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Simulation of Synchronous-Hysteresis

Superconducting Machine

Bárbara M. O. Santos1, Fernando Dias1,3, Felipe Sass2, Guilherme Sotelo2,

Alexander Polasek3 and Rubens de Andrade Jr1

1Federal University of Rio de Janeiro (UFRJ)

2Federal Fluminense University (UFF)

3Electric Power Research Center (CEPEL)

Outline

1. Motivation

2. Studied prototype

3. Objectives

4. Simulation Models

5. Results

6. Conclusion

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Simulation of Synchronous-Hysteresis Superconducting Machine 2

Motivation

• Several works in the literature have proposed replacing HTS bulks

by HTS 2G tapes in trapped field motors*

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Simulation of Synchronous-Hysteresis Superconducting Machine 3

Trapped field rotors

With bulks With HTS tapes

*G.G. Sotelo, F. Sass, M. Carrera, J. Lopez-Lopez and X. Granados. Proposal of a Novel Design for Linear Superconducting Motor Using 2G Tape Stack. IEEE Transactions on Industrial Electronics., vol 65, no 9, Sept. 2018.

Studied Prototype

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Simulation of Synchronous-Hysteresis Superconducting Machine 4

Prototype built at UFRJ and CEPEL. Non-superconducting three-phase stator and

rotor made of two rings of nine turns of HTS 2G tapes wrapped around a

ferromagnetic cylinder.

Maximum radius 56 mm

Length 28 mm

Tape SuperPower

SF12050

Phases and Poles 3 Phases, 6 Poles

Critical current

measured

377 A

Adapted from a 0.47Nm

Permanent Magnet Machine

Studied Prototype

Trapped Field Motor with HTS 2G Tapes

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Simulation of Synchronous-Hysteresis Superconducting Machine 5

Superconductor is magnetized by the rotating magnetic field applied

The mode of operation depends

on the mechanical torque

𝜏𝑚𝑒𝑐 < 𝜏𝑝𝑖𝑛𝑛𝑖𝑛𝑔 𝜔𝑚𝑒𝑐 = 𝜔𝑠𝑖𝑛𝑐

𝜏𝑚𝑒𝑐 > 𝜏𝑝𝑖𝑛𝑛𝑖𝑛𝑔 𝜔𝑚𝑒𝑐 < 𝜔𝑠𝑖𝑛𝑐

Synchronous machine

Hysteresis machine

Studied Prototype

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Simulation of Synchronous-Hysteresis Superconducting Machine 6

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

T o rq

u e (

N m

)

Speed (rpm)

Torque vs Speed

94,9 189,5

284,5 379,4

473,8 568,1

663,6 757,7

852,2

948,3 1043,5

1135,4

0

200

400

600

800

1000

1200

100 200 300 400 500 600 700 800 900 1000 1100 1200

M e a s u re

d s

p e e d (

rp m

)

Synchronous speed (rpm)

Measured speed vs Synchronous speed

5% slip appeared in the torque vs

speed curve

Mechanical torque applied.

Experimental data

Objectives

• Observe the induced current density in the rings at locked

rotor

• Analyse machine behavior at synchronous speed

• Analyse the dynamic response

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Simulation of Synchronous-Hysteresis Superconducting Machine 7

H Formulation

A-V Formulation

Mixed A-V-H Formulation

Simulation Models

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Simulation of Synchronous-Hysteresis Superconducting Machine 8

Simulation Models: H Formulation

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Simulation of Synchronous-Hysteresis Superconducting Machine 9

COMSOL’s Magnetic Field Formulation

𝐸 𝐽 = 𝐸𝑐 𝐽

𝐽𝑐

𝑛−1

∇ × H = J

μ𝜕H

𝜕t + ∇ × E = 0

At the boundary, 𝐻𝑥 = 𝐻𝑦 = 0

Homogeneized𝐽𝑐

Air

Steel

Superconductor

Copper windings

36-slot stator

72-slot stator

Linear B-H curve for all

materials

Considering Flux-Creep region,

zero field cooling

Simulation Models: A-V Formulation

COMSOL’s Rotating Machinery, Magnetics

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Simulation of Synchronous-Hysteresis Superconducting Machine 10

