2144 IEEE Transactions on Power Apparatus and Systems, Vol. PAS-97, No.

6, Nov/Dec 1978

TRANSFORMER DIAGNOSTIC TESTING BY FREQUENCY

RESPONSE ANALYSIS

E.P. Dick, Member and C.C. Erven, Member

Ontario Hydro
Toronto, Canada

/3
ABSTRACT PREPARATION OF TRANSFORMER FOR TEST
Winding deformation in power transformers can be measured
externally using a new frequency response analysis (FRA) method Pror to making FRA measurements on any transformer m service,
Field experience since 1975, on five separate transformers up to 550 the transformer was isolated and physically disconnected from the
MVA rating,230kVclassindicatesthatthismethod hasadvantagesover buswork at all bushing terminals. This preparation was necessary to
the low voltage impulse (LVI) method as a practical maintenance tool. minimize the effects of bus capacitance, which could be variable and
Results on suspect transformers indicate that benchmark reference unbalanced depending on location.
data is not always necessary to identify certain kinds of mechanical Transformertappositionwascheckedandsettofullwindingtapon
damage. all phases. This permitted us to standardize all measurements to full
winding response.
INTRODUCTION Some sources have recommended using coaxial ground shields
When a transformer is subjected to high through fault currents the over each bushing to minimize the effects of stray capacitance to
mechanical structure and the windings are subjected to large nearby grounded structures. We later observed that complete removal
mechanical stresses. These stresses may cause serious deformation of of the coaxial ground shields on the bushings did not affect the
the winding and precipitate a transformer failure. sensitivity and repeatability of the FRA measurement at the frequencies
used.
Winding deformation is difficult to determine by conventional
measurements of ratio, impedance and inductance. However, INSTRUMENTATION
deformation results in relative changes to the internal inductance and
capacitance of the winding structure. These changes can be detected The instrumentation system used for frequency response analysis
externally by frequency response analysis (FRA) or in the time domain is easily portable,.and can be readily set up and operated by two people.
by the low voltage impulse (LVI) method. Figure 1(a) shows a 3 0, 550 MVA generator step-up transformer
The first application of LVI was, made in Poland in 1966(1). The undergoing FRA testing before repair in our maintenance shops.
method wasfurtheradvanced and refined in Britain (2) and in the United
States (3, 4). The main purpose in most of these applications, however,
was to assist in determining whether transformers under short circuit
test had passed or failed. The LVI method has now been incorporated
into the IEEE Power Transformer Short Circuit Test Guide and Test
Code (5, 6).
The alternative to time domain testing is frequency response
analysis (FRA). The FRA method uses a sweep generator to apply
sinusoidal voltages at different frequencies to one terminal of a
transformer winding. Amplitude and phase of signals obtained from
selected terminals of the transformers are plotted directly as a function
of frequency.
Since 1975 we have tested 5 different transformers to evaluate the
LVI and the FRA method as a field maintenance tool. Our experience
with LVI indicates that it is subject to interference effects and extensive
calibration procedures. Furthermore, it requires a specially constructed
and finely trimmed instrumentation system to obtain repeatable results.
This report shows that the FRA method removes many of these
difficulties while increasing the sensitivity of detecting winding
deformation.
Fig 1(a). 550 MVA Transformer Under Repair
and FRA Testing
Network Analyzer
The heart of the FRA method is the network analyzer, Figure 1 (b),
which incorporates three separate instruments. These include a sweep
generator, a dual channel detector, and a hard copy pen-type plotter.
The system provides a sinusoidal output signal whose frequency can be
programmed from a keyboard to vary overany range between 50 Hzand
F 78 024-2. A paper recommended and approved by the IEEE 13 MHz. Simultaneous
difference between twomeasurement of amplitude
received signals, ratioa and
produces phase
display of
Transformers Committee of the IEEE Power Engineering Society for amplitude ratio in dB and phase difference in degrees, coincident with
presentation at the IEEE PES Winter Meeting, New York, NY, the corresponding dc output signals which are used to drive the "X" -
January 29-February 3, 1978. Manuscript submitted September 6, "Y" plotter. The stated dynamic range for our analyzer is 120 dB
1977; made available for printing November 1, 1977. with 0.01 dB resolution and 0.010 phase resolution.

0018-9510/78/1100-2144$00.75<@ 1978 IEEE

 2145
The use of coloured pens on the plotter can be used to identify different
phase winding measurements so that direct comparisons can be made
without further processing of the results. A separate output signal
whose dc level is proportional to the swept frequency is used to drive the
"X"-axis of the plotter. A damping resistor of 1 kS2 is connected from
each unused terminal of the transformer to tank ground. These resistors
help to damp out secondary oscillations in non-excited windings and to
minimize stray capacitance at the bushing terminals.
As a precaution against station wiring surges and external
interference the 60 Hz, 115 V, power to drive the complete
instrumentation system was supplied through a shielded isolating
transformer. All instrument chassis, coaxial cable shields, and the
isolating transformer shield were connected to the tank ground of the
transformer under test.

OPERATION OF TEST EQUIPMENT

Operation of the network analyzer was simplified by several
automatic and pre-programmable features. The sweep generator
IENERE | | This to signal level was normally set to 0 dBm referred to 50 5 load.
anoutput
Coresponds
This corresponds to an output signal level of 0.224 V rms.
