AC loss part I - KIT · AC loss –part I Fedor Gömöry Institute of Electrical Engineering Slovak Academy of Sciences Dubravska cesta 9, 84101 Bratislava, Slovakia [email protected]

AC loss – part I

Fedor Gömöry

Institute of Electrical Engineering

Slovak Academy of Sciences

Dubravska cesta 9, 84101 Bratislava, Slovakia

[email protected] www.elu.sav.sk

mailto:[email protected]

Outline of Part I:

1. What is AC loss

2. Dissipation mechanisms: Resistive

Eddy currents

Flux pinning

Coupling currents

3. Possibilities for AC loss reduction

4. Methods to measure AC loss

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



What is understood under AC loss

= amount of heat

released during operation in cyclic (or transient) regime

it does not appear in DC regime

is not a property of material but of a (superconducting) object

operating in well defined conditions

(temperature, transported current, applied magnetic field)

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Resistive AC loss

does not fall under the definition of AC loss

because it is due to static E(j) relation

can be calculated from E(j)

should be marginal in nominal operating regime

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

10 100

I rms [A]

P [

W/m

]

36 Hz

72 Hz

144 Hz

36 Hz

72 Hz

144 Hz

36 Hz

72 Hz

144 Hz

P res

P mag

P tran- data

P tran- model

j

E

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Eddy current loss

induced currents in metallic parts

treated in textbooks of electromagnetism (skin effect, inductive heating)

penetration depth

shielding of magnetic field if d << wall thickness

negligible if d >> thickness of metallic object

should be marginal in nominal operating regime

d

0

2

metal resistivity

frequency (angular)

magnetic permeability of vacuum

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Hysteresis loss in superconductor

because of magnetic flux pinning in superconductor

(the mechanism securing high current transport capacity i.e. large critical current density in magnetic fields >> 1 T )

“hard” = type II superconductor with flux pinning

critical state model – Ch. P. Bean 1962:

cj

j0 in the places that never experienced electrical field

elsewhere

simplest version: jc independent of E, B

jc = const. sometimes call “the Bean model”

Transport of electrical current

e.g. the critical current measurement

0 A 20 A 100 A

80 A 20 A 0 A

j =+ jc

j =- jc

j =0

I

Transport of electrical current

AC cycle with Ia less than Ic : neutral zone

80 60 -80 -60 0 A

T

IdIUdtQ

neutral zone:

j =0, E = 0

U

t

ΦU

check for hysteresis in I vs. plot

AC transport in hard superconductor : is it still without dissipation?

AC transport loss in hard superconductor

-1.5E-05

-1.0E-05

-5.0E-06

0.0E+00

5.0E-06

1.0E-05

1.5E-05

-150 -100 -50 0 50 100 150

[V

s/m

]

I [A]

hysteresis dissipation AC loss

AC transport loss in hard superconductor

hysteresis dissipation AC loss

-1.5E-05

-1.0E-05

-5.0E-06

0.0E+00

5.0E-06

1.0E-05

1.5E-05

-150 -100 -50 0 50 100 150

[V

s/m

]

I [A]

Hard superconductor in changing magnetic field

0 30 50 40 mT

0 -50 -40 0 50 mT

volume loss density Q [J/m3]

magnetization:

Hard superconductor in changing magnetic field

dissipation because of flux pinning

MBV

Qad

S

yxyxjxM dd),(.

Ba

x

y

Round wire from hard superconductor in changing magnetic field

-3.E+04

-2.E+04

-1.E+04

0.E+00

1.E+04

2.E+04

3.E+04

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

M [

A/m

]

B [T]

Bp

Ms

Ms saturation magnetization, Bp penetration field

Round wire from hard superconductor in changing magnetic field

-3.E+04

-2.E+04

-1.E+04

0.E+00

1.E+04

2.E+04

3.E+04

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

M [

A/m

]

B [T]

estimation of AC loss at Ba >> Bp

saMBV

Q4

Slab in parallel magnetic field – analytical solution

saMBQ 4

j

B penetration field

w

20

wjB cp

2

3

0

3

42

3

2

1

pap

p

a

BBB

B

B

V

Q

024

p

cs

BwjM

Slab in parallel magnetic field – analytical solution

saMBQ 4

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Q/V

[J/m

]

Ba [T]

jc=10^8 A/m2, w=1 mm (Bp = 63 mT)

jc=10^8 A/m2, w=0.1 mm (Bp = 6.3 mT)

jc=10^7 A/m2, w=1 mm (Bp = 6.3 mT)

jc=10^7 A/m2, w=0.1 mm (Bp = 0.63 mT)

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Coupling loss - two parallel superconducting wires in metallic matrix

coupling currents

Ba

0 20 80 60 mT

in the case of a perfect coupling:

Magnetization of two parallel wires

-2.E+05

-1.E+05

-5.E+04

0.E+00

5.E+04

1.E+05

2.E+05

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

M [

A/m

]

B [T]

coupled:

uncoupled:

how to reduce the coupling currents ?

