Modelling and Stability of Time-Delayed Microgrid Systems*

In this paper stability of inverter based microgrid system with time delay in voltage phase angle is analysed. It is observed that this delay in voltage angle damages the frequency synchronization of microgrid, which is undesirable. To maintain the grid synchronization frequency, in the presence of delay a condition on droop gain is proposed. Assuming the microgrid is lossless and have constant voltage amplitude at every node Lure system model with input delay is proposed. To check the stability of time-delayed system, a Lyapunov-Krasovskii(L-K) functional is constructed. Based on a L-K functional a Linear Matrix Inequality (LMI) is formed. LMIs are easy to verify, which makes the verification of local stability of time-delayed system easy. It is proved if the LMI is satisfied then the Lyapunouv functional so formed also exist, in turn assuring the local stability of a system.