Energy and Power Engineering, 2011, 3, 585-591
doi:10.4236/epe.2011.34073 Published Online September 2011 (http://www.SciRP.org/journal/epe)
Detection of Mechanical Deformation in Old Aged Power
Transformer Using Cross Correlation Co-Efficient
Analysis Method
Asif Islam1, Shahidul Islam Khan2, Aminul Hoque2
1Energypac Engineering Ltd., Dhaka, Bangladesh
2Department of Electrical & Electronic Engineering, Bangladesh University of
Engineering & Technology, Dhaka, Bangladesh
Received May 25, 2011; revised June 28, 2011; accepted July 9, 2011
Abstract
Detection of minor faults in power transformer active part is essential because minor faults may develop and
lead to major faults and finally irretrievable damages occur. Sweep Frequency Response Analysis (SFRA) is
an effective low-voltage, off-line diagnostic tool used for finding out any possible winding displacement or
mechanical deterioration inside the Transformer, due to large electromechanical forces occurring from the
fault currents or due to Transformer transportation and relocation. In this method, the frequency response of
a transformer is taken both at manufacturing industry and concern site. Then both the response is compared
to predict the fault taken place in active part. But in old aged transformers, the primary reference response is
unavailable. So Cross Correlation Co-Efficient (CCF) measurement technique can be a vital process for fault
detection in these transformers. In this paper, theoretical background of SFRA technique has been elaborated
and through several case studies, the effectiveness of CCF parameter for fault detection has been represented.
Keywords: Core Damage, Radial Deformation, Axial Deformation, Sweep Frequency Response Analysis,
Cross Correlation Co-Efficient, Power Transformer
1. Introduction
Nowadays, reliability is an inevitable part of power sys-
tem studies and operation, due to significant increase in
the number of industrial electrical consumers. Power
transformer is one of the major and critical elements in
power system [1] in the area of reliability issue, since
their outage may result in costly and time-consuming
repair and replacement. Power transformers are specified
to withstand the mechanical forces arising from both
shipping and subsequent in-service events, such as faults
and lightning. Once a transformer is damaged either
heavily or slightly, the ability to withstand further inci-
dents or short circuit test [2] becomes reduced. There is
clearly a need to effectively identify such damage. A
visual inspection is costly and does not always produce
the desired results or conclusion [3-10]. During a field
inspection, the oil has to be drained and confined space
entry rules apply. Often, a complete tear down is re-
quired to identify the problem. An alternative method is
to implement field-diagnostic techniques that are capable
of detecting damage such as Frequency Response Analy-
sis (FRA) [11-16].
FRA is a generally well-known testing technique
within the industry to determine a transformer winding
deformation, e.g. coils, turns, layers, HV leads, .etc,
owning to short-circuit currents (faults), impact during
transportation and aging [11]. Dick and Erven were the
first to use the FRA method to detect the transformer
winding deformation in 1978 [10]There are basically two
techniques used for FRA measurements on power trans-
formers; Low Voltage Impulse (LVI) based FRA and
Sweep Frequency Response Analysis (SFRA) [16]. The
two techniques are also termed FRA-I (impulse method)
and FRA-S (swept-frequency method) [17]. The com-
mon strategy for both methods [18] is that the trans-
former impedance is measured at several different fre-
quencies. The impedance will vary from one frequency
to another due to the internal constitution of the trans-
former.

A. ISLAM ET AL. 586
2. SFRA Theory
When a transformer is subjected to FRA testing, the
leads are configured in such a manner that four terminals
are used. These four terminals can be divided into two
unique pairs [6,8,19], one pair for the input and the other
pair for the output. These terminals can be modeled in a
two-terminal pair or a two-port network configuration.
Figure 1 illustrates a two-port network where Z11, Z22,
Z12 and Z21 are the open-circuit impedance parameters.
The transfer function of this network [20] is repre-
sented in the frequency domain and is denoted by the
Fourier variable H(jω), where (jω) denotes the presence
of a frequency dependent function and ω = 2πf. The Fou-
rier relationship for the input/output transfer function is
given by Equation (1).
 

