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The Effect of Inrush Current on Transformer
Protection
Li-Cheng Wu,,Student Member,IEEE, Chih-Wen Liu,Senior Member,IEEE,
Shih-En Chien,Student Member,IEEE,Ching-Shan Chen,Member,IEEE
Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan
characteristics of iron core can be expressed by equation (1) [8]
which can show the excitation curve as Fig.2. Due to the
Abstract—Transformers are key components for electrical non-linear of transformer iron core, this will result in excitation
energy transfer in power system. Stability and security of and saturation problems of transformer in power systems.
transformer protection are important to system operation; we According to different operation point of transformer core as
found that many mal-trip cases of transformer protection are Fig.3, we can get different excitation current on transformer.
caused by inrush current problems. The phenomenon of When switched to a no-load transformer, this will result in
transformer inrush current has been discussed in many papers transformer’s working in saturation area of excitation curve
since 1958 [1-5]. Therefore, this paper will only discuss and
(see Fig.3) in which creates high magnitude asymmetrical
analyze inrush current problems. Finally, this paper will also
present two cases that were analyzed with the use of digital current with a high harmonic and a high direct current
simulation technique to make COMTRADE files, to provide components. This may cause mal-operation of over-current
over-current protection and differential protection tests and the protection or differential protection. Typically, for steady state
analysis of the effect of inrush current on transformer protection. operation, the excitation current of transformer is slightly less
than 5% of the rated current (see Fig.3). In practice, the
magnitude and duration of transient inrush current depend on
Index Terms—Over-current protection, Differential Protection,
Inrush Current, COMTRADE files.
the following [9]:
Circuit breaker switching angle when the transformer is
energized
I. INTRODUCTION
The value and sign of the residual flux linkage in the
In power systems, differential protection is applied for transformer core
transformer capacity above 10MVA, while over-current
protection is used for transformer with the banks below The saturation characteristic of the transformer core
10MVA for main protection that includes simple theory and Source impedance
best protection results. However, the transformer will create
large inrush currents when the transformer operates on no-load
energizing condition. This inrush currents involves a large and
long lasting dc component, which is rich in harmonics, assumes
large peak values at the beginning about 6 to 30 times of the
rated value. This condition causes unbalance of current loop of
differential relay that will occur with mal-trip. In order to
prevent false tripping due to an inrush current, a technique
using the content of the second harmonic component in the Fig.1 Equivalent circuit of a two-winding transformer
current waveform is commonly used. However, this method
ϕ = −s *[Isat *tan−1 (−s *(dϕ dI )* Ie + Ic ) − s *ϕr * Ie + ϕsat ] (1)
cannot provide total solution for inrush current. Therefore, we
present digital simulation method to analyze and to test to know
the best transformer protection schemes.
Where： s =1 for an ascending trajectory, s =-1 for a
descending trajectory
II. SIMULATION AND ANALYSIS OF INRUSH CURRENT I sat for saturation current of transformer
The equivalent circuit of transformer model shown as Fig.1 dϕ for slop of excitation curve of transformer
consists of an ideal transformer of ratio N1 : N 2 and parameter dI
of elements. The model takes into account the winding I e for excitation current
resistances ( R p , Rs ), the leakage inductances ( L p , Ls ) and I c for coercive current
the excitation characteristics of iron core. The excitation ϕr for residual flux
ϕ sat for saturation flux of transformer
values of inrush current vs. residual flux (from -1 to 1 pu) when
1.5
CB1’s closed angle is 0 degree and 90 degrees respectively.
The simulation results show that the inrush current can be
1 reduced by controlling CB1’s closing time and residual flux.
