Environmental Engineering Reference
In-Depth Information
19.5.1 Real Power Sharing
Substituting (19.5) into (19.3), the real power of the two inverters can be obtained as
E
∗
cos
δ
i
−
V
o
P
i
=
V
o
.
(19.9)
n
i
cos
δ
i
+
R
oi
/
Substituting (19.9) into (19.5), the voltage amplitude deviation of the two inverters is
E
∗
cos
E
∗
cos
δ
1
−
V
o
δ
2
−
V
o
E
=
E
2
−
E
1
=
−
.
(19.10)
R
o
1
n
1
V
o
R
o
2
n
2
V
o
cos
δ
1
+
cos
δ
2
+
It is known from (Tuladhar
et al.
1997) that the voltage deviation of the two units leads to
considerable errors in load sharing. Indeed, in order for
P
1
S
1
=
P
2
S
2
n
1
P
1
=
n
2
P
2
or
to hold, the voltage deviation
E
should be 0 according to (19.5). This is a very strict condition
because there are always numerical computational errors, disturbances, parameter drifts and
component mismatches. This condition is satisfied
1
if
n
1
R
o
1
=
n
2
R
o
2
(19.11)
and
δ
1
=
δ
2
.
(19.12)
In other words,
n
i
should be chosen to be proportional to its output impedance
R
oi
.
Taking (19.7) into account, in order to achieve accurate sharing of real power, the (resistive)
output impedance should be designed to satisfy
R
o
1
S
1
R
o
2
S
2
.
=
(19.13)
Since the per-unit output impedance of Inverter
i
is
R
oi
S
i
(
E
∗
)
2
,
R
oi
E
∗
/
γ
i
=
I
i
=
the condition (19.13) is equivalent to
γ
1
=
γ
2
.
1
Note that this set of conditions is sufficient but not necessary.
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