AC loss – part I
Fedor Gömöry
Institute of Electrical Engineering
Slovak Academy of Sciences
Dubravska cesta 9, 84101 Bratislava,
Slovakia
elekgomo@savba.sk
www.elu.sav.sk
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
Eddy currents
Flux pinning
Coupling currents
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
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
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
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
j
can be calculated from E(j)
1.E+02
P res
36 Hz
1.E+01
P mag
72 Hz
144 Hz
36 Hz
P [W/m]
1.E+00
P tran - data
72 Hz
144 Hz
1.E-01
P tran - model
36 Hz
72 Hz
144 Hz
1.E-02
1.E-03
1.E-04
10
E
100
I rms [A]
should be marginal in nominal operating regime
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
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
d
2
0
metal resistivity
frequency (angular)
magnetic permeability of vacuum
shielding of magnetic field if d << wall thickness
negligible if d >> thickness of metallic object
should be marginal in nominal operating regime
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
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:
0
j 
 jc
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
0A
20 A
I
100 A
j =+ jc
j =0
80 A
20 A
j =- jc
0A
Transport of electrical current
AC cycle with Ia less than Ic : neutral zone
80

60

-80

-60

0 A
AC transport in hard superconductor : is it still without dissipation?
Q   IUdt   Id
T
neutral zone:
j =0, E = 0

U
check for hysteresis in I vs.  plot
Φ
U 
t
AC transport loss in hard superconductor
1.5E-05
1.0E-05
 [Vs/m]
5.0E-06
-150
0.0E+00
-100
-50
0
50
-5.0E-06
-1.0E-05
-1.5E-05
I [A]
hysteresis  dissipation  AC loss
100
150
AC transport loss in hard superconductor
1.5E-05
1.0E-05
 [Vs/m]
5.0E-06
-150
0.0E+00
-100
-50
0
50
-5.0E-06
-1.0E-05
-1.5E-05
I [A]
hysteresis  dissipation  AC loss
100
150
Hard superconductor in changing magnetic field
0
0


30

50
-50

-40


40 mT
0

50 mT
Hard superconductor in changing magnetic field
dissipation because of flux pinning
Ba
y
x
volume loss density Q
magnetization:
Q
  Ba dM
V
[J/m3]
M    x. j ( x, y )dxdy
S
Round wire from hard superconductor in changing magnetic field
3.E+04
Ms
2.E+04
M [A/m]
1.E+04
Bp
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
B [T]
Ms saturation magnetization,
Bp penetration field
Round wire from hard superconductor in changing magnetic field
estimation of AC loss at Ba >> Bp
3.E+04
2.E+04
M [A/m]
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
B [T]
Q
 4 Ba M s
V
0.2
0.25
Slab in parallel magnetic field – analytical solution
B
penetration field
w
B p   0 jc
2
w Bp
M s  jc 
4 20
w
j
3

2 Ba
Q 1 
3 Bp


V 0 
4 2
2 B p Ba  B p

3
Q  4Ba M s
Slab in parallel magnetic field – analytical solution
1.E+05
Q  4Ba M s
1.E+04
1.E+03
1.E+02
1.E+01
Q/V [J/m]
1.E+00
1.E-01
jc=10^8 A/m2, w=1 mm
(Bp = 63 mT)
1.E-02
1.E-03
jc=10^8 A/m2, w=0.1 mm
(Bp = 6.3 mT)
1.E-04
1.E-05
jc=10^7 A/m2, w=1 mm
(Bp = 6.3 mT)
1.E-06
jc=10^7 A/m2, w=0.1 mm
(Bp = 0.63 mT)
1.E-07
1.E-08
1.E-05
1.E-04
1.E-03
Ba [T]
1.E-02
1.E-01
1.E+00
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
Eddy currents
Flux pinning
Coupling currents
Coupling loss - two parallel superconducting wires in metallic matrix
Ba
coupling currents
in the case of a perfect coupling:
0

20

80

60 mT
Magnetization of two parallel wires
2.E+05
1.E+05
M [A/m]
5.E+04
uncoupled:
0.E+00
-5.E+04
-1.E+05
coupled:
-2.E+05
-0.15
-0.1
-0.05
0
0.05
0.1
B [T]
how to reduce the coupling currents ?
0.15
Composite wires – twisted filaments
lp
 B
1 
good interfaces  t   m
1 
1 
t   m
bad interfaces
1 
S SC

Sm
B
j
j 
l p B
2t
Composite wires – twisted filaments
coupling currents (partially) screen the applied field
Bi  B   B
0

2 t
 lp

 2



 - time constant of magnetic flux diffusion
2
Q B
2

2 2
V
0 1   
2
max
round 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
 0
Q B

