Energy and Power Engineering, 2013, 5, 1109-1114
doi:10.4236/epe.2013.54B212 Published Online July 2013 (http://www.scirp.org/journal/epe)
Influence of Phase Compensation Method on
Magnetizing Inrush Identification
Xiangfei Sun, Jianping Zhou
Department of Electrical Power Engineering, Kunming University of Science and Technology, Kunming, China
Received April, 2013
ABSTRACT
The effect of different phase compensation methods on second harmonic ratio of magnetizing inrush is investigated.
The flux linkage expression of switching on an unload transformer is deduced and influence factors of inrush current
are analyzed firstly. Then the difference of two kinds of phase compensation methods, from star to delta and from delta
to star connection, is compared. The second harmonic ratio of symmetric inrush is analyzed specially. Using inrush
waveform of a real transformer, second harmonic ratio of phase inrush and that of differential current under two kinds
of phase compensation methods are calculated respectively. Furthermore, based on the calculation results, the effect of
two kinds of phase compensation methods on the inrush current identification is proved. The analysis and calculation
results show that the second harmonic ratio of symmetric inrush caused by phase compensation method, from star to
delta, is not low. Moreover, the split-phase blocking scheme should not be adopted for differential protection of from
delta to star compensation. Using the phase current without compensation to calculate the ratio of second harmonic is
inadvisable too.
Keywords: Transformer; Differential Protection; Magnetizing Inrush ; Second Harmonic; Phase Compensation
1. Introduction
When an unload transformer is energized, it will create a
large magnetizing inrush, which will cause the mal- op-
eration of transformer differential protection. In order to
prevent mal-operation, many techniques have been in-
vestigated in the design and operation of transformer
differential protection [1-3]. However, the inrush current
identification algorithm that has been widely used is still
the second harmonic restraint scheme [4-6].
Second harmonic restraint mainly includes two schemes.
One is single phase blocking three-phase scheme, i.e. all
three-phase differential relays will be blocked when any
phase second harmonic ratio is larger than setting valve.
The other is split-phase blocking scheme, i.e. only the
relay of the phase whose second harmonic ratio is larger
than setting valve will be blocked.
In practice, for Y-delta connected transformers, which
are used widely in power system, phase compensation
should be carried out to eliminate the imbalance current
in the circuit loop of transformer differ ential relays [7-9 ].
Phase compensation mainly includes two methods, one is
from star to delta phase compensation, the other is from
delta to star phase compensation. As a result, different
phase compensation methods will lead to different influ-
ence on the differential current of transformer differential
protection.
Therefore, which second harmonic blocking scheme
should be adopted need to be researched [10-13]. How-
ever, the previous researches have some opposite view-
points. Literature [10] presents that from star to delta
phase compensation method will lead to symmetric in-
rush, which results in inrush characteristic is not obv ious
and the second harmonic content of differential current
reduced. So split-phase blocking scheme is not adopted.
Literature [11] indicates that split-phase blocking scheme
is suitable for from delta to star phase compensation me-
thod. Literature [12] proposes that the two phase com-
pensation methods have similarities in inrush identifica-
tion, and split-p hase blocking scheme may mal operation
under the both two methods. Literature [13] presents that
the two compensation methods both can change the har-
monics of differential current, so directly take the un-
compensated current to calculate the second harmonic
ratio can achieve split-phase brake scheme.
Aim to investigate the influence of different phase
compensation methods on second harmonic restraint
scheme; the paper analyzes the influencing factors of
magnetizing inrush firstly. Then the difference of two
kinds of phase compensation methods are compared,
especially focus on the analysis of the second harmonic
ratio in symmetric inrush. Based on the inrush waveform
of a real transformer, influence of two phase compensa-

