Research Article Robust Fault Detection of Wind Energy ...downloads.hindawi.com/journals/cin/2014/580972.pdf · Robust Fault Detection of Wind Energy Conversion Systems Based on Dynamic

Research ArticleRobust Fault Detection of Wind Energy Conversion SystemsBased on Dynamic Neural Networks

Nasser Talebi Mohammad Ali Sadrnia and Ahmad Darabi

School of Electrical and Robotic Engineering University of Shahrood PO Box 3619995161 Shahrood Iran

Correspondence should be addressed to Nasser Talebi ntalebilivecom

Received 1 October 2013 Accepted 3 February 2014 Published 11 March 2014

Academic Editor Christian W Dawson

Copyright copy 2014 Nasser Talebi et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Occurrence of faults in wind energy conversion systems (WECSs) is inevitable In order to detect the occurred faults at theappropriate time avoid heavy economic losses ensure safe system operation prevent damage to adjacent relevant systems andfacilitate timely repair of failed components a fault detection system (FDS) is required Recurrent neural networks (RNNs) havegained a noticeable position in FDSs and they have been widely used for modeling of complex dynamical systems One methodfor designing an FDS is to prepare a dynamic neural model emulating the normal system behavior By comparing the outputs ofthe real system and neural model incidence of the faults can be identified In this paper by utilizing a comprehensive dynamicmodel which contains both mechanical and electrical components of the WECS an FDS is suggested using dynamic RNNs Thepresented FDS detects faults of the generatorrsquos angular velocity sensor pitch angle sensors and pitch actuators Robustness of theFDS is achieved by employing an adaptive threshold Simulation results show that the proposed scheme is capable to detect thefaults shortly and it has very low false and missed alarms rate

1 Introduction

Nowadays the economy and daily life rely on power dis-tribution networks such that occurrence of a fault in anycomponents of them can affect performance of the overallsystem In general a fault is a phenomenon that changes thebehavior of a system in such away that it is not able to performits tasks [1] A feature which is very important for everystructure is reliability and it can be insured by removing theearlier weaknesses and faults One way to achieve reliability isimplementation of condition monitoring systems and FDSsRecently the problem of fault detection for industrial appli-cations namely applications where lives are not at risk hasgained extreme importance In such systems user satisfactionand economic issues are important Among these systemselectricalmachines [2 3] power systems building ventilationsystems andWECSs [4ndash15] can bementioned Repair actionscan be performed in a timely manner without the need foran immediate action and this fact is extremely importantfor off-shore plants where bad conditions (such as storm)can delay any repair operation for several weeks [16 17]Although initially FDSs implementation requires investment

producing energy continuously without any interruptionswill compensate for initial investment costs Hence an FDSfor a WECS has advantages such as avoidance of prematurebreakdown reduction of maintenance costs supervision atremote sites remote diagnosis improvement of the capacityfactor and support for further development of a WECS [16]

In general fault detection techniques can be categorizedinto two categories hardware redundancy (HR) and ana-lytical redundancy (AR) Furthermore the AR techniquescan be classified as quantitative model-based methods andqualitative model-based ones In recent years extensiveresearches have been performed on quantitativemodel-basedmethods [18 19] and qualitative model-based methods [20ndash22] Generally these methods can be classified as observer-based signal processing expert system and artificial intel-ligence approaches Over the past two decades artificialneural networks have been studied extremely by researchersand they have been used successfully for modeling andcontrol of dynamical systems [20 23] Also they were usedto design FDSs [20 22] Among the many structures forneural networks two notable structures are the feedforwardand recurrent ones Feedforward networks are used typically

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2014 Article ID 580972 13 pageshttpdxdoiorg1011552014580972

2 Computational Intelligence and Neuroscience

for pattern recognition purposes while recurrent ones areused to prepare dynamical model of a process Among neuralnetworks that have been used frequently in FDSs multilayerfeedforward neural networks (MFNNs) radial basis functionneural (RBFN) networks and globally and locally recurrentnetworks can be mentioned

