numerical simulation of the performance of hts coils
TRANSCRIPT
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Numerical simulation of the performance of HTS coils
Bulk Superconductivity Group, Department of Engineering
Dr Mark Ainslie Royal Academy of Engineering (UK) Research Fellow
Co-authors: Di Hu, University of Cambridge Victor Zermeno, Karlsruhe Institute of Technology Francesco Grilli, Karlsruhe Institute of Technology
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Presentation Outline
• Electrical engineering applications of superconductivity
• Numerical modelling of HTS coils
• Case study 1: DC characterisation of HTS coils
• Case study 2: Use of flux diverters to improve coil performance
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Electrical Engineering Applications
• Energy security & supply is a crucial 21st century challenge
• US DOE estimates > 35 trillion kWh required worldwide by 2035 [1]
• 1.8 billion middle-class consumers + 3 billion by 2030 [2]
• 90% of this growth from Asia-Pacific region
• Existing methods of electricity supply & usage are unsustainable
• Superconductors offer an opportunity for a step change in power system technology
• Improved efficiency, lower carbon emissions, increased power-density
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[1] http://www.eia.gov/forecasts/ieo/world.cfm [2] Professor Sir David King, “The Politics of Climate Change”
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Electrical Engineering Applications
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Almost all aspects of electric power systems have a superconducting equivalent: • Transformers, cables, electric machines (motors & generators) New technologies enabled by superconductors: • Superconducting magnetic energy storage • Superconducting fault current limiters
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Superconducting Machine Research
• Electric motors & systems they drive are single largest electricity end-use
• 43-46% of global electricity consumption, 6 Gt of CO2 emissions [1]
• Using superconductors can increase electric / magnetic loading of an electric machine
• Higher current density increased power density reduced size & weight
• Lower wire resistance (zero for DC) lower losses & higher efficiency / better performance
• Coils are an integral part of electric machines: stator and/or rotor
[1] Organisation for Economic Co-operation and Development (OECD) / International Energy Agency (IEA), “Energy-efficient policy opportunities for electric motor-driven systems,” 2011
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Superconducting Materials
• Superconductor properties vary with magnetic field & temperature Jc(B, T) dependence
Electromagnetic & thermal considerations
• HTS coils can operate in complex electromagnetic environments
• Transport current (DC or AC)
• Static / dynamic background magnetic fields
• Numerical models are needed! • Can simulate more practical & complex
situations than analytical methods
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Critical parameters for a superconducting material
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Numerical Modelling of HTS Coils
• Numerical modelling plays a number of crucial roles:
• Interpret experimental results & physical mechanisms of superconducting material behaviour
• Simulate accurate current & magnetic field distributions
• Reducing costs & time required for costly & complex experiments
• Design & predict performance of practical superconductor-based devices
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HTS Coil Modelling – What Do We Want To Know?
• DC properties
• Critical current (maximum allowable current)
• AC properties
• AC loss
• Magnetic field
• I vs Bcentre (peak central field)
• Field distribution, incl. homogeneity
• Optimisation of coil geometry
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• Effect of critical current density anisotropy Jc(B,θ)
• Effect of inhomogeneities
• Width, length
• Effect of magnetic materials
• Magnetic substrates
• External flux diverters
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Numerical Modelling of HTS Coils
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• HTS coil geometries take a number of different forms: circular (2D axisymmetric), racetrack & triangular (3D)
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
H = [Hr, Hz] J = [Jφ] E = [Eφ] H = [Hx, Hy, Hz]
J = [Jx, Jy, Jz] E = [Ex, Ey, Ez]
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Numerical Modelling of HTS Coils
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Finite element method is commonly used & well developed (other techniques do exist) Governing equations: Maxwell’s equations (H formulation) Other formulations also exist (A-V, T-Ω, Campbell’s equation) Can be implemented in commercial software or self-programmed
Ampere’s Law
Faraday’s Law
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Numerical Modelling of HTS Coils
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HTS materials Kim-like model: BSCCO:
Šouc et al. Supercond. Sci. Technol. 22 (2009) 015006
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Numerical Modelling of HTS Coils
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HTS materials (RE)BCO coated conductors:
Pardo, Grilli SuST 25 (2012) 014008 Hu, Ainslie et al. IEEE 26 (2016) 6600906
Measured Jc(B,θ) for
SuperPower’s SCS4050-AP
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Numerical Modelling of HTS Coils
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• Some software packages, e.g., COMSOL, allow direct interpolation of experimental data without need for data fitting:
• Hu, Ainslie et al. Supercond. Sci. Technol. 28 (2015) 065011
• Hu, Ainslie et al. IEEE Trans. Appl. Supercond. 26 (2016) 6600906
• Computation can be > order of magnitude faster
Comparison of Ic (left) & AC loss (right) for data fitting & interpolation
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Numerical Modelling of HTS Coils
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E-J power law • Conventional conductors non-linear
permeability, linear resistivity • Superconductors linear permeability (µ0), non-
linear resistivity • Non-linearity is extreme: power law with n > 20
I-V curves for different n values
E = ρJ
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Numerical Modelling of HTS Coils
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Boundary conditions & constraints • Transport current
DC (ramped) or AC, DC with AC ripple, etc.