output
input
V
V
j
Hj j



 (1)
when a transfer function is reduced to its simplest form,
it generates a ratio of two polynomials. The main char-
acteristics, such as half-power and resonance of a trans-
fer function occur at the roots of the polynomials. The
roots of the numerator are referred to as “zeros” and the
roots of the denominator are “poles” [21]. Zeros produce
an increase in gain while poles cause attenuation.
The goal of FRA is to measure the impedance model
of the test specimen. When the transfer function H(jω) is
measured, it does not isolate the true specimen imped-
ance Z(jω). The true specimen impedance Z(jω) is the
RLC network which is positioned between the instru-
ment leads and it does not include any impedance sup-
plied by the test instrument. Figure 2 illustrates the RLC
circuit with shunt resistor.
From the figure, Voltage division formula gives
 
21
1
1
111
2
R
R
jC
R
jVj
jL
V







The transfer function is:
Figure 1. Two port network.
Figure 2. RLC circuit and shunt re sistor.




21
11
2
1
2
1
2
2
1
2
2
1
2
1
11
11
11 1
1
1
VR
VR
jC
RjL
RjC
RjL jL
jL
RjC
RjL
L
Rj LC
R
L
RjLC L
Hj
R
j
j
j










 





 



















If R2 would be removed from the circuit then the term
2
L
jR
 disappears from the expressions above. It is now
easy to see where the resonant frequency must occur:
21
10
rr
LC LC  
At resonant frequency the transfer function is

1
2
1
2
1
21
112
2
11
11
1
H
L
Rj
RLC
LL
Rj j
RLC LC
R
RR
RRR
j
R
r







 







What is really measured over the shunt resistor R1 is
the current I. So, the transfer function describes the ad-
mittance:
1
I
YV

. The impedance is thus: 1
V
Z
I

The impedance at resonance (including the shunt re-

A. ISLAM ET AL.587
sistor) is

12
1
RR
Zr R 


The preferred method of engineers is to use the Bode
Diagram. The Bode Diagram plots the magnitude and
phase as follows:
  
  
10
1
20 log
tan
A
dBH j
AHj





The Bode Diagram [22] takes advantage of the as-
ymptotic symmetry by using a logarithmic scale for fre-
quency. It is more advantageous to plot H(s) logarithmi-
cally over large frequency spans. The logarithmic plot
helps to maintain consistent resolution. Plots ranging
from 10 Hz to 10 MHz can be displayed as a single plot
if they are formatted logarithmically. Figure 3 shows a
typical response for a high voltage star connected wind-
ing. The frequency range of interest is between 20 Hz
and 2 MHz.
Experience has shown that different sub-bands are
dominated [23] by different internal components of the
transformer and are subsequently more sensitive to dif-
ferent types of failures, as summarized in Table 1.
Measurements above 2 MHz tend to be dominated by
Figure 3. Frequenc y analysis bands.
Table 1. Frequency sub-band se nsitivity.
Region Frequency
Sub-Band Component Failure Sensitivity
1. <2 kHz
Main core bulk
and winding
inductance
Core deformation,
open circuits, shorted
turns and residual
magnetism
2. 2 kHz to 20 kHz
Bulk component
and shunt
impedances
Bulk winding
movement between
windings and clamping
structure
3. 20 kHz to 400
kHz Main windings Deformation within the main or top windings
4. 400 kHz to 1
MHz
Main windings,
top windings and
internal leads
Movement of the main
& top winding, ground
impedance variations
variations in grounding practices for test leads.
3. Measurement Procedure
The FRAX “Generator” (Gen.) generates (Figure 4) a
sinusoidal voltage at a selected frequency and measures
the input voltages, amplitude and phase, on two input
channels “Reference” (Ref.) and “Measure” (Meas.). The
instrument stores “Amplitude” and “Phase” data for both
“Reference” channel and “Measure” channel as well as
the ratio “Measure” divided by “Reference”. The values
can be plotted and exported as Magnitude, Phase, Im-
pedance, Impedance-Phase, Admittance and more. The
“Custom models” function makes it possible to calculate
almost any parameter based on the measured/stored data.
FRAX uses the sine correlation technique [24]. This
means that the input voltages are multiplied by a sine and
a cosine, and then averaged over an integer multiple of
the interval of time. The sine, cosine and the voltage ap-
plied have exactly the same frequency. The sine correla-
tion technique is well known and is suitable for Sweep
Frequency Response Analysis (SFRA) measurements.
Since the signals on the two input channels are treated
the same way, the phase resolution between these two
channels is very high. The rejection of DC offset and
harmonics—referred to as the applied voltage—are in
theory infinite. By increasing the integration cycles, the
rejection gradually improves.
The IF Bandwidth is commonly used as a parameter
defining the bandwidth around the applied signal ana-
lyzed. An IF bandwidth of 10% of the active frequency is
equivalent to 12 cycles of integration. When considering
SFRA measurements, winding measurements realisti-
cally consist of three categories. The winding categories
are high-voltage, low-voltage, inter winding. (Figures 5
-7)
Figure 8 presents a high-voltage winding trace, a
low-voltage winding trace and an inter-winding trace
together from a common test specimen. This illustrates
their general relationship.
4. Response Analysis
For the analysis of a measured response, the response in
Figure 4. SFRA terminal connection.