The frequency of the output signal can be varied in discrete steps
Fig 1(b). Frequency Response Test Equipment over a wide frequency range. We normally chose a frequency window
extending from 10 kHz to 1 MHz. The sweep was divided into 1000
discrete steps with a step duration of 100 milliseconds. It took 100
seconds to complete a record of amplitude or phase as a function of
frequency.
feuny
Measurement Circuit For one set of FRA measurements the detector was arranged to
The arrangement of the FRA instrumentation and test connections measure amplitude ratio of the winding output voltage to winding input
used on a typical transformer winding are shown in Figure 2. Four voltage Vo/Vi and the corresponding phase difference for each of the
standard 502 coaxial cablesof suitable length are used toconnectthe windings. The plotter was calibrated to read amplitude ratio in dB and
network analyzer to the selected transformer terminals. All cables are phase difference in degrees. By exchanging some of the cable
terminated in their characteristic impedance to minimize reflection connections on the transformerterminalsand analyzer, a measurement
problems. One of the cables is used to carry the output signal from the of voltage to current input ratio Vi/li, or impedance, along with the
network analyzer to an input transformer terminal. The other three phase could be similarity obtained at any terminal.
cables are used to carry the voltage and current input signal and the
voltage output signal from otherterminals back tothe network analyzer.
Voltage signals are measured directly at the bushing terminals with FREQUENCY RESPONSE OF TEST TRANSFORMER
respect to tank ground. A high frequency current transformer, whose Voltage Ratio Measurements
output is matched to the characteristic impedance of the cable, is used The frequency response for one of the high voltage (HV) winding
to measure current. of an 8 MVA, 110/22 kV, wye-delta powertransformer is shown in Figure
The amplitude ratio and phase difference between two compared 3. Thevoltagestimulussignal, Vi, wasapplied between the HV neutral of
signals are available as calibrated dc output signals from the network the winding, Ho, and tank ground. The response was obtained by
analyzer. These are used alternately to drive the 'Y'-axis of the plotter. measuring the ratio of the outputvoltage toground at HV terminal H3, to
the input voltage, Vo/Vi. Amplitude and phase has been plotted over
three separate frequency ranges to showthe behaviourfrom 1 kHz to 10
MHz.
Figure 3(a) shows the results from 1 kHz to 100 kHz. In the low
CT - frequency range the response wascharacterized by resonance at24,43,
63 and 87 kHz. These resonant frequencies correspond to the half-wave
space harmonics in the winding due to the low impedance terminations
of the measuring circuit. Below 20 kHz the phase remained essentially
constant at -90°, indicating that the transformer winding response was
dominated by inductance. As the frequency increased the phase lag
increased as more space harmonics built up in the winding.
TRANSFORMER Figure 3(b) shows the response of the same winding in the medium
S~i a-.................. frequency range from 10 kHz to 1 MHz. Multiple resonances can be
observed over the entire frequency range. Although amplitude and
I..I I I I H( + AH t I I I I I phase were recorded for each test on the transformer, the figure shows
lll | 1 = i Ahllll only amplitude due to space limitations.
The high frequency amplitude response of the winding from 100
50l
CABLE
l kHz to 10 MHz is shown in Figure 3(c). Up to 1.5 MHz there were about
55 space harmonics present in the winding. At the higher frequencies
the distributed capacitance in the transformer tended to shunt the
Vaf winding inductance and resonance was much less pronounced. Also
V1 I,I
PLOTTER I IX- v |
winding lead effects appear to affect the results in the higherfrequency
I IINPUTH I o
I I I Y-INPUIT I I I region.
Impedance Measurements
The input impedance measured at the H2 terminal of the 8 MVA test
transformer is shown in Figure 4. These results were obtained by
AMPLITUDE - PHASE measuring the voltage to current ratio Vi/li and phase difference as a
A
l lI B | he | function of frequency for a signal applied from the terminal to ground.
We observed a dominant capacitance effect for most of the
frequency range shown. The impedance continues to decrease with
SINEWAVE SWEEP frequency and the phase remained close to -90o. The equivalent input
OUTPUT G EN ERATOR capacitance from the high voltage terminal to ground on the 8 MVA test
transformer was approximately 700 pF in the frequency range above
400 kHz. The 115 kV bushing which hasa nominal capacitanceof 400 pF
tended to obscure the striking resonant effects which appeared in the
Fig. 2 Arrangement of Test Equipment and Transformer voltage ratio results.
 2146

0(LD C bJ~~~~~~~~~~~~~~~~~~
n

20
) 40 60 80 10 ) ;! S) 20K
U~~~~~~~~~~~~
>~~~~~~~~~~~~~~~~~9 [L
1. 20K Amplitude0
1a

2. &
>
- . a

~~~~~~~~~~~~~200
---. -...-- ..9Phas

-9&cPW
10 20
I600
40 60 80 100
(nIII
I0 200
--II
400 600 800 11000
FREQUENCY kHz - (LFREQUENCY - kHz
Ho~~~~~~~~~~~~~
V rnfreH3 toL t 2 rnfre
1. Amplitude 1. Magnitude
2. Phase ........2. Phase

Fig 3(a) Low Frequency HV Winding Response, Fig 4. Medium Frequency HV Winding Impedance
Ho to H3, 8 MVA Transformer at H2, 8 MVA Transformer

EQUIVALENT CIRCUIT OF TRANSFORMER WINDING

A simplified equivalent circuit for one outside phase of the HV
winding of the 8 MVA test transformer, using cascaded IT sections is
-40 shown in Figure 5. The model consists of 116 sections, equal to the
number of winding discs in the transformer. The parameters for the
equivalent circuit are calculated in Appendix A from the results shown
V ~~~~~~~~~~~~~~~~~~in
Figure 3.
