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Fault Detection and Isolation of the Wind Turbine Benchmark: an Estimation-based Approach
Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011
Fault Detection and Isolation of the Wind Turbine Benchmark: an Estimation-based Approach Xiaodong Zhang ∗ , Qi Zhang ∗ Songling Zhao ∗ Riccardo Ferrari ∗∗ Marios M. Polycarpou ∗∗∗ , and Thomas Parisini ∗∗∗∗ ∗
Dept. of Electrical Engineering, Wright State University, USA ∗∗ Danieli Automation, Buttrio (UD), Italy ∗∗∗ Dept. of Electrical and Computer Engineering, University of Cyprus, Cyprus ∗∗∗∗ Imperial College London (UK) and University of Trieste (Italy) Abstract: In this paper, a fault detection and isolation (FDI) method is developed for wind turbines based on a benchmark system model. The FDI method follows a general architecture developed in previous papers, where a fault detection estimator is used for fault detection, and a bank of fault isolation estimators are employed to determine the particular fault type/location. Each isolation estimator is designed based on a particular fault scenario under consideration. Some representative simulation results are given to show the effectiveness of the FDI method. 2. BENCHMARK SYSTEM DESCRIPTION
1. INTRODUCTION
2.1 System Overview 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 diagnosis and accommodation techniques is a crucial step in achieving reliable operations of wind turbines. During the last two decades, there has been significant research activity in the design and analysis of fault diagnosis and accommodation schemes (see, for instance, Blanke, et al. [2006], Gertler [1998]). Several researchers have also investigated wind turbine fault diagnostics (e.g., Dobrila and Stefansen [2007], Hameeda et al. [2009], Odgaard and Stoustrup [2009], Wei et al. [2008]). The main challenges of FDI design for wind turbines include: (1) the aerodynamic rotor torque is not measured; and (2) the wind speed is only measured at the hub position with high noise. In this paper, a fault diagnosis method is presented for wind turbines by utilizing the benchmark system model developed by Odgaard et al. [2009]. The FDI architecture follows the general methodology presented in previous papers by Zhang et al. [2002, 2008]. A fault detection estimator is used to monitor the occurrence of a fault, and a bank of fault isolation estimators are employed to determine the particular fault type/location. Each isolation estimator is designed based on a particular fault scenario under consideration. The paper is organized as follows. Section 2 introduces the wind turbine benchmark system used for this research work. The general FDI architecture is given in Section 3. Sections 4 - 6 describe the FDI method for the pitch systems, the drive train, and converter, respectively. Some representative simulation results are given in Section 7. Finally, some concluding remarks are given in Section 8. 978-3-902661-93-7/11/$20.00 © 2011 IFAC
A wind turbine converts wind energy to electrical energy. In the benchmark model developed by Odgaard et al. [2009], a three blade horizontal axis turbine is considered. The wind turbine benchmark 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 at 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 from wind energy to mechanical energy is controlled by pitching the blades or by controlling the rotational speed of the turbine relative to the wind speed. The controller is designed to make the system track a given power reference. 2.2 System Model Each of the three hydraulic pitch systems is represented by its closed-loop system dynamics. The state space representation of the nominal pitch system dynamics is: x˙ pb = Apb xpb + Bpb (βr + βf ) (1) ypb = Cpb xpb
where the state vector xpb = [β˙ i βi ] is comprised of the pitch angular speed β˙ i and position βi (i = 1, 2, 3), and ypb ∈ is the measured pitch position, βr ∈ is the reference position signal provided by the controller, and βf ∈ 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 benchmark model. For redundancy consideration, each of three pitch positions
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is measured with two identical sensors, represented by βi,m1 and βi,m2 , i = 1, 2, 3, respectively. The nominal dynamics of the drive train are described by τ x˙ dt = Adt xdt + Bdt r τg (2) ydt = Cdt xdt
where the state vector xdt = [ωr ωg θΔ ] includes the rotor speed ωr , the generator speed ωg , and the torsion angle of the drive train θΔ . The input signals are the aerodynamic rotor torque τr and the generator torque τg . The output ydt represents measured speeds of the rotor and the generator. For redundancy consideration, the generator speed and rotor speed are measured with two identical sensors, respectively. Specifically, ωr,m1 and ωr,m2 are the two rotor speed measurements; and ωg,m1 and ωg,m2 are the two generator speed measurements.
The fault isolation decision scheme is based on the following intuitive principle: for s = 1, · · · , N , if fault s occurs at time T0 and is detected at time Td , then a set of threshold can be designed for the s-th isolation estimator, such that each component of its output estimation error remains below its corresponding threshold, for all t > Td . Consequently, for each isolation estimator, such a set of thresholds can be associated with its output estimation error. In the fault isolation procedure, if for each isolation estimator r ∈ {1, · · · , N }\{s} , at least one component of its output estimation error exceeds its threshold, then the possibility of the occurrence of fault r can be excluded. To summarize, we have the following: Fault Isolation Decision Scheme: Assume that fault s ∈ {1, . . . , N } occurs at time T0 and is detected at time Td . If, for each FIE r, r ∈ {1, · · · , N }\{s} , there exist some finite time tr > Td , such that at least one component of its output estimation error exceeds the corresponding threshold, then the occurrence of fault s is concluded.