A. ISLAM ET AL. 588
Figure 5. HV winding response.
Figure 6. LV winding response.
Figure 7. Inter winding response.
Figure 8. Complete response.
compared with one of the following:
 An earlier result [25] for the same phase tested with
the same tap changer position.
 If no earlier result is available then another phase [23]
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.
It is found that Cross Correlation [20] coefficient
(CCF) is the most reliable statistical indicator to extract
information from comparison method. The CCF is de-
fined as:



1
2
CCF
*





n
ii
ii
iXY
X
Y
XY
X
2
Y
(2)
where Xi and are Yi are the two series (or trace in the case
of SFRA) being compared at each individual frequency
‘i’ and X-bar and Y-bar are the means. Equation (2) as-
sumes 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 SFRA analysis
negative CCF are not common but they do occur on oc-
casion. Regardless, negative correlation coefficients are
not considered acceptable when trying to look for devia-
tions between traces.
Normalizing the results to the individual power spec-
trums is what allows this resulting waveform to be ex-
pressed in a simple single coefficient. Table 2 helps pro-
vide a rough estimate of what the CCF means in simple
language.
5. Fault Diagnosis
The following two case studies (Table 3) demonstrate two
scenarios where SFRA response has been used to detect
deformation or damage taken place in transformers.
Case 1: 41.67 MVA, 132/33 kV, 3φ Power Trans-
former at 132 kV Substation
The results here are from a three phase 25/41.67 MVA,
Table 2. Outcome of CCFs value.
Decision 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 3. Case study of fault condition.
Case Capacity
MVA
HT Voltage
kV
LT Voltage
kV Year of manufacture
141.67 132 33 1998
214 33 11.6 1991

A. ISLAM ET AL.589
132/33 kV (vector group Dyn-1) power transformer
manufactured by EMCO Transformers Ltd. (Maharastra,
India) at 1998 for Bangladesh Power Development
Board (BPDB) 132 kV sub-station. The transformer had
tripped out of service on protection. No reference factory
results were available for this unit. The phase-to-phase
HV results didn’t show typical variations from standard
HV delta winding response. An overall look at the LV
winding has showed several shifts between 200 kHz and
2 MHz. This is shown in Figure 9 where it is clear that
H3-H0 has consistently shifted at higher frequencies with
respect to H2-H0 and H1-H0.
This is an indication of axial winding movement at X3
(Blue/C phase) phase. From CCF analysis method results
(Table 4), this prediction can be more confirmed.
From the table, it is clearly visible that CCF values of
phase A and phase B fulfill “Good Match” criteria in all
4 frequency sub-band regions. CCF values of phase C
both with phase A or phase B meet up either “Good
Match” or “Close Match” criteria in all bands except
region 3. At region 3, both CCF values of phase C
(0.7263 and 0.7681) drops down vigorously at “Poor
Match” level.
Removing the transformer top cover, the active part was
brought out and after a through physical inspection, the
prediction became true with damage of LV (phase C)
coil (Figure 10).
Case 2: 14 MVA, 33/11.6 kV, 3φ Power Trans-
former at 33 kV Substation
Figure 9. Close zoom of LV winding response (100 kHz - 1
MHz).
Table 4. Test result of LV winding keeping HV open.
CCF results
Frequency Sub-band X1 - X0,
X2 - X0
X2 - X0,
X3 - X0
X3 - X0,
X1 - X0
0 - 2 kHz 0.9981 0.9925 0.9954
2 kHz - 20 kHz 0.9943 0.9868 0.9736
20 kHz - 400 kHz 0.9853 0.7263 0.7681
400 kHz - 1 MHz 0.9892 0.9475 0.9424
The subjected transformer was running at Dhaka Power
Distribution Company (DPDC). It is a 10/14 MVA,
33/11.6 kV (vector group - YNd11) power transformer
manufactured by Brush Transformers Ltd. (Loughbor-
ough, England) at 1991. Due to its age of 20 years, fre-
quency response of this transformer was taken to predict
its aging effect. At first, test was carried on HV side
keeping LV side open followed by LV side shorted.
Corresponding Bode Plot response has been shown in
Figures 11 and 12.
From the CCF result (Tables 5 and 6), it is easily
viewable that the matching is very poor at low frequency
region (0 - 2 kHz). This may be due to core deformation
Figure 10. Damaged LV (phase-C) coil.
Figure 11. HV winding response (LV open).
Figure 12. HV winding response (LV short).

