Frequency Response Analysis Results Research Articles

Quality Index for Assessment of the Mechanical Condition of Transformers’ Active Part with Frequency Response and Vibroacoustic Measurements

The paper describes the application of the numerical tool quality index for an objective evaluation of complementary frequency response analysis (FRA) and vibroacoustic method (VM) test methods. These diagnostic methods are used in the industrial practice of transformer diagnostics for the assessment of the mechanical condition of windings and a core. The quality index is based on a numerical comparison of the curve obtained from measurements and the reference curve in a frequency domain. The quality index is based on estimators for the covariance, variance, and expected values. First, both methods of analysis were applied to a group of transformers of similar construction, leading conclusions on quality index values being quickly drawn. Next, it was applied to another transformer’s FRA and VM measurement results. The results showed problems with its mechanical condition, thus confirming that the proposed methods can be used in the practical assessment of transformers with these two diagnostic methods. The assessment of transformer’s active-part mechanical condition with complementary FRA and VM methods can be performed much more easily with the proposed quality indices.

Cut‐set matrix methods for frequency response analysis curves of lumped parameter equivalent circuit model of three‐winding power transformer

SummaryTo accurately and efficiently calculate the frequency response of the lumped parameter equivalent circuit model (LPECM) of a transformer winding is the basis for studying the simulation method of the frequency response analysis (FRA). In this paper, two different cut‐set matrix (CSM) methods, including fundamental cut‐set (FCS) and independent cut‐set (ICS) matrix methods, are proposed to calculate the FRA curves of the LPECM of a three‐winding power transformer. First, based on graph theory and electrical circuit laws, the basic CSM equation is deduced. Second, four different FCS matrix selection methods of the LPECM are introduced and the best FCS matrix is determined by deeply analyzing their characteristics. Then, an ICS matrix method is proposed to obtain the ICS of the LPECM. Furthermore, FCS and ICS are taken into the CSM equation to calculate the FRA results of the LPECM, respectively. Finally, the accuracy of the proposed methods is validated by Multisim software and the performance of these two methods is compared with node voltage matrix (NVM) method by analyzing the calculation time. The results show that FCS and ICS matrix methods both can be used to accurately obtain the FRA results of the LPECM of the three‐winding power transformer, but ICS is more simple than FCS matrix method due to avoiding the procedure for the selection of the tree. In addition, since ICS matrix method has the shortest running time among these methods, it can be used to improve the calculation efficiency of the FRA curves of the LPECM of a three‐winding power transformer.

Transformer Winding Fault Classification and Condition Assessment Based on Random Forest Using FRA

At present, the condition assessment of transformer winding based on frequency response analysis (FRA) measurements demands skilled personnel. Despite many research efforts in the last decade, there is still no definitive methodology for the interpretation and condition assessment of transformer winding based on FRA results, and this is a major challenge for the industrial application of the FRA method. To overcome this challenge, this paper proposes a transformer condition assessment (TCA) algorithm, which is based on numerical indices, and a supervised machine learning technique to develop a method for the automatic interpretation of FRA results. For this purpose, random forest (RF) classifiers were developed for the first time to identify the condition of transformer winding and classify different faults in the transformer windings. Mainly, six common states of the transformer were classified in this research, i.e., healthy transformer, healthy transformer with saturated core, mechanically damaged winding, short-circuited winding, open-circuited winding, and repeatability issues. In this research, the data from 139 FRA measurements performed in more than 80 power transformers were used. The database belongs to the transformers having different ratings, sizes, designs, and manufacturers. The results reveal that the proposed TCA algorithm can effectively assess the transformer winding condition with up to 93% accuracy without much human intervention.

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.

Feasibility Study on the Detection of Turn-to-Turn Fault Severity in the Transformer Winding by Frequency Response Analysis and Numerical Indices

Frequency response analysis (FRA) provides valuable information on internal electrical and mechanical faults in a transformer. This information can also be used to diagnose the turn-to-turn fault (TTF) in a transformer winding. This paper concentrates on using numerical indices for the evaluation of FRA to diagnose the TTF severity of the transformer winding. This evaluation is essential for expanding the knowledge toward the interpretation of FRA results. In this paper, the FRA traces of a winding are obtained in the laboratory for a healthy and faulty transformer with various TTF severities. The test results are analyzed using the indices related to all points of FRA characteristic and the indices related to the resonance and anti-resonance points. In this analysis, the possibility of diagnosing the TTF severity is addressed. To confirm the experimental results, simulation models of different windings are implemented to repeat the evaluation. By choosing an appropriate frequency range for the evaluation, the numerical indices demonstrate a monotonic performance versus the fault severity, i.e., the TTF severity can be determined in a transformer winding by assessing the FRA results with numerical indices.

