Question

There are two generators in a power system. No-load frequencies of the generators are 51.5 Hz and 51 Hz, respectively, and both are having droop constant of 1 Hz/MW. Total load in the system is 2.5 MW. Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in Hz in the steady state is ___________.

Answer 1

Let the frequency of the power system be = f Hz.  Then both generators must synchronize to that frequency, when they are connected to the grid.

Let the load on the generator1 be  L  MW.  Load on generator2 will be (2.5 - L) MW.

Then the droop in frequency of generator 1 at load L:   L * 1 Hz/MW =  L
The droop in frequency of generator 2:   (2.5 - L) * 1 Hz /MW  = 2.5 - L

Frequency of operation = f = 51.5 - L  = 51 - (2.5 - L)
                               0.5 = 2 L - 2.5
                                 L = 1.5 MW
                         So    f = 51.5 - 1.5 = 50 Hz
  Then droop on generator 1 is 1.5 Hz and droop in the second one is 1 Hz