Knowledge Bases for the Interpretation of the Frequency Response Analysis of

Power Transformers

Juan L. Velsqueza Miguel A. Sanz-Bobib Miguel Gutierrezc Alexander Kraetgea aOMICRON Electronics GmbH, Oberes Ried 1 , A-6833 Klaus, Austria

bUniversidad Pontificia Comillas, Instituto de Investigacin Tecnolgica, IIT, Santa Cruz de Marcenado 26, 28015 Madrid, Spain

cOMICRON Electronics Corp., 12 Greenway Plaza, Suite 1510, Houston Texas juan.velasquez@omicron.at, Miguel.gutierrez@omicronusa.com

Abstract

The FRA method provides comprehensive and unique

information about the mechanical and electrical

integrity of the active part of transformers. For taking

advantage of the potential of this method, certain

knowledge bases are necessary in order to assist the

automatic process of diagnosis. In this work such bases

are presented from the point of view of the

understanding of the waveform of the plots and from the

standpoint of assessment of the results. Moreover, an

attempt for the characterization of different failure

modes by using transformer-specific sub-bands is also

provided as well as an overview to the effects of the

factors affecting the repeatability of FRA results. At the

end the formulation of algorithms for automatic

detection of abnormalities and its relationship to the

development of an expert system is presented.

1. Introduction to the FRA method The Frequency Response Analysis (FRA) has been proven to be a powerful tool for the detection and diagnosis of the active part of power transformers [1]. In contrast to traditional diagnostic methods, the FRA method is able to detect geometrical deformations in the windings before the occurrence of a major or catastrophic failure. When talking about FRA it is important to distinguish between Impulse Frequency Response Analysis (IFRA) and Sweep Frequency Response Analysis (SFRA). This work focuses the attention on the SFRA method. As illustrated in Fig.1, the SFRA consists in applying a frequency variable low-level sinusoidal signal "U" at one end of a winding and from this point a reference signal "U1"is measured. Simultaneously the output or response signal at the other end of the winding "U2" is measured. Subsequently, the transfer function H(f) is computed. It can be easily demonstrated that H(f) corresponds to the

expression (1). This means that the H(f) is only dependant on the measurement resistance of the FRA instrument (Rm) and on the impedance of the transformer (Ztra). The most common way of representing the results is as bode diagrams as shown in Fig. 2. In the majority of the cases only the plot of the magnitude is used for interpretation purposes. Nevertheless, the plot of the phase also provides valuable information. The magnitude and the phase are computed according to the equations (2) and (3).

RMC

RLC Network

U1 Rref=50 U2Rm=50

50

U

CMC

Figure 1. Measurement setup

f/Hz1.000e+002 1.000e+003 1.000e+004 1.000e+005

dB

-100

-90

-80

-70

-60

-50

-40

-30

-20

H0 H1 H0 H2 H0 H3

f/Hz1.000e+002 1.000e+003 1.000e+004 1.000e+005

100

150

Ma

gn

itu

de

(d

B)

Ph

as

e (

)

tram

m

ZR

R

fU

fUfH

+==

)(

)()(

1

2 (1)

)/(log20 1210 UUk = (2)

)/(tan 12

1UU = (3)

Figure 2. Graphical representation of FRA results

2. Bases to the interpretation In this section the term "interpretation" is analyzed from two points of view: from the point of view of the understanding of the waveform of the plots and from the point of view of the assessment of the results. 2.1. Understanding of the plots Taking into account that a power transformer from the electrical standpoint, is a complex network of resistances, inductances and capacitances, the frequency response of these elements are the foundations for the understanding of the transformer response. The response of a resistance is a straight line with a constant attenuation along the frequency range. The response of inductances and capacitances is governed by the equations (4) and (5) respectively.

fLLX L pi 2== (4)

CCXC pi 2

11== (5)

If traZ = LX in equation (1), it can be said that as long

as the frequency increases, H(f) decreases. This explains the typical increase in the attenuation of an inductance as

illustrated in Fig. 3(a). In contrast, if traZ = CX in (1), as

long as the frequency increases, the attenuation decreases as depicted in Fig. 3(b). Other aspect of major importance for the interpretation is the concept of resonance. In an RLC network the resonances are series or parallel resonances. Series resonances are related to a maximal transfer of energy between two systems, that is, to the minimal impedance at a determined frequency. While a parallel resonance is related to minimal transfer of energy between two systems (maximal impedance). In the plot of the amplitude, minimal impedances are seen as minimal attenuations while maximal impedances as minimal attenuations according to (1). In Fig. 3(c) and 3(d) the responses of RLC networks connected in parallel and in series are shown. The simulations were done using an inductance of 50 mH. In conclusion, the maximal peaks in the frequency response are created by series RLC networks and the minimal peaks by parallel RLC networks. However, it is worth to mention that in the frequency response not all the maximal and minimal peaks are resonances. The best way of recognizing resonances is by taking a look at the plot of the phase. When a resonance is present, the phase should be zero, what means that the response is 100% resistive. If now the physical components of the active part of a transformer are associated to RLC elements, an equivalent circuit as the one shown in Fig. 4 can be used for a qualitative explanation of the frequency response of a real transformer.

