Smart Grid Command Center: State Estimation & Cyberattack Detection

SECURE — no bad data

Grid Loading

Load / generation spread 1.00×

Sensor noise σ 0.020 pu

Attack on Command Center Data

Target line meter L1 (0–1)

Injection magnitude a 0.00 pu

State Estimator (WLS)

χ² residual J

0.00

Detection threshold

0.00

State error (RMS)

0.0 mrad

Meters / redundancy

9 / 4

How it works

A command center never sees the grid directly — it sees noisy sensor readings and must estimate the true state. This uses a linearised (DC) power-flow model on a 6-bus, 9-line network with bus 0 as the reference (θ₀ = 0):

line flow:  f_ij = B_ij (θ_i − θ_j)
measurement: z_k = f_ij + noise_k,  noise_k ~ N(0, σ²)
in matrix form:  z = Hθ + e

The estimator solves the weighted least-squares problem, with W = diag(1/σ²):

θ̂ = (HᵀWH)⁻¹ HᵀWz     (solved live by Gaussian elimination, 5×5)
residual:  r = z − Hθ̂
χ² test:   J(θ̂) = Σ rₖ²/σ²  vs threshold ≈ dof + 3√(2·dof)

If J exceeds the threshold, the command center flags bad data. A naive spoof adds an offset to one meter directly — it breaks the flow-consistency equations, spikes the residuals, and trips the alarm. A stealthy false-data injection (FDIA) instead adds an error vector c = Hâ built from a fake angle shift â: because c lives inside the column space of H, the estimator "explains" it as a perfectly consistent — but wrong — grid state, and the residual (and χ²) barely move. This is the textbook unobservable-attack result from power-system security research (Liu, Ning & Reiter, 2011): an attacker who knows the network topology can corrupt the state estimate without tripping a single alarm.

Grid loading — rescales bus power injections, re-solving the true DC flow and regenerating fresh noisy measurements every frame.
Sensor noise σ — the assumed/actual meter noise; also sets the χ² threshold via W.
Target line meter + magnitude — choose which of the 9 line-flow sensors to corrupt and by how much.
Naive spoof vs Stealthy FDIA — same magnitude, two different injection geometries; watch χ² and the estimated-angle error respond completely differently.

Bus (height = estimated θ̂) Line — low residual Line — high residual

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.