1. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
5
Fault Detection and Isolation in Wind Turbine
Based on Modified Kalman Filter
*G.Noshirvani J.Askari
Isfahan University of Technology,
Electrical and Computer Engineering Department
Isfahan, Iran
Isfahan University of Technology,
Electrical and Computer Engineering Department
Isfahan, Iran
g.noshirvani@ec.iut.ac.ir j-askari@cc.iut.ac.ir
Keywords- Fault Detection; Wind Turbine;
Modified Kalman Filter; Fault Isolation;
Abstract-In this paper, a fault detection and
isolation (FDI) method is developed for sensor
and actuator of a wind turbine. This study is
based on modified Kalman filter with
considering to the correlation between process
and measurement noises for fault detection, also
a bank of fault isolation estimators is employed
to determine the particular fault type and the
location. Each isolation estimator is designed
based on a particular fault scenario under
consideration.
Introduction
As one of the alternative energy sources, wind
turbines are starting to contribute to a more
significant part of the world’s power production.
The wind turbines need to operate reliably at all
times, despite the possible occurrence of faulty
system components and sensors. Therefore, the
design of fault detection and diagnosis techniques is
a crucial step in achieving reliable operations of
wind turbines.
In order to detect, diagnose and correct these
abnormal process behaviors, the use of efficient and
advanced diagnostic systems is of great importance
to modern industries. The main objective of fault
detection and isolation (FDI) is to provide early
warnings to operators, such that appropriate actions
can be taken to prevent the breakdown of the
system. This will improve the reliability and safety
of the system, and avoid unnecessary and costly
downtimes.
During the last two decades, there has been
significant research activity in the design and
analysis of fault detection and diagnosis schemes.
In [1], a survey on the failures of wind turbine
systems in Sweden, Finland and Germany is done,
where the data are from the maintenance records in
the last two decades. In [2–4] and the references
therein, the rotor condition monitoring and some
other topics for improving the reliability and safety
of offshore wind energy converters are presented.
Model-based fault detection for wind turbine
systems has also received some attention in recent
years. In [5], the pitch sensor and actuator faults are
considered based on the Kalman filter technique
and the multiple model estimation technique
respectively.

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The observer based approach is popular for
developing FDI techniques [6-7]. It mainly consists
of two stages. The first one is to generate residuals
by computing the difference between the measured
output and the estimated output obtained from the
dynamic system by an observer. And the second
one any departure of the residuals from zero
indicates that a fault has likely occurred [8].
The Kalman Filter (KF) is an efficient
recursive filter that estimates the state of a
dynamic system from a series of noisy
measurements. There are many examples where
the KF is used for fault detection. W. C. Merrill, J.
C. Delaat, and W. M. Bruton used a bank of
Kalman filters for FDI aircraft engine sensors [9].
This study successfully improved control loop
tolerance to sensor failures, which were
considered the most likely engine failures to
happen under the uncorrelated measurement and
process noise operating environment. In [10] the
residual generation is designed based on observer
to detect and isolate the sensor faults in the pitch
system of a wind turbine.
However, there are some hypotheses for the
Kalman filter. Such as, the sequences of process
and measurement noise subjected to Gaussian
distribution and independent, respectively [11]. If
the process or measurement noise is colored or
correlated noise, the standard Kalman filter has
been suboptimal.
The system under study is a wind turbine and
the winds are buffeting the blade. An anemometer
is used to measure wind speed as an input to the
KF. Thus, the random gusts of wind affect both
the process (i.e. The blade of wind turbine
dynamics) and the measurement (i.e. The sensed
wind speed). In this case, there is a correlation
between the process noise and the measurement
noise.
According to the research conducted to date,
when the process noise and the measurement noise
are correlated in industrial applications, the
general method to reformulate the state transition
equation and make the correlation in the new state
transition equation has been few discussed.
Recently, Song and colleagues [12] proposed
methods to deal with cross-correlated sensor noise
under condition of multi-sensor for measurement
and process parts. In [13] the authors considered
dynamic systems with correlated random
parameter matrices, i.e., transition matrices and
measurement matrices.
In order to test various detection, isolation, and
accommodation schemes for the wind turbine
application, this paper presents a model of the
pitch system, containing the sensor and actuator
faults of a wind turbine constructed by MAPNA
Group and inaugurated in Iran.
This model describes a realistic generic three
blade horizontal variable-speed wind turbine with
a full-scale converter coupling. This generic
turbine has a rated power of 2.5 MW. Since this
model works at the system level, the fast control
loops of the converters are not considered.
Wind turbines are complicated machines;
therefore it was decided to keep the model simple
so that all wind-turbine experts can use it. Blades
and tower are assumed rigid, and aerodynamics
are described by a static model. The wind turbine
controller included in the model is also simple,
leaving out some typical features; however, it
controls the wind turbine with acceptable
performance. In this paper, the model is extended
with even more faults and test sets, and described
in more detail, so that a better understanding of the
model is provided. Additional test sets are
introduced to test the robustness of solutions
toward different points of operation at which
faults are introduced. This paper also presents
some of the best FDI solutions applied to this

3. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
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model.
In this paper, a fault detection estimator is used
to monitor the occurrence of a fault, and a bank of
KF estimators is employed to determine the
particular fault type/location by considering to the
correlation between process and measurement
noises. Each isolation estimator is designed based
on a particular fault scenario under consideration.
Since the wind speed can only be roughly
measured and there is a large risk of an offset in
this measurement, so it will be considered as a
disturbance in this paper. Since this disturbance
influences the pitch subsystem. Then, diagnostic
observer based residual generator has been
designed, which can decouple the disturbance and
simultaneously achieve the optimal residual
generation in statistical sense.
Based on the statistical properties of the
residual signals, generalized likelihood ratio test
and cumulative variance index are applied. For the
fault isolation purpose, a bank of residual
generators based on dual sensor redundancy is
designed.
System modelling for Fault Detection
The wind turbine model mainly consists of four
components: blade and pitch system, drive train,
generator and converter, and controller. The blades
connected to the rotor shaft are facing the wind
direction, and the wind turns the wind turbine
blades around. A generator fully coupled to a
converter is used to convert the mechanical energy
to electrical energy. In order to upscale the
rotational speed to the needed value of the
generator, a drive train is introduced. The converter
can be used to set the generator torque, which
consequently can be used to control the rotational
speeds of the generator and the rotor. The
conversion of wind energy to mechanical energy is
controlled by pitching the blades.
This paper considers a generic wind turbine,
constructed by MAPNA Research Group based on
the benchmark wind turbine described in [14]. The
turbine is a variable speed three bladed pitch
controlled, with a front horizontal axis rotor. An
overview of the model can be seen in figure 1, in
which νw denotes the wind speed, τr denotes the
rotor torque, ωr denotes the rotor speed, τg denotes
the generator torque, ωg denotes the generator
speed, βr denotes the pitch angle control reference,
βm denotes the measured pitch angles, τω,m denotes
the estimated rotor torque, ωr,m denotes the
measured rotor speed, τg,m denotes the measured
generator torque, ωg,m denotes the measured
generator speed, Pg denotes the measured
generated electrical power, τg,r denotes the
generator torque reference, and Pr denotes the
power reference. Each element of the model is
subsequently shortly described. The rotor speed,
the generator speed, and the pitch positions of all
blades are measured with two sensors.
Fig. 1. An overview of a wind turbine system [14]
 Wind Model
The wind speed is given by a wind model
including mean wind trends, turbulence, wind
shear and tower shadow effects [15].
 Pitch sensor model
Each of the three hydraulic pitch systems is
represented by its closed-loop system dynamics.
The state space representation of the sensor pitch
system dynamic is:
 pb pb pb pb r f
pb pb pb
x A x B
y C x
   

(1)
where the state vector pb i ix     
is comprised
of the pitch angular speed i and position
( 1,2,3)i i  , and pby R is the measured pitch
position, r R  is the reference position signal

4. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
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provided by the controller, and f R  is an internal
variable used to model the pitch position error
caused by sensor faults. The values of the (Apb, Bpb,
Cpb) triple are defined in the model. For
redundancy consideration, each of three pitch
positions is measured by two identical sensors,
represented by , 1i m and , 2i m , i = 1, 2, 3,
respectively.
 Pitch actuator model
The three hydraulic pitch driver is modeled as a
closed loop transfer function between the pitch
angle  and its reference r:
 
 
2
2 2
2
n
r n n
s
s s s
 
  

 
(2)
Where  is the damping factor and ωn the natural
frequency that take the nominal values 0.3 and 8.31
rad/s respectively. The pitch rate may take values
between -4 and 4 deg/s and the pitch angle between
-2 and -90 deg.
 Generator and convertor model
The generator and convertor torques are modeled
by a first order transfer function:
 
 ,
g gc
g r gc
s
s s
 
 


(3)
Where gc = 31.2 is the combined convertor and
generator model parameter. The power produced
by the generator is given by:
     g g g gP t t t   (4)
Where g=0.91 is the generator efficiency.
 Drive Train Model
The drive train, which is used to increase the speed
from rotor to generator, is modeled with a flexible
two-mass system. The drive train model includes
the inertia of the rotor (which includes blades and
the main shaft) and generator [15].
 Controller
The wind turbine operates in principle in 4 regions:
Region 1 in which wind speeds are too low for the
wind turbine to operate, Region 2 in which the
turbine operates up to a nominal wind speed
(partial load), Region 3 between nominal and rated
wind speed, where the nominal power can be
produced, Region 4 above rated wind speed, where
the wind turbine is closed down in order to limit
extreme loads on the wind turbine. The controller
is active in Region 2 & 3. In Region 2, the optimal
rotor speed is obtained by using the converter
torque as a control signal. In Region 3 the rotor
speed is kept at a given reference value by pitching
the blades, (the converter keeps the power at the
reference taking care of fast variations in the
speed) [16].
Kalman filter design with considering
process and measurement noises
Consider the discrete system for filtering;
Where xk denotes state vector at time k and zk
denotes the corresponding measurement. Fk
represents the state transition matrix and Hk
represents the measurement matrix. ωk is the
process or system noise and vk is the
measurement noise. These signal are subjected
to the Gaussian distribution as:
T T
k j kj k j
T
kj k j kj
E Q E
R E U
    
   
       
   
(7)
Where δ denotes Kronecker-delta function, and
T
k j kjE U     
indicates cross-correlated noise
sequences, a nonzero cross-correlation between the
process and measurement noise sequences.
However, the diagnosis approaches based on
Kalman filter require some hypotheses. Such as,
the sequences of process and measurement noises
subject to Gaussian distribution and independent,
respectively. If the process or measurement noise
is colored or correlated, the standard Kalman filter

5. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
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has been suboptimal [11].
The approach is addressed to this issue needs
reformulate the dynamic equation and make the
noise sequences independent with each other.
An item which consists of observation equation
and equals to zeroes is added to the right hand of
(5). The equation is:
1
(8)
Where Jk−1 is a coefficient matrix to be
determined, which is called one step prediction
g a i n matrix. We define the new state transition
matrix
*
1, kkF and dynamic noise *
1k as:
1
The equation (8) is determined by control item
1 1k kJ z  . The expectation of
*
k is calculated by:
11
The correlation between process noise *
k in (8)
and measurement noise vk in (6) is calculated by
1
Where,
1
For Obtaining the independency between the
process noise and measurement noise, the
coefficient matrix Jk is determined by Uk − Jk Rk =
0. Rearranging the equation above, we obtain:
1
Substituting (14) into (13), we can get
1
1
From the above analysis, when we have the initial
conditions as, xˆ0 =E[x0], P0 = var[x0], and we can
get the recursive equations by using the
standard Kalman filter.
Step 1: calculate the coefficient matrix Jk by (14);
Step 2: one step prediction stage:
1
1
Step 3: the Kalman gain is evaluated as
1
Step 4: one step update stage:
Fault Detection Algorithm for Sensor
and Actuator
In this paper, a model based approach is
applied for sensor fault detection and isolation
using a bank of Kalman filter. Each Kalman filter
is designed for specific sensor and actuator fault.
Fault1 is a fixed value sensor fault on pitch1
position sensor1 (β1,m1) and fault2 is a scaling error
sensor fault on pitch2 position sensor2 (β2,m2). In
addition, two actuator faults in the pitch systems
are defined; fault 3 associated with pitch actuator 2
caused by high air content in oil, and fault 4 is
associated with pitch actuator 3 caused by dropped
main line pressure.
In the event that a fault does occur, all filters
using the correct hypothesis will produce large
estimation errors. By monitoring the residual of
each filter, the specific fault that has occurred can
be detected and isolated.
For each Kalman filter, the residual vector:
i i
e x x  (21)
When we got the residual, the Weighted Sum
Square Residuals (WSSR) for each of Kalman filter
were calculated as:
  1Ti i i i
WSSR V e e
  (22)
Where  2
diag   . The vector δ is the noise

