Geomagnetically Induced Currents — Mesh Network Nodal Analysis (2D)

Storm Drivers

Ground dB/dt 150 nT/min

Storm field azimuth 90°

Neutral grounding resistance 2.0 Ω

Live Readouts

Geoelectric field E—

Effective dB/dt—

Peak line GIC—

Worst neutral current—

Core saturation—

How it works

The 3D twin of this simulator treats each transmission line as an independent lumped Ohm's-law circuit. Real grids are meshed — lines share substations and form loops — so this 2D companion solves the actual Kirchhoff nodal-analysis equations for a six-substation network with two independent loops (a hexagonal ring plus a diagonal cross-tie):

for every line i→j:  EMF_ij = E·L_ij·cos θ_ij   (E = k·dB/dt)
node equation:  Σⱼ (Vᵢ − Vⱼ + EMF_ij)/R_ij + Vᵢ/R_ground,ᵢ = 0
             → solve the resulting 6×6 linear system for every node voltage Vᵢ

Line current then follows directly: I_ij = (Vᵢ − Vⱼ + EMF_ij)/R_ij. Because the network has real loops, a line's current depends on every other line's resistance and orientation, not just its own — rotate the storm azimuth and watch current redistribute between the ring and the cross-tie rather than simply switching on and off line-by-line.

The quantity that actually saturates a transformer core is the current through its grounded neutral — not the line current passing through it. This model reads that off each node's own ground branch, V_i / R_ground,i, and feeds the single worst-loaded neutral into a genuine saturable-core model:

φ(t) = φ_dc(I_neutral) + φ_ac·sin(ωt)
i_mag(φ) = atanh(φ/φ_sat)     [odd, ≈linear for small φ, diverges as φ→φ_sat]

Unlike an arbitrary polynomial kink, atanh is the textbook idealized saturable-inductor characteristic: linear response for a weak flux, and a genuine divergence as flux approaches the core's saturation limit — exactly the half-cycle saturation mechanism behind events like the 1989 Hydro-Québec blackout.

dB/dt slider — storm intensity; severe storms reach several hundred to ~1000+ nT/min at auroral latitudes.
Azimuth slider — rotates the storm's geoelectric field; watch current shift between the ring and the diagonal cross-tie as it sweeps.
Grounding resistance — the resistor utilities add in transformer neutrals specifically to throttle GIC; raising it cuts every neutral current at once.
Substorm impulse — a sudden-impulse-style transient spike in dB/dt, as real substorms produce.

Line (color/width = |current|) Substation node (size = |neutral I|) Storm field direction