Download Magnetic Saturation Effect of the Iron Core in Current Transformers

TRANSACTIONS ON ELECTRICAL AND ELECTRONIC MATERIALS
Vol. 18, No. 2, pp. 97-102, April 25, 2017
pISSN: 1229-7607 eISSN: 2092-7592
DOI: https://doi.org/10.4313/TEEM.2017.18.2.97
OAK Central: http://central.oak.go.kr
Magnetic Saturation Effect of the Iron Core in Current
Transformers Under Lightning Flow
Young Sun Kim
Department of Electrical and Electronic Engineering, Joongbu University, Goyang 10279, Korea
Received January 17, 2017; Revised January 21, 2017; Accepted January 31, 2017
A current transformer (CT) is a type of sensor that consists of a combination of electric and magnetic circuits,
and it measures large ac currents. When a large amount of current flows into the primary winding, the alternating
magnetic flux in the iron core induces an electromotive force in the secondary winding. The characteristics of a CT
are determined by the iron core design because the iron core is saturated above a certain magnetic flux density. In
particular, when a large current, such as a current surge, is input into a CT, the iron core becomes saturated and the
induced electromotive force in the secondary winding fluctuates severely. Under these conditions, the CT no longer
functions as a sensor. In this study, the characteristics of the secondary winding were investigated using the timedifference finite element method when a current surge was provided as an input. The CT was modeled as a twodimensional analysis object using constraints, and the saturation characteristics of the iron core were evaluated using
the Newton-Rhapson method. The results of the calculation were compared with the experimental data. The results of
this study will prove useful in the designs of the iron core and the windings of CTs.
Keywords: Current transformer, Iron core, Electromotive force, Surge, Finite element method, Fourier series
1. INTRODUCTION
magnetic field analysis was conducted while considering the
magnetic nonlinearity of the iron core. Furthermore, the area
in which the induced electromotive force was generated was
regarded as a winding using the variation of the electric scalar
potential as a constraint condition. To express the surge current
as a function, the amplitude of the frequency harmonics was
extracted through the development of the 8/20 μs waveform of
the standard surge wave as a Fourier series and its application to
the surge analysis [3-6]. In the surge current analysis, 1,000 A and
5,000 A were applied as input currents to the primary winding of
the CT before the magnetic core became saturated, and 50,000
A was also applied, at which point the magnetic core became
saturated [7,8].
An experiment was conducted using three through type CTs,
and the results were compared with those from the numerical
analysis. At 1,000 A and 5,000 A before the saturation, the shapes
of the induced electromotive forces are similar. At 50,000 A, only
the numerical analysis results could be evaluated because the
experiment could not be conducted. The proposed algorithm
will be useful for the design of CTs in accordance with their use
and purpose while the characteristics of the electromotive power
characteristics are considered.
A current transformer (CT ) is composed of a primary
winding through which the current flows, a magnetic core,
and a secondary winding in which an induced electromotive
force is generated. In addition, a CT has electric and magnetic
currents that induce an electromotive force in the secondary
winding. When a surge, such as an inrush current, is input into
the primary winding of the CT, the magnetic core becomes
saturated and the magnetic flux density no longer increases.
This distorts the induced electromotive force of the secondary
winding and causes the malfunction and time delay of the
device [1-3].
A two-dimensional magnetostatic field analysis was
conducted using the time difference finite element method,
and the results were compared with the experiment results. The
Author to whom all correspondence should be addressed:
E-mail: [email protected]
Copyright ©2017 KIEEME. All rights reserved.
This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial
License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted noncommercial use, distribution,
and reproduction in any medium, provided the original work is properly cited.
97
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98
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
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derivative
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s 
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over
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is
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in
Fig.
1.
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equation
for
the
electromagnetic
A

original
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between
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temporal
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magnetic field,
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S stEq.
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The
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When
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is
When a conductor
or
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the micro-time
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can
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as
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method
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dsit discretizes
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based present
on by
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In
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
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A
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under
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that
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(eddy
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is
induced
it
by
temporal
∇φ
substituted
in
the
governing
equation,
is
follows:
governing
equation
of thedstime-varying
field becomes as(4) eliminated and the
dimensional field changes over time is shown in Fig. 1.
.




governing
of
the time-varying
field becomes as
potential
canaxis,
be equation
expressed
as follows:
analyzed
by the
△t of the
micro-time
and itmethod
changes
linearly
within
each
time
segment.
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sdiscretizes
follows:
changes in the magnetic field, and the direction
of the
magnetic
governing
of the
the time-varying field becomes as follows:
t enables
Sequation
In thesolutions.
the
adifferential
nonlinear equation
analysis including
transient
However,
this gradient of the electric scalar
under thefollows:
assumption
that the
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
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
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1

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. enables
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as follows: ds  J .
method
several
disadvantages,
asThis
a long
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linearly
within
each time
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A
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When
of the
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s winding
A
1the
Stwo-dimensional
s 
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time,
and flux
the
accuracy
solution
onthis
the
a plane)
nonlinear
analysis
A
1Sis2constraint
magnetic field. The relationship between
the (x-z
magnetic
andincluding
theof thetransient
tA
∇φ
tAds
1governing
2dependent
solutions.
A
tHowever,
JJs . . and(5)(5)
A
(5)
substituted
in
the
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eliminated
the(4)

