Environmental Engineering Reference
In-Depth Information
Straightforward computations yield the following expression for the log-like-
lihood ratio s(k) in Eq.
10.5
:
p
r
ð
k
Þ
2
T
s
r
2
1
6c
1
1
s
ð
k
Þ¼
ln
ð
10
:
21
Þ
2
6
This method is illustrated by a case study in the next section.
10.3.2 Application to Incremental Encoder Fault
The detection of excessive noise is applied to generator speed measurements for a
wind driven DFIG. Such measurements are typically determined from an incre-
mental encoder. The generator speed estimate, X
g
ð
k
Þ
, is then obtained by com-
puting the frequency of the encoder pulses over a time window T
sc
as
X
g
ð
k
Þ¼
60DN
ð
k
Þ
N
p
T
sc
½
rpm
where N
p
is the number of pulses per revolution and DN
ð
k
Þ
is the measured
number of pulses over the time window.
The quantization error on this speed estimate is given by q
h
¼
60
N
p
T
sc
½
rpm
,[
12
].
An excessive noise can be due to imperfections of the encoder code wheel. For
instance, when a portion g
2
0
;
1
½
of the bars of the code wheel is damaged, a
reduction to
ð
1
g
Þ
N
p
of the number of pulses per revolution can be induced. This
imperfection generates an increase of the quantization error to q
f
¼
60
ð
1
g
Þ
N
p
T
sc
½
rpm
.
To illustrate the algorithm for excessive noise detection, a wind turbine is
simulated with the AERODYN and FAST software [
13
]. The main data of the
variable-speed variable-pitch wind turbine are represented in Table
10.1
. The
weather conditions correspond to a mean wind speed equal to 14.2 m/s and a 18 %
wind turbulence intensity. The incremental encoder parameters are N
p
¼
1
;
024
and T
sc
¼
0
:
01 s. In the wind turbine simulator, the quantization error on the
generator speed measurement is modeled by an additive uniformly distributed
white noise in the interval [-q, 0], namely L
ð
v
ð
kT
s
ÞÞ ¼
U
ð
q
;
0
Þ
[
12
]. q is equal
to q
h
(q
f
) when the encoder is healthy (faulty). The simulation represents the
occurrence of an excessive noise with g equal to 10 % at time instant 10 s.
The algorithm described by Eqs.
10.5
-
10.8
, in which Eq.
10.21
is substituted
for the log-likelihood ratio, is applied to r(k) with r
2
¼
q
h
=
12 and the increase
factor in the variance c
¼
1
=ð
1
g
Þ
2
. Note that the division by T
s
is omitted in the
computation of Eq.
10.20
for r
ð
k
Þ
. g is set to 10 % as the algorithm is intended to
detect a damage affecting at least 10 % of the bars of the code wheel.
