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

Real power grids are meshed, not a chain of independent lines — a substation can sit on several transmission paths at once, and current redistributes across the whole network rather than following each line in isolation. This 2D companion to the 3D GIC simulator models that directly: a six-substation grid with two independent loops (a hexagonal transmission ring plus a diagonal cross-tie) is solved as a genuine Kirchhoff nodal-analysis circuit — a 6×6 linear system for every substation's ground potential — so a line's current depends on the whole network's topology, resistances and the storm field's orientation all at once. The worst-loaded transformer neutral's current then drives a real saturable-core model (an odd, divergent atanh magnetizing-current characteristic) rather than an ad-hoc curve, showing exactly how a quasi-DC geomagnetic current pushes a 50/60 Hz transformer core into half-cycle saturation. Sweep storm intensity, field azimuth and neutral grounding resistance to watch current shift between loops and saturation build or clear.