Environmental Engineering Reference
In-Depth Information
as long as
K
e
is the same for all inverters. This guarantees the accurate sharing of reactive
power in proportion to their ratings. As long as the system is stable, which leads to the same
frequency, the real power can be guaranteed as well (Zhong 2012c).
According to (19.18), the output voltage is
n
i
K
e
n
i
Q
i
K
e
E
∗
E
∗
−
E
∗
−
E
∗
,
V
o
=
Q
i
=
which can be maintained within the desired range via choosing a big
K
e
. Hence, the control
strategy has very good capability of voltage regulation as well, in addition to the accurate
power sharing.
The droop coefficients
n
i
and
m
i
can then be determined as usual by the desired voltage
drop ratio
n
i
Q
i
K
e
E
∗
and the frequency drop ratio
m
i
P
i
ω
∗
, respectively, at the rated reactive power
Q
∗
and real power
P
∗
.
19.8.2 Simulation Results
A system that consists of two single-phase inverters powered by two separate 42 VDC voltage
supplies was used to carry out simulations to verify the design. The capacity of Inverter 1 is
25 VA and the capacity of Inverter 2 is 50 VA, with the rated power factor of 0
.
9. It is expected
that
P
2
=
2
P
1
and
Q
2
=
2
Q
1
. The switching frequency is 7
.
5 kHz and the frequency of the
system is 50 Hz. The rated voltage is 12 V and
K
e
=
20. The filter inductor is
L
=
2
.
35
mH with a parasitic resistance of 0
.
1
and the filter capacitance
C
is 22
μ
F. Without any
ω
∗
)
inner-loop controller, the output impedance of the inverter is about
Z
o
(
j
=
j
0
.
74
, which
is inductive.
Assume that the desired voltage drop ratio
n
i
Q
i
K
e
E
∗
is 10% and the frequency drop ratio
m
i
P
i
ω
∗
is 1%, respectively, at the rated real power
P
i
9
S
i
and reactive power
Q
i
436
S
i
.As
=
0
.
=
0
.
a result,
n
1
=
.
2 and
n
2
=
.
1;
m
1
=
.
14 and
m
2
=
.
2
1
0
0
07.
19.8.2.1 With a Linear Load
Simulations were carried out for a linear load with
R
L
=
. The results for L-inverters and
R-inverters are shown in the left and right columns of Figure 19.19, respectively. The system
performed very well in both cases. It is worth noting that the output voltage of the L-inverters
was slightly higher than the rated voltage because the reactive power is capacitive due to the
filter capacitor.
9
19.8.2.2 With a Non-linear Load
The same simulations were carried out for a full-bridge rectifier load with an LC filter
L
=
150
. The results for L-inverters and R-inverters are shown
in the left and right columns of Figure 19.20, respectively, with the steady-state performance
shown in Table 19.1 with comparison to C-inverters. Again, the system performed well in both
μ
H,
C
=
1000
μ
F and
R
L
=
9
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