10

210

410

6-150

-100

-50

0

Frequency (Hz)

Am

plit

ude

[dB

]

L=200 mH

L=2 mH

L=20 H

(a)

10

210

410

6-200

-150

-100

-50

0

Frequency (Hz)

Am

plit

ud

e [d

B]

C=1uFC=20nF

C=1pF

(b)

10

210

410

6-30

-25

-20

-15

-10

-5

0

5

Frequency (Hz)

Am

plit

ud

e [

dB

]

C=1nF

C=10nFC=50nF

(c)

10

210

410

6-140

-120

-100

-80

-60

-40

-20

Frequency (Hz)

Am

plit

ud

e [d

B]

C=1nFC=10nF

C=50nF

(d)

Figure 3. Series and parallel resonances of RLC networks

Cg1

CHL

Cs1

HV Winding

LV Winding

Cg2

L1, R1

L2, R2

Cs2

R1: resistance of the HV winding

L1: leakage inductance of the HV windingR2: resistance of the LV winding

L2: leakage inductance of the LV winding

Cs1: series capacitance of the HV windings

Cs2: series capacitance of the LV windingsCg1: parallel capacitance of the HV windings with

respect to ground

Cg2: parallel capacitance of the LV windings with respect to core

C12: capacitance between HV and LV windings

L1R1

Cg1

Lm

L2 R2

Rn

C12

Cs1 Cs2

Cg2

Figure 4. Physical components of the transformer

as RLC network The FRA response of a transformer can hardly be generalized since the response highly depends on the design of the windings, their connections (Y or D), etc. In this work only the FRA response of power transformers with windings connected in YN is described. In general, the response of YN connected windings can be classified in two groups: response of HV windings and response of MV or LV windings. For the HV windings normally inter-shielded or inter-leaved windings are used in order to get a high series

capacitance (Cs). This is done for allowing a uniform distribution of the voltage along the windings. For many transformers, the pattern of the FRA plots can be divided in sub-bands where there are specific dominant elements of a transformer as indicated in Table 1. For accounting on the differences among transformers, an automatic identification of these sub-bands is highly recommended as it will be presented in section 3, these bands provide the bases for the detection of failure modes from the FRA plots. The band B1 occurs normally between 20 Hz and 200 Hz and here mainly it is present the inductive behavior of the magnetizing inductance. In the band B2, between 200 Hz and approximately 3 kHz the parallel capacitance Cg highly influence the response. Between 3 kHz and 200 kHz the band B3 is defined for characterizing the interaction between windings. This band is sensitive to bulk winding deformations. The band B4, between 200 kHz and 1 MHz exhibits an accentuated capacitive response caused by the series resonance Cs. This band is sensitive to localized deformations in the windings. Finally, the band B5 between 1 MHz and 2 MHz exhibits an inductive behavior that is highly influenced by the inductance of the internal leads of the transformer and by the measurement setup.

f/Hz1.000e+002 1.000e+003 1.000e+004 1.000e+005

dB

-70

-60

-50

-40

-30

-20

-10

Magnetizing inductance (Lm)

Parallel capacitance (Cg)

Series capacitace (Cs)

Measure

ment

setu

p a

nd leads

Iteraction between windings

B

C

D

E

A

F

Figure 5. Relationship between the FRA plot of a

220 kV winding and the physical components of one transformer

Table 1. Typical sub-bands in the FRA plots Band From Til

l Dominant elements

B1 A B Lm B2 B C Lm and Cg B3 C D L1, Cg, and mutual couplings B4 D E Cs B5 E F Internal leads

For the MV windings a high Cs is not a requirement and that's why other kinds of winding design are used such as continuous disk windings. In Fig. 6 a typical response of MV windings is shown. For MV windings is much more difficult to identify the sub-bands where the elements of the transformer domain. Because for these windings Cg is comparable to Cs, there is a big interaction among the capacitances and it is not possible to get a sub-bands

where only the Cs domains the response as in the case of HV windings. The strong interaction between the inductances and capacitances gives place to multiple peaks at high frequencies. For LV windings normally helical windings are used. Similar to disk windings, these windings also have a small Cs and a strong interaction with Cg. Cs and the inductances occur as in disk windings as illustrated in Fig. 7.