A

ds
.S s t




ds
s
has
several
disadvantages,
such
as
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long
calculation
method
regarding
the
selection
of
△t.

t

b) Eddy current
and distribution
of the
magnetic flux
induced
current
when the
magnetic
flux for a two-dimensional field When
the
t time-varying
S s t fieldwinding
governing
equation
oftthe
becomes
S sof
the 
constraint
is as
time, and the accuracy of the
solution
is dependent
on two-dimensional
the
follows:
changesfluxover
time
is shownvarying
in Fig.
1.
substituted
the governing
equation,
∇φ is eliminated and the
2.3
finite
method regarding
ofTime
△t.in
t  tthe selection
t difference
t  t
t element analysis
Fig. 1. Magnetic
and eddy
current in time
fields.
b) Eddy current
and distribution
of the magnetic
flux
Time
AWhen
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A time-varying
the
ofelement
the two-dimensional
 A  a time-governing
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 equation
ofthe
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as t is
2.3
difference
finite
method
discretizing
derivative
termwinding
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When a current density Js is given in an analysisregion,
, the
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1
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)
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2.3
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substituted
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iselement
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and
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model
(x-z plane) 



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
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
A
1

a current
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in
an
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a
The
method
discretizing
the
time
derivative
term
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t the
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
t
t
based
on
the
time
difference
in
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(5)
is
a
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2.3
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
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t
t
Fig.When
1.varying
Magnetic
flux
and
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in
time
varying
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
t

t

t
field is formed by the temporal change in the current,
and  
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method
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time derivative
equation

the
dsfield
 J term
. ∂A/∂
(5)t
A 
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A
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governing
the
time-varying
s becomes
time-varying field is formed by the temporal change in the
that
divides
the
temporal
of
to be as
based
the
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(5)sthe
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,ininEq.
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magnetic
(
1

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


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t
S

based
on
the
time
difference
Eq.
(5)
is
a
calculation
method
the
induced
current
flows
are
due
to
the
effect
of
this
field,
 t 
 follows:
1by the
current,
the induced
flows in
areandue
to the region,
effect (x-z
ofa plane)
When and
a current
densitycurrent
Js is given
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Analysis
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]{A}t ,
(7)

A
1 canthe


2
1  Ni N j Ni N j 
e
 current
A  is ignored,

  J s . equation of(2)the
displacement
the governing
where,
S
dxdy


t


t
t
ij
 field can beexpressed
t

time varying
bythe following Eq. (2) :
C]{xA}x {F
(7)
y ]{ A} ,
y}  [C
A
1
where, [S 






2. MATHEMATICAL MODELING








 









 
 
 
 



 
 
 
 
 
 


 
 
 
 


(b)



 2 A  
    J s .
 1
t  A  

  2 A  
    J s .

 t


(2)
1  N N j Ni N j  
e
Sij where,
dxdy
   i

e  1 x  Nx Ny Ny N 
j
j
(2)
i
i
Sij   
dxdy

   x x
y y 

Cije    Ni N j dxdy
Cij   t Ni N j dxdy
 t
e
Fie   Ni J s dxdy .

Fe i  Ni J s dxdy .
Cij    Ni N j dxdy
 t
force
2.4 Electromotive
e Electromotive
Fig. 2, the linkage
flux inside the core that is induced by
force
2.4In
F Fig.
dxdy
. expressed
i J slinkage
 2,Ncurrent
theiInprimary
can be
using
vector
the
flux
inside the
corethe
thatmagnetic
is induced
by
e
Fig. 1. Magnetic flux and eddy current in time varying fields. (a)
Analysis model (x-z plane) and (b) eddy current and distribution of
the magnetic flux.
2.2 Constraints on the induced current in the
secondary coil
In the two-dimensional finite element analysis, the induced
current region consists of two windings in opposite directions,


N
t
t
Ea  l N j Aat  Aat
S
Ea  l a j Aa  Aa
Sa
.
.
2.5 Fourier series expansion for the
N
t
t
Fourierseries
series
for
a randomfor
2.5The
the
. period
j Aexpansion
EFourier
a l
a   Aa 
S a equation
The Fourier
series for that
a random
periodth
develop
an
describes
follows: an equation that describes th
develop

follows:

