Environmental Engineering Reference
In-Depth Information
i
K
i
-
u
v
r
Figure 7.2
Controller to achieve a resistive output impedance
Since the average of
u
f
over a switching period is the same as
u
, there is approximately
v
r
−
K
i
i
=
sLi
+
v
o
,
which gives
v
o
=
v
r
−
Z
o
(
s
)
·
i
with
Z
o
(
s
)
=
sL
+
K
i
.
If the gain
K
i
is chosen big enough, the effect of the inductance is not significant and the
output impedance can be made nearly purely resistive over a wide range of frequencies. Then,
the output impedance is roughly
Z
o
(
s
)
≈
K
i
,
which is independent of the inductance. However, a big
K
i
causes considerable harmonic
components in the output voltage for non-linear loads and, hence, small
K
i
is preferred in
order to achieve low THD in the output voltage. How to reduce the THD of the output voltage
while using large
K
i
will be discussed in Chapter 20. Note that when
K
i
=
0, the output
impedance becomes inductive and the inverter becomes an L-inverter.
With the above control strategy, the inverter can be approximated as a controlled ideal
voltage supply
v
r
cascaded with a resistive output impedance
R
o
described as
v
o
=
v
r
−
R
o
i
(7.1)
with
R
o
=
K
i
.
Such inverters are called R-inverters. Note that
v
o
≈
u
=
v
r
if no load is connected.
7.2.2 Stability Analysis
If the controller is implemented using analogue electronic circuits, then the control loop
is stable for a very large gain
K
i
. However, if it is implemented with a digital controller,
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