Transformer Frequency Response Analysis Research Articles

Parameter identification of transformer lumped element network model through genetic algorithm‐based gray‐box modelling technique

AbstractThe lumped element network model has been proven to be an efficient tool for the interpretation of transformer Frequency Response Analysis. However, it is challenging to obtain parameters of the model if transformer design information is unavailable. In such a case, optimisation algorithms can be used for gray‐box model parameter estimation. A methodology is developed by the authors to establish a transformer network model without winding design data, and instead, end‐to‐end open circuit Frequency Response and other terminal test results are utilised; and Genetic Algorithm is applied to approximate the unknown parameters of the model. The modelling approach developed is independent of the unit number of the network model and therefore guarantees the accuracy of optimisation. Furthermore, it can deal with transformers with a complicated winding structure such as interleaved disc type winding. Two single windings, helical and interleaved disc type, and a single‐phase 144/13 kV 60 MVA transformer are used to demonstrate the method. FRA spectra produced by the best estimated gray‐box model and the corresponding white‐box model are compared. The main features in amplitude and phase spectra are well matched, with low values of Relative Standard Deviation, for both single windings and transformer. Estimated electrical parameters show a high consistency with reference values, which are calculated based on winding design data. This validates the methodology and gives confidence to apply grey‐box modelling for FRA interpretation.

Transformer's frequency response analysis results interpretation using a novel cross entropy based methodology

Transformer defects can be identified by the FRA (frequency response analysis) that is a promising diagnostic technique. Despite the standardization in FRA measuring technique, its results interpretation is yet a research area. Because different faults types can be identified in various frequency bounds of the FRA signatures, it is necessary to identify the possible relationships between specific failures and frequency ranges in this contribution. For this purpose, a real transformer is used to conduct the essential tests, which include both healthy and faulted circumstances (axial displacement (AD), radial deformation (RD), and short-circuits (SC)). To identify efficient characteristics from the produced frequency response traces and improve interpretation accuracy of such traces, a new hyperbolic fuzzy cross entropy (FCE) measure is demonstrated and then utilized for the aim of discrimination and classification of transformer winding defects in pre-defined frequency ranges. After normalizing FRA results of the transformer under healthy and various fault circumstances the lower bounds from such responses have been extracted and then utilized to construct the desired form of the fuzzy sets of healthy and faulted circumstances. Then, a new hyperbolic FCE measure-based discrimination and classification of winding faults methodology is offered on the basis of highest and lowest FCE measure values. The highest FCE measure value between the fuzzy sets of healthy and faulted circumstances such as AD, RD and SC is designated to confirm the occurrence of winding faults in a suitable frequency range. The suggested methodology ensures smart interpretation of FRA signature and accurate classification of winding faults as it can effectively discriminate both healthy and faulted circumstances in the desired frequency ranges. The proposed approaches' performance is tested and compared by applying the experimental data after feature extraction.

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.

Fault Diagnosis of Transformer Windings Based on Decision Tree and Fully Connected Neural Network

While frequency response analysis (FRA) is a well matured technique widely used by current industry practice to detect the mechanical integrity of power transformers, interpretation of FRA signatures is still challenging, regardless of the research efforts in this area. This paper presents a method for reliable quantitative and qualitative analysis to the transformer FRA signatures based on a decision tree classification model and a fully connected neural network. Several levels of different six fault types are obtained using a lumped parameter-based transformer model. Results show that the proposed model performs well in the training and the validation stages, and is of good generalization ability.

Understanding the Influence of Power Transformer Faults on the Frequency Response Signature Using Simulation Analysis and Statistical Indicators

Frequency Response Analysis (FRA) is the most reliable technique currently used to evaluate the mechanical integrity of power transformers. While the measurement devices have been well developed over the past two decades, interpretation of the FRA signatures is still challenging regardless of the several papers published in this regard. This paper adds an attempt to understand the power transformer FRA signatures through experimental and simulation analyses. In this context, experimental FRA measurements are conducted on a 33/11 kV, 30 MVA transformer under various faults, including winding deformation, the short circuit turns, loss of clamping, and bushing fault. At the same time, the high-frequency transformer model that comprises series capacitance, self-inductance, series resistance, and mutual inductance is simulated using MATLAB / Simulink to compare simulation and experimental results. The correlation between physical circuit parameters and various faults facilitates a better understanding of each fault's effect on the FRA signature. To quantify the impact of such faults, correlation coefficient, the absolute sum of logarithmic error, standard deviation, and sum square error are calculated with respect to the healthy signature at three frequency regions. Results show that using statistical coefficients over three frequency ranges of the FRA signature facilitates better fault identification and quantification.

