900
A. Contin et al.: Frequency-response Analysis of Power Transformers by Means of Fuzzy Tools
Frequency-response Analysis of Power Transformers
by Means of Fuzzy Tools
Alfredo Contin, Germano Rabach
DEEI University of Trieste
Via A.Valerio, 10
34127 Trieste, Italy
Johnny Borghetto, Michele De Nigris
R.S.E. spa
Via Rubattino, 54
20134 Milano, Italy
Renzo Passaglia and Giuseppe Rizzi
Consultants R.S.E. spa
Via Rubattino, 54
20134 Milano, Italy
ABSTRACT
A novel Fuzzy algorithm for the automatic analysis of frequency response of power
transformers is described in this paper. It relies on the values of two parameters able to
quantify the difference between the present and a reference frequency response, over
three frequency ranges. These ranges are associated with different defect types, i.e.,
short circuits between turns, radial and axial displacements. Training examples
obtained mainly from experimental results have been used to select the different
ranges. Fuzzy-Logic has been adopted to reflect the uncertainty in the analysis of the
differences between the two curves in the defect-identification results. Practical
applications are also discussed to show the efficiency of the proposed diagnostic
method.
Index Terms — Power transformers, insulation, frequency response, faults
prediction, diagnostics.
1 INTRODUCTION
TRANSFORMERS are essential elements of power
delivery and their failure can cause serious problems in
electric utility operations. Among the causes of transformer
failure, those related directly or indirectly to the deformation
of windings due to bad assembly or after transportation or an
accident, are outstanding. Therefore, the development of
diagnostic methods for the identification of winding
deformations is of practical value to avoid unexpected
accidents. Short-circuit inductance measurement is widely
used to test the transformer conditions and threshold levels
have been established for pass/not pass criteria, depending
from the transformer typology [13]. Even if widely used, this
diagnostic technique does not provide details about the
potential defect typology. The Sweep Frequency Response
Manuscript received on 29 October 2010, in final form 10 February 2011.
Analysis (SFRA) gained popularity for its ability to point out
geometrical deformations, winding displacements and internal
short-circuits between turns by means of the interpretation of
the modifications in frequency-response characteristics [1, 2].
Diagnostics based on SFRA method is thus carried out
comparing the present frequency response with a reference
one that reflects the good conditions of the transformer.
Relating the curve comparison with potential internal defects
requires skilled operators and a wide specific experience [3,
4]. This fact promotes investigations having the purpose of
finding methods and algorithms that allow the automatic
interpretation of SFRA results.
The purpose of the paper is to discuss a Fuzzy-Logic
Algorithm (FLA) for the automatic analysis of frequencyresponse measurements of power transformers. It is based on
the evaluation of the curve obtained subtracting the present
and the reference frequency-response (comparison curve) over
three different frequency ranges, each one associated with a
1070-9878/11/$25.00 © 2011 IEEE
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 18, No. 3; June 2011
particular defect type, i.e., short circuit between turns, radial
and axial displacements. These frequency ranges have been
selected considering mainly SFRA experimental results
performed on transformers whose conditions were wellknown. FLA has been adopted to take into account the
uncertainty in the identification of the different defects in
these three frequency ranges (partially overlapped). Using this
approach, the different defect types are identified by means of
“defuzzyfication”, into different predicates. Each predicate is
associated to a specific defect with a membership function that
indicates the confidence degree of the output. Examples of
FLA outputs relevant to SFRA measurements carried out on
site on real transformers, are also discussed to show its
effectiveness.
2 BASICS OF SFRA
Important mechanical stresses are due to electro-dynamic
forces linked to short circuits currents. The axial forces
compress the windings while the radial ones act to buckle the
inner and open the outer windings [5]. The mechanical
stresses can affect the tightness of the connections in the
windings. Axial and radial deformations are the premises to a
mechanical and/or electrical collapse of the transformer
windings, thus representing an important indicator of an
incipient fault. Short-circuit currents can generate breakdowns
of the insulation between turns due to overheating of weak
points and can modify the residual magnetization (the latter
being a harmless effect) [1-4].
The measurement of the short-circuit inductance, widely
adopted in industry for checking the presence of such
internal defects, is effective but not sensitive enough to
distinguish among the different defect types [13]. The SFRA
method was developed to cope with this lack of sensitivity.
