Power Grid Synchronization: Swing-Equation Cascade

Every bus in this meshed 12-bus, 20-line network is modeled as its own rotating mass obeying the real electromechanical swing equation, coupled to its neighbors through the true nonlinear AC power-angle relation and integrated live with a 4th-order Runge-Kutta solver — not re-solved as a linear snapshot after each change. Trip a single transmission line and watch the network's rotor angles and frequencies swing in real time as power reroutes, overcurrent relays trip further overloaded lines after a realistic inverse-time delay, and any bus whose local frequency collapses far enough triggers automatic under-frequency load shedding. The Kuramoto order parameter tracks how tightly the whole grid stays phase-locked, falling visibly the moment synchronism is lost — the same electromechanical mechanism (not a mere overload) behind real transient-stability blackouts.