Distributed control based on tie-set graph theory for smart grid networks

This paper introduces tie-set graph theory and its application to smart grid networks. Tie-sets stand for loop structure in a network. Tie-set graph theory, which aims to realize distributed control in local units, provides the theoretical nature of loops. In mesh topological networks, all the nodes and links are covered with a fundamental system of tie-sets, which is created by a tree defined by graph theory. If tie-sets are used as local management units in a network, an entire network can be controlled in an orderly fashion due to the graph theoretical basis. Distributed control based on tie-sets has some merit such as easy communication and reduction of electricity loss. In this paper, we propose the unique graph theory on tie-sets, its relationship with smart grid networks, and autonomous configurations based on tie-sets. In addition, we suggest distributed algorithms for an electricity distribution problem as a conceivable issue, and basic simulations and experiments are also conducted.