such as the IEEE standard [1], the CIGRE standard [2], the IEC standard [3], and the DL/T 911 standard [4] are available, there are still difficulties in identifying and quantifying transformer winding faults [5]. The other drawback of the FRA technique as a diagnostic tool is that standard procedures do not yet define the measured data.
For identifying and quantifying various transformer faults, numerical indices are used, such as the correlation coefficient (CC). Sum square error (SSE) or mean squared error (MSE), the absolute sum of logarithmic error (ASLE), minimum-maximum ratio (MM), and spectrum deviation (SD) have also been presented in the literature [6][7][8]. The CC can calculate the variation between two FRA traces. If the two responses are identical, the CC is 1; otherwise, it is 0. The CC is sensitive to changes in response resonance and anti-resonance frequencies, and it is widely used for FRA. The SSE can show the deviation between normal and faulty responses. The ASLE is highly recommended in the latest studies and is reported to be more pertinent than the SSE. SD has also been used to detect variation between frequency responses for normal power transformers and winding deformation [9]. Typically, SD shows similar sensitivity to the ASLE.
On the other hand, some methods have been proposed for a more objective interpretation of FRA measurements, as elaborated below.
Past studies adopted a transformer-equivalent high-frequency circuit by representing the winding using resistance, inductance, and capacitance (RLC) ladder circuit [10][11][12], due to the difficulty of staging physical faults on real transformers. The equivalent circuit enables understanding of the changes in response due to specific faults that might otherwise be impossible to reproduce on actual winding. Several transformer faults can be simulated using the equivalent circuit, including short circuit turns, inter-disk deformation, axial displacement, buckling faults, bushing and insulation faults, and clamping pressure loss [13][14][15].
In the mathematical models presented in the literature, the frequency response is modeled as a rational function with actual coefficients. For comparison purposes, the parameters of the model can be indicated, but their sensitivity to various types of faults is not stated [16,17]. The disadvantage of using this numerical method is the time-consuming nature of solving complex mathematical equations [18].
The use of artificial neural networks (ANNs) to identify transformer failure is also reported. Essentially, ANNs are used to estimate transformer parameters over a wide frequency range. ANNs are also used as a complementary technique to statistical indicators to improve the FRA interpretation process's reliability [19,20].
Digital image processing has been used on 2D and 3D FRA plots to extract unique features for each fault type [21]. In [21], a three-dimensional-FRA trace in one plot that includes frequency, magnitude, and phase is presented. Compared to the current interpretation practice, which relies only on the magnitude plot, more features can be extracted from the proposed 2D and 3D FRA signature, hence increasing the accuracy of the FRA classification.
Previous works in [22][23][24] investigate the impact of winding deformation, bushing, and inter-disk faults on the FRA signature. The effects of tap changer variation and the loss of clamping pressure on the FRA signature were also studied in [25][26][27][28][29]. These studies were based on statistical indicators and necessary visual inspection. A comparison between the latest proposed methods for FRA interpretation is given in Table 1.  This paper aims to take a step towards establishing guidelines for FRA interpretation. The proposed guidelines are designed to facilitate an uncomplicated way to identify fault types within power transformers. The proposed guidelines are developed by reviewing major studies and standards for FRA interpretation. The effect of various faults on a transformer FRA signature is categorized into three frequency bands: low, mid, and high. Classification is also categorized into three states: no variation, small variation, and large variation, through CC calculation. Non-expert users can use these guidelines to interpret the measured FRA responses. The proposed guidelines are validated through experimental testing on a three-phase 11/0.433 kV, 500 kVA distribution transformer with a short circuit fault. The step-by-step research progress of the proposed method is shown in Figure 1.