• External field DC or AC, DC with AC ripple, etc.
COIL GEOMETRY
ELECTROMAGNETIC FORMULATION
BOUNDARY CONDITIONS & CONSTRAINTS
Jc(B,θ)
E-J POWER LAW
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Case Study 1:
DC characterisation of HTS coils
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Triangular, Epoxy-Impregnated HTS Coil
• Prototype triangular, epoxy-impregnated HTS coil for an axial-gap, trapped flux-type superconducting machine
• Wound using SuperPower’s SCS-4050AP coated conductor
• 10 bar overpressure with N2, 4-5 hrs rotary baking, Stycast W19 w/catalyst 11 (100:17)
• Ten voltage taps, spaced every 2 m
• 9 individual voltage sections can be analysed
• First tap 1 m from current contact, last tap 0.2 m from current contact
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Triangular HTS Coil Modelling
• 3D H-formulation
• 1/6th of coil modelled using symmetry
• Jc(B,θ) data from short sample
• Input using direct interpolation
• DC transport current problem
• Integral constraint on each tape: ramped current 7 A/s
• Boundary conditions, air sub-domain: Hx = Hy = Hz = 0
• Meshing is important!
• Mapped mesh in HTS tapes, scaled mesh between tapes, swept mesh along each turn, free triangular mesh outside of coil (in 2D)
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Experimental & Simulation Results
B S G Hu, Ainslie et al. Supercond. Sci. Technol. 28 (2015) 065011
Experimental & simulation results assuming uniform Jc(B,θ)
Experimental results for each third of the HTS coil
2D:
3D:
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Experimental & Simulation Results
B S G Hu, Ainslie et al. Supercond. Sci. Technol. 28 (2015) 065011
I-V curve for non-uniform region V3 New simulated I-V curve for non-uniform region V3 and region V13 (one third)
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Case Study 2:
Use of flux diverters to improve coil performance
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AC Losses in HTS Coils
• Many power applications require AC (alternating current, time-varying)
• Finite AC loss appears for time-varying current and/or magnetic field
• Amplified at low temperatures: e.g., Ptotal ≈ 20 P77 K
• Must take into account Carnot efficiency & cryocooler efficiency
Instantaneous AC loss for a stack of 32 tapes in a transport current case Zermeno et al. J. Appl. Phys. 114 (2013) 173901
AC loss is hysteretic First ½ cycle is “transient,” ignore Tapes magnetised from virgin state Self-field: loss = 2 x 2nd ½ cycle loss In-field: loss = 2nd & 3rd ½ cycle loss
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AC Losses in HTS Coils
• How to reduce AC loss?
• Striation into narrow filaments
• Can introduce coupling loss between filaments
• Roebel transposition
• Conductor cut/punched into shape before winding
• Twisted with full transposition
• Averaged over length, no net mutual flux linkage occurs
• All these techniques involve modification of conductor itself degradation?
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AC Losses in HTS Coils
• How to reduce AC loss?
• External flux diverters
• Use ferromagnetic materials to modify magnetic flux profile of coil
• Doesn’t require modification of conductor can be used ‘as is’ (off the shelf)
• Ideal diverter: high saturation field, low remnant field (small hysteresis loop)
Without diverter
With diverter
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Flux Diverter and DC Performance
• Diverter placed on both sides of a 50 turn coil
• 1 mm thickness, 1 mm gap
• Strong magnetic material: Bsat = 1.7 T µr,max ≈ 12,440 @ 75 A/m
• Effect on DC performance, both self-field and in-field?
• Contrary to hypothesis, DC critical current is reduced
I-V curves with & without flux diverter, self-field & in-field
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Flux Diverter and DC Performance
• Why does this occur?
• Circular coil: comparatively higher local magnetic field at innermost turn reduced Jc
• Flux diverter increases field here lower Ic of coil
• Geometric optimisation needed!
Without diverter
With diverter
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Flux Diverter and AC Performance
• AC loss is reduced, even accounting for diverter’s hysteretic loss
• Loss calculated using measured hysteresis loop & peak field seen
• Difficult to calculate diverter loss in-field due to asymmetric hysteresis loop
• Complex interaction between DC background field & self-field from coil
• Diverter effectiveness maximised when below saturation limit of material used
Raw transport AC loss with & without diverter
Total AC loss incl. diverter hysteretic loss, self-field
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Presentation Outline
• Electrical engineering applications of superconductivity
• Numerical modelling of HTS coils
• Case study 1: DC characterisation of HTS coils
• Case study 2: Use of flux diverters to improve coil performance
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Thank you for listening Contact email: [email protected] Website: http://www.eng.cam.ac.uk/~mda36/