Short-circuit faults are the most commonly occurring faults in an electrical power system. Traditionally, circuit breakers, fuses or similar protective devices are used to safeguard sensitive equipment from these faults by disconnecting the supply. An alternative approach for protection against shortcircuit faults is using fault current limiters (FCL), which suppress the large magnitude currents created by the fault to manageable values. This fault limiting action not only prevents damage to delicate equipment but also aids in providing uninterrupted power supply to the consumers. A promising FCL design is the saturated iron-core superconducting fault current limiter (SISFCL), which uses the property of its ferromagnetic core to suppress high-magnitude currents. In this paper, the performance of an open-core type three-phase SISFCL is analysed in response to variation of three model parameters. The parametric analysis is performed on the SISFCL under the effects of a symmetric-type three line to ground (LLLG) fault and an asymmetric-type single line to ground (SLG) fault. A finite-element modelling (FEM) approach is used in the design and simulation of the model in ANSYS Maxwell software. Following the parametric analysis, an optimization of the design of the SISFCL is performed using the Quasi-Newton Gradient Search method, in order to improve its performance against both LLLG and SLG faults.