Environmental Engineering Reference
In-Depth Information
15
Current Proportional-Integral
Control
Proportional-integral (PI) controllers are so far the most widely applied controllers in industry.
In this chapter, a PI controller is applied to grid-connected inverters to track a reference current
so that a desired current can be injected into the grid. This is done in the synchronously rotating
reference (
dq
) frame. Its equivalent in the natural (
abc
) frame is also discussed. Experimental
results are provided to demonstrate the performance of the PI control scheme.
15.1 Control Structure
15.1.1 In the Synchronously Rotating Reference (dq) Frame
The transfer function of a PI controller (Astrom and Hagglund 1988, 1995, 2006; Tan
et al.
1999; Visioli 2006; Yu 1999) is given by
K
i
s
,
C
PI
(
s
)
=
K
p
+
(15.1)
where
K
p
and
K
i
are the proportional and integral gains, respectively. As discussed in Chap-
ter 2, three-phase signals in the natural frame can be transformed into DC signals in the
synchronously rotating reference (
dq
) frame. Hence, for inverters, PI controllers are normally
designed in the synchronously rotating reference (
dq
) frame (Teodorescu and Blaabjerg 2004;
(Timbus
et al
. 2006c, 2009).
The block diagram of a current-controlled VSI in the synchronously rotating reference (
dq
)
frame is shown in Figure 15.1. A PLL is adopted to provide the phase information of the grid
voltage, which is needed to transform the grid currents into their
dq
components
I
d
and
I
q
in the
dq
frame and then transform the voltage control signal back to the
abc
frame. Two PI
controllers are adopted to regulate
I
d
and
I
q
according to the current references
I
d
and
I
q
,
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