Abstract: Based on the Lyapunov stability theory analysis method, the problem of the frequency dynamic response of the time-delay microgrid LFC considering VIC is studied. Firstly, the LFC model of the time-delay microgrid with VIC is constructed. Secondly, by constructing a time-delay product augmented Lyapunov-Krasovskii functional that takes into account more state information of time-delays and combining the generalized free matrix integral inequality method to precisely define the derivative of the functional, a stability criterion with lower conservatism is obtained. Finally, experiments and simulations are conducted using Matlab, the relationship between the upper bound of the maximum allowable time-delay in a time-delay microgrid system incorporating VIC and the control gains K_P and K_I under both constant and time-varying delay scenarios is analyzed. The results confirm that VIC not only significantly enhances the dynamic performance of the system but also influences the upper bound of the maximum allowable time-delay.