Thermal instability and current–voltage scaling in superconducting fault current limiters

We have developed a computer model for the simulation of resistive superconducting fault current limiters in three dimensions. The program calculates the electromagnetic and thermal response of a superconductor to a time-dependent overload voltage, with different possible cooling conditions for the surfaces, and locally variable superconducting and thermal properties. We find that the cryogen boil-off parameters critically influence the stability of a limiter. The recovery time after a fault increases strongly with thickness. Above a critical thickness, the temperature is unstable even for a small applied AC voltage. The maximum voltage and maximum current during a short fault are correlated by a simple exponential law.