The　secondary　control　plays　an　important　role　in　ensuring　the　power　quality　of　AC　island　microgrid.　Since　the　traditional　time-driven　secondary　control　strategy　will　cause　communication　redundancy,　the　event-triggered　mechanism　has　been　widely　studied.　Under　the　event-triggered　mechanism,　the　DG　performs　necessary　communication　only　when　its　own　triggering　condition　is　met.　This　paper　studies　the　problem　of　secondary　voltage　control　under　periodic　event-triggered　mechanism,　which　can　restore　the　output　voltage　to　the　reference　value.　At　the　same　time,　considering　that　each　DG　has　a　different　sampling　and　checking　period,　this　is　a　more　general　asynchronous　communication　problem.　In　the　stability　analysis,　the　conditions　of　event　detection　period　and　event　parameters　to　ensure　the　realization　of　secondary　control　are　given.　Finally,　the　effectiveness　of　the　mechanism　is　verified　by　several　simulations.