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standard deviation and the additional weight Vi
is the weighting factor.
The statistical function as in (22) has χ2
distribution consider the following two
hypotheses.
H0: system operates normally; H1: fault occurs in
the system.
Confidence probability consists of a range of values
(interval) that act as good estimates of the
unknown population parameter; however, the
interval computed from a particular sample does
not necessarily include the true value of the
parameter.
The desired level of confidence is set by the system
operators (not determined by data). If a
corresponding hypothesis test is performed, the
confidence level is the complement of the
respective level of significance, i.e. a 95%
confidence interval reflects a significance level of
0.05. The confidence interval contains the
parameter values that, when tested, should not be
rejected with the same sample. Greater levels of
variance yield larger confidence probability, and
hence less precise estimates of the parameter.
The confidence probability is given by expert
operators, the threshold can be found as in [17].
The following gives the detection theory:
0 1: ; :i i
i iH WSSR H WSSR   (23)
Where i is the threshold.
Fault 3 corresponds to pitch actuator fault
due to hydraulic pressure drop (abrupt change).
Fault 4 corresponds also to pitch actuator fault,
but due to increased air content in oil (slow
change). They are both modeled by varying ωn
and  in (2) but abruptly for fault 4 and more
smoothly for fault 3.
As can be seen, (2) is a second order linear
relation between (and r. In case of modification
in the parameters ωn and , the stationary state
does not change, but the transient dynamics
change. In order to estimate these dynamics, the
transient behavior should be included in the
estimation procedure, which might increase
importantly the data volume and it remains
difficult due to correlated measurement and
process noises. Since the mechanical model is
known, it is more obvious in this case to develop
a model-based method, such as observers, for
fault detection of these actuators.
Considering (2) and by applying the following
change of coordinates 1 ix  , 2 ix  , fu  for
i=1,2,3. One gets the following state equations:
1 2
2 2
2 1 22n n n
x x
x x x u  


   
(24)
To estimate the parameter ωn and ζ, we construct
the following augmented system:
1 2
2 4 1 3 2 4
3
4
0
0
x x
x x x x x x u
x
x

    


 
(25)
With x3=2ζωn and 2
4 nx 
Where,
 2 2 2
1 0 11n f n f nf       (26)
 2 0 0 21n n f n f f nf          (27)
 1 0 1f  and  2 0 1f  are the fault indicators.
In the real system, the two faults always occurs
together when the dynamics of the actuator systems
change. So these fault scenarios can be simplified
into a single fault for each case as described by:
 2 2 2
01n f n f nf       (28)
  0 01n n f n f f nf          (29)
Where  0 1f  is the fault indicator,
0f  and 1f  are the corresponding fault-
free and full fault cases, respectively.
When a large discrepancy between commanded

7. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
7
and true actuator positions does exist due to an
actuator fault, it cause significant error. A
modified Kalman filter may be designed in order
to isolate the actuator faults.
Table 1. Pitch actuator system parameters
Pressure
Normal (100%) Low (50%)
Air Content in oil
Normal (7%)
11.11( / )n rad s 
0.6n 
3.42( / )n rad s 
0.9n 
High (15%)
5.73( / )n rad s 
0.45n 
2.5( / )n rad s 
0.45n 
A Kalman filter that satisfies the Dolye-Stein
condition is referred to as Robust Kalman Filter
(RKF). The Dolye-Stein condition is expressed as
follow [18].
   