2.3 Fault Scenarios 4. FDI METHOD FOR PITCH SYSTEMS The following faults are considered in the wind turbine benchmark model. • Faults in the pitch systems. Sensor faults in the pitch position measurements are either electrical or mechanical faults in the position sensors. Fault 1 is a fixed value sensor fault on pitch 1 position sensor 1 (β1,m1 ); Fault 2 is a scaling error sensor fault on pitch 2 position sensor 2 (β2,m2 ); Fault 3 is a fixed value sensor fault on pitch 3 position sensor 3 (β3,m1 ). In addition, two actuator faults in the pitch systems are defined: Fault 6 associated with pitch actuator 2 caused by high air content in oil, and Fault 7 is associated with pitch actuator 3 caused by dropped main line pressure. • Faults in the drive train system. Fault 4 is a fixed value sensor fault on rotor speed sensor 1 (ωr,m1 ), and Fault 5 is a scaling error sensor affecting both rotor speed sensor 2 and generator speed sensor2 (ωr,m2 , ωg,m2 ). • Faults in the generator and converter system. Fault 8 is a converter fault, representing an offset in the internal converter control loops. 3. FDI ARCHITECTURE In the benchmark model, it is assumed that only a single fault can possibly occur at any time. The presented FDI method is based on the general architecture developed in Zhang et al. [2002]. The FDI architecture consists of a fault detection estimator (FDE) and a bank of N fault isolation estimators (FIEs), where N is the number of faults under consideration. The FDE is used to detect the occurrence of a fault, and the FIEs are used to determine the particular fault type/location that has occurred. Each FIE is designed based on a particular fault scenario or hypothesis under consideration. Fault Detection Decision Scheme: The decision on the occurrence of a fault (detection) is made when the modulus of at least one component of the fault detection residual exceeds its threshold.
In this section, we will present the FDI design for each pitch system by using the general architecture described above. 4.1 Pitch System Faults The potential faults considered in the pitch systems include several sensor faults and actuator faults. Specifically, the faults considered in each pitch system of the benchmark model are: sensor fault 1 in pitch system 1, sensor fault 2 and actuator fault 6 in pitch system 2, as well as sensor fault 3 and actuator fault 7 in pitch system 3. 4.2 FDI Method for Pitch System 1 The objective of FDI design for Pitch system 1 is to timely detect and isolate a fixed value position fault in one of the two pitch position sensor signals (i.e., fault 1 in β1,m1 or β1,m2 ). Fault detection can be achieved by simply checking the consistency between these two sensor signals based on | β1,m1 −β1,m2 |. After fault detection, in order to determine which sensor is faulty, two FIEs are designed. Each FIE is based on one of the following two possible fault scenarios: • Case 1: Sensor 2 is faulty, and sensor 1 is healthy; • Case 2: Sensor 1 is faulty, and sensor 2 is healthy As described above, the variable βf is used to model pitch position error as a result of sensor faults. For the ith pitch system, i = 1, 2, 3, βf is given by 1 βf = βi − (βi,m1 + βi,m2 ) . 2
(3)
By substituting (3) into (1), we obtain 1 x˙ pb = Apb xpb + Bpb βr + Bpb βi − (βi,m1 + βi,m2 ) (4) 2 Under the fault scenario 1 described above, we have
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β1,m1 = β1 = Cpb xpb .
(5)
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
Thus, by using (1), (4), and (5), the dynamics of pitch system 1 under fault scenario 1 is x˙ pb = (Apb + 0.5Bpb Cpb )xpb + Bpb (βr − 0.5β1,m2 ) (6) β1,m1 = Cpb xpb . Analogously, under fault scenario 2, we have β1,m2 = β1 = Cpb xpb ,
(7)
and the dynamics of pitch system 1 under fault scenario 2 is given by x˙ pb = (Apb + 0.5Bpb Cpb )xpb + Bpb (βr − 0.5β1,m1 ) (8) β1,m2 = Cpb xpb . Therefore, based on (6) and (8), the following two FIEs for pitch system 1 are chosen: 1 xˆ˙ pb = (Apb + 0.5Bpb Cpb )ˆ x1pb + Bpb (βr − 0.5β1,m2 ) + Lpb (β1,m1 − βˆ1,m1 )
ˆ1pb , βˆ1,m1 = Cpb x and
where x ˆpb and yˆpb are the estimated system states and output, respectively, and Hpb is the observer gain chosen to ensure the stability of the matrix Apb −Hpb Cpb . Clearly,
the output estimation error y˜pb = ypb − yˆpb converges to zero in the absence of faults. By using similar methods as reported in Section 4.2, two FIEs are designed for pitch system 2. FIE 1 corresponds to the fault scenario of faulty sensor 2 and generates a residual β˜2,m1 , and FIE 2 corresponds to the fault scenario of faulty sensor 1 and generates a residual β˜2,m2 (see (9) and (10)). Note that, for this specific problem under consideration, the fault isolation architecture is simplified by using two FIEs instead of three FIEs. After fault detection, if we can exclude the two cases of potential faulty sensors, then the occurrence of the third fault (i.e., actuator fault) considered is concluded. Specifically, the following fault isolation decision logic for pitch system 2 is employed:
(9)
• If the residual | β˜2,m1 | is close to zero, and | β˜2,m2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If | β˜2,m2 | is close to zero, and | β˜2,m1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty; • If both | β˜2,m1 | and | β˜2,m2 | are significantly non-zero, then it is concluded that the actuator is faulty.
2 xˆ˙ pb = (Apb + 0.5Bpb Cpb )ˆ x2pb + Bpb (βr − 0.5β1,m1 ) + Lpb (β1,m2 − βˆ1,m2 )
ˆ2pb , (10) βˆ1,m2 = Cpb x where βˆ1,m1 is the estimate of output β1,m1 provided by FIE 1, and βˆ1,m2 is the estimate of output β1,m2 provided by FIE 2, and Lpb is an observer gain matrix designed to make the matrix Apb + 0.5Bpb Cpb − Lpb Cpb Hurwitz. Clearly, if sensor 2 is faulty (i.e., fault scenario 1 is true), then the output estimation error β˜1,m1 = β1,m1 − βˆ1,m1 associated with FIE 1 converges to zeros. Analogously, if sensor 1 is faulty (i.e., fault scenario 2 is true), then the output estimation error β˜1,m2 = β1,m2 − βˆ1,m2 associated with FIE 2 converges to zeros. Hence, by following the fault isolation decision scheme described in Section 3, we have: • If | β˜1,m1 | is close to zero, and | β˜1,m2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If | β˜1,m2 | is close to zero, and | β˜1,m1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty.