In structure of recurrent neural networks dynamic neu-rons replace the standard ones In one type of dynamicneurons the dynamics are applied by introducing an IIR filterinto the neuron structure This network structure does nothave any global feedbacks In fact this network has a structurethat is somewhere in between a feedforward and a globallyrecurrent structure [20]The recurrent neural network with aneuron model using the IIR filter has been used successfullyfor modeling fault detection and time series prediction In[20 24] this kind of network was used for fault detectionof a sugar evaporation process Also in [20] applicationsfor fault detection by using the mentioned network werepresentedThis network was utilized to detect faults in a fluidcatalytic cracking and a DC motor In [2] this network wasused for fault detection and isolation of induction motorsIn [25] by using this network an FDS for protecting andmonitoring systems of power networks was designed in sucha way that reliability of the power grid has risen up In [26]by combining the RBFN and the neuron model with the IIRfilter a network was proposed and it was used to predict timeseries In [27 28] it was utilized to predict both the windspeed and power in wind farms Finally in [29] it was usedto detect faults of a turbocharger

In addition fault detection of theWECSs has attracted theattention of many researchers in recent years For instancein [4 7] using a linear model of mechanical parts of a windturbine (electrical parts were neglected) a fault-tolerant con-troller was presented by utilizing the linear parameter varyingcontrol which was replaced with the reference controller Inthese two researches the occurred faults were diagnosed andthen the controller was reconfigured In [5] fault detectionof a wind turbine was performed using the linear modelof the mechanical parts and only occurrence of a fault wasconsidered In [6] faults of the induction generator wereconsidered Also the linearmodel of themechanical parts wasused to detect two categories of faults using the Kalman-filterin [8] Utilizing the supervisory control and data acquisition(SCADA) in [9] the occurred faults in a wind turbine weredetected In [10] by using the data-mining approach bearingfaults were detected In [11] utilizing the real data obtainedfrom a condition monitoring system faults of the brakingsystem of a wind turbine were detected In [12] a faulttolerant controller was proposed using fuzzy observers In[14] utilizing the Set-Membership approach and a modelfor the mechanical parts various faults of a wind turbinewere detected Also in [15] numbers of faults were detectedusing amodel for themechanical parts and the counter-basedresidual thresholding method

As it is obvious in researches that have been performedso far either a small number of faults have been studied orthe WECS has not been modeled completely or the linearmodels have been used to design the FDS It is obvious thatusing the more accurate nonlinear model will lead us to the

results which are closer to the real ones Another importantissue is robustness of the proposed scheme Robustnesscan be achieved either by active approaches or by passiveones [20] Active approaches consider the desired robustnessfrom the beginning of the design procedure [30ndash32] whilepassive approaches utilize adaptive thresholds architecturein decision making block to achieve the desired robustness[20] In this paper by utilizing a comprehensive nonlinearmodel of the WECS an FDS is suggested which has thecapability to detect faults in the generatorrsquos angular velocitysensor pitch sensors and pitch actuatorsThe presented FDSis composed of the dynamic neural network with the IIRfilter as the dynamic neuronmodel Additionally an adaptivethreshold is employed to achieve the anticipated robustnessThe proposed FDS can be utilized to detect the faults in otherparts of the WECS

The structure of this paper is organized as followsdynamic model of the WECS is presented in Section 2 InSection 3 the RNN with the IIR filter as neuron model isintroduced Section 4 presents the design procedure of theFDS In Section 5 the robustness of the proposed FDS isinvestigated

2 Dynamic Model of the WECS

The block diagram of the considered model in this paperis shown in Figure 1 In this figure the yaw mechanismis neglected and wind speed is the exogenous input Theaerodynamic torque of the turbinersquos rotor119879

119903(119905) is transferred

to the generator through the drive train The drive trainincludes a high speed shaft a low speed shaft and a gearboxThe induction generator converts the mechanical energy tothe electrical one and is connected to the power grid Aninterface is used for calculation of the active and reactivegenerated power The grid model includes a local loadtransformers transmission lines and the infinite-bus at theend Converters a dc link rotor and grid side controllers aremodeled in this study

Equations for modeling of the mechanical parts of theWECS are as follows [4 33ndash36]

V119908(119905) = V

119908(119905) + V

119908119904(119905) + V

119905119904(119905) + V

119905119906(119905) (1)

where in (1) which is related to the modeling of the windV119908(119905) is the wind speed including the tower shadow wind

shear and turbulence components In this equation V119908(119905) is

the mean wind speed V119908119904(119905) is the wind shear component

V119905119904(119905) is the wind speed tower shadow component and V

119905119906(119905)

is the wind speed turbulence component Consider

119875119903(119905) = 05120588119860V3

119903(119905) 119862119901(120582 (119905) 120573 (119905))

119879119903(119905) =

119875119903(119905)

120596119903(119905)

=1

120596119903(119905)