2.5 Fourier series expansion for the su
2.4
Electromotive
force
the
primary
potential,
as current
follows:can be expressed using the magnetic vector
f ( x)  a   (an cosperiodic
nx  bf
The Fourier series0 for a random
potential, as follows:
f ( x)  a0  nthat
1 ( an cos nx  bn
develop an equation
describes the
2.4 Electromotive force
n 1
In Fig. 2,
the flux
linkage the
flux inside
the core
thatwhere
is induced
a0 denotes by
the magnitude
of the dc c
In Fig.2,the
 Nlinkage
B( x, y)inside
 ds   core
N that
A(isx,induced
y)  dl ,by (8) follows:
where
the magnitude
the cosin
dc c
bn are athe
coefficients
of the sineofand
0 denotes
scurrent
coil
primary
can
be
expressed
using
the
magnetic
vector
thethe
primary
current
can
be
expressed
using
the
magnetic
vector
   N B( x, y)  ds   N A( x, y)  dl , (8) bFigure
coefficients
of the
and cosin
3)shows
the 8/20
μcos
ssine
standard
surg
n are the
s
where as
B is
the magnetic
flux density of coil
the core, A denotes the
potential,
follows:
f
(
x

a

(
a
nx

b
potential,
as follows:
n si
Figure
3 shows
8/20 nμThis
s standard
were used
in 0thethe
testing.
means surg
that
where
B isvector
the magnetic
density
of the
core, A
the
magnetic
potentialflux
of the
winding
region,
anddenotes
± denotes
n 1
were
used current
in the testing.
means thati
magnetic
vector
of thecurrent
windinginregion,
and ± denotes where
the direction
ofpotential
the induced
the two-dimensional
the asurge
reachesThis
its maximum
0 denotes the magnitude of the dc com
direction
  N ofB(the
x, yinduced
)  ds current
 N inAthe
( x, two-dimensional
y)  dl , (8) b are
the
analysis.
the
surge
current
reaches
its
maximum
(8)
point
when
it becomes
halfsine
of the
the
coefficients
of the
andmaximum
cosine is
t
n
s
coil
analysis.
point3when
it becomes
of the maximum
Figure
shows
the 8/20 half
μs standard
surge
where B is the magnetic flux density of the core, A denotes the
wereAused
in the testing.
magnetic
of the winding
and ±of
denotes
wherevector
B ispotential
the magnetic
fluxregion,
density
the core,
denotes
the This means that th
the direction of the induced current in the two-dimensional
the surge current reaches its maximum is 8
magnetic
vector
potential
of
the
winding
region,
and
±
denotes
the
analysis.
point when it becomes half of the maximum is






direction of the induced current in the two-dimensional analysis.





Cij  
e

E l
N
 t Ni NNj dxdy
B( x, y)  ds   N  A( x, y)a  dl S,a

t
t

(11)
of the dc component, and an and
j Aa where
Aa . a0 denotes the magnitude
(8)
bn are the coefficients of the sine and cosine terms, respectively.
e
N
t
t
e
F
Ni isJ N
dxdy
.
Figure
i  B
s the
. 3 shows the 8/20
(11) μs standard surge current waves that

j

A
 Aafor
E
l
where
magnetic
flux
density
of
the
core,
A
denotes
the
C
N
dxdy



a
a
ij
the surge inflow
2.5 Fourier series
 t i j
S a expansion
were
used function
in the istesting.
magnetic vector potential of the winding region,The
and
± denotes
Fourier
series for a random periodic
used to This means that the time point when
e
develop an equation that the
describes
surge current,
as its maximum is 8 μs, and the time
Electromotive
2.4F
J s force
dxdy
.
the
of the
induced current in the two-dimensional
surgethe current
reaches
i direction
theNilinkage
follows:
2.5
Fourier
series expansion for the surge inflow
In Fig. 2,Trans.
flux Electron.
inside the core
that is18(2)
induced
Electr.
Mater.
97by(2017):
Y. S. Kim
analysis.
99
point
when
it
becomes
half
The Fourier series 
for a random periodic function is used to of the maximum is 20 μs.
the primary current can be expressed using the magnetic vector
develop
describes
surge current,(12)
as
potential,
as follows: force
f ( xan
)  equation
a0   (that
an cos
nx  bthe
2.4 Electromotive
n sin nx) ,
s
coil
In Fig. 2, the linkage flux inside the core that is induced by
the primary current can be expressed using the magnetic vector
 as N
B( x, y)  ds   N A( x, y)  dl , (8)
potential,
follows:
s
coil


where B is the magnetic flux density of the core, A denotes the
magnetic vector potential of the winding region, and ± denotes
   N B( x, y)  ds   N A( x, y)  dl , (8)
the direction of sthe induced current incoil
the two-dimensional
analysis.
where B is the magnetic flux density of the core, A denotes the
magnetic vector potential of the winding region, and ± denotes
the direction of the induced current in the two-dimensional
analysis.




