Environmental Engineering Reference
In-Depth Information
23
Sinusoid-locked Loops
Several conventional synchronisation methods are discussed in Chapter 22. Simulation and
experimental results have shown that these methods have difficulties in providing the infor-
mation on the voltage when there are frequency variations and/or harmonics, etc. Moreover,
the response is not fast enough. In this chapter, a sinusoid-locked loop (SLL) that is able to
quickly track the amplitude, frequency and phase of the fundamental component of a signal is
presented. This is based on the idea of mimicking a grid-connected synchronous machine that
does not exchange power with the grid because such a machine generates the same instanta-
neous voltage as the grid voltage. That is, the voltage amplitude, the phase and the frequency
of the generated voltage are the same as those of the grid voltage. Following the idea of
synchronverters (Zhong and Weiss 2011) discussed in Chapter 18, the mathematical model of
a synchronous machine can be adopted as the core of an SLL to lock with the fundamental
component of the voltage. The control objective of the SLL is then to zero the real power and
reactive power exchanged with the input voltage. Because the dynamics of a tiny machine can
be very fast, the SLL is able to provide very fast response. Both simulation and experimental
results are presented.
23.1 Single-phase Synchronous Machine (SSM) Connected to the Grid
The simplified model of an SSM connected to the grid is depicted in Figure 23.1, where the
grid voltage is
v
=
v
m
sin
θ
g
and the SSM is modelled as a voltage source
e
=
E
sin
θ
, which
represents the generated voltage, in series with the synchronous reactance
X
s
.
The real power
P
and reactive power
Q
flowing out of the SSM are (Singh
et al
. 2009;
Wildi 2005)
sin
θ
−
θ
g
,
=
v
m
E
2
X
s
P
(23.1)
and
2
X
s
E
cos
θ
−
θ
g
−
v
m
.
v
m
=
Q
(23.2)
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