We have analyzed operating characteristics of transformer-type superconducting fault current limiter (SFCL) according to the serial or parallel connections of secondary coils with $YBa_2Cu_3O_7$ (YBCO) thin films. The turn ratio between the primary and secondary coils was 63:21. Transformer-type SFCL using a transformer with secondary winding of serial or parallel coils could reduce the unbalanced quench caused by differences of the critical current density between YBCO thin films. We found that transformer-type SFCL having serial or parallel connections induced simultaneous quench between the superconducting units. The limiting current in the transformer-type SFCL with a parallel connection was lowered to 30 % compared to the SFCL with a serial connection. In the meantime, when the currents generated in the superconducting units were similar, the voltage value in the parallel connection was 60 % as low as that in the serial connection. However, the voltage generated in the primary winding was some higher. In conclusion, we found that transformer-type SFCL with parallel connection of secondary coils was more effective in fault current limiting characteristics and in the reduction of the consumption power for superconducting units compared to those of the transformer-type SFCL with serial connection of secondary coils.