Singular Perturbation-Based Capability-Aware Frequency Control for Microgrids with Ramp-Rate-Limited Generation

This paper presents a capability-aware frequency control strategy for microgrids comprising a ramp-rate-limited synchronous generator (SG) and a bounded inverter-based resource (IBR). In contrast to conventional droop and virtual inertia methods, the proposed design activates IBR support according to whether the required power-rate exceeds the ramp-rate capability of synchronous generation. A smooth activation mechanism detects when the required power-ramp demand exceeds the SG ramp-rate limit. The IBR is then engaged to supply the excess ramping requirement while providing additional damping through frequency-deviation feedback. A two-timescale model is formulated, where the IBR power-tracking dynamics evolve on a fast boundary-layer timescale. In contrast, the SG regulation loop evolves on a slow electromechanical timescale. Using singular perturbation theory combined with Lyapunov and input-to-state stability (ISS) analysis, local practical stability of the closed-loop system is established for sufficiently fast IBR dynamics. The proposed framework yields a physically interpretable coordination mechanism that exploits the fast response of IBR without introducing artificial inertia or frequency-domain disturbance splitting.