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Transformer failure diagnosis based on parameter analysis
Conference Paper · November 2012
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Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
Transformer failure diagnosis based on parameter analysis
D. A. K. Pham1, 2 (*), T. M. T. Pham1, 2, M. H. Safari1, A. Kazemi1, H. Borsi1, E. Gockenbach1
1
Leibniz Universität Hannover, Schering-Institut, Hannover, Germany
2
Ho Chi Minh City University of Technology, Vietnam
E-mail (*): pham@si.uni-hannover.de
Abstract
There are currently several methods applied to diagnose failures on the active part of power transformers, which can be
categorized into two main groups: traditional- and advanced methods. Traditional methods include measurements of
transformer ratio, exciting current, magnetic balance, winding resistance, short-circuit impedance etc. Advanced methods consist of tests of Frequency Response Analysis (FRA), Frequency Response of Stray Losses (FRSL), Frequency
Response of Leakage Inductance (FRLI) etc. Results derived from these methods reflect transformer parameters in
open- and short-circuit configurations. In general, these methods should be performed and combined to enhance the accuracy of failure diagnosis for power transformers.
In order to reduce the number of tests while keeping the diagnostic quality, this paper introduces a study case in which a
new method based on only the driving-point impedance test analysis is applied to determine transformer parameters
from which results of almost above-mentioned tests are recovered appropriately. In addition, the tendency of parameter
change in regard with different failures, which may be valuable for diagnosis quality improvement, is also researched.
In the study case, experimental measurements are performed on a 200 kVA 10.4/0.4 kV YNyn6 opened distribution
transformer which is simulated under healthy- and faulty conditions.
1
Introduction
To improve the diagnosis quality for transformer failures,
the combination of traditional- and advanced diagnostic
techniques is required. That is understandable since the
transformer is a complex object and each technique reflects only certain response from all transformer components at fixed frequencies. However, there is always a
demand to develop more techniques for better diagnosis
as well as to improve the interpretation of all measured
results.
In transformer structure, the most important part is the
active part which includes mainly windings and the core.
Failure modes on the transformer active part consist of
electrical, thermal, mechanical and degradation/aging [1].
Among these failure modes, electrical failure is of importance since it reveals first signals of abnormal conditions
of transformers; and in case there is no appropriate
“treatment”, other failures can appear.
In order to fulfill the demand in developing a new technique for better diagnosis and comprehensive interpretation of electrical failures on the active part of power transformers, this paper proposes a new method based on only
driving-point impedance test analysis to determine physical transformer parameters. Once these parameters are
reasonable derived, the interpretation of results of other
diagnostic methods such as magnetic balance tests, FRLI,
FRA etc can be reached. Furthermore, several physical
parameters might be helpful for failure diagnosis since
they are good indicators for detecting failure modes.
The test object of this paper is a 200 kVA 10.4/0.4 kV
YNyn6 opened distribution transformer which is changed
ISBN 978-3-8007-3465-8
from Yzn5 vector group. The transformer has no tank and
also no insulating liquid. Electrical failures simulated on
the transformer active part consist of open-circuit, shortcircuit between discs, short-to-ground (HV windings) and
loss of core ground.
Driving-point impedance tests are performed by mean of
the vector-network analyzer (VNA) named “FRAnalyzer”
of Omicron. Different equivalent impedances of the test
transformer are measured under different combinations of
terminal conditions such as being excited by the instrument, opened (left floating), shorted together or grounded.
For all connections, coaxial cables are used to avoid interferences and additional external coupling. Frequency
range for all tests is from 20 Hz to 2 MHz. Open-circuit
voltage of the instrument is 1 V. Receiver bandwidth is
chosen as 30 Hz for better denoising effect.
2
Transformer parameter determination based on driving-point impedance analysis
As mentioned in the introduction section, there are two
kinds of conditions investigated on the test transformer:
healthy and faulty. For healthy condition, reference [2]
presents an equivalent transformer circuit and a simple
procedure for determining circuit parameters for the purpose of frequency response analysis and hence this procedure is briefly recalled and improved in section 2.1. The
parameters in the equivalent circuit are then called as
physical transformer parameters since they represent
physical structure parts of the transformer. Afterwards,
© VDE VERLAG GMBH ∙ Berlin ∙ Offenbach
Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
section 2.2 illustrates verifications of these parameters
through comparisons of frequency responses which are
measured through other diagnostic methods and recovered
from the physical equivalent circuit. Finally, in section
2.3, attempts in detecting simulated failures based on
physical parameter analysis are presented.
