Quasi-Synchronization of Heterogeneous LC Circuits in Grid-Connected Systems With Intentionally Time-Varying Lumped Delays

This article is concerned with quasi-synchronization of grid-connected systems in electrical networks, where heterogeneous Inductance-Capacitance (LC) oscillators are coupled via electrical inductance subject to time-varying delays. Note that complete synchronization fails to be accomplished due to the existence of nonidentical parameters and quasi-synchronization cannot be achieved via non-delayed inductive coupling. A configuration of multiple heterogeneous LC oscillators with inductive coupling subject to time-varying lumped delay is first constructed by introducing an active delay intentionally. Then the complete-type Lyapunov-Krasovskii functionals (LKF) are constructed to investigate the exponential convergence of quasi-synchronization of LC oscillators in the presence of parameter mismatches utilizing the positive effects of interval time-varying delays. Some feasible synchronization criteria are derived. The gain matrix can be designed by solving a set of linear matrix inequalities combining an optimization algorithm. Finally, a numerical example of five LC oscillators in photovoltaic grid-connected system is given to demonstrate the effectiveness of the proposed method.