Isochronous generator transient response

An isochronous generator is a generating unit whose governor is isochronous (integral type, zero droop). It keeps the speed and frequency exactly at the set value for any load within its rating. It is used for a single unit supplying an isolated load, or for one unit that controls frequency in a small system.

Governor law: $\Delta Y(s) = -\dfrac{K}{s}\,\Delta\Omega(s)$, so the gate keeps moving as long as there is any speed error.

Transient response to a step increase in load

 power
 P0+dPL     .________________ Pe
            |      __.-- Pm -> Pe
            |   _.'
 P0   ______|__/  (Pm)
          t = 0
 speed
 w0   ______.            .---- w0 (restored)
             \         .'
              '.____.-'
          t = 0                 time

1. At $t = 0$ the electrical output $P_e$ jumps by $\Delta P_L$; $P_m$ is unchanged, so the rotor decelerates and speed falls (slope $-\Delta P_L/2H$).
2. The integral governor opens the gate; $P_m$ rises (a hydro turbine first dips a little).
3. When $P_m > P_e$ the rotor speeds up again. Because the integrator acts until the error is zero, the speed returns exactly to $\omega_0$.
4. Final state: $\Delta\omega = 0$ and $\Delta P_m = \Delta P_e = \Delta P_L$. Frequency error is zero, unlike a droop governor which leaves $\Delta\omega_{ss} = -\Delta P_L/(D + 1/R)$.