Composite wires – twisted filaments

B

j

B

lp

t

pBlj

2

1

1

1

1

mt

mtgood interfaces

bad interfaces

m

SC

S

S

Composite wires – twisted filaments

coupling currents (partially) screen the applied field

BBBi - time constant of magnetic flux diffusion

2

0

22

p

t

l

22

0

2

max

1

2

B

V

Q22

0

0

2

max

1

B

V

Q

round wireflat wire

A.Campbell (1982) Cryogenics 22 3

K. Kwasnitza, S. Clerc (1994) Physica C 233 423

K. Kwasnitza, S. Clerc, R. Flukiger, Y. Huang (1999)

Cryogenics 39 829

Around2

0

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Hysteresis loss:

at large fields proportional to Bp ~ jc w

= loss reduction by either lower jc or reduced w

lowering of jc would mean more superconducting material required to transport the same current

thus only plausible way is the reduction of w

width of superconductor

(perpendicular to the applied

magnetic field)

effect of the field orientation

saMBV

Q4

-2.E+05

-1.E+05

-5.E+04

0.E+00

5.E+04

1.E+05

2.E+05

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

M [

A/m

]

B [T]

perpendicular field

parallel field

Magnetization loss in strip with aspect ratio 1:1000

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Hmax [A/m]

Q/V

[J/m

3]

parallel

perpendicular

H

H

saMBV

Q4

in the case the tape orientation is not a free parameter

= reduction of the tape width

striation of CC tapes

BB

~ 6 times lower hysteresis loss

striation of CC tapes

but in operation the filaments are connected at magnet terminations

BB

coupling loss will be the main issue

Coupling loss:

at low frequencies proportional to

= filaments (in single tape) or tapes (in a cable)

should be transposed

= low loss requires high inter-filament or inter-tape resistivity

but good stability needs the opposite

transposition length

effective resistivity

2

0

22

p

t

l

Outline of Part I:

1. What is AC loss


Eddy currents

Flux pinning

Coupling currents



Experimental methods for AC loss determination

• Tape

• Cable

• Magnet


Shape of the excitation field (current) pulse

transition unipolar harmonic

relevant information can be

achieved in harmonic regime

final testing necessary in

actual regime


1.Thermal a) cooling power (large devices)

b) boil-off

c) temperature profile

2. Electrical - lock-in technique

- Y(I) hysteresis loop registration

temperature profile method

Thermocouple

Voltage

taps

Thermal

insulation

Current DC,

AC

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1 10 100

Irms [A]

P [

W/m

]

P thermal

P electrical

y = 0.1677x + 0.1452

0

1

2

3

4

5

6

0 5 10 15 20 25 30

P [mW/m]

Utc

[uV

]

Series1

Linear (Series1)

P = (Utc-.145)/.168

P~T

AC power

supplyAC power flow

AC loss in

SC object

cycleAC1

ower.dtPQ

Tt

t

tUQ (t)I(t).d„Power meter“

Lock-in amplifier

Electrical method

Electrical method

Lock-in amplifier

(phase sensitive detection at fundamental component)

so called in-phase and out-of-phase signals

2

0

2

0

dcos)(1

dsin)(1

tttuU

tttuU

mC

mS

reference signal necessary to set the

frequency

phase

taken from AC current

um - measured voltage

Fundamental problem of electrical methods for AC loss determination

AC power

supplyAC power flow

AC loss in

SC object

Solution 1- detection of power flow to the sample

AC power

supplyAC power flow

AC loss in

SC object

Solution 2- elimination of parasitic power flows

AC power

supplyAC power flow

AC loss in

SC object

ideal magnetization loss measurement:

tBB aext cos

Area A

)()(d)(1

)(

d

)(d

d

)(d)(

int tMtBAtBA

tB

t

tBA

t

ttu

ext

A

mm

pick-up coil wrapped around the sample

induced voltage um(t)

macroscopic magnetization of the

sample

contains higher harmonics

dt

tdM

dt

tdBAtu ext

m

)()()(

( )

1

sin"cos')(n

nna tntnBtM

tttB

tt

MtBMBQ

T

a

T

d)cos(")cos(dd

d)(

1d

1

00

2

000

H

M

= 0

=

= /2

= 3/2

"0

2

aBQ

Lock-in amplifier

Real magnetization loss measurement:

Pick-up coil

sample

Calibration necessary

tuCM d

by means of:

measurement on a sample

with known properrties

calibration coil

numerical calculation

…

Loss measurement from the side of AC power supply:

AMPLIFIER

LOCK-IN

channel A

channel B

generator

Rogowski

coil

transformer

LN2

Im sample

Bmsample UIP power supply

Loss measurement from the side of AC power supply:

Y(I) hysteresis loop registration for superconducting magnet (Wilson 1969)

Y

dtU

I

RI

x

y

AC loss part I - KIT · AC loss –part I Fedor Gömöry Institute of Electrical Engineering Slovak Academy of Sciences Dubravska cesta 9, 84101 Bratislava, Slovakia [email protected]

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