For example, according to Fig. 1, we can write equations as
follows:
0.5
dI p dϕ m
ex c itatio n flux (p u)
Vp = Rp I p + Lp + N1 (2)
0 dt dt
dI dϕ
Vs = Rs I s + Ls s + N 2 m (3)
-0.5 dt dt
-1 When the transformer is energized in no-load, the equation
(3) can be expressed by:
1
N2 ∫
-1.5
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02
ϕm = Vs dt (4)
excitation current (pu)
Fig.2 Excitation curve of transformer Here, we want to get CB1 optimal closed time in the main
flux ( ϕ m ) close to zero. Because the number of turns of
∫
primary N1 is larger than the item of R p I p dt and L p I p , we
can modify the equation (4) as follows:
1 ⎡ 1
ϕm =
N1 ⎣ ∫ (Vp − Rp I p )dt − Lp I p ⎤ ≅ N1 ∫ Vp dt
⎦
(5)
Therefore, the value of main flux ( ϕ m ) can be calculated at
any instant using equation (5). In order to reduce inrush
currents, we can use the main flux information combined with
zero-crossing detector to determine the CB1 closing time,
which is at main flux ( ϕ m ) zero. The simulation result is shown
in Fig. 10. The all of the inrush currents are reduced by
controlling CB1’s closing time.
Table 1 The parameters of the simulation system
Fig.3 The operation point of excitation curve determines the magnitude
of the excitation and inrush current
Fig.4 shows the simplified single-line diagram of
transformer protection scheme used in TPC’s (Taiwan Power
Company) substation. We will simulate a transformer running
in no-load situation. Table 1 shows the parameters of
simulation system. Typically, the simulation results of the
inrush current are shown in Fig.5. At the same time, the field
test result is presented in Fig.6. Those currents of all figures are
used to CT (Current Transformer) secondary values whose
ratio is 1200:5. The inrush current is about 5 times larger than
the rated current of the transformer. The large inrush current
will hit transformer protection, which causes mal-trip for
different protection or over-current protection. We will discuss
these issues in the next section. Here, inrush currents are
formed based on the following three major factors: the
transformer energized angle, residual flux of iron core and
structure. Fig. 7 shows the relations between peak values of
three-phase inrush currents and CB1 closed angles when the
residual flux of transformer is zero. Fig. 8 and Fig. 9 show Peak
Fig. 6 Inrush current field test result
CB Switching degrees vs. peak values of Inrush current when residual flux is zero.
10
9
8
7
6
5
A
4
3
Fig.4 Simplified single-line diagram of transformer protection 2
Ia
1 Ib
Ic
0
High Voltage Side 0 50 100 150 200 250 300 350
15 degrees
Phase A
Phase B
Phase C
Fig. 7 Peak values of inrush current vs. CB1 closed angles
10
Residual flux vs. peak values of Inrush current
20
Ia
5
18 Ib
Ic
16
0 14
A
12
10
A
-5
8
6
-10
4
2
-15
0 1 2 3 4 5 6 7 8 9 10 0
Cycles -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Residual (pu)
Fig. 8 Peak values of inrush current vs. residual flux(from -1 to 1 pu) when
Fig. 5 Inrush current simulation result
CB1’s closed angle is zero degree
Residual flux vs. peak values of Inrush current transformer neutral line is caused by transformer when it is
20
Ia energized in no-load.
18 Ib
Ic
16 Case I: The connection diagram of differential relay of
transformer is as shown in Fig. 4. The basic theory of
14
differential relay is formed with the use of current balancing of
12 transformer of the two-sides as a trip signal. When the
10
unbalance currents of transformer of the two-sides is larger
A
than the pick-up setting of differential relay, the trip signal will
8
be sent from differential relay to trip circuit breaker (CB) for
6 isolated fault. From the basic differential theory, we know that
4 the inrush currents only go through one of the transformer
winding when the transformer is energized in no-load. At this
2
time, if the differential relay of transformer doesn’t include the
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
best blocking function of the inrush currents, than the mal-trip
Residual (pu) will occur. The differential relay of transformer use either
harmonic or blocking principles for inrush currents of
Fig. 9 Peak values of inrush current vs. residual flux(from -1 to 1 pu) when
transformer. Generally speaking, the second-harmonics content
CB1’s closed angle is 90 degrees of inrush currents of transformer usually is 15% larger than the
fundamental component. Therefore, the setting of the
second-harmonics of differential relay is usually set at 15%.
In the Fig.4, the frequent mal-trip of differential relay is
caused by the inrush currents when the transformer is energized
10
in no-load. Here, the differential relay is electrical-mechanical
0 type that utilizes the second-harmonic blocking for inrush
A
current restrain. The setting of the second-harmonic is at 15%.
