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In this paper, two-level decentralized optimization power dispatch control strategies are proposed in an islanded microgrid without communication network to ensure frequency security and economic benefit. First, the secondary-level decentralized optimization control strategy is designed only by using local measurement regarding frequency deviation. It is able to implement the optimal power dispatch for all dispatchable distributed generation units in a coordinated way in order to completely restore the system frequency with minimum operation cost. Then, the first-level decentralized droop compensation control strategy is designed to implement real-time optimal power sharing among all energy storage units in order to quickly compensate large supply-demand imbalance and ensure frequency security. Moreover, the proposed control strategies are proved to be able to meet the requirements of the 'plug and play' operation in the absence of communication network. Simulation results verify the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]