Economical RoCoF-Gated Virtual Inertia with DC Energy Buffering and PV Curtailment Reserve for Inverter-Dominated Grids

As synchronous generation is displaced by inverter-based resources, aggregate system inertia falls, the rate of change of frequency (RoCoF) following a disturbance rises and the frequency nadir deepens. Hybrid virtual-inertia schemes that permanently engage a battery buffer restore frequency performance, but impose continuous cycling on the storage asset, and a permanently deloaded photovoltaic (PV) plant forgoes energy revenue, whether or not a severe event is actually in progress. This paper proposes and evaluates an economical virtual-inertia scheme organised as a cost hierarchy: inverter synthetic inertia, which draws only on existing converter headroom, is always active, while a DC battery/supercapacitor buffer and a curtailment-based PV reserve are held dormant and released by a RoCoF-triggered mode-switching supervisor with hysteresis and a dwell-time lockout. The scheme is modelled as an aggregated swing equation with governor droop, explicit state-of-charge dynamics and a first-order PV ramp lag, and is implemented independently in a MATLAB time-domain script and a Simulink block model that agree to within 0.02 Hz. For a 100 MW loss of generation on a 1000 MVA system with H = 5 s, the gated scheme reproduces the entire peak-RoCoF reduction of an always-engaged buffer (-0.470 to -0.158 Hz/s, 66%) while consuming approximately one quarter of the battery state of charge (1.05 against 4.35 percentage points), at the cost of a partial rather than complete nadir recovery. Eigenvalue analysis confirms every configuration stable with monotonically improving damping, and the reported improvements are robust to plus/minus 30% variation in the control gains.