Environmental Engineering Reference
In-Depth Information
v
a
v
b
v
c
]
T
As discussed in Chapter 2, a three-phase voltage vector
v
abc
=
[
in the natural
frame can be transformed into a vector [
V
d
V
q
]
T
in the synchronously rotating reference
frame by first using the Clarke transformation
⎡
⎣
⎤
⎦
v
abc
=
1
2
1
2
v
α
v
β
1
−
−
2
3
v
αβ
=
=
√
3
2
√
3
2
T
αβ
×
v
abc
,
(22.2)
0
−
and then the Park transformation
V
d
V
q
cos
θ
−
sin
θ
=
v
αβ
=
T
dq
v
αβ
.
(22.3)
sin
θ
cos
θ
For a voltage vector
⎡
⎣
⎤
⎦
E
cos(
θ
g
)
E
cos
⎡
⎤
v
a
v
b
v
c
2
3
θ
g
−
⎣
⎦
=
,
E
cos
2
3
θ
g
+
there is
V
d
V
q
E
cos(
θ
−
θ
g
)
=
.
θ
−
θ
g
)
E
sin(
Hence, [
V
d
V
q
]
T
is a vector with two DC components
V
d
and
V
q
in the SRF. In order to lock
into the phase of the input signal, i.e. to achieve
θ
=
θ
g
,
the
V
q
component can be fed into a
PI controller to achieve
V
q
=
0 in the steady state. The output of the PI controller is actually
the estimated frequency, which is integrated to obtain the estimated phase angle
,asshown
in Figure 22.3. The estimated amplitude
E
of the voltage vector can also be obtained, via
θ
V
d
=
+
V
q
.
E
(22.4)
When the phase is locked,
E
=
V
d
. Hence, the frequency, the amplitude and the phase are all
available from the SRF-PLL.
Comparing Figure 22.3 to the basic PLL shown in Figure 22.2(a), the transformation from
abc
to
dq
with the estimated
plays the role of the phase error detection. Because
V
q
is already
a DC component, the loop filter is simply a unity gain. The PI controller and the integrator
actually play the role of the VCO to generate the frequency and the phase.
θ
Search WWH ::
Custom Search