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Diagnosing Transformer Faults
Using Frequency Response
Analysis
Key Words: Frequency response analysis, diagnostics, transformer faults, correlation coefficient,
loose turns, winding damage
F
requency response analysis, generally known
within the industry as FRA, is a powerful diagnostic
test technique. It consists of measuring the impedance of a transformer winding over a wide range of frequencies and comparing the results with a reference set.
Differences may indicate damage to the transformer,
which can be investigated further using other techniques
or by an internal examination.
Fundamentals
As already mentioned, FRA essentially consists of measuring the impedance of transformer windings over a
wide range of frequencies and comparing the results with
a reference set. There are two ways of injecting the wide
range of frequencies necessary, either by injecting an impulse into the winding or by making a frequency sweep
using a sinusoidal signal. The former method is sometimes known as the impulse response method and the
latter as the swept frequency method.
A detailed evaluation of the relative merits of the two
methods can be found in [1]. Briefly, the main advantage
of the impulse response method over the swept frequency
method is a shorter measurement time. The main advantages of the swept frequency method over the impulse response method are as follows:
●
better signal to noise ratio
●
equal, or nearly equal, accuracy and precision across the
whole measurement range
●
a wider range of frequencies are injected
●
less measuring equipment is required.
The author (and most others) uses the swept frequency
method. All of the results shown in this article were obtained using the swept frequency method.
So far as is known to the author, the swept frequency
method was invented by Dick and Erven of Ontario Hydro Research Laboratories (now Kinectrics) between
16
S.A. Ryder
Alstom Transformer Research Centre
Saint-Ouen, France
Frequency response analysis consists of
measuring the impedance of a
transformer winding over a wide range
of frequencies and comparing the
results with a reference set.
1975 and 1977, and the first description of the method to
appear in the literature is [2]. An introduction to the
method for the nonspecialist may be found in [3].
Measurement Method
The swept frequency method for FRA requires the use
of a network analyzer to generate the signal, make the
measurements, and manipulate the results. A number of
suitable network analyzers are presently commercially
available.
Figure 1 shows engineers making measurements on a
test transformer as part of a research program. The author is on the right.
The basic measurement circuit is shown in Figure 2.
The tested impedance, in this case the transformer
winding, is ZT. The standardized test impedance, in this
case the impedance of the measurement cables is ZS. The
injected signal is S, the reference measurement is R and
the test measurement is T.
A number of different methods are used for presenting
the results. Following the lead of Dick and Erven [2], the
author uses the modulus-argument form.
The modulus is defined as:
0883-7554/03/$17.00©2003IEEE
IEEE Electrical Insulation Magazine
k = 20 log 10 (T / R ),
(1)
using the same notation as Figure 2, which is equivalent
to


ZS
k = 20 log 10 
,
 ZS + ZT 
(2)
also using the same notation as Figure 2.
The modulus is variously called the amplitude, the
voltage ratio, the voltage gain, the impedance, and the admittance. The author prefers amplitude, which is used
throughout this article. Voltage ratio and voltage gain can
be seen to be descriptive. Impedance and admittance can
also be seen to be descriptive, but can also be slightly misleading, as k is the ratio of two admittances or impedances.
The argument is defined by
φ = ∠(T / R ),
(3)
again using the same notation as Figure 2. The argument
is usually called the “phase.”
The measured frequency range is usually rather large
(5 Hz to 20 MHz in the tests reported
here) and so the results are usually presented on a graph of amplitude or phase
against frequency. The phase-frequency
graph does not contain as much useful information as the amplitude-frequency
graph does, so it is often not plotted or
analyzed.
It is possible to use either a linear scale
or a logarithmic scale for frequency in
the graphs. A logarithmic scale has the
advantage of allowing all of the information to be presented on a single graph
(with linear scales it is often necessary to
use a separate plot for each decade
examined).
nance. The first resonant frequencies can vary with the
state of residual magnetization of the core. They will also
be different on sister transformers, where manufacturing
differences in the core joints will give different
reluctances.