f/Hz1.000e+002 1.000e+003 1.000e+004 1.000e+005

dB

-60

-50

-40

-30

-20

x0 01 x0 x2 x0 x3 Figure 6. Typical FRA response of 110 kV

windings

f/Hz1.000e+002 1.000e+003 1.000e+004 1.000e+005

dB

-40

-35

-30

-25

-20

-15

-10

x0 x1 x0 x2 x0 x3 Figure 7. Typical FRA response of 12.47 kV

windings 2.2. Assessment of results FRA is a comparative measurement method. This means that results of an actual test are compared to a reference or baseline. Three methods are commonly used to assess the measured traces:

1. Time-based (current FRA results will be compared to previous results of the same unit)

2. Construction-based (FRA of one transformer will be compared to another of the same design)

3. Phase comparison (FRA results of one phase will be compared to the results of the other phases of the same transformer)

The preferred method is the time-based comparison. Unfortunately the so called fingerprint is in the majority of the cases not available. Nevertheless, by a simple comparison of the FRA plots of the phases or by type-

based comparison, a successful assessment of the results can be achieved. Even if a fingerprint of the transformer is available, the experience has demonstrated that the comparison has to be carried out carefully because in some cases the deviations observed are not related to deformations, but to measurements under different conditions or due to measurement mistakes. For overcoming theses misleading factors, the comprehensive time-based comparison concept is proposed in this work. The flow diagram of this concept is shown in Fig. 8. The method is based on the comparison between the FRA plot of each phase of the actual test (Test 2) and its fingerprint (Test 1). Then an analysis of deviations is performed by means of the algorithms of automatic detection described in section 5. The key point is to determine if the same kind of deviation is detected or not in the three phases. If the same deviation takes place in the three phases and in the same frequency range, there are very likely no deformations in the transformer, but different conditions in the transformer or just a measurement mistake in one of the tests. In order to find out weather the deviations are or not related to deformations, a comprehensive phase-based comparison of the regions of deviations is here proposed. As can be noted in Fig. 9, the comprehensive phase-based comparison is based on the comparison of the phases of both Test 1 and Test 2 and an analysis of deviations observed.

Time-based Comparison

B1 vs.B2A1 vs.A2 C1 vs.C2

Core integrity is suspected

Core deformation is suspected

Winding's integrity is suspected

Deformation in windings is suspected

Connection lead's integrity is suspected

Deformation in connection's leads is suspected

Clamping structure's integrity is suspected

Deformation in the clamping structure is suspected

Test 1

Trace Phase A1

Trace Phase B1

Trace Phase C1

Test 2

Trace Phase A2

Trace Phase B2

Trace Phase C2Analysis of Deviations by means of Algorithms of

automatic detection

No deviationsDeviations

Similar three-phase deviations

Single-phase or Bi-phase deviations

Expert System

Phase comparison for

further investigation is

required

Active's part integrity is suspected

Figure 8. Comprehensive time-based comparison

Test 1

Trace Phase A1

Trace Phase B1

Trace Phase C1

Test 2

Trace Phase A2

Trace Phase B2

Trace Phase C2

Phase-based

comparisonA1 vs B1 B1 vs C1

C1 vs A1

Analysis of

Deviations by means

of Algorithms of

automatic detection

Analysis of

Deviations by means

of Algorithms of

automatic detection

Analysis of

Deviations by means

of Algorithms of

automatic detection

Analysis of

Deviations by means

of Algorithms of

automatic detection

Expert System

No deviations Deviations No deviationsDeviations

Tests under different

conditions

Measurement

mistakes

Three-phase

deformationActive's part integrity

is suspected

Construction-based

comparison

A1 vs A3 B1 vs B3

C1 vs C3

Test 3

Trace Phase A3

Trace Phase B3

Trace Phase C3

Phase-based

comparisonA3 vs B3 B3 vs C3

C3 vs A3

Construction-based

comparison

A2 vs A3 B2 vs B3

C2 vs C3

Figure 9. Comprehensive phase-based comparison

If there are not deviations found in the comparison of the phases of the Tests 1 and Test 2 in the regions of

deviations , there are two possible sceneries for explaining the deviations found in the time comparison. One possibility is that there is integrity of the active part and in this case the deviations could be due to different conditions of the transformer or due to measurement mistakes. The other possibility is that there is a deformation in the three phases of the transformer, this is not very likely but it should be considered as possible scenery. In these cases, the easiest way for determining the presence of tests under different measurement conditions, measurement mistakes or simultaneous three-phase deformations, is by means of a construction based comparison with a twin o sister transformer (represented in Fig. 9 as Test 3). As result it can be distinguished between deformations and tests under different conditions or measurement mistakes. Otherwise, if there are not deviations found in the phase comparison of the Test 1/Test 2 , but in the phase comparison of the Test 2/Test 1 deviations are found, the likelihood of deformations in the Test 2/Test 1 is high and further investigations are necessary. The construction based comparison is also a powerful tool in these cases.