4.4 FDI Method for Pitch System 3 The objective of FDI design for Pitch system 3 is to timely detect and isolate the following two faults: • A fixed error fault in one of the two pitch position sensor signals (i.e., fault 3 in β3,m1 or β3,m2 ). • An actuator fault caused by low presure (i.e., fault 7) The FDI design can be carried out by following a similar method to that of pitch 2 reported above. 5. FDI METHOD FOR DRIVE TRAIN SYSTEM 5.1 Drive Train Faults For the rotor and generator speed measurements in the drive train system, we consider the following sensor faults in the drive train system:
4.3 FDI Method for Pitch System 2
• A fixed value sensor fault on one of the rotor speed sensor (i.e., fault 4 on ωr,m1 or ωr,m2 ) , • A scaling error sensor affecting one of the generator speed sensor (i.e., fault 5 on ωg,m1 or ωg,m2 ).
The objective of FDI design for Pitch system 2 is to timely detect and isolate the following two faults: • A scaling error fault in one of the two pitch position sensor signals (i.e., fault 2 in β2,m1 or β2,m2 ), • An actuator fault caused by high air content in oil (i.e., fault 6). Based on the FDI architecture described in Section 3, a FDE and two FIEs are designed. In the absence of faults, βf = 0. Thus, by using (1), the FDE is chosen as x ˆ˙ pb = Apb xpb + Bpb βr + Hpb (ypb − yˆpb ) (11) ˆpb , yˆpb = Cpb x
5.2 FDI Method for Rotor Speed Sensor Fault One of the difficult issues of FDI design for the drive train system is that the rotor speed ωr in (2) is controlled by the unknown aerodynamic rotor torque τr . It is also difficult to accurately estimate τr , since it involves the wind speed, which is only measured at the hub position with high noise. To overcome this issue, we note that in model (2), the input matrix Bdt and output matrix Cdt take the forms of
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⎡ Bdt
⎢ ⎢ = ⎢ ⎣
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and ω ˜ g2 = | ωg − ω ˆ g2 |, the following isolation decision scheme is used:
,
where Adt4 ∈ 2×2 and Adt3 ∈ 2×1 , we have ω˙ g ωg = Adt4 + B1 τg + B2 ωr θΔ θ˙Δ
(14)
0] and B2 = Adt3 . By defining the
state vector zdt = [ωg θΔ ] and by taking into account the measurable generator speed signal ωg , we have z˙dt = Adt4 zdt + B1 τg + B2 ωr ωg = C¯dt zdt ,
(15)
where C¯dt = [1 0]. Now, the inputs τg and ωr in (15) are both available, and the pair (Adt4 , C¯dt ) is observable. It is worth noting that the rotor speed sensor fault shows up in (15) as an “actuator fault” (associated with the input signal ωr ). Then, FDI design in the drive train can be carried out based on (15). The rotor speed sensor fault can be detected by designing a FDE based on (15) or by simply checking the consistency between the two sensor measurements ωr,m1 and ωr,m2 . Two FIEs are designed based on the following two possible fault scenarios: Case 1: Sensor 2 (i.e., ωr,m2 ) is faulty, and sensor 1 (i.e., ωr,m1 ) is healthy. Thus, by using (15), we obtain z˙dt = Adt4 zdt + B1 τg + B2 ωr,m1 (16) ωg = C¯dt zdt . Case 2: Sensor 1 (i.e., ωr,m1 ) is faulty, and sensor 2 (i.e., ωr,m2 ) is healthy. Analogously, we have z˙dt = Adt4 zdt + B1 τg + B2 ωr,m2 (17) ωg = C¯dt zdt . Then, based on (16) and (17), the two FIEs are chosen as: 1 1 zˆ˙ dt = Adt4 zˆdt + B1 τg + B2 ωr,m1 + Ldt (ωg − ω ˆ g1 ) ω ˆ 1 = C¯dt zˆ1 , g
5.3 FDI Method for Generator Speed Sensor Fault The generator speed sensor fault (i.e., fault 5 in the benchmark model) can be detected and isolated using a simple method based on the system dynamics given in Odgaard et al. [2009]. Specifically, we have Pg = ηgc τg ωg , where Pg is the electric power and ηgc is the generator efficiency. Since Pg , ηgc , τg are all measured or known, an estimate of the generator speed is given by Pg ω ˆg = , ηgc τg where ω ˆ g is the estimated generator speed. By comparing ω ˆ g with the two sensor measurements ωg,m1 and ωg,m1 , the generator speed sensor fault can be diagnosed. It is worth noting that the generator speed sensor fault may also affect the residuals ω ˜ g1 and ω ˜ g2 used for FDI of rotor speed sensor. From simulation studies of the benchmark model, it is observed that such effect is very small for the generator speed sensor fault magnitude considered. Nevertheless, even in the presence of a very significant generator speed sensor fault, we can always first apply the FDI method presented here to decide the presence of a generator sensor fault before diagnosing the rotor speed sensor, hence avoiding false alarms. 6. FDI METHOD FOR CONVERTER SYSTEM In the benchmark model, a converter fault (i.e., fault 8) is considered, representing an offset in the internal converter control. The converter dynamics is described by τ˙g = −αgc τg + αgc τgr + θαgc τgr ,
dt
2 2 zˆ˙ dt = Adt4 zˆdt + B1 τg + B2 ωr,m2 + Ldt (ωg − ω ˆ g2 ) ω ˆ 2 = C¯dt zˆ2 , dt
ˆ g2 are the generator speed estimates prowhere ω ˆ g1 and ω vided by FIE 1 and FIE 2, respectively, and Ldt is an
(18)
where αgc = 50, τg is generator torque, τgr is the generator torque reference, and θ is a constant offset as a result of the fault (θ = 0 in the absence of the fault). Since τg is measured, a fault detection estimator can be designed as τg − τg ) − αgc τg + αgc τgr , τˆ˙ g = −λ(ˆ
and
g
• If |˜ ωg1 | is close to zero, and |˜ ωg2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If |˜ ωg2 | is close to zero, and |˜ ωg1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty.