SFRA is based on the assumption that any mechanical
deformation as well as changes in the number of turns and
residual magnetization, modify the inductive/capacitive
couplings within the transformer. In particular, radial and
axial deformations affect the coil-to-ground and coil-to-coil
capacitances, respectively, while short circuits between turns
and variations of the residual magnetization modify the self
and mutual inductance of the windings. Some electric
models, based on equivalent ladder network circuits have
been proposed to simulate the effects of the winding
displacements, [6]. The connections of the transformer
windings in a two-port configuration allow a description of
the machine based on a transfer function whose features are
related to its zeros and poles values (the latter showing the
resonant peaks). Any winding deformation can be described
in terms of pole displacements (modification of the transferfunction resonant peaks) which correspond to a modification
of the response curve. SFRA diagnostic methods try to infer
the specific causes of modification of the response-curve
since internal short-circuits affect mainly the low-frequency
winding impedance (poles in the low-frequency range),
while radial and axial displacements modify mainly the
phase-to-ground and coil-to-coil capacitance (variations in
pole position in the middle and high frequency ranges
respectively) [6].
901
3 EXPERIMENTAL SETUP
SFRA method requires connecting the windings of the
transformer as a two-port configuration. A sinusoidal sweepfrequency generator supplies the input port while the response
of the transformer is recorded at the output terminals
connected to a suitable impedance (R=50 :) [1-3]. The
experimental transfer-function is obtained in terms of
amplitude ratio and phase delay between the output, Vout(f),
and input, Vin(f), signals [4]. The use of a sinusoidal signal is
preferred to the impulse wave-shape since the applied sweep
maintains the same voltage level for each selected frequency.
This allows obtaining a more accurate and reproducible results
both in low- and high-frequency range [12, 14]. The
frequency span adopted here, ranges from 10 Hz to 5 MHz
and the signal amplitude is constantly set at 10 Vp-p. SFRA
was carried out mainly on high power and high voltage (up to
400 kV) three-phase transformers (auto, two- and threewinding transformers, transformers with three and five limbs).
Different test setup configurations can be considered
depending on the connection of the winding terminals (star or
delta connections) and the availability of the neutral terminal.
If all the terminals are available, the different windings can be
tested one by one (end-to-end). SFRA can be applied to
evaluate the same winding before and after a potentially
damaging event such as an external short circuit or, in the
absence of reference measurements, to compare the response
of the different windings within the same transformer or with
the response of transformer of the same type and ratings [4].
When the windings are star-connected, each winding can be
tested leaving floating the other terminals of the star, or
alternatively, connecting them to ground. In the latter case,
residual magnetization is minimized. If the transformer is
delta-connected, the frequency-response of a given winding is
influenced by the other two that are connected in parallel.
Two configurations can be considered for the winding
opposite to the tested one: i.e. winding open and floating and
winding short-circuited. These test conditions allow the
selective evaluation of the presence of defects. In fact, in the
conditions in which the opposite winding is open and floating,
the effect of the mutual coupling between the two windings
can be seen in addition to the effect of the magnetic circuit. In
the other test configuration (short-circuited winding) the
effects of the mutual coupling and the magnetic circuit are
masked and the effect of the single winding is evidenced.
It is to be underlined that special precaution shall be adopted
with concern to the screening of measuring cables to avoid
interferences and noise in the frequency range above 500 kHz.
If the back-ground noise is minimized, the same testing
accuracy can be obtained in the laboratory and in the field [3].
It can be concluded that SFRA can offer reliable results
whenever the reference and the present curves are recorded in
the same setup conditions (i.e., the tap position, terminals
grounded, shorted or floating).
All the experimental test results, collected in a homogeneous
database, have been used to develop the proposed algorithm
for the evaluation of the comparison curve [12]. The measured
and the reference curves are reported in a Bode plot and
902
A. Contin et al.: Frequency-response Analysis of Power Transformers by Means of Fuzzy Tools
mutually compared to point out any significant differences.
Let us consider Vin(jZ) and Vout(jZ) the input and the output
signals, respectively. The transfer function H(jZ) is expressed
by:
H ( jZ )
Vout ( jZ )
Vin ( jZ )
(1)
The Bode diagrams are plotted considering both the
magnitude and phase as follows:
Adb ( Z )
20 log 10 H ( jZ )
AT ( Z ) tan 1 ( H ( jZ ))
(2)
Let Ar(f) and Ae(f) be the magnitude diagrams of Equation
(2) relevant to the reference and present conditions of the
investigated transformer, respectively. The comparison curve,
ǻ(f), is defined as:
'( f )
Ae ( f ) Ar ( f )
(3)
Both the Bode diagrams as well as the comparison curve are
reported in the same plot to facilitate the comparison. Changes
in the resonant peaks due to mechanical displacements or
short circuits between turns, reflected on the ǻ(f) plot, have
been analyzed deeply to extract diagnostic information.
4 FAULT CLASSIFICATION
A set of about 250 SFRA test results, obtained mainly from
tests carried out on transformers whose conditions are known,
have been studied to extract diagnostic information and
classify them into good or faulty categories.
