ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED ...

3. FUNDAMENTALS OF DVR Mustafa İNCİ
V
i
i
[ k ( V −V
) + k k ( V −V
) − i ]
= k
{ }
(3.22)
f
ref
s
c
v
ref
l
c
The load side voltage for this control configuration is given by (3.23)
Vload
Gclose
1
Vref
+ Gclose2
= V
(3.23)
s
Where G
close1
is the closed-loop transfer function from the reference signal
V
ref
to V
load
while G
close2
is the closed-loop transfer function from the supply voltage
V
s
to V
load
. These transfer functions (3.24) and (3.25) (Vilathgamuwa et al., 2002) :
G
( nk k k + nk )( L s + r )
i c v i l l
close1 ( s)
= (3.24)
3
2
a1
ncvs
+ a2ncvs
+ a3ncvs
+ a4ncv
G
close 2
( s)
LL C s +
2
( L r + Lr + kk L ) C s + ( r rC + (1−
nk)
L + kk rC ) s+
( 1−nk)
3
l f f f l l f i c l f f l f i l i c l f
i l
= (3.25)
3 2
a1
ncvs
+ a2
ncvs
+ a3
ncvs
+ a4
ncv
r
Following a similar analysis as in open loop control method, it can be seen
the real root of the characteristics equation can be approximately located at
−
2
2
( r + n r )/( L + n L )
l
t
L
(Vilathgamuwa et al., 2006).
t
. Factorization of the characteristics equation yields
2
2 2
( L + n L ) s + ( r + n r ) ( s + b s bncv)
3 2
a1 ncv
s + a2ncvs
+ a3
ncvs
+ a4ncv
≈ b1
ncv{ l t l t
}
2ncv
+ (3.26)
Where
b b ncv 2ncv
1
, and b 3 ncv
are given in the Appendix.
The expressions for the coefficients
b b ncv 2ncv
1
, and b 3 ncv
show that the two
dominant complex poles depend largely on the values of the filter inductance, filter
resistance as well as the capacitor current loop gain k
c
. Furthermore it can be shown
that the real part of these poles is − ( rf
+ kikc
)/
2L
f
. This is a very useful feature
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