A quadratic convex framework with bigger freedom for the stability analysis of a cyber-physical microgrid system

Information exchange between a microgrid central controller and local controllers is supported by low-bandwidth communication channels, leading to an inevitable delay with time-varying characteristics that adversely affect the microgrid dynamics and even cause instability. This study addresses the problem of stability analysis for a load frequency control (LFC) microgrid system with the interval time-varying delay. First, a modeling approach is proposed for the cyber-physical microgrid, in which the physical interconnection between the cyber-physical components is established. Given that a quadratic function is often introduced in stability analysis and the negative determination is crucial to reducing the conservatism, a novel quadratic convex framework with adjustable free parameters that relaxes the quadratic function negative-determination conditions is developed. Next, the delay-dependent stability criterion of the cyber-physical LFC microgrid is obtained on the basis of augmented Lyapunov-Krasovskii functional and Bessel-Legendre inequality together with mixed convex combination techniques. This reduces the conservatism without requiring extra decision variables. Finally, two types of case studies demonstrate the merits of the proposed scheme.