At medium frequency there is a group of resonances,
corresponding to the interaction of the shunt capacitance
and air-cored inductance of the windings. These are generally the most repeatable. Slight differences may exist
between sister transformers, owing to the effect of manufacturing differences in the windings. More significant
differences may be found between windings on different
phases of three-phase transformers, owing to different
lead configurations or different winding external
clearances.
At high frequency there is a more confused group of
resonances, corresponding to the interaction of the shunt
and series capacitances and air-cored inductances of parts
of the windings. The high-frequency response is affected
by manufacturing differences, lead configuration, and
winding external clearances in much the same way as is
the medium-frequency response. At the highest frequencies the influence of the measurement cables can become
important, especially on large transformers. Grounding
Characteristics of
Figure 1. Making measurements on a test transformer.
Winding Frequency Response
Results of FRA measurements made
on the LV winding of a 60 MVA trackside
ZS
transformer made before and after a short-circuit withstand test are shown in Figure 3. The transformer withstood the applied short-circuits without damage, which is
why there are no significant differences between the
results.
R
S
The low-frequency response is typically characterized
by decreasing amplitude reaching a minimum in a resonance at or below 1 kHz. This resonance is caused by the
interaction of the shunt capacitance of the windings with
the magnetizing inductance. If there are two flux paths in
the core of different lengths, then it will be a double resoFigure 2. Measurement circuit.
March/April 2003 — Vol. 19, No. 2
ZT
ZS
T
ZS
17
low-frequency response. Circulating
currents loops, if they are sufficiently
0
large, redirect leakage flux into the core
−10
and also change the low-frequency response. An ungrounded core changes the
−20
shunt capacitance of the winding closest
to the core and also the low-frequency
−30
response.
The medium-frequency response is
−40
sensitive to faults that cause a change in
the properties of the whole winding. A
−50
significant increase in the medium-frequency resonances normally indicates
−60
axial movement of a winding. A signifiBefore Test
−70
cant decrease normally indicates radial
After Test
movement of the inner winding (hoop
−80
buckling). Slight differences are often acFrequency (Hz)
cepted as being a result of “windings
settling into place.”
Figure 3. Frequency response of LV winding.
The high-frequency response is sensitive to faults that cause changes in the
properties of parts of the winding. Localized winding
damage causes seemingly random changes in the
high-frequency response, often leading to the creation of
new resonant frequencies. The high-frequency response
may also be affected by the tank or cable grounding. Poor
tank grounding is easy to spot, as it affects all windings,
whereas damage is usually confined to one winding or at
worst one phase. Poor cable grounds are more difficult to
detect, as they may cause changes to just one winding, but
are unlikely to lead to the creation of new resonant
frequencies.
The comparison is best made using measurements
made earlier on the same winding. Where appropriate,
both sets of measurements should be made on the same
Figure 4. Loosened turns on 100 kVA distribution transformer.
tap position and with the same accessories, such as bushings, fitted. If the transformer is oil filled, then the oil
of the transformer and the cable screens can also have an
should have the same relative permittivity as previously.
important influence. The upper limit of the reproducible
Relative permittivity is influenced by the type of oil, the
range is likely to be at least 1 MHz, probably rather more
relative humidity (itself a function of temperature and the
for small transformers. For more details on factors
absolute humidity) and so-called “normal aging.” If it is
limiting the repeatable range, see [4].
suspected that the oil has been changed since the baseline
measurement was made or that there has been a signifiDiagnosing Faults
cant change in the relative humidity, then caution is necAs has been stated above, FRA consists of measuring
essary
and it may be advisable to make inter-phase
the impedance of transformer windings over a wide range
comparison
to supplement the comparisons with the
of frequencies and comparing the results with a reference
baseline
measurement.
set. To be detectable a fault must cause either the inducInter-phase comparison is possible with three-phase
tance or the capacitance of a significant part of the windtransformers.
