Effect of excitation on steady state stability

For a generator connected to an infinite bus, the power transferred is

$$P_e = \frac{E\,V}{X}\sin\delta, \qquad P_{max} = \frac{EV}{X}$$

The steady-state stability limit is $P_{max}$, reached at $\delta = 90^\circ$. Excitation sets the internal emf $E$, so it changes this limit directly.

Increase in excitation (over-excitation)

• $E$ increases, so $P_{max} = EV/X$ increases and the power-angle curve becomes taller.
• For the same mechanical input $P_m$, the operating angle $\delta = \sin^{-1}(P_m X/EV)$ becomes smaller.
• The synchronising power coefficient $P_s = (EV/X)\cos\delta$ becomes larger.
• The steady-state stability margin $(P_{max}-P_m)/P_{max}$ increases. The machine also supplies lagging reactive power to the bus.

Decrease in excitation (under-excitation)

• $E$ falls, $P_{max}$ falls, and $\delta$ rises toward $90^\circ$ for the same $P_m$.
• $P_s$ becomes small, so the machine is weakly held in synchronism.
• If excitation is reduced too far, $P_{max}$ drops below $P_m$ and the machine pulls out of step. Under-excitation limiters guard against this.

 Pe
  |      ___  E2 > E1 (higher excitation)
  |    /     \
  |   / __    \   E1
  |  / /  \    \
 Pm-+-*---*-----\----------
  | /d2  d1      \
  +--------90------180-- delta

Effect of the AVR

A fast automatic voltage regulator raises $E$ when the load angle increases. This effectively holds the terminal voltage, and the practical stability limit rises above the value set by a fixed $E$ (dynamic stability limit). Too high an AVR gain can, however, reduce damping, which is why power system stabilisers are used.