Simulation of Synchronous-Hysteresis Superconducting Machine · Simulation of...
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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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Motivation
• Several works in the literature have proposed replacing HTS bulks
by HTS 2G tapes in trapped field motors*
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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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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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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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0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
Torq
ue (
Nm
)
Speed (rpm)
Torque vs Speed
94,9189,5
284,5379,4
473,8568,1
663,6757,7
852,2
948,31043,5
1135,4
0
200
400
600
800
1000
1200
100 200 300 400 500 600 700 800 900 1000 1100 1200
Measure
d s
peed (
rpm
)
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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H Formulation
A-V Formulation
Mixed A-V-H Formulation
Simulation Models
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Simulation Models: H Formulation
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COMSOL’s Magnetic Field Formulation
𝐸 𝐽 = 𝐸𝑐𝐽
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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𝜎𝜕𝐴
𝜕𝑡+ ∇ × 𝐻 = 𝐽𝑒𝑥𝑡
𝐵 = ∇ × 𝐴
∇ ⋅ μ0μrH = 0
𝜎 =𝐽𝑐𝐸𝑐
𝐸 + 𝐸0𝐸𝑐
1−𝑛𝑛
At the boundary, 𝐴𝑧 = 0
Air
Steel
Superconductor
Copper windings
Homogeneized𝐽𝑐 𝐵 =𝐽𝑐0
1 +𝐵𝑟𝐵0
𝛽
Considering Flux-Creep region, zero field cooling
Simulation Models: Mixed Formulation*
COMSOL’s General and Coefficient PDEs
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*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
𝐻𝑡𝐴 = 𝐻𝑡
𝐻 𝜌(𝐽) =𝐸𝑐𝐽𝑐
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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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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Results: H Formulation Model
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Magnetic Field along the air gapInduced Current Density – z component
along the supercondutor ring
Influence of field harmonics are low in the induced
current density
𝐽𝑐 = 2.98 𝑥 107 Τ𝐴 𝑚2 , f = 60Hz, n=25, locked rotor
Results: A-V Formulation Model
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Magnetic Field along the air gapInduced Current Density along the
Superconductor ring
𝐽𝑐0 = 2.98 𝑥 107 Τ𝐴 𝑚2 , B0= 0.5T, 𝛽 = 1, f = 60Hz, n=25, synchronous speed
Results: A-V Formulation Model
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• Many disturbances at synchronous speed, but amplitude stays the
same
• Many convergence problems arise
Results: Mixed Formulation Model
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𝐽𝑐0 = 3.437 𝑥 107 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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𝐽𝑐0 = 3.437𝑥 107 Τ𝐴 𝑚2 , f = 60Hz, n=25, no load condition
Torque vs Time Speed vs Time
Results: Mixed Formulation Model
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𝐽𝑐0 = 3.437𝑥 107 Τ𝐴 𝑚2 , f = 60Hz, n=25, load condition
Magnetic Field – radial component Current Density along the Superconductor ring
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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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Thank You!
Bárbara M. O. SantosMSc. Student
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