Owing to differences in the magnetizing ining to change by a significant amount. Faults that do not
ductance
between
the three phases, there will be differcause such changes (partial discharge is probably the best
ences
between
the
FRA results at low frequencies. At
example) are not detectable. Such faults may become demedium and high frequencies, the results usually agree
tectable if they become sufficiently severe to cause detectable secondary damage (short-circuited turns, severe
quite well, although not so well as different results from
local winding damage, etc.).
the same winding. For some designs the agreement is not
as good, owing either to differences in the lead configuraFaults, such as short-circuited turns, change the magtions or in the winding external clearances. See [5] for an
netizing characteristics of the transformer and, hence, the
10
100
1000
10,000
100,000
1,000,000 10,000,000
Amplitude (dBm)
1
18
IEEE Electrical Insulation Magazine
nances and relies on there being sufficient resonances to
give useful information but not so many as to cause confusion. This method can be difficult for computers to apply, because they tend to confuse noise for resonances,
especially at the edges of the reproducible range.
An alternative, which the author has been involved in
promoting, is to calculate statistical indicators of the
amount of agreement or disagreement between the two
sets of measurements. This amounts to a more objective
and transparent way of performing the first part of the
graphical comparison described above (and if the changes
are large enough, the other two as well). This extracts information from the results across the whole of the repeatable range and is easily applied by computers.
10
100
1000
10,000
100,000
Amplitude (dBm)
example of differences in medium- and high-frequency
FRA results between the phases of a new transformer.
Comparison between sister transformers is also possible. It can be particularly useful for single-phase transformers forming three-phase banks. There may be quite
large normal differences in the low-frequency results, but
at higher frequencies the results tend to agree quite well,
although not so well as different results from the same
winding. See [4] for an example of normal differences between FRA results from sister transformers.
The faults causing changes to the low-frequency response can all be reliably detected using other means:
short-circuited turns by magnetizing current or turns ratio measurements, circulating currents by DGA or a thermal scan, and no core earth by
capacitance measurement. The faults
causing changes at medium and at high
1
frequency are difficult to detect using
0
other means: turns ratio, capacitance
measurement, and leakage impedance
−20
measurement are effective in some cases
but not all. For a detailed evaluation of
−40
FRA for fault diagnosis see [6]. For a particularly spectacular example of FRA
succeeding where other methods fail see
−60
[7].
The rest of this article, and the practi−80
cal examples presented, will concentrate
on the detection of winding damage.
March/April 2003 — Vol. 19, No. 2
Baseline
Loosened
Loosened,
Moved Down
−100
Loosened,
Moved to Ends
−120
Frequency (Hz)
Figure 5. Frequency response for HV A-B – 10 Hz to 10 MHz.
100,000
−10
1,000,000
10,000,000
−15
Amplitude (dBm)
Comparison Methods
The comparison of results is usually
made by plotting a graph of the amplitude against frequency for both sets of
measurements. An experienced observer
then examines the two curves for any significant differences. Significant differences are usually understood to be:
●
changes to the shape of the curve
●
the creation of new resonant frequencies or the elimination of existing resonant frequencies
●
large shifts in existing resonant frequencies.
The main problem with this method of
comparison is that the expert’s opinion
may lack both objectivity and transparency.
One way of addressing both problems
is to note down all of the resonant frequencies. This gives objective and transparent information on the number of
resonances that have been created or eliminated, and how far any resonances may
have shifted. However, it can only extract
information from the results at the reso-
1,000,000 10,000,000 100,000,000
−20
−25
−30
−35
Baseline
Loosened
Loosened,
Moved Down
Loosened,
Moved to Ends
−40
Frequency (Hz)
Figure 6. Frequency response for HV A-B – 100 kHz to 10 MHz.
19
Table I. Correlation coefficients for 100 kVA distribution transformer.
