The　adoption　of　the　droop　control　provides　a　feasible　scheme　for　the　distributed　generation　connected　to　the　utility　grid.　Nevertheless,　it　does　not　contribute　to　the　inertia　and　damping　factor　necessary　for　power　systems.　In　order　to　achieve　increased　stability　of　microgrids,　some　scholars　simulate　the　operating　characteristics　of　traditional　synchronous　generators　through　control　equations,　thus　virtual　synchronous　generator　control　(VSG)　was　developed.　Firstly,　the　small　signal　models　of　inverter　based　on　droop　control　and　VSG　control　are　built　in　grid-connected　(GC)　state　and　stand-alone　(SA)　state　to　compare　the　dynamic　response　when　load　transition　and　power　reference　change.　And　we　can　deduce　that　in　terms　of　dynamic　response　neither　of　these　two　control　strategies　can　simultaneously　satisfy　the　stringent　requirements　of　different　modes　of　operation.　Then,　by　integrating　the　advantages　of　the　traditional　droop　control　and　VSG　control,　inertial　droop　control　is　introduced　in　this　paper.　The　presented　inertial　droop　control　not　only　features　virtual　inertia　but　also　adds　compensators　to　the　output　power　part　of　the　active　power　control　loop　to　ensure　the　dynamic　response　of　the　system.　In　the　GC　state,　inertial　droop　control　helps　to　restrain　power　oscillations,　shorten　power　adjustment　time,　and　minimize　frequency　fluctuations　to　maintain　frequency　stability.　In　the　SA　state,　the　inertial　droop　control　enables　to　achieve　high　enough　inertia　and　damping　properties.　Finally,　this　paper　demonstrates　the　superiority　of　the　inertial　droop　control　by　means　of　simulation　results.　©　2020　The　Author(s)