Power Systems Lab · 18 modules · all computed in your browser
Transient stability
Swing equation (RK4) and the equal-area criterion.
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Power Systems Lab · 18 modules · all computed in your browser
Swing equation (RK4) and the equal-area criterion.
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Single machine – infinite bus · swing equation & equal-area criterion
Result
STABLE
δ₀
26.4°
δ critical (EAC)
81.3°
δ at clearing
41.1°
Red = accelerating area A1 (Pm > Pe while faulted). Green = decelerating area available A2. Stable if A2 ≥ A1.
Learn it
During a fault the generator can’t push its power into the grid, but the turbine keeps driving it, so the rotor speeds up and its angle δ grows. Once the fault clears, the electrical power is higher than the mechanical power and brakes the rotor. If the braking energy available (A2) is at least the energy gained (A1), the machine swings back. Otherwise it slips a pole and must be tripped.
That’s why fast protection, such as instantaneous Zone 1 and 87L, and fast breakers matter so much at 500 kV: clearing time directly sets A1.
Quiz · 0/3
1. Increasing H (more inertia) makes the critical clearing time…
2. Clearing faster primarily reduces…
3. Why does tripping the faulted line lower post-fault Pmax?