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The displacement of synchronous generators by converter interfaced energy renewable resource essentially reduces the system inertia, which can trigger under-frequency load shedding relay. To support the frequency containment, virtual inertia control (VIC) and fast frequency control (FFC) based on energy storage system (ESS) have been developed. Most of the existing VIC did not take into account the power constraints of the ESS. Although some of the FFC methods account for the ESS constraints, they ignore the intermediate steady-state (ISS) operating point of the primary frequency response (PFR). To counteract these problems, a model predictive control (MPC) based FFC, which considers the power limitations of the ESS, the frequency deviation constraint, and the ISS frequency tracking capability, is proposed in this paper. The proposed MPC only requires few local measurements, and the system parameters including inertia constants, onset time of inertia response and the ISS time of the PFR can be accurately estimated. To achieve the optimal control action and reduce computational burden, quadratic programming (QP) is incorporated in the proposed MPC. The proposed MPC is tested on a real Taiwan power system. The fast response and robustness of the proposed MPC has been justified by comparing with the state-of-the-art method. [ABSTRACT FROM AUTHOR]