X. F. SUN, J. P. ZHOU
1110
tion methods on identifying magnetizing inrush is ana-
lyzed in depth, and problems of transformer differential
protection device on the second harmonic restraint
scheme is investigated.
2. Influence Factors of Magnetizing Inrush
Equivalent circuit of single-phase transformer switching
on without load is sh own in Figure 1. As the second side
of transformer is unloaded and core loss is small, the
equivalent resistance R
m which represents core loss can
be ignored. Assuming that voltage source us is a sine
voltage, i.e. us=Umsin(
 t+  ), where Um and  are volt-
age amplitude and closing angle respectively. Rs and L
s
are the equivalent resistance and inductance of system
respectively, R
σ and L σ are the equivalent leakage resis-
tance and leakage inductance of transformer respectively.
Lm is equivalent magnetizing inductance.
Defining ψ is the total equivalent flux linkage of the
circuit, i.e. ψ=ψs+ψσ+ψm, where ψs, ψσ and ψm are cre-
ated by Ls, Lσ and Lm respectively. R is the total equiva-
lent resistance of the circuit, i.e. R=Rs+Rσ. Voltage equa-
tion of the circuit shown in Figure 1 can b e e x p r es s ed as
d
sin( )d
sm m
uUtRi t

  (1)
In Equation (1), ψ=ψs+ψσ+ψm=(Ls+Lσ+Lm)im=Lim,
where im is magnetizing current. Since Ls and L
σ can be
regarded as constant, the relationship between ψm and im
is the magnetization curve

m=f (im). When transformer
is saturated, the relationship between ψm and im will be
nonlinear, which means Lm is a nonlinear inductance. So
the solution of Equation (1) is hard to obtain. Because
voltage mainly varies with the flux linkage, and R has
little effect on the voltage. Therefore Lm can be consid-
ered as an average inductance of the transformer tran-
sient process. Thus L can be regarded as constant. The
simplified equation will be
dsin( )
dm
RUt
Lt


   (2)
The solution of Equation (2) consists of the steady
component
  and the transient component  , that is
1
22
sin(tg )
()
e
m
Rt
L
UL
Lt
R
RL
C

 




 


-
(3)
L
s
R
s
u
s
R

L

L
m
K
i
m
Figure 1. Equivalent circuit of single-phase transformer
switching on without load.
In Equation (3), C is integration constant, which is
depended on initial condition. Considering that R<<
 L,
so it will be
1
tg 90
L
R

 (4)
22
()
mm
m
UU
L
RL




 (5)
In equation (5),

m is the amplitude of flux linkage
that transformer is in steady operation. Thus Equatio n (3)
can be expressed as
cos() e
R
t
L
mtC
 

  (6)
The integration constan t C is depended on the residual
magnetism ψr that switching on moment t=0, that is
cos
m
Cr



 (7)
Therefore, the solution of flux linkage can be obtained
cos() (cos)e
R
t
L
mm
t  

r (8)
According to Equation (8), it is can be seen that the
essential reason for occurring magnetizing inrush is the
saturation of transformer core, which caused by an ape-
riodic flux that generated to restrain the flux mutation
when energizing an unload transformer. Moreover, as
Equation (8) expresses, the factors that mainly affect the
magnetizing inrush are closing angle
 , the amplitude
and polarity of residual magnetism ψr. Obviously, mag-
netizing inrush will be maximum when closing angle
 =0°. And magnetizing inru sh will be zero when closing
angle
 =90°. If the polarity of magnetizing fluxes when
transformer switching on is same with that of residual
magnetism, saturation of transformer core may be more
serious. On the contrary, if the polarities of magnetizing
flux and residual magnetism are opposite, it will be help
to reduce magnetizing inru sh.
3. Influence of Phase Compensation Methods
on Characteristics of Magnetizing Inrush
For Y-delta connected transformers, which are used
widely in power system, the phase angle of current in
star(Y) side lags 30°than that in delta(△) side. In order
to eliminate the imbalance current in the circuit loop of
transformer differential relays, the amplitude and phase
angle of current should be corrected before the trans-
former differential protection discrimination. The correc-
tion of current amplitude and phase angle is called as
phase compensation.
The traditional phase compensation method is carried
out by adjusting the mode of connection of current
transformers (CT), i.e. three CTs on transformer Y side is
connected into a delta, while CTs on transformer delta

