Transformer Frequency Response Research Articles

Fault Identification Method of Transformer Winding based on Gramian Angular Difference Field and Convolutional Neural Network

Background:: As the frequency of transformer winding faults becomes higher and higher, the frequency response analysis used to detect the winding status has attracted more and more attention. At present, there is still a lack of reliable and intelligent technologies for detecting the state of transformer windings in this field. Objective:: This paper focuses on studying a high-precision method for transformer fault diagnosis, which can be easily and effectively applied to daily life. Methods:: By changing the detection method, the traditional detection method can not distinguish the problem that the detection data are highly overlapping when identifying the same fault of the head and tail symmetric points, and the problem that the phase is too similar is changed. In order to solve the problem that the fault samples of transformer frequency response curve are scarce and the one-dimensional data cannot be read by partial deep learning method, the one-dimensional data of frequency response curve is first converted into characteristic index and then into a three-dimensional image by moving window calculation method and Gramian Angular difference field transformation. The fault classification is realized by a convolutional neural network. Results:: The accuracy of the final model for slice classification reached 100%. Conclusion:: Illustrative examples show that the method is distinguishable from different fault types. The traditional method only uses the amplitude of the frequency response curve, but this method displays the two features of the amplitude-phase together in the image. Compared with the traditional method, more features and samples are added to further improve the accuracy of the method. The accuracy of diagnosis results reached 100%, which showed the feasibility of the method.

Measurement Based Linear and Nonlinear Time Invariant Representations for High Voltage Inductive Transformer Frequency Response up to 10 kHz

Measurement Based Linear and Nonlinear Time Invariant Representations for High Voltage Inductive Transformer Frequency Response up to 10 kHz

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.

Optimizing Instrument Transformer Performance through Adaptive Blind Equalization and Genetic Algorithms

In real-world scenarios, deviations in the frequency response of instrumentation transformers can lead to distorted harmonic measurements, highlighting the critical role harmonic measurement plays in assessing power quality. The blind channel equalization technique offers a potential solution to improve the frequency response of a large number of instrumentation transformers already installed in substations. These transformers were designed to accurately measure only the fundamental phasor component. Therefore, in order to use them for harmonic phasor measurement, methodologies for reducing frequency distortion must be applied. In this work, we propose a novel approach to improve the frequency response of the instrument transformer using adaptive blind equalization. The blind technique can compensate for distortions caused by voltage and current transducers without requiring prior knowledge of input signals or circuit characteristics. The proposed methodology uses a Linear Prediction Filter to convert the colored noise present at the channel output into white noise. Furthermore, a genetic algorithm is used to find a pole to cancel possible zeroes present in the frequency response of some transducers. The main advantage of blind equalization with the genetic algorithm is its independence, operating without clear information about the channel or the input signal. Through extensive experimentation, we demonstrate the effectiveness of the proposed methodology in significantly reducing the absolute error in ratio and phase caused by current and voltage transformers. Simulated and laboratory experiments are presented in this paper.

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.

The Power Transformer Winding Input Admittance and Frequency Response

The frequency response analysis is increasingly more widely used to estimate the electrical and mechanical condition of power transformer windings. The frequency response measurement procedure has been prescribed in the existing international and national standards. However, the interpretation of measurement results still remains a subject of discussion. Various approaches have been used to interpret the results, including an analysis of transformer windings’ complex impedances and admittances obtained by calculations from frequency responses. To improve the frequency response interpretation, the article presents an analysis of power transformer winding input and output currents and admittances based on simplified equivalent circuits. Qualitative and quantitative results are presented, which show that the admittances obtained from measured frequency responses differ essentially from the true input admittances of the windings. The main factors causing the differences between these winding admittances are considered. It is shown that despite the existing differences, the current through the neutral and the winding admittance determined from the measured frequency response can also be used in practice to determine the power transformer winding natural oscillation frequencies.

머신러닝 기법을 이용한 변압기 주파수 응답 모델 파라미터 추정

Examining power transformer faults is crucial for maintaining the reliability of the power system. The most popular methods for detecting power transformer fault include thermal analysis, vibration analysis, partial discharge analysis, dissolved gas analysis(DGA), and sweep frequency response analysis(SFRA). Especially, the SFRA test is examined to detect transformer internal fault such as winding fault. Simulation-level frequency response analysis enables inspection of the power transformer before connecting to the grid. This paper proposes a parameter estimation method using machine learning for the power transformer frequency response equivalent model.

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.

