ELECTRICAL PARAMETERS IN MULTISTRAND SUPERCONDUCTING CABLES AND THEIR EFFECT ON STABILITY

1
ELECTRICAL PARAMETERS IN MULTI-STRAND
SUPERCONDUCTING CABLES AND THEIR EFFECT ON
STABILITY

• Bing Lu and Cesar Luongo
• Department of Mechanical Engineering
• FAMU-FSU College of Engineering, and
• Center for Advanced Power Systems
• Tallahassee, Florida, USA

Presented at the CHATS on Applied
Superconductivity Workshop, Berkeley, California,
September 5-7, 2006
This work was supported by the Center for
Advanced Power Systems through a grant from the
Office of Naval Research
2
Outline

• Introduction
• Theoretical Approach
• Experiment
• Results and Discussion
• Conclusions

3
Introduction Superconducting Cables

• Superconducting cables are widely used in large
  scale magnet applications.
• ? MRI ? SQUID ? Particle Accelerator
• ? Power Systems ? Magnetically levitated
  vehicles
• Multi-strand superconducting cables
• Higher stability
• Larger current carrying capability

4
Introduction Stability of CICC

• Stability is one of the key issues for
  continuous and reliable operation of CICC
• Stability events involve the response of the
  cable to thermal, fluid dynamic and electric
  transient phenomena

Flow model
Electrical model
Volumetric flow
Pressure
Thermal model
Temperature
L. Bottura, C. Rosso, B. Breschi, Cryogenics
40617-626, 2000
5
Introduction Influence of Non-uniform Current
Distribution on Stability

• Non-uniform current distribution is caused by
• External disturbances
• Transient current and field
• Different interstrand conductance
• Other boundary conditions
• Non-uniform current distribution may lead to
  premature quench
• Non-uniform current distribution causes ramp rate
  limitation

6
Introduction Stability Improvement by Current
Re-distribution

• Efficient current re-distribution improves cable
  stability
• Time constant for current transfer must be
  smaller than time constant for thermal diffusion
• Time constant for current transfer is dominated
  by interstrand conductance g
• Trade-off between stability and coupling loss

7
Introduction Electrical Parameters in
Superconducting Cables

• Any analysis of current distribution and
  re-distribution in multi-strand superconducting
  cables depends on the electrical characteristics
  of the cable.
• Strand longitudinal resistance r
• zero in superconducting state
• Self and mutual inductances l
• influence dynamic response of cable
• Interstrand conductance g
• influences cable stability and AC loss
• Trade-off between stability and AC loss

8
Introduction Interstrand Conductance (I)

• Interstrand conductance g has major influence on
  coupling loss and stability
• Factors that determine interstrand conductance
• surface layer properties
• crystalline structure
• degree of oxidation
• interstrand micro-sliding
• interstrand contact condition
• cable geometry
• mechanical loading
• Strong interest in directly measuring g at
  different cable stages to correlate mechanical
  cable configuration and electrical properties

9
IntroductionInterstrand Conductance (II)
Four-point method the widely used experimental
method for studying interstrand conductance
Example of results
g 1/Rc (W-1 m-1)

• Difficult to obtain fine detail of g from Rc
  data (especially in large cables)

10
Introduction Summary

• Stability is one of the key issues for CICC
• Stability is largely dominated by the
  thermo-hydraulics of helium in the cable space,
  but it is also influenced by the transient
  current distribution among strands during a
  stability event
• Accurate evaluation of the cable electrical
  parameters is very useful for understanding
  current distribution in superconducting cables
  and how that influences stability, as well as AC
  losses, ramp-rate limitations, and n-value of
  cable
• Objective to develop a new approach to evaluate
  the interstrand conductance in CICC that will
  allow for fine details of g in-situ (e.g. under
  different mechanical loads, temperatures, etc.)
• Will use distributed parameter circuit model plus
  parametric estimation method (from control
  theory) to develop new approach to measure g

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Overview of the Parameter Estimation Model

• Use distributed parameter circuit model (1) to
  calculate the voltage differences at cable ends
• Design experiment to measure strand voltage
  differences at cable ends
• Apply least squares method to estimate the
  interstrand conductance by minimizing the norm of
  least squares criterion J matrix with respect to
  g

r strand longitudinal resistance r l self and
mutual inductances g interstrand conductance
(1)
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Distributed Parameter Circuit Model (I)
Kirchhoff's laws Conservation of
current Assuming uniform interstrand
conductance v voltage i current vext
external voltage source r longitudinal
resistance l inductance g interstrand
conductance
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Distributed Parameter Circuit Model (II)
Strand voltage
Strand current
External voltage source
Vext0 in our experiment
inductance
Longitudinal resistance
Interstrand conductance to be measured
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Basic Least Squares Method (I)
The voltage difference equation can be derived
from the equation of voltage

• Output (voltage difference with respect
  to reference strand) can be measured by
  experiment
• Input can be calculated from system
  equation
• The parameter matrix can then be estimated by
  least squares method

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Basic Least Squares Method (II)
With m sets of data, the voltage equation becomes
matrix form
Measured voltage differences
Calculated current derivative
Parameter to be estimated

