Environmental Engineering Reference
In-Depth Information
19.6.2 Error Due to Inaccurate Voltage Measurements
The only possible error in the real power sharing comes from the error in measuring the RMS
value of the load voltage. From (19.16), the real power deviation
P
i
due to the error
V
oi
in
the measurement of the RMS voltage is
K
e
n
i
P
i
=−
V
oi
.
For two inverters operated in parallel with
P
1
+
P
2
, the relative real power sharing
error due to the error in the measurement of the RMS voltage
P
2
=
P
1
+
V
o
=
V
o
2
−
V
o
1
is
K
e
E
∗
n
i
P
i
P
1
P
1
−
P
2
=
P
2
P
1
P
1
−
P
2
P
2
V
o
E
∗
.
e
P
%
=
=
This characterises the percentage error
e
P
% of the real power sharing with respect to the
percentage error
V
o
E
∗
of the RMS voltage measurement. The term
K
e
E
∗
n
i
P
i
is the inverse of the
voltage drop ratio with respect to the rated voltage at the rated power. If all inverters measure
the voltage at the same point accurately, then the error
V
o
can be made zero and exact
proportional sharing can be achieved.
In order to achieve exact power sharing, all the inverters need to share and measure the
same load voltage
0
◦
accurately. In order to measure the same load voltage, each
inverter can provide an extra terminal, which is not internally connected to the output terminal,
for voltage measurement. This voltage measurement terminal can be connected to the load
terminal with a separate wire to measure the load voltage. In this way, the accuracy of the
voltage measured is not affected by the current flowing through the feeder line and hence the
effect of the feeder line on the power sharing accuracy and voltage regulation is eliminated.
Moreover, the THD of the voltage at the load terminal instead of the inverter terminal is
maintained, which reduces the THD of the load voltage. If needed, the voltage measurement
terminal can be connected to the output terminal externally to measure the local voltage if the
performance is acceptable. When the inverters and/or the loads are spatially distributed, it may
be difficult to measure the voltage at the same point. This causes an error in the power sharing
but in most cases this is acceptable because the resulting relative error of (real) power sharing
is the relative error of the voltage measurement divided by the voltage drop ratio at the rated
power, as characterised above. The voltage drop ratio at the rated power in these applications
can be designed to be bigger than the ones in applications where the loads/inverters are close
to each other so that the system is less sensitive to the error in voltage measurement.
v
o
=
V
o
∠
19.6.3 Voltage Regulation
The strategy also reduces the load voltage drop. From (19.16), the load voltage is
n
i
K
e
n
i
P
i
K
e
E
∗
E
∗
−
E
∗
−
E
∗
,
V
o
=
P
i
=
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