CB1 uncontrolled Phase A
-10 CB1 controlled Phase A Fig. 11 shows the situation when the traces of inrush current is
entering the protection zone of differential relay during the
0 1 2 3 4 5 6 7 8 9 10
Cycles
transformer is energized in no-load. Fig. 12 is the
CB1 uncontrolled Phase B second-harmonic contents of the inrush currents after it is
10
CB1 controlled Phase B transferred by Fourier transfer. We can see the
0
second-harmonic contents of the inrush currents of phase A, B
A
and C at 10~12%, 20~23%, and 19~35% respectively. It is very
-10 obvious that the second-harmonic contents of phase A is less
than 15%, so the mal-trip of differential relay of phase A
0 1 2 3 4 5 6 7 8 9 10
Cycles
usually occurs in transformer when it is energized. In order to
improve this situation, we adjusted the setting of the
10 CB1 uncontrolled Phase C
CB1 controlled Phase C second-harmonic from 15% to 10% and since then the
0
differential relay has never mal-tripped during the time when
A
the transformer is energized in no-load.
-10 2
10
0 1 2 3 4 5 6 7 8 9 10 Characteristic curve of differential relay
Cycles IA
IB
IC
Fig. 10 Inrush currents compare CB1 uncontrolled with CB1
controlled 1
10
Idiff (A)
III. PRACTICAL EXAMPLES AND RESULTS OF THE EFFECT OF
INRUSH CURRENT 0
10
In this section, we will use two cases to explain and
analyze how and why the protective relay mal-trip occurs in 0 1 2
10 10 10
inrush currents. Case I for the mal-trip of differential protection Ires (A)
relay occurs during the time when transformer is energized in Fig. 11 the traces of inrush currents
no-load. Case II for the mal-trip of over-current relay of
Waveform of TR-SW1 neutral-line
30 15
IA Field test
20 IB 10 Simulation result
Inrush current (A)
IC
10 5
0 0
A
-10 -5
-20 -10
-30 -15
0 1 2 3 4 5 6 0 5 10 15
cycles cycles
2sd Harmonic content (% of fundamental
RMS values of Waveform of TR-SW1 neutral-line
40 10
IA Field test
IB 8 Simulation result
30 IC
6
20
A
4
10
2
0 0
0 1 2 3 4 5 6 0 5 10 15
cycles cycles
Fig. 12 Second harmonic contents of inrush currents Fig. 14 Current of neutral line of TR-SW1 when TR2_CB1 is opened
Fig. 13 shows one-line diagram of generator ‘s cooling
pump systems at a power plant in Taiwan. Here, the cooling Waveform of TR-SW2 neutral-line
15
system is very important for generators. If the cooling system Field test
10
shut down, then all the generators will be tripped by Simulation result
5
over-heating. The loss power of the load of transformer
0
(TR-SW2) results from the mal-operation of TR2_CB1 by
A
operators and the factor that the TR2_CB2 remains closed. At -5
the same time, the transformer (TR-SW2) only produces inrush -10
current when the Tie CB is closed. The inrush currents results -15
0 5 10 15
in the mal-trip of over-current relays (50/51Z, the relay setting cycles
RMS values of Waveform of TR-SW2 neutral-line
is 4A for instant trip) of two transformers’ (TR-SW1 and 10
TR-SW2) neutral-line. The current waveforms are shown in 8
Field test
Simulation result
Fig. 14 and Fig.15. In order to solve the mal-trip of 50/51Z, we
6
designed an inter-lock logic of the Tie CB as Fig. 16 for
A
security and reliability of a power plant. This logic can keep Tie 4
CB working in normal condition. In general condition, when 2
we close the Tie CB, the currents waveforms of the 0
transformers’ (TR-SW1 and TR-SW2) neutral line are shown 0 5 10 15
cycles
in Fig.17 and Fig 18. The results are satisfying because the
magnitude currents are less than the setting (4A) of the relay. Fig. 15 Current of neutral line of TR-SW2 when TR2_CB1 is opened
Therefore, the systems can work in the best condition.
Fig. 16 Improvement logic of case study of inrush currents
Fig. 13 Single-line diagram of case II
Waveform of TR-SW1 neutral transient data exchange (COMTRADE, IEEE C37.111) for a
1.5 standard format for the exchange of data in 1991. Here, we will
TR-SW1-50N
1
use digital simulation to produce COMTRADE file for
transient tests of differential protection.
