This paper presents a study on protection coordination of over current relays (OCRs) in a distributed system by considering its different operating modes. Two different case studies which are considered in present work for protection coordination include: (i) DG interfaced distribution system in grid connected mode and (ii) DG interfaced distribution system in islanded mode of operation. The proposed approach is tested on the Canadian urban benchmark distribution system consisting of 9 buses. On the occurrence of fault, level of fault current changes which in turn changes the operating time of various OCRs. Therefore, it is important to calculate and suggest method of the relay setting in order to minimize the operating time of relays and also to avoid its mal-operation. In this paper, the protection scheme is optimally designed by taking into account the above mentioned conditions. The operating time of relays can be decreased and, at the same time, coordination can be maintained by considering the optimum values of time dial setting (TDS). Genetic Algorithm (GA) has been used for determining the optimum values of TDS and hence operating time.