Characteristics of Inrush Current of Present Designs of Power Transformers
Ramsis S. Girgis, Fellow, IEEE
Ed G. teNyenhuis, Member, IEEE
ABB Inc.
ABB Inc.
Abstract: Accurate calculation of peak and % 2nd harmonic
current in
order to design the relaying to properly differentiate between
inrush and short circuit incidents. Also, a proper calculation
of the minimum % ratio of 2nd harmonic content of inrush
current is an especially important parameter for this
differentiation.
of inrush current is critical to appropriate selection of relay
protection of a power transformer. In this paper, a
description is given of a rigorous calculation of magnitude
and wave-shape of inrush current as a function of the
transformer design parameters as well as parameters of the
system to which the transformer is connected. A comparison
is given between magnitudes of peak inrush currents
calculated using the presented calculation method and the old
formula commonly used in the industry. Also, advancements
made to transformer technology in the past three decades
have changed the characteristics of the transformer inrush
current. The second part of this paper presents the impact
of these design, material, and system parameters on the peak
value and minimum % ratio of 2nd harmonic content of inrush
current of transformers of small, medium, and large power
transformers. Parameters studied are core design induction,
core material, core joint geometry, power rating, winding
connections, and number of phases. These studies have been
performed using the newly developed calculation.
Keywords: Transformers, Inrush
Transformer cores, Magnetics
Current,
Remnant
In this paper, a description is given in section II of a newly
developed calculation of magnitude and wave-shape of
inrush current as a function of the transformer design
parameters as well as parameters of the system to which the
transformer is connected. A comparison is given in section
III between magnitudes of peak inrush currents calculated
using the presented calculation method and the old formula
commonly used in the industry. In section IV, dependence of
peak value and 2nd harmonic content of inrush current on
angle of energization are presented. Section V presents the
impact of a number of transformer design and core material
parameters on peak value and minimum % ratio of 2nd
harmonic content of inrush current of transformers of small,
medium and large power transformers.
Flux,
II. CALCULATION OF INRUSH CURRENT
I. INTRODUCTION
The simplified equation that has been used in the industry
to calculate the peak value of the first cycle of inrush current
in Amps is as follows:
Inrush Current is a form of over-current that occurs during
energization of a transformer and is a large transient current
which is caused by part cycle saturation of the magnetic core
of the transformer. For power transformers, the magnitude
of the first peak of inrush current is initially several times the
rated load current but slowly decreases by the effect of
oscillation damping due to winding and magnetizing
resistances of the transformer as well as the impedance of the
system it is connected to until it finally reaches the normal
exciting current value. This process typically takes several
minutes. As a result, inrush current could be mistaken for a
short circuit current and the transformer is erroneously taken
out of service by the over - current or the differential relays.
The transformer design and station installation parameters
affect the magnitude of the inrush current significantly.
Therefore, it is important to have an accurate calculated
value of the magnitude and other parameters of inrush
I pk =
2U
(ω ⋅ L )2 +
⎛ 2 ⋅ BN
⎜
⎜
R2 ⎝
+ BR − BS
BN
⎞
⎟
⎟
⎠
(1)
Where:
U
L
R
BR
BS
BN
= Applied voltage [Volts]
= Air-core inductance of the transformer [Henry]
= DC resistance of the transformer windings [Ohms]
= Remnant flux density of the core [Tesla]
= Saturation flux density of the core material [Tesla]
= Normal rated flux density of the core [Tesla]
In reality, the above equation does not give sufficient
accuracy since a number of transformer and system
parameters, which affect the magnitude of inrush current
significantly, are not included in the calculation. As well,
this equation does not provide information on the subsequent
oscillations throughout the duration of the inrush current
transient. An improved, more rigorous, calculation for inrush
current has been developed by ABB. This calculation
provides the magnitude of inrush current versus time t; hence
the entire wave-shape of the inrush current can be
_________________________________________________
Dr. Ramsis Girgis is presently the Technical manager at the
ABB Power Transformer plant, Saint Louis, MO
Mr. Ed teNyenhuis is presently the Technical manager of the
ABB TRES (Transformer Remanufacturing and Engineering
Solutions) organization located at Brampton, ON, Canada
1
1-4244-1298-6/07/$25.00 ©2007 IEEE.
