Frequency Response Analysis Data Research Articles

Transformer winding faults diagnosis using the transfer function of its high-frequency lumped equivalent model from the measured FRA data

The frequency response analysis (FRA) of the transformer is the data obtained in a wide frequency range that represents the transfer function (TF) that reflects the physical behavior of its coil. However, it can be considered one of the best tools for a better understanding of the electromagnetic characteristics of the winding. This article proposes the TF as a tool to locate and assess transformer winding failures. So, an autonomous algorithm has been developed to construct the TF in ‘s domain’ proposed in previous research. The TF has been determined from experimental measured FRA data from an isolated air-core winding, where the TF has been calculated for the axial defects (AD) realized on the winding discs. Besides, the diagnostic approach is based on the scaling factor (K) and the real zero (τ) of the TF that can be obtained from the measured equivalent capacitance, equivalent inductance, and the DC resistance of the winding in high and low-frequency ranges. However, the K, τ, and the slope of the equivalent inductance characteristics as a function of the winding defects degree have been used for locating and assessing the severity of the winding faults.

Derivation of transformer winding equivalent circuit by employing the transfer function obtained from frequency response analysis data

AbstractPrecisely interpreting frequency response analysis (FRA) curves is crucial when investigating mechanical malfunctions in power transformer windings (TWs). However, many conventional explanations of FRA features cannot be validated by an equivalent circuit (EC) that represents winding structures using resistance, inductance, and capacitance components in a ladder network. Incorrect interpretation can lead to misdiagnosis and confusion in asset management. Previous ECs are often proposed by analysing winding structures without rigorous verification compared to the corresponding FRA data. The specific EC is acquired using the transfer function (TF) derived from the measured FRA data. This allows for the establishment of the relationship between TW FRA curves, TF equations, and EC topologies. The precise interpretation of FRA curves can be achieved by closely observing the FRA curves created from TFs and ECs. The remarkable similarity between the measured and modelled FRA curves verifies the authenticity of the derived ECs. This significant achievement clarifies many misunderstandings regarding FRA and represents a substantial advancement in FRA technology.

Application of generative AI-based data augmentation technique in transformer winding deformation fault diagnosis

Accurately diagnosing various winding deformation faults is significant in power transformer maintenance. Among the different fault diagnosis methods, frequency response analysis (FRA) is widely used but still poses challenges. Artificial intelligence (AI)-based methods have recently been proposed to interpret FRA data. Nevertheless, these approaches are either complicated or exhibit limited generalization performance due to real-world FRA fault data scarcity. Inspired by AI-generated content (AIGC), this study proposes a data augmentation technique named conditional Wasserstein generative adversarial network with gradient penalty (Conditional-WGAN-GP) combined with fault diagnosis model. Numerous FRA-based data are automatically generated using the proposed data augmentation technique based on real FRA data obtained from a specially designed 10 kV transformer. The augmented dataset is then used to train fault diagnosis models to detect winding deformation faults. The trained fault diagnosis model is subsequently applied to assess two actual transformers. Experimental results demonstrate that when combined with the proposed method, even simpler fault diagnosis models can achieve high accuracy, exhibiting an improvement of approximately 5 % compared to the previous baseline model. The fault diagnosis models combined with the proposed data augmentation technique demonstrate improved generalization and robustness. (GitHub code: https://github.com/cy1034429432/Diagnosing-Transformer-Winding-Deformation-Fault-Types-from-FRA-Based-on-Conditional-WGAN-GP-/tree/main).

Diagnosis method of transformer winding mechanical deformation fault based on sliding correlation of FRA and series transfer learning

Frequency response analysis (FRA) is a common method for diagnosing transformer winding faults. There are many ways to interpret FRA, however, extracting fault features from FRA still faces challenges because the FRA signature of each transformer is different, which can make the generalization of FRA diagnosis difficult. Based on this, this paper proposes a diagnosis method based on FRA sliding correlation and series transfer learning. The study collected FRA data from three transformers, two obtained through simulation, while the third obtained through experiment. During the simulation, the synthetic minority over-sampling technique (smote) algorithm was used to expand the data set to solve the problem of unbalanced and insufficient data sets for different fault types. The FRA signature was processed by sliding correlation to extract fault features, and the FRA sequence data was transformed into a heat map with correlation coefficient values distinguished by color. Next, the AlexNet network was transferred twice using the simulation data, and the experimental data was used for the third transfer learning. The experimental results showed that the diagnosis method has high accuracy and strong generalization.

