1. AC Loss For YBCO Coated Conductor In Utility Power Applications
M. Sumption, Milan Majoros and E.W. Collings
1LASM, MSE, Ohio State University
                                                                  
Sixth Annual EPRI Superconductivity Conference and Task Force Meeting (Sep'06)
Acknowledgements: V. Selvamanickam (S-power), Funded by AFSOR Phase II (LEI) and previous Phase I (HTR). Also, Summer Research Faculty, ARFL
Department of Materials Science and Engineering

2. Representative Applications
1. Transmission Line
2. Transformer
3. Fault Current Limiter
4. Motor/Generator

3. Loss Types in YBCO Transport Loss External Field Loss
Combined Transport and Field Loss
Transmission Configuration
Special Considerations for YBCO

4. Transport Loss AC Current only (No Field)
Hysteretic Losses (mostly), eddy current loss
P  I/Ic4 for strip, also P  w2
Filamentarization + twist does not help
Filamentarization + Braid works

5. External Field Loss Hysteretic Ferromagnetic Substrate
Loss 500 Hz/ 1 T
1 kW/m
70 mW/m
20 W/m
Hysteretic
Ferromagnetic Substrate
Normal Metal Eddy Currents
Coupling Eddy Currents
Cu I2R loss = some W/cm3
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6. Combined Transport and Field Loss
IDC + BAC
IAC + BDC
IAC + BAC
Relative Phase
Relative Size

7. Transmission Lines -- I
Approximate as thin-wall, hollow tube
Losses go down as h (SC thickness)
Losses go up with I3, down as R2
Current into page
Implication – (1) YBCO Q < BSCCO Q (2) I/Ic fraction again important, striping, cutting, not needed to first order.

8. Transmission Lines II -- GAPS
Losses << transport Q of isolated tapes,
Q  width  B
BUT, gaps let field through, so
More SC exposed to B and thus Q increases
Q gap2 in end regions
Make Gaps small, route field to keep it out

9. Special Considerations for YBCO
Influence of high Aspect Ratio
Influence of ferromagnetic (Even “soft” ferromagnetic elements)
Transposition
Stability
Protection

10. Representative Applications
1. Transmission Line
2. Transformer
3. Fault Current Limiter
4. Motor/Generator
T- Line Configuration
Stray External Field Dominated
Resistive – Transport, inductive external field
Rotor – DC + Negligible ripple unless shielding removed

11. Transformer Loss small where B  thin side Loss large when B 
Bstray – T
B main – 1-2 T
Can either reduce width or stripe – but striping requires transposition

12. Externally Applied Field Loss at OSU–4 cm Sample Solenoid Rig
Primary coil: at least 200 Hz at 140 mT, built for 500 Hz
Pick-up
Compensation
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13. (2) Racetrack Primary – 20 cm samples active field
Applied Fields of 100 mT, 2% field homogeneity

14. Power Loss for Unstriped and 40 Stripe Conductors
striping
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15. Transposition Can either twist
Or transpose using small resistive links

16. Fault Current Limiter Two types Resistive –Transport loss only
Inductive – saturated or non-saturated Fe – back to the case of the transformer

17. Transport and Helmholtz Rig
AC Current only (No Field)
Hysteretic Losses (mostly), eddy current loss
P  I/Ic4 for strip, also P  w2
Filamentarization + twist does not help
Filamentarization + Braid works

18. YBCO Coated Conductor Transport Loss
More or less follows Norris cubic equation (ellipse)
But why ellipse
Not perfect agreement
Reasons
Substrate ferromagnetism
Non-uniform Jc
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19. Field Enhancement due to Ferromagnetic layer
Tape width = 5 mm
YBCO film thickness = 1 m
Buffer layer thickness = 0,
Substrate thickness = 100 m,
YBCO film Jc=1010 A/m2

20. Transport Loss Increase with Ferromagnetic Layer

21. Motor/Generator Rotor DC element with AC ripple only Stator
High External Field in Regions (1-2 T)
Combined with transport current

22. Section III: Coil Data and Dynamic R
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23. Dynamic Resistance: Full Penetration
Interactions of DC current and AC field in superconductors leads to a loss.
Energy for “Alternating Field Loss” is provided by the magnet
Energy for this latter loss is provided by the DC power Supply, and is interpreted as a resistance
This is the dynamic resistance, and is given by the equation at right
This model is valid for Full Penetration
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24. Dynamic Resistance: Partial Penetration (Heuristic)
SI unit
Let the penetration along the width be x
Let the critical penetration be x* = w-a
Where a is the region of loss-less current flow at the sample interior
Clearly a = (I/Ic)w leading to
K  1
Using Bm=K0Jcx*, we can find that
A criterion for Ic reduction based on Hm
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25. Dynamic Resistance in CoilsIf
Note: This is DC current and AC field, but AC current and DC field has similar properties, also AC current and field
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26. Looking More Closely at Dynamic Resistance Onset
This leads to 1/(JcwK) = 50
Which means that if K  1 and w = is 2m.
But this should be no surprise, since really, the thickness is controlling the penetration
Slope = -50
This leads to a good fit for the experiment to the theory, but now

