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Converters are the key for increasing the development of renewable energy generation but their dynamic interaction with the grid has an important impact on stability. Oscillatory instabilities in different grid-connected converter systems at several frequency ranges are reported. In particular, sub and supersynchronous oscillatory instabilities in AC power systems with type-3 and type-4 wind turbine generators (WTGs) were recently registered at several wind farm areas. A number of works based on eigenvalue analysis and frequency domain approaches are carried out to analyse this new stability issue and more research is going on to analyse in detail the electric and control parameters that may affect this phenomenon. This study contributes analysing in detail the influence of system parameters on the subsynchronous oscillations (SSOs) in AC power systems with type-4 WTGs. This study is based on a new approach for subsynchronous stability assessment which could also be used for analysing other types of SSOs (e.g. subsynchronous control interactions between doubly-fed induction generators and series-compensated networks) as well as supersynchronous oscillations. A representative example of weak AC grids with type-4 WTGs is used to illustrate the contributions of the study. Results are validated with PSCAD/EMTDC time-domain simulations.