Transformer Frequency Response Analysis
The principal function of the FRA is to detect winding and core deformation. Nowadays, the FRA test is recommended to be performed before and after transportation or relocation, on suspected units, and during regular offline maintenance.
The transformer frequency response is obtained by injecting a low (<20 V) AC input signal, 'V in ', of varying frequency at one terminal of a transformer winding [30]. The output voltage, 'V out ', is measured at the other terminal of the same winding, as shown in Figure 2. The frequency response, usually the transfer function, 'H(f)', of V out to V in , is plotted as phase, 'θ(f)', and magnitude, 'K(f)', in dB, in a frequency range of 2 MHz as given by (1) and (2). The most commonly used plot for analyzing the response is the magnitude plot. FRA test configuration refers to the connection of the frequency response analyzer to the transformer. According to CIGRE WG A2/26 [2], IEEE Std. C57.149-2012 [1], and IEC 60076-18 [3], four different configurations can be used to perform FRA measurement. These are the end-to-end open circuit test, the end-to-end short circuit test, the capacitive inter-winding test, and the inductive inter-winding test.
The end-to-end open circuit configuration is performed by injecting the signal into one end of the winding and measuring the transmitted signal at the other end of the same winding. This configuration is commonly used because it can provide more information regarding the winding and core. An example of a typical frequency response using end-toend open circuit configuration is shown in Figure 3a. On the other hand, in the end-to-end short circuit configuration, the secondary winding of the same phase is shorted to eliminate the influence of the core on the measurement, since the low-frequency response results from the magnetizing inductance of the iron core [25]. The typical frequency response of end-to-end short circuit configuration is shown in Figure 3b.
To interpret the FRA signature, it is necessary to analyze all frequency ranges. The frequency response can be divided into three regions as per IEC 60076-18 [3]: the lowfrequency (LF) region, the mid-frequency (MF) region, and the high-frequency (HF) region, as shown in Figure 4. These responses are from measurements using end-to-end open and short circuit tests. However, there is no general frequency limit specified for each region as this mainly depends on the size and rating of the transformer. In the IEEE std. C57.104 [1], the frequency sub-bands are divided into four regions. The fourth region is for frequencies above 1 MHz, in which the effects of measurement and grounding leads are considerable.
It is crucial to analyze each frequency region because each frequency region is affected by different transformer faults. The core dominates the LF region, the MF region is dominated by the parallel capacitance and mutual inductances, while the HF region is influenced by the winding capacitance [25,31].  Essentially, the frequency response of a transformer can be simulated based on a complex circuit consisting of resistances, inductances, capacitances, and mutual inductances, as shown in Figure 5. Each of the circuit elements is related to the physical geometry of the transformer winding [32,33].
In the transformer-equivalent high-frequency circuit shown in Figure 5, Rs, Cs, and Ls are the winding series resistance, capacitance, and self-inductance, respectively. Cg and Gg are the ground capacitance and conductance that represent the dielectric insulation system. M ij is the mutual inductance. C HL and G HL are the capacitance and conductance between high voltage and low voltage windings.
Any changes in the winding will affect the RLC network, thereby altering the original or baseline frequency response [34]. The simulated frequency response of a simple RLC circuit is shown in Figure 6a. The winding resistance, 'R', contributes to the horizontal line, as shown in Figure 6b. The winding inductance, 'L', influences the negative slope illustrated in Figure 6c, at the low-and mid-frequency regions. The capacitive effect due to winding insulation affects the positive slope, shown in Figure 6d, at the mid-and high-frequency regions.

Fault Extent Methodology
This paper proposes three steps, or phases, for interpreting the FRA measurement, as shown in Figure 7. In phase 1, the response is divided into three frequency regions: the low-frequency region (LF < 2 kHz), the mid-frequency region (2 kHz < MF < 20 kHz) and the high-frequency region (HF > 20 kHz). Phase 2 determines the level of variation between the measured response and the reference signature by calculating the correlation coefficient (CC) that results in three categories. In [35][36][37], three CC limits are suggested to identify the transformer condition. The transformer is considered in good condition for a CC more than 0.98. The transformer health state is considered marginal for a CC in the range (0.96-0.97), and the transformer calls for further investigation for a CC less than or equal to 0.96. These limits are categorized based on the variation between the measured and reference responses, which can be categorized into no variation, small variation, and large variation. The limits or range for the CC variation are given in Table 2.  No variation means that the compared FRA responses are identical with a calculated CC of more than 0.98, as shown in Figure 8a. The small variation refers to cases when the CC ranges between 0.96 and 0.97. For large variation, the difference between the measured and baseline responses results in a CC less than 0.95, as shown in Figure 8b. In phase 3, the fault is estimated based on the CC levels for each frequency region.
Equation (3) is used to calculate CC. The value approaches 0 or 1 when the two responses are uncorrelated or identical, respectively. In Equation (3), n is the number of frequency points, and x(i) and y(i) are the two compared responses.

