Coupled Magnetodynamic and Electric Circuit Models for ......14 Oct 2011 1 Coupled Magnetodynamic and Electric Circuit Models for Superconducting Fault Current Limiter Presentation

14 Oct 2011 1

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

Comsol Conference 2011

Presented at the 2011 COMSOL Conference in Boston

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

2 14 Oct 2011 Comsol Conference 2011

Inductive Superconducting FCL

14 Oct 2011 Comsol Conference 2011 3

Stack of SC rings

Primary coilMagn. flux lines

~ ZLoad

ZSource LSFCL

USource

Fault t

LSFCL

faultnormal

• Problem: Increasing levels of fault currents in power grids

• SFCL limits fault current without negative impact at normal operation

– Low voltage drop during normal operation

– Low reactive power • Inductive SFCL provide

operational advantages: – No heat influx into cryostat

through current leads – No Joule heating in cryostat

Shielding Properties of HTS


0

20

40

60

80

100

0 2 4 6 8 10

Shie

ldin

g Fa

cto

r [%

]

External Magnetic Field [mTRMS]

8.26 mT

%100ext

intext

B

BBS

• Measured with the exact same ring of HTS as later used for the validation experiment

• Hall probes inside and outside the ring pick up the magnetic field

• Operation frequency differs slightly from 60 Hz to reduce noise

Finite Element Model

• Shielding properties of HTS modeled by

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

• Primary coil: Multi-turn coil domain with 60 turns of 1 mm Cu wire

• Liquid nitrogen (LN2) in open bath at 77 K (µr = 1; σ = 0 S/m)


LN2

HTS

Prim. coil

0.1

43 35

66.2 72.5

2

AB

JBvHA

e

t

operation.lt quench/fauin S/m 105.2

operation, normalin S/m 105.20

14

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

~

25 kW inverter with output filter and resistive grounding

~ ~

Step down transformer

11

1 7

9 10

8

2 3 4 5 6

12

0

iSFCL & protec. resistor

LS

CS RG

Lh

LL LL RW RW

RL LSFCL

1.35 mH 1.35 mH

9.545 H 100 Ω

10 kΩ 60 µF · 7.52

0.6 mH

0...240 VRMS (phase-to-phase)

7.52

7.52

7.5

1.34 Ω 1.34 Ω 7.52 7.52 7.52

7.52

7.52

14 Oct 2011 6 Comsol Conference 2011

~ ~ ~ =

• 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

iSFCL for FEA Validation: Pulse Pattern

7

Time [ms]

Pulse/Fault

Voltage 12 VRMS 84 VRMS 12 VRMS

Recovery Normal Normal

Conductivity

Inductance 0.3 mH 0.3 mH 0.7 mH

2.5·1014 S/m 2.5 S/m 2.5·1014 S/m

14 Oct 2011 Comsol Conference 2011

iSFCL for FEA Validation: Magnetic Flux Density

8

a) After fault but before recovery of superconduction (quenched)


b) Normal operation (shielding)

Bmax = 10.2 mT Bmax = 41.5 mT

L = 0.7 mH L = 0.3 mH

• Primary purpose of this small-scale iSFCL: Validation of FEA model (i.e. conductivity-based magnetic shielding)

iSFCL for FEA Validation: Construction

9

LN2

HTS

Prim. coil

0.1

43 35

66.2 72.5

2

14 Oct 2011

HTS ring (single layer)

Primary coil on G10 former


iSFCL for FEA Validation: Voltage, Current, and Inductance

10

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-50

0

50

Quench of Benchtop FCL (Experimental vs Simulation)

FC

L P

rim

ary

Curr

ent,(A

)

time,(s)

FEA Simulation

Experimental

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-20

-10

0

10

20

FC

L P

rim

ary

Voltage,(

V)

time,(s)

FEA Simulation

Experimental

0.4 0.45 0.5 0.55 0.6 0.65 0.7

-20

-10

0

10

20

Recovery of Benchtop FCL (Experimental vs Simulation)

FC

L P

rim

ary

Curr

ent,(A

)

time,(s)

FEA Simulation

Experimental

0.4 0.45 0.5 0.55 0.6 0.65 0.7

-10

0

10

FC

L P

rim

ary

Voltage,(

V)

time,(s)

FEA Simulation

Experimental

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.71

2

3

4

5

6

7

8

x 10-4

time,(s)

Calc

ula

ted Inducta

nce,(

H)

FEA Simulation

Experimental

14 Oct 2011

• FEA results compared to measurements around instant of fault (above, left), instant of recovery (above, right), and ratio of inductance (right)

• Convincing agreement of model and measurement


11

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


Additional Slides


13

Coreless Model: Parameters

14 Oct 2011

• 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


14

Coreless Model: Equations and BCs

0

0

Jn

An Magnetic and electric insulation

0

0

coiltot AIj DEJ External current density

All vectors are in cylindrical coordinates

Axis of symmety

0

0

0

2

coiltotr AIj BvHA

Multi-turn coil domain

AB

AE

DEJ

JH

J

jV

AIj coiltot

0

0

0

Governing equations

HB

ED

r

r

0

0

Material equations


15

Coreless Model: No-Fault Condition

LCoil = 0.96 mH

ρSC = 10−15 Ωm ICoil = 500 A

Model input

Model output

mH 00.1

22

0

2

Coil

SCCoil

h

rrNL

Cross-validation by adapted formula for long cylindrical coil:


16

Coreless Model: Fault Condition

ρSC = 1 Ωm ICoil = 20 kA

Model input

LCoil = 2.19 mH

mH 78.2

2

0

2

Coil

Coil

h

rNL

Cross-validation by simple formula for long cylindrical coil:

Model output


17

Coreless Model: Inductance Ratio wrt. Gap Distance

• Primary winding: rCoil = 0.5 m (const) • SC stack radius: rSC = 0.30, 0.32, ...0.48 m

Corresponds to 20 cm gap

Corresponds to 2 cm gap

0

0.5

1

1.5

2

2.5

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48

Radius [m]

Ind

uc

tan

ce

[m

H]

L_nonFault [mH]L_Fault [mH]

0

1

2

3

4

5

6

7

8

9

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48

Radius [m]

Ra

tio

(L

_n

on

Fa

ult

/L_

Fa

ult

)

ratio


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

18 14 Oct 2011 Comsol Conference 2011

Documents

Coupled Magnetodynamic and Electric Circuit Models for ......14 Oct 2011 1 Coupled Magnetodynamic and Electric Circuit Models for Superconducting Fault Current Limiter Presentation