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.

Locating Inter-Turn Faults in Transformer Windings Using Isometric Feature Mapping of Frequency Response Traces

Power transformers usually confront various mechanical and electromagnetic stresses during an operation that may lead to defects in their windings. The short circuit in the windings is one of those severe defects. Early detection of short-circuits is necessary as extra heating in the shorted location can lead to progressive damage in windings insulation. Frequency response analysis (FRA) is a well-known method to diagnose short-circuits in transformers. Despite the accuracy of FRA, the interpretation of the obtained frequency response traces (FRTs) is still an intricate task. Due to the unknown impact of faults on FRTs, extracting efficient features from such traces is necessary for the interpretation of transformer's frequency response. In this article, an isometric feature mapping (Isomap) is used as a nonlinear dimensionality reduction technique to locate interturn faults in transformer windings due to its capability of capturing the nonlinear phenomena in FRT of power transformers. It is revealed that, after constructing the isometric mapping for a transformer, there is no need for any expertise to detect fault location even in nondirect (high impedance) short-circuits. In other words, it can be the first step for the automated interpretation of FRA of power transformers.

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.

Estimating Power Transformer High Frequency Model Parameters Using Frequency Response Analysis

Frequency response analysis (FRA) has become a widely accepted technique by worldwide utilities to detect winding and core deformations within power transformers. The main drawback of this technique is its reliance on the personnel level of expertise more than standard or automated codes. To establish reliable FRA interpretation codes, accurate high frequency transformer model that can emulate the frequency characteristics of real transformers in a wide frequency range is essential. The model can be used to investigate the impact of various winding and core deformations on the transformer FRA signature. The transformer equivalent high frequency electric circuit parameters can be calculated based on design data, which are rarely available, especially for old transformers. As such, this paper presents an artificial intelligence technique to estimate these parameters from the transformer FRA signature. The robustness of the proposed technique is assessed through its application on three, 3-phase power transformers of different ratings, sizes, and winding structures to estimate their high frequency electric circuit parameters during normal and fault conditions. Results show that the proposed technique can estimate equivalent circuit parameters with high accuracy and helps interpret the FRA signature based on the numerical changes of these parameters. The main advantage of this approach is the physical meaning of the model parameters facilitates reliable identification of various faults and hence aids in establishing reliable interpretation codes for transformer FRA signatures.

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.

High frequency electric circuit modeling for transformer frequency response analysis studies

Power transformers are subject to winding and core deformations due to short circuit faults and other environmental conditions. Majority of these faults are of progressive nature and should be rectified as soon as they emerge. Frequency response analysis (FRA) has been widely accepted as a reliable diagnostic tool to detect such faults. As reliable interpretation codes for FRA signatures have not been fully developed and accepted yet, researchers have put much effort to investigate the impact of various mechanical deformations on the transformer FRA signature. Because of the intrusive nature of such faults when staged on a real transformer, most of the studies in the literatures were conducted on a transformer high frequency electric circuit model. Simplifications assumed in these models by ignoring the turn-to-turn capacitance, not taking into account the detailed winding structure and not considering all mutual inductances between coils in various phases have reduced the accuracy of the obtained results. To establish reliable FRA interpretation codes, it is essential to develop electric equivalent circuit models that can yield FRA signature as close as possible to the FRA signature trend of the real transformer. This paper proposes a detailed transformer high frequency electric circuit model which considers the winding structure, inter-turn capacitance and all mutual inductances. Calculation details of the model’s parameters are presented. The accuracy of the proposed model is assessed by comparing its FRA signature with that of an equivalent transformer hardware model during healthy, short circuit disks, radial deformation and axial disks buckling fault.

Investigating the applicability of the finite integration technique for studying the frequency response of the transformer winding

The frequency response analysis (FRA) is a promising diagnostic method for detecting mechanical faults inside a power transformer. Despite the standardization of the FRA measurement procedure, the interpretation of the results is still a subject of study. The reason lies in the fact that the frequency response is different from case to case. Therefore, for interpreting a transformer FRA result, the effects of various possible mechanical changes on the FRA trace of that particular transformer should be known. Additionally, real mechanical deformations cannot be executed for obtaining the required information due to the destructive nature. Hence, the transformer winding models are utilized instead to study the frequency response. While the circuit model has been extensively discussed in the literature, there is little focus on the numerical methods for the FRA purpose. To take a step forward, this contribution investigates the applicability of the finite integration technique for the FRA studies. The presented model can simulate different fault types for the FRA interpretation while it has also other applications regarding the frequency response. In this contribution, the FRA traces are derived directly from a finite integration model which is an important improvement compared with the previous papers. The agreement between the simulation results and the experimental data indicates that the proposed model has the potential of providing a powerful tool to decipher the transformer frequency behavior.