Decade Band
10 Hz-100 Hz
100 Hz-1 kHz
1 kHz-10 kHz
10 kHz-100 kHz
100 kHz-1 MHz
Loosened
0.9999
0.9652
1.0000
0.9991
0.9827
Correlation Coefficient Between Baseline Results and:
Loosened, Moved Down
Loosened, Moved to Ends
0.9998
0.9998
0.9893
0.9737
1.0000
1.0000
0.9994
0.9996
0.9886
0.9908
Trials by the author indicate that the correlation coefficient is the most reliable statistical indicator. Full results
of an evaluation may be found in [8]. The mathematical
definition of the correlation coefficient is given in the
Appendix.
Case Studies
A small number of case studies are presented to show
the application of different comparison methods to the
diagnosis of real and simulated faults on transformers.
Case Study 1—Loosened Turns on 100 kVA
Distribution Transformer (Simulated)
This case study concerns a fault that was simulated on
the 100 kVA distribution transformer, shown in Figure 1.
The fault was simulated by cutting away the cotton tape
holding the outside of the A phase HV winding in place
and manually displacing turns from the outer layers of the
winding. This is intended to simulate localized winding
damage that might result from a through fault. Figure 4
shows the damage created (the damaged phase is on the
right, the visible damage on the other phases was part of
another experimental program not described here).
The frequency response of the A-B phase of the HV
winding, before, during, and after the fault simulations,
which were made in three stages, is shown in Figure 5.
The double-decade band from 100 kHz to 10 MHz,
where the changes caused by the damage are most apparent, is shown in Figure 6.
Figure 7. Damage to LV winding of 440 MVA generator transformer.
20
The changes to the FRA results take the form of seemingly random changes in the amplitude, which are highly
characteristic of this type of fault. The existing resonances are shifted around, but there is no creation of new
resonances. Creation of new resonances is a common
symptom of winding damage on large transformers, but
not on small distribution transformers such as this.
The correlation coefficients between the baseline measurement and the three measurements made during the
damage simulation, calculated in decade bands, are
shown in Table I.
For most windings the correlation coefficients between results from undamaged transformers are very
close to unity from 1 kHz up to 1 MHz. The author considers that a correlation coefficient of less than 0.9950 in
this range, between different measurements on the same
winding, merits further investigation.
In this case study the correlation coefficient for the
100 kHz-1 MHz decade band is low enough to merit further investigation in all three cases.
Case Study 2—Hoop Buckling Failure of LV
Winding in 440 MVA Generator Transformer
This case study concerns a 440 MVA 21/245 kV generator transformer. The transformer was originally installed at a generating station in Germany in 1969. It was
damaged by a through fault and was rewound in 2000.
The frequency response of the three phases of the LV
winding is shown in Figure 8. The measurements were
made after the windings had been removed from the
core; the low-frequency response was largely absent and
was therefore cropped from the graph.
The changes to the FRA results take the form of decreases in the first two resonant frequencies (from about
62 kHz to 56 kHz and from about 222 kHz to about 207
kHz) and the creation of two new resonant frequencies
(at about 370 kHz and at about 700 kHz). These changes
are quite typical of what can be expected from hoop
buckling associated with winding damage, i.e., decreases
in the medium-frequency resonances and the creation of
new resonances at high frequencies.
The correlation coefficients between the measurements, calculated in decade bands, are shown in Table II.
In this case study the correlation coefficients between
the undamaged phases 1 and 3 may be used as a baseline. It
can be seen that the correlation coefficients with the damIEEE Electrical Insulation Magazine
20
10
1,000
0
Amplitude (dBm)
aged phase 2 are very much lower than
those between the undamaged phases in
both the 10 kHz-100 kHz and 100 kHz-1
MHz decade bands. This is a good indication of abnormal differences, which merit
further investigation. Note that the correlation coefficients between the two undamaged phases are rather lower than in
Case Study 1, partly owing to manufacturing differences between the two phases
and partly owing to the less than ideal
measurement conditions. See [9] for another example of a hoop buckling failure.