2.1
Parameter analysis in healthy condition
2.1.1 Equivalent transformer circuit
An appropriate equivalent circuit in which most physical
parameters of transformers appears logically is the first
important thing to deal with. In [2] the duality-based
equivalent circuit adapted from the one developed for the
purpose of transient analysis seems to be the most appropriate circuit. Figure 1 presents this circuit for the test
transformer in a context of a driving-point impedance test
performed on the winding of phase A at HV side. In this
test configuration, the VNA source is connected to the
HV terminal of phase A while the HV neutral is
grounded. Then the measured impedance is the equivalent
impedance of the transformer observed at the excited terminal.
vant LV winding. The inter-winding capacitances between HV windings such as CAB and CBC have insignificant influences but make the calculation more complicated; thus they can be neglected.
2.1.2 Parameter determination from short-circuit
tests at HV side
In a normal short-circuit test at HV side, each singlephase winding at LV side, e.g. an, is shorted whereas the
relevant HV winding, i.e. AN, is excited by the VNA instrument (HV neutral is grounded). The measured impedance consists of equivalent resistance from stray losses
(Rsl) in real part and total leakage reactance (L3total from
L3H and L3X) in imaginary part. With appropriate factors,
resistance and equivalent leakage inductance of HV- and
LV windings (RH/RX and L3H/L3x) are reasonably derived
[3]. Afterwards, frequency-dependent functions RH(f),
RX(f) and L3H(f), L3X(f) for each phase are developed
based on measured values. They are valid from 20 Hz to
at least 30 kHz since the inductive feature of the measured
impedance can be observed within this frequency range.
Figure 3 shows a verification of measured- and recovered
impedances from the HV winding of phase A in whole
frequency range, i.e. from 20 Hz to 2 MHz.
L4
VNA
A
RA
50
RH L3H
R4
R1
CA
B
N
RB
RH L3H
R4
CB
L4
RX a
L3X
RX b
L1
Ly
NH:NH
L3X
NH:NX
Ry
R1
L1
n
Ly
NH:NH
C
RC
RH
L3H
R4
L4
Ry
NH:NH
L3X
C1
R1
CC
NH:NX
RX c
L1
N1
NH:NX
Figure 1 Simple duality-based equivalent transformer circuit of a YNyn transformer seen from HV side in lowand mid frequency ranges [2]
In Figure 1:
- Z1 = R1//L1 : non-linear core leg impedance
- Zy = Ry//Ly : non-linear core yoke impedance
- RH and RX : resistances of HV- and LV windings
- L3H and L3X : leakage inductances at HV- and LV sides
- Z4 = R4//L4 : zero-sequence impedance
- ZA = RA//CA : total capacitive impedance of phase A
- ZB = RB//CB : total capacitive impedance of phase B
- ZC = RC//CC : total capacitive impedance of phase C
Due to the fact that the HV neutral is grounded in most
measurement configurations, total capacitive impedance
of a HV winding consists of different capacitances such
as series-, ground capacitances of this winding and the
combination of inter-winding capacitance between HV
and LV sides, series- and ground capacitances of the rele-
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Figure 3 Verification of equivalent impedances in the
short-circuit test on phase A between measurement and
recovery at low- and mid frequency ranges.
2.1.3 Parameter determination from zero-sequence
test at HV side
In the zero-sequence test at HV side, three HV terminals
are all excited in the same time by the instrument while
the HV neutral is grounded (LV windings are opened). At
low frequencies, the total zero-sequence current from the
instrument is divided into three parts each of which flows
through RH and L3H of each phase winding and Z4 (if
there are three equal Z4 in the core circuit) [4]. There is
© VDE VERLAG GMBH ∙ Berlin ∙ Offenbach
Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
almost no current flowing through core impedances Z1
and Zy since magnitude of Z4 is much lower than those of
Z1 and Zy (see Figure 1). From that, Z4 of each phase is
determined thanks to available RH and L3H from shortcircuit tests. Afterwards, like in the short-circuit test, frequency-dependent functions R4(f) and L4(f) for HV side
are developed appropriately based on calculated values.
Figure 4 presents a comparison of measured- and recovered equivalent impedances in the zero-sequence test. It
can be concluded that all frequency-dependent functions
developed from short-circuit and zero-sequence tests are
reasonable derived within frequency range from 20 Hz to
at least 3 kHz.