3. Detection of failure modes with FRA plots The failure modes that can be detected in the active part of transformers using the FRA methods are multiple. Depending on the nature of the deformation (electrical or mechanical) its effects on the FRA plot can be assigned to specific sub-bands. The bases of knowledge for interpreting FRA results reside on the capability of the expert in recognizing the pattern of specific failure modes in FRA plots. A generalization of the patterns of failures is a cumbersome task because the patterns of the FRA response of the transformer itself depend on the type of transformer and design considerations. Nevertheless, in this section an attempt to the characterization of the failure modes along the frequency spectrum is presented. Such characterization is given with base on the split of the frequency spectrum in transformer-specific sub-bands as presented in section 2.1. In Table 2 a list of the electrical failures that can be detected by FRA is presented. Actually the majority of electrical failures can also be detected by traditional diagnostic methods. The advantage of FRA is that taken just one measurement, the same information is obtained that using several traditional diagnostic methods. Additionally FRA allows for the detection of other failures modes that can be hardly detected by traditional methods as ungrounded core, ungrounded electromagnetic screens and short-circuits in current transformers placed at the bushings.

Electrical failures characterize themselves for affecting the magnetizing inductance of the transformer and the winding resistance as well as the self-inductance of the windings. This is the reason why their effects are visible at low frequencies as indicated in Table 2. Table 2. Electrical failure modes and sub-band of detection Detectable failure mode B1 B2 B3 B4 B5 Short-circuit between strands / turns

Short-circuit between windings and core

Ungrounded core Ungrounded electromagnetic screen

Shorten core laminations Open-circuit High impedance Multiple core grounding Short-circuits in bushing's CT Shorten leads The mechanical failure modes and the sub-bands in which these can be observed in the FRA plots are shown in Table 3. The failure modes related to deformations in windings are visible in the sub-bands B3 and B4. Radial deformations as the hoop tension failure are mainly detected in the sub-band B4. In the sub-band B3 it might be also possible to observe the effects of a buckling, but normally in this region the changes are minimal this is the reason why the sun-band B3 should only be used as secondary evidence. Typically the FRA plots of buckling failures are related to horizontal deviations of the FRA plot to the right in the region B4. Other typical symptoms could be the creation of new peaks in the region B4, depending on the severity of the deformation. Other failure modes related to radial deformations are the radial compression failures. Tilting of conductors is caused by the axial cumulative compression applied to the conductors via any axial spacers or stampings. These deformations affect mainly the series capacitance of the windings (Cs) and for this reason its effects can be appreciated in the sub-band B4. The axial telescoping failure refers itself to two phenomena: a) movement of individual winding relative to one another, and b) axial instability of a single winding (outer turns moving upward or downward relative to inner turns), that's why is sometimes also called axial collapsed. This kind of deformations affects both the sub-band B3 and the sub-band B4. On one hand, the bulk movement of a winding modifies the interaction among windings and hence the mutual couplings. And on the other side, this kind of deformations produce a decreasing in the series capacitance of the windings what causes a typical shift of the peaks to the left in the FRA plot. Other failure modes such as break of clamping

plates and loose clamping structure can be appreciated in the FRA plot in the sub-band B4. Regarding to geometrical deformations of internal leads, such as the connection leads between the regulating windings and the tap changers and the leads between the windings and the bushings, it can be said that these changes can be appreciated in the sub-band B5. Table 3. Mechanical failure modes and sub-bands of detection

Detectable failure modes B1 B2 B3 B4 B5 Radial compression failure (Buckling in inner windings)

Hoop tension failure (Buckling in outer windings)

Tilt in conductors Axial collapse (Telescoping failure)

Break of clamping plates Loose clamping Spiral tightening Shifted regulating winding leads

Distorted leads

4. Factors affecting the repeatability As discussed in the section 2.2, the comparison of FRA results measured under different conditions is one of the possible causes of deviations that could lead to an erroneous assessment of FRA results. In this section, the basic knowledge base is presented for the identification of the effects that different factors have in the FRA plots. Such factors are classified into three groups as shown in Fig. 10. The conditions of the transformer (group A) are of major importance. Not always the transformer is tested under the same conditions and if this is the case, the conditions have to be properly documented in order to allow a reliable interpretation. The oil temperature does not affect the results considerably, but it is recommended to be documented. The experience has shown that in many cases, the connection of the tertiary windings during measurements in the primary or secondary windings is one of the factors leading to wrong interpretation of the results.