1,000,000
−10
−20
−30
−40
Case Study 3—Axial Collapse of
Series Winding in 300 MVA
Autotransformer (Suspected)
100,000
−50
Phase 1
Phase 2
(Damaged)
Phase 3
−60
Amplitude (dBm)
This case study concerns a 300 MVA
Frequency (Hz)
400/220 kV autotransformer. The transformer was originally installed at a substation in France in 1980. It remained in Figure 8. Frequency response for LV winding.
service there until 1998, when it was replaced by a higher-capacity transformer
1,000
10,000
100,000
1,000,000
10
100
and transferred to the reserve. The HV
0
and LV bushings were removed and the
−10
transformer was stored under dry nitrogen. In 2000, the transformer was moved
−20
to a different substation, where it was reassembled and the bushings refitted.
−30
Shortly after its return to service the
transformer was tripped by various pro−40
tective relays. FRA measurements were
made to see whether the windings had
−50
been damaged. The incident is described
A⋅a
in more detail in [10].
−60
C⋅c
The frequency response of A-a and
−70
C-c phases of the series winding is shown
in Figure 9. Earlier measurements (deFrequency (Hz)
scribed in [10]) had identified the C
phase as damaged and had eliminated the Figure 9. Frequency response for series winding.
possibility of damage to the common
winding.
The correlation coefficient reaches very low values in
The differences in the FRA results take the form of an
the 1 kHz-10 kHz decade band, where the changes
increase in the frequency of the main medium-frequency
caused by the axial displacement are most apparent, and
resonance on C-c winding with respect to A-a winding
in the 100 kHz-1 MHz decade band, where the changes
(1640 Hz on A-a winding, 1830 Hz on C-c winding) and
caused by the consequent winding damage are most apthe creation of several new resonant frequencies above
parent. The correlation coefficient in the 10 kHz-100
100 kHz on C-c winding (175 kHz, 190 kHz, 443 kHz,
kHz decade band is close to normal. See [5], [9], and [11]
637 kHz, 679 kHz, and 843 kHz). These changes are
for further examples of axial collapse of windings.
quite typical of what can be expected from axial displacement associated with winding damage, i.e., increases in
Conclusions
the medium-frequency resonances and the creation of
Frequency response analysis is a proven and effective
new resonances at high frequencies. This diagnosis has
means of detecting faults in transformers. The main interyet to be confirmed by an internal inspection.
est of the method lies in its ability to find faults, princiThe correlation coefficients between the measurepally mechanical damage to the windings, which cannot
ments, calculated in decade bands, are shown in Table III.
always be detected using other means. Results can be
March/April 2003 — Vol. 19, No. 2
21
Table II. Correlation coefficients for 440 MVA generator transformer.
Decade Band
10 kHz-100 kHz
100 kHz-1 MHz
Phase 1 – Phase 2
0.8618
0.7761
Correlation Coefficient Between Results
Phase1 – Phase 3
Phase 2 – Phase 3
0.9953
0.8923
0.9626
0.7779
Table III. Correlation coefficients for 300 MVA autotransformer.
Decade Band
Correlation Coefficient
10 Hz-100 Hz
0.9908
100 Hz-1 kHz
0.9918
1 kHz-10 kHz
0.7483
10 kHz-100 kHz
0.9797
100 kHz-1 MHz
0.8577
compared by eye, by noting down the resonant frequencies, or by using statistical indicators. Statistical indicators are particularly useful as they add objectivity and
transparency.
Acknowledgments
This article is published with the permission of Alstom
Transformer Research Centre and Electricité de France
Recherche. The author gratefully acknowledges the contributions of his colleagues Dominique Lacaze, Michael
Rösner, and Stefan Tenbohlen.
