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JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 6, NO. 2, JUNE 2008
High Temperature Superconducting Magnetic Energy
Storage and Its Power Control Technology
Xiao-Yuan Chen, Jian-Xun Jin, Kai-Meng Ma, Ju Wen, Ying Xin, Wei-Zhi Gong,
An-Lin Ren, and Jing-Yin Zhang
Abstract⎯High temperature superconducting (HTS)
power inductor and its control technology have been
studied and analyzed in the paper. Based on the results
of simulations and practical experiments, a controlled
release scheme has been proposed and verified for
developing a practical HTS SMES prototype.
Index Terms⎯Electronic switch, SMES, high
temperature superconducting (HTS) inductor, uninterruptible power system (UPS).
1. Introduction
The power inductor energy storage technology has
important applications in the modern scientific and
technical field, i.e., high-energy physics, high-energy laser,
electromagnetic propulsion, etc. Superconducting magnetic
energy storage (SMES) devices can store the excessive
electronic energy as electromagnetic energy in the
superconducting inductor and release the stored energy if
required. The advantages of SMES devices comparing with
other energy storage devices include high energy storage
density, high energy storage efficiency, long application
life-time and few environmental pollution. With the
development
of
applicable
high
temperature
superconducting (HTS) materials, SMES technology has
been progressed actively and is expected to apply in
commercial applications[1]-[4].
In this paper, a HTS inductor design is introduced, with
its geometry design and magnetic field analysis presented.
Based on the results of simulations and experiments, a
controlled release scheme is proposed to discharge the
Manuscript received March 1, 2008; revised April 1, 2008.
X.-Y. Chen, J.-X. Jin, K.-M. Ma, J. Wen are with the Center of Applied
Superconductivity and Electrical Engineering, University of Electronic
Science and Technology of China, Chengdu, 610054, China (e-mail:
cxy_yjs@yahoo.com.cn, jxjin@uestc.edu.cn and hanqinmount@sina.com.
cn 83201229).
Y. Xin, W.-Z. Gong, A.-L. Ren, and J.-Y. Zhang are with Department of
Development of Innopower Superconductor Cable Co. Ltd., Beijing,
100176, China (e-mail: yingxin@innopower.com, gong_weizhi@
innopower.com and ren_anLin@innopower.com).
stored energy steadily and a simulation analysis on an
uninterruptible power system (UPS) is also presented to
verify the controlled release scheme for SMES applications.
2.
HTS Inductor Design
In this section, three HTS solenoid coils with different
configurations are designed and analyzed. A common
configuration of HTS solenoid coil is shown in Fig. 1.
2.1 Specifications of HTS Conductor
Practically, Bi-2223 multifilament HTS tape conductor
is chosen to deign a HTS solenoid coil. Its main
specifications are: width a is 4.23 mm, thickness b is 0.23
mm, critical current Ic is 100 A (77 K, 0 T), and critical
current density Je is 10 kA/cm2.
2.2 Inductance Calculation
A formula for inductance calculation is given by [5]
and can be expressed as follows
L = 2πμ 0 N c2 R15 T ( p, q)
(1)
where μ0 = 4π × 10−7 , parameter Nc is given by
Nc =
N
( R2 − R1 ) D
(2)
where N is the number of coil turns, and T(p, q) is the
function of size ratio p(=R2/R1), q(=D/R1).
According to (1) and (2), there is
2
⎡
⎤
N
L = 2πμ0 R T ( p, q) ⎢
⎥ .
⎣ ( R2 − R1 ) D ⎦
5
1
(3)
Considering the filling factor K for practical design, there is
Nab = ( R2 − R1 ) DK .
(4)
The total length of conductors S is given by
R − R1 ⎞ ⎤
⎡ ⎛
S = N ⎢ 2π ⎜ R1 + 2
2 ⎠⎟ ⎥⎦
⎣ ⎝
(5)
2.3 Design of HTS Solenoid Coils
For practical design of HTS solenoid coil, three
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JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 6, NO. 2, JUNE 2008
different coils with same inner radius R1 and section area
(R2−R1)D are analyzed in this section. The main geometries
of the three HTS solenoid coils are shown in Table 1.
Fig. 3. Magnetic field distribution of the HTS coil in Case 2.
D
C. Case 3
Referring to (3) and (4), the inductance L3 in Case 3 is
1.53 H and the length of HTS conductors S3 is 2224 m. The
magnetic distribution is shown in Fig.4.
