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Grid
Inertia constant H
Model checks
The science
Swing equation
Rotating machines store kinetic energy. When generation and load differ, the shared rotor speed (grid frequency) changes: 2H/f0 · df/dt = (Pgen − Pload)/S. The 3D lab uses the same simplification: the target rate of change of frequency is RoCoF = (ΔP/500 MW) · (10/2H) Hz/s, low-pass filtered with a 1/3 s time constant. Larger H (more spinning mass) means a smaller RoCoF.
Droop / automatic frequency response
Governors and batteries add or remove power in proportion to the deviation: target = 140 MW per Hz (limited to ±400 MW), approached with a 0.83 s time constant. The frequency settles where the controller exactly covers the imbalance: fss = 50 − (Pload − Pgen)/140. Without it the frequency keeps ramping until protection would trip.
Honest simplifications: a single-area model, constant load damping ignored, no under-frequency load shedding, no network losses, no secondary (AGC) control. Real grids hold 50 ± 0.2 Hz; the numbers here are illustrative.
What to try
- Press Trip a generator with medium inertia and watch the drop and recovery.
- Switch the controller off: frequency ramps without limit.
- Compare Low and High inertia on the same trip: only the RoCoF changes, the final value does not.