Environmental Engineering Reference
In-Depth Information
Hence, the THD of
v
o
is in proportion to the inductance
L
of the inverter LC filter. A small
L
not only reduces the cost but also improves the voltage quality. Moreover, since
1
C
o
L
,
a small
L
leads to a small gain for the integrator, which improves the stability of the current
loop. However, a small
L
leads to a high
d
d
t
for the switches and large current ripples.
If the distribution of the harmonic components is not known, then it can be assumed that
the even harmonics are zero (which is normally the case) and the odd harmonics are equally
distributed. As a result, the optimal
C
o
can be chosen, according to (7.5), as
∼
ω
∗
)
2
L
h
=
3
,
5
,
7
, ...,
N
h
2
1
C
o
=
N
h
(
N
1
=
3
,
5
,
7
, ...,
ω
∗
)
2
L
h
=
3
,
5
,
7
, ...,
N
h
2
1
=
.
(
(
N
−
1)
/
2
This can be written as
1
3
2
+
1
1
1
5
2
+···+
1
N
2
C
o
=
,
(
ω
∗
)
2
L
(
N
−
1)
/
2
where (
N
−
1)
/
2 is the number of terms in the summation. The corresponding
f
(
C
o
)is
h
2
1
h
2
h
=
3
,
5
,
7
, ...,
N
(
N
−
1)
/
ω
∗
L
)
2
f
min
(
C
o
)
=
(
h
=
3
,
5
,
7
, ...,
N
−
.
1
h
2
If a single
h
-th harmonic component is concerned, then the optimal
C
o
is
1
C
o
=
ω
∗
)
2
L
.
(
h
This forces the impedance at the
h
-th harmonic frequency nearly 0 and hence no voltage at
this frequency is caused.
7.4.2 Special Case I: to Minimise the 3rd and 5th Harmonic Components
In most cases, it is enough to consider the 3rd and 5th harmonics only. This gives the optimal
capacitance
17
225(
C
o
=
ω
∗
)
2
L
.
As a result, the output impedance of the inverter is
j
1
ω
Z
o
(
j
ω
)
=
ω
L
−
C
o
ω
∗
L
ω
ω
∗
ω
225
17
=
ω
∗
−
.
j
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