Proposed Fault Identification Guidelines
The most common transformer faults and their impacts on various frequency bands based on extensive literature studies are listed in Table 3. Only end-to-end open and short circuit tests are considered in the study, as these are the most common essential test configurations as per the IEEE and IEC standards. Each of the faults listed in Table 3 has a distinct effect on the transformer frequency response. For example, core defects show a large variation at the low-frequency region, small variation at the mid-frequency region, and no variation at the high-frequency region.  The proposed flowchart shown in Figure 9 is constructed based on Table 3. This flowchart can be adopted to determine the possible type of fault when comparing the FRA measurements at different frequency regions. The flowchart may indicate an "undefined" condition for certain frequency response variations that have not been recorded previously.  Table 4 provides additional information for FRA interpretation. It shows the change in the frequency response due to various faults. The proposed table describes how each fault type impacts the frequency and magnitude by using a simple arrow, the direction of which indicates the deviation of the measured response compared to the reference FRA signature. Right direction arrows show that the measured response is shifted towards higher frequencies, while left direction arrows indicate a lower frequency movement. On the other hand, up and down arrows indicate an increase and decrease in response magnitude. The severity of variation is identified by the arrow shading degree, as shown in Table 4.

Case Study: Short Circuit Fault
For examining the feasibility of the proposed flowchart in Figure 9, laboratory testing was conducted on an 11/0.433 kV, 500 kVA transformer, as shown in Figure 10. The transformer windings were lifted from the main tank to access the tap changer. A short circuit fault in the winding was then created by shorting tap terminals 2-7 in-phase (R), as shown in Figure 11. A turns ratio test was performed on the transformer before and after applying the fault. The results of the measured V-ratio are presented in Table 5.
The FRA measurement was performed using a commercial frequency response analyzer on the tested winding open-circuit configuration before and after applying the short circuit fault, as shown in Figure 12. The fault causes shifting of the response at the low and mid-frequency regions toward higher frequencies, which is attributed to the reduction in the inductive components due to the shorted turns. Similarly, within the low and midfrequency regions, the magnitude increases due to reduced inductance from the shorted turns. These changes align well with the variations listed in Table 4.
The CC between the FRA signatures for normal and short circuit faults was calculated to quantify the fault severity, and the result is shown in Table 6. Based on the proposed CC margins given in Figure 8 and Table 2, the results show a small variation at the lowfrequency region, large variation in the mid-frequency region, and no variation in the high-frequency region. This is consistent with the short circuit fault identification using the proposed flowchart in Figure 9.

Conclusions
FRA is a reliable tool for the assessment of power transformer mechanical integrity. However, FRA signature interpretation is still challenging due to the lack of easy and straightforward guidelines. This paper proposes an easy-to-use flowchart and characteristic table as a guideline to facilitate the identification and quantification of FRA signatures. The proposed guidelines are achieved according to the following points:

•
The proposed guidelines are established based on the review of previous extensive research presented in the literature, along with various FRA international standards.

•
The flowchart is developed based on three frequency regions and three levels of variations based on CC calculation.

•
The characteristic table is presented graphically with arrows to provide a simple interpretation scheme for an inexperienced user.

•
An experimental case study conducted on an 11/0.433 kV 500 kVA transformer with normal and short circuit faults is presented to verify the feasibility of the proposed guidelines.
Experimental results show that the variations within the three frequency regions of the measured response are consistent with the proposed guidelines. The proposed FRA guidelines can be used to identify approximately twenty-two transformer faults and conditions. Further feasibility studies should be conducted to investigate the accuracy of using the proposed method in practical case studies. Additionally, proposed guidelines should be analyzed and tested on different power transformers of various ratings and winding configurations. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data presented in this study are available in this article.