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.
determined. The calculation incorporates the following
important transformer and system parameters, which have
been proven to have as much as 60% impact on the
magnitude of inrush current:
IV. EFFECT OF VOLTAGE ENERGIZATION ANGLE
ON INRUSH CURRENT PARAMETERS
Shown in Figure 2 below are calculated magnitudes of
peak inrush currents and corresponding 2nd harmonic values,
all as a function of voltage energization angle. It should be
noted that both the maximum magnitude of inrush current as
well as the minimum % ratio of the 2nd harmonic content
occur when the transformer is energized at the time instant
when the voltage is crossing the zero line, as shown in Figure
2 and Figure 3 below .
The magnetizing inductance of the transformer core
adjusted for the transient nature of the inrush current
phenomenon.
Impedance and short circuit capacity of the system.
Core geometry, winding configurations, and winding
connections in 3 phase transformers, e.g., 1- vs. 3-phase,
Y- vs. Delta windings connections, Grounded vs. non
grounded Y connections, etc.
4500
4000
Below in Figure 1, is shown the first 5 cycles of the inrush
current wave-shape for a large power transformer calculated
using the new method of calculation.
Peak current amps
3500
2000
1800
Current [Amperes]
1600
3000
2500
Peak of Inrush
2000
Peak of Second Harmonic
1500
1400
1000
1200
500
1000
0
0
800
600
20
40
60
Voltage angle °
80
Figure 2 – Calculated magnitudes of peak and 2nd harmonic
of inrush current
400
200
0
30%
0
0.02
0.04
0.06
Time [s]
0.08
0.1
25%
III.
% 2nd Harmonic / Peak
Figure 1 – Calculated Inrush Current Wave-shape for a 50
Hz Large Power transformer
MAGNITUDE OF PEAK INRUSH CURRENT
A comparison between magnitude of the peak of the first
cycle of inrush current as calculated by the old formula in
equation [1] above versus that calculated using the rigorous
ABB method is given in Table 1 below. As can be seen from
these values, including the above mentioned parameters
provides a much lower magnitudes of the first peak of inrush
current compared to that calculated using the old formula.
20%
15%
10%
5%
0%
Table 1 – Calculated First Peak of Inrush Current, Amps
Simplified Equation
New Equation
Example 1
4941
1984
0
Example 2
1755
1094
20
40
60
Voltage angle °
80
Figure 3 - % of 2nd Harmonic / Peak Inrush Current
2
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.
V. EFFECT OF TRANSFORMER DESIGN
PARAMETERS ON INRUSH CURRENT
size transformers, the peak inrush current can reach levels
greater than the SC current.
In order to study the impact of design features of today’s
power transformers on parameters of inrush current,
extensive calculations were made of ratio of peak inrush
current / rated current and minimum % ratio of 2nd harmonic
of inrush current for transformers at different flux densities,
core materials, and power capacities. This section presents
the results of this study. Also discussed is the effect of core
joint geometry.
Min % 2nd Harmonic vs Peak Inrush
30%
A. Effect of Core Induction
As shown in Figure 4 below, peak inrush current increases
as the design induction level increases. This is caused by
core saturation for a greater part of the voltage cycle. For the
same reason, the minimum % 2nd harmonic / peak inrush
current ratio decreases with induction as shown in Figure 5
below. Modern transformers generally operate at higher flux
density values since higher grain oriented steels are used
more and more. It thus results that modern transformers will
have higher inrush currents due to the higher rated design
induction value but lower minimum % 2nd harmonic / peak
inrush current ratio.