-60 [9 b b [1 A W V'< H Also calculated in the Appendix is the equivalent input capacitance,
O |60 250 pF which is obtained from the ladder network of all series and
parallel capacitances of the winding. If we add to this the nominal
bushing capacitance of 400 pF, we find that this agrees with the 700 pF
W 11 of equivalent input capacitance as shown in the impedance
F
O-80 characteristic of Figure 4.
The equivalent circuit is useful in modelling the sensitivity of FRA to
o winding changes. Conversely, a change in response could be related to
> a calculated amount of winding deformation.
-100 0ll
200 400 600 800 1000
FREQUENCY - kHz
Vi Ii Ls Ls Ls VO
Fig 3(b) Medium Frequency HV Winding Response, I 2 116
Ho to H3, 8 MVA Transformer
Cs Cs C
Ri

Cb TC9 Cg Cg C9 C Ro

Vo -40 -
Cs Se 1
Cs Series Capacitance
7.0 nF per section
t -60
-

LA Cg - Ground Capacitance
9.2 pF per section
Cb - Bushing Capacitance 400 pF
Ls - Winding Inductance 3.5 mH per section
Ri - Input Impedance 36 2
0 Ro - Output Impedance 36 S2

0 2 4 6 8 10 of 8 MVA Transformer
FREQUENCY - MHz

Fig 3(c) High Frequency HV Winding Response, SENSITIVITY OF FREQUENCY RESPONSE ANALYSIS
H0 to H3, 8 MVA Transformer The practical application of any diagnostic technique to detect
mechanical damage in a transformer depends on its sensitivity to
changes in the distributed inductance and capacitance.
 lo~ ~ ~ ~ ~ ~ ~ m
2147
Inter-disc Capacitance Inter-winding Capacitance
Since the 8 MVA test transformer had been declared surplus, we During our field testing program we also did tests on several 550
were able to disturb the winding insulation, and introduce additional MVA, 230/22 kV, wye-delta generator step-up transformers. Figure 7
inter-disc capacitance as shown in Figure 6(a). These capacitors were shows the effect of removing the ground connection toa metallic shield
added to simulate a change in the distributed series capacitance of the which was located between the LV winding and a part of the HV winding.
winding. This change in inter-winding capacitance showed the greatest effect
above 200 kHz.
15 WInding Inductance
To determine the sensitivity of the FRA method to changes in
winding inductance, we examined the effect of changing transformer
-:
E tap position. Figure 7 shows the effect of introducing a 2.5% change on
one phase of the HV winding of the 550 MVA transformer. The effect is
again more noticeable in the frequency range above 200 kHz.
10_
=1 r s~~~~~~~~i ~~~~20llll
= _

-30
I-~~~~~~~~~~~~~~~~~~~~~~
Fi6) Caaio Ade to Inte-dis

winding sections
40 and 41 of te w4
° I l- . I, 'V .
Fig 6(a). Capacitor Added to Inter-disc l | :
Capacitance on 8 MVA Transformer l.\J

Figure 6(b) shows the effects of adding 100, 250 and 1000 pF -60_
between winding sections 40 and 41 of the 116-section HV winding.
Since the distributed capacitance, as indicated by the model, is about
7000 pF per disc section, the 100 pF capacitor represents a 1.4% change
in inter-disc capacitance. -70 [
0 100 200 300 400 500
FREQUENCY - kHz
1. Reference
............... Ground Shield Isolated
.3. Tap Change
40 III
Fig 7. Effect of Ground Shield and Tap Change
on HV Winding Response, 550 MVA Transformer
M-50 X

'~ - \ ,\Other Transformer Effects

-0 \i ' / \\ 0 During ourfield testing program wetested one of the550 MVAstep-
2 \ | \ \^yup
%\ij 8
transformers with the bushings removed, oil removed from the tank
and cover removed from the tank. Although the overall response for all
windings was noticeably altered, a high degree of consistency was
* ,Z~lmaintained among the phase winding responses. These changes would
> _70 -_ I invalidate benchmark comparisons but do not detract from the value of
.j comparisons among phase windings.
.. Effects of Instrumentation Changes
-80 | Changes were also made to the test equipmentconnections and the
600 700 800 measuring system to determine theireffect. The results of some of these
FREQUENCY- kHz changes are shown in Figure 8.
- 1. No Capacitance Trace 1 The response of the Ho-H1 winding with a normal
. ----------2.
100 pF Between Discs 40 - 41 instrumentation set-up as shown in Figure 2 including
------ 3. 250 pF Between Discs 40 - 41 coaxial ground shields on the three HV bushings.
4. 1000 pF Between Discs 40 - 41 Trace 2 Conditions as in Trace 1 without the HV bushing shields. The
change is not noticeable below 400 kHz.
Trace 3 Conditions as in Trace 1 with a 72 5 coaxial cable system
cable system. This change hada
pronounced effecton 50Q
replacing the normal
Fig 6(b). Effect of Additional Capacitance on HV thefrequency response overtheentire
Winding Response, 8 MVA Transformer range.
