Parallel PI Voltage-H Current Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 215

20

0

−20

−40

−60

1440

C 7
C 5
C 3
C 1

1080

720

360

0

−360

10 0 10 1 10 2 10 3 10 4 10 5

Frequency (rad/sec)

Figure 13.5 Bode plots of the current controllers designed

The Bode plots of these controllers are shown in Figure 13.5. It can be seen that high gains
appear at the harmonic frequencies included in the corresponding weighting function W ,
which helps reduce the harmonic components in i C . These controllers can be discretised for
digital implementation. With a sampling frequency of 5 kHz, the discretised controllers can
be obtained, e.g. by using the MATLAB R

c 2 d (ZOH) algorithm, as

0 . 013755( z − 1 . 011)( z 2 − 1 . 937 z + 0 . 9425)

C 1 ( z ) =

9994) ,

(13.13)

( z − 0 . 7951)( z − 0 . 9835)( z 2 − 1 . 995 z + 0 .

018)( z 2 9426)( z 2 0 . 017515( z − 1 . − 1 . 937 z + 0 . − 2 . 003 z + 1 . 03)

C 3 ( z ) =

9981) ,
(13.14)

( z − 0 . 7674)( z − 0 . 9857)( z 2 − 1 . 995 z + 0 . 9994)( z 2 − 1 . 963 z + 0 .

02)( z 2 9427)( z 2

0 . 018432( z − 1 . − 1 . 937 z + 0 . − 2 . 007 z + 1 . 034)

C 5 ( z ) =

( z − 0 . 7598)( z − 0 . 9862)( z 2 − 1 . 995 z + 0 . 9994)( z 2 − 1 . 963 z + 0 . 9981)

( z 2 − 1 . 93 z + 1 . 021)

×

9969) ,

(13.15)

( z 2 − 1 . 899 z + 0 .

021)( z 2 9428)( z 2

0 . 018805( z − 1 . − 1 . 937 z + 0 . − 2 . 009 z + 1 . 036)

=

C 7 ( z )

9865)( z 2 9994)( z 2 ( z − 0 . 755)( z − 0 . − 1 . 995 z + 0 . − 1 . 963 z + 0 . 9981)

( z 2 025)( z 2

− 1 . 933 z + 1 . − 1 . 844 z + 1 . 027)

×

9956) .

(13.16)

( z 2 − 1 . 899 z + 0 . 9969)( z 2 − 1 . 806 z + 0 .