Transformer fault type discrimination based on window calculation method and frequency response analysis

Frequency response analysis (FRA), one of the methods for the diagnosis of transformer mechanical faults, is improving quickly to result in easier fault detection. Recently, the window calculation method has been introduced in the literature to interpret the FRA results. In this method, the interpretation algorithm divides the transfer function (TF) into small frequency windows and analyses overall behavior of these windows. This contribution studies the window method on a test transformer in which three mechanical defects are exerted to determine the type of winding fault. For this purpose, various numerical indices acquire the corresponding window curves from TFs obtained in four different connections. Afterward, the trend of the generated curves is utilized to give an interpretation of the results. In this regard, two novel numerical indices, based on the trend of maximum points of window curves, are introduced that facilitate the discrimination of the winding fault type.

Formation of band gaps in periodic composite beams by finite element analysis

It is known that a filtering phenomenon, called a band gap, occurs in structures in which materials or structures with different properties are repeated, and vibration propagation is suppressed in the band gap frequency. This study intends to realize the band gap phenomena using composite beams consisting of metallic materials. First, the wave finite element analysis (WFEM) is applied to derive a dispersion curve, which indicated the conditions for the formation of a band gap. Next, by comparing the results of frequency response analysis using Ansys, the formation of band gaps is confirmed by showing no resonant peaks exist in the frequency bands where band gaps are predicted. By evaluating several periodic composite beams, it was found that the condition for widening the frequency band in which the band gap is formed is a large difference between the EI/ρA values of the two phases. Furthermore, by replacing the hollow beams with solid beams with ρA and EI set to be equivalent, it was shown that it is possible to predict the formation of a band gap by dispersion analysis using WFEM for beams with a complex structure.

Frequency Response Analysis (FRA) Fault Diagram Assessment Method

Frequency response analysis (FRA) is an extended technique for transformer condition assessment. In recent times, its proven sensitivity for detecting different type of faults have generated interest for rotating machine applications. However, at present, the interpretation of FRA results is mostly made by visual inspection of curves and is a hard task for nonexpert maintenance personnel. This article presents a mathematical model to simplify diagnostic tasks from FRA results. The developed model is called “Fault Diagram” and it is conceptualized to be applied to any coil, so it could be extensive to any type of machine. The fault diagram is based on a paradigm which states that a healthy machine is a machine with infinite impedance fault. The model uses a first-order frequency response for the purpose of fitting a linear function ∊ R3. The input of the model is the FRA curve of the machine, and the output is a point in a three-dimensional space. This approach can give an accurate diagnosis without ambiguous interpretations about if the machine is healthy or not and can provide an estimation of the fault location in case of damage. For validating the method, it was applied in a pole of a 40 MVA synchronous generator.

Transformer Winding Condition Assessment Using Feedforward Artificial Neural Network and Frequency Response Measurements

Frequency response analysis (FRA) is a well-known method to assess the mechanical integrity of the active parts of the power transformer. The measurement procedures of FRA are standardized as described in the IEEE and IEC standards. However, the interpretation of FRA results is far from reaching an accepted and definitive methodology as there is no reliable code available in the standard. As a contribution to this necessity, this paper presents an intelligent fault detection and classification algorithm using FRA results. The algorithm is based on a multilayer, feedforward, backpropagation artificial neural network (ANN). First, the adaptive frequency division algorithm is developed and various numerical indicators are used to quantify the differences between FRA traces and obtain feature sets for ANN. Finally, the classification model of ANN is developed to detect and classify different transformer conditions, i.e., healthy windings, healthy windings with saturated core, mechanical deformations, electrical faults, and reproducibility issues due to different test conditions. The database used in this study consists of FRA measurements from 80 power transformers of different designs, ratings, and different manufacturers. The results obtained give evidence of the effectiveness of the proposed classification model for power transformer fault diagnosis using FRA.

Winding deformation classification in a power transformer based on the time-frequency image of frequency response analysis using Hilbert-Huang transform and evidence theory

This study presents a novel fully-automated technique to interpret a frequency response analysis (FRA) of a power transformer, using a combined method based on digital image processing and evidence theory. Power transformers are widely used in power systems, and their continuous operation depends on proper monitoring and maintenance. While FRA is considered an efficient method for detecting minor damage in the windings of a power transformer in industrial applications, there is no universally accepted method for interpreting FRA results, and this crucial task relies on the opinion of an error-prone human expert. Our method first obtains a time-frequency image using the Hilbert-Huang transform. Next, the image’s histogram is imported into an evidence theory-based classifier, which ultimately detects radial and axial deformation faults, and their severity. The proposed method is shown to report faults with remarkable accuracy by a finite element model of a three-phase 125 MVA, 230/132/20 kV autotransformer, in which various faults with different severities are simulated and tested.

