With　the　large-scale　access　of　renewable　energy,　the　problem　of　sub-synchronous　oscillation　(SSO)　caused　by　the　interaction　between　the　direct-drive　permanent　magnetic　synchronous　generators　(D-PMSGs)-based　wind　farm　and　weak　AC　grid　has　attracted　people＇s　attention.　Focusing　on　this　topic,　the　study　presents　an　analysis　of　the　SSO　mechanism　by　establishing　the　double　input　and　double　output　transfer　function　of　the　d　axis　and　q　axis　currents.　Because　of　the　dynamic　characteristics　of　PLL　and　the　existence　of　grid-connected　inductance,　d　axis　and　q　axis　current　transfer　functions　are　coupled　and　asymmetric,　which　introduced　positive　feedback　into　the　closed-loop　negative　feedback　system　of　current　transfer　functions.　The　positive　feedback　is　related　to　controller　parameters,　PLL　parameters,　grid-connected　inductance　and　operation　conditions.　The　combination　of　some　parameters　may　cause　oscillation　or　instability　of　the　system.　In　this　paper,　the　root　locus　method　is　used　to　analyze　the　influence　of　these　parameters　on　the　stability　of　the　system.　Finally,　eigenvalue　analysis　and　electromagnetic　transient　simulation　are　used　to　verify　the　correctness　of　the　method.　©　2019　IEEE.