Electricity: electrical systems and devices – Safety and protection of systems and devices – Superconductor protective circuits
Reexamination Certificate
1997-06-25
2001-05-22
Sherry, Michael J. (Department: 2836)
Electricity: electrical systems and devices
Safety and protection of systems and devices
Superconductor protective circuits
C361S141000, C361S093900
Reexamination Certificate
active
06236545
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to a current limiting device of the kind comprising a superconducting element for connection in an electrical circuit, the superconducting element having a critical current density.
DESCRIPTION OF THE PRIOR ART
Current limiting devices of the kind described known as fault current limiters (FCL) have been recently proposed and we describe some examples in WO-A-96/30990. In a typical example, a length of high temperature (HTc) superconductor is placed into the circuit carrying the current. HTc materials have a critical temperature which is relatively high (typically equivalent to a liquid nitrogen temperature) and have a critical current (strictly current density) which varies inversely with an applied magnetic field. If the current carried by the superconductor exceeds the critical current then the material of the conductor makes a transition to a resistive state which acts to limit the current being carried. The critical current value at which this transition occurs can be changed by changing the applied magnetic field.
In WO-A-96/30990, we describe a way of resetting such a current limiting device after the superconductor has transformed into a resistive state.
We have recently been investigating the process during which a superconducting element converts from its superconducting state to its resistive state. We have found that the change is progressive along the length of the superconducting element due to constraints in heat conductive properties of the element and in some cases could result in the generation of very high power densities within the element and possible failure of the device.
We set out below our analysis:
The following symbols are used with typical values:
&rgr;
resisitivity
10
−6
&OHgr;− m
K
thermal conductivity
0.5
Wm
−1
K
−1
C
p
specific heat
150
Jkg
−1
K
−1
&ggr;
density
6300
kgm
−3
h
heat transfer to coolant
200
Wm
−2
K
−1
&thgr;
0
coolant temperature
77
K.
&thgr;
c
superconducting critical temperature
90
K.
&thgr;
max
maximum safe temperature
800
K.
&thgr;
temperature variable
J, J
c
current density, critical current density
&dgr;
width of the superconducting transition
I
max
, I
f
trip current, limited current
R
0
nominal normal-state resistance
L, A
length, cross-sectional area
For a “series resistor” type of FCL system:
I
max
=
J
c
A
(
peak
)
I
f
=
V
ρ
L
/
A
I
f
I
max
=
V
ρ
J
c
L
Thermal diffusivity
m
=
K
γ
C
p
=
5.3
10
-
7
ms
-
1
This implies that in 0.01 s, a thermal disturbance will travel only 5 nanometres. We can therefore ignore the AC heating effect of the supply current, and use the appropriate RMS value in thermal calculations.
If we consider an HTC element consisting of a slab or a film, with one face cooled, then under normal-state conditions, the temperature distribution is described by:
K
∂
2
θ
∂
x
2
-
γ
C
p
∂
θ
∂
t
=
J
2
ρ
2
At x=0, the heat flow is
Q=
h
(&thgr;−&thgr;
0
)
and at t=0,&thgr;=&thgr;
0
everywhere.
This was solved numerically for current densities of 10
8
and 10
9
Am
−1
, The temperature profiles across a 200 micron thick film are shown in
FIGS. 1 and 2
.
It can be seen that the heat transfer to the (film boiling) nitrogen is much less than the rate of heat generation. Hence for most purposes, the system can be regarded as adiabatic.
Protection against burn-out
Consider an FCL which includes in essence, a high-temperature-superconducting element in series with the line (or in the case of the screened inductor type is inductively coupled to the line current). This element is sufficiently long that, in the normal state, its resistance is high enough to limit the current through it to a low value. In the superconducting state, it can carry a current up to a value Ic without dissipation of power.
In practice, the superconducting element will not be uniform and some parts will have a lower critical current density than others. If a fault occurs, such as a short circuit, the current attempts to exceed Ic, with its rate of rise determined by the system inductance, or by the part of the alternating it is current cycle at which the fault occurs. Initially, it is sufficient the element will become resistive to produce a resistance that limits the current to the critical value.
If, instead of a short circuit, the fault gives rise to a small overload, or the fault current ramps up relatively slowly, then because of the non-uniformity of the element, some of the superconductor will become normal (resistive), but much of it will remain superconducting.
As shown above, the propagation velocity is so low that in a time comparable to the alternating current period, the resistive region does not grow. The resistance simply tracks the current as it rises, and “latches” at its maximum value when the current falls in its cycle.
These effects can be modelled as follows:
Assume that the critical current has a normal distribution:
F
(
J
c
)
=
1
δ
π
exp
[
-
(
J
c
-
J
c0
)
2
δ
2
]
R
=
R
0
∫
0
I
/
A
F
(
J
c
)
ⅆ
J
c
FIG. 3
shows the V/I characteristic for an element with J
c0
=10
8
A/m
2
, &dgr;=10
7
A/m
2
, sized to have R
0
=100 &OHgr; and I
max
=1000 A.
If the load resistance is r, and the system voltage is V
0
I
(
R
+
r
)
=
V
0
sin
(
2
π
f
t
+
φ
)
2
V
0
sin
(
2
π
f
t
+
φ
)
I
[
R
0
erf
(
I
J
c0
I
max
δ
-
J
c0
δ
)
+
R
0
erf
(
J
c0
δ
)
+
2
r
]
=
1
This equation can be solved graphically for I. Representative plots of I against time are shown in
FIG. 4
, for V
0
=24 kV and for different values of r from 1 &OHgr; (≈short circuit), 20 &OHgr; (moderate overload) to 40 &OHgr; (normal).
It can be seen that the current has been limited to just below the nominal trip value, I
max
.
The corresponding resistances are shown in FIG.
5
.
Left to itself, therefore, the FCL element will limit the current to approximately the value of its critical current.
Unfortunately, this will generally be rather large for a resistive conductor, and represent a very high power density.
The time taken to reach the maximum safe temperature is
δ
t
=
(
θ
max
-
θ
0
)
γ
C
p
ρ
J
2
/
2
This is 140 ms at J=10
8
Am
−2
and 1.4 ms at J=10
9
Am
−2
, The implication is that at 10
9
Am
−2
, the superconductor can be destroyed in less than one cycle of the supply current.
The protection problem is likely to be most severe when the fault results in a very slight overload, so that only a small region only becomes resistive. Because this is so small it is difficult to detect, in the limiting case of a tiny resistive region, we must wait until it has grown before it can be detected.
Resistance Growth
Following Broom and Rhoderick (Brit J Appl Phys, 11, 292, 1960), the rate at which a normal region propagates is given by:
v
q
=
J
/
2
γ
C
p
ρ
K
θ
c
-
θ
0
This is 0.014 ms
−1
at J=10
8
Am
−2
and 0.14 ms
−1
at J=10
9
Am
−2
, which is extremely slow compared with the familiar low-temperature superconductors.
During the time to reach the maximum safe temperature, the length of the resistive region, its resistance and the voltage across it grow to:
δ
L
=
θ
max
J
K
ρ
(
θ
c
-
θ
0
)
δ
R
=
θ
max
J
A
ρ
Hanley Peter
McDougall Ian Leitch
Huynh Kim
Oxford Instruments PLC
Sherry Michael J.
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