TRANSMISSION
Transformer sweep frequency
response analysis (SFRA)
by G M Kennedy, A J McGrail and J A Lapworth, Doble Engineering,
Sweep frequency response analysis (SFRA) is one of the most powerful diagnostic tools for assessing mechanical damage to a transformer
winding. Analysis of the results, which are in the form of frequency response traces can, however, be daunting to new users.
One approach is to attempt automated
analysis, and this paper presents an approach
using crosscorrelation coefficients. This is a
power signal processing tool that can simplify
result interpretation in some cases and allow
limits to be created.
A common failure mode for power transformers
is consequent to mechanical deformation
of the core or windings. Core damage is
more likely as a result of transportation, while
winding damage is more likely to be caused
by short circuit type forces. Consequently,
the requirements are for transformer to be
checked before and after a new delivery or
re-location, and also after any major fault.
The latter might be after faults on a cable
connected to the low voltage winding, or
on a measurement transformer on the high
voltage, or a tap changer or bushing failure.
These close-up faults may be so severe as
to initiate protection and then the need is to
assess the damage to the transformer.
Alternatively, there could be lesser damage
in the form of deformation. This would reduce
the capability of the winding to withstand
any further faults i.e. the winding is bent but
not broken. Knowledge of such damage is,
therefore, part of a risk assessment process
to be applied for critical units.
Within IEC and IEEE standards, various
diagnostic techniques are described,
and these are to be used after routine or
type testing. Two relevant to this discussion
include turns ratio to detect if the winding
has faulted, and leakage reactance to
identify deformation. Over the years the
measurement of leakage reactance
(or short-circuit impedance) has proven
valuable, particularly when used during withstand evaluation in high power laboratories.
The impedance change allowed post fault
can be defined as being less than a 2%
change (see IEC60076-5). Provided the
test is done correctly this provides a clear
definition for acceptability. However, for
in-service assessment it is considered by
some that this method is insensitive. In the
1990s a group from the major utilities in
northern Europe evaluated an alternative
method involving the injection of a low
voltage swept frequency sine wave into
each winding in turn. They met as a working
group of EuroDoble and at the end of the
1990s documented their experience in a
Doble test guide and several papers at
the annual Doble conferences [1], [2].
Today, groups within IEEE and Cigré are
working to introduce the method into IEEE
and IEC standards, and several companies
now produce instruments to replace
the laborator y equipment used earlier.
Over these recent years the technique
has gained acceptability with a much
larger and rapidly expanding group (and
including the recent-entr y suppliers of
equipment). But this has created some
problems for these new users and suppliers
relating to the interpretation of the results.
The experience is that this is a transitional
phase and new users can acquire the skill
within a short time.
But for that first phase there is an interest
in having an analytical method, ideally
producing a number, ideally as simple as
that from leakage reactance.
The nature of SFRA results
The sweep frequency response analysis (SFRA)
test involves injecting a signal at one end
of a winding and measuring the response
at the other end. Responses with large
variations in attenuation over the measured
frequency range are obtained as a result of
variations in the impedance of the complex
L-C-R distributions of the windings. Since
capacitances and inductances depend on
detailed winding geometry, any movement
results in changes in the frequencies at which
resonances occur. It is the identification
of changes in frequency response that
is the essence of analysis and diagnosis
of mechanical integrity. This is currently
achieved with the expert eye - but the aim
is to use some processing to yield numerical
evaluation of changes.
But differences in response also occur for
reasons other than deformation. These include
differences between individual phases, tap
changer position and configurations of internal
leads between the bushings and windings- as
well as whether the oil was present or absent.
Unsuitable test equipment, lead connections
and layout can produce repeatability issues.
These issues present considerable challenges
when contemplating any automation of the
analysis.
Fig. 1: Frequency analysis bands.
