Application Of Inclusion Principle Based On Graph Theory In Interconnected Large-scale Systems

From the view of graph theory, dynamic graphs can describe the interconnected large-scale systems. Based inclusion principle, the interconnected large-scale systems can be decomposed a group of pair-wise subsystems. The research on connective stability and overlapping decentralized control of interconnected large-scale systems is advanced and valuable.The purpose of this paper includes three aspects as follows:First, based on the dynamic graph and inclusion principle, this paper presents a kind of decomposition method about dynamic graphs of interconnected large-scale systems. The results show that this method is useful for overlapping decentralized control of interconnected large-scale systems.Second, based inclusion principle, this paper presents a kind of judging method of connective stability for a class of linear interconnected large-scale systems. First, a class of linear interconnected large-scale system is decomposed into a group of subsystems, and then each of the subsystems is associated with stability analysis and judgment. Then a group of judgment matrices can be obtained. After permuted and corrected, these judgment matrixes form an extended judgment matrix. Under the constraints of inclusion principle, this paper can turn the extended decision matrix into a judgment matrix. If the judgment matrix is diagonally dominant and it is an M-matrix, the author can judge that the linear interconnected large-scale system is connective stability,or not. Parameters of judgment matrixes were derived from each subsystem, easy to be obtained and the calculation is simple. The Matlab simulation results show that this method is benefit to judge the connective stability of a class of linear interconnected large-scale systems.Third, this paper also proposes a kind of overlapping decentralized control scheme and applies it to four regional interconnected power systems in automatic generation control. Based on the inclusion principle, system in the extending space is divided into a set of pair system. Then, through the LQ control law, this paper design a group of decentralized controller for each pair-wise subsystem. Finally, under contains conditions, this paper can obtain an overlapping decentralized controller. The Matlab simulation results show that this method not only guarantees the quality of AGC, but also can effectively control some structural perturbations caused by disconnection of certain regions.