Characterizing transformer HV–LV winding FRA curves through derivation of transfer functions from FRA data

Mechanical malfunctions pose a significant threat to the reliability of power transformers. Frequency Response Analysis (FRA) of transformer windings (TWs) serves as a predictive technology, allowing the assessment of mechanical conditions based on collected FRA data. Changes in the winding structure manifest in FRA characteristics, making it possible to detect incipient faults. This paper presents the derivation of transfer functions (TF) equations through processing FRA data, aiming to investigate and interpret the characteristics of TWs. The derived TFs are utilized to mathematically describe FRA curves, enabling the characterization of winding structures by observing the FRA curves generated from these TF equations. Not only do the derived TFs yield very similar FRA curves, but the TF estimation also provides valuable insights for assessing TW malfunctions. The similarity analysis, using calculated RMSE and MAE values of 0.4807 and 0.2020, respectively, demonstrates a strong correlation between the derived TF curves and the measured FRA curves. This affirms the validity of TF estimation and underscores its significant impact on the advancement of FRA technology.

A confidence level estimation technique for reliable Data-Driven FRA interpretation in air-core winding faults

Frequency response analysis (FRA) data interpretation is among highly challenging tasks in transformer fault diagnosis. Among different quantitative methods, employing statistical indicators on FRA results for mechanical integrity assessment is well-stablished. However, the boundary values of indices that differentiate normal/healthy, suspicious, and abnormal transformer operating conditions are not yet agreed upon. This will make the FRA data interpretation using SIs subjective and unreliable. In this study, data-driven critical boundaries of the most frequently used SIs are introduced. To address the uncertainty of the decision boundaries, a confidence level estimation technique is developed to quantify the probability of a transformer being in a particular operating condition. Reporting a confidence level along with the classified conditions facilitates objective decision-making that can support utility operators during on-site transformer evaluation. The confidence level estimation technique proposed in this work was inspired by bolstered error estimation method widely applied in pattern recognition. Moreover, this study provides a new comprehensive technique of transformer winding fault modeling using SPICE netlists. The proposed analytical winding model is validated through practical FRA measurements with high precision. It is further used to generate various scenarios of common active part faults, such as disk space variation, radial displacement, and disk tilting. Consequently, the proposed method of confidence level estimation is examined on different winding deformations and demonstrated a high potential for comprehensive transformer winding diagnosis.

A Novel Approach to Assess Power Transformer Winding Conditions Using Regression Analysis and Frequency Response Measurements

A frequency response analysis (FRA) is a well-known technique for evaluating the mechanical stability of a power transformer’s active part components. FRA’s measuring practices have been industrialised and are codified in IEEE and IEC standards. However, because there is no valid coding in the standard, the interpretation of FRA data is still far from being a widely acknowledged and authoritative approach. This study proposes an innovative fault segmentation and localisation technique based on FRA data. The algorithm is based on regression analysis to estimate the repeatability and relationship between the FRA fingerprint and the latest measured data. Initially, the measuring frequency is discretised into three regions to narrow the location of the fault; the regression model of the fingerprint and current FRA data are then evaluated. As a benchmark, two statistical indicators are the employed benchmark against the proposed method. Finally, the proposed scheme identifies and characterises various transformer conditions, such as healthy windings, axial and radial winding deformations, core deformation and electrical faults. The database used in this study consists of FRA measurements from 70 mineral-oil-immersed power transformers of different designs, ratings and manufacturers that were physically inspected for various faults and comparable frequency regions. The results achieved corroborate the efficacy of the proposed regression analysis fault recognition algorithm (RAFRA) model for transformer fault diagnosis using FRA. Further recommendations are made to address the reproducibility concerns induced by multiple FRA testing conditions.

