Abstract The time delay between distributed generation sources puts the frequency stability at risk. Moreover, increasing the number of distributed generation sources in islanded microgrids due to the lack of inertia has undesirable effects on frequency stability. In this article, the notion of a virtual synchronous generator which follows the characteristics of a conventional synchronous generator is introduced. Virtual inertia control can be implemented on sources of energy storage. In this article, the problem of designing a Virtual Inertia Control method is based on Robust Model Predictive Controller (RMPC), considering the time delays in microgrids is addressed. To model the uncertainty of the system, employed the polytopic model and the Sedumi solver to solve the Linear Matrix Inequalities (LMI), in a shorter time. Compared the results of the proposed controller under several different scenarios with virtual inertial control schemes based on the optimized-PIcontroller (Genetic algorithm), the H-infinity controller, and the control free procedure, considering uncertainties in microgrid parameters, time delays and input disturbances. The efficiency of the RMPC method has been indicated via the simulations performed in MATLAB.
