Every source and load on this island shares one system frequency, governed by the classic power-system swing equation integrated live, not solved as a static snapshot:
2H·dΔf/dt = P_gen − P_load − D·Δf
P_gen = P_diesel + P_solar + P_battery(droop)
Δf is the deviation from 50 Hz, H is the combined rotating/virtual inertia of whichever sources are currently synchronized, and D is frequency-dependent load damping. The battery inverter is grid-forming: it energizes the dead bus at 50 Hz and supplies fast droop power P_battery = K·(−Δf), clipped by how much state of charge you've reserved. The diesel genset needs several seconds of battery-fed cranking before it synchronizes; once online, its governor chases a droop-commanded target with a first-order lag, and a slow secondary-control term nudges its base dispatch to match connected load.
The restoration mechanic:
- Begin Black Start — the battery energizes the island and starts cranking the diesel generator (draining SoC); after the crank time the diesel synchronizes and starts responding to frequency error.
- Restore Critical / Essential / Full — closes a breaker, stepping up connected load instantly. The swing equation then decides the transient: enough spinning reserve and battery droop headroom holds frequency inside band; too little and it sags.
- Under-frequency load shedding — if frequency stays below 49.0 Hz for more than 1.5 s, protection relays automatically reopen the most recently closed stage, exactly like real UFLS relays sacrificing load to save the island.
- Island collapse — drop below 47.5 Hz and the whole island blacks out again: every stage sheds and the diesel drops offline, forcing a fresh black start.
The 3D version of this sim renders a decorative particle-flow scene with cosmetic sliders that don't drive any shared power-balance state; this 2D companion instead runs the real swing-equation feedback loop the title describes, so restoring load too fast genuinely can — and does — trip a stage back off.