Transformer Oil Diagnosis Based on a Capacitive Sensor Frequency Response Analysis

Condition monitoring of large power transformers is of paramount importance in power systems. One of the most common indicators of transformer aging is moisture content in oil. In this article, a capacitive sensor able to online measuring moisture content is presented. The output of this sensor is recorded using a Frequency Response Analysis (FRA) device. Comparing the FRA results of a degraded oil with a reference FRA test, moisture content can be determined. A prototype sensor has been designed, built and tested. The performance of this sensor was simulated and laboratory tested with different moisture content oil samples. The results confirm that the proposed sensor can determine moisture content in oil. Therefore, it allows estimating oil degradation.

Transformer Winding Faults Detection Based on Time Series Analysis

Monitoring of winding faults is of great significance for the assessment of the transformer maintenance status. In this study, the time series analysis is combined with frequency response analysis (FRA) for better interpretation and analysis of FRA results. Here, healthy baseline residual data are modeled using the time series analysis for faults detection of the transformer winding. Different statistical software, such as R 4.0.2 and ITSM2000, are used to analyze measured data. To detect the transformer’s winding faults, various analyses, such as the autocorrelation and partial autocorrelation functions plot, the Box–Pierce test, the Ljung–Box test, the McLeod–Li test, the turning points test, the Wallis and Moore phase–frequency test, and the Jarque–Bera test, and the order of minimum corrected Akaike’s information criteria are used. The simulation results show that the suggested method is able to classify and discriminate mechanical and electrical faults of the transformer’s winding with good accuracy.

Optimization of Transformer Winding Deformation Assessment Criterion Considering Insulation Aging and Moisture Content

Frequency response analysis is widely used to diagnose transformer winding deformation faults due to its high sensitivity, strong anti-interference capability, and equipment portability, but the results of frequency response analysis can be affected by insulation aging and moisture in the transformer, leading to errors in the diagnosis of winding deformation faults. Currently, there is no effective method to prevent such errors. This paper focuses on optimizing the criterion for diagnosing winding deformations when insulation aging and moisture are present. First, the winding frequency response curves of oil-paper insulation were determined by combining insulation aging and moisture tests of the oil-paper insulation with frequency response simulations of the transformer winding. Next, the winding deformation criterion predicting the likelihood and extent of errors diagnosing transformer winding deformations due to the insulation aging and moisture content is discussed. Finally, the corresponding criterion optimization method is proposed. The corresponding results show that insulation aging and moisture can lead to errors when using the correlation coefficient R criterion to diagnose the transformer winding deformations. Moreover, the possibility of winding deformation errors caused by the change of insulation state can be reduced by introducing the corresponding auxiliary criterion through comparing the capacitance change rate based on the frequency response method and that based on the dielectric spectrum method.

FEM Modelling of the Influence of the Remaining Windings on the Frequency Response of the Power Transformer

One of the standard diagnostic methods for power transformers is frequency response analysis (FRA). This paper deals with progress in the frequency response interpretation of these very important appliances in the power network. Simulations of the frequency response of the transformer windings are a useful way to improve the correct assessment of FRA results. One of the disadvantages of FRA modelling is time-consuming analysis, especially of large multilayer windings. The aim of this article is to develop a numerical model, which would reduce the duration of the electromagnetic field analysis of the winding with hundreds of turns. The approach introduced in the paper describes the simple two-dimensional (2D) finite elements method (FEM) model, which provides the results comparable to the three-dimensional (3D) model. Moreover, the paper presents the numerical models, which demonstrate the influence of the remaining windings on the inductance of tested winding. As a result of the conducted research, the comparison of inductance curve obtained from FRA measurement on the physical model with modelled resonance slope is presented, both for 2D and 3D cases.

FRA lookup charts for the quantitative determination of winding axial displacement fault in power transformers

Frequency response analysis (FRA) has gained attention as a reliable diagnostic tool, to assess the mechanical integrity of power transformers, due to standardised FRA measurement methods. However, the assessment of FRA results is still a challenge as it demands skilful personnel for diagnosis. Since there is no definitive and reliable code available for FRA interpretation. In this study, the three-dimensional (3D) finite integration technique is used to simulate the physical geometrical dimensions of a three-phase transformer which emulate the behaviour of real transformer and frequency response measurements. This novel method eliminates the need for lumped parameter circuit models, as it provides the ability to extract the FRA signatures directly from the 3D winding model. Axial displacement of different levels is simulated in several connection schemes. It was found that variation of the inter-winding capacitance due to the axial displacement possesses a linear relationship with the degree of axial displacement fault. This provides the possibility for the quantitative determination of winding axial displacement fault using FRA. A simple mathematical relation is derived for calculating the variation of inter-winding capacitance and a geometrical factor is introduced to generalise the method. Finally, lookup charts are introduced to diagnose axial displacement fault in different transformers.