4.1 GOOD CONDITIONS
The perfect overlapping of the present and reference SFRA
curves produce a null function of the comparison curve
(equation (3)) thus indicating the perfect invariance of the
winding conditions. Deviations between the two frequency
responses can be found during on-site SFRA measurements on
transformers in good conditions. In fact, an increase of
residual magnetization can be found after an external short
circuit as well as differences in SFRA curves due to different
magnetization can arise when internal and external windings
of the same machines are compared. Even if the instrument is
equipped with shielded connections, external high frequency
noise can affect the measurements and the comparison curve
can be distorted in the high frequency region.
The analysis of a large set of SFRA measurements
performed on transformers in good conditions was used to
evaluate the acceptable level of noise and the curve
modifications due to the residual magnetization, below 10
kHz.
Results of SFRA measurements carried out on a three phase
transformer rated 58 MVA, 15/230 kV, delta/star connected,
are explicative in this respect. Since no reference data existed
for this specific machine, diagnostic tests were carried out
comparing the SFRA curves of the different windings. Tests
were carried out connecting the instrument to two terminals
and leaving all the others floating. Test results obtained
connecting the instrument to two low-voltage terminals are
reported in Figure 1 as an example. Similar results were
obtained using other test setup configurations. An accurate
inspection carried out after SFRA measurements confirmed
that the transformer was in good condition. The differences
were linked to the different magnetization level (below 10
kHz), while probable noise and small geometric differences
affected the curves above 100 kHz. SFRA carried out on a
large number of power transformers in good condition
allowed to establish specific threshold levels to be applied to
the comparison curve to discriminate between the “good” and
“faulty” conditions.
4.2 FAULT CONDITIONS: SINGLE DEFECTS
A wide set of transformers that showed modifications in
SFRA curves, has been analyzed deeply with the purpose to
relate these changes to their specific causes.
According to the results reported in the literature, it was
found that the short circuits between turns change the
equivalent number of turns of the winding and, as a
consequence, the total inductance. Moreover, the higher
currents associated with the short circuit between turn(s)
modify also the magnetization and structural deformations in
the magnetic circuit can produce variation in the
magnetization reluctance values. Since these defects are
linked with the magnetization field, SFRA curve
modifications can be evidenced in the low-frequency range
(below 10 kHz). An example of the effects due to a short
circuit between turns is shown in Figure 2. SFRA carried out
on a three-phase autotransformer rated 250 MVA, 400/35 kV,
before and after a short circuit test, is reported in Figure 2A
while the picture of the fault is shown in Figure 2B. As can be
seen, SFRA curves differ mainly below 10 kHz. The response
to higher frequencies is not substantially affected, thus
excluding geometrical deformations of the windings. In fact,
the short circuit occurred between the connection cables.
Analyzing the data-base, similar deviations were found in the
same range of frequencies, due to short circuits between turns
without significant geometric deformations.
Radial deformations modify mainly the phase-to-phase
and phase-to-ground capacitance distributed along the
whole windings. The resonant peaks linked with these
deformations affect mainly the medium-frequency
response. Radial deformations can be localized in a
restricted section of turns/coils or distributed along several
coils. These deformations can be pronounced or negligible.
These characteristics can be evidenced by the modification
of the resonant peaks in the medium-frequency range:
marked the former, spread the latter. Slight differences in
the resonant peak positions are often accepted as being
linked with the winding setting process. Analyzing
transformers having only radial deformations, it was found
that SFRA changes its shape in the frequency range of
about 5 – 500 kHz.
Weaknesses in upper/lower coil pressure plates and in
spacing blocks, can produce axial movements of the windings.
This can cause changes in the high frequency response (above
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 18, No. 3; June 2011
Figure 1. Comparison of SFRA measurements carried out on two phases of
LV windings delta connected while the HV terminals are open and floating.
903
A
B
A
Figure 3. Comparison of SFRA measurements carried out on a phase of a
transformer rated (60 MVA, 400 kV) before and after a breakdown event, (A),
and picture of the fault, (B).
frequency modifications as well as medium or high frequency
(or both) SFRA curve coexist.
B
Figure 2. Comparison of SFRA measurements carried out on a single phase
of a transformer before and after a breakdown event, (A), and picture of the
fault between the connecting cables (B).
400 kHz) often leading to the creation of new resonant
frequencies.
4.3 FAULT CONDITIONS: MULTIPLE DEFECTS
Faults can often produce complex deformations such that
shown in Figure 3. In this example, a single phase transformer
with two secondary windings positioned on separated
columns, was subjected to short circuit. SFRA was carried out
before and after the short circuit to check the possible effects.
The two curves differ in the range of 20 kHz – 5 MHz (Figure
3A). The machine was successively inspected and an
important deformation was found on the low-voltage winding
(see Figure 3B) due to the breaking of the axial support on the
top-end of the coil which generated also a radial deformation.