25%
20%
15%
10%
5%
0%
1
1.1
1.2
1.3 1.4 1.5 1.6
Flux Density [T]
1.7
1.8
1.9
Figure 5 - % Minimum 2nd Harmonic / Peak Inrush Current
Ratio for a 100 MVA Transformer
4.0
6.0
100 MVA
3.5
70 MVA
Inrush Current/Peak Rated Current
Inrush Current/Peak Rated Current
100 MVA
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.8 0.9
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Flux Density [T]
5.0
100 MVA
224 MVA
4.0
3.0
2.0
1.0
0.0
0.8 0.9 1
Figure 4 - Calculated Peak Inrush Current vs. flux density for
a 100 MVA Transformer
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Flux Density [T]
B. Effect of MVA
Figure 6 - Calculated Peak Inrush Current for Different Size
Transformers
In order to study the effect of MVA on the magnitude of
peak inrush current and % 2nd harmonic, calculations were
made for 3 transformers of 70, 100, and 224 MVA, for the
same core material. As can be seen in Figure 6, the ratio of
peak inrush current / rated load current is higher for smaller,
lower capacity, transformers. It follows that, for distribution
The MVA size has negligible impact on the % 2nd harmonic,
as shown in Figure 7, since the harmonic content is
dependent on the wave-shape itself which is in - turn a
function of only the rated flux density and parameters of the
core material, namely, the saturation flux density and the
remnant flux density.
3
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.
reluctance than a step-lap joint, it follows that a core with the
step-lap joint would have much higher magnitudes of peak
inrush current and a much lower minimum % of 2nd harmonic
/ peak current ratio than those of a core with a non step-lap
joint.
25%
4.5
20%
R Material
4.0
Inrush Current/Peak Rated Current
Min % 2nd Harmonic vs Peak Inrush
30%
15%
10%
70 MVA
100 MVA
5%
224 MVA
0%
1
1.1
1.2
1.3 1.4 1.5 1.6
Flux Density [T]
1.7
1.8
1.9
H & D Materials
3.5
3.0
2.5
2.0
1.5
1.0
0.5
nd
Figure 7 - % Minimum 2 Harmonic / Peak Inrush Current
Ratio for Different Size Transformers
0.0
0.8 0.9
C. Effect of Core material
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Flux Density [T]
Figure 8 – Calculated Peak Inrush Current versus Rated Flux
Density for Different Core Materials
In order to study the effect of core material on the
magnitude of peak inrush current and % 2nd harmonic,
calculations were made for two material types for the same
transformer. A new feature of modern transformers is the use
of Highly grain oriented (H) and Domain – refined (D)
electrical steel type materials which have a higher value of
saturation flux density, a larger linear portion of the
magnetization curve, and a lower remnance flux density
compared to Regular Grain Oriented (R) type materials.
Thus, these higher grain orientated materials would be
associated with lower peak inrush currents & higher
minimum % 2nd harmonic / peak inrush current ratios. This
can be seen in Figure 8 and Figure 9 below, respectively.
For the same flux density, the H material has a somewhat
lower magnitude of the peak inrush current but appreciably
greater minimum % 2nd harmonic / peak inrush current ratio
than the R material. As the Domain-refined materials are
basically highly grain oriented materials enhanced with
domain orientations, they have the same characteristics of
inrush current as those for the base highly grain oriented
material of these grades.
30%
Min % 2nd Harmonic vs Peak Inrush
H & D Materials
25%
R Material
20%
15%
10%
5%
0%
1.0
1.1
1.2
1.3
1.4 1.5
1.6
Flux Density [T]
1.7
1.8
1.9
Figure 9 - % Minimum 2nd Harmonic / Peak Inrush Current
Ratio versus Rated Flux Density for Different Materials
D. Effect of Core Joint Type
Until a decade or two ago, the non step-lap type joint was
commonly used in transformer cores, however modern
transformers use the step-lap type joint. Because of the high
reluctance of the core joints, the remnance flux density levels
of a transformer core are significantly lower than that of the
core material itself. As the non-step lap joint has a greater
E. Inrush current in 1- versus 3- Phase transformers
In a single phase transformer, the winding inrush current is
clearly the same as the line inrush current. In a three - phase
circuit, only one phase experiences inrush current. Hence,
the magnitude of the line current in a 3 – phase transformer
4
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.
will be almost equal to the inrush current of 1 - phase
transformer of 1 /3 its MVA capacity. However, the ratio of
inrush current / rated line current in a 3 phase transformer
will be 1 / SQRT (3) of the 1 - phase value of this ratio.