(13)
where Jg and Jr are the moment of inertia of the high speed shaft and rotor shaft. From (2), (12), and (13), it is observed that the τr only directly affects the first state variable ωr , which is measured. Therefore, by partitioning the state matrix Adt ∈ 3×3 in (2) into: Adt1 Adt2 Adt = , Adt3 Adt4
with B1 = [− J1g
observer gain designed to make the matrix Adt4 − Ldt C¯dt stable. Clearly, in the presence of a rotor sensor fault, the output estimation error associated with the matched FIE should converge to zero. Then, by defining ω ˜ g1 = | ωg − ω ˆ g1 |
(19)
where τˆg is an estimate of τg , and λ > 0 is a filter pole. Clearly, in the absence of not only faults but also modeling error and noise, the estimation error τ˜g = τg − τˆg converges to zero, which can be used for fault detection. Note that among all the faults under consideration, only this fault will affect the residual τ˜g . Hence, this fault can also be isolated by using τ˜g .
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7. SIMULATION RESULTS
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Next, some FDI simulation results are given to show the effectiveness of the FDI method. A wind speed profile of 4400 seconds defined in the benchmark model is used.
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Figure 1 shows the FDI results of an offset in converter torque control (i.e., fault 8). The fault occurs between 3800 and 3900 seconds. As described in Section 6, the single residual chosen is sufficient to detect and isolate this fault. The top plot in Figure 1 illustrates the behaviors of the residual throughout the simulation run, and the bottom plot gives an enlarged view of the residual in a shorter time interval within which the fault is present. As we can see, due to the presence of sensor noise, the residual is not zero in the absence of the fault. The residual significantly increases after the fault occurs. The fault is detected and isolated in approximately 0.01 seconds.
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Figures 2 - 5 describe the FDI results in the drive train system. Specifically, Figure 2 and Figure 3 correspond to the case of a fixed value fault on rotor speed sensor 1 (fault 4), which occurs between 1500 and 1600 seconds. The timebehaviors of the residual throughout the simulation run is shown in Figure 2, and an enlarged view of the residuals in a shorter time interval within which the fault is present is shown in Figure 3. As can be seen, the fault is timely detected by the detection residual (top plot in each of the two figures). Additionally, the first isolation residual takes significantly large value after fault occurrence, while the second isolation residual remain around zero. Based on the presented isolation decision scheme, we can determine that the fault is on sensor 1. The fault is detected and isolated in approximately 0.35 seconds. Figure 4 and Figure 5 correspond to the case of a scaling error fault on generator speed sensor 2 (fault 5), which occurs between 1000 and 1100 seconds. As described in Section 5.3, a simplified FDI method with two residuals is used for diagnosing this fault. The time-behaviors of the residuals throughout the simulation run are shown in Figure 4, and an enlarged plot is given in Figure 5. As we can see, the FDI results are satisfactory. The fault is detected and isolated in approximately 0.01 seconds. 7.3 FDI Results in Pitch Systems As described in Section 4, the FDI method for the three pitch systems are similar. For the sake of space limitations, here only the simulation results of pitch 3 are presented. Two faults in pitch 3 are considered during the simulation run of 4400 seconds, including a fixed value fault (i.e., fault 3) on position sensor 1 in the interval of 2600 2700 seconds and an incipient actuator fault (i.e., fault 7) developing gradually in the interval of 3400 -3500 seconds. Figure 6 and Figure 7 are plots for the overall simulation run and an enlarged short time interval, respectively. Both faults are timely detected. The fault detection times for fault 3 an fault 7 are approximately 0.02 seconds and 4
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Fig. 1. Case of an offset in converter torque control: complete plot (top), enlarged plot (bottom). seconds, respectively. Additionally, when the sensor fault is detected in the interval of 2600 - 2700 seconds, the isolation residual generated by FIE 1 significantly increases (middle plot), while the other isolation residual generated by FIE 2 always remain around zero (bottom plot), hence allowing the isolation of the fault in sensor 1. It is worth noting that, even though the residual generated by FIE 1 goes to zero after a transient, this is sufficient to exclude the fault case corresponding to FIE 1 based on the isolation decision scheme. Moreover, in the presence of the actuator fault (3400 - 3500 seconds), we can see both isolation residuals significantly increase. Therefore, the cases of a fault in sensor 1 or sensor 2 can be excluded, which indicates the occurrence of the third fault type (i.e., actuator fault). The fault isolation times for fault 3 an fault 7 are approximately 0.5 seconds and 10 seconds, respectively. 8. CONCLUSIONS In this paper, a FDI method is presented for wind turbines by following the general methodology presented in Zhang et al. [2002, 2008]. By utilizing certain structure of system model, the FDE and FIEs are designed without the need of estimating the unknown wind speed and aerodynamic rotor torque. Future research work will include the integration of diagnosis and fault-tolerant control design. REFERENCES M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki. Diagnosis and Fault-Tolerant Control. Springer, Berlin, 2006. C. Dobrila and R. Stefansen. Fault Tolerant Wind Turbine Control. Masters thesis, Technical University of Denmark, Kgl, Lyngby, Denmark, 2007.
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J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, New York, NY, 1998. Z. Hameeda, Y. Honga, Y. Choa, S. Ahnb, and C. Song, “Condition monitoring and fault detection of wind turbines and related algorithms: a review,” Renewable and Sustainable Energy Reviews, 13(1):139, January 2009. P. F. Odgaard, J. Stoustrup and M. Kinnaert, “Fault Tolerant Control of Wind Turbines a benchmark model,” Proceedings of IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes: SAFEPROCESS, pp. 155-160, Barcelona, Spain, 2009. P. F. Odgaard and J. Stoustrup, “Unknown input observer based scheme for detecting faults in a wind turbine converter,” Proceedings of IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes: SAFEPROCESS, pp. 161-166, Barcelona, Spain, 2009. X. Wei, M. Verhaegen, and T. van den Engelen, “Sensor fault diagnosis of wind turbines for fault tolerant,” Proceedings of the 17th IFAC World Congress, pp. 3222– 3227, Seoul, South Korea, 2008. X. Zhang, M. M. Polycarpou, and T. Parisini, “Design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems,” IFAC Annual Reviews in Control, vol. 32, pp. 107-121, 2008. X. Zhang, M. M. Polycarpou, and T. Parisini, “A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems,” IEEE Trans. on Automatic Control, vol. 47, pp. 576-593, 2002.
