Abstarct: Nowadays, with the development of the power grids and more complex interrelations of the systems to supply the reliable energy for the customers, the necessity for the appropriate protection of the power grid is more felt. The overall objective of the protection system of the power grid is to maintain the power system through isolation of the systems of the error and keep under operation the most possible parts of the grid. In this study, after the literature review and introduction of the basic concepts, we will study the overcurrent relays and the coordination of these relays in the power system. Relay coordination is the setting of the current and time of the overcurrent relays with the aim of achieving the desired function of the relay. In other words, relays in power system should be able to react rapidly when fault happens and also there should not be any interference and only one small part of the grid should be disconnected.Distributed Generation(DG) establishment in the grid can cause several problems in the malfunction of the protection system. In the new structure of the grid with the added DGs, the aim is the fast performance of the relays. So, setting of the relay coordination will change and therefore the cost will increase. In the proposed plan, in addition to assurance for fast and proper operation of the relays, the number of the relays that undergo setting changes will be added to the objective function. In this way, in addition to the proper operation of the protection system, the number of set relays will also decrease. The proposed plan was simulated using MATLAB and DigiSilent software and the results of the proposed genetic algorithm proved its efficacy. The results of the simulation shows that the costs for resetting the relays in the proposed method is less than the method in which all the relays will be reset and on the other hand, the costs have decreased significantly.