follows:
n 1
Table
the harmonics for a lighting surge with the

where a0 denotes the magnitude
of the 1.
dc Coefficients
component, and aof
n and
f (coefficients
x)  a0  of the
(ansine
cosand
nxcosine
A bmaximum
nxrespectively.
) , current
(12) (type: 8/20 μs).
bn are the
terms,
50,000
n sin
n 1 μs standard surge current waves that
Figure 3 shows the 8/20
Sine
Cosine
whereused
a0 denotes
magnitude
of the that
dc component,
and awhen
were
in the the
testing.
This means
the time
point
n and
bn are
the current
coefficients
of the
and Order
cosine
respectively.
Coefficients
Order
Coefficients
μs, and
the
time
the
surge
reaches
itssine
maximum
is 8terms,
Figure
3 shows
the 8/20
standard
surge
that
point
when
it becomes
half μofs the
maximum
20 μs. waves20,870
a1 iscurrent
b1
-6,330
were used in the testing. This means that the time point when
3,280
b2
-6,530
a
the surge current reaches its maximum 2is 8 μs, and the time
a3 is 20 μs.
340
b3
-3,700
point when it becomes half of the maximum

a4
-265
b4
-1,300
a5
-140
b5
-800
a6
-60
b6
-605
a7
-145
b7
-445
a8
-120
b8
-245
a9
80 wave used in the
b9 numerical analysis
-180 (8/20
Fig. 3. Standard
surge current
a
0
b
-155
10
10
μs).
Fig. 2. Schematic diagram of the magnetic flux linkage to the
Fig. 2. Schematic diagram of the magnetic flux linkage to the secondary
secondary winding to calculate the induced voltage.
Fig. 3. Standard surge current wave used in the numerical analysis (8/20
winding to calculate the induced voltage.
For the harmonic analysis of the surge waveform, the Fourier
Figure
shows thefor
8/20
standard
current waves
series
was3developed
theμscase
where surge
the maximum
currentthat
is
the
harmonic
ofwere
the
the
Fourier
used
in the
testing.
meansfor
that
the
time point when
the
Standard
surge analysis
current wave
usedsurge
in
thewaveform,
numerical
analysis
(8/20This
The induced emotive force is calculated Fig.
byFor3.the
temporal
1
A.
The
use
of
the
input
current
the
electromagnetic
field
The induced emotive force is calculated by theseries
temporal
change
was developed
for the case where the maximum current is
μs).
surge current
its maximum
8 μs, and the
time
when
change
theofforce
magnetic
flux
intothethe
the
iron core.
The
analysis
its reaches
multiplication
by theismaximum
value
ofpoint
the actual
The
inducedof
emotive
is calculated
by
temporal
1 A.induced
The
use voltage
of in
thethe
input current
for theiselectromagnetic
field
Fig.
2. Schematic
diagram
the magnetic
flux
linkage
secondary
of
the
magnetic
flux
in
the
iron
core.
The
voltage
it
becomes
half
of
the
maximum
is
20
μs.
change
of calculate
the in
magnetic
fluxvoltage.
in the iron
core. The
voltage
winding
to
the
induced
analysis
is its
multiplication
the
maximum
value
of
the
actual
For the
the
harmonic
analysisby
of
the
surge
waveform,
the
Fourier
induced
the
secondary
winding
is expressed
by
temporal
surge current. Table 1 lists the magnitudes of the harmonics
secondary
winding
is expressed
temporal
change
of the
induced
in the secondary
winding
is expressed byby
thethe
temporal
current.
Table
1forlists
the For
magnitudes
of the harmonics
series
was developed
the case
wherethe
the harmonic
maximum
current
is
analysis
the surge
Fourier
change
of emotive
the magnetic
flux
inasaby
closed
loop, assurge
follows:
when
the
maximum
surge ofcurrent
is waveform,
50,000 A.theThe
dc
change
of
the magnetic
flux
in a closed
loop,as
follows:
The
induced
is calculated
the temporal when
the use
maximum
surge
current
is 50,000
A. The field
dc
magnetic
flux in
aforce
closed
loop,
follows:
1 A. The
of the input
current
for the
electromagnetic
series
was
developed
for
the case
change of the magnetic flux in the iron core. The voltage component
component
this
is 22,305
A. where the maximum current
in this
case is 22,305
A. maximumin
analysis is its
multiplication
by
the
value
of case
the actual
Fig. 2. Schematic diagram of the magnetic flux linkage to the secondary
winding to calculate the induced voltage.
μs).
induced in the secondary
winding is
A. The use
of harmonics
the input current for the electromagnetic field
the1magnitudes
of the
d
d expressed by the temporal surge current. Table 1 lists is
,
(9)
A  dl
N
 dsina N
(9)
changeEofa the
magneticBflux
closed loop,
as follows:
when
maximum
current for
isisa50,000
A.surge
Thewith
dc
Table
of surge
the harmonics
lighting
analysis
its
multiplication
by the maximum value of the actual
, 1.theCoefficients
(9)
dt c
adt s
Table
the harmonics for a lighting surge with
component
this case is
22,305
A. 1.
s
c
the
50,000 Ainmaximum
current
(Type:
8/20Coefficients
μs). Table 1 of
where N is the number of turns, B is the linkage flux density,
surge
current.
lists
the magnitudes of the harmonics when
d
d
Sine
Cosine
the 50,000 A maximum current (Type: 8/20 μs).
and where
s isEtheN
area
ofthe
the
Stokes’
theorem,
number
turns,
B ,isB
theislinkage
flux density,
and s is
(9)linkage
Nisisthe
B
ds  NofUsing
A
winding.
 dl
where
N
number
of
turns,
thethe
flux density,
theOrder
maximum
surge
current
is 50,000 A. The dc component in this
a
Table
of the harmonics
for a lighting
surge
with
s
c
Order1. Coefficients
Coefficients
Coefficients
dt
EMF equation candt
be rewritten
as follows:
Sine
Cosine
the
area
ofthe
thearea
winding.
Using
Stokes’Using
theorem,
the
EMF
equation
the
50,000
A
maximum
current
(Type:
8/20
μs).
and
s
is
of
the
winding.
Stokes’
theorem,
the
case
22,305
A. -6,330
a1
20,870
bis
where N is the number of turns, B is the linkage flux density,
1
Sine
Cosine
rewritten
as
follows:
Order
Coefficients
Order
Coefficients
a2
3,280
b2
-6,530
andcan
s is be
theequation
area
winding.
Using Stokes’
theorem, the
EMF
be rewritten
as follows:
N ofdthecan
Order
Coefficients
Order
Coefficients
a3
340
b3
-3,700
EMF equation
ds 
Az ds  , (10)
Ea  l can be rewritten
 S  Aasz follows:
a
20,870
b
-6,330
1
1
S