0.5
Fig. 19 shows a transient test structure of differential relay
A
0 for transformer protection. We use simulation tools of PSCAD
and MATLAB to simulate a number of different fault types and
-0.5
to produces COMTRADE files for transient test of differential
-1 relay. The transient tests of open loop are used to input
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
times (sec) COMTRADE file to wave amplifier that produce real currents
RMS values of waveform of TR-SW1 neutral
0.5
or voltages to inject into protection devices for performance
TR-SW1-50N evaluations of protective relay. In addition, this method can be
0.4
combined by GPS (Global Position System) for end-to-end test.
0.3 Fig. 20 shows the inrush current for differential relay test. A
A
0.2
transient test of transformer internal-fault (AG) is shown in Fig.
21. The differential relay is operated because the differential
0.1
current trace of phase A falls into the operation area of
0 differential curve. On the contrary, in Fig. 22, the differential
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
times (sec) relay is of no-trip when the external fault occurred in out of the
protection zone of differential relay of transformer. The
Fig. 17 Current of neutral line of TR-SW1 when TR2_CB1 is closed
transient test can nearly simulate real situation of differential
protection of transformer to clearly show whether the
Waveform of TR-SW2 neutral differential relay should be operated or not in the internal or the
1.5
TR-SW2-50N external faults. However, the traditional steady-state test cannot
1 control dynamic processes, namely, internal faults, external
0.5
faults, energized and saturation of transformers. Usually, it is
discussed when the faults are occurred. From the above
A
0 discussion, the transient test of protective relay is important for
-0.5
power systems protection.
-1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
times (sec)
RMS values of waveform of TR-SW2 neutral
0.5
TR-SW2-50N
0.4
0.3
A
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
times (sec)
Fig. 18 Current of neutral line of TR-SW2 when TR2_CB1 is closed
IV. TRANSIENT TEST ON DIFFERENTIAL PROTECTION
Nowadays, the fault and transient data recording are widely
used in power systems. Their data are being used with various
devices to enhance and automate the analysis, testing,
evaluation, and simulation of power systems and related Fig. 19 the structure of transient test for differential relay
protection schemes during fault and disturbance conditions. In
order to get a bridge between different electric devices, IEEE
defines a common language that is a common format for
20
HV Phase A
LV phase A
0
A
-20
0 2 4 6 8 10 12
Cycles
20
HV Phase B
LV Phase B
0
A
-20
0 2 4 6 8 10 12
Cycles
20
HV Phase C
LV Phase C
0
A
Fig.20 Transient test of differential protection -20
0 2 4 6 8 10 12
Cycles
1
Phase A trip
Phase B trip
T rip s ignal
100 Phase C trip
HV Phase A 0.5
LV phase A
0
A
0
0 2 4 6 8 10 12
-100 Cycles
0 2 4 6 8 10 12
Cycles
10
HV Phase B
LV Phase B
Characteristic Curve of Differential Relay
0 30
A
Phase A
Phase B
-10 Phase C
0 2 4 6 8 10 12 25
10 Cycles
HV Phase C
LV Phase C
20
0
A
Idiff
15
-10
0 2 4 6 8 10 12
Cycles
1
Phase A trip 10
Phase B trip
Trip signal
Phase C trip
0.5
5
0
0 2 4 6 8 10 12
Cycles
0
0 2 4 6 8 10 12 14 16 18 20
Ires
Characteristic Curve of Differential Relay
30 Fig. 22 A transient test of external-fault (ABCG) for transformer
Phase A
Phase B
25 Phase C
20 V. CONCLUSIONS
This paper provides detail analysis of simulation and field
Idiff
15
measurement for problems of inrush current and transformer
10 protection. At the same time, we have also identified mal-trip
factors from our case studies in differential relay and
5 over-current relay, as well as resolutions for improvement. In
addition, in protection test field, we present advanced transient
0
0 2 4 6 8 10 12 14 16 18 20 test method that is applied in the setting of relay, fault analysis
Ires
and new algorithms research of relay and so on, which will
Fig. 21 A transient test of Internal-fault (AG) for transformer
result in better performance in transformer protection and thus
salability, reliability and security of power systems operation Taiwan University of Science and Technology in 2002, and
can be reached. M.S. degree in electrical engineering from National Taiwan
University in 2004. He is currently working toward his Ph.D.
