© [2007] IEEE. Reprinted, with permission, from Zhao, C; Wang, Songnian; Qiu,
Jie; Zhu, Jianguo; Guo, Youguang; Gong, Wz; Cao, Zj. 2007, 'Transient Simulation
And Analysis For Saturated Core High Temperature Superconducting Fault Current
Limiter', IEEE Transactions On Magnetics, Vol. 43, no. 4, pp. 1813-1816. This
material is posted here with permission of the IEEE. Such permission of the IEEE
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PF8-5
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Abstract—In this paper, the transient performance of a
magnetic core fault current limiter (FCL) saturated by high
temperature superconducting (HTS) DC bias winding is
investigated by using both 3-dimensional (3D) field-circuit
coupled simulation and magnetic circuit analysis. A high voltage
is induced on the DC HTS winding during the fault current state.
The induced voltage is computed and a short circuit coil for the
reduction of induced voltage is studied. The numerical
computations are verified by the experiment results on an FCL
prototype.
Index Terms—Fault current limiter, high temperature
superconductor, saturated core, field-circuit coupled simulation,
magnetic circuit analysis.
I. INTRODUCTION
S
the results of the development of large-scale and
complex implementation of power systems, the
influence of the fault currents, such as short-circuit current and
grounding current, has become one of important problems for
electric appliances, e.g. the circuit breakers, transformers, and
so on. All devices of the power system have to be designed to
withstand the high mechanical and thermal stresses caused by
the short circuit currents. There is a big demand for fault
current limiters (FCLs), which has a negligible influence on a
power system in normal condition, but can limit the current
within a pre-defined value in fault condition.
High temperature superconducting fault current limiters
(HTS FCL) are researched worldwide for their prospective
commercial application in power system. Due to the
superconductor and its special structure, the superconducting
fault current limiter (SCFCL) will be a kind of innovative
protection apparatus for high voltage grids [1]-[2]. It works
automatically, further more, it offers many advantages: rapid
reaction to fault current, low impedance in normal conditions,
and large impedance during fault conditions. With the wide
application of high temperature superconducting techniques,
Manuscript received Apr. 24, 2006.
C.X Zhao, S.H. Wang, and J. Qiu are with Xi’an Jiaotong University,
China (phone: +86-29-82668630-106, e-mail: shwang@mail.xjtu.edu.cn).
J. G. Zhu, and Y.G. Guo are with University of Technology, Sydney,
Australia (e-mail: joe@eng.uts.edu.au).
W.Z. Gong and Z.J. Cao are with Innopower Superconductor Cable Co.,
Ltd, Beijing, China (e-mail: gong_weizhi@innopower.com).
FCLs with diverse principles have been proposed, such as
resistive, inductive, magnetic shielding and saturated core
FCLs, etc. [3]-[5]. Most of them are based on the principle of
the transition from the Superconducting to Normal conducting
state (SN transition). However, the saturated core HTS FCL
achieves the purpose of limiting short current not by using the
SN transition, but by the nonlinear permeability of the
magnetic core, which does not have the problem of recovery
times. At the same time, the high temperature superconducting
coils are supplied by DC source, hence do not have AC power
loss, so more and more scholars have paid attention to this
type of FCL.
There have been reports on analyzing the superconducting
FCL by performing prototype experiment, as well as circuit
model with Ψ-i curve of FCL. The finite element analysis
(FEA) considering E-J characteristics of superconductor has
also been developed in simulation of magnetic shielding type
FCL [4]. In this paper, both methods of the equivalent
magnetic circuit simulation and 3D transient magnetic field
simulation are used to transiently simulate the saturated core
FCL. To consider the nonlinearity of the magnetic core, in
circuit simulation, an equivalent magnetization curve is used.
This paper also utilizes the numerical simulation for the
performance of HTS FCL by using 3D transient magnetic field
computation directly coupled with circuit equations of AC
windings, which is integrated in ANSYS. The results of the
field and circuit variables are solved simultaneously. All of
computed results and experimental results will be compared.
The flux change of core will induce an undesirable high
voltage in the DC coil, which may destroy the DC coil. In this
paper, the induced voltage in the DC HTS bias winding is
computed and analyzed in detail by using the transient FEA. A
short-circuit coil will be investigated for limiting the induced
AC voltage in HTS bias coil.
II. T
RANSIENT SIMULATION AND ANALYSIS OF THE
SATURATED CORE FCL
A. Analysis of the saturated core FCL by equivalent
Magnetic circuit method
1) Structure of saturated core FCL
The structure of the saturated magnetic core HTS FCL is
shown in Fig. 1, which is composed of two magnetic cores and
a superconducting DC bias coil. Although the permeability of
Transient Simulation and Analysis for Saturated
Core High Temperature Superconducting Fault
Current Limiter
Cuixia Zhao, Shuhong Wang, Jie Qiu, Jian Guo Zhu, Senior Member IEEE, Youguang Guo, Member
IEEE, Weizhi Gong, and Zhengjian Cao
A
PF8-5
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the magnetic core is nonlinear, in order to analyze
theoretically, the Ψ-i curve of the both AC windings of FCL
can be described approximately by five linear segments with
different slopes, as shown in Fig. 2. Curve 1 illustrates the
magnetization curve of single core without the DC bias, where
I
c
is a critical saturated current, and
Ψ
c
is the flux linkage.