It can happen to find both axial and radial deformations
associated to short-circuited turns or coils. In this case, low-
4.4 DISCUSSION
The experimental data gathered showed that the different
defect types can be classified into three different ranges:
4.4.1 FREQUENCY RANGE BELOW 10 KHZ
Phenomena linked with the transformer magnetic core and
circuits, in particular short circuits between turns, are
evidenced in this range of frequencies. The residual
magnetization which can slightly modify SFRA curves must
be taken into consideration in the same range of frequencies
but this is a harmless phenomenon;
4.4.2 FREQUENCY RANGE BETWEEN 5 KHZ AND
500 KHZ
In this range phenomena linked with radial relative
geometrical movements between windings, are evidenced;
4.4.3 FREQUENCY RANGE ABOVE > 400 KHZ
Axial deformations of each single winding are evidenced
in this range of frequencies.
As can be seen, the frequency intervals are partially
overlapped. This implies a potential ambiguous identification
when modifications of SFRA curves fall in these overlapped
ranges. The transition from good to faulty conditions is not
necessarily abrupt but progressive degradation processes can
be evidenced resulting “negligible” in the first instance,
“potentially damaged” in a second instance and “certainly
damaged” as the final condition. Any diagnostic algorithm
904
A. Contin et al.: Frequency-response Analysis of Power Transformers by Means of Fuzzy Tools
must interpret correctly the indicators by adopting suitable
criteria to distinguish between the three different conditions. It
is to be noticed that the criteria at the base of operative
decisions (run, refurbish, replace) are closely linked to the risk
evaluation policy of the user.
Since modifications in the SFRA can also be linked with
harmless causes, i.e. residual magnetization and noise in low
and medium/high frequency, respectively, three different
tolerance belts (expressed in dB) are associated to the
different frequency ranges: the tolerance is larger in lowfrequency to take into account the residual magnetization,
thinner in medium and intermediate in high frequency ranges.
5 THE “FUZZY” ALGORITHM
Fuzzy Logic (FL) is adopted here to organize information
in a context characterized by a level of uncertainty. Initially,
the lack of information linked with the limited number of
cases is normally coped with relying on experts. About ten
clear examples for each defect typology have been selected to
build up the “knowledge-base” of FLA, that is, the ranges of
the parameter values and the rules adopted to discriminate
between the different good and fault conditions. As the
knowledge evolves, FLA can be updated including the new
information. The FLA has the purpose to automatically
identify different defect types, such as short circuited turns as
well as radial and axial displacements, giving rise to
parameters able to characterize the comparison curve.
5.1 PARAMETER SELETION
Among the different parameters proposed in the literature,
only those able to consider simultaneously both
pronounced/slight and concentrated/distributed deformations
have been considered [7]. Attention was given to the
evaluation of the comparison curve defined by equation (3). In
particular, the mean:
m
¦
N
i
'( f i )
1
N
N
Ae ( f i ) Ar ( f i )
i 1
N
¦
(4)
and the standard deviation:
V
2
1
N
¦
N
i 1
'( f i ) m
is given in an interval of {0 – 1} by using the oblique sides of
the trapezium with the limit that the sum of the different
memberships be always 1. An example of “fuzzyfication” of a
generic parameter P is reported in Figure 4. A given value P*
is associated to the attribute “Low” with a membership PL and
to “Medium” with membership PM (PL+PM=1). The choice of
the values that establish the membership limits are derived
from the heuristic analysis of the parameter/defect relationship
obtained during the analysis of the experimental results (see
section 4). In particular, the frequency range has been
partitioned according to section 4.4, while m and V2 have been
partitioned differently over the three frequency ranges
according to the experience of RSE, taking also into account
the influence of the background noise. The selected limits can
be updated easily when new information is obtained after new
data-set acquisitions.
A tri-dimensional input space is thus constituted by the
connection of the three “fuzzified” parameters. By using these
attributes, the input space is partitioned in sub-spaces each one
associated to the vector whose components are the linguistic
attributes of the input parameters and the relevant membership
values.
The output linguistic predicates (i.e., Good Conditions (G),
Slight (S) and Pronounced (P) displacement) are connected
with the input space by means of appropriate rules based on
IF..THEN..ELSE conditions. The association between
input/output predicates and the limits for the linguistic
attributes is performed on the base of the training test results
and reflects the experience of RSE.
Figure 4. Example of “Fuzzy-Set” selection of a generic parameter P:
w (L), Medium (M) and High (H).
2
(5)
have been considered to evaluate the comparison curve over
the three different frequency ranges of section 4.4. In
particular, m takes into account the amplitude dispersion and
V the frequency shift due to resonant peak displacements.