V
 0 1   2 2
2
max
flat wire
   round
0
2
A
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
Eddy currents
Flux pinning
Coupling currents
Hysteresis loss:
at large fields proportional to Bp ~ jc w
width of superconductor
(perpendicular to the applied
magnetic field)
= 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
effect of the field orientation
perpendicular field
2.E+05
1.E+05
parallel field
M [A/m]
5.E+04
0.E+00
-5.E+04
-1.E+05
-2.E+05
-0.15
-0.1
-0.05
0
B [T]
Q
 4 Ba M s
V
0.05
0.1
0.15
Magnetization loss in strip with aspect ratio 1:1000
1.E+07
1.E+06
Q
 4 Ba M s
V
H
1.E+05
1.E+04
1.E+03
Q/V [J/m 3]
1.E+02
H
1.E+01
1.E+00
1.E-01
1.E-02
parallel
1.E-03
1.E-04
perpendicular
1.E-05
1.E-06
1.E-07
1.E+00
1.E+01
1.E+02
1.E+03
Hmax [A/m]
1.E+04
1.E+05
1.E+06
in the case the tape orientation is not a free parameter
= reduction of the tape width
striation of CC tapes
B
B
~ 6 times lower hysteresis loss
striation of CC tapes
but in operation the filaments are connected at magnet terminations
B
B
coupling loss will be the main issue
Coupling loss:
at low frequencies proportional to
0  l p


2  t  2



2
transposition length
effective resistivity
= 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
Outline of Part I:
1.
What is AC loss
2.
Dissipation mechanisms:
3.
Possibilities for AC loss reduction
4.
Methods to measure AC loss
Resistive
Eddy currents
Flux pinning
Coupling currents
Experimental methods for AC loss determination
•
Tape
•
Cable
•
Magnet
Experimental methods for AC loss determination
Shape of the excitation field (current) pulse
transition
unipolar
harmonic
relevant information can be
achieved in harmonic regime
final testing necessary in
actual regime
Experimental methods for AC loss determination
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
Voltage
taps
1.E-01
Current DC,
AC
P thermal
1.E-02
P electrical
P [W/m]
1.E-03
1.E-04
Thermal
insulation
1.E-05
Thermocouple
1.E-06
1
10
Irms [A]
P~T
6
Utc[uV]
Series1
Linear (Series1)
5
y = 0.1677x + 0.1452
4
P = (Utc-.145)/.168
3
2
1
0
0
5
10
15
P [mW/m]
20
25
30
100
Electrical method
AC power
supply
AC power flow
AC loss in
SC object
 Power.dt
Q
1 AC cycle
t T
Q   U (t)I(t).dt
t
„Power meter“
Lock-in amplifier
Electrical method
Lock-in amplifier
(phase sensitive detection at fundamental component)
so called in-phase and out-of-phase signals
US 
UC 
1

1

2
 um (t ) sin tdt
um - measured voltage
0
2
u
m
(t ) costdt
0
reference signal necessary to set the
frequency
phase
taken from AC current
Fundamental problem of electrical methods for AC loss determination
AC power
supply
AC power flow
AC loss in
SC object
Solution 1- detection of power flow to the sample
AC power
supply
AC power flow
AC loss in
SC object
Solution 2- elimination of parasitic power flows
AC power
supply
AC power flow
AC loss in
SC object
ideal magnetization loss measurement:
Bext  Ba cos t
pick-up coil wrapped around the sample
induced voltage um(t)
=
um (t )  
B (t ) 
M
dm (t )
dB (t )
 A
dt
dt
 = /2
1
Bint (t )d A  Bext (t )  M (t )

AA
H
 = 3/2
 dB (t ) dM (t ) 
um (t )   A ext 
dt 
 dt
Area A
=0

M (t )  Ba  ( n ' cos nt   n " sin nt )
macroscopic magnetization of the
sample
contains higher harmonics
T
n 1
T
Ba2
dM
Q
BdM   B(t )
dt  
cos(t ) " cos(t )dt


0
0 0
dt
0 0
1
1
Lock-in amplifier
Q
Ba2
0
 "
Real magnetization loss measurement:
Pick-up coil
Calibration necessary
M  C  udt
sample
by means of:
measurement on a sample
with known properrties
calibration coil
numerical calculation
…
Loss measurement from the side of AC power supply:
LOCK-IN
Rogowski
coil
LN2
channel A
channel B
generator
transformer
Im
AMPLIFIER
power supply
Psample  I mU B
sample
Loss measurement from the side of AC power supply:
Y(I) hysteresis loop registration for superconducting magnet (Wilson 1969)
 Udt
Y
RI
I
y
x