05120588119860V3119903(119905) 119862119901(120582 (119905) 120573 (119905))

(2)

Equations (2) are used to model wind turbinersquos aerody-namic where 119875

119903(119905) is the captured power by the turbinersquos

rotor 120573(119905) is the pitch angle 120582(119905) is the tip-speed ratio119862119901(120582(119905) 120573(119905)) is the power coefficient 119860 is the rotor swept

area V119903(119905) is the rotor effective wind speed 120588 is the air

Computational Intelligence and Neuroscience 3

Wind model

Aerodynamics

Pitch system

Tower

Drive trainInductiongenerator

Interface

Rotor side converter

DC link and grid

side converter

Rotor sideconvertercontroller

Grid model

Grid sideconvertercontroller

r(t)

120573(t)

Ft(t)

Tr(t)

120596r(t)

120573ref (t)

120596g(t)

Tg(t)

Qlowastg(t)

Plowastg (t)

Qg(t)

Pg(t)

Vlowastdqr

Vdqr

idqs

Vdqs

idqr

Vdqg

Vlowastdqg

Vdc

Vlowastdc

ilowastqg

Vabc Iabc

Pitch anglecontroller

minus

+vw(t) v v

w(t)Σ

Figure 1 Block Diagram of the dynamic model of the WECS

density and 119879119903(119905) is the aerodynamic torque which is applied

to the turbinersquos rotor Equation (3) represents the aerody-namic thrust where 119862

119905(120582(119905) 120573(119905)) is the thrust coefficient

119862119901(120582(119905) 120573(119905)) and 119862

119905(120582(119905) 120573(119905)) can be utilized by look-up

tables in simulations Consider

119865119905(119905) = 05120588119860V2

119903(119905) 119862119905(120582 (119905) 120573 (119905)) (3)

By drive train the aerodynamic torque is transferred tothe generator The gearbox scales up the rotational speed tothe required generatorrsquos angular velocity by a factor that iscalled gear ratio Equations (4) are used to model the drivetrain which includes a low speed shaft a gearbox and ahigh speed shaft In these equations 119869

119903is the inertia of the

rotor 119879119903is the torque acting on the low speed shaft 120596

119903is the

turbinersquos rotor speed 119870119889119905is the spring stiffness coefficient of

a massless viscously damped rotational spring 119861119889119905is viscous

damping parameter119873119892is the gear ratio 119869


gearbox high speed shaft and generator 119879119892is the generator

torque and 120596119892is the rotational speed of the generatorrsquos rotor

Consider

119869119903119903= 119879119903minus 119870119889119905120579120575minus 119861119889119905

120579120575

119869119892119873119892119892= minus119879119892119873119892+ 119870119889119905120579120575+ 119861119889119905

120579120575

120579120575= 120596119903minus

120596119892

119873119892

(4)

The thrust makes the tower to sway back and forth Thetower is modeled by a mass-spring-damper according to (5)In this equation 119865

119905ℎ(119905) is the force acting on the tower at hub

height 119861119905is the tower damping coefficient 119870

119905is the tower

spring coefficient119872119905is the topmass of the tower and 119909

119905(119905) is

the displacement of the nacelle from its equilibrium positionThe swaying of the tower changes the effective wind speed

seen on the turbinersquos rotor The rotor effective wind speed ismodeled using (6) Consider the following

119872119905119905(119905) = 119865

119905ℎ(119905) minus 119861

119905119905(119905) minus 119870

119905119909119905(119905) (5)

V119903(119905) = V

119908(119905) minus

119905(119905) (6)

The pitch system is a hydraulic system and it can bemodeled using (7) where 120573ref(119905) is the reference pitch angle120596119899is the natural frequency of the pitch actuator model and 120577

is the damping ratio of the pitch actuator model Equation(7) explains the operation of the pitch actuators when itoperates within limitations so physical limitations should beconsidered in modeling

120573 (119905) = minus2120577120596119899

120573 (119905) minus 1205962

119899120573 (119905) + 120596

2

119899120573ref (119905) (7)

Equations for modeling of the electrical parts of theWECS are as follows [37ndash39]

119881119902119904= 119877119904119894119902119904+

119889

119889119905120593119902119904+ 120596119904120593119889119904

119881119889119904

= 119877119904119894119889119904+

119889

119889119905120593119889119904minus 120596119904120593119902119904

119881119902119903= 119877119903119894119902119903+

119889

119889119905120593119902119903+ (120596119904minus 120596119903) 120593119889119903

