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Renewable energy sources (RESs) are growing rapidly and highly penetrated in microgrids (MGs). As a result of the replacement of the synchronous generators with a large amount of RESs, the overall system inertia might be dramatically reduced which negatively affected the MG dynamics and performance in face of uncertainties, leading to weakening of the MG stability, which considers being a serious challenge in such grids. Therefore, in order to cope with this challenge and benefit from a maximum capacity of the RESs, robust control strategy must be applied. Hence, in this paper, a new application of robust virtual inertia control-based coefficient diagram method (CDM) controller is proposed in an islanded MG considering high-level RESs penetration for enhancement the system's validity and robustness in face of disturbances and parametric uncertainties. The proposed controller's proficiency has been checked and compared with H-infinite controller using MATLAB/Simulink which approved that the CDM controller achieved superior dynamic responses in terms of accurate reference frequency tracking and disturbance reduction over H-infinite in all test scenarios. Thus, the proposed controller alleviates the difficulties of H-infinite controller such as the experience and necessary abilities to design the form of the weighting functions for the system. Consequently, the frequency stability is improved and approved that the proposed CDM-based virtual inertia controller can significantly support a low-inertia islanded microgrid against RESs and load fluctuations. INDEX TERMS Virtual inertia control, renewable energy sources, coefficient diagram method (CDM), frequency control. I. INTRODUCTION Recently, there is a growing interest in integrating Renewable Energy Sources (RESs) into the electrical power grids as a future solution for the reduction of greenhouse gas emissions generated by conventional power plants, such as carbon dioxide and nitrogen oxide which have bad environmental consequences [1]. As a result, several conventional generation units are being replaced by the concept of Distributed Generators (DGs)/ RESs such as solar, wind energy, microturbine, and small thermal power plants. In other words, small power generation sources such as wind turbines and photovoltaic (PV) are connected to close distributed sites. Although, this concept has a lot of merits such as reduction of the voltage droop and transmission system losses, and enhancing system reliability, it has some impacts on the performance of the modern power systems such as lack of system inertia [2], [3]. Microgrid (MG) has considered providing an appealing infrastructure for overcoming the challenges of integrating RESs/DGs to the grid [4]. Where the MG acts as a single controllable entity with respect to the grid and that connects and disconnects from such grid to enable it to operate in

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