5.2 FUZZIFICATION AND DEFUZZIFICATION
Each of the three parameters f, m and V2 was “fuzzyfied”,
i.e. partitioned in three ranges, according to FL theory and
past experiences [8-11]. Three linguistic attributes (i.e., Low,
Medium and High) have been associated to each partition by
means of a characteristic function (membership function, P)
here composed of a sequence of trapezium shapes. When two
attributes range in overlapped intervals, a partial membership
The most common Fuzzy-Logic procedure that associates
logical AND to the minimum membership value while logical
OR to the maximum one, has been adopted here to provide
membership profiles to the output linguistic predicates, [9]. In
this way, the uncertainty of the result is taken into account
assigning membership values <1 (and >0) to more than one
predicate with the constraint 6P=1. In general, a P-value close
to 1 gives an indication that the output predicate has a high
confidence degree to be true. Lower P-values are related to
ambiguous situations since different outputs are activated.
Through this approach the user decision is strongly
facilitated since, if P=1, the identification is accurate while
P<1 indicates that different options should be taken into
account. As an example, if m is “Low” with membership 0.2
and “Medium” with membership 0.8 while f and V2 are “Low”
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 18, No. 3; June 2011
with membership 1, the output of FLA will be “Residual
Magnetization”: “Slight” with membership 0.8”. This result
indicates that the reference and investigated-transformer
SFRA differ because of a harmless phenomenon and the
transformer can be considered in good conditions.
6 APPLICATIONS OF THE FUZZY TOOL
FLA has been first tested by using the training examples and
validated later by processing SFRA curves recorded on field.
6.1 THE UNCERTAINTY MANAGEMENT
Among these results, specific examples are discussed here
to point out the advantages of using FLA when applied to
analyze practical cases where the curves are of difficult
reading even for a skilled operator.
The effectiveness of the FLA is evident considering SFRA
such those obtained testing a transformer rated 250 MVA,
400/135 kV. The present results, recorded after an external
short circuit event, are compared with the frequency response
of earlier tests considered as a reference. The instrument was
connected between the HV terminals and the neutral point,
leaving floating the LV terminals. The test result related to the
W-phase is plotted in Figure 5. As can be seen, it is quite
difficult to formulate any conclusion looking only at the
differences between the two curves. The comparison curve
shows slight variations over the three different frequency
ranges. The FLA output, reported in Table 1, helps
considerably in the interpretation of this test result. Neither
short circuit nor residual magnetization were found (Table 1:
Good Conditions with P=1 for both cases). Changes in the
position of the resonant peaks around 5 kHz and over 400 kHz
determine an almost negligible modification in the medium
(Table 1: slight radial displacement P=0.1) and more evident
curve modification in the high frequency range (Table 1:
pronounced axial displacement, P=0.8). The value of P=0.8
offers an idea of uncertainty in the FLA results.
This means that the axial deformation is not granted but it is
realistic to suppose that some mechanical support has been
loosened. A variation of 1.9% in the short-circuit inductance
nameplate value supported the decision to leave the machine
in service (the prescriptions of [13] and the uncertainty related
the real and the nameplate value of the reactance are also
taken into consideration). As can be seen by comparing the
information provided by the two methods, FLA shown more
detailed information. It must be pointed out once again that
the P values depend both on the training examples and on the
operator experience in SFRA analysis. Other experts can
calibrate FLA in a different way reflecting their experience.
Similar test results, but different conclusions, can be drawn
looking at SFRA carried out on the low-voltage windings of a
transformer rated 200 MVA, 400/15 kV before and after a
short circuit event. The same setup of the former example has
been used in the test. The most significant SFRA is plotted in
Figure 6 while the output of the algorithm is reported in Table
2. Changes in a resonant peak appear at 100 kHz: this may be
905
linked to a slight displacement of few turns. The FLA output
indicates a “slight” and “pronounced” radial displacement
with P=0.8 and P=0.2 respectively. Even if some changes in
the transformer geometry has been detected, RSE experts
suggest to leave the transformer in service since P=0.8 is
associated to slight deformation. The residual magnetization
appears to be negligible.
6.2 A CASE STUDY
The FLA results can considerably help also to decide upon
the measurement procedure, as shown in the next example. A
three-phase step-up transformer rated 150 MVA and 400/20
kV was artificially subjected to an internal short circuit on
phase W, HV side. SFRA was carried out adopting the phaseto-phase connection since the HV windings were connected in
star configuration and the neutral was not available. UW, UV
and VW phases were compared to each other because no
previous reference curves were available. Tests were carried
out leaving the low-voltage terminals open and floating. The
result of the comparison of the connections (UV in good
conditions and UW containing the faulted phase, W) is
reported in Figure 7. The large discrepancy between the two
frequency responses is evident in the low-frequency range
(below 5 kHz), thus indicating an internal short circuit. The
same output as of Table 3 also indicate a pronounced axial
displacement with P=0.3. Since the P value indicates an
uncertain condition, SFRA was repeated in the same setup
conditions but shorting out the LV windings.
