Effect of the Conductor Length on the Hot-Spot Regime for Resistive-Type Superconducting Fault Current Limiter Applications

The design of the conductor of a resistive-type superconducting fault current limiter (R-SFCL) using the second generation of high-temperature superconductors (2G HTS) tapes is driven by two operation regimes. On one hand, when the quench occurs on the overall conductor (i.e., the limitation regime), it should withstand the highest possible electric field to reduce its length and make it cost-effective. On the other hand, it has also to cope with the hot-spot regime. Fault currents in the range of the critical current I c can lead to localized dissipation along the length of the conductor over the parts showing the lowest I c values. The almost nonlimitation of the current coming from the low normal zone propagation velocity of 2G HTS tapes causes temperature elevations in these zones, which highly threaten their integrity. To summarize, the conductor architecture is adapted to withstand a high electric field and to obtain a nondestructive value of the maximum temperature in a hot-spot regime. However, the I c variations, causing this last-mentioned regime, depend on the position along with the tape. This article aims to qualify the effect of a variable conductor length on the I c variations and, as a consequence, on the hot-spot regime. We first study the influence of the length on the I c variations. The minimum critical current tends to decrease when the conductor length increases. This behavior can be modeled by a Weibull distribution assuming a minimum critical current different from zero with an infinite length of the conductor. To assess this impact on the hot-spot regime, we develop a probabilistic approach using the deterministic one-dimensional modeling of 2G HTS conductor considering the I c inhomogeneity along its length to simulate a R-SFCL behavior. It appears that the more the conductor is long, the more the maximum temperature in the hot-spot regime is high. Moreover, the fact that two I c measurements corresponding to the same length of conductor present different maximum temperatures in hot-spot regime leads to present a method to design large-scale manufacturing conductors of the desired length, robust to survive hot-spot regime due to any I c variations.