degree at Electrical Engineering Department of National
REFERENCES Taiwan University. At present, his interested research includes
[1] Saied, M.M., “A study on the inrush current phenomena in transformer
power system protection and relay testing.
substations”, IEEE , Volume: 2 , 30 Sept.-4 Oct. 2001 Pages:1180 - 1187
vol.2 Ching-Shan Chen was born in Taichung, Taiwan, in 1976. He
[2] Stringer, N.T., Lawhead, L., Wilkerson, T., Biggs, J., Rockefeller, G.D.， received the B.S. degree in electrical engineering from National
Testing and performance of transformer differential relays ，
Taiwan University of Science and Technology, Taipei, Taiwan,
IEEE , Volume: 3 , Issue: 4 , July-Aug. 1997 Pages:36 – 42。
[3] Stringer, N.T., Lawhead, L,; Wilkerson, T.; Biggs, J., Rockefeller, G.D.，
and the M.S. and Ph.D. degrees in electrical engineering from
Real-time National Taiwan University, Taipei, Taiwan, in 1998, 2000,
transient testing and performance of transformer differential relays， and 2003, respectively.
IEEE , Volume: 2 , 8-12 Oct. 1995 Pages:1142 - 1150 vol.2。 At present, he works at Industrial Technology Research
[4] Bronzeado, H., Yacamini, R.,”Phenomenon of sympathetic interaction Institute and his research interests include distributed
between transformers caused by inrush transients”, IEE , Volume: generation systems and computer relaying.
142 , Issue: 4 , July 1995
Pages:323 – 329
[5] Yabe, K., “Power differential method for discrimination between fault and
magnetizing inrush current in transformers”, IEEE Transactions
on , Volume: 12 , Issue: 3 , July 1997 Pages:1109 – 1118
[6] IEEE Standard “Common Format for Transient Data Exchange
(COMTRADE) for Power Systems” , IEEE Std C37.111-1999 ,
[7] IEEE WG116 Report “Understanding Microprocessor-Based Technology
Applied to Relaying”, February 2004
[8] Casoria, S., P. Brunelle, and G. Sybille, "Hysteresis Modeling in the
MATLAB/Power System Blockset," Electrimacs 2002, École de
technologie supérieure, Montreal, 2002.
[9] K.S. Smith , C.Eng., MIEE ,”Transformer Inrush Studies for Wind Farm
Grid Connections”, International Conference on Power Systems
Transients (IPST’05 June 2005)
[10] Guzman, A.; Zocholl, S.; Benmouyal, G.; Altuve, H.J.,”a current-based
solution for transformer differential protection-part I: Problem Statement",
IEEE Transactions on Power Delivery ,Volume 16,October 2001
Page(s):485-491
[11] Guzman, A.; Zocholl, S.; Benmouyal, G.; Altuve, H.J.,”a current-based
solution for transformer differential protection-part II: relay description
and evaluation", IEEE Transactions on Power Delivery ,Volume
17,October 2002 Page(s):886-893
Li-Cheng Wu received his B.S and M.S. degrees in electrical
engineering from National Taiwan University of Science and
Technology, Taipei, Taiwan, in 1997 and 1999, respectively.
He is currently pursuing the Ph.D. degree at National Taiwan
University, Taipei, Taiwan. Between 1997 to 2002 he worked
as an electrical engineer in the Department of relay, Taiwan
Power Company.
His main research interests are power electronics, high voltage
test and power system protection.
Chih-Wen Liu (S’93-M’96-SM’02) was born in Taiwan, in
1964. He received the B.S. degree in electrical engineering
from National Taiwan University (NTU), Taipei, Taiwan, and
the M.S. and Ph.D. degrees in electrical engineering from
Cornell University, Ithaca, NY, in 1987, 1992, and 1994,
respectively.
Since 1994, he has been with NTU, where he is a Professor of
electrical engineering. His main research interests include
application of computer technology to power system
monitoring, protection, and control. His other research interests
include motor control and power electronics.
Shih-En Chien was born in Keelung, Taiwan in 1980. He
received his B.S. degree in electrical engineering from National
