A Stability Analysis of Hybrid Control System Based on Microgrid Considering Asymmetric Synthetic Inertia with Time Delay

In this paper, an asymmetric synthetic inertia control based on the external storage system with time delay is considered as the frequency regulation approach for the microgrid system. Alternating inertia constants which are dependent on the system frequency and the rate of change of frequency are applied in the control. The alternative inertia constants are generated based on the discrete dynamics therefore, the microgrid is regarded as a hybrid system because there is an interaction between continuous and discrete dynamics. The alternating signal describes the trend of change of frequency deviation, moving away from the nominal value or turning to the nominal value. The quadratic stability of such hybrid systems is discussed by using the common Lyapunov approach. Sufficient conditions are established in terms of linear matrix inequalities for piecewise quadratic Lyapunov functions with arbitrary switching signals. The permissible boundary for inertia constant is also discussed. In addition, the supplies of the proposed microgrid involve diesel engine generators, wind turbines, and photovoltaics.