Robust μ-Synthesis Grid-Side Control for Inverter-Based Resources in Weak Grids

With the increasing penetration of inverter-based resources (IBRs), modern power systems are experiencing undesirable dynamics, such as sub-synchronous oscillations in weak grids. Conventional PI control schemes, however, exhibit limited robustness against nonlinearities arising from varying operating points in weak grids, leading to instability. To address this challenge, we propose a robust controller for the outer loop of grid-side converters in IBRs based on robust μ-synthesis control theory. Specifically, this paper utilizes μ-synthesis to handle linearized model parameters associated with operating-point variations. The proposed controller replaces the PI controllers in the outer loop while retaining the established dq-frame control philosophy. Furthermore, during controller synthesis, the controller is optimized with a 2-by-2 multi-input multi-output structure to explicitly account for cross-coupling effects between the d- and q-axes. Finally, the proposed controller was validated using electromagnetic transient simulations of a detailed type-IV wind farm model implemented in MATLAB/Simulink R2025a, and its performance was compared with that of a conventional PI-based outer control loop. The wind farm was tested under very weak grid conditions, and the proposed controller demonstrated robust stability against varying operating points by providing superior damping performance.