aa41
-265
bb41
-1,300
a

S a dt  a
20,870
-6,330
a2bb52
3,280
b2
-6,530
aa52
-140
-800
3,280
-6,530
N d
 , (10)
aa63
-60
bb63
-605
340
-3,700
a
340
b
-3,700
 length

Az dswinding
A
ds
l

3
3
(10)
where lE
isathe
of
the
secondary
region,
S
+
is
the
z
, (10)
-145
bb74
-445
aS dt  Sa 
z a
zaa74
Sa 
-265
-1,300
Sa 
Sa 
a area in the positive direction,
area of the winding
and Sa- is the
a
-265
b
-1,300model
A
through-type
CT
was
selected
as
the
numerical
analysis
4
4
a
-120
b
-245
8
8
a
-140
b
-800
5
5
area of the winding area in athe negative direction. The above
aa96
80
-180
-140of the CT. First,b5the primary current
-800for the
-60
-605
5bb96 surge analysis
forathe
equation
can
be
reorganized
using
the
complex
approximation
where
l
is
the
length
of
the
secondary
winding
region,
S
+
is
the
the
where l is the length of the secondarya winding region,
Sa+ is-145
aa107
0
-155
-445
a6bb107
-60 was inputbas
6 a sinusoidal ac-605
experimental
verification
voltage. A
method
area of as
thefollows:
winding area in the positive direction, and Sa- is the
a8 Sa- S
b
-245
where
is the
length
of in
thethe
secondary
winding region,
is-120
the
isa+
the
area
area
of lthe
winding
area
positive direction,
and
a7b89current was also
-145applied to analyze
b7 the characteristics
-445 of the
area of the winding area in the negative direction. The above 3. NUMERICAL
a9
80
-180
surge
ANALYSIS
of
the
area using
in
the
negative
direction.
area
ofwinding
thereorganized
winding
area
the positive
direction,
and Sequation
3 TheAaabove
equation
can
be
thein
complex
approximation
a- is the
-155
a8b10as thefield
-120
b8
-245
numerical
analysis and the induced
10through-type CT0 was selected
magnetic
distribution
electromotive
force.
method
follows:
can
reorganized
complex
approximation
method
as
areaasbe
of
the windingusing
area the
in the
negative
direction. The
above
d
d
E  N  B ds  N  A  dl
dt
dt




N d
E l 
  A ds  
S dt  
3. NUMERICAL ANALYSIS
A ds 

a9
3. NUMERICAL
ANALYSIS
follows:
equation can be reorganized using the complex
approximation
a10
3
method as follows:
N
t
t
j Aa  Aa
Ea  l
is induced by
magnetic vector
is induced by
magnetic vector
, y)  dl , (8)
A denotes the
, (8)
,and
y) ±dldenotes
wo-dimensional
A denotes the
and ± denotes
wo-dimensional
to the secondary
temporal
tothe
the secondary
. The voltage
y the temporal
the temporal
ollows:
. The voltage
y the temporal
(9)
llows:
e flux density,
’ theorem, (9)
the
A through-type CT was selected
the numerical
3.1asAnalysis
model

.
(11)


(11)
Sa
N
t
t
j Aa  Aa .
Ea  l series
2.5 Fourier
S a expansion for the surge inflow
80
0
analysis
(11)
The2.5
Fourier
series forseries
a randomexpansion
periodic function
Fourier
foris used
the tosurge inflow
develop an equation that describes the surge current, as
follows:
Fourier series expansion for the surge inflow
2.5
Fourier
forperiodic
a random
 series
The The
Fourier
series for
a random
functionperiodic
is used to function is used to
develop
equation
describes
surgethe
as
f ( xan) an
a0equation
 that
(an cos
 bthe
)current,
, surge
(12)
develop
thatnxdescribes
current, as follows:
n sin nx
follows:
n 1