In this way, the influence of the magnetic core (residual
magnetization and consequently the visibility of the internal
short-circuit) is removed. Hence, the frequency response in
the low-frequency range was almost deleted as can be seen in
Figure 8 where the SFRA test results with shorted LV
terminals, are reported.
In fact, when the windings opposite to the tested one are shortcircuited, the inductive coupling is very much affected and the
sensitivity at low frequencies lowers significantly. Moreover,
being the short-circuit reactance much smaller than the no-load
reactance, the signal attenuation in the low-frequency range is
much smaller. The FLA output, reported in Table 4 and related to
the data reported in Figure 8, shows a reduction of the warning
level (Slight axial displacements with P=0.95 instead of
Pronounced with P=0.3). In this way, the assumption that the
machine is in good conditions becomes stronger.
6.3 SFRA TESTS ON SISTER UNITS
It often happens that the reference curves or the phase-tophase connections are not available, as in the case of the
single-phase HV transformers discussed here. Thus, the
comparison of the frequency response of sister units
(transformers having the same design) is the only possible
option to predict the transformer conditions. However,
experience has shown that sister units may show little
variations that must be taken into account. The comparison
with a sister unit has several benefits in that reference results
may be determined for a number of transformers at one time.
906
A. Contin et al.: Frequency-response Analysis of Power Transformers by Means of Fuzzy Tools
Figure 5. Comparison of SFRA measurements carried out on a single
phase of a transformer rated 400/135 kV, before and after an external short
circuit.
Table 1. Final test results of SFRA measurements of Figure 5.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0
0.9
1
1
Slight
0.2
0.1
0
0
Pronounced
0.8
0
0
0
Figure 7. Comparison of SFRA measurements carried out on a step-up
transformer rated 150 MVA, 400/20 kV, after an internal short circuit, using a
phase-to-phase configuration (UV vs. UW connections). The LV terminals are
open and floating.
Table 3. Final test results of SFRA measurements of Figure 7.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0
1
0
1
Slight
0.7
0
0
0
Pronounced
0.3
0
1
0
good conditions by the experts of RSE. It must be pointed out
that, in few cases, the FLA applied to transformers having
nominally the same design but some differences in their
construction can give false indications. Consequently, caution
is suggested when FLA is applied to analyze SFRA carried
out on sister units.
Figure 6. Comparison of SFRA measurements carried out on a single
phase of a transformer rated 400/15 kV, before and after an external short
circuit.
Table 2. Final test results of SFRA measurements of Figure 6.
Type of Fault
Good Cond.
Slight
Pronounced
Axial Displ.
1
0
0
Radial Displ.
Short Turns
Residual Magn.
0
1
0
0.8
0
0.77
0.2
0
0.23
Three single-phase transformers rated 100 MVA, 135/18 kV
were compared to a spare unit, never used before, and therefore
considered in good conditions. The FLA outputs related to
SFRA carried out on the three machines are reported in Table 5
while the SFRA curves related to the test carried out comparing
the machine connected to the S phase and the spare unit, are
plotted in Figure 9. As can be seen, different residual
magnetization affect the FLA output in all the measurements.
Even if these machines show successive serial numbers, the
frequency response is characterized by several resonance-peak
shifts. The FLA has been designed to take into account also
these differences and the FLA output assigning a very low P
value to R- and T-Ref. (see Table 5) while a higher value was
assigned to S-Ref.: the three machines were considered in
6.4 COMPARISON BETWEEN SFRA AND SHORTCIRCUIT INDUCTANCE TEST RESULTS
A comparison between short-circuit inductance and SFRAFLA test results appears interesting to better understand the
differences in terms of diagnostic information provided by the
two methods. The short-circuit inductance variations relevant
the two transformers of Figure 2 (section 4.2) and Figure 3
(section 4.3) were found 3.4% and 6%, respectively. Both
these values indicate fault conditions but FLA test results
address to specific defect typologies named “short circuit” the
former and “axial” and “radial” displacement, the latter, thus
facilitating the user decision.
A three-phase transformer rated 200 MVA, 400/20 kV was
subjected to short circuit withstand tests and SFRA method
was used in addition to the short-circuit inductance
measurement to assess the condition of the windings after the
tests. An anomalous behavior was notified comparing SFRA
measurements obtained adopting the phase-to-phase
connection (the HV windings are star connected and the
neutral is not available). In the absence of previous reference
curves, SFRA curves of the different connections were
compared to each other. Tests were carried out leaving the LV
terminals floating. A variation of 2.7% in the short-circuit
inductance measurement suggested to open the machine and a
fault, whose picture in reported in Figure 11, was found on
phase U. FLA was verified by using this information and the
results are reported in Table 6. As can be seen, a pronounced
radial displacement is indicated with a P=0.8 while the axial
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 18, No. 3; June 2011
Figure 8. Comparison of SFRA measurements carried on a step-up
transformer rated 150 MVA, 400/20 kV, after an internal short circuit, using a
phase-to-phase configuration (UV vs. UW connections). The LV terminals are
short circuited.
