The coordination of a large number of protective relays in an interconnected power system is a crucial task. In recent years, researchers have adopted various approaches to attain minimal discrimination time between primary and backup relay pairs for directional overcurrent relay coordination. Researchers have suggested various objective functions to overcome relay mis-coordination and to achieve optimum value of relay plug setting and time multiplier settings. This paper discusses an approach to improve the mathematical formulation for the coordination of directional overcurrent relay for an interconnected power system. Various objective functions reported in the literature are compared with the proposed objective function precisely adopting the overcurrent relay coordination philosophy. To check & analyze the robustness and suitability of the proposed objective function, a modified IEEE14-bus distribution system & IEEE 30-bus system, and IEEE8- bus system is employed. A comparative analysis of the proposed objective function and reported objective functions is presented.