Control and Design of Microgrid Components - Power Systems ...

ω
Unit 2 Max
Unit 2
ω
o
Unit 1
ω
1
ω
2
ΔPmax
ΔPmax
Δωmax
P
P = 0
Output Power
Within Limits
Pmax
Figure 3.16 Effectively Limiting Pmax on Output Power Control.
Figure 3.16 shows two units in island mode operating at the frequency ω1 (circles) where unit 2
has:
P1(at ω1) = P1_1
P2(at ω1) = Pmax + ΔPmax
Here, ΔPmax is the amount of power that is given in excess of Pmax. The main idea is that a
change must be performed so that at the final operating point unit 2 is injecting Pmax (and no
more), while unit 1 injects the amount of power that it had previously added of the excess of
power (ΔPmax ) of unit 1:
P1(at ω2) = P1_1 + ΔPmax
P2(at ω2) = Pmax
Frequency ω2 is also shown on Figure 3.16 and the corresponding power outputs are shown with
squares. Notice that the sum of power injected does not (and must not) change between the two
frequencies, since the overall sum of the load demand has not changed. The question now is how
to make sure that unit 1 (that reaches max) will rearrange its frequency as to end up at frequency
ω2 and not ω1. The reason why it would reach ω1 in the first place is because of the droop
equation, reported here for convenience:
i
= o o , i
( P P )
ω ω − m −
Eq. 3.4
i
33