Influence of pulse rise time and duty cycle on distribution of transients along the wind turbine step-up transformer windings

A transformer is one of the most important assets in an electric power generation system. Wind turbine step-up transformers have recently seen premature failures due to high-frequency repetitive transients. The high-frequency transients under resonance can severely damage the insulation of the transformer. Thus the paper initially analyses the distribution of transformer frequency response to identify critical resonance frequencies for the two transfer function frequency responses; namely, impedance frequency response and voltage ratio response. Transformer frequency response is compared with transient response to understand the influence of repetitive transient parameters; namely applied voltage amplitude, rise time, and duty cycle, on transient distribution along the transformer winding. Based on three variable experiments, the range of rise time was considered as less than 300 ns and 1000 ns, applied voltage considered was 100 V and 1000 V, and duty cycle considered was 10% and 50%. For the current transformer model, both the experimental and PSCAD simulation results indicated that a duty cycle of 50% and rise time < 300 ns were critically damaging to transformer insulation. The research helps in designing transformer insulation stressed under different transient parameters.

Investigations on using white noise as a test signal for performing frequency response measurements on transformers

White noise is a random signal mathematically analogous to an impulse function in time and flat spectrum in frequency. Naturally, the white noise may be used as an alternative test signal for determining the frequency response analysis (FRA) of transformers. Such an attempt not only enhances the power of FRA testing but also enable development of an online diagnostic test method. At present, the concept of using white noise is well-defined, but the crucial knowledge of applying the same on a real-time power transformer is currently not available or at least in the public domain. The study attempts to bridge this gap between theoretical contribution and practical requirement. The mathematical concept, experimental illustrations, and onsite / field validation altogether provides a complete insight into the identified problem. In this regard, an experimental study that investigates on using white noise as a test signal in determining the frequency response of a two-winding transformer is initiated. First, the possibilities of application of theoretical and mathematical concepts of using white noise as a test signal for measuring the frequency response of winding-core assembly is verified. Following this, the white noise signal applied to the circuit model and the corresponding response is recorded and the arbitrary choice of data samples measured from the circuit model is ensured using brute-force approach. In this procedure, the number of samples are manually increased until the magnitude and natural frequencies of resonant peaks matches atleast within 2 % accuracy with conventional FRA measurements. This is performed to ensure the repeatability of the method. Later, the time and frequency dependent statistical properties of the measured signals are computed and the respective transfer function is obtained. Subsequently, the transfer function obtained from the white noise method and the respective natural frequency (tabulated) are compared with the values measured using conventional FRA method. Once this is accomplished, these findings are experimentally validated on an actual high voltage transformer.

Multi-Conductor Transmission Line Model of Split-Winding Transformer for Frequency Response and Disk-to-Disk Fault Analysis

For transformer designers, split-winding transformer modeling in different frequency ranges is of great importance. In this paper, for the first time, a multi-conductor transmission line model is proposed for high-frequency modeling of the split-winding transformer. In this model, all the turns in layers and disks have been considered and the model's parameters have been calculated using the finite element method. In order to validate the proposed model, the results are compared with the result of a model, which is based on finite element and coupled field-circuit. It is shown that the introduced model has good accuracy and it can be employed for split-winding transformer modeling in different frequency ranges. In addition, using the validated multi-conductor transmission line model, the frequency response of the split-winding transformer and disk-to-disk short circuit fault are analyzed.

Аналіз отриманих частотних характеристик силового трансформатора та визначення його технічного стану з їхньою допомогою

The decommissioned 10 kV power transformers, which are stored at the repair sites of JSC "Vinnytsiaoblenergo", among others, are damage to the windings and magnetic circuit, which can be detected by analyzing the frequency characteristics of the transformer. An exemplary graph of the frequency response of a power transformer used in the diagnostic process may be a graph showing the average values of the test signal transfer factor of the FRAnalizer through a power transformer for different types of serviceable transformers depending on the frequency of the test signal. Only those transmission measurement results are taken into account and only the number of measurements in which the deviation of the current values does not exceed the FRAnalizer error (2&nbsp;%). The frequency of the test signal, which must be taken into account for detecting a defect, corresponds to the frequency at which the deviation of the value of the transmission coefficient of the frequency response of the transformer under study differs from the value of the transmission coefficient (frequency response built from the average values of the same type of serviceable transformers) by more than 2&nbsp;%. Determining the value of the informative frequency, which correlates with the defect, is carried out by own observations and analysis of literature sources. On the example of the studied power transformer type TMG 1000/10 U1 its actual technical condition is established. However, in the frequency range 6060…7010 Hz, abrupt deviations were observed, which are proposed to be preliminarily removed from the calculations, considering them to be mistakes.

Harmonic Synchrophasors Measurement Algorithms With Embedded Compensation of Voltage Transformer Frequency Response

The widespread diffusion of nonlinear power electronics-based devices in distribution grids has raised the interest toward power quality monitoring. In this respect, the estimation of synchronized harmonic phasors would enable the employment of algorithms that allow identifying the sources of harmonic disturbances, which, until now, have only been tested through numerical simulations or implemented on small-scale. However, the impact of the uncertainty due to the employed voltage transformers (VTs) and to the other devices that compose the measurement chain has to be analyzed. In this framework, the present article proposes a class of harmonic synchrophasor estimation algorithms that allows compensating the frequency response function of the instrument transformer. The technique has been tested and validated under realistic conditions considering an inductive VT. Experimental results highlight its effectiveness, especially when taking into account its ease of implementation. The black-box approach allows abstracting from the operating principle of the VT.