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Fault Detection and Isolation of the Wind Turbine Benchmark: an Estimation-based Approach Xiaodong Zhang ∗ , Qi Zhang ∗ Songling Zhao ∗ Riccardo Ferrari ∗∗ Marios M. Polycarpou ∗∗∗ , and Thomas Parisini ∗∗∗∗ ∗
Dept. of Electrical Engineering, Wright State University, USA ∗∗ Danieli Automation, Buttrio (UD), Italy ∗∗∗ Dept. of Electrical and Computer Engineering, University of Cyprus, Cyprus ∗∗∗∗ Imperial College London (UK) and University of Trieste (Italy) Abstract: In this paper, a fault detection and isolation (FDI) method is developed for wind turbines based on a benchmark system model. The FDI method follows a general architecture developed in previous papers, where a fault detection estimator is used for fault detection, and a bank of fault isolation estimators are employed to determine the particular fault type/location. Each isolation estimator is designed based on a particular fault scenario under consideration. Some representative simulation results are given to show the effectiveness of the FDI method. 2. BENCHMARK SYSTEM DESCRIPTION
1. INTRODUCTION
2.1 System Overview 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 diagnosis and accommodation techniques is a crucial step in achieving reliable operations of wind turbines. During the last two decades, there has been significant research activity in the design and analysis of fault diagnosis and accommodation schemes (see, for instance, Blanke, et al. [2006], Gertler [1998]). Several researchers have also investigated wind turbine fault diagnostics (e.g., Dobrila and Stefansen [2007], Hameeda et al. [2009], Odgaard and Stoustrup [2009], Wei et al. [2008]). The main challenges of FDI design for wind turbines include: (1) the aerodynamic rotor torque is not measured; and (2) the wind speed is only measured at the hub position with high noise. In this paper, a fault diagnosis method is presented for wind turbines by utilizing the benchmark system model developed by Odgaard et al. [2009]. The FDI architecture follows the general methodology presented in previous papers by Zhang et al. [2002, 2008]. A fault detection estimator is used to monitor the occurrence of a fault, and a bank of fault isolation estimators are employed to determine the particular fault type/location. Each isolation estimator is designed based on a particular fault scenario under consideration. The paper is organized as follows. Section 2 introduces the wind turbine benchmark system used for this research work. The general FDI architecture is given in Section 3. Sections 4 - 6 describe the FDI method for the pitch systems, the drive train, and converter, respectively. Some representative simulation results are given in Section 7. Finally, some concluding remarks are given in Section 8. 978-3-902661-93-7/11/$20.00 © 2011 IFAC
A wind turbine converts wind energy to electrical energy. In the benchmark model developed by Odgaard et al. [2009], a three blade horizontal axis turbine is considered. The wind turbine benchmark 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 at 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 from wind energy to mechanical energy is controlled by pitching the blades or by controlling the rotational speed of the turbine relative to the wind speed. The controller is designed to make the system track a given power reference. 2.2 System Model Each of the three hydraulic pitch systems is represented by its closed-loop system dynamics. The state space representation of the nominal pitch system dynamics is: x˙ pb = Apb xpb + Bpb (βr + βf ) (1) ypb = Cpb xpb
where the state vector xpb = [β˙ i βi ] is comprised of the pitch angular speed β˙ i and position βi (i = 1, 2, 3), and ypb ∈ is the measured pitch position, βr ∈ is the reference position signal provided by the controller, and βf ∈ 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 benchmark model. For redundancy consideration, each of three pitch positions
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is measured with two identical sensors, represented by βi,m1 and βi,m2 , i = 1, 2, 3, respectively. The nominal dynamics of the drive train are described by τ x˙ dt = Adt xdt + Bdt r τg (2) ydt = Cdt xdt
where the state vector xdt = [ωr ωg θΔ ] includes the rotor speed ωr , the generator speed ωg , and the torsion angle of the drive train θΔ . The input signals are the aerodynamic rotor torque τr and the generator torque τg . The output ydt represents measured speeds of the rotor and the generator. For redundancy consideration, the generator speed and rotor speed are measured with two identical sensors, respectively. Specifically, ωr,m1 and ωr,m2 are the two rotor speed measurements; and ωg,m1 and ωg,m2 are the two generator speed measurements.
The fault isolation decision scheme is based on the following intuitive principle: for s = 1, · · · , N , if fault s occurs at time T0 and is detected at time Td , then a set of threshold can be designed for the s-th isolation estimator, such that each component of its output estimation error remains below its corresponding threshold, for all t > Td . Consequently, for each isolation estimator, such a set of thresholds can be associated with its output estimation error. In the fault isolation procedure, if for each isolation estimator r ∈ {1, · · · , N }\{s} , at least one component of its output estimation error exceeds its threshold, then the possibility of the occurrence of fault r can be excluded. To summarize, we have the following: Fault Isolation Decision Scheme: Assume that fault s ∈ {1, . . . , N } occurs at time T0 and is detected at time Td . If, for each FIE r, r ∈ {1, · · · , N }\{s} , there exist some finite time tr > Td , such that at least one component of its output estimation error exceeds the corresponding threshold, then the occurrence of fault s is concluded.
2.3 Fault Scenarios 4. FDI METHOD FOR PITCH SYSTEMS The following faults are considered in the wind turbine benchmark model. • Faults in the pitch systems. Sensor faults in the pitch position measurements are either electrical or mechanical faults in the position sensors. Fault 1 is a fixed value sensor fault on pitch 1 position sensor 1 (β1,m1 ); Fault 2 is a scaling error sensor fault on pitch 2 position sensor 2 (β2,m2 ); Fault 3 is a fixed value sensor fault on pitch 3 position sensor 3 (β3,m1 ). In addition, two actuator faults in the pitch systems are defined: Fault 6 associated with pitch actuator 2 caused by high air content in oil, and Fault 7 is associated with pitch actuator 3 caused by dropped main line pressure. • Faults in the drive train system. Fault 4 is a fixed value sensor fault on rotor speed sensor 1 (ωr,m1 ), and Fault 5 is a scaling error sensor affecting both rotor speed sensor 2 and generator speed sensor2 (ωr,m2 , ωg,m2 ). • Faults in the generator and converter system. Fault 8 is a converter fault, representing an offset in the internal converter control loops. 3. FDI ARCHITECTURE In the benchmark model, it is assumed that only a single fault can possibly occur at any time. The presented FDI method is based on the general architecture developed in Zhang et al. [2002]. The FDI architecture consists of a fault detection estimator (FDE) and a bank of N fault isolation estimators (FIEs), where N is the number of faults under consideration. The FDE is used to detect the occurrence of a fault, and the FIEs are used to determine the particular fault type/location that has occurred. Each FIE is designed based on a particular fault scenario or hypothesis under consideration. Fault Detection Decision Scheme: The decision on the occurrence of a fault (detection) is made when the modulus of at least one component of the fault detection residual exceeds its threshold.