119881119889119903

= 119877119903119894119889119903+

119889

119889119905120593119889119903minus (120596119904minus 120596119903) 120593119902119903

(8)

Equations (8) are stator and rotor voltages of the induc-tion machine in the synchronous reference frame In thismodel the synchronous reference frame was used to trans-form variables from the 119886119887119888 frame to the 119889119902 referenceframe All electrical variables are referred to the stator Inthese equations 119877

119904and 119877

119903are stator and rotor resistance

respectively 120596119904is the synchronous angular velocity 120596

119903is the

electrical angular velocity 120593119889119904and 120593

119902119904are the stator 119889 and 119902


axis fluxes and 120593119889119903

and 120593119902119903are the rotor 119889 and 119902 axis fluxes

Consider the following

120593119902119904= 119871119904119894119902119904+ 119871119898119894119902119903

120593119889119904

= 119871119904119894119889119904+ 119871119898119894119889119903

120593119902119903= 119871119903119894119902119903+ 119871119898119894119902119904

120593119889119903

= 119871119903119894119889119903+ 119871119898119894119889119904

(9)

Also the stator and rotor fluxes are expressed by (9)where 119871

119904= 119871119897119904+ 119871119898is the total stator inductance and 119871

119903=

119871119897119903+ 119871119898is the total rotor inductance The electromagnetic

torque is expressed by (10) where 119901 is the number of polepairs Consider

119879119890= 15119901 (120593

119889119904119894119902119904minus 120593119902119904119894119889119904) (10)

Two equations of the mechanical parts of the machineare as (11) where 119867 is the combined rotor and load inertiaconstant 119865 is the combined rotor and load viscous frictioncoefficient 119879

119892is the mechanical torque 120596

119892is the angular

velocity of the rotor and 120579119892is the rotor angular position

119889

119889119905120596119892=

1

2119867(119879119890minus 119865120596119892minus 119879119892)

119889

119889119905120579119892= 120596119892

(11)

Equations (12) can be used to model the grid sideconverter (GSC) and DC link capacitor where 119877

119892and 119871

119892are

the resistance and inductance of the circuit between the GSCand the grid119862 is the DC link capacitance119881

119889119888is the capacitor

voltage 119875119903is the active power exchanged between the rotor

and the rotor side converter (RSC) and119875119892is the output active

power of the GSC

119881119889119892

= 119877119892119894119889119892

+ 119871119892

119889

119889119905119894119889119892

minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881119902119892

= 119877119892119894119902119892

+ 119871119892

119889

119889119905119894119902119892

+ 120596119904119871119892119894119889119892

+ 119881119902119904

119875119892=

3

2(119881119889119904119868119889119892

+ 119881119902119904119868119902119892)

119889119881119889119888

119889119905=

119875

119881119889119888119862

=

119875119903minus 119875119892

119881119889119888119862

=

119875119890minus 119875119904minus 119875119892

119881119889119888119862

(12)

The WECS contains three categories of controllers RSCcontroller GSC controller and pitch angle controller Tocontrol the RSC the following equation can be used [39]

119881lowast

119889119903= 1205901198711199031198811015840

119889119903+ 119877119903119894119889119903minus 119904120596119904120590119871119903119894119902119903minus 119904120596119904(119871119898

119871119904

)120593119902119904

119881lowast

119902119903= 1205901198711199031198811015840

119902119903+ 119877119903119894119902119903+ 119904120596119904120590119871119903119894119889119903+ 119904120596119904(119871119898

119871119904

)120593119889119904

(13)

where control voltages 1198811015840119889119903and 119881

1015840

119902119903can be obtained using the

PI controllersThese voltages are calculated by comparing 119894119889119903

and 119894119902119903currents with reference 119894lowast

119889119903and 119894lowast

119902119903as follows

1198811015840

119889119903=

119889119894119889119903

119889119905= 1198701198751

(119894lowast

119889119903minus 119894119889119903) + 1198701198681int (119894lowast

119889119903minus 119894119889119903) 119889119905

1198811015840

119902119903=

119889119894119902119903

119889119905= 1198701198751

(119894lowast

119902119903minus 119894119902119903) + 1198701198681int (119894lowast

119902119903minus 119894119902119903) 119889119905

(14)

where1198701198751is the proportional gain and119870

1198681is the integral gain

of the PI controller The following equations can be used tocontrol the GSC [39]

