Environmental Engineering Reference
In-Depth Information
system of the form presented in Sect.
10.3.2
. r
ð
k
Þ
is a 6-dimensional vector when
using the GOS, and a three-dimensional vector when using the DOS. The residual
vector resulting from these two schemes can be written as:
r
ð
k
Þ¼
r
0
ð
k
Þþ
m
'
C
'
1
f
k
k
0
g
ð
10
:
43
Þ
where r
0
ð
k
Þ
can be considered as a zero-mean Gaussian white noise sequence with
known variance R
r
ð
k
Þ
that corresponds to fault free measurements, C
'
is the
'
-th
column of the incidence table and m
'
stands for the magnitude of the fault effect on
the residual. m
'
is supposed to be constant and equal to its steady state value, for the
sake of simplicity. Transient effects could be accounted for as in [
11
].
Thus the fault detection/isolation problem can be stated as the following
hypothesis test.
Choose between:
H
0
L
ð
r
ð
i
ÞÞ ¼
N
ð
0
;
R
r
ð
i
ÞÞ
for
i
¼
1
;
...
;
k
H
'
;'¼
1
;
...
;
n
f
L
ð
r
ð
i
ÞÞ ¼
N
ð
0
;
R
r
ð
i
ÞÞ
for
i
¼
1
;
...
;
k
0
1
¼
N
ð
m
'
C
'
;
R
r
ð
i
ÞÞ
for
i
¼
k
0
;
...
;
k
where k
0
is the unknown fault occurrence time.
This is exactly the form of the problem statement in Sect.
10.3.2
, except that the
variance of the residual is time-varying. Yet this can be accounted for in a
straightforward way in the computation of the the log-likelihood ratios [
14
,
15
].
Remark Due to the fact that R
w
and R
v
i
are used as tuning parameters for the
Kalman filters, the whiteness of the residual sequence is not guaranteed. However,
the CUSUM algorithm is known to be robust to this hypothesis [
20
].
In the next section, a validation example for voltage and current sensor FDI on
a DFIG is presented.
10.5.3 Fault Detection and Isolation in the Stator Voltage
and Current Sensors of a Wind Driven DFIG
The presentation of the case study consists of the problem statement, the design of
the residual generator and the decision system, and their validation in simulation.
10.5.3.1 Problem Statement
The controlled DFIG depicted in Fig.
10.5
is considered. The rotor side controller
(RSC) aims at reaching the desired reference generator torque T
g
and the stator
