Minimum Breakpoint Set Determination for Directional Overcurrent Relay Coordination in Large-Scale Power Networks via Matrix Computations

Determination of the minimum breakpoint set (MBPS) is essential for optimum coordination of directional protection relays. However, in modern large-scale power networks, this task poses serious difficulties and becomes time consuming. This paper addresses such deficiencies and proposes a numerically efficient algorithm. Despite being derived from graph theory, the proposed algorithm functions via a series of matrix computations, that is, reduction, permutation, and LU factorization of the branch to bus incidence matrix of a given network. At first, parallel branches are united via the reduction step. Then, branches and buses are reset to form spanning trees of the network via the permutation step. Finally, MBPS is determined via the LU factorization step. Experimental results obtained by implementing the proposed algorithm in various test systems are presented to illustrate its computational performance.