Factors

affecting the

Repeatability

Electromagnetic environment

Remanence

Oil Insulation degradationTemperatureCore grounding

Moisture

Tap changer position

Tank

Bushings

Measurement cables

FRA instrument

Reverse connection

Tester

Arrangement of

cables

Measurement

mistakesC Stochastic factors

B Tester and instrument related factors

A Transformer conditions

Tertiary windings

Injection point

Figure 10. Factors affecting the repeatability

Regarding to the tester and instrument related factors; the connection technique of the FRA instrument plays a very important role in the reproducibility. The connection technique with aluminum braids has been recommended by the CIGR WG A2.26 [2]. Table 3. Characterization of the effects of the factors affecting the repeatability in sub-bands

Factors B1 B2 B3 B4 B5 Moisture Temperature Oil level Insulation degradation Tertiary windings Core grounding Bushings Tank Tap changer position Remanence Electromagnetic environment FRA instrument Measurement cables Injection point Reverse connection Arrangement of cables Measurement mistakes

5. Algorithms for automatic detection and

diagnosis Different algorithms are proposed in this work for the required analysis of deviations presented in section 2.2. These algorithms can be structured in three groups as can be observed in Fig. 11. As part of the statistical algorithms, the cross-correlation, the standard deviation and the covariance can be used as general indicators of deviations. But for a more reliable detection, feature extraction algorithms are also necessary, especially for the detection of localized deviations. As a complement, modeling techniques, such as mathematical modeling of the transfer function by means of a rational functions and circuit synthesis or network realizations provide also very important information for the detection.

Statistical algorithms Feature Extraction

Modeling

Physical

2210

2210

sBsBB

sAsAAZ

++

++=

2210

2210

sBsBB

sAsAAZ

++

++=

Mathematical

Circuit synthesis with

physical meaning

Circuit synthesis

without physical

meaning

Figure 11. Algorithms for automatic detection

For the diagnosis, a link between the algorithms and the real failure modes has to be established. For this purpose, the development of an expert system is also proposed. The application of the algorithms to FRA data of healthy and failed or distorted transformers provides the knowledge base for training the expert system.

6. Conclusions An understanding of the frequency response of RLC networks constitutes the bases for understanding the FRA response of a real transformer. A generalization of the FRA response of transformers is difficult, but for transformers of the same family is possible to describe general patterns. Identification of transformer-specific sub-bands is a key element for the automatic detection and diagnosis of FRA results. Patterns of the effects of both failure modes and factors affecting the repeatability of FRA results in the sub-bands can be built by means of algorithms and subsequently be used as input to an expert system for an automatic and reliable diagnosis of the results what is one of the biggest challenges of the FRA method.

7. References [1] S.A. Ryder, Diagnosing Transformer Faults Using Frequency Response Analysis, IEEE Electrical Insulation Magazine March/April 2003. Vol. 19, No. 2, pp.16-22 [2] CIGRE WG A2.26, "Mechanical condition assessment of transformer windings: guidance, April 2008.

8. Curriculum Vitae

Juan L. Velsquez received the B.Sc. degree in Electrical Engineering from the Universidad Antonio Jos de Sucre in Barquisimeto, Venezuela in 2002. In October 2008 he jointed Omicron Electronics GmbH in Austria, where he works as product manager of diagnostic instruments for high voltage assets. Dr. Miguel A. Sanz Bobi is professor at the Computer Science Department and also researcher at the Institute for Research and Technology (IIT) both inside the Engineering School of the Pontificia Comillas University, Madrid (Spain). Miguel Gutierrez Received his Bachelor in electronic and Licenciatura in Power System from the University of Costa Rica in 1985 and 1988 respectively. He worked as a field engineer since 1985 to 1996 at the Costa Rican Institute of Electricity in Costa Rica. In 1997 he worked for Rochester Instruments Systems (USA) as a testing

engineer and Since 1999 he has been working for OMICRON electronics (USA) as a sales and application engineer for Latin America. He is member of the IEEE. Dr. Alexander Kraetge received the Doctoral degree in Electrical Engineering from the Technical University of Berlin, Germany in 2007. From 2006 he jointed Omicron Electronics GmbH in Austria, where he works as product manager of diagnostic instruments for high voltage assets.