2148
-20 _________________________________________________ above theorem implies that the input and output terminals of the
l l l transformer winding may be interchanged without affecting the
response. Our test results confirmed that our measuring circuit
approached the necessary conditions.
V 30 Accordingly, all tests above the diagonal produce duplicate results
1 X§9 85 ,^ / l v ; to those below, and we can eliminate 28 measurements from the 64
indicated by the matrix. A further reduction of test data results if only
terminal pairs separated by one high voltage or one low voltage winding
0 {Z , / A , / I I are tested. For example testing between H. and H2 would place two HV
1/ 5 4 1 a/ N { / ; t windings on two different limbs in series which would make any
40 l distortion in either winding more difficult to determine.
W | w 2Of ltthe remaining 24 entries in Table 1,21 of these are grouped in sets
\\,\
of three by the dashed lines. Phase symmetry in transformer winding
arrangement will yield similar response characteristics within each
J group. Thus records can be more easily compared to detect small
> 50 _; changes in response if traces in each group are overlapped directly on
the plotter and identified by suitable colours. Our results suggest that
this technique can be useful in assessing the condition of transformer
windings without the benefit of original benchmark data.
In our test program we identify each test by the standard
-60 | | transformer terminal designations, with the terminal input preceding
0 100 200 300 400 500 the terminal output for a given winding test. Groups H and X emphasize
FREQUENCY - kHz winding end effects, whereas groups HOH and XOX emphasize internal
effects in the HV and LV windings respectively. Groups HOX, HXO, HX,
1. Reference emphasize capacitive coupling between HV and LV windings. The HO,
*---.--------- 2. No Bushing Shields XO, and HOXO groups are supplementary measurements which can be
useful if benchmark data is available. Table 11 shows the modified group
- 3. Change in Type of Co-Axial Cable structure for testing a wye-delta transformer. Since the wye-delta
transformer has only one neutral, 22 tests are sufficient.
Fig 8. Effect of Test Equipment Change on HV
Winding Response, 550 MVA Transformer TABLE 11
Standard Test for Y- A
Transformer

PROPOSAL FOR A STANDARDIZED TEST Output Input Terminal

Oneof the objectives in ourtestprogramwastoreducethenumber Terminal HO Hi H2 H3 Xl X2 X3
of tests to a minimum and to group those test results which would be
expected to be similar due to phase symmetry in the transformer. HO HO
Table I shows the 8 terminals of a Y/Y transformer arranged
horizontally and vertically in a matrix format for a voltage ratio test. Any HOHHiH
one of these terminals can be selected for a signal input and any other
for signal output. In addition, current can be measured at the same H2 HOH H
terminal as the voltage for an input impedance test.
H3 HOH H

Xl HOX HXFHXO X XOX

TABLE I ,,
Standard Test for Y-Y X2 HOX HXO HX, X XOX
Transformer "'
X3 HOX HXO HX XOX 'X
Output Input Terminal
Terminal HO Hi H2 H3 XO X1 X2 X3

HO HO
APPLICATION OF THE METHOD TO SUSPECT TRANSFORMERS
Hi HOH H One of the 3 0, 550 MVA, 230/22 kV generator step-up transformers
was taken out of service for repairs to defective ground shields. FRA tests
H2 HOH H were made before and after repairs according to the above schedule.
AThe HOH response of the three HV windings are shown before repair in
H3 HOH H3 HOH HFigure 9(a) and after repair in Figure 9(b). Since the consistency after
H repair is greatly improved this winding shield problem was easily
XO HOXO HXO-HXO-HXO XO detected.
A second transformer of the same rating had suffered a fault in one
xl HOX XOX phase of the low voltage delta winding. About 10% of the winding was
H. ,
HX X
later found to be short-circuited. The XOX response of the three LV
is shown in Figure 10(a) and after repairs in
Figure 10(b). Therepairs
windings
X2 H9X HX XOX X before disparity shown in Figure 10(a) by this drastic fault
d X , Aimplide Ontario
that less major damage can also be detected.
Hydro our objective is to find a relatively simple and
l X3 |HOX HX XOX |At
reliable field maintenance tool, so that diagnosis of the mechanical
state of suspect transformers can be made on location. Including set-up
time, but not including transformer preparation, each of the above
suspect transformers was completely tested in about two hours. Our
The theorem of reciprocity states that if a voltage applied in one programme will also continue with measurements on key transformer
branch of linear, bilateral, passive network produces certain current units as part of their maintenance outage schedule. More testing
in any other branch of the network, the same voltage applied in the experience will enable us to relate anomalies in frequency response to
second branch will produce the same current in the first branch. Since the extent of winding deformation. Consideration is being given to
low impedance connections are used in our measuring circuit, the replacing plotted records with digital data storage.
 2149

-20 _

-10
-30 I

IM~~~~~~~~~~
-40 / ' F

I Q~~~~~~~~~~~~-30
£k-50
° O 2030 40 0
LI) 0

1 ~~~~~~~~~~~~~-40
> -60 l. Ho- Inut, H.- Otput '
I-. OH 100 o 200Il, 300 400 500
Li : 0 100 200 300 400 500

FREQUENCY- k~z FREQUENCY - kHz

100 200 300 400
0 1A~~~~~~~~~~~~~~~~~~~~Wnig 500 1 l X2 Input55 , X,- Output
V rnfre -
Xi X2 X3
,- k- 2. X3 -
FREQUENCY "T X?- "
Hi H2H3 .............