In this section, we will present the FDI design for each pitch system by using the general architecture described above. 4.1 Pitch System Faults The potential faults considered in the pitch systems include several sensor faults and actuator faults. Specifically, the faults considered in each pitch system of the benchmark model are: sensor fault 1 in pitch system 1, sensor fault 2 and actuator fault 6 in pitch system 2, as well as sensor fault 3 and actuator fault 7 in pitch system 3. 4.2 FDI Method for Pitch System 1 The objective of FDI design for Pitch system 1 is to timely detect and isolate a fixed value position fault in one of the two pitch position sensor signals (i.e., fault 1 in β1,m1 or β1,m2 ). Fault detection can be achieved by simply checking the consistency between these two sensor signals based on | β1,m1 −β1,m2 |. After fault detection, in order to determine which sensor is faulty, two FIEs are designed. Each FIE is based on one of the following two possible fault scenarios: • Case 1: Sensor 2 is faulty, and sensor 1 is healthy; • Case 2: Sensor 1 is faulty, and sensor 2 is healthy As described above, the variable βf is used to model pitch position error as a result of sensor faults. For the ith pitch system, i = 1, 2, 3, βf is given by 1 βf = βi − (βi,m1 + βi,m2 ) . 2
(3)
By substituting (3) into (1), we obtain 1 x˙ pb = Apb xpb + Bpb βr + Bpb βi − (βi,m1 + βi,m2 ) (4) 2 Under the fault scenario 1 described above, we have
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β1,m1 = β1 = Cpb xpb .
(5)
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
Thus, by using (1), (4), and (5), the dynamics of pitch system 1 under fault scenario 1 is x˙ pb = (Apb + 0.5Bpb Cpb )xpb + Bpb (βr − 0.5β1,m2 ) (6) β1,m1 = Cpb xpb . Analogously, under fault scenario 2, we have β1,m2 = β1 = Cpb xpb ,
(7)
and the dynamics of pitch system 1 under fault scenario 2 is given by x˙ pb = (Apb + 0.5Bpb Cpb )xpb + Bpb (βr − 0.5β1,m1 ) (8) β1,m2 = Cpb xpb . Therefore, based on (6) and (8), the following two FIEs for pitch system 1 are chosen: 1 xˆ˙ pb = (Apb + 0.5Bpb Cpb )ˆ x1pb + Bpb (βr − 0.5β1,m2 ) + Lpb (β1,m1 − βˆ1,m1 )
ˆ1pb , βˆ1,m1 = Cpb x and
where x ˆpb and yˆpb are the estimated system states and output, respectively, and Hpb is the observer gain chosen to ensure the stability of the matrix Apb −Hpb Cpb . Clearly,
the output estimation error y˜pb = ypb − yˆpb converges to zero in the absence of faults. By using similar methods as reported in Section 4.2, two FIEs are designed for pitch system 2. FIE 1 corresponds to the fault scenario of faulty sensor 2 and generates a residual β˜2,m1 , and FIE 2 corresponds to the fault scenario of faulty sensor 1 and generates a residual β˜2,m2 (see (9) and (10)). Note that, for this specific problem under consideration, the fault isolation architecture is simplified by using two FIEs instead of three FIEs. After fault detection, if we can exclude the two cases of potential faulty sensors, then the occurrence of the third fault (i.e., actuator fault) considered is concluded. Specifically, the following fault isolation decision logic for pitch system 2 is employed:
(9)
• If the residual | β˜2,m1 | is close to zero, and | β˜2,m2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If | β˜2,m2 | is close to zero, and | β˜2,m1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty; • If both | β˜2,m1 | and | β˜2,m2 | are significantly non-zero, then it is concluded that the actuator is faulty.
2 xˆ˙ pb = (Apb + 0.5Bpb Cpb )ˆ x2pb + Bpb (βr − 0.5β1,m1 ) + Lpb (β1,m2 − βˆ1,m2 )
ˆ2pb , (10) βˆ1,m2 = Cpb x where βˆ1,m1 is the estimate of output β1,m1 provided by FIE 1, and βˆ1,m2 is the estimate of output β1,m2 provided by FIE 2, and Lpb is an observer gain matrix designed to make the matrix Apb + 0.5Bpb Cpb − Lpb Cpb Hurwitz. Clearly, if sensor 2 is faulty (i.e., fault scenario 1 is true), then the output estimation error β˜1,m1 = β1,m1 − βˆ1,m1 associated with FIE 1 converges to zeros. Analogously, if sensor 1 is faulty (i.e., fault scenario 2 is true), then the output estimation error β˜1,m2 = β1,m2 − βˆ1,m2 associated with FIE 2 converges to zeros. Hence, by following the fault isolation decision scheme described in Section 3, we have: • If | β˜1,m1 | is close to zero, and | β˜1,m2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If | β˜1,m2 | is close to zero, and | β˜1,m1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty.
4.4 FDI Method for Pitch System 3 The objective of FDI design for Pitch system 3 is to timely detect and isolate the following two faults: • A fixed error fault in one of the two pitch position sensor signals (i.e., fault 3 in β3,m1 or β3,m2 ). • An actuator fault caused by low presure (i.e., fault 7) The FDI design can be carried out by following a similar method to that of pitch 2 reported above. 5. FDI METHOD FOR DRIVE TRAIN SYSTEM 5.1 Drive Train Faults For the rotor and generator speed measurements in the drive train system, we consider the following sensor faults in the drive train system:
4.3 FDI Method for Pitch System 2
• A fixed value sensor fault on one of the rotor speed sensor (i.e., fault 4 on ωr,m1 or ωr,m2 ) , • A scaling error sensor affecting one of the generator speed sensor (i.e., fault 5 on ωg,m1 or ωg,m2 ).
