Modelling of Power Transformer Winding Faultsfor Interpretation of Frequency Response Analysis

(FRA) MeasurementsAlmas Shintemirov

School of Science and Technology, Nazarbayev UniversityAstana, Kazakhstan

Email: ashintemirov@nu.edu.kz

Abstract—This paper discusses the possibility of utilizingpower transformer modelling for interpretation of frequencyresponse analysis (FRA) measurements. FRA is a reliable tech-nique for power transformer winding distortion and deformationassessment and monitoring. A lumped parameter model of athree phase power transformer is briefly presented and applied tosimulate frequency responses at various winding fault conditionssuch as short-circuited turns, axial displacements and radial de-formations. Simulations and discussions are presented to explorethe potentials of the model to transformer fault detection basedon FRA measurements.

I. INTRODUCTION

Frequency response analysis (FRA) is widely recognized asa reliable technique for power transformer winding distortionand deformation assessment and monitoring. The analysisof the response shapes in higher frequencies provides infor-mation about the changes of internal distances and profilesin a transformer winding which characterizes its deviationor geometrical deformation [1]–[3]. Thus, the simultaneousmeasurements of amplitude ratio and phase difference betweenthe input and output signals of a transformer winding give itsfrequency response in a wide range up to several mega hertzusing the Fourier transform.

Despite of extensive FRA practice, transformer windingcondition assessment is usually conducted by experts ortrained on-site engineers. The obtained FRA traces are com-pared with the various reference ones taken from the samewinding during previous tests (“time-based” (reference) com-parison) or from the corresponding winding of a “sister”transformer (“type-based” (sister unit) comparison), or fromother phases of the same transformer (“construction-based”(phase) comparison) [1]–[9]. The shifts in resonant frequenciesand magnitude of FRA traces indicate a potential windingdeformation. However, the questions of potential deformationlocation in a winding are still required to be investigated.

In practice, each section of an equivalent circuit representsone or a few discs in the case of a disc type windings andone or a few turns of helical type windings [10]–[12]. Thelumped parameter simplified models for one phase transform-ers have been used to analyse axial and radial displacementsof the model transformer windings [13]–[15]. However, theseworks neglected the effect of transformer core on frequencyresponses at frequencies above several kHz, which should be

Fig. 1. FEM geometry of the experimental transformer in a draw mode (ahalf of the geometry is shown).

taken into account for more accurate modeling of three-phasepower transformers [16].

In this paper, a lumped parameter equivalent model of athree phase power transformer with the magnetic core effectincluded is applied to FRA simulation of various windingfault conditions. Simulations and discussions are presented toexplore the potentials of the proposed model to transformerfault detection.

II. TRANSFORMER MODEL

The lumped parameter model, presented in [11], [12], of a 3-phase experimental transformer (400 kVA, 15/0.4 kV) having aΔ-Y winding configuration is employed to simulate frequencyresponses due to its high degree of simulation accuracy incomparison with experimental measurements. The geometricaldimensions of the transformer are presented in [17] and usedfor hierarchical FEM computation of inductive and resistive

(a) (b)

Fig. 2. Magnetic flux density distribution in the experimental transformer core at frequencies f = 300 Hz (a) and f = 664 kHz (b).

parameters of the lumped parameter model [17]–[19]. Capac-itance and conductances of the model are estimated using theanalytical expressions and measurements of dielectric materialproperties presented in [16].

Using the graphical interface of the COMSOL Multiphysicsfinite element method (FEM) software [20] the FEM geometryof the transformer core with LV and HV winding sectionshas been drawn as shown in Fig. 1. The previously obtainedmagnetic properties of the core and winding conductors areset up alongside with the governing equations and internalparameters of the program. The software generates a meshto divide the FEM geometry of the transformer into finiteelements and solves numerically the magnetostatic problemdescribed in [17], [18] at different frequencies in the range ofinterest (Fig. 2).