3. XI -VTX
I. Ho - Input ,Hi Output
---2. Ho - ,2
H T

............ 3. Ho- 3,7J

H- ,"TV
Ho
Fig 10(a). LV Winding Response with Faulted LV
Winding, 550 MVA Transformer
Fig 9(a). HV Winding Response with Damaged Ground
Shield, 550 MVA Transformer

-6 I I .II
-20

-30 IM~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10
IX -30F
0 -50~~~~~~~~~~~~~~~~~~~~~~~~-

-601~~~~~~~~~~~~~~~~~~~~~~~~~~~:
1-~ ~ ~ RQUNY ~ FRQENY-I ~

LiFo(- n
Inut,
TV)
Hi-Otu i

?
2H
? fi
2

Inu2I0OtptX I3
2X
2150

CONCLUSIONS 4. High Frequency Impedance: Ls is neglected. The input capacitance

1. Frequency response analysis has been applied successfully as a of an infinitely long ladder network of capacitors is:
diagnostic method for detecting mechanical deterioration in q =
suspect power transformers.
2. Our experience supports the development of FRA as a field
maintenance tool. Frequency response analysis instrumentation is = F000 x 9.2 x 10-
well developed and commercially available. It is portable, and
relatively easy to set up and operate to give repeatable results. = 250 pF
3. The FRA method is inherently a powerful diagnostic method. The
input signal is concentrated ata single frequency allowing filtering
of the received signals to reduce noise. Since the useful frequency
range is below 1 MHz it is not so susceptible to lead effects as REFERENCES
impulse or step input signals. Benchmark reference data is not (1) W. Lech, L. Tyminski, "Detecting Transformer Winding Damage-
always necessary to identify certain kinds of damage. The Low Voltage Impulse Method". Electrical Review, No. 21, Vol.
4. FRA results can be used to construct models of transformer 179, November 1966, pp 768-772, (ERA Translation).
windings. These models can be used to relate frequency response (2) M. Waters, A. Stalewski, J.C. Farr, J.D. Whitaker, "Short-Circuit
data to the transformers' mechanical structure and to quantify Testing of Power Transformers and the Detection and Location of
significant winding changes. Damage". CIGRE, Paper No. 12-05, 1968.
5. Furtherdevelopmentisencouragedtocorrelatedegreeofdamage (3) E.J. Rogers, L.E. Humbard, D.A. Gillies, "Instrumentation
to test results. Techniques for Low Voltage Impulse Testing of Power
Transformers". IEEE Transactions PAS-91, No. 3, May/June 1972,
pp 1281-1293.
APPENDIX A (4) D.A. Gillies, L.E. Humbard, E.J. Rogers, "Bonneville Power
Administration Transformer Short Circuit Test Results -
CALCULATION OF EQUIVALENT WINDING Comparison of Winding Inspection with Diagnostic Methods". IEEE
MODEL FOR 8MVA TRANSFORMER Transactions PAS-92, No. 3, pp 934-942.
1. Low frequency response: Cs and Cg are neglected (see Figure 5). (5) IEEE Task Force of the Performance Characteristics Sub-
The 3651 termination resistance Ro and the 116 winding sections committee of the IEEE Transformers Committee, "Power
form a voltage divider. Transformer Short Circuit Strength - Requirements and Test
Code". IEEE Trans PAS-91, No. 3, May/June 1972, p 1294, C.R.
V French, W.J. McNutt, E.J. Adolphson, R.B. Pherson, D.C. Johnson,
Ro J.E. Dind.
Vi RO + j2n f x 116 Ls (1) (6) IEEEWorking GrouponShort-CircuitStrength,TestCodeandTest
Guide of the Performance Characteristics Sub-committee of the
IEEE Transformers Committee, "Distribution and Power
From Figure3(a), Vo/Vi is-45 dBat2.5kHz. Neglectingtherealpart Transformer Short Circuit Test Guide". D262(a) 1/D6, January
in the denominator of (1) and solving for Ls: 1977.
L 13 x 102.25 = 3.51 mH E. P. Dick (M'77) was born in Waterloo, On-
52rt x2500x 116 tario in 1948. He received the B.A.Sc in 1971
Total series inductance is 116 x 3.51 mH = 0.41 H. from the University of Waterloo and the
M.A.Sc in 1973 from the University of British
2. Medium Frequency Response: Cs is neglected. The increase in Columbia specializing in dual field machine con-
phase lag between 2 resonant peaks (24 kHzfrom Figure3(a))is 180 trol. Following a year at the Eidgenossische
degrees or ~ radians per winding section. ___Technische Hochschule in Zurich, Switzerland,
he worked on high energy switching at the Karl-
TZ 2 =2ntfV/ Ls g ~~~~~~~~~~~~~~~~sruhe
Kernforschungzentrum in Germany.
sTruheSince 1975 Mr. Dick has been with the
Thus Cg = 1 (2) Research Division of Ontario Hydro. He is cur-
(116 x2f)2 Ls rently working on transformer modelling techniques for both digital
and analog computers.
1 Mr. Dick is a Registered Professional Engineer in the Province of
(116 x 48000)2 x 3.51 x 10-3 Ontario, Canada.
