Simulation of cascading failures in power grids using percolation theory on 2D lattice networks, identifying critical tolerance thresholds for system-wide blackouts.
Modern electrical grids are vulnerable to cascading failures, where a single transmission line fault can trigger widespread outages. This project models such failures using percolation theory, exploring whether power grid cascades exhibit phase-transition behavior similar to classical percolation systems.
Using a 2D lattice network representation of a power grid, this simulation investigates how tolerance margins (capacity buffers) influence the likelihood of large-scale failures.
Does the margin between operating load and transmission capacity exhibit a critical threshold beyond which cascading failures are avoided?
- Grid: ( L \times L ) 2D lattice
- Nodes: substations
- Edges: transmission lines
- Boundary: non-periodic
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Initial Failure
- Random edge removal
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Load Redistribution
- Failed edge load redistributed to neighboring edges
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Failure Check
- Edges exceeding capacity fail
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Iteration
- Repeat until equilibrium
| Parameter | Values |
|---|---|
| Grid Size (L) | 12, 20, 30 |
| Tolerance ( \tau ) | 0.1 → 0.9 |
| Step Size | 0.04 |
| Trials per config | 15 |
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Identified a critical tolerance: [ Tau ~ 0.42 ]
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Regimes:
- Fully Cascaded: ( Tau < 0.14 )
- Partial Cascades: ( 0.14 < Tau < 0.42 )
- Stable: ( Tau > 0.42 )
- Small increases in tolerance dramatically reduce cascade risk
- Larger grids are more vulnerable to cascading failures
- Behavior resembles—but differs from—classical percolation
- Sharp transition near ( Tau ~ 0.42 )
- Rapid drop-off in failures as tolerance increases
git clone https://github.com/yourusername/power-grid-cascade-percolation.git
cd power-grid-cascade-percolation
pip install numpy networkx matplotlib