Fast virtual inertia support for AC-excitation synchronous condensers based on dual frequency-locked loops

The increasing integration of inverter-based resources into modern power systems has substantially reduced the overall rotational inertia, posing critical challenges to grid frequency stability. The AC-excitation synchronous condenser, which employs a doubly-fed induction machine with a high-inertia rotor and a three-phase inverter for excitation, has emerged as a promising device for reactive power compensation and voltage support. However, its conventional grid-following control lacks the capability to provide inertial response during frequency disturbances. To address this limitation, this paper proposes a virtual inertia injection strategy based on dual frequency-locked loops with distinct response dynamics. The fast loop rapidly tracks the grid frequency to ensure prompt inertial response, while the slow loop, incorporating a second-order low-pass filter, emulates the rotor dynamics of conventional synchronous condensers. This architecture eliminates the noise amplification and response delays inherent in derivative-based virtual inertia methods, while enabling independent adjustment of the virtual inertia constant and damping coefficient through explicit parameter mapping. The mathematical equivalence between the proposed dual-loop structure and the swing equation of synchronous condensers is rigorously established under both over-damped and under-damped conditions. Simulation results demonstrate that the proposed strategy achieves an inertial response settling time of approximately 35 ms, which is 24% faster than the conventional derivative-based method, and maintains stable operation during severe grid faults including three-phase voltage sags and phase jumps. Experimental validation on a 5.5 kW prototype demonstrates that the proposed strategy achieves a rise time of 120 ms with oscillation-free power output, representing a 68% improvement over the virtual synchronous machine method, while maintaining robust operation under harmonic-distorted grid conditions.