R2
R1
0.772
0.647
0.523
0.398
0.273
0.148
0.024
Fig. 1. Scheme of HTS solenoid coils.
0.732
0.586
0.440
0.294
0.149
0.074
0.024
Table 1. Main geometries of the three HTS coils
R1 (mm)
R2 (mm)
D (mm)
Case 1
81
162
81
Case 2
81
81
121.5
162
243
40.5
Case 3
Fig. 4. Magnetic field distribution of the coil in Case 3.
A. Case 1
From Table 2, the size ratios (p, q) in Case 1, 2, and 3
are (2, 1), (1.5, 2), (3, 0.5), respectively. According to [6],
T(p, q) in Case 1, 2, and 3 are 0.3290, 0.2046, and 0.5028,
respectively. A solenoid coil having the size ratio of (2, 1) is
a so-called Brooks coil, which can give a maximum
inductance for a given length of conductor.
In the design of Case 1, the HTS coil should be wound
with a certain insulating layer. The total width and
thickness of Bi-2223 HTS conductor with insulating layer
are 6 mm and 0.6 mm, respectively. Therefore, a reasonable
filling factor is 32.2%. Referring to (3) and (4), the
inductance L1 in Case 1 is 1 H and the number of turns N1 is
2186. Referring to (5), the total length of HTS wires S1 is
1668 m.
To realize some magnetic specifications of the designed
coil, QuickField software is introduced. Assume that the
current through the designed coil I1 is 100 A, the magnetic
field distribution is generated as shown in Fig. 2.
Line a
0.866
0.656
0.445
0.234
0.142
0.054
0.020
Fig. 2. Magnetic field distribution of the coil in Case 1.
B. Case 2
The filling factor K1, the length of HTS wires S1, and
the current through the designed coil I1 in Case 1 are also
used to deign the coils in Case 2 and Case 3, with an aim to
optimize practical inductor design.
Referring to (3) and (4), the inductance L2 in Case 2 is
0.62 H and the length of HTS conductors S2 is 1390 m. The
magnetic field distribution is shown in Fig. 3.
From the designs above, the main specifications of the
three deigned coils are summarized as shown in Table 3.
Table 3: Main geometries of the three HTS coils
Turns
number
Volume (m3) Inductance (H) Wire length (m)
Case 1
2186
0.005
1
1668
Case 2
2186
0.004
0.62
1390
Case 3
2186
0.007
1.53
2224
From Table 3, a Brooks coil is chosen to obtain
maximum inductance for HTS conductors with a given
length. The required volume and HTS conductor length of
the coil in Case 2 are minimum values in three coils,
however the inductance in Case 2 is lowest. The inductance
of the coil in Case 3 can obtain maximum inductance
within the same section area of the three coils, but the
required volume and wire length are maximum values,
which may lead to largest placement volume and highest
cost to fabricate a practical coil.
2.4 Magnetic Field Analysis
The maximum flux density of the solenoid coil is
normally located at the cross circle of the central plane of
the solenoid coil and its inner cylindrical surface.
Assume that the center coordinates of magnetic
distributions in Fig. 2, Fig. 3 and Fig. 4 are (0, 0) and the
coil was symmetrically placed around (0, 0), a line a from
(−80, −100) to (−80, 100) is added to analyze the flux
density distributions, as shown in Fig. 2. Parallel flux
density Bx1 in Case 1, parallel flux density Bx2 in Case 2 and
parallel flux density Bx3 in Case 3 are shown in Fig. 5.
Bx (//c) decreases the HTS conductor Ic more severely
than the B and By (⊥c). Quench occurs when the current
value through the HTS coil reach or exceed the Ic value. It
is essential to reduce Bx so that the operating current of a
practical HTS coil can reach a larger value. In Fig. 5, Bx3 is
B
B
B
B
B
B
B
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CHEN et al.: High Temperature Superconducting Magnetic Energy Storage and Its Power Control Technology
lowest and therefore the operating current can reach largest
value in practical application.
Bx1
Bx2
Bx3
10
5
0
−0.25
-0.25
00
Y (mm)
50
50
30.4
t (s)
(b)
30
30.8
B
i (A)
100
5
0
50
0
30.8
30.4
t (s)
(a)
30
30
30.4
t (s)
(b)
30.8
Fig. 8. Discharging current waveforms with different charging
current I: (a) I=10 A and (b) I=100 A.
