Two synchronous generators operating in parallel supply a common

SOLUTION

Given that: two synchronous generators are operating in parallel.

Frequency power characteristics have same slope 1 MW/Hz (1/1 MW/HZ = 1 Hz/MW)

No-load frequencies are:

For generator 1, f₀₁ = 51.5 Hz

For generator 2, f₀₂ = 51 Hz

Load sharing by both generator = 2.5 MW

Load shared by Generator 1 = P₁ MW

Load shared by generator 2 = 2.5 – P₁ MW

Let the frequency of system be f Hz and both generators synchronize to this frequency when connected to the grid.

Now, the droop of generator 1 at P₁ = P₁ × 1 Hz/MW = P₁

And droop of 2^nd generator (2.5 – P₁) = (2.5 – P₁) × 1 Hz = 2.5 – P₁

Given that both have same droop slope

Now, the frequency of operation f,

f = (51.5 – P₁) = 51 – (2.5 – P₁)

⇒ 0.5 = 2P₁ – 2.5 ⇒ P₁ = 1.5 MW