Simulation of Synchronous-Hysteresis Superconducting Machine Simulation of Synchronous-Hysteresis Superconducting

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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

    20:38

    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

    20:38

    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

    20:38

    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

  • 20:38

    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

    Support