Presented at the 2011 COMSOL Conference in Boston

Coupled Magnetodynamic and Electric Circuit Models

for Superconducting Fault Current Limiter

Presentation at the COMSOL Conference 2011

Boston, 13 – 15 October 2011

L. Graber1, J. Kvitkovic1, T. Chiocchio1, M. Steurer1, S. Pamidi1, A. Usoskin2

1Center for Advanced Power Systems, Florida State University

2Bruker Energy & Supercon Technologies

14 Oct 2011 Comsol Conference 2011 1

 Contents

• Basics of superconducting fault current limiters (SFCL)

• Shielding properties of superconductors
• FEA magnetic model
– Implementation of shielding properties
• Electric circuit model (“SPICE”)
• Model validation
– Experiment with benchtop model
– Measurements
• Conclusion

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 Inductive Superconducting FCL

• Problem: Increasing levels of

Magn. flux lines fault currents in power grids
Primary coil
• SFCL limits fault current without
negative impact at normal
operation
– Low voltage drop during normal
operation
Stack of SC rings – Low reactive power
• Inductive SFCL provide
operational advantages:
LSFCL
ZSource LSFCL – No heat influx into cryostat
~ USource ZLoad through current leads
Fault t – No Joule heating in cryostat
normal fault

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 Shielding Properties of HTS

100 • Measured with the exact

8.26 mT same ring of HTS as
80
later used for the
Shielding Factor [%]

validation experiment
60
• Hall probes inside and
40 outside the ring pick up
the magnetic field
20
• Operation frequency
0
differs slightly from 60 Hz
0 2 4 6 8 10
to reduce noise
External Magnetic Field [mTRMS]

Bext  Bint
S  100%
Bext

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 Finite Element Model

• Shielding properties of HTS modeled by

0.1 conductivity of HTS
2
– Exact value of conductivity is not critical
– Factor 100 lower due to increased thickness in model
HTS

43 35 2.5 1014 S/m in normal operation,

 
 2.5 10 S/m in quench/fau lt operation.
0

66.2 Prim. coil

72.5 • Primary coil: Multi-turn coil domain with 60
LN2
turns of 1 mm Cu wire
• Liquid nitrogen (LN2) in open bath at 77 K
A (µr = 1; σ = 0 S/m)
    H   v  B  Je
t
B   A

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 iSFCL for FEA Validation:
Equivalent Circuit

• Electric circuit with lumped elements (“SPICE”), coupled to the FEA model
• Transformer ratio: 240 V : 32 V = 7.5

=
~
~
~

LS RW LL LL RW
1 2 3 4 5 6
7 8
9 10 1.34 Ω 1.35 mH 1.35 mH1.34 Ω
7.52 7.52 7.52 7.52 RL LSFCL
0.6 mH
7.52 Lh
~ ~ ~ CS RG 9.545 H
7.52 100 Ω
60 µF · 7.52 10 kΩ
0 7.52
11 12
0...240 VRMS (phase-to-phase)
7.5 iSFCL &
25 kW inverter with output filter and resistive grounding Step down transformer protec. resistor

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 iSFCL for FEA Validation:
Pulse Pattern

• Input parameters
– Applied voltage (pulse of 7× nominal simulates a fault situation)
– HTS conductivity
• Output parameters
– Inductance of the iSFCL as a function of time

Normal Pulse/Fault Recovery Normal

Voltage 12 VRMS 84 VRMS 12 VRMS

Conductivity 2.5·1014 S/m 2.5 S/m 2.5·1014 S/m

Inductance 0.3 mH 0.7 mH 0.3 mH

Time [ms]

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 iSFCL for FEA Validation:
Magnetic Flux Density

a) After fault but before recovery of b) Normal operation (shielding)

superconduction (quenched)

Bmax = 10.2 mT Bmax = 41.5 mT

L = 0.7 mH L = 0.3 mH

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 iSFCL for FEA Validation:
Construction

• Primary purpose of this small-scale iSFCL:

Validation of FEA model (i.e. conductivity-based magnetic shielding)

HTS ring (single layer)

0.1
2
HTS

43 35

66.2 Prim. coil

72.5
LN2 Primary coil
on G10 former

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 iSFCL for FEA Validation:
Voltage, Current, and Inductance
Quench of Benchtop FCL (Experimental vs Simulation) Recovery of Benchtop FCL (Experimental vs Simulation)

