⚡ Power Grid Flow

DC power flow is a linearised approximation of the full AC power-flow equations that assumes small angle differences between buses and ignores reactive power and losses. It reduces the flow problem to a simple linear system P = B·θ, where B is the network's susceptance matrix and θ is the vector of voltage angles at each bus, solvable directly by Gaussian elimination. It is the standard tool grid engineers use for fast contingency screening because it captures the essential redistribution behaviour of a real grid without the computational cost of a full AC solution.

Each transmission line has a thermal capacity based on a nominal 62 MW rating scaled by the Line capacity slider. After solving the flow, the simulation checks every line's loading ratio (flow ÷ capacity); if any line exceeds 100%, the single most overloaded line is removed from the network and the DC power-flow equations are re-solved from scratch. Because power must still get from generators to loads, the tripped line's flow redistributes onto the remaining lines — which can now push previously safe lines over their own limit, repeating the cycle up to 40 times and building the "cascade depth" stat.

An overloaded grid (max line loading above about 85%) still delivers all its power but with little safety margin left. A blackout occurs when the cascading trips split the network into separate "islands" — the simulation checks network connectivity after every re-solve, and any island that ends up without a generator inside it has no way to serve its loads, so that entire island's demand is shed. The "Load served" percentage falls below 100% precisely when islanding has cut some buses off from every generator.

Raising System demand pushes more power through every line to satisfy the extra load, so the network starts closer to its collective thermal limit even before anything trips. Lowering Line capacity shrinks every line's thermal rating directly, so the same power flow that was previously safe now exceeds the (smaller) limit. Both sliders reduce the margin between normal operating flow and the trip threshold, which is exactly why the Stress test button ramps demand upward — to find the point where that margin runs out.

The N−1 criterion is the standard grid-planning rule that a transmission network must be able to lose any single line or generator and still serve all its customers without cascading failure. The 2003 Northeast America blackout and the 2006 European blackout both began with a single line trip (from a tree contact and a planned disconnection respectively) whose power rerouted onto neighbouring lines that were already running close to their limits, triggering exactly the trip-reroute-overload sequence this simulation reproduces — proof that even networks designed to N−1 standards can fail if operating margins have already eroded.