Environmental Engineering Reference
In-Depth Information
Fig. 10.5
Faults affecting the three-phase signals in a controlled DFIG
10.5.3.2 Residual Generator and Decision System Design
Let us denote by f
1
, f
2
, and f
3
the faults affecting u
s
;
a
, u
s
;
b
and u
s
;
c
respectively, and
by f
4
, f
5
, and f
6
the faults affecting i
s
;
a
, i
s
;
b
, and i
s
;
c
. Then by combining two GOS
schemes, one for monitoring the stator voltages and one for monitoring the stator
currents, a 12-dimensional residual vector is obtained that complies with the
incidence matrix of Table
10.4
. Indeed, each observer output r
'
ð
k
Þ
, where
' 2
f
1
;
2
;
3
g
for the stator voltages and
' 2f
4
;
5
;
6
g
for the stator currents, is a two-
dimensional vector. Both three-phase systems are assumed to have constant fre-
quency x
e
¼
2pf
s
rad/s, with f
s
¼
50 Hz the synchronous frequency for the design
of the Kalman filter based on model described by Eqs.
10.33
and
10.35
.
The residual vector can be processed by the multi-CUSUM algorithm described
by Eqs.
10.11
-
10.13
to detect and isolate faults. To this end, the mean and
covariance of the residual vector have to be evaluated in fault free mode and for
the nominal fault to be detected.
From a first set of 5 s of simulated data in healthy conditions, with the system in
its rated operating point, the value of the covariance matrix (R) for the residual
vector r(k) is obtained. The residual mean presents negligible values, so l
0
is set to
zero. On the basis of the indicated minimum fault magnitudes, each l
'
, for
' ¼
1
;
2
;
...
;
6, is calculated, assuming that vector C
'
is the
'
-th column in
Table
10.3
. The thresholds are set to h
'
¼
3
10
4
for
' 2
1
;
2
;
3 and h
'
¼
6
10
3
for
' 2f
4
;
5
;
6
g
, to comply with the required mean detection/isolation delay.