A. ISLAM ET AL. 590
as a result of axial stress because the transformer is run-
ning for a long time (20 years). Again, poor matching at
higher region (400 kHz - 1 MHz) indicates main coil
deformation either by radial stress or by axial stress. This
deformation is more severe for A phase (Red phase).
From LV winding response (Figure 13) and corre-
sponding CCF calculation (Table 7), the previous as-
sumption becomes stronger. Poor matching at low fre-
quency region (0 - 2 kHz) and high frequency region
(400 kHz - 1 MHz) again spans the prediction of core
damage and main winding movement firmly. After re-
placing the transformer from the system, it was dissected
and both the prediction became true
6. Conclusions
Sweep frequency response analysis method has been
applied to a number of three phase and single phase
Table 5. CCF of HV winding keeping LV open.
CCF results
Frequency Sub-band X1 - X0,
X2 - X0
X2 - X0,
X3 - X0
X3 - X0,
X1 - X0
0 - 2 kHz 0.7981 0.7825 0.9914
2 kHz - 20 kHz 0.9743 0.9841 0.9736
20 kHz - 400 kHz 0.9523 0.9267 0.9081
400 kHz - 1 MHz 0.8394 0.8975 0.8427
Table 6. CCF of HV winding keeping LV short.
CCF results
Frequency Sub-band X1 - X0,
X2 - X0
X2 - X0,
X3 - X0
X3 - X0,
X1 - X0
0 - 2 kHz 0.9981 0.9925 0.9954
2 kHz - 20 kHz 0.9743 0.9861 0.9786
20 kHz - 400 kHz 0.9354 0.9283 0.9217
400 kHz - 1 MHz 0.8113 0.8671 0.8039
Figure 13. LV winding response (HV open).
Table 7. CCF of LV winding keeping HV open.
CCF results
Frequency Sub-band X1 - X0,
X2 - X0
X2 - X0,
X3 - X0
X3 - X0,
X1 - X0
0 - 2 kHz 0.8381 0.8325 0.9907
2 kHz - 20 kHz 0.9943 0.9921 0.9936
20 kHz - 400 kHz 0.9825 0.9867 0.9781
400 kHz - 1 MHz 0.8493 0.9275 0.8027
power transformers of different vector groups. This me-
thod is also applicable for mechanical deformation and
damage diagnosis in distribution transformers. The pa-
rameter Cross Correlation Co-efficient (CCF) is found to
vary significantly and consistently with mechanical dis-
placements taken place in transformers. So it can be con-
sidered as the most effective indicator to predict the in-
ternal physical condition of the active part of a trans-
former.
7. Acknowledgements
The authors would like to acknowledge the contributions
made by Mr. Rashiduzzaman Bulbul, Assistant Engineer
(Testing, Transformer), Energypac Engineering Ltd. for
his logistic and data support. They are also grateful to
Energypac Engineering Ltd. for frequent high voltage
instruments using facility.
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