where a0 denotes the magnitude of the dc component, and an and
f ( xcoefficients
)  a0  of (the
ansine
cosand
nx cosine
 bn sin
nx)respectively.
,
(12)
bn are the
terms,
(12)
n 1 μs standard surge current waves that
Figure 3 shows the 8/20
where
a0 denotes
magnitude
of the dc
component,
and awhen
were used
in thethe
testing.
This means
that
the time point
n and
bthe
the coefficients
of thethe
and cosine
respectively.
where
a0 denotes
magnitude
dc time
component, and an and
n are
s, the
and
the
surge
current
reaches
itssine
maximum
is terms,
8 μof
Figure
3 shows
the 8/20
s standard
point
it becomes
halfμof
the
20 μcosine
s.waves that
bnwhen
are
the
coefficients
ofmaximum
thesurge
sineiscurrent
and
terms, respectively.
were used in the testing. This means that the time point when
the surge current reaches its maximum is 8 μs, and the time
point when it becomes half of the maximum is 20 μs.


b9
b10
-180
-155
3. NUMERICAL
ANALYSIS
A commonly used
model was selected to investigate the
A through-type
CTsaturation
was selected
numerical
analysis
characteristics
of the
and as
thethe
induced
electromotive
force of the iron core when a surge is applied to the CT. A twodimensional time varying field finite element analysis was
conducted using the time difference method. When considering
the magnetic saturation characteristics of the soft iron of the core,
the hysteresis curve shown in Fig. 4 was used. To apply the input
current to the primary coil, the surge current waveform that was
developed into the Fourier series was used.
Figure 5 shows the distribution of the shape and the equipotential line distribution of the analyzed CT. The specific
dimensions and simulation parameters are listed in Table 2.
Fig. 3. Standard surge current wave used in the numerical analysis (8/20
μs).
the harmonic
analysis
of the
the Fourier
Fig.For
3. Standard
surge current
wave
usedsurge
in the waveform,
numerical analysis
(8/20
series was developed for the case where the maximum current is
μs).
1 A.
The3.use
of the input
current
for the electromagnetic
Fig.
Standard
surge
current
wave used infield
the numerical analysis
For theisharmonic
analysis by
of the maximum
surge waveform,
analysis
its multiplication
value ofthe
theFourier
actual
(8/20 μs).
surge was
current.
Table for
1 lists
the where
magnitudes
of the harmonics
series
developed
the case
the maximum
current is
1when
A. The
of the input
current
for the
theusemaximum
surge
current
is electromagnetic
50,000 A. Thefield
dc
analysis
is its
by the
component
inmultiplication
this case is 22,305
A.maximum value of the actual
surge current. Table 1 lists the magnitudes of the harmonics
when
theCoefficients
maximum ofsurge
current is
A.surge
The with
dc
Table 1.
the harmonics
for 50,000
a lighting
component
in maximum
this case iscurrent
22,305(Type:
A.
the 50,000 A
8/20 μs).
Sine
Cosine
Fig. 4. Hysteresis curve used in the time difference finite element
analysis.
Trans. Electr. Electron. Mater. 18(2) 97 (2017): Y. S. Kim
100
(a)
3.3 Surge analysis
(b)
Fig. 5. (a) Analysis model and (b) distribution of the magnetic flux in
the current transformer.
The time difference finite element analysis was conducted using
the coefficients of the surge current waveform that was developed
using the Fourier series. Figure 7 shows the lines of the magnetic
force at specific times based on the surge current in the results of
the magnetic field analysis.
Figure 8 shows the magnetic flux density distribution in the CT
core when the surge current of 8/20 μs and the maximum value of
50,000 A were applied to the primary winding of the CT. Because
the induced coil part (EMF part) generates a magnetic field in the
opposite direction via the induced current, the magnetic field is
smaller than the core part. The magnetic flux density appeared the
largest near 8 μs, which is the maximum input value of the inrush
current.
Figure 9 shows the instantaneous induced EMF of the
secondary winding when the maximum values of the surge input
current are 1,000 A and 5,000 A. Figure 10 shows the waveforms
of the input current and the induced EMF when the maximum
value of the input current is 5,000 A. In this case, the induced EMF
is large in the early stages when the surge was increasing rapidly,
and a negative induced EMF appears in the part where the surge
decreases.
Table 2. Specifications of the analyzed current transformer.
Spec.
Outer diameter of core [mm]
Inner diameter of core [mm]
Diameter of primary conductor [mm]
Diameter of EMF coil [mm]
Relative permeability (linear region)
Conductivity of EMF coil [S/m]
Primary current (time harmonic) [A]
Frequency of primary current [Hz]
Surge current (max.) [A]
Dimension & Values
63
44
6
1.5
1,000
5 × 107
500
60
5 × 104
(a)
(c)
(b)
a) 2 μs
a) 2 μs
(d)
b) 8 μs
b) 8 μs
3.2 Time difference finite element analysis for the AC
field
The numerical analysis for the ac magnetic field was analyzed
using the time difference finite element method.
Then, the induced EMF characteristics were investigated when
the maximum input sine-wave current is 500 A. Figure 6 shows the
