Grid Inertia & RoCoF 2D: Multi-Machine Network Desynchronization

Grid Setup

Renewable penetration 30%

Contingency size (lost generation) 6%

Network coupling (tie-line strength) 8 pu

Governor / frequency response 1.5 pu

Live Readouts

⚠ A node crossed the under-frequency load-shedding threshold (49.5 Hz) — distributed generation there would trip offline.

Grid-average frequency

50.000 Hz

RoCoF at epicenter

0.000 Hz/s

Coherence spread

0.000 Hz

Worst-node nadir

50.000 Hz

How it works

This is a genuine multi-machine model, not a single lumped grid: every node on the ring is its own generator running its own swing equation, coupled to its two ring neighbors through a tie-line. Node i's frequency deviation Δf_i evolves as:

2H_i · d(Δf_i/f0)/dt = P_i − D·(Δf_i/f0) + K · Σ_j sin(θ_j − θ_i)
dθ_i/dt = 2π·f0·(Δf_i/f0)

H_i   = that node's inertia constant (turbines: 5.5 s · inverters: 0.4 s)
P_i   = local power imbalance (only the tripped node carries one)
K     = tie-line synchronizing strength — how tightly neighbors are coupled
θ_i   = node i's rotor angle relative to nominal

Because the coupling term is exactly antisymmetric between any two neighbors (what one node gains the other loses), the network-wide average frequency always follows the same swing-equation math as a single lumped grid — but individual nodes do not have to move together. Trip one generator and the epicenter node's RoCoF spikes immediately while a distant node barely notices at first; the disturbance then radiates outward through the tie-lines, and how far it gets before decaying depends on K. With strong coupling the whole ring locks into one coherent frequency, just like a healthy interconnected grid. Weaken the tie-lines (or cluster renewables — which carry almost no inertia and add nothing to K) and the ring desynchronizes: some nodes recover while others keep sliding toward the 49.5 Hz load-shedding line, exactly the kind of regional split-and-shed event real grid operators most fear.

Renewable penetration — converts an arc of the ring from spinning turbines (H = 5.5 s) to inverter-based sources (H = 0.4 s); it lowers local inertia exactly where those nodes sit, not the whole grid uniformly.
Contingency size — how much power the tripped node suddenly loses.
Network coupling — tie-line synchronizing strength K; weak ties let a local trip stay local (and desynchronize), strong ties spread the disturbance so the whole ring absorbs it together.
Governor / frequency response — how strongly every node's own governor pushes its local frequency back toward 50 Hz.

Synchronous turbine node Inverter-based renewable node Tripped epicenter

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