X. F. SUN, J. P. ZHOU. 1111
side is connected into a star. With the development of
microcomputer protection, phase compensation can be
achieved by software program expediently. The software
phase compensation method mainly includes two kinds,
one is from star to delta phase compensation, the other is
from delta to star phase compensation.
3.1. From Star to Delta Phase Compensation
From star to delta phase compensation method is that
each current of transformer Y-side is calculated by each
two-phase current of three-phase current subtraction,
while delta-side current is still original phase current.
The compensated current in Y-side can be expressed as
'
'
'
110
101 1
310 1
aa
b
c
c
I
b
I
I
I
I
I




 

 

 
 

 



(9)
where IaY, IbY and IcY are original phase current in Y-side,
IaY’, IbY’ and I
cY’ are compensated phase current. From
Equation (9), by from star to delta method, if two phase
original inrush current are in the same direction, their
subtracted current, i.e. differential current after compen-
sation, may be a symmetric inrush.
The following theoretical analysis is about the second
harmonic ratio characteristics of symmetrical inrush. For
the convenience of analysis, supposing original current
of phase A and B are in the same direction, and funda-
mental component amplitude and second harmonic ratio
of the two currents are respectively equal. Frequency of
second harmonic is double that of fundamental harmonic,
so the phase vector is shown as Figure 2. As seen from
Figure 2, the fundamental wave amplitude of the differ-
ential current 1AB1
I
I

 is 3 times that of IA1 (IB1),
the second harmonic amplitude of the differential current
2AB2
I
I

 is 3 times that of IA2 (IB2). Therefore, the
second harmonic ratios of symmetry inrush and single
phase inrush are equal. For the more general analysis,
subtracted current amplitudes of fundamental wave IA1
(IB1) and second harmonic IA2 (IB2) between any
two-phase currents are all equal as above discussed. Ob-
viously, because of the uncertainty of the fundamental
and second harmonic amplitudes of single phase inrush,
2
A
I

2B
I

22AB
I
I


1
A
I

1B
I

11AB
I
I


Figure 2. Phase vector of the fundamental and second har-
monic in differential current of two same direction inrush.
when inrush subtracted in couples, the second harmonic
ratio of differential current may become larger, or may
become smaller.
3.2. From Delta to Star Phase Compensation
With this method, original phase current of transformer
delta-side will be subtracted in couples in a negative
phase sequence. Delta-side currents can be expressed as
'
'
'
10 1
111 0
3011
aa
bb
c
c
I
I
I
I
I
I





 

 

 
 

 


(10)
where I
a
△
, Ib
△
and Ic
△
are original phase currents in
transformer delta-side, Ia
△
’, Ib
△
’ and Ic
△
’ are compensated
phase currents.
Due to zero sequence current caused by Y-side exter-
nal ground fault would lead to transformer differential
protection mal-operation, Y-side current will be adjusted
by minus the zero sequence current. Y-side currents can
be expressed as
'
0
'0
'0
100
010
001
211
1
121
3112
aa
bb
c
c
a
b
c
I
I
I
I
II
I
I
I
I
I
I







 
 

 

 
 




 
 




(11)
where I0 is zero sequence current in Y-side. According to
Equation (11), IaY’, IbY ’ and IcY’ all consist of IaY, IbY and
IcY, thus the three currents are linear dependence, and
second harmonics may offset each other under certain
conditions. Therefore, second harmonic ratio of com-
pensated differential current may be very low. Conse-
quently, if the second harmonic blocking scheme is split-
phase blocking, it would result in the failure of second
harmonic bl o cking m e t h od.
4. Calculation Results and Analysis
Based on the following field data of differential protec-
tion mal-operation caused by magnetizing inrush, second
harmonic ratio of differential current fewer than two
kinds of phase compensation methods are calculated re-
spectively. Then the above analysis about effect of dif-
ferent phase compensation methods on the inrush current
identification will be further confirmed.
Three phase inrush of a real 220 kV tran sformer when
the transformer was energized were recorded by the fault
recorder, shown as Figure 3. It is worth emphasizing that
this 220 kV transformer adopted double differential pro-
tections with second harmonic restraint. And both dif-

