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Grid-connected large-scale power converter-based intermittent renewable energy sources (RES) reduce system inertia, increase frequency fluctuation, and increase the rate of change of frequency (RoCoF). An energy storage system (ESS) is an indispensable component of a smart grid, and is used to overcome low-inertia problems. However, the capital and maintenance costs of ESS are high and high RoCoF events are less frequent in power systems. Therefore, the introduction of a virtual energy storage system (VESS) to provide the function of a conventional ESS for power system ancillary services is an innovative and cost-effective method. This study investigated a VESS using photovoltaic (PV) generators and inverter air conditioners (IACs) to provide virtual inertia and frequency regulation for a low-inertia microgrid. A model predictive control (MPC)-based VESS regulates indoor temperature, microgrid frequency, and RoCoF. The impact of parameter variation, that is, the microgrid frequency weight, indoor temperature weight, virtual inertia gain, and number of IACs, was studied and selected by considering the ability of the parameters to provide virtual inertia and frequency regulation. Finally, the efficiency and robustness of the proposed MPC-based VESS technique are compared with those of a conventional VESS. Simulation results revealed that the proposed MPC-based VESS can improve the virtual inertia, reduce the frequency deviation, and reduce the RoCoF of the studied microgrid. In addition, the proposed method is robust to variations in the system parameters.INDEX TERMS Virtual energy storage system, virtual inertia emulator, load frequency control, inverter air conditioner, photovoltaics generator, microgrid

-This paper proposes a simultaneous control of frequency deviation and electric vehicles (EVs) battery state of charge (SOC) using load frequency control (LFC) and EV controllers. In order to provide both frequency stabilization and SOC schedule near optimal performance within the whole operating regions, a multiple-input multiple-output model predictive control (MIMO-MPC) is employed for the coordination of LFC and EV controllers. The MIMO-MPC is an effective modelbased prediction which calculates future control signals by an optimization of quadratic programming based on the plant model, past manipulate, measured disturbance, and control signals. By optimizing the input and output weights of the MIMO-MPC using particle swarm optimization (PSO), the optimal MIMO-MPC for simultaneous control of the LFC and EVs, is able to stabilize the frequency fluctuation and maintain the desired battery SOC at the certain time, effectively. Simulation study in a two-area interconnected power system with wind farms shows the effectiveness of the proposed MIMO-MPC over the proportional integral (PI) controller and the decentralized vehicle to grid control (DVC) controller.