119881lowast

119889119892= 119877119892119894119889119892

+ 1198711198921198811015840

119889119892minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881lowast

119902119892= 119877119892119894119902119892

+ 1198711198921198811015840

119902119892+ 120596119904119871119892119894119889119892

+ 119881119902119904

(15)

where the control voltages1198811015840119889119892

and1198811015840119902119892are obtained using the

PI controller as follows

1198811015840

119889119892=

119889119894119889119892

119889119905= 1198701198752

(119894lowast

119889119892minus 119894119889119892) + 1198701198682int(119894lowast

119889119892minus 119894119889119892) 119889119905

1198811015840

119902119892=

119889119894119902119892

119889119905= 1198701198752

(119894lowast

119902119892minus 119894119902119892) + 1198701198682int (119894lowast

119902119892minus 119894119902119892) 119889119905

(16)

The pitch angle controller is responsible for increment ordecrement of the pitch angle and it can be implemented by aPI controller This controller acts on the difference betweenthe reference angular velocity and the measured angularvelocity of the generator In modeling of the WECS it isusual to neglect the dynamics of the sensors because they aremuch faster than the dynamics of the wind turbine The onlyexpectation is the anemometer which is modeled as a first-order low-pass filter with a half a second time constant [3] Inthis study allmeasured signalswere emulated by adding zero-mean Gaussian distributed noise to deterministic values

3 Dynamic Neural Network

In recurrent neural networks the dynamic neurons replacethe standard static ones In the structure which is utilized inthis paper dynamics are created by introducing an IIR filterinto the neuron architecture where the neuron reproducesits own past inputs and activations by using the input signal119906119894(119896) for 119894 = 1 2 119899 and the output signal 119910(119896) The

structure of the considered neuron model is shown in Figure2 First the weighted sum of inputs is calculated according tothe following equation [20 29]

120593 (119896) =

119899

sum

119894=1

119908119894119906119894(119896) (17)

The weights of this network are such as the weightsof static feedforward networks The weights and activationfunction are responsible for approximation properties ofthe model The IIR filters are linear dynamic systems ofdifferent orders which consist of feedback and feedforwardpaths weighted by the weights 119886

119894 119894 = 1 2 119903 and 119887

119894


u1(k)

u2(k)

un(k)

W1

W2

Wn

sum(k) z(k)IIR

g1

g2

120590() y(k)

middotmiddotmiddot

120593

Figure 2 Structure of the neuron model with the IIR filter

119894 = 0 1 119903 respectively The behavior of this linear systemcan be expressed by the following equation

119911 (119896) =

119903

sum

119894=0

119887119894120593 (119896 minus 119894) minus

119903

sum

119894=1

119886119894119911 (119896 minus 119894) (18)

where 120593(119896) is the filter input and 119911(119896) is the filter outputEventually the output of the neuron is obtained by thefollowing equation

119910 (119896) = 120590 (1198922(119911 (119896) minus 119892

1)) (19)

where120590(sdot) is a nonlinear activation function and1198921and1198922are

the bias and the slope parameters of the activation functionThere are different methods to train these networks thethreemajormethods are extended dynamic back propagation(EDBP) adaptive random search (ARS) and simultaneousperturbation stochastic approximation (SPSA) Each of thesemethods has its own advantages and disadvantages The ARSmethod was used in this paper to train the network Theadvantage of this method is that it is easy to implement andit has very wide applicability The information required toimplement this method is only the input-output data wherethe parametersrsquo vector 120579 is the input and the cost function 119869(120579)is the output All network parameters can be represented bythe parametersrsquo vector 120579 The main purpose of training is toadjust the elements of the vector 120579 so that the cost function isminimized as follows [20]

120579lowast

= min120579isinC

119869 (120579) (20)

where 120579lowast is the optimal network parameter vector 119869 R119901 rarr

R1 is the cost function to be minimized 119901 is the dimensionof the vector 120579 and C sube R119901 is the constraint set defining thepermissible values for the parameters 120579The cost function canbe defined as follows

119869 (119897 120579) =1

2

119873

sum

119896=1

(119910119889(119896) minus 119910 (119896 120579))

2

(21)

where 119910119889(119896) and 119910(119896 120579) are the desired output of the network

and the actual response of the network on the given inputpattern119906(119896)119873 is the dimension of the training set and 119897 is theiteration indexThe above cost function should beminimizedbased on a given set of input-output patterns In the ARSmethod it is not required to compute the gradient of 119869 Table1 represents the ARS training algorithm [20] Assuming thatthe sequence of solutions 120579

