Multi-Objective Optimization of an Actively

Shielded Superconducting Field Winding

David Loder

Dr. Kiruba Haran

1

Outline

Design Concept

Field Computation

Optimization Scheme– Constraints

– Design Space

– Fitness Formulation

Results & Validation

Conclusions

Future Work

2

Background & Motivation

Demand for high power density

Air-core superconducting machines

Containment of magnetic fields

– Eddy Current Shields [1]

– Magnetic Shields (steel)

– Active Shielding [2]

Fig.1. Actively Shielded Air-Core Superconducting Machine

3

Design Concept

Fig.2. Cross Section Flux Density

Fig.3. Main Coils Only Excited

Fig.4. All Field Coils Excited 4

Field Computation

Fig.5. Radial Flux Density along D-axis Fig.6. Radial Flux Density at Armature

2-D Simplification of Biot-Savart (1)

5

Superconducting Constraints

Fig.7. Flux Density in Main Coil

Fig. 8. Nb3Sn Critical Surface [3]

HyperTech T1505 Wires Selected

50% Safety Margin included

0.1% Strain Allowance6

Optimization Design Space

Fig.9. Design Parameters

Field Winding Design Space (2)7

Input θWinding

Geometry Valid?

Armature flux density met?

Within critical surface?

Assign small fitness

Compute Fitness (3)

Return fitness

Increasing Computational

Intensity

No

No

No

Yes

Yes

Yes

Fig.10. Fitness Formulation

Fitness Vector (3)

Define fitness to:– Maximize shielding

– Minimize coil usage

Bmax contained by stator (to below 0.5 mT): 35 mT

[5]

Min. fundamental of radial armature flux density: 2 T

Optimization Scheme: Evolutionary Algorithm [4]

8

Preliminary Results

Fig.11. Pareto-Optimal Front

Design #39 vs. Optimized Uncompensated– 32 % ↓ Rmin

– 33% ↑ Coil Usage9

Validation

Fig.12. Design #39 FEA

Armature flux density: 6% error

Main coil peak flux density: 2% error

Fig.13. Operating Points [6]

10

Conclusions

Combined shielding

– 97% Reduction in stator yoke

– 27% increase in coil usage

– Main coil peak field ↓ 5%

Fig.14. Passive Shielding Fig.15. Combined Active/Passive Shielding

11

Stator Yoke

Future Work

Include End Windings

Include Stator Yoke in Optimization

Expand design space

– Pole Count

– Armature

– Stator Yoke

Incorporate manufacturing considerations in winding geometry constraints [7]

12

[1] H. Woodson, “Eddy-current shield superconducting machine,” U.S. Patent 3772543 A, Nov 13, 1973.J. Clerk Maxwell, A Treatise on E lectricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.

[2] M. Steckner and B.C. Breneman, “MRI magnet and MRI system with optimized fringe, fields, attractive forces and spatial constraints,” U.S. Patent 8729899 B2, May 20, 2014.

[3] J.W. Ekin, “Four dimensional JBT critical surface for superconductors,” J. Appl. Phys., vol. 54, no. 1, pp. 303-306, Sep. 29, 1982.

[4] S.D. Sudhoff, “Optimization-Based Design,” in Power Magnetic Devices: A Multi-Objective Design Approach. Hoboken, New Jersey: Wiley, 2014.

[5] ICNIRP, “Guideline to limits of exposure to static magnetic fields,” Health Phys., vol. 66, pp. 113-122, 1994.

[6] M.D. Sumption, S. Bhartiya, C. Kovacks, et. al., “Critical current density and stability of Tube Type Nb3Sn conductors,” Cryogenics, vol. 52, no. 2-3, pp. 91-99, Dec. 22, 2011.

[7] W. Stautner, K. Sivasubramaniam, S. Mine, J. Rochford, E. Budesheim, and K. Amm, “A cryo-free 10 T high-field magnet system for a novel superconducting application,” IEEE Trans. Aplied Superconductivity, vol. 21, pp. 2225-2228, Jun. 2011.

References