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Fig. 1 shows a typical response for a high
voltage star connected winding. The
frequency range of interest is between
20 Hz and 2 MHz. Experience has shown
that different sub-bands are dominated
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Region
Frequency
sub-band
Component
Failure sensitivity
Core deformation, open circuits, shorted turns
and residual magnetism
1
< 2 kHz
Main core bulk
winding
inductance
2
2 kHz to
20 kHz
Bulk component
shunt
impedances
Bulk winding movement between windings and
clamping structure
3
20 kHz to
400 kHz
Main windings
Deformation within the main or tap windings
Main windings,
tap windings
and internal leads
Movement of the main and tap windings,
ground impedances variations
4
400 kHz to
~1 MHz
Table 1: Frequency sub-band sensitivity.
by different internal components of the
transformer and are subsequently more
sensitive to different types of failures, as
summarized in Table 1. Measurements above
2 MHz tend to be dominated by variations in
grounding practices for test leads.
Normal practice is to separate the response
into frequency bands and relate the analysis
to features in each band, as indicated in
Table 1. The first resonance, here at around
600 Hz, is where the change from inductive
to capacitive impedance occurs. The
resonances at higher frequencies relate
to the winding configuration. The above
regions are a general rule of thumb
dependent on transformer design and test
conditions.
lie not in the capability of the calculation or
the application, but in three main areas:
• Large generic differences between
responses of different winding types.
This means that setting cross-correlation
bands ‘universally ’ is difficult, if not
impossible; hence the recommendation
in this paper to make sure the user is
able to set the band limits to match the
transformer and winding under test.
• The fact that some differences between
responses are inevitable and must be
allowed e.g. due to measurement
limitations or manufacturing tolerances.
Unless appropriate allowances are made,
Sub-bands should be modified and adjusted
by the user based on the observed waveform.
For instance, the low frequency Region 1
could be changed to include all frequencies
between the lowest and the first dominant
pole, to completely encapsulate the core
effect, or a sub band within Region 3 could
be chosen that includes a series of dominant
resonances.
In the analysis a response may be compared
with one of the following:
• An earlier result for the same phase tested
with the same tap changer position.
• If no earlier result is available then another
phase of the same transformer, tested at
the same occasion.
• The same phase, same tap changer
position but on a unit believed to be of
the same design group and made at the
same factory.
The preference for selection of options is in
the order as given.
Cross correlation analysis
Several attempts have been made over
the years at creating automated or semiautomated SFRA analysis tools. Nearly all
have been unsuccessful. The reasons for this
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dependent on transformer designs and
manufacturers, there is a risk that there
will be false positives in the analysis.
• The subtle nature of some failures, which
mean that the SFRA traces are ‘almost
acceptable’, leading to a possible false
negative in the analysis.
The traditional view of the Doble team, some
of whom have been reviewing data for almost
20 years, is that where unusual results are
obtained, any decision must always be made
by the expert to evaluate the existence of
interferences from issues listed above. Where
automated systems can help is as a short term
crutch for the new user. Most applications will
be for fingerprinting sound transformers where
there should be good overlay between other
phases, sister units, etc.
Here some comfort factor will be a help to
the new user since it will be able to identify
the normal low level differences between
traces being compared. The method can
act as a filter so that the engineer can use
their limited resource of time looking at the
most important traces. The output should
not be “pass/fail” but “pass/investigate”. The
goals are to express results as “pass” where
variations are within normal bounds for the
configuration and a means to communicate
results to end-customers who are not so
familiar with SFRA.
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CCF
Good match
0,95 – 1,0
Close match
0,90 – 0,94
Poor match
< 0,89
No or very poor match
< 0,0
Table 2: Example CCFs explained.
CCF
Good
0,95 – 1,0
Marginal
0,90 – 0,94
Investigate
<0,90
Fig. 2: Cross correlation analysis of the H2-H0 winding
to benchmark results.
Cross correlation coefficients (CCFs) are
already used in a variety of industries, primarily
telecom, where knowing the quality of signals
is important. They are already well understood
and provide the type of analysis needed
without blurring the analysis with “go/no-go”
type outputs.