The fault simulation program on the 100 kVA distribution transformer was undertaken as part of a joint project
between Alstom Transformer Research Centre and
Electricité de France Recherche. Some of the experiments
described in this article were carried out by Vincent
Bergaud as part of a final year project while he was a student with IUT Paris Jussieu.
Simon A. Ryder (M ’03) was born in England in 1973. He
graduated from St. John’s College, Oxford University,
with an MEng. in Engineering Science in 1996. He joined
Alstom later that year. He is presently working as a research engineer at Alstom Transformer Research Centre.
His main areas of interest are frequency response analysis, thermal characteristics of transformers, and winding
technology. He is a member of IEEE-PES and of IEE
(U.K.), a personal member of CIGRÉ, and a chartered engineer (U.K.).
References
[1] S. Ryder and S. Tenbohlen, “Comparison of swept frequency and
impulse response methods for making FRA measurements,” paper
to be presented at 2003 Conference of Doble clients, Boston, 2003.
[2] E.P. Dick and C.C. Erven, “Transformer diagnostic testing by
frequency response analysis,” IEEE Trans. PAS, vol. 97, pp.
2144-2153, Nov./Dec. 1978.
[3] S. Ryder, “Frequency response analysis for diagnostic testing of
power transformers,” Electricity Today, vol. 13, no. 6, pp. 14-19,
2001.
[4] S. Ryder, “Experimental investigations of the repeatability of
[frequency response analysis] measurements,” paper presented at
2002 Conference of Doble clients, Boston, 2002.
22
[5] J.A. Lapworth and T.J. Noonan, “Mechanical condition assessment
of power transformers using frequency response analysis,” paper
presented at 1995 Conference of Doble clients, Boston, 1995.
[6] T.J. Noonan, “Power transformer condition assessment and
renewal. Frequency response analysis update,” paper presented at
1997 Conference of Doble clients, Boston, 1997.
[7] J.A. Lapworth, “Transformer fails seven years after close-up faults.
FRA diagnoses the problem,” paper presented at 2002 Conference
of Doble clients, Boston, 2002.
[8] S. Ryder, “Methods for comparing frequency response analysis
measurements,” in Proc. 2002 IEEE Int. Symp. Electrical
Insulation, Boston, MA, 2002, pp. 187-190.
[9] J.A. Lapwoth, “Detection of winding movement in power
transformers by frequency response analysis (FRA),” presented at
the Int. Conf. Power Transformers, Kolobrzeg, Poland, 1999.
[10] J.P. Taisne, A. Tanguy, J.P. Patelli, E. Chemin, F. Devaux, and S.
Ryder, “French experience with decision making for damaged
transformers,” presented at the International Council on Large
Electric Systems (CIGRÉ), Paris, France, 2002.
[11] M. Stace and S.M. Islam, “Condition monitoring of power
transformers in the Australian state of New South Wales using
transfer function measurements,” in Proc. 5th ICPADM, Seoul,
Korea, 1997, pp. 248-251.
[12] S. Ryder, “Diagnosing transformer faults using frequency response
analysis: Results from fault simulations,” paper presented at IEEE
Power Engineering Society Summer Meeting, Chicago, IL, 2002.
[13] D.K. Xu, C.Z. Fu, and Y.M. Li, “Application of the artificial neural
network to the detection of the transformer winding deformation,”
presented at the International Symposium on High Voltage
Engineering, London, U.K., 1999.
Appendix: Mathematical Definition
of the Correlation Coefficient
Consider two sets of n numbers, X {x 1, x 2, x 3, … x n}
and Y{y1, y2, y3, … y n}. The correlation coefficient between these two sets of numbers is defined by
ρ=
n
n
n
x =i
x =i
x =i
∑ x i y i / ∑ x i2 ∑ y i2 .
(A1)
The correlation coefficient was first applied to the analysis of FRA results by Xu, Fu, and Li in [13]. A detailed
evaluation of its performance may be found in [8].
IEEE Electrical Insulation Magazine