10
i (A)
Based on the above analysis, conclusions can be made
as follows: 1) The Brooks coil in Case 1 can obtain
maximum inductance for HTS conductors with a given
length, but its energy storage may not be maximum value
because of its high Bx; 2) The HTS coil in Case 2 is better
for cooling and requires shortest conductor length and
lowest placement volume, but its inductance is a minimum
value and not ideal for obtaining high energy storage; 3)
Though the required volume and conductor length of the
HTS coil in Case 3 are maximum values, its inductance and
operating current can reach maximum values, which are
more suitable to obtain maximum energy storage.
10
5
0
30.05
t (s)
(a)
30
30.1
5
0
30
30.4
t (s)
(b)
30.8
Fig. 9. Discharge current waveforms with different Rs: (a) Rs=10
Ω and (b) Rs=1 Ω.
3.1 Theoretical Analysis and Simulation
The electromagnetic energy stored in the inductor E(J)
can be described by
(6)
E = 1 / 2(Ls I 2 )
where Ls(H)is the inductance of the inductor, I(A) is the
charging current.
The current i (t ) in the discharging circuit can be
described by
t
(7)
where t is the discharging time, τ (=Ls/Rs) is the time
constant. The discharging time becomes longer while τ
increases.
The principle of charging and discharging circuit is
shown in Fig. 6. Ls is assumed to be the ideal inductor and
Rs is the resistance of practical inductor. The inductor is
charged while the switch S is on, and discharged through
the diode D while S is off. Some simulation results are
shown in Fig. 7, Fig. 8 and Fig. 9. The simulation results
conclude that the discharging time becomes longer while Ls
increases or Rs decreases, however it is independent of the
charging current.
3.2 Experimental Test and Analysis
Practically a circuit test platform is designed and built
to verify the simulation results. A 0.2 H Cu inductor is
chosen to analyze charging and discharging tests. The
resistance of the inductor Rs decreases while the operating
temperature decreases. Its value is 5.6 Ω and 1.6 Ω at room
temperature and liquid nitrogen (LN2) temperature,
respectively. The Cu inductor is charged by a 70 V power
supply and discharged through the diode D while the switch
K is on and off, respectively. The discharging waveform is
shown in Fig. 10. The discharging current decreases
exponentially and can not be used effectively, which
matches with the theoretical analysis using (7). The
operating temperature increases along with LN2
evaporation. The above simulation results are well verified
by the relational curves among different parameters, as
shown in Fig. 11.
40
i (A)
3. Inductive Energy Release
τ
0
30.8
10
B
−
30.4
t (s)
(a)
5
Fig. 7. Discharging current waveforms with different Ls: (a) Ls=
0.2 H and (b) Ls=0.02 H.
100
100
Fig. 5. Bx distribution of the designed three HTS coils.
i (t ) = Ie
30
i (A)
−50
-50
10
i (A)
00
−0.5
-0.5
−100
-100
Ls
D
Fig. 6. The principle of a charging and discharging circuit.
i (A)
Bx (T)
0.25
0.25
Rs
i (A)
0.5
0.5
S
DC
20
0
0.032
0.5
t (s)
1.0
Fig. 10. Discharging current waveform (Rs=1.6 Ω).
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JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 6, NO. 2, JUNE 2008
filter, R is the load.
50
im(A)
t (ms)
t(ms)
500
300
DC
10
100
1
3
Rs (Ω)
5
1
3
Rs (Ω)
(b)
(a)
S3
Lf
R
Cf
D2
D1
Fig. 12. A controlled release circuit.
Based on the above simulation and experimental analysis,
conclusions can be made as follows: 1) The charging
current i(t) is directly related to the. charging current I, but
the discharging time t is not affected by I; 2) The
discharging time t becomes longer while Ls increases or Rs
decreases, and it is expected to enlarge the inductance or
reduce the resistance for practical applications. The circuit
in Fig. 6 can not satisfy the requirements for practical
applications, the power release control strategy should be
developed to improve its performance.
4. A Controlled Release Scheme
It has been verified that energy release without any
control is useless and it is expected to develop a controlled
release scheme for practical applications. Assume that the
inductor can be discharged with a constant power P0(W)
within a time period ts(s), the stored energy E(t) at t(<ts) can
be described by
E (t ) = E − P0 t .