= 9.2 pF
afford C. Erven (M'63) was born in South
3. High Frequency Response: Ls is neglected. An infinitely long ladder River, Ontario, Canada on July 5, 1937. He
network of capacitors has an output after n sections: received the B.Sc degree from Queen's Universi-
ty, Kingston, Ontario and the M.A.Sc degree in
V° = On Electrical Engineering from the University of
-i (3) _
_i
l _ Waterloo, Ontario, in 1959 and 1970 respectively.
After joining Ontario Hydro in 1959, he has
where istlosesetnCssaspent
of his career
mostLaboratories at the inOntario Hydro
where r is the loss per section.
related to Cg and )' by
Cbyisapproximately _ l _
Research engaged the study
analysis of electrical transients on power systems
and

r2 associated with switching and faults. His current

Cs, _ Cg (4) activities include the development of improved transformer models for
(4)z)2 use in analog and digital simulation studies, the transient behaviour of
From Figure 3(c) Vo/Vi is -36 dB at 3.2 MHz. Thus station grounding systems and diagnostic techniques for detecting
transformer winding damage. From 1965 to 1972 he was part of a team
116 which developed a prototype high-speed synchronous vacuum circuit
10=Oand= 0.9649 breaker using a pulsed electromagnetic repulsion drive.
Mr. Erven is a Registered Professional Engineer in the Province of
Cs 9 (0.0351)2 7.0 nF Ontario, Canada.
 2151
Discussion One disadvantage is the large exposure to EMI and the low signal levels
of FRA. We would conclude, because of low level signals, the
FRA method will not be applicable for every transformer or in every
E. J. Rogers and D. A. Gillies (Bonneville Power Administration, Van- location.
couver, Washington): The authors have added a second alternative
method to LVI for the detection of winding movement and winding REFERENCE
deformation in large power transformers. The other alternative is "Fre-
quency Domain Analysis of LVI" (1). (1) A. G. Richenbacher, "Frequency Domain Analysis of Responses
The FRA method inserts a sinusoidal voltage with a multiplicity of from LVI Testing of Power Transformers." DOBLE Conference
discrete frequencies between one winding terminal and transformer 43AIC76, Transformers, See 6-201.
case. The output voltage at a second terminal is compared to the input
signal-both phase shift and output to input voltage ratio is measured. Manuscript received February 21, 1978.
For example, the voltage ratio in Figure 7 varies between -23db to
-67db. For a 0db level of 0.224 Volts, this would correspond to output
voltage levels of 16 mV to 100 uV. Signals at this level are difficult to R. C. Degeneff (General Electric Company, Pittsfield, MA): The
measure with the test transformer in the proximity of energized bus. authors are to be congratulated on a clear and interesting paper describ-
High voltage bushings and exposed test cables are good antennas for ing a method for detecting transformer winding deformation by
ambient noise, switching transients, carrier, microwave, radio and TV measuring the transformer's terminal frequency response characteristic.
stations. Prior to the FRA testing, is the magnitude of the interference Historically, transformer manufacturers have also been interested in
voltage at each frequency in the frequency window measured? For identifying the frequency response of power transformers. Their in-
transformers above 230 kV, output db will probably vary to less than terest was not, however, to assess possible winding deformation, but
-100db or below 2.24 uV. At these low signal levels, both input and out- rather to insure the insulation integrity of their windings. These efforts
put, connections at transformer terminals, transformer case, coaxial have proceeded hand-in-hand with the development of techniques to
cable connectors and measuring equipment terminals will have to be determine the transient voltage response of those same transformer
clean and tight. Any connection impedance will affect repeatability. windings. In the past decade a significant amount of progress has been
Inspection and disassembly of a transformer are costly. Do the made in the area of analytically predicting both the transient voltage
authors make any repeatability checks prior to testing? response and the frequency characterisic of power transformer win-
The examples cited in the paper, while demonstrating the FRA, dings (1, 2). This has been made possible by the development of very
would have been detected by more mundane methods (impedance, sophisticated lumped parameter mathematical models of windings
capacitance, resistance). Have the authors used FRA during short- along with numerical tools to calculate the transient voltage and fre-
circuit tests to determine more subtle changes in winding condition? quency response of those same windings (3, 4). At present most
We were surprised to read in the Introduction that the authors have transformer manufacturers have some degree of capability in this
had difficulty with the LVI technique. The method is used extensively in regard.
both the USA and abroad. We have used LVI tests to evaluate winding Upon reading this paper I felt it would be a worthwhile addition to
condition during 19 short-circuit tests and for bench mark compare the analytically predicted transient voltage and natural fre-
measurements of a 3-phase 230-kV transformer, three single-phase quency response of a typical power transformer when the model was
500-kV transformers and 19 Celilo converter transformers. For the lat- subjected to known disturbances such as winding deformation, faulty
ter, LVI tests were even successful when performed on three single- shield connections, or internal winding faults.
phase transformers located between two operating groups. EMI levels Figure 1 is a line diagram of a single leg of a three-phase 2-winding
are high and variable in the converter transformer yard. 477 MVA 500 kVGry/288.7 kV - 20.9 kV Delta transformer. For this
The authors have developed an equivalent circuit for their 8-MVA example Xl is the excited terminal and Ho, H1, and X. are terminated as
test transformer consisting of 116 cascaded Pi-elements. To conform to shown in Figure 1. Figure 2 compares the calculated transient voltage
a cascade of Pi-elements, shouldn't the input and output capacitors in response at Ho when the ground shield separating the primary and
Figure 5 be Cg/2? Determination of each component of the Pi from secondary windings is first solidly grounded (curve 1) and then floating
FRA measurements requires clarification. (curve 2) when a full wave is applied to Xl. Clearly, there is a marked
1. Ls is calculated at 2.5 kHz (Ls = 3.51 mH). On what basis did difference in the transient voltage response. Figure 3 compares the im-
the authors select 2.5 kHz? For example, at 1 kHz, Ls = 4.94 mH.
