A Contribution to the Analysis of Frequency Response and Impedance Measurements to

Evaluation and Diagnostic of Power Transformers

Helvio J. A. Martins Bruno Urbani Cintia de Faria Ferreira CEPEL – Brazilian Electric Power Research Center

Av. Olinda s/n – Adrianópolis Zip Code 26053-121 – Nova Iguaçu, RJ, Brazil

Abstract-. This paper has an objective to show a developed

quantitative criterion, based in two mathematical variables that explicit the deviation degree of a normal situation, applying simultaneously data from terminal impedances and frequency response. Based in more than 100-measured equipment, of different applications (step-up transformer, transmission transformer, etc.,), for a period of 10 years, the work presents some examples of practical application of this methodology in Brazilian Electrical System.

I. INTRODUCTION

Among the various techniques available for the monitoring and diagnosis of equipment, the Frequency Response and Terminal Impedance measurements have been used in a wide application form, in particular for power transformers, focusing mainly the following aspects: Evaluation during type tests, identification of natural resonances and anti-resonances frequencies, support to equipment modeling for electromagnetic transient studies and evaluation of geometric displacements of the windings. Geometric changes of windings are sometimes associated with electromechanical efforts due to short-circuits that occur in the neighborhood of substation where the equipment is installed. An usual cause refers to the phase-to-ground short-circuit resulting from an atmospheric discharge. These changes are cumulative and not detected by any other technique, are aggravated by natural vibration associated to a natural ageing of the solid insulation causing a significant reduction clamping pressure, consequently decreasing the short-circuits tolerability of the transform, without being characterization as defect. So, the transformer remains in operation until this condition may migrate to a dangerous situation and an “unexplained” failure occur. Another fact is that power transformers are specified and designed to support short-circuits effects (of short duration) during its whole life, but in case of large power transformers the performance about this situation is rarely tested.

Another important aspect is related to transportation (roads, railways and ships), where sometimes the equipment is subjected to excessive vibrations, fallings, collisions and other situations inherent to loadings and unloading procedures. These situations must be considered before putting the equipment in operation and in some cases another tests must be performed.

Traditionally the analysis of results for these two techniques (FRA and Impedance) is made visually, qualitatively, in a comparative mode.

II. DATABASE

During the last 10 years, almost one hundred equipment (transformers and autotransformers) from various powers, voltage classes and manufacturers, have been measured by CEPEL staff and the informations were consolidated in a database. Before storage, the data were previously criticized, qualified and in some cases filtered or discarded in function of the any occurrence (example – excessive noise) which makes difficult the future utilization.

These data have been used as a source of reference for utilities and manufacturers of equipment for evaluation and diagnosis. Another aspect concerns the analysis of these results in search of identifying patterns of normality, since most of the data refers to new or used equipment in good conditions, allowing some analyses, such as: Identification of standards of normality, from the verification of characteristic response of determinate family of equipment; Comparison between equipment from different or same families and correlation between equipments. The Figures 1 to 6, show some examples of equipment families, concerning frequency response and impedance measurements. In Figures 1, 2, 5 and 6, the voltage signal was applied in H1-H0 terminals, while for Figure 3, was applied in X1-X2 terminal.

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2008 International Conference on High Voltage Engineering and Application, Chongqing, China, November 9-13, 2008

The graphics related to frequency response are normalized to

the 60 Hz frequency response, while for impedance the results are showed in Ohms.

III. EVALUATION AND DIAGNOSTIC

Usually the evaluation of some equipment using transfer functions, obtained from measurements of frequency response or terminals impedance, is made comparatively and qualitatively. The procedures adopted for implementation of appropriate analysis of the results generally follow one of the situations:

- If the sample is unique, that is, unknown to any other similar, and it is an 3 equipment, one may consider the symmetry comparison of outer phases results to the central phase; - Where it is possible to identify a family to which the equipment belongs one can compare it to others; - Where there is an equipment’s measurement historical, it makes no matter whether it is unique or belongs to a particular family, it is possible an analysis by comparison during its lifetime.

Following, it will be showed two modes normally mentioned in the literature for representative curves comparison of transfer

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functions. The correlation coefficient (-1 r 1) can be used to measure the affinity between two curves of the transfer functions, denoted by x and y, with n points of each frequency, as the following equation (1).

)var()var( y

yy

x

xx

nr i

n

i

i

1

1 (1)

Where, x and y - are relatives values to the function’s averages x

and y; and - are the variances of the functions x and y;

n - number of points measured in each transfer function.

)var(x )var(y

The application of the correlation coefficient for

comparison between curves from experiments on terminal impedance’s measurements is cited in [2], where the author suggests those correlations less than 0.9950 are indicative of defects. In a deeper research on ways of comparing curves [3], there is an important limitation of this method, which is related to how the curves are compared. Multiple curves of each other, although displaced in amplitude or phase, may lead to correlation coefficients equal to 1, generating a false diagnosis.

Another approach for comparing the two curves is used in [4] using equation for spectrum’s deviation, which measures the affinity between a given curve and an average curve obtained from the set of interesting curves, with no limits on information from of which sets itself is an indicative of a defect. In this work, in the formula (2) below, "m" was considered equal to 2.

n

i

m

ii

iii

m

ii

iii

yx

yxy

yx

yxx

n 1 2

2

2

21

/)(

/)(

/)(

/)( (2)

When using any method chosen for comparison between the

curves, it is essential that the data have been treated and qualified before, eliminating at the stage of measuring, possible interference’s sources and the conditions in which the results were obtained are the same, with guaranty of repeatability. This stage is crucial, so much, that a work carried out by CIGRÉ, for comparison of measuring terminal impedance’s curves for a particular equipment [5], involving laboratories of some authoritative international staffs, resulted in that occasion obtaining similar results until the 300 kHz frequency.