III. SIMULATIONS OF TRANSFORMER WINDING FAULTS

The transfer function responses, simulated with the lumpedparameter model of the 3-phase experimental transformer, areemployed to study the effect of major winding faults such asshort-circuited turns, axial displacements and radial deforma-tions on frequency responses. These winding conditions areanalysed using the case studies reported in other publicationsand the simulations with the 3-phase lumped parameter modelin the frequency range limited by 1 MHz.

A. Normal Winding

The normal state of a winding usually corresponds to aconsistent response shape and resemblance between several

responses at cross-comparison.

B. Short Circuited Turns

To simulate short-circuited turns, a large admittance(low impedance) is added between the nodesrepresenting adjacent ends of two sections of the3-phase lumped parameter model. This has been performedin several different positions along the HV and LV windingsin order to observe the differences.

The LV winding transfer function responses of the exper-imental transformer are illustrated in Figs. 3(a) and 3(b). Asseen from the figures this fault type is clearly detectable withindifference to the fault location due to disappearance of thefirst resonance points at low frequencies associated with thetransformer core. Therefore, this fault can easily be detectedeven using the “construction-based” (phase) comparison with-out additional expert analysis or comparison with referenceresponses [7].

C. Axial Displacement

Right shifts in medium frequency resonances may indicatepotential axial displacement, also known as axial collapse,of a winding with respect to other transformer windings. Inaddition, new resonances may appear at higher frequencies [1],[5], [21], [22]. Similar to a hoop buckling, this failure usuallyattributes no clear indication at low frequencies.

To simulate different scenarios of an axial displacementfault, the whole LV winding of experimental transformer isassumed to be shifted on 17.4 mm upwards and downwards,

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Fig. 3. “Time-based” (reference) comparison of the LV winding responses of the 3-phase experimental transformer: short-circuited turns 10-11 in LV winding(a) and short-circuited discs 15-16 in HV winding (b)

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Fig. 4. “Time-based” (reference) comparison of the LV winding responses of the 3-phase experimental transformer: axial shift up on 17.4 mm of LV winding(a) and axial shift down on 17.4 mm of LV winding (b) with respect to HV winding

which approximately corresponds to 3.5% of the windingheight. The phase A parameters of the 3-phase lumped pa-rameter model are correspondingly modified to introduce thechanges in impedances and admittances between the HV andLV windings.

Figures 4(a) and 4(a) illustrate the transfer function re-sponses simulating upward and downward shifts of the LVwinding with respect to the HV winding respectively. As seenfrom the figures there are clear shifts to right in resonancefrequencies in both the cases, which supports the above

classification hypothesis.

However, the shifts in resonance frequencies appear not onlyin the middle-frequency range but also at low frequencies.This can be explained by the fact that the whole LV windingdisplacement is modelled with respect to the HV winding.Potentially, this may cause a clamping failure of a transformerand, therefore, be expressed as resonance shifts at low frequen-cies [8].

On the other hand, in many cases an axial displacementfault is accompanied by winding compressing or, otherwise,

Core

HV winding side LV winding

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Core

LV windingHV winding side

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Fig. 5. Electrical potential distribution in the 3-phase experimental transformer (the space between HV and LV windings and between LV winding and core,radial deformation of LV winding): buckling degree 1 (a) and buckling degree 3 (b)

stretching (telescoping), characterised by the correspondingdistance changing between sections of the faulty winding.This may cause more significant deviations of resonancefrequencies or new resonance points appearances at higherfrequencies.

D. Radial Deformation (Hoop Buckling)

Severe radial deformation of a winding, known as hoopbuckling, leads to a bent winding, being not broken. Thesedeformations normally occur in inner (usually LV) windingsand show significant decrease (shift to left) of the medium-frequency resonance points while low frequency open circuitresponses usually indicate no difference [1], [14]. In addition,short-circuit FRA test results may indicate increased inputimpedance of the damaged phase with respect to other phasesof a transformer [5], [6].