0 1205791 120579

119896is obtained already to

achieve the next point 120579119896+1

the following equation is used[20]

120579119896+1

= 120579119896+ 119903119896 (22)

where 120579119896is the estimate of 120579lowast at the 119896th iteration and 119903

119896

is the perturbation vector generated randomly according tothe normal distribution N(0 V) The new solution 120579

119896+1is

accepted when the cost function 119869(120579119896+1

) is smaller than 119869(120579119896)

otherwise 120579119896+1

= 120579119896 In order to start the optimization pro-

cess it is necessary to specify the initial value 1205790and the

variance 120592 Assuming 120579lowast is a global minimum that should befound when 120579

119896is far away from 120579

lowast 119903119896should have a large

variance to allow large displacements This causes to escapelocal minima However when 120579

119896is close to 120579lowast 119903

119896should have

a small variance to allow precise exploration of the parameterspace Far from its convenience of training the algorithmhas the global convergence property and adaptive parametersof the algorithm reduce the possibility of trapping in localminima [20]

4 FDS Scheme

In this research among the possible faults of the WECSthe pitch sensors generatorrsquos angular velocity sensor andpitch actuators faults were studied because according to theinformation of the fault analysis which is given in [4] thesethree categories of faults have more severity and occurrenceindices than the other faults Internal faults of the generatorand converter were not studied in this research in orderto prevent the research from becoming too complex andextensive It is also assumed that no fault has occurred in thecontrol systems of the WECS and they continue to functionproperly Thus it can be said that the normal operationconditions of the WECS are as follows

(i) the control systems are healthy(ii) any type of faults has not occurred in the WECS(iii) any fault has not occurred in the power grid con-

nected to the WECS

Also the faulty operation conditions are as follows

(i) the control systems are healthy and they continue toact normally when a fault has occurred

(ii) one of the faults in the pitch sensors pitch actuatorsor generatorrsquos angular velocity sensor has occurred it


Table 1 The ARS training algorithm

Step Operation(1) Initialization phase 120579

0 119899max 1205920 and 119869min should be selected and 119899 = 1 120579best = 120579

0

(2) Variance selection phase

119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)

The trial point algorithm is executed119896 = 119896 + 1

end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end

(3) Variance exploration phase

119896 = 1 120579119896= 120579best 119894 = 119894best

while (119896 le 100)The trial point algorithm is executed119896 = 119896 + 1

endif ((119899 = 119899max) or (119869(120579best) lt 119869min))

Breakelse 120579

0= 120579best 119899 = 119899 + 1 and go to Step 2

end

The trial point algorithm

120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end

is assumed that these faults do not occur at the sametime

(iii) any fault has not occurred in the power grid con-nected to the WECS

In design of the FDS studying the two signals of thegeneratorrsquos angular velocity and pitch angles causes to detectthe faults in the pitch system and generatorrsquos angular velocitysensor According to themodel of theWECS bothmentionedsignals can be considered as a nonlinear function of theturbinersquos rotor speed and the measured wind speed Thesetwo measurements are available from the healthy sensorsBecause the closed-loop control system performance variesunder different wind speeds the wind speed is regarded as aninput of the nonlinear functions So the following relationscan be considered

120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)

where ℎ1(sdot) and ℎ

2(sdot) are nonlinear functionsThus according

to the measured values of the signals in the input of thesefunctions their outputs can be estimated by the mentioneddynamic neural networkThese neural models can be used toemulate the normal system behavior The neural models arethen placed in parallel with the system and fault detectionis acquired by comparing the outputs of the neural modelswith the real system outputs First the generatorrsquos angular

velocity is modeled by neural network The process to bemodeled is described by (23) This process has two inputsand one output The training process was carried out off-lineusing the ARS algorithm The learning set consisted of 1000samples for different mean wind speeds whilst the testingset consisted of 2000 samples for the mean wind speed of16ms First these samples were converted to the pu accord-ing to their base values and then the pu values were used totrain the network The best model was selected by using twoinformation criteria These criteria are the Akaike informa-tion criterion (AIC) and the final prediction error (FPE)The AIC determines the model complexity by minimizingan information theoretical function 119891AIC which is definedas follows [20]

119891AIC = log (119869) + 2119870

119873 (25)

where 119869 is the sum of squared errors between the desiredoutput 119910119889

119894 and the network output 119910

119894 119873 is the number of

samples used in the computation of 119869 and119870 is the number ofmodel parameters Another criterion is the FPEwhich selectsthe model order minimizing the function FPE 119891FPE which isdefined as follows [20]