Shown in Figure 10 below is a comparison of peak inrush
current for a three - phase transformer and a single – phase
transformer having the same winding per phase and the same
core material, i.e. MVA of the 3 - phase transformer is 3
times that of the 1 - single phase transformer. The 3 phase
transformer is connected in Delta.
7.0
Inrush Current/Peak Rated Current
6.0
9.0
Single Phase
Inrush Current/Peak Rated Current
8.0
Energised Winding - Delta Connected
Energised Winding - Wye Connected
Three Phase
7.0
5.0
4.0
3.0
2.0
6.0
1.0
5.0
0.0
0.8 0.9
4.0
3.0
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Flux Density [T]
Figure 11 - Calculated Peak Inrush Current for transformers
with windings connected D /Y versus Y /Y
2.0
The % 2nd harmonic would not be impacted by the winding
connection or number of phases since as earlier discussed. It
is only a function of the rated flux density and material
parameters (saturation flux density, and the remnant flux
density).
1.0
0.0
0.8 0.9
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Flux Density [T]
Figure 10 - Calculated Peak Inrush Current ratio for a single
phase transformer and a Delta-connected 3 Phase
transformer
VI. CONCLUSIONS
The old formula for calculating peak of first oscillation of
inrush current of power transformers provides magnitudes as
much as twice the magnitudes calculated using the more
accurate equation recently developed by ABB. This
calculation accounts for a number of important transformer
and system parameters that significantly impact the
magnitudes and wave - form of inrush current. Predicting the
accurate peak inrush current is very critical in designing and
determining the settings of the over - current / differential
relaying used with a power transformer. Also, the new
calculation provides the function of inrush current versus
time throughout the duration of the transient as well as the
magnitude of the 2nd harmonic of the inrush current, which is
the parameter commonly used today to differentiate between
short circuit and inrush current occurrences, hence
preventing erroneously taken out a power transformer of
service by the over current or the differential relays.
It has been confirmed by this calculation that the
maximum magnitude of inrush current as well as the
minimum % ratio of the 2nd harmonic content occur when the
transformer is energized at the time instant when the voltage
is crossing the zero line
Also, in a Wye – connected winding, it can be shown that the
line inrush current is 2 / 3 of the peak inrush current of a
single phase transformer of 1/3rd of its MVA rating. The
same is true in a 3 - phase system made of three single phase
transformers connected in Delta. The line inrush current is 2
/ 3 of the peak inrush current of the single phase transformers
making up the system.
Additionally, in a 3 – phase transformer, connection of the
primary and secondary windings and the grounding of any
Wye connections will dictate the distribution of the
developed inrush current in one winding to the other phases
and the line currents. This is illustrated in Figure 11, where
the energized primary winding is Delta - connected versus
another where the energized winding is Wye - connected.
For both transformers, the secondary winding is connected in
an ungrounded Wye, which allows the currents in the
primary winding to redistribute between the phases. The line
current of the Wye connected primary winding will see the
full winding inrush current. For the delta connected primary
winding, the line current will be reduced since the inrush
current can enter the other phases.
5
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.
Inrush current parameters (Peak, 2nd harmonic and
duration) of today’s power transformers differ significantly
from those of older designs due to the use of higher grain
oriented core steels, the step-lap core joint type, and higher
rated design core induction values. This, in-turn, should
have a significant impact on selecting the proper relaying
protection for the transformer.