The objective of FDI design for Pitch system 2 is to timely detect and isolate the following two faults: • A scaling error fault in one of the two pitch position sensor signals (i.e., fault 2 in β2,m1 or β2,m2 ), • An actuator fault caused by high air content in oil (i.e., fault 6). Based on the FDI architecture described in Section 3, a FDE and two FIEs are designed. In the absence of faults, βf = 0. Thus, by using (1), the FDE is chosen as x ˆ˙ pb = Apb xpb + Bpb βr + Hpb (ypb − yˆpb ) (11) ˆpb , yˆpb = Cpb x
5.2 FDI Method for Rotor Speed Sensor Fault One of the difficult issues of FDI design for the drive train system is that the rotor speed ωr in (2) is controlled by the unknown aerodynamic rotor torque τr . It is also difficult to accurately estimate τr , since it involves the wind speed, which is only measured at the hub position with high noise. To overcome this issue, we note that in model (2), the input matrix Bdt and output matrix Cdt take the forms of
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⎡ Bdt
⎢ ⎢ = ⎢ ⎣
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(12)
and ω ˜ g2 = | ωg − ω ˆ g2 |, the following isolation decision scheme is used:
,
where Adt4 ∈ 2×2 and Adt3 ∈ 2×1 , we have ω˙ g ωg = Adt4 + B1 τg + B2 ωr θΔ θ˙Δ
(14)
0] and B2 = Adt3 . By defining the
state vector zdt = [ωg θΔ ] and by taking into account the measurable generator speed signal ωg , we have z˙dt = Adt4 zdt + B1 τg + B2 ωr ωg = C¯dt zdt ,
(15)
where C¯dt = [1 0]. Now, the inputs τg and ωr in (15) are both available, and the pair (Adt4 , C¯dt ) is observable. It is worth noting that the rotor speed sensor fault shows up in (15) as an “actuator fault” (associated with the input signal ωr ). Then, FDI design in the drive train can be carried out based on (15). The rotor speed sensor fault can be detected by designing a FDE based on (15) or by simply checking the consistency between the two sensor measurements ωr,m1 and ωr,m2 . Two FIEs are designed based on the following two possible fault scenarios: Case 1: Sensor 2 (i.e., ωr,m2 ) is faulty, and sensor 1 (i.e., ωr,m1 ) is healthy. Thus, by using (15), we obtain z˙dt = Adt4 zdt + B1 τg + B2 ωr,m1 (16) ωg = C¯dt zdt . Case 2: Sensor 1 (i.e., ωr,m1 ) is faulty, and sensor 2 (i.e., ωr,m2 ) is healthy. Analogously, we have z˙dt = Adt4 zdt + B1 τg + B2 ωr,m2 (17) ωg = C¯dt zdt . Then, based on (16) and (17), the two FIEs are chosen as: 1 1 zˆ˙ dt = Adt4 zˆdt + B1 τg + B2 ωr,m1 + Ldt (ωg − ω ˆ g1 ) ω ˆ 1 = C¯dt zˆ1 , g
5.3 FDI Method for Generator Speed Sensor Fault The generator speed sensor fault (i.e., fault 5 in the benchmark model) can be detected and isolated using a simple method based on the system dynamics given in Odgaard et al. [2009]. Specifically, we have Pg = ηgc τg ωg , where Pg is the electric power and ηgc is the generator efficiency. Since Pg , ηgc , τg are all measured or known, an estimate of the generator speed is given by Pg ω ˆg = , ηgc τg where ω ˆ g is the estimated generator speed. By comparing ω ˆ g with the two sensor measurements ωg,m1 and ωg,m1 , the generator speed sensor fault can be diagnosed. It is worth noting that the generator speed sensor fault may also affect the residuals ω ˜ g1 and ω ˜ g2 used for FDI of rotor speed sensor. From simulation studies of the benchmark model, it is observed that such effect is very small for the generator speed sensor fault magnitude considered. Nevertheless, even in the presence of a very significant generator speed sensor fault, we can always first apply the FDI method presented here to decide the presence of a generator sensor fault before diagnosing the rotor speed sensor, hence avoiding false alarms. 6. FDI METHOD FOR CONVERTER SYSTEM In the benchmark model, a converter fault (i.e., fault 8) is considered, representing an offset in the internal converter control. The converter dynamics is described by τ˙g = −αgc τg + αgc τgr + θαgc τgr ,
dt
2 2 zˆ˙ dt = Adt4 zˆdt + B1 τg + B2 ωr,m2 + Ldt (ωg − ω ˆ g2 ) ω ˆ 2 = C¯dt zˆ2 , dt
ˆ g2 are the generator speed estimates prowhere ω ˆ g1 and ω vided by FIE 1 and FIE 2, respectively, and Ldt is an
(18)
where αgc = 50, τg is generator torque, τgr is the generator torque reference, and θ is a constant offset as a result of the fault (θ = 0 in the absence of the fault). Since τg is measured, a fault detection estimator can be designed as τg − τg ) − αgc τg + αgc τgr , τˆ˙ g = −λ(ˆ
and
g
• If |˜ ωg1 | is close to zero, and |˜ ωg2 | significantly deviates from zero, then it is concluded that sensor 2 is faulty; • If |˜ ωg2 | is close to zero, and |˜ ωg1 | significantly deviates from zero, then it is concluded that sensor 1 is faulty.
