Determination of the Minimum Breakpoint Set of Directional Relay Networks Based on k-Trees of the Network Graphs

We propose a new graph theory-based algorithm for the determination of the minimum breakpoint set of meshed systems. We show that if there is a k-tree in the graph
G
(
V
,
E
) associated with the system, then the minimum breakpoint set has a cardinality of |
E
|-|
V
|+
k
. The proposed algorithm implements an iterative procedure to identify such a k-tree and having minimum
k
. It is found that the cardinality of the minimum breakpoint set is 9 for the IEEE 14-bus system and 16 for the IEEE 30-bus system. These minimum values are smaller than the previously best reported results of 10 and 18 for the same systems.