Have the authors measured the winding inductance with an inductance
bridge to confirm calculated value(s)? What effect does the core have
on this inductance?
2. Cg is determined in the medium frequency range by neglecting
Cs. This implies: coLs<<1/cwCs or f <<Y2n(LsCs)'2.
The impedance of Ls and Cs will become comparable with each other
in the 10-30 kHz range. Above this range, the "Cs" impedance will / oQ io1000Q
decrease and "Ls" will increase. Will the authors indicate at what fr- x0 0H B C A
quencies in Figure 3a the 180°-phase lag is determined? Winding
capacitance-to-ground (116 x Cg) can be verified by measuring with a
P.F. test set or a 1000-Hz bridge.
3. At 3.2 MHz "Ls" is neglected and the equivalent circuit
becomes a Pi-cascade of capacitance. Vo/Vi = vn is only true if the
capacitance ladder is terminated in its characteristic impedance; (name- 2
ly, l/jcO[Cg(Cs + Cg2/4)I"/2. Actually the output load shown in Figure 0 U
5 is 36 Ohms, which is resistive and much lower than l/jco[Cg(Cs + La

Cg2/4)]' 12. Therefore, the overall attenuation will be increased over that
due to the 116 Pi-sections. Also, because of the resistive load on a
capacitive source, measured phase angle will be shifted. Both attenua-
tion and phase shift vary with frequency as a result of transformer
parameters and output loading. Thus, the phase angle at resonance in- / 11 11 1 11 l 1 H1 1000 L
flections will be shifted./, *W -
4. It appears incorrect exponents were substituted in equation (5). fl|' PRIMARY
Calculated value of (5) is 254 nF the correct answer, as shown, is 254 /^ lt E CD
pF. CORE\
The authors are to be congratulated in pioneering the application 'SHIELD
of network analyzers and sweep generators to power transformers for
the detection of winding shift and winding deformation. One advantage Fig. 1. Single Leg of a 2-winding three-phase 500 kV/288.7 kV
of the FRA method is single-phase units are tested individually. GrY-20.9 kV delta 477 MVA transformer.
2152
pedance versus frequency characteristic of Ho when Xl is excited for the Using the same transformer as an example it was found that reduc-
cases of the shield solidly grounded (curve 1) and floating (curve 2). The ing the low voltage winding radius by as little as .050 inches (while
value of impedance and its associated phase angle are determined by holding all other dimensions fixed) was detectable and that a relocation
dividing the voltage at terminal Ho by the current injected at terminal X, of the low voltage winding by 100 mils was clearly visible in both the
at frequency co. Once again, the difference in response is clearly visible. transient voltage and frequency response.
This confirms the experience of the authors and of those in-
vestigators of the LVI technique for detection of winding deformations.
70 CURVE 2 It appears, then, that both frequency domain and time domain
measurements are equally valid. Which is preferred in practice will de-
60 pend on the depend on the reliability of measurement techniques.
Having the capability to predict analytically the effect of small winding
so. X \ ~^ x~x-x \deformations on the terminal frequency response is a potentially
X
r _,
valuable
, xS tool. It should make it possible to measure changes in
x~ x~xx\
4011 r transformer frequency characteristic in the field and then correlate
a X
x' these changes with the results of analytical predictions based on
,f,x A/ \\ / ,xAx assumed sets of winding deformities. Ultimately, this ability may allow
0 3- Xr \ At,x C~vex-. 5 ~ >, involved engineers to develop a "feel" for where the problem exists in
> \A' yX A ,gx x x much the same way that transformer test engineers can predict problem
S
20.g Ox ' /
-6 SHIELD UNGROUNDED locations from small variations on impulse waves or neutral current
oscillograms.
10 . / CURVE 1 REFERENCES

0 { (l) R. C. Degeneff, "A General Method for Determining Resonances

In Transformer Windings", IEEE PAS-96, pp. 423-430.
-10 (2) W.J. McNutt, T.J. Blalock, R.A. Hinton, "Response of
Transformer Windings to System Transient Voltages", IEEE
-201_0 10 20 30 40
Trans. PAS, Vol. 93, pp. 457-467.
(3) R. C. Degeneff, "Reducing Storage and Saving Computational
so
Time with a Generalization of the Dommel (BPA) Solution
TIMEposec Method", PICA-77 Conference Proceedings pp. 307-313.
(4) H. W. Dommel, W. S. Meyer, "Computation of Electromagnetic
Transient",
983-993. Proceedings of IEEE, Vol. 62, No. 7, July 1974, pp.
Fig. 2. Transient voltage response versus time at H, with X1 impulsed
with a full wave.
Manuscript received February 24, 1978.