1 1
1K H K B H B
 
    (30)
Here K is the Kalman filter gain,  
1
sI A

   , A
is the system matrix a continuous time, and B is
the control distribution matrix in continuous
time. H is the system measurement matrix. If the
Kalman filter process noise intensity matrix is
defined as:
2
0
T
qQ Q q BVB  (31)
Where Q0 and R0 are a noise intensities matrix of
the nominal plant also, V is a positive definite
symmetric matrix. With these selections, then
the RFK is obtained despite the dependence
between process noise and measurement noise
with (14-20). The value of the q must be chosen
carefully, if q is chosen small, the RFK becomes
sensitive to actuator failures, on the other hand,
if it is chosen large, noise effects increase and
unexpected result occur in the Kalman filter.
When the residual vector for actuator fault is
created, the Weighted Sum Square Residuals for
each of the Kalman filter were calculated. Also,
Because of gradual fault type in fault 3, the
threshold must be set differently to the other
faults.
The performance of any fault detection scheme is
measured by its detection delay, its propensity to
issue false alarms, and whether it permits a
failure to go undetected. For actuator2 fault
detection procedure, it is qualitatively clear that
the balance between “low detection delay” and
“low false alarm rate” is ensured by the threshold
. A higher level of , to which the overlap test is
compared, corresponds to larger confidence
regions and so to a higher degree of robustness
with respect to unknown inputs such as
uncertainties in the nominal model, system
noise, and measurement noise. The risk of false
alarms is then reduced, but the detection interval
(from the time that failure occurs to the time it is
detected) increases. In practice, for the fault
detection scheme proposed in this paper, the
design parameter for achieving a specified
measure of performance can be provided
through the present knowledge about the
underlying application. This can be done by
process simulation and physical behavior
analysis by an expert hydraulic engineer under
various types of failures (for instance, gradually
increase air content in oil of hydraulic pitch
actuators).
5- Simulation Result
This section gives the simulation results of the
proposed algorithm for fault detection in a wind
turbine with rated power at 2.5 MW.
The continuous model of the system is
discretized using the zero order hold discretization
method with considering 0.1s for sample time.
The FDI requirements are listed in section2, where
the goal is to motivate solutions that are realistic for
the wind industry. The detection times (TD) for the
respective faults are defined in terms of the
sampling time for the control system Ts=0.1s then
the time of detection is as follow [19]:
• Faults 1 and 2 must satisfy TD < 10 · Ts
• Fault 3 must satisfy TD < 8 · Ts
• Fault 4 must satisfy TD < 100· Ts
The proposed algorithm assumes that measurement

8. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
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noise is white and bounded, but in the simulink
model of the benchmark, sensor noises are Gaussian
white and hence theoretically bounded. In this
paper, based on modified and more precise isolation
algorithm the noises are assumed correlated with
±10σ bound. The simulation is performed by a wind
input sequence demonstrated in figure 2.
Fig. 2 Wind speed input sequence used in the benchmark
simulation model
A. FDI Residual for Pitch1 System
Sensor fault, represented by a fixed value on
pitch1 position sensor1 (β1,m1=3˚ in the time period
2000s-2100s). As specified in the benchmark
model, a fixed value sensor fault occurs during
2000-2100s in one of the position sensors in pitch
system1 during the simulation run. In figure 3 when
the sensor fault is detected, the isolation residual
generated by MKF1 (Modified Kalman Filter)
significantly increased (middle plot), while in
position sensor2 the isolation residual generated by
MKF2 remains around zero (bottom plot).
Fig.3. Case of a fixed value fault on position sensor 1 in pitch 1
B. FDI Residual for Pitch2 System
Faults in pitch 2 system are a scaling error
sensor fault (β2,m2=0.9 ⨯β2) during the time period
of 2300-2400s and an actuator fault during the time
period of 2900-3000s. Figure 4 shows the entire
simulation run corresponding to the cases of the
sensor fault occurring in pitch 2 position sensor2.
Also, it indicates that the sensor fault is in pitch2
position sensor2 for when a fault is detected (top
plot), the isolation residual generated by MKF1 still
remains around zero (middle plot) while the
isolation residual generated by MKF2 can be
distinguished from zero (bottom plot).
It is worth noting that fault 2 is not detected during
the entire fault occurrence time interval. This is
because sometimes the actual signal is 0 in the
presence of the scaling sensor fault, which hides the
effect of the fault.
Fig.4. Case of a scaling error fault on position sensor2 in pitch2
C. Actuator Fault Scenario
To simulate fault 3, the parameter  is changed from
its nominal value 0.6 to 0.45 and ωn from its
nominal value 11.11 to 5.73 linearly as a result of
high air content in oil between the time period
2900s-3000s.
To simulate fault 4, these parameters are changed
abruptly to =0.9 and ωn=3.42 as a result of drop
pressure in hydraulic pitch system.
As figure 5 presented, this fault is detected from
2900-3000s (top plot) the two residuals generated
0 1000 2000 3000 4000
2
4
6
8
10
12
14
16
18
Time[s]
WindSpeed[m/s]
0 500 1000 1500 2000 2500 3000 3500 4000
0
10
Sensor Fault Detection Residual for Pitch1
0 500 1000 1500 2000 2500 3000 3500 4000
0
10
Isolation Residual Generated by MKF1 for sensor1 of Pitch1
0 500 1000 1500 2000 2500 3000 3500 4000
0
10
Isolation Residual Generated by MKF1 for sensor2 of Pitch1
Time[s]
0 500 1000 1500 2000 2500 3000 3500 4000
0
1
2
Sensor Fault Detection Residual for Pitch2
0 500 1000 1500 2000 2500 3000 3500 4000
0
1
2
Isolation Residual Generated by MKF1 for sensor1 of Pitch2
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
1.5
Isolation Residual Generated by MKF2 for sensor2 of Pitch2
Time[s]

9. ‫ایران‬ ‫بادی‬ ‫انرژی‬ ‫کنفرانس‬ ‫چهارمین‬–5931‫ایران‬ ،‫تهران‬
3
by MKF1 and MKF2 are all significantly over zero
which indicate actuator fault is present in the
system.
To simulate fault 4, these parameters are changed
abruptly to =0.9 and ωn=3.42 as a result of drop
pressure in hydraulic pitch system.
As figure 5 presented, this fault is detected from
2900-3000s (top plot) the two residuals generated
by MKF1 and MKF2 are all significantly over zero
which indicate actuator fault is present in the
system.
Fig.5. Case of an actuator fault in pitch2
Fig.6. Case of an actuator fault in pitch3
For experimental study, fault 3 and 4 can be added
to any blade, but in this paper, fault 3 is added to the
actuator of blade 2 and fault 4 to the actuator of
blade 3. In theory, the same observer can be applied
to any blade. It can also be seen that by comparing
the estimated signal  ˆ t the actual measured  t
is highly influenced by sensor noise. However, if the
noise level is different between the blades, a
different filter constant and different observer gain
might be necessary.
6- Conclusion
A novel approach has been proposed to detect
and isolate the hydraulic pitch system's sensor and
actuator failures. A bank of Kalman filters was used
to detect and isolate sensor failures. Each of the
Kalman filter is designed based on a specific
hypothesis for detecting a specific sensor fault. In
the situation that a fault does occur, all filters except
the one using the correct hypothesis will produce
large estimation errors, from which a specific fault
is isolated. Failures in the sensors and actuators
affect the characteristics of the residual signals of
the Kalman filter. When the Kalman filter is used,
the decision statistics change regardless the faults in
the sensors or in the actuators. While a Robust
Kalman filter is used, it is easy to distinguish the
sensor and actuator faults. The results are
appropriate to the original navigation and
application that motivated the precursor studies.
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0 500 1000 1500 2000 2500 3000 3500 4000
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Actuator Fault Detection Residual for Pitch2
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Isolation Residual Generated by MKF1 for Actuator of Pitch2
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