Stability limits and enhancement techniques

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 $X$:

$$P_{max} = \frac{EV}{X} \quad (\text{at } \delta = 90^\circ)$$

• 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.

Limits for a machine on an infinite bus

 Pe
  ^      steady state limit EV/X
  |          .-''-.
  |        .'      '.
  |------.'---------'.---- transient limit
  |     /             \    (lower; depends on fault)
  |    /               \
  +---+--------+--------+--> delta
      0       90       180

• Steady state limit: $P_{ss} = EV/X$; operation is stable only where $dP_e/d\delta > 0$, i.e. $\delta < 90^\circ$.
• Transient limit: the largest $P_m$ for which, after the given fault and clearing time, the equal area condition $A_1 = A_2$ can still be met.

Techniques for enhancing transient stability