Determination of optimal breakpoint set of overcurrent relays using modified depth-first search and mixed-integer linear programming

In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate MBPS is an issue which must be considered. This paper proposes a prioritization between different MBPSs based on the sum of operating times of OCRs. In this case, a set which results the minimum sum of operating times is selected as the appropriate MBPS. For this purpose, the proposed method combines two problems: Determination of MBPS and coordination of OCRs, and is expressed in mixed-integer linear programming (MILP) form. Also, a modified depth-first search (DFS) algorithm is applied to determine the OCRs contained loops of studied networks. It is shown that the proposed method has the capability to be combined with previous defined expert rules in this field in order to consider the network conditions in the process of determination of optimal breakpoint set (OBPS). The proposed method has been implemented on various size networks, and the results show the effectiveness of proposed method in determining breakpoint set with the least number in first priority and minimum operating times of relays in second priority.