Transient Stability Analysis

Method & Assumptions

This tool uses the classical one-machine infinite-bus (OMIB) swing equation model for single-generator transient stability analysis.

The swing equation:

M × d²δ/dt² = Pm − Pe
where M = 2H / ωs,  Pe = Pmax × sin(δ)

Three operating periods are modeled:

  1. Pre-fault: normal operating power flow establishes δ₀
  2. During fault: reduced electrical power transfer (Pmax_fault), rotor accelerates
  3. Post-fault: fault cleared, power transfer restored (Pmax_post)

Integration method: 4th-order Runge-Kutta at 1 ms time steps.

The Critical Clearing Time (CCT) is found by bisection: the latest clearing time at which the system remains stable (δ < 180°).

The Equal-Area Criterion (EAC) provides a fast analytical estimate of CCT, valid for OMIB systems.

Inputs are in per-unit (pu) on the machine's rated MVA base.

References: Kundur (1994), Anderson & Fouad (2003), IEEE Std 1110-2002.

Machine Parameters

Machine inertia constant. Typical values: hydro generators 2–4 s, steam turbines 4–8 s, gas turbines 3–6 s.

Affects the machine inertia coefficient M = 2H/ωs.

Pre-disturbance generator loading. Assumed constant during the transient. Typical: 0.7–1.0 pu. Do not exceed pre-fault Pmax.

Network Power Transfer (pu)

Maximum power transfer Pmax = E'V / X depends on the transient reactance E' (assumed = 1.05 pu), terminal voltage V (1.0 pu), and the Thevenin reactance between generator and infinite bus. Enter directly from a load flow study or reactance calculation.

E'V / X_pre (normal network). Must be ≥ Pm for a stable operating point.

E'V / X_fault (reduced — fault depresses terminal voltage). Bolted 3-phase fault at generator bus → Pmax_fault = 0.

E'V / X_post (post-fault network, e.g. after line tripped). Must be > Pm for stable post-fault equilibrium to exist.

Simulation Parameters

Time from fault inception to circuit breaker interruption. Typical: 3–6 cycles (0.05–0.10 s) for high-speed relaying. Enter 0.083 s for 5-cycle breaker at 60 Hz.

Total simulation time. 2–3 s is sufficient for most transient stability studies.