133
Appendix E
Quench Detection Study for HTS Coil
E.1 Quench Detection
As a well-known problem for the HTS coil, the quench protection is very challenging due to the very slow normal quench propagation, which is 2-3 order of magnitude slower than those in LTS conductor [123], in particular, for a coil has high inductance.
Since the normal zone propagates slowly, the joule heating is considered to be dominated by the operation current, in which the hot spot temperature can be suppressed below an allowable temperature if the current is discharged as soon as possible. Thus the quench detection is a major problem for protecting a HTS coil since the coil voltage is too low to be detected in a process of premature quench. The hot spot temperature for HTS coil increases immediately when the operation current is closed to its critical current, and the coil may be burnout at the moment when the quench signal is detected. Here, assuming the current can be reduced in a short duration, the thermal runaway analysis is performed to validate the possibility of quench detection when a quench is occurred in this HTS coil.
E.1.1 Simulation Model
As mentioned in Sec. 6.1, the double pancake coil has 166 turns along the radius direction and wound with a 4 mm wide and 0.1 mm thick ReBCO conductor, of which the copper ratio is 6:4 (hastolly:Cu) and hastolly is assumed to be stainless steel. The insulation is assumed to be 50 µm between turn to turn as well as that between the single pancake. The 340 mm long coil is simplified to one double pancake coil since the quench propagation of HTS coil is enough slow. The thermal conductivity (kz, kθ, kr) are averaged with the materials of stainless steel, copper (RRR = 50) and G10 for the conductor
The magnetic field is assumed to be a uniform field of 3.5 Tesla because the hot spot is set in the inner surface of coil, and the normal zone propagates slowly so that the voltage rise mainly relies on the magnetic field around the hot spot. The outermost layer of double pancake coil is fixed to 20 K, and the boundary is switched to an adiabatic condition when a quench is detected. A hot spot is heated with a virtual heater, and located at innermost
layer of HTS coil with a cross-sectional area of 0.1×4 mm2 and a length of 11 mm (dθ = π/50) determined by MPZ along the azimuth. The critical current of ReBCO coated tape (SuperPower, SCS4050) is calculated from a fit function as described in Appendix B, and
the n-value is assumed to be 40.
Similar to the simulation model described in chapter 5, the heat generation during the quench is calculated as
Q=
(I·(I−Isc)·RCu, Ic > 0
I2RCu, Ic = 0 (E.1)
where Isc (ICu) is the current in superconductor (copper),I is the operation current, and RCu is the resistance of copper, respectively. The current in superconductor and copper is calculated by solving the following nonlinear equation with a Newton-Raphson method:
f(Isc) = Ec·(Isc
Ic)n−(I−Isc)·RCu. (E.2) Here the critical current that magnetic field parallel to the c-axis of HTS tape is utilized to give a conservative analysis.
T
ISc ICu
V 0.1 V Iop = 140 A
T
ISc ICu
V 0.1 V Iop = 100 A
Figure E.1: The evolution of current sharing, coil voltage and hot spot temperature for a operation current of 100 A (left) and 140 A (right). The green and red line indicate the current in the superconductor and copper respectively. The black and blue line are the hot spot temperature and coil resistive voltage. The red and blue axis shows a scale for current and voltage.
E.1.2 Result
The nominal current as well as an elevated operation current is examined to understand the process of quench in HTS coil by assuming the voltage threshold is 0.1 V and detection time is 0.1 sec. Figure E.1 shows the calculated current sharing, coil voltage and hot spot temperature before the thermal runaway. As the hot spot temperature is increased, the current in superconductor starts to share with the copper stabilizer. For a case with lower
Appendix E. Quench Detection Study for HTS Coil
operation current, the voltage grows up slowly so that an elevated hot spot temperature is predicted when the coil voltage reaches to 0.1 V. After the current totally flows to the copper stabilizer, the hot spot temperature increases immediately as well as coil voltage.
Compared with lower operation current, the hot spot temperature grows substantially in a short duration for a high operation current case.
20 40 60 80 100 120 140 160 180 200 Temperature [K]
0 100 200 300 400 500 600
Resistive Voltage [mV]
100 A 140 A 150 A
160 A 170 A
20 40 60 80 100 120 140 160 180 200 Temperature [K]
0.6 0.4 0.2 0.0 0.2 0.4
t
−t
det[s ec ]
Figure E.2: The resistive voltage (left) and the elapsed time after the quench detection (right) as a function of peak hot spot temperature, in whichtis the global time, and tdet is the time when the coil resistive voltage reaches to the threshold of 100 mV. The dashed line is the criteria of 0.1 sec.
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 X [m]
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20
Y [m]
Time = 1.20 sec
20 22 24 26 28 30 32 34
Temperature [K]
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 X [m]
0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20
Y [m]
Time = 1.20 sec
20 21 22 23 24 25 26 27 28 29
Temperature [K]
Figure E.3: R-θ view of the temperature distribution in double pancake at the operation current of 100 A. The hot spot is located at the innermost layer of first single pancake coil (left).
The right one shows the temperature in the second single pancake coil. The mesh of single pancake coil is cut to be 120 along the azimuth and 166 along the radius.
Then, in order to investigate the possibility of quench detection, the hot spot temper-ature against coil voltage and detection time is plotted in Fig. E.2 (similar method is described in Ref. [124]). With a criteria of quench detection, the lower operation current
can be easily detected before the thermal runaway. However, as for a high operation current, for instance to 160 A, the hot spot temperature reaches to 200 K when the quench signal is fully detected. A higher operation current such as 160 A is possible to be achieved, however, the detection time must be reduced lower than 50 msec, otherwise, the voltage threshold should be reduced. A novel method to reduce the detection noise with a co-winding coil [125] may be a candidate for the further studies. Therefore, the quench in this HTS coil is capable of being detected with its nominal current of 105 A before the thermal runaway.
137
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