primary current and EMF wave of the secondary winding.
Because the ac field was analyzing using the time difference
finite element analysis, the size of the induced electromotive
force is approximately 0.07 V, and the phase of the induced
electromotive force is behind the input current by approximately
90°.
c) 20 μs
d) 34 μs
Fig. 9. Insta
Fig.
9. for
Insta
inflow
al
inflow for a la
c) 20ofμsthe magnetic flux density
d) 34 μsin the core with
Fig. 7. Distribution
respect
to
the
time
during
the
surge
inflow:
not
Fig. 7. Distribution of the magnetic flux density in (a)
the the
core core
with is
respect
Distribution
of the
magnetic
flux
density
core
with respect
saturated
in the
stage
in 2 μs,
saturated
state
with
1.58
T
toFig.
the7.time
duringinitial
the
surge
inflow:
a)(b)
the
coreinisthe
not
saturated
in the
to thethe
time
during
the is
surge
a) theincore
notthe
saturated
in the
when
surge
inflow
at itsinflow:
maximum
8 μs,isthe
(c)
surge
inflow
initial
stage,
b) saturated
state
with
1.58
[T] when
surge
inflow
is at
initial stage, b) saturated state with 1.58 [T] when the surge inflow is at
is
of its maximum
value
andisthe
is not
saturated
inand
20 μs,
itshalf
maximum,
c) the surge
inflow
halfcore
of its
maximum
value
the
its maximum, c) the surge inflow is half of its maximum value and the
core (d)
is not
d) the
endinflow
stage of
surge inflow
(max.:
and
the saturated,
end stageand
of the
surge
in the
34 μs (max.:
50,000
A,
core is not saturated, and d) the end stage of the surge inflow (max.:
50,0008/20 μs).
A, wave: 8/20 μs).
wave:
50,000 A, wave: 8/20 μs).
Fig. 10.
10. InI
Fig.
electromotiv
electromotive
Fig.
parts (core
(core part
part and
and
Fig. 8.8. Magnetic
Magnetic flux
flux density
density in
in the
the specific
specific two
two parts
EMF
EMFpart)
part)with
withrespect
respect to
to time.
time.
Fig. 6. Primary current (max.: 500 A, freq.: 60 Hz) and electromotive
force of the secondary windings.
Fig.Figure
8. Magnetic flux density
in the specific two parts (core
EMFpart
of and
the
Figure 99 shows
shows the
the instantaneous
instantaneous induced EMF
of
the
EMF
part)
with
respect
to
time.
secondary winding when the maximum values of the surge input
secondary winding when the maximum values of the surge input
current
shows the
the
current are
are 1,000
1,000 A
A and
and 5,000
5,000 A. Figure 10 shows
waveforms
when the
the
waveforms of
of the
the input
input current
current and the induced EMF when
maximum
this case,
case, the
the
maximumvalue
value of
of the
the input
input current
current is 5,000 A. In this
induced
surge was
was
induced EMF
EMF isis large
large in
in the
the early stages when the surge
increasing
appears in
in the
the
increasing rapidly,
rapidly, and
and aa negative
negative induced EMF appears
4. EXPERIM
EXPERI
4.
To
verify
To verify
and the
the algo
alg
and
based on
on t
based
electromoti
electromotiv
compared bb
compared
current teste
test
current
measureme
measuremen
the conduct
conduc
the
performed
performed
winding of
of
winding
Specs
Winding ratio
Trans. Electr. Electron. Mater. 18(2) 97 (2017): Y. S. Kim
(a)
Model 1
Model 2
Model 3
75:5
80:5
100:5
Class
3.0
3.0
3.0
Frequency [Hz]
50/60
50/60
50/60
5101
1,150
2nd current [A]
5
5
Max. voltage [V]
1,150
1,150
Table
Specifications
of the load 17
current tester.17.5
Inner3.dia.
of core [mm]
Outer dia. of Specs
core [mm]
Power
Width ofInput
corevoltage
[mm]
Output
current
Radius of core [mm]
Timer
No. of turns
(a)
24.5
23
0.5
14
(b)
Values
27.5
1.2 kVA
1φ AC22
220 V, 60 Hz
1φ AC
0.50 ∼ 400 A
Set. 99 h 59 min.
17.5
27.5
22
0.5
15
20
(c)
(b)
a)
b)
c)
Fig.CTs
12.used
CTs in
used
the experiment:
a) 75:5,
80:5,
and
100:5.
Fig. 12.
theinexperiment:
(a) 75:5,
(b) b)
80:5,
and
(c)c)100:5.
First, for the experiment to measure the electromotive force
induced
electromotive force of the secondary winding was measured
Specs
Values
with a digital multi-meter while
current
primary
Modelthe
1 input
Model
2 to the
Model
3
winding
was varied
range of 0 A 100:5
to 400 A
Winding
ratio over the ac-maximum
75:5
80:5
for the three
models.
Class
3.0
3.0
3.0
The
saturation
induced electromotive
Frequency
[Hz] characteristics
50/60 of the 50/60
50/60
5 The
force 2nd
forcurrent
the [A]
three models5 are shown5 in Fig. 13.
Max. voltageof
[V]the induced
1,150
1,150force can1,150
characteristics
electromotive
be seen
Inner dia.
core [mm]current because
17
17.5
17.5
through
theof induced
the voltage
is proportional
Outer
dia.
of
core
[mm]
24.5
27.5
27.5
to the current.
Width of core [mm]
23
22
The
experiment results show
that the22secondary induced
and 4.saturation
characteristics
theexperiment.
CT, the
Table
Specifications
of the CTs usedof
in the
Fig. 9. Instantaneous induced electromotive force during the surge
inflow for a large current of: (a) 1,000 A and (b) 5,000 A (type 8/20 μs).
Radius of core [mm]
No. of turns
0.5
14
0.5
15
0.5
20
Fig. 10. Input surge current (max.: 50,000 A, type: 8/20 μs) with
electromotive force during the surge inflow.
4. EXPERIMENT
To verify the saturation characteristics of the magnetic core and