907
Figure 10. Comparison of SFRA measurements carried out on a three-phase
transformer rated 200 MVA, 400/20 kV, using a phase-to-phase configuration
(UV vs. UW connections). The LV terminals are open and floating.
Table 6. Final test results of FRA measurements of Figure 7.
Table 4. Final test results of FRA measurements of Figure 8.
Type of Fault
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0.05
1
1
1
Slight
0.95
0
0
0
Pronounced
0
0
0
0
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0
0
1
0
Slight
Pronounced
1
0.2
0
1
0
0.8
0
0
Figure 11. The picture of the fault of the transformer of Figure 10.
Figure 9. Comparison of SFRA measurements carried out on two singlephase sister transformers rated 100 MVA, 135/18 kV.
Table 5. Comparison of FLA outputs relevant to three single-phase sister
transformers. Output S-Ref. is relevant to SFRA measurements of Figure 9.
S-Ref.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
1
0.1
1
0
Slight
0
0.9
0
0
Pronounced
0
0
0
1
R-Ref.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0.7
1
1
0
Slight
0.3
0
0
0
Pronounced
0
0
0
1
T-Ref.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0.7
1
1
0
Slight
0.3
0
0
0
Pronounced
0
0
0
1
displacement is considered “slight”. The residual
magnetization is negligible.
SFRA test can be conveniently adopted for the quality check
of new transformers, just installed. This is the case of the
transformer rated 150 MVA, 400/15 kV. SFRA tests were
carried out comparing phase-to-phase. An anomalous
behavior was found on the phase V (HV side). SFRA test
results obtained comparing U and V phases are reported in
Figure 12.
A variation of 3% in the short-circuit inductance relevant to
phase V, compared with the other phases, motivated to open
the machine and an axial deformation was found on the phase.
FLA results clearly indicated a pronounced axial displacement
as reported in Table 7 where the FLA results are summarized.
7 CONCLUSION
The experience acquired through the extended application
of SFRA both in laboratory and in the field with different
types of defects, has allowed to establish general rules for the
interpretation of SFRA. A Fuzzy-Logic Algorithm for the
automatic analysis of the frequency response in presence of
uncertain conditions has been developed. The uncertainty is
908
A. Contin et al.: Frequency-response Analysis of Power Transformers by Means of Fuzzy Tools
[3]
[4]
[5]
[6]
[7]
[8]
Figure 12. Comparison of SFRA measurements carried out on a three-phase
transformer rated 200 MVA, 400/20 kV, using a single-phase configuration
(U vs. V connections). The LV terminals are open and floating.
Table 7. Final test results of SFRA measurements of Figure 12.
Type of Fault
Axial Displ.
Radial Displ.
Short Turns
Residual Magn.
Good Cond.
0
0
1
0.8
Slight
0
0.7
0
0.2
Pronounced
1
0.3
0
0
[9]
[10]
[11]
[12]
[13]
[14]
M. DeNigris, R. Passaglia, R.Berti, L.Bergonzi and R.Maggi, "Application of
Modern Techniques for the Condition Assessment of Power Transformers”,
CIGRE, Paris, France, paper A2-207, 2004.
S. A. Ryder, “Diagnosing Transformer Faults Using Frequency Response
Analysis”, IEEE Electr. Insul. Mag., Vol. 19, No.2, pp. 16-22, 2003.
S. V. Kulkarni and S.A. Khaparde, Transformer Engineering, Design and
Practice, Marcel Dekker Inc., New York 2004.
J L.Satish and S.K.Sahoo, "An Effort to Understand What Factors Affect the
Transfer Function of a Two-Winding Transformer", IEEE Trans. Power
Delivery, Vol. 20, pp. 1430-1440, 2005.
W. Kim, B.K. Park, S.C. Jeong, S.W. Kim and P.G. Park, "Fault Diagnosis of a
Power Transformer Using an Improved Frequency-Response Analysis", IEEE
Trans. Power Delivery, Vol. 20, pp. 169-178, 2005.
J. M. Mendel, “Fuzzy Logic Systems for Engineering: A Tutorial”, Proc. IEEE,
Vol. 83, pp. 345-377, 1995.
F. Russo, “Fuzzy Model Fundamentals”, in Wiley Encyclopedia of Electrical
and Electronics Engineering, Vol.8, pp. 158-166, J. Wiley & Sons, New York,
USA, 1999.
M. M. A. Salama and R. Bartnikas, “Fuzzy logic applied to PD pattern
classification”, IEEE Trans. Dielectr. Electr. Insul., Vol. 7, pp. 118 – 123, 2000.
