Subsynchronous　oscillations　(SSOs)　induced　by　the　interaction　between　wind　farms　based　on　direct-drive　permanent　magnet　synchronous　generators　(D-PMSGs)　and　weak　grids　have　attracted　extensive　attention.　To　better　understand　this　SSO　phenomenon,　this　paper　derives　multi-input　multi-output　(MIMO)　transfer　functions　between　the　references　of　the　current　controller　and　the　current　of　a　grid-connected　converter　in　the　d-q　frame,　where　the　dynamic　of　PLL　is　considered.　The　dynamic　of　PLL　lead　to　positive　feedback　in　the　MIMO　transfer　function,　which　impairs　the　stability　of　the　overall　system　and　induces　the　SSO　phenomenon.　Using　the　classical　root　locus　method,　the　influence　of　correlated　control　parameters　and　different　operation　conditions　on　the　system　stability　is　substantially　analysed.　It　is　found　that　heavy　load,　low　short　circuit　ratio　(SCR)　will　intensify　the　SSO　instability　of　system.　Nonlinear　electromagnetic　transient　simulations　of　a　D-PMSG-based　weak-grid-connected　wind-farm　system　using　PSCAD/EMTDC　software　effectively　verify　the　correctness　of　the　model　proposed　in　the　SSO　analysis.　©　2013　IEEE.