(13)
where Jg and Jr are the moment of inertia of the high speed shaft and rotor shaft. From (2), (12), and (13), it is observed that the τr only directly affects the first state variable ωr , which is measured. Therefore, by partitioning the state matrix Adt ∈ 3×3 in (2) into: Adt1 Adt2 Adt = , Adt3 Adt4
with B1 = [− J1g
observer gain designed to make the matrix Adt4 − Ldt C¯dt stable. Clearly, in the presence of a rotor sensor fault, the output estimation error associated with the matched FIE should converge to zero. Then, by defining ω ˜ g1 = | ωg − ω ˆ g1 |
(19)
where τˆg is an estimate of τg , and λ > 0 is a filter pole. Clearly, in the absence of not only faults but also modeling error and noise, the estimation error τ˜g = τg − τˆg converges to zero, which can be used for fault detection. Note that among all the faults under consideration, only this fault will affect the residual τ˜g . Hence, this fault can also be isolated by using τ˜g .
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7. SIMULATION RESULTS
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Next, some FDI simulation results are given to show the effectiveness of the FDI method. A wind speed profile of 4400 seconds defined in the benchmark model is used.
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Figure 1 shows the FDI results of an offset in converter torque control (i.e., fault 8). The fault occurs between 3800 and 3900 seconds. As described in Section 6, the single residual chosen is sufficient to detect and isolate this fault. The top plot in Figure 1 illustrates the behaviors of the residual throughout the simulation run, and the bottom plot gives an enlarged view of the residual in a shorter time interval within which the fault is present. As we can see, due to the presence of sensor noise, the residual is not zero in the absence of the fault. The residual significantly increases after the fault occurs. The fault is detected and isolated in approximately 0.01 seconds.
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Figures 2 - 5 describe the FDI results in the drive train system. Specifically, Figure 2 and Figure 3 correspond to the case of a fixed value fault on rotor speed sensor 1 (fault 4), which occurs between 1500 and 1600 seconds. The timebehaviors of the residual throughout the simulation run is shown in Figure 2, and an enlarged view of the residuals in a shorter time interval within which the fault is present is shown in Figure 3. As can be seen, the fault is timely detected by the detection residual (top plot in each of the two figures). Additionally, the first isolation residual takes significantly large value after fault occurrence, while the second isolation residual remain around zero. Based on the presented isolation decision scheme, we can determine that the fault is on sensor 1. The fault is detected and isolated in approximately 0.35 seconds. Figure 4 and Figure 5 correspond to the case of a scaling error fault on generator speed sensor 2 (fault 5), which occurs between 1000 and 1100 seconds. As described in Section 5.3, a simplified FDI method with two residuals is used for diagnosing this fault. The time-behaviors of the residuals throughout the simulation run are shown in Figure 4, and an enlarged plot is given in Figure 5. As we can see, the FDI results are satisfactory. The fault is detected and isolated in approximately 0.01 seconds. 7.3 FDI Results in Pitch Systems As described in Section 4, the FDI method for the three pitch systems are similar. For the sake of space limitations, here only the simulation results of pitch 3 are presented. Two faults in pitch 3 are considered during the simulation run of 4400 seconds, including a fixed value fault (i.e., fault 3) on position sensor 1 in the interval of 2600 2700 seconds and an incipient actuator fault (i.e., fault 7) developing gradually in the interval of 3400 -3500 seconds. Figure 6 and Figure 7 are plots for the overall simulation run and an enlarged short time interval, respectively. Both faults are timely detected. The fault detection times for fault 3 an fault 7 are approximately 0.02 seconds and 4
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Fig. 1. Case of an offset in converter torque control: complete plot (top), enlarged plot (bottom). seconds, respectively. Additionally, when the sensor fault is detected in the interval of 2600 - 2700 seconds, the isolation residual generated by FIE 1 significantly increases (middle plot), while the other isolation residual generated by FIE 2 always remain around zero (bottom plot), hence allowing the isolation of the fault in sensor 1. It is worth noting that, even though the residual generated by FIE 1 goes to zero after a transient, this is sufficient to exclude the fault case corresponding to FIE 1 based on the isolation decision scheme. Moreover, in the presence of the actuator fault (3400 - 3500 seconds), we can see both isolation residuals significantly increase. Therefore, the cases of a fault in sensor 1 or sensor 2 can be excluded, which indicates the occurrence of the third fault type (i.e., actuator fault). The fault isolation times for fault 3 an fault 7 are approximately 0.5 seconds and 10 seconds, respectively. 8. CONCLUSIONS In this paper, a FDI method is presented for wind turbines by following the general methodology presented in Zhang et al. [2002, 2008]. By utilizing certain structure of system model, the FDE and FIEs are designed without the need of estimating the unknown wind speed and aerodynamic rotor torque. Future research work will include the integration of diagnosis and fault-tolerant control design. REFERENCES M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki. Diagnosis and Fault-Tolerant Control. Springer, Berlin, 2006. C. Dobrila and R. Stefansen. Fault Tolerant Wind Turbine Control. Masters thesis, Technical University of Denmark, Kgl, Lyngby, Denmark, 2007.
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J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, New York, NY, 1998. Z. Hameeda, Y. Honga, Y. Choa, S. Ahnb, and C. Song, “Condition monitoring and fault detection of wind turbines and related algorithms: a review,” Renewable and Sustainable Energy Reviews, 13(1):139, January 2009. P. F. Odgaard, J. Stoustrup and M. Kinnaert, “Fault Tolerant Control of Wind Turbines a benchmark model,” Proceedings of IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes: SAFEPROCESS, pp. 155-160, Barcelona, Spain, 2009. P. F. Odgaard and J. Stoustrup, “Unknown input observer based scheme for detecting faults in a wind turbine converter,” Proceedings of IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes: SAFEPROCESS, pp. 161-166, Barcelona, Spain, 2009. X. Wei, M. Verhaegen, and T. van den Engelen, “Sensor fault diagnosis of wind turbines for fault tolerant,” Proceedings of the 17th IFAC World Congress, pp. 3222– 3227, Seoul, South Korea, 2008. X. Zhang, M. M. Polycarpou, and T. Parisini, “Design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems,” IFAC Annual Reviews in Control, vol. 32, pp. 107-121, 2008. X. Zhang, M. M. Polycarpou, and T. Parisini, “A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems,” IEEE Trans. on Automatic Control, vol. 47, pp. 576-593, 2002.
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