Detecting incipient radial deformations of power transformer windings using polar plot and digital image processing

One of the main drawbacks of the frequency response analysis (FRA) technique that is widely accepted as the most reliable tool to detect transformer internal mechanical deformations is the inconsistent interpretation of the measured signature because of its reliance on personal expertise more than standard codes. Moreover, conventional FRA signature has a very low accuracy in detecting incipient and low mechanical fault levels. In order to avoid inconsistent interpretation for the transformer FRA signatures and improve its accuracy to detect minor fault levels, a reliable automated technique has become essential. This study investigates the feasibility of utilising FRA polar plot to detect minor radial deformation levels within two, three-phase power transformers of different ratings and winding configurations simulated using three-dimensional finite-element analysis software. Simulation results are validated through experimental measurements. Results of this study are also compared with the results obtained for other types of transformer winding deformations that are published in the literature in order to identify unique impact for each fault type on the proposed method. Findings reveal the superiority of the proposed approach over existing conventional technique in terms of accurate identification and quantification for minor transformer winding deformations.

Performance evaluation of online transformer internal fault detection based on transient overvoltage signals

Winding deformation is a critical power transformer issue that needs to be detected as soon as it emerges due to its progressive nature and severe consequences it may lead to. Frequency response analysis (FRA) is the only reliable technique currently used to detect such deformation. However, the technique is conducted offline that may cause interruption to the electricity grid when taking an operating transformer out of service for testing. Moreover, as the current FRA technique is only conducted on suspected units, a mechanical fault may emerge and progress before the utility becomes aware of. To overcome these limitations, this paper presents a practical feasibility study to detect transformer winding deformations online. The technique relies on utilizing transient overvoltage signals that a transformer is subjected to during its normal operation as a natural variable frequency excitation source. The feasibility of utilizing various transient overvoltage signals as excitation source for transformer FRA signature measurement is firstly investigated and optimum signal parameters are recommended based on signal voltage and energy spectrum analyses. Secondly, the proposed technique is verified through simulation analysis by comparing the transformer frequency response signatures when transient overvoltage and conventional sweep frequency voltage are used as excitation sources. Also, experimental testing is conducted to assess the feasibility of the proposed technique to identify various winding deformations such as radial buckling, telescoping and short circuit turns. Custom-made capacitive voltage divider is developed to accurately detect the response of transient overvoltage signals generated due to environmental conditions or power system switching operations. The proposed technique along with the developed capacitive voltage divider is implemented on a 3-phase Wye-Delta, 50 Hz, 31.5 MVA, 110/10.5 kV power transformer to measure the frequency response signatures of the high voltage winding.

Loss of low-frequency data in on- line frequency response analysis of transformers

Power transformers are a key component of the electricity supply grid. Monitoring and assessment of their condition has always been of great concern [1]. In critical situations, transformer failures can cause irreversible damage and considerable financial loss to the grid stakeholders or even the end-users [2], [3]. In this regard, mechanical defects are considered a major problem in distribution and power transformers [4]. Consequently various diagnostic techniques have been developed to identify transformer mechanical defects and winding deformation.

Application of DIP to Detect Power Transformers Axial Displacement and Disk Space Variation Using FRA Polar Plot Signature

While frequency response analysis (FRA) technique has been successfully used to assess the mechanical integrity of active parts within power transformers, it still exhibits some drawbacks including its inability to detect incipient and minor winding deformations and the requirement for an expert to analyze the results. Although several papers have investigated the impact of various faults on the transformer FRA signature, no attempt was made to automate and improve the fault detection accuracy of the current technique. The main contribution of this paper is the presentation of a new approach for the FRA technique through incorporating the magnitude and phase angle plots that can be measured using any commercial frequency response analyzer into one polar plot. Contrary to the current industry practice that only relies on the magnitude of the measured FRA signature for fault identification and quantification, the proposed polar plot that comprises more features than the magnitude plot will facilitate the use of digital image processing (DIP) techniques to improve the detection accuracy, standardize, and automate the FRA interpretation process. In this regard, three-dimensional models for two three-phase power transformers of different ratings, sizes, and windings structures are modeled using a finite element analysis technique to simulate various levels of axial displacement (AD) and disk space variation (DSV) at different locations of the transformer windings. Impact of minor fault levels on the proposed polar plot signature is investigated through the application of various DIP techniques. Simulation results are validated through practical measurements on a scaled-down transformer. Results show that the proposed polar plot along with the DIP technique is able to detect minor fault levels of AD and DSV with high accuracy.

