Environmental Engineering Reference
In-Depth Information
the error of
ω
1% in the frequency setting would lead to a 100% of error in the reactive
power sharing! Hence, the accuracy of reactive power sharing is very sensitive to the accuracy
of the global setting for
ω
∗
=
ω
∗
, which should be made very accurate.
Similarly, according to (19.16), the real power deviation
E
i
in
E
i
P
i
due to the error
is
K
e
n
i
E
i
.
P
i
=
P
1
P
2
, the relative real power sharing
For two inverters operated in parallel with
P
1
+
P
2
=
+
E
∗
=
E
2
−
E
1
=
E
2
−
E
1
in the global settings of
E
∗
error due to the error
is
P
2
=
−
K
e
E
∗
n
i
P
i
E
∗
E
∗
.
P
1
P
1
−
P
2
P
1
P
1
P
2
P
2
=
=−
e
P
%
For a typical voltage drop ratio at the rated power of
n
i
P
i
E
∗
E
∗
10%, a 10% error in
K
e
E
∗
=
would
100% error in the real power sharing. Although the error in
E
∗
is less sensitive than
the error in
lead to a
−
ω
∗
, it is still quite significant. Hence, in practice, it is very important to make sure
that the global settings are accurate. Anyway, this is not a problem at all.
19.6.5 Experimental Results
The above strategy is verified in a laboratory set-up consisting of two single-phase inverters
controlled by dSPACE kits and powered by separate 42 VDC voltage supplies. The inverters
are connected to the AC bus via a circuit breaker CB and the load is assumed to be connected
to the AC bus. The values of the inductors and capacitors are 2
.
35 mH and 22
μ
F, respectively.
The switching frequency is 7
.
5 kHz and the frequency of the system is 50 Hz. The rated voltage
is 12 VRMS and
K
e
=
10. The droop coefficients are:
n
1
=
0
.
4 and
n
2
=
0
.
8;
m
1
=
0
.
1 and
m
2
=
2
Q
2
. Due to the configuration of the
hardware set-up, the voltage for Inverter 2 was measured by the controller of Inverter 1 and
then sent out via a DAC channel, which was then sampled by the controller of Inverter 2. This
brought some latency into the system but the effect was not noticeable.
0
.
2. Hence, it is expected that
P
1
=
2
P
2
and
Q
1
=
19.6.5.1 Inverters Having Different per-unit Output Impedances with a Linear Load
Both
K
i
were chosen as 4 for the two inverters to intentionally make the per-unit output
impedances of the two inverters significantly different. In reality, this could be due to different
feeder impedances or component mismatches.
A linear load of about 9
was connected to Inverter 2 initially. Inverter 1 was connected
to the system at around
t
5 s. The relevant
curves from the experiment with the robust droop controller are shown in the left column
of Figure 19.8 and the relevant curves from the experiment with the conventional droop
controller are shown in the right column of Figure 19.8. In both cases, the reactive power was
shared accurately (in the ratio of 2 : 1), although the actual values were different (because
=
3 s and was then disconnected at around
t
=
10
.
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