Environmental Engineering Reference
In-Depth Information
v
=
v
sin
θ
i
X
e
=
E
sin
θ
g
s
~
SSM model
~
Figure 23.1
Model of an SSM connected to the grid
The factor 2 in the denominator is because E and
v m are peak amplitude values instead of
RMS values. The SSM is considered to be synchronised and floating on the grid (Wildi 2005)
if and only if
E
= v m ,
θ = θ g .
(23.3)
In this case, P
0. In other words, if P and Q are driven to zero, then the condition
(23.3) is satisfied and the generated voltage e is the same as the input (terminal) voltage
=
0 and Q
=
v
.
23.2 Structure of a Sinusoid-locked Loop (SLL)
As mentioned above, the idea of the SLL is to operate a virtual (single-phase) synchronous
generator with P
0 so that the generated voltage e is the same as the fundamental
component of the terminal (or input) voltage
=
0 and Q
=
. Hence, the controller of the synchronverter
shown in Figure 18.4 can be adopted to implement it after making some necessary changes.
The resulting SLL is shown in Figure 23.2(a), which is able to provide the frequency ˙
v
θ
, phase
θ
.
As discussed above, the desired real power and reactive power should all be set as 0. For
single-phase applications, the instantaneous values of T e and Q given in (18.7) and (18.9) are
pulsating. Hence, their average values
, voltage amplitude E and a recovered voltage e for the voltage
v
t
1
T
T e =
M f i f i sin
θ
dt
,
(23.4)
t T
t
1
T
˙
Q
=−
θ
M f i f i cos
θ
dt
,
(23.5)
t T
2
˙
where T
=
is the period of voltage
v
, should be used. The amplitude of the generated
θ
voltage e is
˙
E
=
θ
M f i f
and the instantaneous value of the generated voltage e is
˙
e
=
θ
M f i f sin
θ =
E sin
θ,
(23.6)
which should track that of the input voltage
v
.
 
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