This paper addresses the distributed frequency control and economic dispatch problem of micro-grid systems. The optimal frequency control problem is formulated considering both frequency regulation and generation cost minimization, by establishing an equivalent nonlinear second-order dynamic model. A distributed finite-time consensus protocol is proposed to solve the optimal frequency regulation problem based on the equivalent model. Despite the nonlinear dynamics, the system frequency

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... to the nominal value and the economic dispatch is achieved both in finite time. It is proved that the equilibrium point of the closed-loop system is the unique optimal solution to the associated economic dispatch problem. Simulation results verify the theoretical analysis and demonstrate the effectiveness of the proposed control method. INDEX TERMS distributed finite-time control, frequency control, economic dispatch problem, micro-grid hierarchical control