119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)

The results of the appropriate network structure selectionto model 120596

119892are presented in Table 2 In this table 119870 is the


Table 2 The training and testing results for the network structure selection to model 120596119892

Network structure 119870Training Testing

119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886

number of network parameters 119869 is the sum of squarederrors and119873

119898

119899V119904(119903) represents the119898 layered dynamic neuralnetwork with 119899 inputs V hidden neurons and 119904 outputs inwhich neurons are of the 119903 order of the IIR filters The bestresults (marked with the bold text) were obtained for the1198732

231(2) structure for the training set However for the test-

ing set1198732231

(1) structure shows better performance Eventu-ally the1198732

231(1) architecture which corresponds to the mini-

mum criteria in testing was selected as optimal to modelbehaviors of 120596

119892 because this structure has better generaliza-

tion capability than the one selected for the training set Eachneuron of the dynamic network model has the hyperbolictangent activation function and is of the first order of the IIRfilter Figure 3 shows the comparison of the real 120596

119892and the

estimated 120596119892by the designed dynamic neural network in the

normal operation conditions As it is obvious the designedneural network estimates 120596

119892desirably and estimation error

is minimal All simulations were carried out inMatlabSimu-link version R2008a environment The parameters of thesystem are presented in the appendix

In order to form the FDS of the generatorrsquos angularvelocity two types of faults were considered which will bediscussed below In the basic FDS the constant threshold wasused to evaluate the residual signals This threshold level wasconsidered equal to plusmn4 rads In the first simulation the +2abrupt proportional fault was introduced at time instant 30 sfor duration of 20 s and theminus5 abrupt proportional fault wasintroduced at time instant 70 s for duration of 20 s Figure 4shows the simulation result in this case

According to Figure 4 in the case of the generatorrsquos angu-lar velocity deviation from its healthy value a residual isobtained by neural model estimator which is compared withthe threshold level hence the fault occurrence is detectableIn this figure between the moments of 30 to 50 secondsand 70 to 90 seconds the obtained residual passes theplusmn4 rads threshold level and this event indicates that a faulthas occurred in the generatorrsquos angular velocity sensor Asa result it can be argued that the FDS has the capability of

020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5

Figure 3 Residual signal of the generatorrsquos angular velocity sensorresulting from the WECS simulation for the mean wind speed of14ms in normal conditions

detecting the abrupt proportional faults in the generatorrsquosangular velocity sensor

The second simulation was performed when an incipientproportional fault occurred in the generatorrsquos angular velocitysensor In this case output of the generatorrsquos angular velocitysensor was deviated from its real value at time instant 30 suntil it reached to 11 times greater than its real value at timeinstant 90 s that is during 60 seconds an incipient fault wasintroduced in the generatorrsquos angular velocity sensor In thiscase the simulation result is presented in Figure 5 Accordingto Figure 5 the FDS has the ability to detect the introducedincipient fault at time instant 407 s It means that it takesabout 11 seconds until the FDS detects this type of fault whichis so desirable in detection of incipient faults Accordingto the obtained results for the abrupt proportional faultincipient proportional fault and fixed output fault (which is aspecial case of the incipient fault) it can be concluded that thedesigned FDS can detect faults well in different wind speeds(which affects the dynamics of the system) This FDS hascapability of the early detection of faultsThe significant pointin this system is a very low number of false alarms which isdesired in any FDSs




119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177

Table 4 Faults specifications in the integrated test

Location Type Start time Stop timeGeneratorrsquos angular velocity sensor Proportional +2 (f 1) 30 70Pitch actuator of the blade 1 Change in 120577 and 120596

119899(f 2) 80 120

Generatorrsquos angular velocity sensor Proportional minus10 (f 3) 120 150Pitch sensor of the blade 1 Positive bias +1∘ (f 4) 160 180Generatorrsquos angular velocity sensor Proportional +5 (f 5) 190 210Generatorrsquos angular velocity sensor Proportional minus2 (f 6) 220 230Pitch sensor of the blade 1 Negative bias minus08∘ (f 7) 240 260Pitch actuator of the blade 1 Change in 120577 and 120596

119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg

Figure 4 The residual of the generatorrsquos angular velocity forthe mean wind speed of 14ms during occurrence of the abruptproportional fault in the generatorrsquos angular velocity sensor