In order to model a radial deformation of the LV windingof the experimental transformer, the following deformationdegrees are considered [14]: deformation of one side of thewinding (degree 1) and deformation of three sides of thewinding with 900 with respect to each other (degree 3) asshown in Figs. 5(a) and 5(b) respectively. The deformationdepth is 1 cm, which is about 8% of the LV winding radius.

In general, deformations of winding geometry result in mod-ification of the corresponding model parameters. Therefore,it is necessary to investigate the effect of radial deformationon the model parameters. The analysis of relative changesof winding self and mutual inductances was presented in[14] using analytical calculations and with FEM in [16].In these works, the inductances of winding sections werecalculated considering different degrees of radial deformation,

TABLE IRELATIVE DEVIATIONS (%) OF LUMPED MODEL PARAMETERS DUE TO

HOOP BUCKLING OF THE LV WINDING OF THE 3-PHASE EXPERIMENTAL

TRANSFORMER

Hoop Buckling Inductances ResistancesMode LLV LLVHV RLV RLVHV

Degree 1 0.37 0.26 0.66 0.39

Degree 3 1.79 0.47 1.84 0.56

Hoop Buckling Geometrical CapacitancesMode CHVLV,geo CLV,geo

Degree 1 4.4 19.29

Degree 3 3.07 58.25

without taking into account the transformer core effect. It wasconcluded that the changes in inductances due to bucklingwere negligible compared to the capacitance changes andmight not be accounted during simulations. Therefore, thisassumption should be confirmed for the case when the coreeffect is taken into account.

In order to model the winding radial deformations accu-rately, the deformed geometries of a LV winding section aremodelled using FEM calculations. 2D FEM models are used tocompute capacitances and conductances of the winding sectionas shown in Figs. 5(a) and 5(b), where the electrical potentialdistributions for the two deformation degrees are illustrated.On the other hand, inductances of the deformed LV windingsections are calculated using 3D FEM model.

Relative deviations of the inductances, resistances and ca-pacitances of the LV winding and between the HV and LVwindings are listed in Table I. As seen from the table, in

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Fig. 6. “Time-based” (reference) comparison of the LV winding responses of the 3-phase experimental transformer (radial deformation of LV winding):buckling degree 1 (a) and buckling degree 3 (b)

general, the capacitances are much more influenced by thewinding buckling than the inductances, showing less then 2%deviations, which are in line with the analysis in [14], [16].Thus, as proposed in [14], [16] the inductance deviationsdue to radial deformation may not be considered in order tosimplify the modelling process. The same assumption maybe applied to resistances, which also deviate insignificantlywith less than 2% relative difference due to introduced radialdeformations.

On the contrary, the capacitances between a LV winding anda core rapidly increase depending on the deformation degree,showing about 19% and 58% changes for the deformationdegrees 1 and 3 respectively. This is due to the LV wind-ing buckling towards the core, which reduces the distancesbetween the corresponding surfaces of the LV winding andthe core.

Figures 6(a) and 6(b) illustrate the transfer function re-sponses simulating hoop buckling of the LV winding with thedeformation degrees 1 and 3 respectively. As seen from thefigures, there are slight shifts to left in resonance frequencies inboth the cases, that support the above classification hypothesis.

IV. CONCLUSION

This paper discusses FRA interpretation criteria related todifferent FRA diagnoses on winding conditions at frequenciesup to 1 MHz using the lumped parameter model. The lumpedparameter model is employed to simulate frequency responsesof a 3-phase experimental transformer with introduced wind-ing faults such as short-circuited turns, axial displacementsand radial deformations. The simulation results show that themodel can correctly reflect the interactions between capaci-tances and inductive elements in power transformer windingsin a wide frequency range up to several MHz and could beused for FRA result interpretation.

On the basis of the simulation study presented in thispaper and analysis of experimental case studies on differentwinding conditions, an evidential reasoning (ER) approachto transformer winding condition assessment based on FRAhas been proposed in [9]. Consequently, further studies willbe concentrated on utilizing of the presented transformermodelling concept for developing a transformer winding de-formation detection procedure upon measurement data.

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