A Bootstrapping Solution for Effective Interpretation of Transformer Winding Frequency Response

The current interpretation procedure for the transformer frequency response analysis (FRA) is practically based on either subjective visual inspection or an observed value of a statistical indicator (SIn) programed in commercial software. However, both solutions are unable to provide very detailed information on transformer conditions in the industry. The former approach highly depends on the experience of the technical personnel, while the latter suffers from uncertainties of SIn-based decision boundaries for classification. This study has specifically focused and introduced a new comprehensive FRA data interpretation and classification method. Evaluation of the proposed technique is performed by emulation of winding short-circuit faults in transformers via a parallel connected rheostat. The method is able to categorize the operational mode of the transformer into the normal, suspicious, and critical classes based on the cumulative effect of 12 frequently used SIns and then provide a confidence level (CL) associated with classification to support operators for making a precise decision. Bootstrap sampling technique is introduced for the first time in FRA data evaluation to simulate the effect of many experiments <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in silico</i> and overcome the difficulty of limited available measured data. Particularly, in a novel approach, a large set of SIn-specific decision boundaries is established by bootstrap sampling of the real experimentally obtained boundaries. In addition, a new transformer condition assessment method that employs the cumulative effect of individual SIns is developed and examined. Classification results and the CLs in FRA evaluation have a substantial practical significance and will support on-site utility managers or engineers for further diagnosis and maintenance.

Confidence Level Estimation for Advanced Decision-Making in Transformer Short-circuit Fault Diagnosis

Frequency response analysis (FRA) is almost certainly the most efficient and well-established method for evaluating the mechanical integrity of transformer active part. FRA has a solid background in both industrial practice and academic research. Besides conventional visual analysis, a statistical analysis has been applied to the FRA data interpretation. The existing standards and recent studies have considered different statistical indicators (SIs) on an individual basis. However, the utility of each SI in its &#x201C;silo&#x201D; may lead to different and possibly contradictory decisions. Inspired by the bolstered error estimation technique used in pattern recognition, this article presents a new method that can utilize multiple SIs obtained from the FRA data to classify transformer operating conditions and estimate the level of confidence in decisions made. The probabilistic method proposed herein is an attempt to bridge the gap between these decision-making silos. The practical implementation of the proposed technique on distribution and power transformers revealed a reliable interpretation and classification results. At the same time, having an estimate for the level of confidence in the decision made by the method further helps engineers and utility operators make informed decisions and have a better understanding of the level of the transformer fault severity.

A Machine-Learning Approach to Identify the Influence of Temperature on FRA Measurements

Frequency response analysis (FRA) is a powerful and widely used tool for condition assessment in power transformers. However, interpretation schemes are still challenging. Studies show that FRA data can be influenced by parameters other than winding deformation, including temperature. In this study, a machine-learning approach with temperature as an input attribute was used to objectively identify faults in FRA traces. To the best knowledge of the authors, this has not been reported in the literature. A single-phase transformer model was specifically designed and fabricated for use as a test object for the study. The model is unique in that it allows the non-destructive interchange of healthy and distorted winding sections and, hence, reproducible and repeatable FRA measurements. FRA measurements taken at temperatures ranging from −40 °C to 40 °C were used first to describe the impact of temperature on FRA traces and then to test the ability of the machine learning algorithms to discriminate between fault conditions and temperature variation. The results show that when temperature is not considered in the training dataset, the algorithm may misclassify healthy measurements, taken at different temperatures, as mechanical or electrical faults. However, once the influence of temperature was considered in the training set, the performance of the classifier as studied was restored. The results indicate the feasibility of using the proposed approach to prevent misclassification based on temperature changes.

Interpretation of transformer winding deformation fault by the spectral clustering of FRA signature

Frequency response analysis (FRA) has been accepted as a widely used tool for the power industry. The interpretation of FRA can be achieved by the conventional mathematical indicators-based method, which is mostly used in the past. The newly developing artificial intelligence (AI)-based method also provides an alternative interpretation. However, in most reported AI techniques, the features of FRA signatures are directly input into the AI model to obtain the classification results. Few studies have concentrated on the separability of winding deformation faults. In this context, a spectral clustering algorithm is studied to aid in FRA interpretation. The electrical model simulation and experimental tests are performed. The FRA data processing results verify the feasibility, effectiveness and superiority of the proposed method.