X. F. SUN, J. P. ZHOU
1112
ferential protections mal-operated at th e same time when
the transformer energizes.
Using three phase inrush data shown as Figure 3,
second harmonic ratio of three phase inrush is calculated.
The calculation results are shown in Figure 4. According
to Figure 4, it is can be seen that second harmonic ratio
of phase B inrush current is very low. As what analyzed
above in section 2, this is because residual magnetism of
phase B is large and polarities of both magnetizing flux
and residual magnetism are the same, thus transformer
core gets serious saturated, resulting in current waveform
is similar to a sine wave, which second harmonic content
is small. Therefore, the method proposed in literature [13 ]
that directly take the uncompensated current to calculate
the second harmonic ratio is still b e problem.
In this case, the microcomputer protection adopts from
delta to star phase compensation method; second har-
monic restraint adopts split-phase blocking logic; the
setting value of operating current is 0.2 times rated cur-
rent; the setting value of second harmonic restraint is
15%. According to Equation (11), three phase differential
current compensated by from delta to star method is
Figure 3. Three phase inrush waveform of a real 220 kV
transformer.
Figure 4. The second harmonic ratio of three phase inrush.
shown in Figure 5, and corresponding second harmonic
ratio are shown in Figure 6. Figure 5 shows that the
amplitudes of three differential current are all more than
0.2 times rated current. Moreover, Figure 6 shows that
second harmonic ratios of three differential current are
all less than 15%. As the result, double differential pro-
tections with split-phase blocking mal-operated at the
same time. It should be noted that this case is identical
with the theoretical analysis discussed in section 3. Thus
it can be seen that the viewpoint proposed in literature
[11], split-phase blocking scheme is suitable for from
delta to star phase compensation method, is incorrect.
As analyzed in section 3, different phase compensation
methods lead to different characteristics of differential
current. If from star to delta phase compensation is
adopted in this case, calculating results of three differen-
tial currents and corresponding second harmonic ratios
are shown in Figure 7 and Figure 8 respectively. Figure
7 shows that compensated differential current of phase C
Figure 5. Three phase differential current used from delta
to star phase compensation method.
Figure 6. The second harmonic ratio of three phase differ-
ential current.