the algorithm of the time difference finite element method based
on the CT capacity, the waveforms of the induced electromotive
force of the secondary winding in each case were compared by way
of an experiment. Figure 11 shows a load current tester, which is
the input device that was used for the measurement of the induced
electromotive force of the CT and the conducting saturation
experiment. This experiment was performed while varying the
Fig. 11. Experimental setup for measuring the electromotive force of
the CTs.
Fig. 13. Saturation characteristics of the iron core using the secondary
current.
input current of the primary winding of the CT from 0 A to 400 A.
Table 3 lists the specifications of the load current tester.
For the experiment, three typical through-type CTs were selected,
as shown in Fig. 12. The specifications and shape dimensions of the
experimental models are listed in Table 4.
First, for the experiment to measure the electromotive force and
saturation characteristics of the CT, the induced electromotive force
of the secondary winding was measured with a digital multi-meter
while the input current to the primary winding was varied over the
ac-maximum range of 0 A to 400 A for the three models.
The saturation characteristics of the induced electromotive force
for the three models are shown in Fig. 13. The characteristics of
the induced electromotive force can be seen through the induced
current because the voltage is proportional to the current.
The experiment results show that the secondary induced current
was saturated when the primary current is around 140 A for model 1,
180 A for model 2, and 230 A for model 3.
These saturation characteristics indicate that the induced
Fig.
In the sec
finite eleme
with the ma
Because
of 180 A in
the applicat
analysis res
and the m
induced elec
The anal
difference f
of the induc
and from t
shapes of th
Trans. Electr. Electron. Mater. 18(2) 97 (2017): Y. S. Kim
102
(a)
(b)
Fig. 14. (a) Simulated and (b) measured electromotive force of the
secondary winding (Model 2, max. 100 A)
current did not increase any further because the magnetic core
became saturated, as the magnetic flux density increased and the
permeability decreased.
The current ratios of model 1, model 2, and model 3 are 75:5,
80:5, and 100:5, respectively. The current ratio of model 3 is large
compared with those of models 1 and 2. Therefore, the saturation
point of the secondary induced current of model 3 is late compared
to those of the other experimental models.
The results of this experiment show that the saturation point of
the magnetic core varies according to the ratio between the primary
and secondary windings.
In the second experiment, the algorithm of the time difference
finite element method was verified by inputting the ac current with
the maximum of 100 A to model 2.
Because the saturation occurred at the primary input current
of 180 A in the case of model 2, the measurement result after
the application of the 100 A was compared with the numerical
analysis result. Figure 14 shows the numerical analysis results and
the measurement results for the characteristics of the induced
electromotive force of the CT.
The analysis results validated the algorithm of the time difference
finite element method, because the maximum values of the
induced electromotive force from the use of this method and from
the experiment are approximately 0.02 V, and the shapes of their
waveforms (schematic shapes) are similar.
5. CONCLUSIONS
A CT is a general measurement instrument for the measurement
of the ac current in various industrial fields. The analysis of the
characteristics of the induced electromotive force and the magnetic
field in the induction coil when a large current, such as a surge
current, flows into a CT is indispensable.
In this study, the characteristics of the magnetic field and the
induced electromotive force in the magnetic core were analyzed
in consideration of the saturation characteristics, and the analysis
results were compared with the experiment results. For the twodimensional analysis of the CT, constraints were applied to the
induced current coil. Furthermore, the time difference finite element
method was used to analyze the transient states, such as the inrush
current. To express the surge current as a function, the sizes of the
harmonics were extracted through the development of the surge
current using the Fourier series, followed by its application to the
surge analysis.
The shape of the induced electromotive force that was measured
through the experiment was compared with that of the simulation
results. When a large current, such as an inrush current, flows into a
CT, the magnetic core becomes saturated and the sensing capacity
of the CT decreases. Therefore, for the optimum design of CTs, the
size of the CT and the characteristics of the magnetic core must be
considered.
ACKNOWLEDGMENT
This paper was supported by Joongbu University Research &
Development Fund, in 2016.
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