Power System Stability

The swing equation describes rotor dynamics:

$\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2} = P_m - P_e \qquad P_e = \frac{EV}{X}\sin\delta$

• Steady-state stability — small slow changes; maximum transferable power is $EV/X$.
• Transient stability — large disturbances like faults; analysed with the equal area criterion: the system remains stable if the decelerating area can equal the accelerating area. Faster fault clearing increases the margin (critical clearing time).
• Voltage stability and frequency stability — related to reactive power support and generation–load balance.

Grids defend stability with fast protection, excitation systems with PSS, automatic generation control and under-frequency load shedding.