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We analyzed the unsymmetrical fault characteristics of resistive superconducting-fault-current-limiters (SFCL) based on YBCO thin films with the unbalanced faults such as a single line-to-ground fault, a double line-to-ground fault, and a line-to-line fault in a three-phase system. The unsymmetrical rates of fault phases were 6.4, 9.2, 8.8 at the fault onset, but decreased by 1.4, 1.5, 3.7 after 50 ms in the fault types, respectively. The positive sequence current I1 was the highest in a double line-to-ground fault, immediately after the fault onset, but that of a line-to-line fault was the highest after 50 ms. This means the current limiting effect was the worst in a line-to-line fault, due to the unbalanced quench between the SFCL units. The negative sequence currents I2 of a single and double line-to-ground faults were relatively low, except for the quench instant, because of the rapid interruption of fault currents by the SFCL. The zero sequence current I0 was similar to the behavior of the negative sequence current. Finally, the positive sequence resistance Z1 was reduced remarkably immediately after the fault but gradually approached the balanced positive sequence resistance prior to the system fault, except during a line-to-line fault. The simultaneous quench between the SFCL units was important for low line-to-line fault currents.