numerical simulation of the performance of hts coils

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

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”

http://www.eia.gov/forecasts/ieo/world.cfm

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

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

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

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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• 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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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



Jc(B,θ)

E-J POWER LAW


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HTS materials Kim-like model: BSCCO:

Šouc et al. Supercond. Sci. Technol. 22 (2009) 015006

COIL GEOMETRY



Jc(B,θ)

E-J POWER LAW


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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



Jc(B,θ)

E-J POWER LAW


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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



Jc(B,θ)

E-J POWER LAW


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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



Jc(B,θ)

E-J POWER LAW


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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



Jc(B,θ)

E-J POWER LAW

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:

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)

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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• 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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• 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

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/

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http://www.eng.cam.ac.uk/%7Emda36/