Environmental Engineering Reference
In-Depth Information
scheme is that it does not depend on the type of the impedance and, hence, it can be used for
any type of impedances. This facilitates the controller design, without the need for checking
the impedance type at the corresponding harmonics, and will be applied to develop a strategy
to improve the voltage THD in this chapter.
Note that
P
=
0 and
Q
=
0 when
E
=
Z
o
I
and
δ
=
θ,
according to (21.2) and (21.3). This is another way to express (21.1) and can be used to reduce
or even eliminate harmonics in the output voltage.
21.3 Reduction of Harmonics in the Output Voltage
As discussed above, in order to force the
h
-th harmonics in the output voltage of an inverter
to be (nearly) zero, the voltage
v
oh
in Figure 21.1(b) needs to be zero. In other words, the real
power and reactive power delivered to the current source
i
h
in Figure 21.1(b) should be 0. As
a result, the voltage set-point
E
∗
for the droop controller obtained in (21.4) should be 0 for the
h
-th harmonics (
h
1). The frequency set-point should simply be set as the
h
-th harmonic
frequency. This leads to the following
h
-th harmonic droop controller:
=
E
h
=−
n
h
P
h
,
(21.6)
ω
∗
−
ω
h
=
h
m
h
Q
h
,
(21.7)
where
P
h
and
Q
h
are the real power and reactive power at the terminal for the
h
-th harmonic
frequency, and
n
h
and
m
h
are the corresponding droop coefficients. Here, the subscripts of
the relevant variables are changed to reflect the
h
-th harmonics. The reference voltage
v
rh
at
the
h
-th harmonic frequency can then be formed with the RMS value
E
h
and the phase angle
generated from the integration of
ω
h
. In practice, instead of generating a harmonic frequency
ω
h
from (21.7), it can be obtained from
h
ω
t
with the addition of
δ
h
, which is integrated from
−
t
is the phase of the voltage reference at the fundamental frequency. This
leads to the
h
-th harmonic droop controller shown in Figure 21.4. As explained above, it does
m
h
Q
h
. Here,
ω
v
o
E
h
P
h
-n
h
v
rh
h
ω
t+
δ
h
Q
h
1
i
-m
h
s
ω
t
h
Figure 21.4
The
h
-th harmonic droop controller (
h
=
1)
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