Optimal Coordination of Directional Overcurrent Relays Considering Different Network Topologies Using Interval Linear Programming

In real power systems, the network topology is subjected to uncertainty due to single-line outage contingencies, maintenance activities, and network reconfigurations. These changes in the network topology may lead to miscoordination of directional overcurrent relays (DOCRs). To overcome this drawback, corresponding to each primary/backup relay pair, a set of inequality coordination constraints which is related to different network topologies should be satisfied. In this paper, a new approach based on the interval analysis is introduced to solve the DOCRs coordination problem considering uncertainty in the network topology. The basic idea is to convert the set of inequality constraints corresponding to each relay pair to an interval constraint. In this situation, the DOCR coordination problem is formulated as an interval linear programming (ILP) problem. Using well-known mathematical theorems, the obtained ILP problem, which has no equality constraints, can be converted to standard linear programming (LP). As a result, the number of coordination constraints is significantly reduced in the proposed methods. The application of the proposed method to the IEEE 14- and 30-bus test systems proves the ability of the interval method in modeling topology uncertainty in the large-scale coordination problem.