As presented in this paper, the study performed on the
impact of the design parameters of the transformer on the
parameters of inrush current showed the following:
VIII. BIOGRAPHIES
Dr. Ramsis S. Girgis (F'93) is
presently Technical Manager at the
ABB Power Transformer factory in St.
Louis, Missouri, USA. He is also the
leader of the global ABB R&D
activities in the Transformer Core
Performance area and Technical SM
activities for electrical steel. He is also
co-leader of the global ABB R&D
activities in the Transformer Noise and
Vibrations area. Dr. Girgis received his
Ph.D. degree from the University of
Saskatchewan, Canada, in Electrical Power Engineering in
1978. He has 40 years of R&D experience in the area of
power, distribution, and high frequency transformers,
rotating machines, and pulse power components. He has
published and presented over 60 scientific papers in IEEE,
IEE, CIGRE, and other international journals. He is
presently the chairman of the IEEE Transformers Subcommittee on Performance Characteristics. He is also a
contributing member of several working groups and
subcommittees in the IEEE Transformers Standards
Committee. He co-authored chapters in two electrical
engineering handbooks on transformer design and
transformer noise. He is the past Technical Advisor
representing the US National Committee in the IEC Power
Transformer Technical Committee (14).
1. At higher design induction levels, peak inrush current is
higher and the minimum % 2nd harmonic / peak inrush
current ratio is lower than those at lower flux densities.
2. For the same flux density, transformers with cores made of
Hi-B and Domain refined electrical steels have 15 – 20
% lower magnitude of the peak inrush current but over
30 % greater minimum % 2nd harmonic / peak inrush
current ratio compared to transformers with regular
grain oriented core steels.
3. For the same core material, higher MVA power
transformers have lower ratio of peak inrush current /
rated load current. The % 2nd harmonic is the same as it
is strictly determined by the type of core material and
the core operating induction level.
4. A core with the step-lap joint would have much higher
magnitudes of peak inrush current and a much lower
minimum % of 2nd harmonic / peak current ratio than
those of a core with a non step-lap joint.
Ed G. teNyenhuis (M’97) is
presently Technical Manager at
ABB
for
Transformer
Remanufacturing and Engineering
Services in Brampton, Ontario. Ed
was born in Barrie, Canada in 1966.
Ed received his B.A.Sc. degree from
the University of Waterloo, Canada,
in 1990 and his M.Eng. Degree from
North Carolina State University,
USA, in 2000, all in electrical
engineering. Ed has worked in the
power transformer industry for 16 years. His past experience
includes positions at ABB Power Transformers in Guelph
Canada, Ludvika Sweden, and at ABB Electrical Systems
Technology Institute in Raleigh, NC, USA. Ed has published
several technical papers in IEEE, SMM, and 2DM pertaining
to power transformers, Magnetics, and electrical steel. He is
presently Chairman of the IEEE Working Group on Loss
Measurement and Tolerances of power and distribution
transformers.
5. The ratio of inrush current / rated line current in a 3 phase
transformer is 1 / SQRT (3) of this ratio for the 1 - phase
transformer of the same power rating / phase.
6. In a Wye – connected winding, the line inrush current is 2
/ 3 of the peak inrush current of a single phase
transformer of 1/3rd of its MVA rating. The same is true
in a 3 - phase system made of three single phase
transformers connected in Delta.
7. Winding connections in 3 - phase transformers, whether it
is a Delta or a Wye, can have as much as 60% effect on
the magnitude of peak inrush current.
VII. ACKNOWLEDGEMENT
The authors would like to thank Mr. Asim Fazlagic for
contributing to the development of the calculation of inrush
currents in 3 - phase transformers. The authors would also
like to thank Mr. Mats Bernesjö for performing a number of
the inrush current design calculations presented in this paper.
6
Authorized licensed use limited to: IEEE Xplore. Downloaded on April 09,2010 at 07:18:07 UTC from IEEE Xplore. Restrictions apply.