Environmental Engineering Reference
In-Depth Information
1.5
Gain: 1.12
Pole: 0.504 + 0.341i
Damping: 0.641
Overshoot (%): 7.23
1
0.5
π
/T
0.6
π
/T
0.4
π
/T
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.7
π
/T
0.3
π
/T
0.5
0.8
π
/T
0.2
π
/T
0.9
π
/T
0.1
π
/T
π
/T
0
π
/T
0.9
π
/T
0.1
π
/T
−0.5
0.8
π
/T
0.2
π
/T
0.7
π
/T
0.3
π
/T
0.6
π
/T
0.4
π
/T
0.5
π
/T
−1
−1.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Real Axis
Figure 16.3
Root locus for the controller design
ξ
=
.
641. Figure 16.4 shows the Bode plots of the open-loop system for different integral
gain
K
i
with
K
p
=
0
.
12, from which the integral gain is chosen as
K
i
=
200. Since the
controller has a very high gain at the resonant frequency, it has a very good ability to reduce
the steady-state error. The resulting controller in the discrete-time domain is
1
12
z
2
1
.
−
2
.
196
z
+
1
.
08
C
PR
(
z
)
=
.
(16.10)
z
2
−
1
.
996
z
+
1
16.4 Experimental Results
The PR controllers implemented in both the
frame and the
abc
frame were evaluated with
the test rig described in Chapter 15 in the grid-connected mode under five different scenarios
to test the steady-state responses without a local load and with a resistive, non-linear and
unbalanced resistive local load connected to the system, and the transient response without a
local load.
αβ
16.4.1 Steady-state Performance
16.4.1.1 Without a Local Load
In the steady state, the grid current reference
I
d
was set at 3 A. The reactive power was set at 0
Va r (
I
q
0). This corresponds to the unity power factor. All the active power was transferred
to the grid via the step-up transformer. The grid current output
i
a
and its spectra, the current
reference
i
ref
and the tracking error
e
i
are shown in the left column of Figure 16.5 for the
=
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