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 Modelling of Transformer Windings Connected in Parallel

This paper describes the approach to the frequency response modelling of transformer windings consisting of coils connected in parallel. At present, computer models are intensively developed with the aim of simulating the influence of faults on the frequency response of the active part of power transformers. Frequency response analysis (FRA) is one of the standard methods used for the assessment of the mechanical condition of a transformer’s windings and core. The interpretation of the FRA results is crucial in the diagnostics of the active part of the transformer. Proper simulations of the FRA results allow the improvement and simplification of the interpretation process of the windings’ faults. Usually only serial winding wires are simulated in computer modelling and parallel wires are simplified, leading to simulation inaccuracies. In this work, a combined electromagnetic field/network method, which includes parallel connections of the coils, is proposed. The method is based on lumped RLC elements. The results of the analysis conducted by the computer model are referred to as the real transformer measurement. The modelling was also performed for the case of a winding with a fault. The results of modelling were assessed with four numerical indices used for FRA interpretation.

Interpretation of frequency response analysis of power transformer based on evidence theory

Power transformers are one of the key components of power systems. Therefore, they must be operated efficiently to obtain satisfactory system performance, since any distortion or failure in power transformer structures may cause drastic damages. In order to detect deficiencies in power transformers, various methods are utilised. Frequency response analysis (FRA) is one of the most well-known methods used for fault detection in power transformers. However, the interpretation of FRA results is subjective, and depends primarily on the opinion of a human expert. In other words, there is no comprehensive, accepted and standardised method to interpret FRA results. Subsequently, fault detection based on FRA is prone to error. In this study, a new mathematical approach is used to interpret the frequency response of power transformers based on evidence theory method. This method is more accurate and less computationally burdensome compared to conventional methods. Simulations are implemented on an operating 125 MVA, 230/132/20 kV autotransformer using finite-element method and the results are compared to the corresponding FRA results of the same autotransformer in order to evaluate the proposed method. The obtained results indicate the efficiency of the proposed method in detecting probable faults of transformer windings through analysing the FRA results.

Validity of frequency response analysis (FRA) for diagnosing large salient poles of synchronouos machines

Frequency Response Analysis (FRA) is a technique under research for its application in rotary electrical machines. Even though FRA has been used for around 40 years in power transformers diagnosis, its application is still brand new in synchronous machines. The FRA technique is based on the comparison to a previous reference test that is done in healthy conditions. This article presents numerous experimental factory tests in a pole of a 40-MVA synchronous machine and onsite tests upon a 106-MVA synchronous generator in a hydro power plant where the FRA test was performed on a pole inside and outside the machine. Furthermore, simulations were executed in order to calculate the impact of the stator core on the FRA reference test. The main contribution of this article is demonstrating that the stator core has a significant influence on poles FRA results. Therefore, FRA tests done inside the machine cannot be compared to FRA tests performed outside the machine or vice versa, in order to avoid fault positives. FRA can be considered a suitable technique for the ground and interturn faults detection in poles of large synchronous machines.

Winding turn‐to‐turn short‐circuit diagnosis using FRA method: sensitivity of measurement configuration

Frequency response analysis (FRA) is increasingly being accepted as an effective technique to diagnose transformer faults. Transformer electric parameters are affected by such faults in a complex manner, and there is yet no standard approach for interpretation of FRA results. Most studies have focused on diagnosing winding and core deformations, but subtle defects in the winding insulation and turn-to-turn short circuits can develop into a more serious fault, and their early diagnosis is equally important. Furthermore, there are several test configurations which have different sensitivities to different faults. This study reports a study where the winding input impedance is measured to diagnose turn-to-turn short circuits using different measurement configurations. A comparison is made between the sensitivities of each measurement configuration to faults of increasing severity. It is found that this fault is detected in the low- and mid-frequency regions as significant reduction in impedance and a shift in resonance peaks towards high frequencies. The results, analysed using different statistical parameters, indicate differences in sensitivities with different levels of short circuits. Marginal variations were found between the sensitivities of statistical parameters in different frequency regions. The study provides useful contribution into interpretation of FRA signatures for turn-to-turn short-circuit diagnosis of transformers.