Several challenges are posed by the escalating complexities of modern power systems, including increased fault levels and fault currents. One efficient solution to the fault current issue is the superconducting fault current limiter (SFCL), which can prevent further increases in fault current caused by the growth in power generation and consumption. The SFCL has a faster response time and can minimize fault current using its quench features. However, relay operation is adversely affected due to delayed tripping time, leading to mis-coordination among primary and backup relays. To address this issue, the voltage component available across the fault current limiters (FCL), which offers a large reactance, is utilized as an input parameter to modify relay characteristics. This helps to reduce tripping time and avoid mis-coordination. Relay characteristics using voltage components derived from SFCL are implemented to tackle this problem. The operational characteristic of the overcurrent relay is changed using this voltage component. In this paper, a new objective function, based on reported relay characteristics, was proposed. A prototype of the ring mains distribution system was developed to evaluate the effectiveness of the reported characteristics and proposed objective function. Furthermore, the reported characteristic and proposed objective function were examined on a 9-bus distribution system. It was found that the application of voltage components in the relay characteristic and proposed objective function was fruitful and did not delay the relay tripping time also there is no miscoordination found in case of reported characteristic and proposed objective functions. To achieve optimum setting of overcurrent relay parameters, a genetic algorithm(GA) was used.