Curves 2 and 3 plot the magnetization curves of two cores,
respectively, when a DC bias current I
d
is imposed. Curve 4 is
the Ψ-i curve of the saturated core FCL, which is achieved by
summation of curve 2 and curve 3.
DC
B
d
B
d
B
c
B
c
i
c
K
u (t)
u
1
u
2
2
Ω
3
4
5
1
2
Fig. 1. Circuit for the current-limiting test
1, 2—AC windings；3, 4—Magnetic cores；
5—Superconducting DC coils
3
1
2
a
1
Ψ
a
2
i
Ψ
c
I
c
I
d
-I
d
Ⅰ
Ⅱ
Ⅲ
Ⅱ
Ⅲ
4
Fig. 2.
Ψ-i
curve of saturated core FCL
In the normal operation, both magnetic cores are driven into
saturation by the DC current. The saturated core FCL works in
line Segment Ⅰ, so the impedance of the FCL is very low.
When a short-circuit current occurs, the rapidly increasing AC
current drives both magnetic cores out of saturation
alternatively during one AC cycle, hence the saturated core
FCL works in line Segment Ⅱ, the impedance of the FCL
becomes so large that the fault current is limited. However, if
the AC current increases unceasingly, the magnetic cores will
be saturated reversely, the FCL works in line Segment Ⅲ，
and will lose the capability of limiting current, due to the low
impedance.
The DC bias winding for FCL is expected to use high
temperature superconductors, which will drive the magnetic
core into saturation with a low DC power supply.
2) Magnetic circuit analysis
The structure and working principle of the saturated core
HTS FCL have been presented in Fig. 1, where the switch K is
employed to simulate the short-circuit fault. The B-H curve of
the core is shown in Fig. 3.
0 50 100 150 200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
B/T
H/A/m
1
2
Fig. 3. B-H curve of magnetic core
In Fig. 3, we divide the B-H curve into two segments
labeled by numbers 1 and 2, respectively, and suppose that the
turns of AC windings of each core and DC coil are N
c
and N
d
,
the mean length of magnetic circuit is
l
, and cross-sectional
area of magnetic core is
A
.
According to Ampere’s circuit law:
1d d cc
N I Ni Hl
−=
(1)
2d d cc
NI Ni Hl+=
(2)
where, I
d
and i
c
are the currents of DC bias winding and AC
winding, respectively, and H
1
and H
2
are magnetic field
intensity of Core 1 and 2, respectively.
The derivatives of H
1
and H
2
can be written as
1
cc
N di
dH
dt l dt
= −
(3)
2
cc
N di
dH
dt l dt
=
(4)
The relationship between magnetic flux density B and H is
BH
µ
=
(5)
The EMF of AC Windings 1 and 2 are shown as
11
11cc
dB dH
e NA NA
dt dt
µ
= =
2
1
c
c
NA
di
l dt
µ
= −
(6)
2
2
2
c
c
NA
di
e
l dt
µ
=
(7)
The induced voltage of AC Winding 1 can be derived as
2
1
11
c
c
NA
di
ue
l dt
µ
=−=
(8)
Similarly, the induced voltage of AC Winding 2 is
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3
2
2
22
c
c
NA
di
ue
l dt
µ
=−=−
(9)
Based on the Kirchhoff’s voltage law, for the circuit in Fig. 1
12
()
c
ut u u iR=++
(10)
Where, R is the sum of load and the resistances of both AC
windings.
Assume μ
n
is the permeability when the core is saturated. In the
normal state
12n
µµµ
= =
(11)
Considering (8)-(11):
2
() 2
c nc
c
N A di
ut iR
l dt
µ
= +
2
2
cc
c
N A di
B
iR
l H dt
= +
1
2tg
c
c
di
iR
dt
α
= +
(12)
However, the permeability becomes μ
f
when the core is not
saturated. In the fault state
1 n
µµ
=
(13)
2 f
µµ
=
(14)
The two magnetic cores are saturated alternately, the voltage
of both AC windings in series can be written as
2
2
()
cf
c nc c
c
NA
N A di di
ut iR
l dt l dt
µ
µ
=++
12
(tg tg )
c
c
di
iR
dt
αα
=++
(15)
3) Numerical result
According to all the above formulations, the dynamic
current waveform is achieved and shown in Fig. 4, by using
the equivalent magnetization curve and parameters of the
saturated core FCL.
Fig. 5 is the measured current waveform under normal state
and fault state. The investigation shows that the calculation
results are in accordance with the experimental ones.
B. Simulation the saturated core FCL by 3D transient
magnetic field coupled with electric circuit
Because of the nonlinear magnetization (B-H) curve, this
paper also employs the numerical simulation for the
performance of the saturated core FCL by using 3D transient
magnetic field computation directly coupled with circuit
equations of AC windings, which is integrated in ANSYS. The
transient magnetic field and circuit variables are solved
simultaneously. The structure of a prototype saturated core
FCL incorporated with DC HTS bias winding is shown in Fig.