𝜎 𝜕𝐴

𝜕𝑡 + ∇ × 𝐻 = 𝐽𝑒𝑥𝑡

𝐵 = ∇ × 𝐴

∇ ⋅ μ0μrH = 0

𝜎 = 𝐽𝑐 𝐸𝑐

𝐸 + 𝐸0 𝐸𝑐

1−𝑛 𝑛

At the boundary, 𝐴𝑧 = 0

Air

Steel

Superconductor

Copper windings

Homogeneized𝐽𝑐 𝐵 = 𝐽𝑐0

1 + 𝐵𝑟 𝐵0

𝛽

Considering Flux-Creep region, zero field cooling

Simulation Models: Mixed Formulation*

COMSOL’s General and Coefficient PDEs

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Simulation of Synchronous-Hysteresis Superconducting Machine 11

*R. Brambilla, F. Grilli, L. Martini, M. Bocchi and G. Angeli. A Finite Element Method Framework for Modeling Rotating Machines With Superconducting Windings. IEEE Trans. Appl. Supercond., vol 28, no 5, Aug. 2018.

𝜎 𝜕𝐴

𝜕𝑡 − 1

𝜇 ∇2𝐴 = 𝐽𝑒𝑥𝑡

𝐵 = ∇ × 𝐴

μ𝜕H

𝜕t + ∇ × E = 0

∇ × H = J

𝐻𝑡 𝐴 = 𝐻𝑡

𝐻 𝜌(𝐽) = 𝐸𝑐 𝐽𝑐

𝐽

𝐽𝑐

𝑛−1

Homogeneized𝐽𝑐

Stator,

Rotor air

gap

Rotor

Considering Flux-Creep region, zero field cooling

Simulation Models: Mixed Formulation*

• A simpler stator was used;

• The stator moves in the opposite direction.

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Simulation of Synchronous-Hysteresis Superconducting Machine 12

A few remarks:

The mechanical model was implemented with COMSOL’s Global ODEs and

PDE’s and Moving Mesh

𝑇𝑒𝑙𝑒𝑐𝑡 − 𝑇𝑚𝑒𝑐 = 𝐽𝑑𝜔

𝑑𝑡

Convergence

Simulation time

Results

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Simulation of Synchronous-Hysteresis Superconducting Machine 13

Results: H Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 14

Magnetic Field along the air gap Induced Current Density – z component

along the supercondutor ring

Influence of field harmonics are low in the induced

current density

𝐽𝑐 = 2.98 𝑥 10 7 Τ𝐴 𝑚2 , f = 60Hz, n=25, locked rotor

Results: A-V Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 15

Magnetic Field along the air gap Induced Current Density along the

Superconductor ring

𝐽𝑐0 = 2.98 𝑥 10 7 Τ𝐴 𝑚2 , B0= 0.5T, 𝛽 = 1, f = 60Hz, n=25, synchronous speed

Results: A-V Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 16

• Many disturbances at synchronous speed, but amplitude stays the

same

• Many convergence problems arise

Results: Mixed Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 17

𝐽𝑐0 = 3.437 𝑥 10 7 Τ𝐴 𝑚2 , f = 60Hz, n=25, no load condition

Magnetic Field – radial component Current Density along the Superconductor ring

Results: Mixed Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 18

𝐽𝑐0 = 3.437𝑥 10 7 Τ𝐴 𝑚2 , f = 60Hz, n=25, no load condition

Torque vs Time Speed vs Time

Results: Mixed Formulation Model

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Simulation of Synchronous-Hysteresis Superconducting Machine 19

𝐽𝑐0 = 3.437𝑥 10 7 Τ𝐴 𝑚2 , f = 60Hz, n=25, load condition

Magnetic Field – radial component Current Density along the Superconductor ring

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Simulation of Synchronous-Hysteresis Superconducting Machine 20

Results: Mixed Formulation Model

Torque vs Time Speed vs Time

Conclusion

• Air-gap magnetic field harmonics have little impact on

the induced current density;

• As speed increases, the current density distribuition

along the ring increases;

• The hysteresis region is larger than expected;

• The speed response is overdamped.

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Simulation of Synchronous-Hysteresis Superconducting Machine 21

Thank You!

Bárbara M. O. Santos MSc. Student

barbara.maria@poli.ufrj.br

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Simulation of Synchronous-Hysteresis Superconducting Machine 22

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