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.

Analysis of Statistical Methods for Assessment of Power Transformer Frequency Response Measurements

Frequency response analysis (FRA) is a widely accepted diagnostic method to assess the mechanical integrity of the active parts within a power transformer. Recent studies in the field of FRA have led to the standardization of its measurement procedure as described in the IEC and IEEE standards. However, the interpretation of FRA results is still limited to the analysis of the experts in the field. Using numerical indices is one of the methods introduced for the FRA interpretation, which quantifies the differences in FRA signatures. There are numerous indices proposed in the literature. However, there is no comprehensive comparison study to assess the sensitivity of these numerical indices against different faults. This contribution is an effort in this direction, which collects all indices on a single platform, compares and categories them based on their characteristics, to announce more appropriate indices as the standard ones. This paper defines the criteria for an appropriate index such as monotonicity, linearity, sensitivity, data-points dependency and index ratio. The evaluation of the indices is performed using 10 case studies from an experimental setup, molded transformer, and real power transformer cases. The results of this paper reveal that some indices stand out from the others in terms of performance and can be considered as the most appropriate ones that can satisfactorily calculate the changes between FRA signatures. The results also provide useful facts and guidelines for the standardization process of numerical indices for their implementation in the FRA studies.

Frequency response analysis for transformer tap changer damage detection

Frequency response analysis (FRA) method has been proven to detect the transformer winding damage. However, there is no practical study which investigates the damages on transformer tap changer even though it has a high failure rate. Hence, this paper investigates normal and faulty transformer tap changer using FRA. The FRA measurements conducted using four different test configurations. Also, normal tap changer, pitting and coking tap changer contact were investigated. In addition to FRA measurement, winding resistance measurement has been conducted. The transformer turn ratio measurement also conducted to identify the taps positions. This study results significant to understand the effect of pitting and coking tap changer on the transformer frequency response. The results showed that pitting has a slight influence on the frequency response. However, coking shows a huge variation in low-frequency response. This effect observed during the winding resistance measurement.

Influence of the Load on the Impulse Frequency Response Approach Based Diagnosis of Transformer’s Inter-Turn Short-Circuit

Frequency Response Analysis (FRA) is an Off-line condition monitoring technique for the transformers and is successful, in diagnosing mechanical faults and inter-turn short-circuits. Only limited literature is available for On-line FRA works, and the effect of the transformer’s load on the fault diagnosing capability of FRA has not yet been analysed. Motivated by this research gap, an experimental investigation was done to analyze the effect of load on IFRA based inter-turn short-circuit diagnosis. A single-phase 1 kVA, 240V/240 V transformer supplying R and R-L loads and a three-phase 5 kVA, 440 V/440 V transformer supplying an induction motor at various load levels were tested. Inter-turn short-circuits were emulated in their windings and, the effectiveness of IFRA in diagnosing the same was investigated. Comparisons were made between the frequency response of the loaded transformers in their healthier conditions and emulated fault conditions, based on the transfer function plots and the statistical parameters. Investigations reveal that the loads alter the useful spectrum of IFRA. The frequency response of the healthier transformer itself varies based on the transformer’s load and necessitates a careful focus on the sensitive frequency spectra for effective inter-turn short-circuit diagnosis in loaded transformers.

Improved Winding Mechanical Fault Type Classification Methods Based on Polar Plots and Multiple Support Vector Machines

The accurate and fast diagnosis of transformer winding deformation faults is of significance to power suppliers and utilities. An improved winding mechanical deformation fault classification method is proposed. In this study, the transformer frequency response data is used to draw polar plots, and then its texture features are extracted for fault classification. The classification model constructed by multiple support vector machines is successfully obtained and shows good classification effect. Besides, this article uses an improved genetic algorithm based on the Emperor-Selective mating scheme and catastrophic operation, to optimize the parameters of support vector machine. The feasibility and accuracy of the proposed method are verified with experimental data obtained from a model transformer, and the proposed method is demonstrated to exhibit better performance compared with the traditional method.

Electromagnetic transients modelling of split‐winding traction transformers for frequency response analysis

High-frequency electromagnetic transients modelling of voltage and current distribution due to electromagnetic transients are of great importance in transformer design. In this study, a 2D and 3D finite-element, coupled field-circuit and modified detailed model is introduced for high-frequency electromagnetic transient studies in split-winding traction transformers. The proposed coupled field-circuit approach uses a 2D finite-element model that is coupled with an external circuit to analyse the electromagnetic transient behaviour of the split-winding traction transformer. Also, a detailed model is introduced for this type of transformer and its results are compared with the introduced coupled field-circuit model and complete 3D finite-element model. After validating the introduced models, the models are employed to analyse the frequency response of the split-winding traction transformer.