Environmental Engineering Reference
In-Depth Information
Define
P
Q
sin
P
Q
θ
−
cos
θ
=
.
(19.2)
cos
θ
sin
θ
Then
⎡
⎣
⎤
⎦
.
EV
o
Z
o
P
Q
sin
δ
=
V
o
Z
o
EV
o
Z
o
cos
δ
−
Hence, for a small
δ
,
EV
o
Z
o
EV
o
Z
o
δ,
P
=
sin
δ
≈
V
o
−
EV
o
Z
o
E
V
o
Q
=
δ
−
Z
o
≈
V
o
,
cos
Z
o
which means
P
and
Q
can be controlled by controlling
and
E
separately. This is the basis of
the widely-used droop control strategies (Brabandere
et al.
2007; Guerrero
et al.
2005, 2006b,
2008; Yao
et al.
2011). What is important is that a transformation involving the impedance
angle
δ
θ
should be applied to calculate the real power
P
and reactive power
Q
.
19.4 Conventional Droop Control
A voltage-controlled inverter can be modelled as an ideal voltage source
v
r
in series with its
output impedance
Z
o
∠
θ
, as shown in Figure 19.2. For different types of output impedances,
different droop control strategies can be obtained.
19.4.1 For R-inverters
When the output impedance is resistive,
0
◦
. Then
θ
=
V
o
Z
o
EV
o
Z
o
EV
o
Z
o
P
=
cos
δ
−
and
Q
=−
sin
δ.
When
δ
is small,
V
o
Z
o
V
o
Z
o
E
EV
o
Z
o
δ,
P
≈
−
and
Q
≈−
and, roughly,
P
∼
E
and
Q
∼−
δ,
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