(8)
When t=ts, the current through the inductor Is is
P
(9)
Is = 0
v
where v(V) is the voltage across the inductor. If the
discharging current drops below Is, the inductor will be
discharged with a reduced power, which depends on the
discharging depth coefficient λ. λ can be described by
P0 t s
E
S2
S1
5
Fig. 11. Relational curves among different parameters: (a)
relational curve between t and R and (b) relational curve between
the peak value of discharging current im and Rs.
λ=
Ls
S
30
(10)
Referring to (6) and (9), the discharging current i (t ) at
S
t
S1
t
S2
t
S3
t
(a)
(c)
(b)
Notes: (a) Energy-charging state, (b) Energy-storing state, (c)
Energy-discharging state.
Fig. 13. The control voltage waveforms on S, S1, S2 and S3.
From Fig. 13, the steady-energy release control circuit
has three operating states: 1) Energy-charging state; 2)
Energy-storing state; 3) Energy-discharging state. In order
to achieve steady-energy release control, the discharging
current IR (or discharging voltage VR) is compared with a
reference current Iref (or reference voltage Vref). If IR > Iref,
(or VR > Vref), the steady-energy release control circuit is
operated in the energy-storing state and IR (or VR) decreases
gradually; If IR < Iref (or VR < Vref), the steady-energy release
control circuit is operated in the energy-discharging state
and IR (or VR) increases gradually. Thus the stored energy is
discharged steadily and a steady current output (steady
voltage output) can be applied in practical applications.
A steady-current release control simulation module is
developed based on Matlab/Simulink. Assume that Ls=0.2
H, Lf=21 mH, Cf=47 μF, R=0.05 Ω , Iref=2A. From Fig. 14,
the steady-current release time increases form 50 ms to 140
ms while the charging current increases from 10 A to 100 A.
So the steady-current output is achieved and the
discharging time increases in direct proportion to the stored
energy in the HTS coil. Based on the above analysis, a
controlled release prototype is developed in Fig. 15.
t
ts
(11)
Referring to the (8) and (10), the stored energy at any
given time t can be described by
Pt
Eλ
t
E (t ) = E −
t = 0 s (1 − λ )
(12)
ts
ts
λ
Based on the above theoretical analysis, a controlled
release scheme is proposed to achieve steady release, as
shown in Fig. 12. Ls is a HTS inductor, switches S1, S2, S2,
S3 and diode D1, D2 are used to form the charging and
discharging circuits, inductor Lf and capacitor Cf form a
2
1
0
i (A)
v 1− λ
1− λ
0.4
0.5
t (s)
0.6
0.1
0.05
0
0.4
0.5
t (s)
(a)
0.6
2
1
0
0.7
v (V)
P0
v (V)
i (t ) =
i (A)
any given time t can be described by
0.7
0.4
0.5
0.6
t (s)
0.7
0.4
0.5
t (s)
(b)
0.7
0.1
0.05
0
0.6
Fig. 14. Steady-current discharging waveforms: (a) the charging
current is 10 A and (b) the charging current is 100 A.
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CHEN et al.: High Temperature Superconducting Magnetic Energy Storage and Its Power Control Technology
because its control technique is rather mature. A chopper
can play a key role in the charging and discharging process
of HTS coil, and provide a stability voltage for the load.
Chopper control algorithms can be operated in three
operation states: energy-charging state, energy-discharging
state and energy-storing state, as shown in Fig. 17. Each
operation state can be achieved by turning on or off the two
control switches in chopper.
Dewar
HTS coils
T4
Current
detector
T1
T2
C
A
B
LS
T3
R
Control board
Load
Cf
Current
detector
Fig. 15. A controlled release circuit prototype.
SMES
5. SMES Application in UPS
5.1 Application Scheme
SMES is expected to be a promising application in UPS.
A SMES-UPS scheme is shown in Fig. 16.
AC
power
SMES
(a)
(b)
(c)
Fig. 17. The three operation states of chopper algorithms: (a)
energy-charging state, (b) energy-discharging state, (c)
energy-storing state.
5.2 Simulation and Analysis
A SMES simulation module is established by using
Matlab/Simulink, as shown in Fig. 18. Its main parameters
are as follows: energy storage inductance L=5 H; the
equivalent resistance of energy storage circuit R1 is 0.1 Ω;
steady charging current I0 is 400 A; a three-phase 380 V
output with its effective power of 50 kW loads in the
three-phase parallel connection RLC circuit. L is discharged
after charging for 0.1 s and its simulation waveforms are
shown in Fig. 19.
Load
SMES
Fig. 16. A SMES-UPS scheme.