C and HV neutral are grounded and other winding terminals are left opened. If one assigns conditions of winding
terminals under order “HV_LV” as “ABCN_abcn” for a
short and convenient configuration name, one would have
the name of this configuration as “EOGG_OOOO” (E–
excited, O–opened, G–grounded). From Figure 1, when
the HV terminal of phase C is shorted to ground, core legand yoke impedances in this phase are bypassed. Hence,
the equivalent impedance observed from the excited
phase winding includes only core leg- and yoke impedances of phases A and B. Therefore, if one performs three
measurement configurations mentioned in Table 1 [2],
one would have a mathematic problem with two variables
and three equations. The best solution for this problem is
a solver of nonlinear least squares problem in which objective functions are differences of real- and imaginary
parts between measured- and calculated equivalent impedances at each frequency point [5].
Index
1
2
3
Configuration
EOOG_OOOO
EGOG_OOOO
EOGG_OOOO
Equivalent impedance
(Z1 // Zy + Z1) // (Z1 // Zy)
(Z1 // Zy) // (Z1 // Zy)
Z1 // (Z1 // Zy)
Table 1 Three measurement configurations for phase A at
low frequencies [2]
Figure 4 Verification of equivalent impedances in the
open-circuited zero-sequence test on HV side between
measurement and recovery at low- and mid frequency
ranges.
2.1.4 Parameter determination from open-circuit
tests at HV side
2.1.4.1 In low frequency range (20 Hz to 400 Hz)
In this frequency range, core effect is dominant. Thus,
core impedances (Z1 and Zy) are main components in the
equivalent circuit in Figure 1. Capacitive impedances can
be neglected since they are much larger than core impedances at low frequencies. According to [2], in case only
Z1 and Zy appear in the circuit for an approximation calculation (RH, L3H and Z4 are bypassed since they have only
little influence), there are three different configurations
required to determine core impedances when a HV winding is excited. The three configurations are necessary
since they provide different core circuits in determining
variables (Z1 and Zy).
Let illustrates a measurement configuration in which the
HV terminal of phase A is excited, HV terminal of phase
ISBN 978-3-8007-3465-8
Core impedances (Z1 and Zy) as results after the solver are
relatively reasonably determined. However, an improvement can be reached if other parameters (RH, L3H, Z4) and
more configurations from other phases are taken into account. Our experience shows that when all measurement
configurations from three phases are supplied as inputs to
the solver, core impedances are best derived and proportionate to each other.
Afterwards, components from Z1 and Zy, i.e. R1(f), L1(f),
Ry(f) and Ly(f), are developed in whole frequency range in
following procedure. At low frequencies, due to the fact
that calculated values vary in an exponential tendency,
they are best fitted by normal exponential functions. At
higher frequencies, since core impedances are no longer
dominant, experimental formulae can be exploited instead. From literatures, there are three main effects contribute to the core losses: eddy current, hysteresis and
anomalous [6]. However, when a transformer is excited
under very low applied voltage, eddy current (skin) effect
in the core is dominant [7] and therefore, skin-effectbased core-section resistance and inductance can be determined thanks to estimated dimensions and material of
core section of the test transformer [8].
2.1.4.2 In mid frequency range (5 kHz to 6.5 kHz)
This frequency range is chosen so as all measured impedances in configurations mentioned in sub-section 2.1.4.1
are capacitive. Therefore, equivalent capacitive impedances (ZA, ZB and ZC) have most influence and can be calculated by mean of a solver of nonlinear least squares
problem [5]. The procedure of calculation is similar like
© VDE VERLAG GMBH ∙ Berlin ∙ Offenbach
Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
that for low frequency range, except equivalent impedance equations are different since all components are involved in the circuit [2]. For illustration of an example of
the difference, let have a look on the equivalent impedance between C1 and N1 in Figure 1. In low frequency
range it is (ZC+RH+jωL3H)//Z1~Z1 because ZC>>Z1;
but in mid frequency range it will be:
(ZC+RH+jωL3H)//Z1~ZC since ZC>>RH+jωL3H and ZC<<Z1
One important thing should be noted that these capacitive
impedances (ZA, ZB and ZC) do not belong to a certain
kind of capacitance such as series- or ground capacitances, but include different kinds of capacitances as abovementioned. Therefore, in order to separate them, capacitive impedance measurements are required.
ISBN 978-3-8007-3465-8
2.2
Diagnostic test recovery via calculated
physical parameters in healthy condition
Once physical parameters are available, several diagnostic
tests such as magnetic balance, FRLI, “standard” FRA etc
can be recovered appropriately. Following figures depict
verifications of these tests whose results are measured by
means of different measurement testing devices and from
the physical parameter recovery.
