Robust Adaptive Supplementary Control for Damping Weak-Grid SSOs Involving IBRs

Subsynchronous oscillations (SSOs) involving grid-following converters (GFLCs) connected to weak grids are a relatively new phenomena observed in modern power systems. SSOs are further exacerbated when grids become weaker because lines are disconnected due to maintenance or following faults. Such undesirable oscillations have also led to curtailment of inverter-based resource (IBR) outputs. In contrast to most literature addressing the issue by retuning/redesigning of standard IBR controllers, we propose a robust adaptive supplementary control for damping of such SSOs while keeping standard controls unaltered. As a result, uncertainty in system conditions can be handled without negatively impacting the nominal IBR performance. To that end, the adaptive control law is derived for a GFLC connected to the grid, where the grid is modeled by the Thevenin's equivalent representation with uncertainty and disturbances. The theoretical result provides dissipativity certificate for the closed-loop error dynamics with sufficient conditions for stability. The effectiveness of the developed controller is validated with several case studies conducted on a single-GFLC-infinite-bus test system, the IEEE $2$-area test system, wherein some of the synchronous generators are replaced by GFLCs, and a modified IEEE $5$-area test system with two GFLCs. The findings demonstrate that under very weak grid conditions, the proposed robust adaptive control performs well in stabilizing SSO modes, which a classical state-feedback control method fails to address.