27. Looking More Closely at Dynamic Resistance
Imperfect extrapolation
Can be usefully re-written
Thus
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28. Operative Equations
This denotes the onset of dynamic resistance. In our case the resistance is large, and this becomes a kind of Ic,eff
The resistance value itself scales with dB/dt and w
Even as w becomes reduced and the onset of dynamic resistance no longer imitates a SC transition, we will have significant losses from this component, given at left
If w = 1 cm, I = 200 A, and Iop = 07Ic, P/L = 0.12 Watts *dB/dt
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29. Loss Numbers for Dynamic Resistance
Dynamic Resistance only calculated for unstriped
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30. Machines and Design for Application
1. What about stability and protection?
2. What are dominant losses in various applications and what kind of conductor are needed for each application?
3. What will the likely operating parameters of the machine be, how is that related to YBCO characteristics
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31. Rotor Fields Rotor scalar fields at right in T
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32. Some Targets and Estimates for Motor/Generator
Barnes, Sumption, Rhodes,
Cryogenics 45 (2005) 670–686
No estimates here of Dynamic resistance effects
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33. Adding in Dynamic Resistance Effects
If w = 1 cm, I = 200 A, and Iop = 07Ic, P/L = 0.12 Watts *dB/dt
Jim Parker [LEI] estimates that unshielded rotors will have a “field” somewhere in the 2 mT range [40 mT peak at worst spots]
Shielded rotors should have this attenuated by a factor of 1000 [J Parker]
dB/dt = 4Bmf = 4*2 x 10-6 * 500 = 10-3 T/s – for unstriped conductor this leads to 0.1 mW/m for shielded rotor, but much larger for all-cryogenic machine (unshielded rotor) – 100 mW/m. Striping will correct this sufficiently
For stators, field is 106 times larger, so filaments 104 times smaller than 1 cm at required at minimum – consistent with constraints from hysteretic loss
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34. Adding Up Losses in a Generator
SC rotor: 0-2 W Rotor shield: 360 W Windage in a cryogenic liquid or gas machine: 1500 W Stator, Cu based: 2000 W
Machine scenarios
Conventional
Hybrid (Cryogenic rotor, oil cooled stator)
All Cryogenic, liquid cryogen
All Cryogenic, Conduction

35. Variants
0. Conventional: Benchmark. All the variants below are assumed to have the target of a greater energy density (as compared to this option) their main goal. Losses are 1500 W W W + normal stator Watts  = nearly = W.
1. Hybrid, SC rotor and Cu stator, the latter oil cooled at RT. Increases powder density, avoids difficulty of stator windings. Losses are = 1500 W W W + [0-2 W * 10] = nearly = W. No real lessening of losses, but increased rotor field, thus machine power, thus power

36. Variants II
2. All SC, operating in liquid cryogen--Losses are unessential, since all in hydrogen ] = [1500 W W W ]*[factor related to inconvenience of hydrogen liquification] = nearly = 4000 W * [very small number] = not important practically, but would be same for Cu system, so must win on power density
3. All SC, operating in a cryocooled state. Losses are = [no windage (assume operate in vacuum) + 2 W (assume non-metallic stator support and low loss stator conductor) + X W from stator ] * [factor of 10 penalty factor] = nearly = stator losses * penalty factor ----But this implies operation in vacuum, ac tolerant SC

37. Integrating the Conductor Into the Machine
Investigations of Winding Geometries
I-V loss Measurements for various diamond stator windings

38. Low Loss Conductors: Will They be “Stable” Enough for Machines?
groove depth extends into substrate Ag
YBCO
Buffer
Substrate
Striped YBCO Layer, striped overlayer, resistive substrate
Can we afford not to stripe Cu overlayer from a stability-protection/current sharing? Can we afford the loss if we don’t?
Department of Materials Science and Engineering

39. Stability/Protection/Current Sharing vs AC loss
Perhaps we can stripe with little or no connection (Some will not agree)
We must remember that YBCO at relevant operation regimes are arguably nearly intrinsically stable (energy margin), but they are very difficult to protect. But this is not directly helped by filament interconnection
Current sharing would reduce possible current distribution inhomogeneity – or Ic inhomogeniety
This can be perhaps addressed with connections that are very high resistance – 400 cm or more
Department of Materials Science and Engineering

40. Summary 1. Transmission Line 2. Transformer 3. Fault Current Limiter
4. Motor/Generator
T- Line Configuration
Stray External Field Dominated
Resistive – Transport, inductive external field
Rotor – DC + Negligible ripple unless shielding removed