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Stability limits and factors affecting transient stability

Short answer

Steady state stability is synchronism under small gradual changes, limit Pmax=EV/X at δ=90°. Transient stability is synchronism after a large sudden disturbance, limit determined by equal area criterion. Factors affecting transient stability include pre-fault loading, fault type and location, clearing time, post-fault reactance, generator inertia, transient reactance, excitation speed, and reclosing schemes.

What do you mean by steady state and transient stability and their limits in a power system? Describe the factors affecting the transient stability of a power system.

Power system stability is the ability of a power system to return to a normal (synchronous) operating condition after being subjected to a disturbance.

  • Steady state stability is the ability of the system to remain in synchronism when subjected to small and gradual changes in load (or generation). The maximum power that can be transmitted through a point without loss of synchronism under such slow changes is the steady state stability limit. For a machine connected to an infinite bus through reactance XX:
Pmax=EVX(at δ=90∘)P_{max} = \frac{EV}{X} \quad (\text{at } \delta = 90^\circ)
  • Transient stability is the ability of the system to remain in synchronism after a large and sudden disturbance such as a fault, loss of a line, sudden loss of large load or generation. It is studied over the first swing (about 1 s). The maximum power that can be transmitted while the system remains stable after a specified large disturbance is the transient stability limit. It is always lower than the steady state limit and depends on the type, location and clearing time of the disturbance.

The limits are shown on the power-angle curve Pe=EVXsin⁡δP_e = \frac{EV}{X}\sin\delta: the steady-state limit is its peak; the transient limit is the largest PmP_m for which the equal area condition (A1=A2A_1 = A_2) can still be satisfied after the given disturbance.

Factors affecting transient stability

FactorEffect on transient stability
Pre-fault loading (PmP_m, δ0\delta_0)Higher loading gives larger δ0\delta_0 and a smaller margin
Type of fault3-phase fault is most severe, then LLG, LL, LG
Location of faultFault near the generator bus reduces PeP_e most (close to zero)
Fault clearing timeLonger clearing increases the accelerating area; critical factor
Post-fault network reactanceHigher reactance after clearing lowers Pmax3P_{max3} and the decelerating area
Inertia constant HHLarger HH slows the rotor swing, giving more time
Generator transient reactance Xd′X_d'Lower reactance raises power transfer
Excitation level and speed of the excitation systemHigher internal emf and fast field forcing raise PmaxP_{max}
Reclosing schemeFast and single-pole reclosing restores transfer capability
Speed of governor/fast valvingQuick reduction of PmP_m reduces acceleration

From the swing equation 2Hωsd2δdt2=Pm−Pmaxsin⁡δ\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2} = P_m - P_{max}\sin\delta, any factor that lowers PmaxP_{max} during or after the fault, or keeps Pm−PeP_m - P_e large for longer, makes the system less stable.

✓ Answer checked by Claude Sonnet 5.5

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