X. F. SUN, J. P. ZHOU. 1113
Figure 7. Three phase differential current used from star to
delta phase compensation method.
Figure 8. The second harmonic ratio of three phase differ-
ential current.
is symmetric inrush, whose amplitude is less than 0.2
times rated current. However, second harmonic ratio of
phase C differential current is much higher than 15%
shown as Figure 8. Theref ore, the viewpoin t propo sed in
literature [10], symmetric inrush characteristic is not ob-
vious and second harmonic content is small, is inappro-
priate.
According to the calculation and analysis above, if the
differential protections adapt from star to delta phase
compensation and single phase blocking three-phase
logic scheme in the case, magnetizing inrush generated
by transformer energized will not cause differential re-
lays mal-operate. However, if transformer is switching
on a fault phase, differential relay will not operate until
magnetizing inrush decayed. Thus, the safety of trans-
former may be endangered.
5. Conclusions
Under from star to delta phase compensation mode, if
two phase magnetizing inrush is in the same polarity, the
differential current may be symmetric. However, because
three phase differential current are obtained by subtract-
ing each two phase inrush, and the fundamental and sec-
ond harmonic amplitudes of single phase inrush are un-
certain, resulting in that the second harmonic ratio of
differential current may become larger, or may become
smaller.
Under from delta to star phase compensation mode,
second harmonics may be offset each other since each
phase of differential current is combined by linear de-
pendence three ph ase magnetizing inrush . Thus the split-
phase blocking scheme should not be ad o pt ed.
Affected by the effect factors such as the closing angle,
the amplitude and direction of the residual magnetism,
transformer core may get serious saturated, which will
lead to magnetizing inrush waveform is similar to a sine
wave and second harmonic component reduced. So un-
compensated phase currents are not appropriate to calcu-
late second harmonic ratio for the inrush restraint
scheme.
6. Acknowledgements
Project Supported by National Natural Science Founda-
tion of China (51007035, U1202233, 51267009); Yun-
nan Natural Science Foundation (2009ZC016M); Kun-
ming University of Science and Technology Talent
Training Foundation (KKZ320201004003).
REFERENCES
[1] J. D. Hang and W. Q. Luo, “New Algorithm to Identify
Inrush Current Based on Improved Mathematical Mor-
phology,” Proceedings of the CSEE, Vol. 29, No. 7, 2009,
pp. 98-105.
[2] M. M. Eissa, “A Novel Digital Directional Transformer
Protection Technique Based on Wavelet Packet Trans-
form,” IEEE Transactions on Power Delivery, Vol. 20,
No. 3, 2005, pp. 1830-1836.
doi:10.1109/TPWRD.2005.848646
[3] D. Z. Chen, J. D. Huang and L. Zhang, “Identification of
Transformer Excitation inrush Based on Correlation
Analysis between Two Fourier Algorithms,” Electric
Power Automation Equipment, Vol. 30, No. 10, 2010, pp.
71-74.
[4] E. Vazquez, I. I. Mijares, O. L. Chacon, etc, “Transformer
Differential Protection Using Principal Component
Analysis,” IEEE Transactions on Power Delivery, Vol.
23, No.1, 2005, pp. 67-72.
doi:10.1109/TPWRD.2007.911149
[5] Z. P. Wang and X. Wang, “Inrush Current Recognition in
Power Transformer Based on Modified Principal Com-
ponent Analysis,” Power System Protection and Control,
Vol. 39, No. 22, 2011, pp. 1-4.
[6] L. D. Wang and Z. C. Duan, “Mal-operation Analysis on

X. F. SUN, J. P. ZHOU
1114
Magnetic Inrush Current of Power Transformer,” Power
System Protection and Control, Vol. 38, No. 10, 2010, pp.
138-140.
[7] H. C. Shu and X. F. Sun, “Wye-delta Current Transform
Effect on Sympathetic Inrush Transfer,” Journal of Elec-
tric Power Science and Technology, Vol. 23, No. 4, 2008,
pp. 33-37.
[8] X. F. Sun and H. C. Shu, “Effect of CT Transient Satura-
tion on Transfer of Sympathetic Inrush,” Electric Power
Automation Equipment, Vol. 29, No. 1, 2009, pp. 83-88.
[9] W. J. Wang, “The Applications of Generator and Trans-
former Relay Protection,” China Electric Power Press,
Beijing, 1998.
[10] X. J. Ge, “Comparison and Calibration of Two Kinds of
Transformer Differential Protection,” Huadian Technol-
ogy, Vol. 33, No. 10, 2011, pp. 51-53.
[11] S. L. Chen, H. Y. Li, Y. Qiao, ect, “RCS-978 Digital
Transformer Protection Set,” Automation of Electric
Power Systems, Vol. 24, No. 22, 2000, pp. 752-55.
[12] X. L. Deng and S. M. Liu, “Comparison of Two Current
Compensation Methods in Transformer Protection,” Re-
lay, Vol. 32, No. 13, 2004, pp. 20-24.
[13] Z. C. Liu, “Analysis of Magnetizing Inrush Current of
Three-Phase Transformer and the Differential Protection
Scheme,” Automation of Electric Power Systems, Vol. 30,
No. 10, 2006, pp. 58-60.