Environmental Engineering Reference
In-Depth Information
S
=
P
+
jQ
i
Z
∠
θ
o
°
I
∠
0
~
↓
E
∠
δ
(
i
)
(
v
)
Figure 21.2
Power delivery to a current source through an impedance by a voltage source
Here,
δ
is the phase difference between the supply (voltage) and the terminal (current). When
δ
is small,
Z
o
I
2
cos
P
≈
EI
−
θ,
Z
o
I
2
sin
Q
≈
EI
δ
−
θ.
Hence, roughly,
P
∼
E
and
Q
∼
δ
for any type of impedance
Z
o
∠
θ
. This is quite different from the case with a voltage source,
where these relationships change with the type of the impedance. The conventional droop
control strategy should then take the form
E
∗
−
E
i
=
n
i
P
i
,
(21.4)
ω
i
=
ω
∗
−
m
i
Q
i
.
(21.5)
This strategy is sketched in Figure 21.3. It is different from any of the droop control strategies
when the power is delivered to a voltage source discussed in Chapter 19. Note that, in order to
make sure that the
P
loop are of a negative feedback, respectively,
so that the droop controller is able to regulate the frequency and the voltage, the signs before
n
i
P
i
and
m
i
Q
i
are all negative, which makes them droop terms. The main advantage of this
−
E
loop and the
Q
−
ω
E
i
ω
i
E
*
*
ω
E
=
E
*
−
n
P
i
i
i
ω
=
ω
*
−
m
Q
i
i
i
Capacitive
Inductive
0
0
P
i
*
P
i
Q
i
*
Q
i
Figure 21.3
Droop control for inverters maintaining a constant output current (for any type of
impedances)
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