Transformer winding type recognition based on FRA data and a support vector machine model

Frequency response analysis (FRA) is regarded as the most effective technique to detect mechanical faults of transformers. Over the years, FRA measurement data have been collected by utilities into transformer asset databases. The characteristic of FRA data is fundamentally determined by the transformer's equivalent electrical circuit, which consists of inductance and capacitance parameters that are windings' design and structure dependent. Different winding types tend to have different FRA characteristics, and a transformer's design information such as winding type, dimension etc. is often not known to the utility but critically important for asset management. This study reviews the state-of-the-art transformer FRA databases and application of machine learning techniques in this field, and proposes to apply a support vector machine (SVM) model onto the FRA data to identify the winding type. The SVM model is first trained by FRA traces of transformers with known winding types, and after testing, the SVM model is then applied to FRA traces with unknown winding information. A set of data from the UK's National Grid FRA database, was used to demonstrate and verify the SVM model. All transformers used in this study are 400/275/13 kV transmission transformers, which were designed using four different winding types, namely multiple layer, plain disc, interleaved disc and single helical windings. The proposed method can successfully identify the correct winding type.

A New Diagnostic Technique for Reliable Decision-Making on Transformer FRA Data in Interturn Short-Circuit Condition

Interpreting results of a transformer frequency response analysis (FRA) is quite challenging. One of the common methods to summarize FRA data is to employ statistical indicators (SIs) over FRA spectra. However, SI-specific boundary conditions for various operational modes of transformers are left unexplored. The lack of such boundary conditions renders interpretation of SIs difficult and subjective. In this article, in an attempt to find data-driven boundary conditions, first the conventional measurement setup of FRA technique is modified to emulate interturn winding short-circuit. Then, the boundary conditions of various SIs for normal, suspicious, and critical operational modes of transformers under fault are obtained. Nevertheless, the price of moving subjective boundaries to their objective data-driven counterparts is paid in an intrinsic uncertainty introduced by the process of data collection per se. In order to capture and quantify this uncertainty, a novel solution inspired by bolstered error estimation used in pattern recognition is proposed. In particular, the proposed method allows reporting the level of confidence that an observed magnitude of SI belongs to a specific operational mode. Having this confidence level is also warranted from an operational perspective because it enables utility operators to enhance the decision-making process and estimate the severity of transformer faulty conditions.

The actual measurement and analysis of transformer winding deformation fault degrees by FRA using mathematical indicators

Since the power transformers are indispensable in power systems, their reliable operation are of significance. Winding deformation is one of the most common failures within transformers. At present, many methodologies have been proposed to detect these faults, and frequency response analysis (FRA) technique is most frequently used because of its low cost, convenience, simplicity and effectiveness. However, there is no standard and reliable code to interpret the mechanical deformations from FRA traces as so far. In this study, an actual transformer experimental platform was used to simulate variable winding deformation faults in order to standardize the interpretation of winding fault degree from FRA data. The measured FRA raw data are processed from the perspective of statistics, and some numerical indices are found to be more suitable for the diagnosis of transformer winding deformation degree.

Spread Spectrum Sensing Techniques for Transformer Frequency Response Data

With the advent of wireless communication, the problem of data security is of greatest interest. In this paper, spread spectrum techniques have been employed due to its advantages in providing data security. Further, the mechanical integrity of a transformer is investigated using an off-line diagnosis test called as Frequency Response Analysis (FRA). The FRA data of a transformer has been taken as the input signal which is being transmitted from the field where transformer is kept and received at the control room. Furthermore, Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS) are employed on FRA data and analyzed the signals by transmitting over Additive white Gaussian noise (AWGN) and Rayleigh faded Channels.

A New Transformer FRA Measurement Technique to Reach Smart Interpretation for Inter-Disk Faults

Transformers are utilized in generation, transmission, and distribution power system network, and face an enormous number of hazards during their course of operation. Frequency response analysis (FRA) is an inexpensive, accurate, and non-destructive technique to explore the transformer mechanical integrity very fast. However, FRA results interpretation is not being automated yet. This study introduces a new setup for FRA measurement that can assist to leave the conventional FRA data interpretation techniques and obtain smart interpretation. Hence, FRA setups and interpretation techniques are studied and formulated in this paper. A new measurement technique is introduced and discussed in detail. Practical studies are performed over distribution and power transformers and FRA data are recorded for inter-disk fault. The analysis of fault severity, which is obatined in this paper, is an advantage of the proposed measurement technique. In this regard, the techniques from machine learning and numerical analysis are employed to train a predictive engine for smart interpretation of FRA data. It is revealed that the proposed intelligent technique is capable of interpreting, detecting, and classifying the transformer winding inter-disk fault and its severity. The new introduced FRA measurement setup is also able to support the online FRA data assessment.