Current state of transformer FRA interpretation: On behalf of CIGRE WG A2.53

Measurement of the frequency response, from a few Hz to a few MHz, is now commonly used in the transformer industry for the condition assessment of transformer windings and has demonstrated its sensitivity for detecting various mechanical and electrical failure modes. The present generally applied practice for interpretation is visual comparison of frequency responses, either with a previous measurement on the same or an identical unit, or between the phases of a three-phase transformer. Examples of curve comparison for typical mechanical and electrical failure modes have previously been published in CIGRE and IEEE guides. Over the last 15 years, numerous technical papers have been published regarding the interpretation of the results in an aim to make it more objective and quantitative. In 2016, CIGRE initiated a new working group titled “Objective interpretation methodology for the condition assessment of transformer windings using Frequency Response Analysis (FRA)”. This paper, written on behalf of the new working group, reviews the basics of FRA interpretation and summarizes the state-of-the-art regarding the potential methods that can be applied to achieve a more objective and quantitative interpretation of the results.

New statistical approach to interpret power transformer frequency response analysis: non‐parametric statistical methods

The frequency response analysis (FRA) test has been recognised as one of the sensitive tools for detecting electrical and mechanical faults inside power transformers. However, there is still no universally systematic interpretation technique for these tests. Many research efforts have employed different statistical criteria in order to aid the interpretative capability of the FRA, but it is shown that the methods used so far are based on parametric statistics, which need a set of assumptions about the normality, randomness and statistical independence of FRA data. Therefore, this study aims to propose some non-parametric statistical methods which are based on explicitly weaker assumptions than such classical parametric methods. The proposed statistical methods are applied to the experimental FRA measurements obtained from two test objects: a three phase distribution transformer (35/0.4 kV, 100 kVA) to study the winding interturn fault and a two winding transformer (1.2 MVA, 10 kV) for the study of radial deformation. The non-parametric statistical methods, namely Spearman correlation coefficient, Wilcoxon signed rank test and Friedman test are used to compare FRA traces. It was found through this research work that the applied non-parametric methods can effectively reflect the differences between compared FRA data and diagnose the fault.

Detection of power transformer bushing faults and oil degradation using frequency response analysis

Frequency response analysis (FRA) has been globally accepted as a reliable tool to detect mechanical deformation within power transformers. However, because of its reliance on graphical analysis, interpretation of FRA signature is still a challenging area that calls for skilled personnel, as so far, there is no widely accepted reliable standard code for FRA signature identification and quantification. While several papers investigating the impact of various mechanical winding deformations on the transformer FRA signature can be found in the literature, no attention was given to investigate the impact of various bushing faults and transformer oil degradation on the FRA signature. This paper introduces a detailed simulation and practical analyses to elaborate the impact of bushing faults as well as transformer oil degradation on the transformer FRA signature. In this regard, the physical geometrical dimension of a three phase power transformer is simulated using 3D finite element analysis to emulate the real transformer operation. Various bushing faults have been emulated on the studied model and oil degradation is implemented through changing oil permittivity. Practical FRA test is conducted on a three phase 132 kV, 35 MVA power transformer to validate the simulation results. Results show that bushing faults and oil degradation can be visibly detected through FRA signature.

Improved power transformer winding fault detection using FRA diagnostics – part 1: axial displacement simulation

Frequency response analysis (FRA) has become a widely accepted tool to detect power transformer winding deformation due to the development of FRA test equipment. Because FRA relies on graphical analysis, interpretation of its signature is a very specialized area that calls for skilled personnel, as so far, there is no reliable standard code for FRA signature identification and quantification. Many researchers investigated the impact of various mechanical winding deformations on the transformer FRA signature using simulation analysis by altering particular electrical parameters of the transformer equivalent electrical circuit. None of them however, investigated the impact of various physical fault levels on the corresponding change in the equivalent circuit parameters. In this paper, the physical geometrical dimension of a single-phase transformer is simulated using 3D finite element analysis to emulate the real transformer operation. A physical axial displacement of different fault levels is simulated in both low voltage and high voltage windings. The impact of each fault level on the electrical parameters of the equivalent circuit is investigated. A key contribution of this paper is the charts it introduces to correlate various axial displacement levels with the percentage change of all transformer equivalent circuit parameters due to the axial displacement fault. In contrary with other researchers who only considered mutual inductance between low voltage and high voltage windings, simulation results shown in this paper reveal that other circuit parameters should be changed by a particular percentage to accurately simulate particular fault level of transformer winding axial displacement. Results of this paper aid to precisely simulating winding axial displacement using transformer equivalent circuit that facilitates accurate qualitative and quantitative analysis of transformer FRA signatures.