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

Given that the generators are in parallel and operate at the same frequency (f) at a steady loss.

Let load on generator G₁ is P₁ and on G₂ is P₂.

Then for G₁ generator

\(\frac{{51.5 - f}}{{{P_1}}}\;\) = constant droop

\( \Rightarrow \frac{{51.5 - f}}{{{P_1}}} = 1\) 

⇒ 51.5 – f = P₁          ---(1)

Now, in steady-state load is 2.5 MW

So, load by G₂ is (2.5 – P₁)

For G₂, \(\frac{{51 - f}}{{2.5{P_1}}} = 1\) 

⇒ 51 – f = 2.5 – P₁      ---(2)

From equation (1) and (2),

51.5 – f + 51 – f = P₁ + 2.5 – P₁

⇒ 102.5 – 2f = 2.5

⇒ f = 50 Hz