• Output (voltage differences measured at
  time t1, t2, tm)
• Input Y calculated from system equation
• is calculated voltage differences

Minimizing
with respect to Q
The least squares estimator is
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Sequential Least Squares Method

• Improve the parameter estimates with fresh
  experimental data
• new estimate old estimate correction term
• P(m) can be updated recursively
• Correction term is proportional to fitting error
• Fitting error is weighted in the correction

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Experiment to Demonstrate Method
Cable sample 656 NbTi CICC used in CAPS SMES
coil

• 1 to 3 digits to specify sub-cables
• First digit third stage sub-cable
• Second digit second stage sub-cable
• Third digit first stage strand
• Examples of interstrand conductance
• g12 g 1-1,1-2 g 1-1,4-1 g
  1-1-1,1-1-2 g 1-1-1, 3-1-1

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Experimental Set-up (I)

• Measurements
• Supply ramp current to one cable end
• Measure Voltage differences at the other cable
  end in transient state
• Measure Operating currents
• Transient data
• General Application of LSE
• Multiple sets of data in each test when the cable
  was in transient state
• different current and voltage differences
• Time constant of cable

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Experimental Set-up (II)

• Repeat experiment in different conditions
• Longitudinal resistance changes with temperature
  and cable length, inductance changes with cable
  length
• g does not change with temperature and cable
  length
• g changes with mechanical load

20
Results Interstrand Conductance Between 3rd
Stage Sub-cable
The 3rd stage sub-cables are wrapped with
stainless steel foil to limit AC loss.
Interstrand conductance (?-1m-1)
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ResultsInterstrand Conductance Between 2nd
Stage Sub-cables
Average 19335 O-1m-1 (intra-bundle)
Interstrand conductance (?-1m-1)
Average 2308 O-1m-1 (inter-bundle)
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ResultsInterstrand Conductance Between 1st
Stage Strands
Average2.97107 O-1m-1
Average19124 O-1m-1
Interstrand conductance (?-1m-1)
Interstrand conductance (?-1m-1)
Average2033 O-1m-1
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Consistency of Results
Results obtained in different conditions
(different temperature, different cable length)
are consistent
Interstrand conductance (?-1m-1)
Interstrand conductance (?-1m-1)
Adds confidence to the validity of the estimation
method
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Summary of Results (No Load)
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Error Analysis

• Error of g

• Error between calculated and measured voltage
  differences

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ResultsEffect of Mechanical Load (I)
Interstrand conductance between 3rd stage
sub-cables
Load
G10
Liquid Nitrogen
Cable
Metal pan
Foam
Fiber glass pan
6
5
G10 insulation
1st cycle
Interstrand conductance (?-1m-1)
Load was applied at 77K

• First cycle configuration
  change plus hysteresis

• Conductance increases with applied
  force

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ResultsEffect of Mechanical Load (II)
Interstrand conductance between 2nd stage
sub-cables within same 3rd stage sub-cables.
6
5
1st cycle
Interstrand conductance (?-1m-1)
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ResultsEffect of Mechanical Load (III)
Interstrand conductance between 2nd stage
sub-cables in different 3rd stage sub-cables
6
5
1st cycle
1st cycle
Interstrand conductance (?-1m-1)
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ResultsEffect of Mechanical Load (IV)
Interstrand conductance between 1st stage strands
1st stage
2nd stage
3rd stage
4th stage
CICC
3
1-1-2
1-2
4
1-3
1-1-3
1
2
2
3
6
1-1-1
4
5
1-1
1-1-6
1-1-5
1-1-4
1-5
1
Copper wire
1-4
6
5
strands in same third stage sub-cables
strands in different third stage sub-cables
1st cycle
1st cycle
Interstrand conductance (?-1m-1)
Interstrand conductance (?-1m-1)
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Comparison with Previous Data (I)
Interstrand contact resistance in various
prototype ITER NbTi conductors and CAPS SMES coil
conductor
Comparison of interstrand conductance (O-1m-1)
A. Nijhuis, Cryogenics 44 319-339, 2004
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Comparison with Previous Data (II)
Similar trend when mechanical load is applied
A. Nijhuis and etc., IEEE Trans. on Appl.
Supercond., Vol. 9, No. 2 754-757, 1999
CAPS data
With our approach, we can show evolution of g at
all stages for varying mechanical load
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Application of Results
Estimated g can be put into electrical model to
study its influence on current distribution, and
on consequent thermal and hydraulic response
Flow model
g
Electrical model
Thermal model
L. Bottura, C. Rosso, B. Breschi, Cryogenics
40617-626, 2000
33
Conclusions

• This is the first time that parametric estimation
  method from system identification theory is
  applied to study the interstrand conductance in
  superconducting cables
• With voltage differences measured at cable ends,
  we used least squares to extract the interstrand
  conductance between sub-cables from the system
  equations
• This method provides a way to evaluate, in-situ,
  the interstrand conductance in multistrand
  superconducting cables under different conditions
  in detail, with a simple experimental set-up