1. 2012 Applied Superconductivity Conference, Portland, Oregon
FEM Studies of AC Loss During Charge and Discharge of a SMES Coil made with CORC (YBCO based) cable
M.D. Sumption, M. Majoros, and E.W. Collings
CSMM, Materials Science Department, The Ohio State University
D. Van Der Laan
Advanced Conductors Inc.
for the
2012 Applied Superconductivity Conference, Portland, Oregon
4LE-06
Funded by an Air Force SBIR

2. SMES modeling based on pre-determined cable length
The Energy and Power of various nominal SMES coil designs are estimated at 4.2 K using various fixed cable lengths.
The strand lengths are fixed at 2.5 km, 5 km, 12.5 km, 25 km, 50 km and 10 km.
The stored energies of the SMES are maximized by varying the coil dimensions (Rin, Rout an h) for each cable length.
The rate at which the SMES can be charged and discharged is calculated from the self-inductance, while setting the maximum voltage at 270 V:
dI/dt = 270/L.
 The operating current of the SMES determines the maximum time and power at which the SMES can be charged or discharged.
Estimations and Target by Advanced Conductors Inc

3. SMES modeling based on pre-determined cable length
There are three different scenarios:
A -- Proven cable technology tape cable with 8 mm OD.
B tape cable-but wound on a larger former that brings the outer diameter of the cable to 16 mm. The benefit of this cable is that the operating field of the SMES is relatively low, which raises the operating current significantly.
C -- a high-Ic , 60 tape cable with 9 mm OD
Main differences are coil dimensions and the maximum discharge power.
SMES made from low-Je (type-B) or high-Ic (type-C) cables can be charged at relatively high rates.
The low-Je SMES (type-B) also has a slightly higher stored energy, but has a relatively large outer diameter times that of the SMES in scenarios (type-A) and (type-C). Its size is a disadvantage.
Estimations and Target by Advanced Conductors Inc

4. Case A: 40-tape cable with 8 mm OD
Nominal Calculations
Estimations and Target by Advanced Conductors Inc

5. Case B: 40 tape cable --16 mm OD
Estimations and Target by Advanced Conductors Inc

6. Case C --High-Ic , 60 tape cable, 9 mm OD
Estimations and Target by Advanced Conductors Inc

7. Summary of Nominal Estimates
At a fixed strand total length of 100 km, and cable lengths between km, the energies of systems A, B, and C were 12,16, and 16 MJ
For these systems, and discharge power, given Air Force voltage limits was 0.8, MW, 1.15 MW, and 1.15 MW (A,B, and C) – about 10 x better than batteries achieve
The SMES will be designed to operate T > 4 K, to avoid cryogens on aircraft, so performance needs to be estimated (and to do this Ic vs B measurements performed at 10 and 20 K)
However, as 4 K data is available for Ic, we will do an initial calculations at 4 K
We are interested in ball-park AC loss estimates, to estimate order-of magnitude temperature rise

8. SMES AC loss at ramp of its current from 0 to Ic - FEM modeling
We adopted the Kim model for the B dependence of the Jc
(1)
Here Jc is the critical current density and B is the magnetic flux density. For a SC slab of width 2b in parallel B, the full penetration field, Bp , in Kim’s model is given by
(2)
For the difference B between the applied magnetic field Ba and the field in the center of the slab we have

9. SMES AC loss at ramp of its current from 0 to Ic - FEM modeling II
In practice, the difference B is usually small as compared with the characteristic scale of variation of the function Jc(B).
This means that the critical current density in the sample varies only slightly, and we can use the Bean’s critical state model with Jc = Jc(Ba)
If Ba rises from Ba = 0 to Ba = Bm we have the hysteresis loss
We considered the winding as a system of superconducting slabs filled with turns with a corresponding filling factor, and used FEM for magnetic field calculation in the winding cross-section.
Bp was calculated from (2) and ac loss calculation using (4), (5) was performed.

10. Jc data and fit
Ic(B) curve of the cable used in the modeling. Blue solid rectangles – experimental data, red continuous line – a fit of the data by Kim’s model (eq. (6)) (I0 = A, B0 = T).

11. SMES Cross Section Cross-section of a SMES solenoid. RI – inner radius
RO – outer radius
h – length of the solenoid.
Because of a cylindrical symmetry only a half of the cross-section is shown.

12. Case A: Field Map, I/Ic =0.4
B(T) in Tesla

13. Case A: Nr=1, full and partial penetration, (I/Ic=0.4)
Loss J/m3
Loss J/m3
Case A (Nr 1): Partial penetration loss distribution in the solenoid winding at I/Ic = 0.4.
Case A (Nr 1): Full penetration loss distribution in the solenoid winding at I/Ic = 0.4.

14. Total Loss Case A I/Ic=0.4
Loss, J/m3

15. Case A: Nr=1, Field Map, I/Ic = 1

16. Case A: Nr=1, full and partial penetration (I/Ic=1)
Loss, J/m3
Loss, J/m3
Case A (Nr 1): Partial penetration loss distribution in the solenoid winding at Ic
Case A (Nr 1): Full penetration loss distribution in the solenoid winding at Ic

17. Total Loss Case A I/Ic=1
Loss, J/m3

18. AC Loss vs I/Ic for SMES (smallest)
AC losses of the SMES solenoid (case A, Nr 1) at different Ic
The black solid lines show the slopes proportional to (I/Ic)3 and (I/Ic)1.
While at the ramp 0 – 0.4Ic the contribution of the partial- and full-penetration loss is more or less equal
At ramp 0 – Ic the full-penetration loss dominates
At right is the whole ac loss curve. It has two characteristic slopes: (I/Ic)3 at low currents and (I/Ic)1 at currents close to Ic.

19. Losses for ramp to full field: Case A Design

20. Losses for ramp to full field: Case B Design

21. Losses for ramp to full field: Case C Design

22. Energy per units length of strand, and Energy per unit volume of coil
Note, power of systems is about constant at 1 MW

23. Estimated Loss, Temperature rise, recovery time, Mode C
Using 7.8 g/cm3 as density
Assuming Cp of steel
Tstart at 20 K
Assuming 50W heat removal at 20 K

24. Summary/Conclusions
Roughly speaking the ac losses represent about 1.5% - 2.5% of SMES stored energy.
Loss is roughly linear with Stored energy, about 0.15 MJ for a 10 MJ system
About 100 km of cable is needed for these designs for 10 MJ
System size is about 0.2 cubic meters for coil only (simple nominal, no added reinforcement)
Cable design allows for 1MW power even at 270 V (good for aircraft)
Simple estimations gave 10 K temperature rise and 45 minute recovery – needs improvement