A voltage-type converter is chosen to design the circuit
ter
R2
Mosfet1
L
Uref Pulses
Gain2
Mosfet2
Saturation
PI
Vc1
C
ter2
Discrete
PI controller
Discrete
PWM generator
Voltage regulator
C
Set current value
1
Vref(pu)
Vabc(pu)
Vd-ref (pu)
Vabc-inv
m
Uref Pulses
v
Vab-inv
A
B
C
50 kW
380 V rms
50 Hz
Fig. 18. A SMES-UPS simulation module.
1/z
ter3
Vab-load
v
Scope1
v
Vdc
Diode1
Diode
0
L1
OR
Mosfet3
PWM generator1
ter1
NOT
R1
Step
Vdc1
SMES
Discrete
Ts=2e006s
Vabc
A
a
B
b
C
c
Measure
A
B
C
A
B
C
LC filter
IGBT
inverter
g
A
B
C
v
1000
0
−1000
Vab-load(V)
0
500
0
−500
0
1
1
1
t(s)
t(s)
t(s)
(a)
2
2
V1(V)
1000
500
0
0
3
1000
500
0
0.1
Vab-inv(V)
JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA, VOL. 6, NO. 2, JUNE 2008
3
1000
500
0
0.1
Vab-load(V)
Vab-inv(V)
V1(V)
142
2
1000
500
0
3
0.1
0.2
t(s)
0.3
0.2
t(s)
0.3
0.2
t(s)
(b)
0.3
Fig. 19. Simulation waveforms in SMES module: (a) the
waveforms of Vc1, Vab-inv and Vab-load, (b) enlargement of (a).
6. Conclusions
A HTS inductor design and the principle of the
charging and discharging of the inductor are studied and
analyzed in the paper. The common power inductor can not
be used in practical applications owning to the exist of
resistance and the stored energy can hardly be utilized if
energy release without any control, a steady-energy release
control method has been proposed and verified by a UPS
simulation. More analysis and SMES prototype design will
be presented in near future.
References
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[8] S. W. Wu, “Inductance tables of air-cored cylindrical coil,”
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Xiao-Yuan Chen was born in Jiangxi Province, China, in
1986. In 2007, he received the B.S. degree from the Chengdu
University of Technology. He is currently pursuing the M.S.
degree with UESTC. His research interest is in high temperature
superconductivity.
Jian-Xun Jin was born in Beijing, in 1962. He received B.S.
degree from Beijing University of Science and Technology in
1985, M.S. degree from University of New South Wales, Australia
in 1994, and Ph.D. degree from University of Wollongong,
Australia in 1997. He was a research fellow and Australian ARC
project chief investigator and senior research fellow with
Australian University of Wollongong from 1997 to 2003. He is
currently a professor and the Director of the Center of Applied
Superconductivity and Electrical Engineering, UESTC. His
research interests include applied high temperature superconductivity, measurement, control and energy efficiency
technology.
Kai-Meng Ma was born in Sichuan Province, China, in 1977.
In 2001, he received the B.S. degree from Tianjin Polytechnic
University. He is currently pursuing the M.S. degree with
University of Electronic Science and Technology of China
(UESTC). His research interest is in superconducting magnetic
energy storage technology.
Ju Wen was born in Hunan Province, China, in 1982. In 2005,
he received the B.S. degree from Henan University of Science and
Technology. He is currently pursuing the M.S. degree with
UESTC. His research interests include control theory and control
engineer.
Ying Xin was born in Heilongjiang Province, China, in 1953.
He received the B.S. degree from Tianjing University, Tianjin, in
1991, and the Ph.D degree from University of Arkansas, in 1991.
He is now working in Innopower Superconducting Cable Co., Ltd.
Dr. Xin is active in high temperature superconductivity.
Wei-Zhi Gong was born in Province, China. He received
the B.S. degree from the University, His research interest is
the electrical application of the superconductor.
An-Lin Ren was born in Hebei Province, China, in 1969. He
received the B.S. degree from the Tianjin University, Tianjin, in
1991. He is now working in Innopower Superconducting Cable
Co., Ltd. His research interests include the electrical application of
the superconducting.
Jing-Yin Zhang was born in Hubei Province, China, in 1979.
He received the B.S. degree in 2001 in mechanical engineering
and M.S. degree in 2006 in electrical engineering, both from the
Beihang University (BUAA), Beijing. His research interests are
superconductor applications in power grid.