Robust damping and decoupling controller for interconnected power network based on distributed energy resources

•Identifying and characterizing the dominant oscillatory modes, which arise as a result of interaction between GFCs in a converter-based power network, which have not been investigated before.•Deriving mathematical modelling to tackle the challenges related to the integrative model of GFCs-based power network such as multiple reference frames and interoperability under different control techniques.•Proposing a hybrid damping method through an oscillation damper and a new decoupling controller for interconnected GFCs-based power network under different control techniques.•Developing design guidelines (based on the pattern search algorithm and participation factor analysis) to optimally identity the parameters of the proposed hybrid damping method.•The system is validated based on DSP and control Hardware in the Loop (CHiL) using OPAL-RT.•Overall, the maximum overshoot and settling time are reduced by 0.25 pu and 0.5 s on average, respectively, using the proposed hybrid method.