Figure 6 compares test results of magnetic balance tests
between a terminal measurement and from the equivalent
circuit recovery at 50 Hz. The terminal test is conducted
by mean of a testing set including a sinusoidal generator
and a 12-bit oscilloscope to measure voltages on winding
terminals at HV side. The applied voltage in the terminal
test is the same with that of the impedance test (1 V). Results confirm that core impedances are well determined
since this test reflects the core behaviour at low frequencies.
100
80
VAN
60
40
VBN
VCN
Phase A
excited
Phase B
excited
Recovered
Measured
Recovered
Measured
Recovered
20
0
Measured
2.1.6 Parameter verification
A simple way to verify the parameters determined in previous sub-sections is to compare measured- and recovered
equivalent impedances. To recover equivalent impedances
for whole range of frequency, frequency-dependent functions of inductive components as well as values of capacitances in Figure 1 are applied in a circuit simulation software. For a better recovery of frequency responses of
equivalent impedances, CA, CB and CC should be replaced
by series-, ground and inter-winding capacitances thanks
to CHG, CLG and CHL.
Figure 5 depicts a verification of a frequency response of
equivalent impedance in the open-circuit test on phase A.
Observed good agreement in low- and mid frequency
ranges proves that parameters are reasonable derived. Besides, deviations of magnitude and phase angle at high
frequencies appear due to the fact that the equivalent circuit is the lumped circuit which does not reflect fully the
distributed behaviour of the real transformer.
Figure 5 Verification of the open-circuit test on phase A
Voltage in percentage (%)
2.1.5 Parameter determination from capacitive impedance tests
There exists a diagnostic test for measuring capacitances
of power transformers performed by mean of an universal
testing device such as the CPC100 of Omicron under
high-voltage applied at low frequencies [9]. Measured results for a two winding transformer consist of HV-toground, LV-to-ground and HV-LV capacitances (CHG,
CLG and CHL respectively). Under assumption that there is
a balanced condition between each phase, corresponding
capacitances of each phase, e.g. CgA, Cga and CAa, can be
calculated as one third of the measured ones.
On the other hand, our experience confirms that those capacitances can be independently determined from drivingpoint impedance tests by mean of the VNA under 1 V excited. Of course those impedance tests should have the
same configurations with the ones from diagnostic test
and thus they are called capacitive impedance tests. Based
on the capacitive tendency of measured impedances at
high frequencies, capacitances CHG, CLG and CHL are reasonably determined.
Phase C
excited
Figure 6 Verification of magnetic balance tests on HV
side
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Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
Figure 7 presents a good verification of FRLI from a
short-circuit test performed by mean of the CPC100 under
1 A current source supplied and the corresponding one
recovered from the calculated physical parameters in frequency range from 20 Hz to 400 Hz.
and reliable information. At high frequency range, interpretation of diagnostic tests requires a more complicated
equivalent circuit with more parameters.
2.3
Parameter analysis in failure condition
There are in total ten failure cases in each of which a single failure is simulated on the active part of the test transformer. Failure modes include open-circuit, short-circuit
between discs, short-to-ground (each failure is simulated
on each HV winding of three phase in succession) and
loss of core ground. Positions of failures on HV windings
are at the middle of the windings for first investigations.
The parameter determination procedure in section 2.1 is
applied for each of all cases appropriately. However, there
is a fact that only a few parameters could be recognized
and determined. Following sub-sections explain more details.
Figure 7 Verification of FRLI from short-circuit test of
phase A at HV side
Figure 8 shows good agreement at low- and mid frequency ranges (until 20 kHz) for the end-to-end opencircuit (EEOC) FRA test between the “standard” FRA
measurement performed by mean of the FRAnalyzer instrument and the recovery result from the physical parameters.
2.3.1 Open-circuit failure on HV windings
From the first step of the parameter determination procedure, i.e. short-circuit test analysis, negative leakage inductances are derived for this failure condition. It is logical since capacitive currents flow in the faulty winding
through the open-circuit position. Therefore, other next
steps are not possible because of negative leakage inductance value and this value is useful to detect an opencircuit failure on a winding.
2.3.2 Short-circuit-to-ground and short-circuitbetween-discs failures on HV windings
From the calculation procedure, it is concluded that one of
physical parameters which are helpful to detect the failures, i.e. being different from those in healthy condition
and having clear tendency, is leakage inductance. It can
be explained that the failures reduce energy in the leakage
channel and hence the leakage inductances decrease [10].
Figure 9 confirms a decrease of energy from 2D-FEM
simulations for the short-circuit tests in different conditions.