In simplest terms, cross-correlation takes two
sets of numbers and looks at how similar they
are. If two series of numbers such as an SFRA
trace perfectly or nearly match, they would
have a CCF very close to 1,0. If two traces
have absolutely no correlation, in other words
are completely random, they would have a
CCF of 0,0. If the two traces are related by
are diametrical, they would have a negative
CCF.
In SFRA analysis negative CCF are not
common, but they do occur on occasion.
Regardless, negative correlation coefficients
are not considered acceptable when trying
to look for deviations between traces. The
CCF is defined [2] as:
(1)
where Xi and are Yi are the two series (or traces
in the case of SFRA) being compared at each
individual frequency ‘i’ and X-bar and Y-bar
are the means.
Equation 1 assumes two real series. In the
case of signal processing the math becomes
a little more involved, but the end results is still
a coefficient between 1 and -1.
In simplest terms cross-correlation of two
traces f and g is:
(f*g)(x) = f*(t)g(x+t)dt
(2)
This results in a new correlation trace that is
then power density normalized to the input
and output signals. The large * indicates
convolution. The mathematics of Equation
2 and subsequent CCF calculation are
beyond the scope of this paper and can be
researched in a variety of mathematical texts
on the subject of signal processing [3].
Normalizing the results to the individual
power spectrums is what allows this resulting
waveform to be expressed in a simple single
coefficient. Table 2 helps provide a rough
estimate of what the CCF means in simple
language.
Calculating cross-correlation coefficients:
Using CCFs to analyze SFRA data first requires
an understanding of what frequency subbands tell us about the physical health of
a transformer. Once the appropriate bands
are selected the CCFs can be evaluated
in the context of the individual parts of a
transformer. The end results will be a series of
CCFs, evaluating different components of
the transformer.
The following traces were obtained using the
Doble SFRA software for M5200/M5300. By
adjusting cursor positions to frequency subbands, new auto-correlation constants can
be calculated. Fig. 2 shows the comparis
on of two phases of a transformer where the
cursors were set to the positions shown in
Table 1. Note that the first five cursor positions
correlate to the regions. The correlation
coefficients are shown below the cursor
positions to indicate the correlation between
the two above frequency regions.
By observing the above two phases of the
same unit, we can see that there are possible
problems noted with the lower correlation
coefficients of 0,9177 and 0,1906. The
variations can be seen in the overlay of the
two phases. Additional analysis and perhaps
narrowing the sub-band could help tell us
more. The Region 4 correlation coefficient
of 0,1906 is most likely due to the mismatch
of resonance in the 600 kHz to 900 kHz
region. It is important to note that this does
not necessarily indicate that the unit is bad
as this highest frequency region is known to
be much more sensitive to tap winding and
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Table 3: Phase A/C or sister unit
(same phase) limits.
CCF
Good
0,98 – 1,0
Marginal
0,96 – 0,97
Investigate
<0,96
Table 4: Benchmark limits.
internal leads. This type of variation could be
normal between phases of the same unit.
Phase to phase comparison can often be
misleading and must be done with care.
There are expected variations between
phase and correlation coefficients limits
should be selected that draw attention to the
analysis, and not necessarily call for failure
of the unit. Based on experience, phase to
phase analysis would need to have the most
forgiving limits. Phase to phase analysis of
the outside core legs will also be the most
credible as these two win dings display the
most geometry symmetry. Comparison to the
middle phase will be difficult with correlation
coefficients and should be analyzed using
traditional SFRA methods.
Sister units can also be used to conduct
correlation coefficient analysis. In this case,
we would expect some variation between
genuine sister units, but the analysis must be
done on the exact same phases of both units
(A to A, B to B, etc.)
The following correlation coefficients limits are
recommended for phase to phase and sister
unit comparison.
The most reliable method of conducting
correlation analysis is using a benchmark
results. Similar to sister unit analysis , the same
phases of the same windings should always
be compared. In addition, the analysis should
be done with the transformer in the same
tap changer positions. The following table
provides recommend correlation coefficients
limits for benchmark comparisons.