FCL Primary Current,(A)

FEA Simulation FEA Simulation
20
FCL Primary Current,(A)

Experimental Experimental
50
10
0

0 -10
-20
0.4 0.45 0.5 0.55 0.6 0.65 0.7
-50 time,(s)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 FEA Simulation

FCL Primary Voltage,(V)

time,(s) Experimental
10
FEA Simulation
20 Experimental
FCL Primary Voltage,(V)

0
10
-10
0
0.4 0.45 0.5 0.55 0.6 0.65 0.7
time,(s)
-10 -4
x 10
FEA Simulation
-20 Experimental
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
time,(s) 8

7
• FEA results compared to measurements

Calculated Inductance,(H)
around instant of fault (above, left),
6

instant of recovery (above, right), and 5

ratio of inductance (right) 4

• Convincing agreement of model and 3

measurement 2

1
0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
time,(s)

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 Conclusion

• HTS conductivity as input parameter to the FEA model is a valid

technique to simulate basic magnetic properties
– Model can be used for parametric studies

• Coupling with circuit model allows interaction with grid components

– Enables power hardware-in-the-loop tests

• Computational very efficient

– A couple of minutes to calculate on a PC
– Would allow to implement geometry of higher complexity

• Regarding the air core iSFCL...

– Ratio of inductance is limited to approx. 1.5 ~ 3 (depends on geometry of primary
coil, cryostat wall thickness, and height to diameter ratio)
– Insertion of an iron core (e.g. I-core) boosts the ratio to 5 ~10

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 Additional Slides

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 Coreless Model: Parameters

• Geometry
– rAir = 2 m; hAir = 5 m
– rCoil = 0.5 m; hCoil = 1.5 m; wCoil =
0.02 m
– rSC = 0.4 m; hSC = 2 m; wSC = 1 mm
– Optional: rCore = 0.42 m; hCore = hSC
– N = 65
– ACoil = 240 mm2
• Material
– Air, HTS, and primary coil:
εr = 1; μr = 1; ρ = {10−15 ; 1} Ωm
– Iron core:
εr = 1; μr = 4000; ρ = 1 Ωm
• Load current in the coil
– f = 50 Hz; Icoil = {0.5 ; 20} kA;
Itot = N·Icoil

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 Coreless Model: Equations and BCs

n  A  0 Magnetic and electric

 n  J  0 insulation

Axis of
Governing equations symmety
J  0
H  J  0 
  External current
J  E  jD   I tot Acoil 
 0  density
 0 
 
J  E  jD   I tot Acoil   
 0 
   0 
 
E  V  jA
 
j    0 r A    H  v  B   I tot Acoil 
2

B   A  0 
 
Material equations Multi-turn coil domain
D   0 r E
B   0 r H

All vectors are in

cylindrical coordinates

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 Coreless Model: No-Fault Condition

Model input
ρSC = 10−15 Ωm
ICoil = 500 A

Model output
LCoil = 0.96 mH

Cross-validation by adapted
formula for long cylindrical
coil:

L  N 0
2 
  rCoil2  rSC 2   1.00 mH
hCoil

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 Coreless Model: Fault Condition

Model input
ρSC = 1 Ωm
ICoil = 20 kA

Model output
LCoil = 2.19 mH

Cross-validation by simple
formula for long cylindrical
coil:
  rCoil2
L  N 0
2
 2.78 mH
hCoil

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 Coreless Model:
Inductance Ratio wrt. Gap Distance

Corresponds to 2 cm gap
• Primary winding: rCoil = 0.5 m (const)
• SC stack radius: rSC = {0.30, 0.32, ...0.48} m
Corresponds to 20 cm gap
2.5 9

Ratio (L_nonFault /L_Fault)

7
Inductance [mH]

6
1.5
5
L_nonFault [mH]
L_Fault [mH]
4
1
3

0.5 2
ratio
1

0 0
0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48
Radius [m] Radius [m]

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 Model with Iron Core

Quenched state (20 kA; 1 Ωm) Normal state (500 A; 10−15 Ωm)

Gap rCoil − rSC = 40 mm rCoil − rSC = 40 mm

LCoil = 11.4 mH LCoil = 0.452 mH
Inductance ratio: 25.2

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