For　inverter　control,　droop　control　is　an　effective　control　scheme,　but　this　scheme　does　not　have　the　inertia　and　damping　of　the　synchronous　generator,　resulting　in　insufficient　frequency　stability.　In　response　to　this　problem,　some　scholars　have　proposed　a　virtual　synchronous　generator　(VSG)　control　method　to　simulate　the　operating　characteristics　of　traditional　synchronous　generators.　In　order　to　analyze　the　advantages　and　disadvantages　of　the　two　control　strategies,　this　paper　first　established　a　small　signal　model　of　the　inverter　based　on　droop　control　and　VSG　control.　The　dynamic　response　of　the　time　is　compared.　We　can　conclude　that　the　droop　control　and　the　VSG　control　have　their　own　advantages　and　disadvantages,　and　cannot　meet　the　strict　dynamic　characteristics　of　the　GC　and　SA　states.　Then,　based　on　the　comparison　between　the　virtual　synchronous　generator　and　the　droop　control,　the　traditional　droop　control　is　improved.　On　this　basis,　an　adaptive　control　is　proposed　to　improve　the　response　characteristics　of　the　output　frequency　and　active　power　when　the　power　command　changes　in　the　grid-connected　mode.　In　the　GC　state,　the　IDC-based　adaptive　control　method　can　improve　the　output　tracking　of　the　input　active　power,　reduce　frequency　fluctuations,　and　ensure　frequency　stability　when　the　power　reference　value　changes.　In　the　SA　state,　the　IDC-based　adaptive　control　method　can　provide　sufficient　inertial　characteristics.　Finally,　the　simulation　results　verify　the　effectiveness　of　the　proposed　control　strategy.　©　2020　IEEE.