Figure 8 Verification of the EEOC-FRA test on phase A
A short conclusion can be drawn: The physical parameters and the equivalent circuit are reasonably determined
for interpretation of several diagnostic test results at lowand mid frequency ranges. These physical parameters can
be therefore investigated under different failure conditions
for a better diagnosis since they may supply important
ISBN 978-3-8007-3465-8
Figure 9 Energy distributions on the gap between HVand LV windings of phase A in healthy-, shorted-disc and
short-to-ground conditions at 50 Hz (from left to right respectively)
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Diagnostik Elektrischer Betriebsmittel ∙ 15. – 16.11.2012 in Fulda
Table 2 introduces a comparison of leakage inductances
between the equivalent circuit recovery and from FEM
simulations at 50 Hz. A clear tendency of value change
between all conditions is observed from FEM-based calculation whereas from the recovery, the shorted-disc- and
short-to-ground failures can not be recognized exactly; in
fact they are only distinguished from the healthy condition and in such case, ground capacitance can be a good
indicator to discriminate them. However, a clear tendency
of leakage inductance change from the recovery like that
from the FEM calculation appear at higher frequencies,
for example at 10 kHz. It recommends that the impedance
measurement performance of the VNA instrument at low
frequencies should be further investigated for better
analysis.
L3total (mH)
Condition
healthy
shorted-disc
short-to-ground
based on FEM
calculation
49
41.6
34.4
2.3.3 Ungrounded core
A parameter which is reliable for detecting this failure
condition is the ground capacitance of the LV windings
since the LV windings are inner windings and core
ground is lost. Table 3 shows a comparison of measured
capacitances between healthy- and failure conditions. As
predicted, total ground capacitance of the LV windings
(CLG) changes significantly whereas there is little change
with inter-winding capacitance (CHL) and ground capacitance of the HV windings (CHG). As a result, it can be the
best indicator to detect this failure mode.
Condition
healthy
ungrounded core
CHL
CHG
CLG
1257
1386
343
264
2843
264
Table 3 Approximate capacitances from capacitive impedance tests
3


4
recovered
from physical
parameters
54.6
45.6
46.5
Table 2 Approximate total leakage inductances at 50 Hz
Capacitance
(pF)

Conclusions
The interpretation of several diagnostic tests until
mid frequency range is now possible thanks to the
physical equivalent circuit with physical parameters.
Number of diagnostic tests may be reduced since
they can be recovered through impedance test analysis. On the other hand, the impedance test analysis
can be considered as a new diagnostic technique
since it supplies more information to the diagnosis
for more reliable interpretation.
A few physical parameters can be good indicators to
detect electrical failures on the active part of power
transformers. Besides, they are also useful in diagnosis of mechanical failures which are not investigated
in this paper.
References
[1] Velasquez, J. L.: Intelligent monitoring and diagnosis of power transformers in the context of an assesst
management model. PhD thesis, Polytechnic university of Catalonia: Spain, 2011
[2] Pham, D. A. K. et. al.: Duality-based lumped transformer equivalent circuit at low frequencies under
single-phase excitation. International conference on
high-voltage engineering and application (accepted),
2012
[3] Martinez, J. A.; Walling, R.; Mork, B. A.; MartinArnedo, J. and Durbak, D.: Parameter Determination
for Modeling System Transients—Part III: Transformers. IEEE Transactions on Power Delivery. Vol.
20, No. 3, July 2005, pp. 2051-2062
[4] Mork, B. A. et. al.: Hybrid transformer model for
transient simulation – Part II: Laboratory measurements and benchmarking. IEEE Transaction on
Power Delivery. Vol. 22, No. 1, January 2007, pp.
256-262
[5] Mathwork Inc.: Curve Fitting Toolbox
[6] ABB: Transformer Handbook. 3th Edition, 2007
[7] Abeywickrama, N.: Effect of dielectric and magnetic
material characteristics on frequency response of
power transformers. Doctoral thesis, Chalmers university of technology: Sweden, 2007
[8] Lammeraner, J.; Stafl, M.: Eddy current. Iliffe
Books, London: U.K. 1996
[9] Krüger, M.: Capacitance and dissipation factor measurement with CPC100 + CP TD1. Omicron Application Guide, 2004
[10] Kulkarni, S. V.; Khaparde S. A.: Transformer engineering design and practice. Marcel Dekker, 2004
The paper introduces a new and comprehensive procedure
in determining physical parameters for power transformers based on only the driving-point impedance tests for
the purposes of test result interpretation and electrical
failure diagnosis. Several main contributions can be
drawn as follows:
ISBN 978-3-8007-3465-8
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