These limits should be used as an aid to
analysis and reporting results but should not
TRANSMISSION
be used in isolation to judge the mechanical
condition of a transformer. A SFRA technician
should still analyze the results and use these
limits as an aid for additional investigation.
Case studies
The following case studies show various
scenarios that a SFRA tester may encounter
in the field and demonstrates how to use
correlation coefficients in the analysis.
Case 1: Benchmark comparison
In this case we have factory and initial field
results available for a 675 MVA generator stepup transformer built in 2002. The transformer
suffered from a fire in the connected
isophase bus and was further tested using
SFRA and other electrical diagnostic tests. This
case was presented as a paper at the 2005
Doble Client Conference.
Variations at low frequencies relate to the
magnetic state of the core of the transformer;
the variation is commonly seen, is well
understood and is acceptable. Minor variations
at the highest frequencies are due to minor
differences in test lead grounding – due to
bushings which had been damaged during the
fire. The main responses overlay very well. This is
strong evidence that nothing has moved within
the transformer. SFRA was used in conjunction
with leakage reactance to propose that the
transformer was mechanically sound and was
worthy of an internal inspection rather than
scrapping. The inspection confirmed the SFRA
diagnosis and the transformer was successfully
returned to service.
Using the cross correlation coefficient analysis
on the H2 - H0 winding and default regions,
we find that the unit was acceptable with the
following cross correlation coefficients.
As mentioned above, the slight dip in the
Region 1 CCF is due to the core magnetization
and there were some minor variations in the
Region 3 but the CCF was still very good
at 0,9882. This helps draw the technician’s
attention to these two sub-bands. The
Fig. 3: Cross correlation analysis of benchmark results H2 - H0 winding.
Fig. 4: Cross correlation analysis of case 2 (phase to phase) scan from 20 Hz - 2 MHz.
Fig. 5: Close-up view of LV winding frequency shifts in 100 kHz – 1 MHz.
magnetization could be easily recognized
and the minor variation in Region 3 ruled out
as an issue. The end result is four figures that
can be used to quantity and report SFRA
findings in an easy to interpret format. All
findings are above the recommended limit of
0,98 CCF for benchmark comparison.
Frequency sub band
CCF
1
0 - 2 kHz
0,9879
Case 2: Bent transformer
2
2 kHz – 20 kHz
0,9964
3
20 kHz – 400 kHz
0,9882
4
400 kHz – 1 MHz
0,9988
The results here are from a 1960s vintage
50 MVA distribution transformer. The transformer
had tripped out of service on protection and
was investigated; no reference results were
available for this unit. The HV results phaseto-phase had typical variation for a HV delta
winding.
Table 5: Case 1 CCF results.
Frequency sub band
CCF
1
0 - 2 kHz
0,9831
2
2 kHz – 20 kHz
0,9868
3
20 kHz – 400 kHz
0,8262
4
400 kHz – 1 MHz
0,9567
Table 6: Case 2 CCF results.
An overall look at the LV windings shows a few
obvious variations, and a trained eye can
see that this is particularly at the resonances
between 200 kHz and 2 MHz where there are
some shifts which are unexpected, Fig 4. If
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we look closer, Fig 5, we can see that it is the
X3 - X0 phase which is consistently shifted to
higher frequencies. This is an indication of a
problem which may relate to axial winding
movement. Note that we are also using the
similarity of the X1 - X0 and X2 - X0 phases
to act as reference traces; if the center and
one outer phase are similar then, generally,
the other phase should also be similar! This
transformer was removed from service and
scrapped.
Using CCF analysis methods, again the regions
were set to the default sub-bands. The phase
A and phase B CCFs were then calculated.
