This work considers the problem of decentralized control of inverter-based ac micro-grid in different operation modes. The main objectives are to (i) design decentralized frequency and voltage controllers

to gather with power sharing

without information exchange between microsources (ii) design passive dynamic controllers which ensure stability of the entire microgrid system (iii) capture nonlinear

interconnected and large-scale dynamic of the micro-grid system withmeshed topology as a port-Hamiltonian formulation (iv) expand the property of shifted-energy function in the context of decentralized control of ac micro-grid (v) analysis of system stability in large signal point of view. More precisely

to deal with nonlinear

interconnected and large-scale structure of micro-grid systems

the port-Hamiltonian formulation is used to capture the dynamic of micro-grid components including microsource

distribution line and load dynamics as well as interconnection controllers. Furthermore

to deal with large signal stability problem of the microgrid system in the grid-connected and islanded conditions

the shifted-Hamiltonian energy function is served as a storage function to ensure incremental passivity and stability of the microgrid system. Moreover

it is shown that the aggregating of the microgrid dynamic and the decentralized controller dynamics satisfies the incremental passivity. Finally

the effectiveness of the proposed controllers is evaluated through simulation studies. The different scenarios including grid-connected and islanded modes as well as transition between both modes are simulated. The simulation conforms that the decentralized control dynamics are suited to achieve the desired objective of frequency synchronization

voltage control and power sharing in the grid-connected and islanded modes. The simulation results demonstrate the effectiveness of the proposed control strategy.