The coordination problem of directional overcurrent relays (DOCRs) is a non-linear and non-convex optimization one. Until now, several methods based on the heuristics and non-linear programming (NLP) approaches have been proposed for solving the problem. Drawback of these methods is that they are likely to be trapped in local minima. In order to overcome the drawback, in this paper, the problem is formulated as a mixed integer linear programming (MILP) while pickup current setting (Iset) and time multiplier setting (TMS) of relays are considered as optimization variables. This formulation is easier to be solved by branch and bound (B&B) approach because at each branch there is a linear and convex sub-problem. Furthermore, for the first time, the proposed method is guaranteed to converge to global optimal values. The proposed method is evaluated using a 3-bus, an 8-bus, the IEEE 14-bus and the modified IEEE 30-bus test systems. The results are compared with some previous heuristics and NLP approaches. Based on the obtained results, it can be seen that better optimal settings for DOCRs are obtained by using the proposed method in comparison with previous methods.

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