Speed droop in sharing common load

Speed droop is the drop in speed (frequency) of a governed unit as its load goes from no load to full load, expressed in per unit of rated speed. It is defined by

$$R = \frac{\Delta f / f_0}{\Delta P / P_r} \quad \text{(pu)}$$

A 4 % droop means the frequency falls by 4 % (2 Hz at 50 Hz) from no load to full load. Droop gives every governor a definite speed–load line, so parallel units share a load change in a fixed, stable ratio. Without droop (isochronous governors), parallel units fight each other and the load division is undefined.

Block diagram (two units on a common bus)

   +-->[1/R1]--+
   |           v -
   |  dPref1->(+)->[Gov1]->[Turb1]--dPm1--+
   |                                      v
   |                        -dPL ------->(S)--+
   |                                      ^   |
   |  dPref2->(+)->[Gov2]->[Turb2]--dPm2--+   |
   |           ^ -                            v
   +-->[1/R2]--+                    [1/(2Hs+D)]
   |                                          |
   +--------------- d(omega) -----------------+

S = summing point: $\Delta P_{m1} + \Delta P_{m2} - \Delta P_L$.

Both units see the same frequency deviation $\Delta f$ because they are synchronised.

Derivation

In steady state, the governor of unit $i$ obeys its droop line:

$$\Delta P_i = \Delta P_{ref,i} - \frac{1}{R_i}\frac{\Delta f}{f_0}P_{ri}$$

With fixed references ($\Delta P_{ref,i} = 0$):

$$\Delta P_1 = -\frac{P_{r1}}{R_1}\frac{\Delta f}{f_0}, \qquad \Delta P_2 = -\frac{P_{r2}}{R_2}\frac{\Delta f}{f_0}$$

The total change must supply the load change:

$$\begin{aligned} \Delta P_L &= \Delta P_1 + \Delta P_2 = -\frac{\Delta f}{f_0}\left(\frac{P_{r1}}{R_1} + \frac{P_{r2}}{R_2}\right) \\ \frac{\Delta f}{f_0} &= \frac{-\Delta P_L}{\frac{P_{r1}}{R_1} + \frac{P_{r2}}{R_2}} \end{aligned}$$

and the ratio of sharing is

$$\frac{\Delta P_1}{\Delta P_2} = \frac{P_{r1}/R_1}{P_{r2}/R_2}$$

If $R_1 = R_2$ (same per-unit droop), $\Delta P_1/\Delta P_2 = P_{r1}/P_{r2}$, i.e. load is shared in proportion to ratings.

 f                     f
 f0|\ unit 1           |\  unit 2
   | \                 |  \
 f'|--*-----common f'--|---*
   |   \               |    \
   +----+---> P1       +-----+---> P2
       P1'                  P2'

Importance

• Gives a unique, stable division of load among parallel units.
• A smaller droop makes a unit "stiffer", so it takes a bigger share of any change.
• Equal per-unit droop on all units makes each carry load proportional to its rating, avoiding overload of small units.
• The frequency drop needed is small (typically 4–5 % droop), and the load reference setting is then used to bring frequency back to nominal.