ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED ...

3. FUNDAMENTALS OF DVR Mustafa İNCİ
For a practical DVR system, it can be shown that the nondominant real root
3 2
(pole) of the system characteristics equation a1 os
+ a2os
+ a3
os
+ a4o
is
2
2
approximately located at − ( r + n r )/( L + n L )
equation can be factorized as (Vilathgamuwa et al., 2006).
l
t
L
t
. Therefore the characteristics
a
2
2 2
( L + n L ) s + ( r + n r ) ( s + b s )
3 2
1 o
s a2os
+ a3os
+ a4o
≈ b10
l t l t
}
20
+
+ { b (3.20)
30
and by equating the coefficients on both sides, the coefficients b
10
, b20,
b30
, ,
and b40
can be determined. They are given in the Appendix (Vilathgamuwa et al.,
2006).
The expressions for b
10
, b20,
b30
reveal that the locations of the remaining two
complex and dominant poles depend on the filter, load, and the series transformer
parameters. Indeed further analysis will show that the real part of the poles is equal
to
− r / 2L
f
f
. As a safeguard against voltage sag, the DVR is expected to be on-line
at all time so that there is minimal delay in providing the voltage support as and
when it is needed. Hence it is desirable that the restorer has low loss and thus the
filter resistance r(f) is kept to as low a value as practicable. This could mean that the
dominant complex poles are located very close to the imaginary axis. Therefore the
transient response of the distribution system following a sag behaves very much like
a second-order system with natural damping frequency of ω
n0
given by
(Vilathgamuwa et al., 2006).
r + n r + n r 1
ω (3.21)
2 2
l t f
n0 =
≈
2
( rl
+ n rt
) L
f
C
f
L
f
C
f
As
r
l
2
2
>> n rt
and rl
n rf
>> .
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