N. C. Sahoo, M. M. A. Salama and R. Bartnikas, “Trends in partial discharge
pattern classification: a survey”, IEEE Trans. on Dielectrics and Electrical
Insulation, Vol. 12, pp. 248 – 268, 2005.
CIGRE Working Group A2.26, “Mechanical-Condition Assessment of
Transformer Windings Using Frequency Response Analysis (FRA)”, CIGRE
Brochure N.342, 2008.
IEC Std., Power Transformers, Part 5: Ability to Withstand Short Circuits, IEC
Standard 60076-5, p.37, Third Edition 2006.
IEC Std., Power Transformers, Part 18: Measurement of Frequency Response,
Draft of IEC Standard 60076-18, First Edition 2009.
Alfredo Contin (M’1987) was born in Udine on 30
January 1955. He is currently an Associate Professor at
the Department of Electric, Electronic and Computer
Science of the University of Trieste (Italy) and he teaches
the courses of Fundamentals and Design of Electric
Machines. His field of interest is characterization, aging
and diagnostics of insulation materials and systems by
means of partial discharges.
Figure 13. The picture of the fault of the transformer of Figure 12.
taken into account by using appropriate membership functions
thus giving the users flexible tools to support the evaluation of
the transformer conditions. The validation tests show that the
algorithm is capable to distinguish between good condition and
different types and levels of winding faults. Moreover, the
algorithm seems to be independent from the connection type
adopted to test the transformers and appears less sensitive to the
background noise or small differences. The use of SFRA with
the proposed algorithm constitutes an important step forward to
the setting up of reliable diagnostics of power transformers.
ACKNOWLEDGMENT
The Ministry of Economic Development with the research
Found for the Italian Electrical System under the contract
agreement established with the Ministry Decree of 23 March
2006, is gratefully acknowledged.
REFERENCES
[1]
[2]
K. G. Nilanga B. Abeywickrama, Y.V. Serdyuk and S. Gubanski,
"Exploring Possibilities for Characterization of Power Transformer
Insulation by Frequency Response Analysis", IEEE Trans. Power
Delivery, Vol. 21, pp. 1375-1382, 2006.
M.Wang, A.J. Vandermaar and K.D. Srivastava, “Transformer Winding
Movement Monitoring in Service – Key Factors Affecting FRA
Measurements”, IEEE Electr. Insul. Mag., Vol. 20, No. 5, pp. 5-12, 2004.
Germano Rabach was born in Pirano on 5 May 1942.
He is currently Full Professor at the Department of
Electric, Electronic and Computer Science of the
University of Trieste (Italy). He teaches the courses of
Materials and Electrical Technologies. His field of
interest is characterization, aging and diagnostics of
insulation materials and diagnostics of electrical systems.
Johnny Borghetto was born in Vigevano (PV) on 10
July 1974. He is graduated in Electrical Engineering at
the University of Pavia (Italy) and he is currently
employed in ERSE, where he deals with diagnostics of
electrical components. His research interests include
partial discharge studies on generators, rotating machines
and power transformers in labs and on plants.
Michel de Nigris – (M’90, SM’94) was born in Brussels
(Belgium) in 1959, received the doctoral degree in
electrical engineering from the University of Genoa ,
Italy in 1983. From 1984 to 2005 he worked with CESI
where he has covered several roles of increasing
responsibility before being appointed as Head of the
Laboratory Division. Since 2006 he works in ERSE
(formerly CESI RICERCA) where he is Director of the
T&D Department.
His fields of interest are surge arresters (he is chairman of IEC TC 37), HV
components (he is the Italian representative in Study Committee A3 of
CIGRE): he heads a group of specialists dealing with research projects on the
lifecycle management of electrical components
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 18, No. 3; June 2011
Renzo Passaglia was born in Piacenza, Italy, in 1948. He
graduated in electrical engineering at the Milan
Polytechnic (Italy). He joined ENEL, Electrical Research
Center, in 1981 where he was mainly engaged in the field
on electrical components, with special reference to power
transformers and electrical rotating machinery. He joined
CESI in January 2000 “Tests and Components”
Business Unit and from 2006 to 2009 he worked in ERSE (formerly CESI
RICERCA) where his main fields of expertise were monitoring and
diagnostics of electrical components. He retired in 2010 and he is presently a
consultant.
909
Giuseppe Rizzi (M’90-SM’95) was born in Milano (MI)
on 1949. He received the doctoral degree in physics from
the University of Milano, Italy in 1974. From 1969 to
2005 he worked with CESI where he has covered several
roles of increasing responsibility. From 2006 to 2009 he
worked in ERSE (formerly CESI RICERCA) where he
was responsible for Asset Management in T&D
Department. He retired in 2010 and he is presently a
consultant. His fields of interest are HV measurements,
diagnostic of HV and MV components (member of
CIGRE WGD1.33)