Complex-Frequency Support Control for Grid-Following Inverter-Based Resources Using an SRF-CFLL

Increasing inverter-based resource (IBR) penetration strengthens the coupling between voltage magnitude and frequency. This study integrates synchronous reference frame complex frequency-locked loop (SRF-CFLL) observation with existing η-control for a single grid-following IBR in a modified WSCC 9-bus system. Joint complex-variable observation replaces the separate PI-tracking front end. An explicit relative-frequency formulation cancels jω0 terms and clarifies the per-unit current-reference interface. Under the original benchmark settings, η-control reduces the local frequency-nadir deviation by approximately 55% and the 70 Ω fault metric μ from 0.03023 to 0.02522 s, an improvement of 16.57%. Simulations reveal trade-offs among transient frequency support, electromechanical damping and settling time under the tested settings. These phasor simulation results provide a reference for integrating complex-frequency observation with grid-following IBR support control and selecting support parameters.