E. P. Dick and C. C. Erven: The authors wish to thank the discussers

400 for their comments on this paper. The presentation of the analytical
IMPEDANCE predictions carried out by Dr. Degeneff is a particularly interesting con-
(MAGNITUDE) tribution. If a satisfactory model can be developed which correlates well
OHMS 1 SHIELD CONDITION with changes in field test data, then it may be possible to predict
300 11 x-- X UNGROUNDED analytically the nature of the deformation from the terminal frequency
response. From the results shown by Dr. Degeneff it is not clear
lI - I GROUNDED whether his model can accommodate all the distributed elements
which give each transformer its unique frequency response. In the low
200 x frequency range the oscillations are most likely to be affected by coil
l I configuration, in the middle range by layer and section effects and at
l higher frequencies by individual turns. We suggest that a model which
can be tuned to accommodate a wide range of these effer- would be
100
CURVE 2
peeaCURVE2 ble to a one-on-one representation for a given transformer.
I ;I
> )I HoIt is evident from our results that much further work is necessary
j- x
K-x-x X.#
x
'
K before a model can be developed which will reproduce the frequency
response of a given transformer with sufficient accuracy to be useful in
CURVE 1 such predictions.
We appreciate the informative discussion and points raised by E. J.
90 Rogers and D. A. Gillies considering the advances that they have
v L 'I pioneered in the development of the LVI method of testing
Al 1LE \ transformers.
r |
DEGREES x
Their concern that the FRA method is handicapped because of a
xHx \
-X/ x-x-X-W-X low signal strength compared to the LVI method has not materialized in
--7x x' I _ any testing that we have carried out. We have had no difficulty in
X~x \ making
< measurements down to - 80 dB (22.4 MV) in the proximity of
energized bus or strong signals from local radio and TV stations. Since
the output signal from the frequency generator is concentrated at a
single frequency for some period of time and since the dual channel
tracking receiver can be closely tuned to reject signals outside a narrow
passband, the signal-to-noise ratio is significantly enhanced. There is
o
10
"
20
|~~~~~~~
30
not likely much difference in the basic requirement for making good
connections whether using LVI or FRA to the same degree of sensitivi-
FREQIUENCY, kHz ty, since both use low impedance terminations. We provide for a simple
calibration check on the measurement system prior to connecting the
transformer under test. This part of the measurement also provides a
Fig. 3. Impedance versus frequency at Ho when X, is excited. repeatability check, although this has not been a problem at the sen-
 2153
sitivities encountered to date. Due to the variety of winding ar- a reduction from the original records. Although we have not checked
rangements used in power transformers at different voltage levels, it is the inductance of the winding with a conventional bridge, it would be of
likely to be the interpretation of the results rather than a specific voltage limited value since the inductance will not be constant with frequency.
class which restricts the usefulness of the FRA method. The core will likely have some effect at the lower frequencies (< 20 kHz)
Our experience to date with both LVI and FRA has been limited to and skin effect will become a factor at higher frequencies.
suspect and critical transformer units on the power system. We do not 2. C9 is determined at a frequency of 24 kHz with the assumption
carry out short circuit tests on such large units, but we do plan to pro- that C, is neglected. This is consistent with techniques applied in the
duce some controlled deformation testing of the 8-MVA unit men- literature [1] even though it appears inconsistent in the simplified
tioned in the paper. Although we do not dispute the fact that some of model. The phase difference in Figure 3(a) is the measured lag between
the examples shown in our paper could have been detected by more con- the output voltage at one terminal of the winding and the input voltage
ventional means, our results do indicate that the method is capable Of at the other. The angle begins at - 900 and continues to increase in a
detecting much less deformation once better correlations have been complex fashion with frequency as more and more standing waves of
established. half-wave multiples are developed within the winding. The suggestion
The simplified equivalent circuit which we included in the paper that the capacitance-to-ground can be verified by measuring with a pf
was not intended to be an accurate model of the transformer winding test set or a 1000 Hz bridge implies that both L, and C, can be neglected.
for predicting the terminal frequency response. Our purpose was simply This would produce a misleading result.
to show how frequency response measurements can be used to advan- 3. At 3.2 MHz we assume L, is neglected and the equivalent circuit
tage in developing models and to give some representative circuit becomes a ladder network of capacitors. Although the network is not
parameter values. The high voltage disc winding of the 8-MVA ideally terminated in its image impedance, the results obtained for the
transformer consisted of 116 coil sections. Therefore, we chose to repre- intersectional capacitance are in reasonable agreement with calculations
sent the capacitance to ground of each section as C, and the capacitance based on geometrical considerations.
between each section as C,. The model should not be construed as being 4. Incorrect exponents did get substituted in equation 5 as in-
a cascaded pi representation of a continuous and uniformly distributed dicated. The corrected expression is:
winding. Since our winding model completely ignores interwinding C, = (7000 x 10-12 x 9.2 x 10-'2)112 = 254 pF
capacitance and all mutual inductance effects as well as damping, it is
obvious that much more effort is needed before trying to correlate the
response of the model to that on a transformer winding.
Notwithstanding the above comments there are some apparent in- REFERENCE
consistencies and typographical errors in the given equivalent circuit
data. 1. P. A. Abetti, F. J. Maginnis. "Fundamental Oscillations of Coils
1. L, was calculated as 3.51 mH from measurement data at 2.5 & Windings". AIEE Transactions. Vol 73. Pt III-A. Power Ap-
kHz. Over the range of frequencies from 1 kHz to 5 kHz the value paratus and Systems, February 1954, pp. 1-10.
drops from 3.7 mH to 3.1 mH. Unfortunately, the resolution at the
lower end of the frequency spectrum shown in the paper suffered from Manuscript received April 28, 1978.