The search for a criterion that can be implemented aiming a diagnosis from the comparison between two situations, expressed by its terminal impedance and / or frequency response’s curves has been the object of study, and an example

of a possible help for diagnosis purpose is shown in the table I below.

TABLE I

DIAGNOSIS CRITERION [6]

Frequency range Indicative

Below 2 kHz Core effect

2 kHz – 20 kHz Interaction between windings

20 kHz – 1 MHz Effect of Winding Structure of the Winding under Test

Beyond 1 MHz Effect of Leads of Taps and Earthing leads

IV. PROPOSAL METHODOLOGY

The curves of each transfer functions (TF) measured are initially compared with the original one, calculating for each frequency’s decade, the correlation coefficient and the spectrum’s deviation in search of any significant change. It is understood that a significant change exceeds a certain limit, for example, the tolerance of project [7], obtained for a group of transformers of same family and manufacture design. In this work, were established two limits: a minimum value of correlation (rmín) and a maximum value for the spectral deviation ( máx), both obtained for each equipment’s family. For evaluation of an equipment condition, was used a composition of these parameters as shown in the table II below:

TABLE II

EVALUATION PARAMETERS

r Situation

> rmin < max Normal

< rmin > max Defect

> rmin > max Defect(*)

(*) - Curves are multiple among themselves.

We might expect, as the equipment becoming older the

original transfer functions will change, being necessary from time to time a system’s calibration associated with any internal inspection unit (if possible).

V. APPLICATION EXAMPLE

As an example of application of this criterion, Figures 7 and 8 show a complex case, which involves changes in two frequency ranges, to a new step-up transformer, 13.8 / 550 kV, 405 MVA, which was damaged during transport between the

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manufacturer and the utility hydroelectric plant. The accident has occurred when one of the wood’s cross support between the tank’s bottom of the transformer and the truck has broken, causing a small fall over the truck’s floor.

For the two curves, one for the frequency response between

the high voltage and low voltage winding, and the other of terminal impedance of high voltage winding, is shown in the table III below the correlation coefficients and spectrum’s deviation.

TABLE III

CORRELATION COEFFICIENTS AND SPECTRUM´S DEVIATION

Frequency Range

Frequency Response

Terminal Impedance

r r

10Hz – 100Hz 1,0000 0,0016 1,0000 0,1190

100Hz – 1kHz 1,0000 0,0019 0,9790 0,1309

1kHz – 10kHz 0,9996 0,0106 0,9998 0,0079

10kHz – 100kHz 0,9999 0,0048 0,9999 0,0102

100kHz – 1MHz 0,9216 0,1305 0,9998 0,0791

1MHz – 4MHz 0,7947 0,4881 0,8951 0,2659

The analysis of the curves of terminal impedance for the first two decades indicates some deviations, signalizing some problem with the core, which was reinforced since the equipment was not energized until that time. The frequency response’s curve has showed some alteration in amplitude and phase in the poles for frequency range above 100 kHz, characterizing some geometric changes in the high voltage winding. Internal inspections have confirmed the diagnostic previously obtained by the techniques and in the case of the core, the damaged caused by the fall was only possible to identify after extracting the active part of the power transformer.

VI. CONCLUSIONS

The work has showed some frequency response and impedance measurements standards for power transformers (core type), which are mainly determined by the power of the equipment than by the kind of manufacturer.

The combined use of correlation coefficient and spectrum deviation may be a useful tool to evaluate and diagnosis power transformers data related to frequency response and impedance measurements.

Finally an example of application of the techniques associated with a criterion was showed using an equipment that has suffered an accident during its transportation, emphasizing that it would be impossible to other techniques to diagnostic the damage in the core bottom of this unit.

REFERENCES

[1] LAPWORTH, J. A, 1995, “Mechanical Condition Assessment of Power

Transformers Using Frequency Response Analysis”. Doble International Conference.

[2] RYDER, S. A., 2002, “Methods for Comparing Frequency Response Analysis Measurements”. IEEE International Symposium on Electrical and Insulating, Boston, USA, 7 – 10 April .

[3] KIM, W. J., PARK, B., SEUNG J., KIM, S., 2005, “Fault Diagnosis of Power Transformer Using an Improved Frequency Response Analysis”. IEEE Transactions on Power Delivery, v. 20, n. 1, January.

[4] BAK-JENSEN, J., BAK-JENSEN, B., MIKKELSEN, S. D., 1995, “Detection of Faults and Ageing Phenomena in Transformer by Transfer Functions”, IEEE Transactions on Power Delivery, v.10, n.1, pp. 308-314, January.

[5] WGA2.26, 2006, “Mechanical Condition Assessment of Transformer Windings using Frequency Response Analysis (FRA)”. Electra, n. 228, pp.30-52, October.

[6] SOFIAN, D. M., “Transformer FRA Interpretation for Detection of Winding Movements”, PhD Thesis, The University of Manchester, July 2007.

[7] CHRISTIAN, J., FESER, K., 2004, “Procedures for Detecting Winding Displacements in Power Transformers by the Transfer Function Method”, IEEE Transactions on Power Delivery, v.19, n.1, pp. 214-220, January.

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