Small signal stability analysis of VSC based DC systems using graph theory

Abstract

This paper presents a new method to evaluate the small signal stability based on state space and graph theory, which not only reduces the computational burden of high-dimensional system, but also has the ability to cope with the uncertain parameters and system structure. The system is first represented by a directed graph. Each node in the directed graph denotes a multi-input multi-output subsystem represented by state, input, and output matrices, and constrained by norm bounded uncertainties. The subsystems are connected by edges through node-edge incidence matrix and edge connection matrices. Then we propose the small signal stability conditions associated with the certain node dynamics, edge connection matrices, the norm bounds of uncertainty, and the maximum degree of the system, independent of the system structure and the number of nodes and edges. We apply our methods to the VSC based DC systems with uncertain parameters and structure. The comparative analysis of simulations results of Bode diagram, state matrix eigenvalues, and the new method validates the effectiveness of the proposed stability conditions.