We can see in Table 6 that there is a large
dip the Region 3 CCF down to 0,8262. Using
the recommended limits for analyzing phase
to phase (Table 3), we can see that Regions
1 and 2 are all within the good limit and do
not warrant continued investigation. Region 4
is below 0,98 but above 0,9 and therefore is
TRANSMISSION
Frequency sub band
CCF
0 - 2 kHz
0,9898
2 kHz – 20 kHz
0,9994
20 kHz – 400 kHz
0,9913
400 kHz – 1 MHz
0,9923
Table 7: Case 3 CCF results –
HV phase A sister units.
marginal and deserves a closer look. Region
3 has dropped into the investigate region
(less than 0,9 CCF). Clearly the region did not
correlate as was discussed earlier.
Case 3: Two large sister transformers
The following case involves the routine test of
two large transformers of 370 MVA 345/14 kV
rating. SFRA tests were used to ascertain the
physical health of the units individually then
sister unit comparison was used to ascertain
the consistency of construction between the
two units. By using both of these techniques it
wa s determined by both phase to phase and
by sister unit comparison that both units were
in good physical condition without indications
of either winding or core deformation.
Comparing sister units must be done with
care to ensure that the units are really
sisters by design. Experience has shown
that it is not unusual for functionally identical
units to have significant design differences,
particularly if some time has elapsed between
constructions. Manufacturers may take the
liberty to tweak the design of a transformer thus
creating physical deviations in the structures.
In this case, they are not sister units. Looking for
successive serial numbers may not guarantee
two or more units are genuine sisters; more
attention should be paid to the date of
manufacture. As a rule of thumb, if more than
six months has elapsed between constructions,
there may be some differences.
Fig. 7: Cross correlation analysis of Case 3 (phase to phase
comparison of HV phase A – sister units)
CCFs should be used with an understanding
of traditional SFRA analysis techniques. There
is no replacing the trained eye of an SFRA
technician as they can recognize the features
and patterns associated with various faulted
conditions. CCF will not tell us the exact
nature of the failure, only draw our attention to
regions of interest for continued analysis and
consideration. Users of this method should
also be aware that it is possible for the CCF to
not indicate a problem when there could be.
Inappropriately assigned region boundaries,
or single resonance shifts for example, could
cause only a minor change to the CCF and
in truth indicate a substantial problem.
The suggested CCF limits should be used
as general rules of thumb and can be
adjusted to fit the scenario in question. For
instance, comparing closely design sister
units may necessitate raising the CCF limits
proposed in Table 3. These “figures of merit”
can help communicate SFRA findings to
end customers. Again, these should serve as
Table 7 and Fig. 7 show an example analysis of
two sister units. As can be seen from the CCFs,
the results show very good correlation. Using
the recommended limits for sister unit analysis
(Table 3), we can see that all correlation
coefficients are well above the recommended
limits and in fact these two units are extremely
close sister units in design.
The slight dip in the Region 1 CCF is most likely
due to a very slight amount of reluctance
variation in the core and is normal.
Conclusion
CCFs can be a useful tool to conduct
specification based analysis of SFRA traces
under a variety of scenarios to include
benchmark results, phase to phase analysis
and sister unit comparison. Care must be
taken to understand the context of the
trace and know that some variation is
expected based on tap changer position,
test conditions and the transformer design.
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starting points for analysis and may change
as more research is done and CCFs are
applied to more transformers.
Acknowledgement
This paper was presented at the IEEE Power
Africa 2007 conference at Wits University,
Johannesburg, in August 2007, and is
republished with permission
References
[1] J A Lapworth and T J Noonan, “Mechanical
condition assessment of power transformers
using frequency response analysis”
Proceedings of the 1995 International
client conference, Boston, MA, USA
[2] G M Kennedy, C L Sweetser and A J McGrail,
“Field Experiences with Sweep Frequency
Response Analysis”, Proceedings of the
2006 International Conference of Doble
Clients. Sec T-6
[3] A V Oppenheim and R Schafer, DiscreteTime Signal Processing, Prentice-Hall Signal
Processing Series, 1989
Contact Steve Svendsen, Eberhardt Martin,
Tel 033 386-0011 v