Environmental Engineering Reference
In-Depth Information
ω
∗
is the rated fundamental frequency and
h
is the harmonic order. In order to minimise
the THD of the output voltage, the virtual capacitor
C
o
should be chosen, according to (2.1),
to minimise
where
h
=
2
I
h
Z
o
(
jh
ω
∗
)
2
because the fundamental component
V
1
can be assumed to be almost constant. This is equiv-
alent to
h
=
2
i
1
h
h
2
1
ω
∗
L
min
C
o
−
,
(7.4)
h
ω
∗
C
o
I
h
where
i
1
h
=
I
1
is the normalised
h
-th harmonic current
I
h
with respect to the fundamental
current
I
1
. Depending on the distribution of the harmonic current components, different
strategies can be obtained.
Assume that the harmonic current is negligible for the harmonics higher than the
N
-th order
(with an odd number
N
). Then
C
o
can be found via solving (7.4). Define
h
=
2
i
1
h
h
2
1
N
ω
∗
L
f
(
C
o
)
=
−
.
ω
∗
C
o
h
Then
C
o
needs to satisfy
2
i
1
h
h
1
h
d
f
(
C
o
)
d
C
o
1
N
h
=
ω
∗
L
=
2
−
ω
∗
C
o
=
0
,
h
ω
∗
C
o
which is equivalent to
2
i
1
h
L
1
h
−
=
0
.
=
(
h
ω
∗
)
2
C
o
Hence,
i
1
h
h
2
,
1
N
h
2
i
1
h
L
N
h
=
ω
∗
)
2
C
o
=
=
2
(
and the optimal capacitance can be solved as
i
1
h
h
2
h
ω
∗
)
2
L
1
=
2
C
o
=
h
=
2
i
1
h
,
(7.5)
N
(
which is applicable for any known harmonic distribution of current
i
. The corresponding
f
(
C
o
)is
⎛
⎞
2
−
ω
∗
L
h
N
h
=
2
i
1
h
⎝
h
⎠
h
=
2
i
1
h
N
ω
∗
L
f
min
(
C
o
)
=
i
1
h
h
2
h
=
2
⎛
⎝
h
⎞
⎠
2
h
=
2
i
1
h
N
h
1
ω
∗
L
)
2
h
=
2
i
1
h
N
=
−
.
(
i
1
h
h
2
N
h
=
2
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