Cascading Power Grid Failure

N-1 Contingency

Initiating line trip

Grid Design

Design security margin 130%

Relay trip threshold 115%

Cascade speed 1.0x

Grid State

Lines active

20 / 20

Cascade trips

Max line loading

—

Unserved load

Grid intact. Select a line and trigger a fault.

How it works

Each bus i has a voltage phase angle θ_i. Under the DC power-flow approximation (small angle differences, flat voltage, lossless lines), real power flow on a line is proportional to the angle difference across it, weighted by the line's susceptance b:

P_ij = b_ij · (θ_i − θ_j)
Nodal balance:  Σ_j P_ij = P_i  (generation − load at bus i)

That balance is a linear system B·θ = P (B is the weighted graph Laplacian, one bus fixed as the angle reference), solved here directly for every topology change — exactly the linearized load-flow used for real-time contingency screening on actual grids.

The cascade mechanic:

Trigger a fault — one line opens. Power that used to flow on it must reroute over the remaining meshed paths, so flows on nearby lines jump immediately, even though nothing there physically changed.
Relay tripping — a line loaded above the protection threshold trips after an inverse-time delay (more overload → faster trip), mirroring real overcurrent relays. Each trip forces another flow redistribution, which can push previously-fine lines over threshold too — the cascade.
Islanding & load shedding — if trips split the network into separate islands, an island with no generator blacks out completely; an island where demand exceeds its generators' output automatically sheds load proportionally (the "unserved load" readout), the same way under-frequency load shedding protects a real island from total collapse.
Design margin — sets every line's thermal capacity as a multiple of its own base-case flow. A tighter margin makes the whole grid more fragile to the same single fault, illustrating why N-1 security margins exist.

This is the same mechanism behind real cascading blackouts (e.g. the 2003 US-Canada or 2003 Italy events): one contingency causes flow redistribution, redistribution causes further trips, and the cascade only stops once every remaining line is inside its rating.

Line <70% loaded 70–100% loaded Overloaded / tripping Tripped / de-energized

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