Answer :
The set-point frequency of the first generator is approximately 47.6 Hz, and the set-point frequency of the second generator is 44 Hz.
To determine the set-point frequency of the first and second generators in order to supply a load of 10 MW, we need to consider their power output and the power drooping slope.
Given:
Load power (P_load) = 10 MW
Power drooping slope (Slope) = 1.25 MW/Hz
Let's denote the power output of the first generator as P1 and the power output of the second generator as P2.
We are given that the first generator supplies three times the amount of the second generator. So we can write:
P1 = 3 * P2
The total power supplied by both generators is equal to the load power:
P1 + P2 = P_load
Substituting the value of P1 from the previous equation:
3 * P2 + P2 = 10
Combining like terms:
4 * P2 = 10
Simplifying:
P2 = 2.5 MW
Substituting the value of P2 into the equation for P1:
P1 = 3 * 2.5
P1 = 7.5 MW
Now, let's determine the set-point frequency for each generator using the power drooping slope.
The change in frequency (Δf) is given by the ratio of the change in power (ΔP) to the power drooping slope (Slope):
Δf = ΔP / Slope
For the first generator:
ΔP1 = P1 - P_load
Δf1 = (7.5 - 10) / 1.25
Δf1 = -2.4 Hz
For the second generator:
ΔP2 = P2 - P_load
Δf2 = (2.5 - 10) / 1.25
Δf2 = -6 Hz
To determine the set-point frequency of each generator, we add the respective Δf values to the nominal frequency (50 Hz):
Set-point frequency of the first generator:
f1 = 50 + Δf1
f1 = 50 - 2.4
f1 ≈ 47.6 Hz
Set-point frequency of the second generator:
f2 = 50 + Δf2
f2 = 50 - 6
f2 = 44 Hz
Therefore, the set-point frequency of the first generator is approximately 47.6 Hz, and the set-point frequency of the second generator is 44 Hz.
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