6. The B-H curve of this magnetic core is shown in Fig. 3.
0.00 0.02 0.04 0.06 0.08 0.10 0.12
-3
-2
-1
0
1
2
b
i/kA
t/s
a
Fig. 4. Computational current by magnetic circuit
PF8-5
4
0.00 0.02 0.04 0.06 0.08 0.10 0.12
-3
-2
-1
0
1
2
a
i/kA
t/s
b
Fig. 7 Computational current by 3D transient FEA
C. Comparison of the result between the experiment and
simulation
In this paper, we employed both methods to simulate the
saturated core HTS FCL, and achieved the transient current,
which are shown in Fig. 4 and 7 respectively. Table I and II
list the results and relative errors of the simulated values and
the measured value at the point “a” and the point “b”, in Fig.
4,5 and 7. It shows good conformity in the results of both
calculation and experiment.
According to Table II, the result of the numerical field-
circuit coupled simulation is better than that of the magnetic
circuit in high precision. Nevertheless, the latter possesses a
better predominance in the aspect of the computing speed.
TABLE I
THE RESULTS AT POINTS “a” AND “b”
i
a
(A)
i
b
(kA)
Test 158.0 -3.09
Circuit
172.0
-3.21
FEA 166.5 -3.13
T
ABLE II
T
HE RELATIVE ERROR BETWEEN THE SIMULATED VALUES AND THE
MEASURED VALUE
Error a(%) b(%) average(%)
Circuit
8.86
3.88
6.37
FEA
5.38
1.29
3.36
III. THE HIGH VOLTAGE PROBLEM OF HTS COILS
Fig. 8 shows the calculated voltage waveform of high
temperature superconducting coils. It can be seen that the
voltage is low in the normal condition. The influence for DC
source can be negligible. However, in the fault condition, the
high induced voltage of high temperature superconducting
coils may destroy the superconducting coil and the DC source.
In order to decrease the induced AC voltage in the DC coil,
a direct method is to reduce the turns of DC coils. However,
this may lead to increasing current value of DC source. And a
voltage-dividing device can be used in the DC circuit, for the
purpose of dividing the voltage of DC source, which will
consume more power.
In this paper, a short circuit coil as magnetic shielding is
placed between the high temperature superconducting coils
and the magnetic core, as shown in Fig. 6. According to
Faraday's law of electromagnetic induction, this method will
achieve the purpose of reducing the high induced voltage, in
DC HTS bias coil. Comparing to both curves of fig. 8, it can
be seen that the induced voltage with magnetic shielding is
much lower than that without magnetic shielding. Thus, the
short-circuit coil has an effect on reducing the induction of
voltage.
0.00 0.02 0.04 0.06 0.08 0.10 0.12
-8
-6
-4
-2
0
2
4
6
8
10
u/V
t/s
magnetic shielding
no magnetic shielding
Fig. 8 Voltage waveform of HT superconducting coils
IV. CONCLUSION
A saturated core FCL with HTS DC bias coil has been
investigated by using the equivalent circuit method and 3D
transient magnetic field simulation coupled with circuit. Good
agreement between the computational and experimental
characteristics confirms the accuracy of both methods. The
saturated core FCL has a fast response to limit the fault current,
because the superconductor has little transition time between
superconducting state and normal conducting state. The high
induced AC voltage in HTS DC bias coil, which may destroy
the DC coil, has been simulated by applying FEA. A short
circuit coil for reducing the voltage has been evaluated and
discussed.
V. REFERENCES
[1] J.X. Jin, S.X. Dou, H.K. Liu and C. Grantham, “Preparation of high Tc
Superconducting coils for consideration of their use in a prototype fault
current limiter,” IEEE Trans. Appl. Superconduct., vol. 5, pp.1051-
1054, June 1995.
[2] H.J. Boenig and D.A. Paice, “Fault current limiter using a
superconducting coil,” IEEE Trans. Magnetics, vol. 19,pp. 1051-1053,
May 1983.
[3] M. Joo and T. K. Ko, “The analysis of the fault currents according to
core saturation and fault angles in an inductive high-T
c
superconducting
fault current limiter,” IEEE Trans. Appl. Supercond., Vol. 6, pp. 62-67,
June 1996.
[4] A. Ishiyama, J. Nakatsugawa, S. Noguchi, H. Kado, and M. Ichikawa,
“Fundamental characteristic estimation based on finite element method
for magnetic shielding type superconducting fault current limiter,”
Electrical Engineering in Japan, Vol. 134, pp. 17-27, 2001.
[5] V. Keilin, I. Kovalev, S. Kruglov, V. Stepanov, I. Shugaev, and V.
Shcherbakov, “Model of HTS three-phase saturated core fault current
limiter,” IEEE Trans. Appl. Supercond., Vol. 10, pp. 836-839, Mar.
2000.
