A　generalized　dq　model　of　the　permanent　magnet　synchronous　motor　(PMSM)　based　on　newly　defined　extended　Park　transformation　is　presented.　The　new　model　can　describes　all　kinds　of　editions　of　the　PMSM　dq　model　together,　such　as　the　edition　based　on　Park　transformation,　the　edition　based　on　the　principle　of　power　invariance,　and　so　on,　for　which　it　can　avoid　confusion　and　prevent　misusing　of　different　editions　at　root.　The　model　equations　derivation　is　shown　step　by　step　and　model　compatibility　is　also　verified.　The　simulation　of　the　vector　controlled　PMSM　drive　based　on　the　new　model,　which　is　instantiated　to　some　edition,　is　performed　to　investigate　the　performance　of　the　drive　in　Matlab.　The　simulation　results　confirm　the　new　model＇s　compatibility　further.