Generic algorithm to calculate Jacobian matrix used for ladder network parameters identification and winding fault diagnosis

Ladder network parameters identification of transformer winding based on frequency response analysis data is crucial to winding fault diagnosis. In the authors’ previous study, the Gauss–Newton iteration algorithm (GNIA) had been proposed to efficiently identify the network parameters. The core in GNIA is the Jacobian matrix, composed of derivative of frequency response function (FRF) to network components. This study proposes a generic algorithm to calculate this Jacobian matrix. Two key problems concerning the algorithm are solved elaborately. The first problem is the method for derivative calculation toward an arbitrary FRF based on adjoint network method (ANM). The other issue is the mathematical model construction of double ladder network and its adjoint network toward different FRFs to obtain all network branch voltages and currents, which are required in the derivative calculation by ANM. This generic algorithm can efficiently and effectively calculate the Jacobian matrix, which can be applied on ladder network parameters identification and winding fault diagnosis.

Transformer Frequency Response Analysis With the Grouped Indices Method in End-to-End and Capacitive Inter-Winding Measurement Configurations

The paper presents a method for assessing the frequency response results of transformers. The frequency response analysis (FRA) method is widely used in the industrial testing of the mechanical condition of transformers, however, there are still some problems with interpreting the test results. The measurements are usually taken only in an end-to-end open measurement configuration, according to the IEC standard. The literature indicates many numerical indices that are used for the assessment of FRA curves. It is not possible to use all of them, especially as they may give different results. The objective of the presented research was to analyze the behavior of 14 of the most popular indices in the medium-frequency range under the influence of deformations. The experiments allowed them to be divided into four groups, based on similar behavior under data recorded in conditions of deformations introduced into windings. All research is performed for two measurement configurations: end-to-end open and capacitive inter-winding. The division into groups is also tested with data recorded on transformers from industry. The proposed grouped indices method needs only four indices for FRA data assessment, while their behavior covers all 14 analyzed formulas.

Classifying Transformer Winding Deformation Fault Types and Degrees Using FRA Based on Support Vector Machine

As an important part of power system, power transformer plays an irreplaceable role in the process of power transmission. Diagnosis of transformer’s failure is of significance to maintain its safe and stable operation. Frequency response analysis (FRA) has been widely accepted as an effective tool for winding deformation fault diagnosis, which is one of the common failures for power transformers. However, there is no standard and reliable code for FRA interpretation as so far. In this paper, support vector machine (SVM) is combined with FRA to diagnose transformer faults. Furthermore, advanced optimization algorithms are also applied to improve the performance of models. A series of winding fault emulating experiments were carried out on an actual model transformer, the key features are extracted from measured FRA data, and the diagnostic model is trained and obtained, to arrive at an outcome for classifying the fault types and degrees of winding deformation faults with satisfactory accuracy. The diagnostic results indicate that this method has potential to be an intelligent, standardized, accurate and powerful tool.

Locating power transformer fault based on sweep frequency response measurement by a novel multistage approach

The windings of the power transformers are prone to deformation or displacement as a result of huge electromagnetic forces. Regular monitoring of transformers for detecting minor winding movements is crucial for preventing them from developing into major faults and eventually, causing an outage. In this study, a novel procedure is proposed to determine the location and severity of the disk space variation, a frequently occurring mechanical damage in transformers, by developing a two-level method. At the first level, an accurate model of the winding is determined from sweep frequency response analysis measured data corresponding to the healthy status. Analysis and interpretation of the obtained results by the proposed fault detector algorithm lead to locating the position and severity of the fault, in the next level. The process of determining the winding model from the frequency response analysis data is achieved by a multistage method utilising an enhanced version of magnetic optimisation algorithm, which comprises of utilising Fourier series coefficients and phase functions, and fast calculation of coupled network matrices. Experimental results of two 64 kV transformer windings verify the effectiveness of the proposed method in detecting the winding faults.