The next phase in design of the FDS is related to thepitch system fault detection In the pitch system the pitchsensors and actuators are subjected to the faults Thereforethe pitch system should be modeled by neural network Theprocess to be modeled is described by (24) The trainingprocess was carried out off-line using the ARS algorithmThe learning set consisted of 1000 samples for different meanwind speeds and the testing set consisted of 2000 samplesfor the mean wind speed of 16ms First these samples wereconverted to the pu values according to their base values

0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4

Figure 5 The residual of generatorrsquos angular velocity for themean wind speed of 12ms during occurrence of the incipientproportional fault in the generatorrsquos angular velocity sensor

and then the pu values were used to train the network Thebest model was selected by using the AIC and FPE criteriaThe results of the appropriate network structure selectionare presented in Table 3 The best results were obtained forthe 1198732

231(2) structure for the both training and testing sets

Thus the 1198732

231(2) architecture was selected as optimal to

model behaviors of the pitch system in the normal operationconditions Each neuron of the dynamic network modelhas the hyperbolic tangent activation function and is of the


0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1

Figure 6 Residual signal of the pitch system of the blade 1 resultingfrom the WECS simulation for the mean wind speed of 14ms innormal conditions

0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731

Figure 7 Residual evaluation by the constant threshold for themean wind speed of 14ms during occurrence of three categoriesof faults in the pitch system

second order of the IIR filter Figure 6 shows the comparisonof the real 120573

1and the estimated 120573

1by the designed dynamic

neural network in normal operation conditions As it can beseen the estimation error is minimal and the designed neuralnetwork has good ability to mimic the pitch angles behaviors

In order to form the FDS of the pitch system three typesof faults were considered Faults of the pitch system werecategorized such that an increase in the output of the blade1 pitch sensor (positive bias) was considered as the category 1a decrease in the output of the blade 1 pitch sensor (negativebias) was considered as the category 2 and faults of the pitchactuator which were modeled by changing the 120577 and 120596

119899were

considered as the category 3 To study the residual signalthe +075∘ bias fault was introduced at time instant 30 s forduration of 10 s the minus1∘ bias fault was introduced at timeinstant 50 s for duration of 10 s and the pitch actuator faultwhich is an abrupt fault was introduced at time instant 70 sfor duration of 30 s Figure 7 shows the residual signal underthese conditions In the basic FDS the constant thresholdcan be used to evaluate the residual signal This thresholdlevel was considered equal to plusmn03∘ As it can be seen theoccurred faults can be detected using the constant thresholdAccording to Figure 7 it takes 13 s 21 s and 25 s to detect thepositive bias the negative bias and the pitch actuator faultsrespectively Using this residual and the constant thresholdthe minimum detectable fault is equal to plusmn05∘ Obviouslythe threshold value can be reduced to further speed up

the detection process however by reducing the detectiontime false alarms will increase In fact a tradeoff should beconsidered between the detection time and false alarms rate

To evaluate the FDS performance in the presence ofthe pitch sensors and actuators and the generatorrsquos angularvelocity sensor faults first it is necessary to point out thatoccurrence of a fault in the angular velocity sensor of thegenerator affects the residual signal of the pitch systemTo investigate this issue the +5 proportional fault in thegeneratorrsquos angular velocity sensor was introduced at timeinstant 30 s for duration of 10 s the +1∘ bias fault in theblade 1 pitch sensor was introduced at time instant 50 s forduration of 10 s and the pitch actuator fault was introducedat time instant 70 s for duration of 20 s Figure 8 representsthe residual signals which were obtained from the FDS Asit can be seen from the results by introducing a fault in thegeneratorrsquos angular velocity sensor the residual signal of theblade 1 pitch sensor was affected and changed Conversely byintroducing a fault in the pitch system the residual signal ofthe generatorrsquos angular velocity was not affected

Consequently to form an integrated FDS it should beconsidered that if both of the residuals have passed thethreshold level it means that a fault has occurred in thegeneratorrsquos angular velocity sensor But if only the residual ofthe blade 1 pitch angle has passed the threshold level it meansthat a fault has occurred in the pitch system The generalalgorithm for detection of the studied faults in the WECS issuggested as follows

(1) if both of the residuals of the generatorrsquos angularvelocity sensor and pitch system remain within thethreshold level no fault has occurred in the WECS

(2) if both of the residuals of the generatorrsquos angularvelocity sensor and pitch system pass the thresholdlevel a fault has occurred in the generatorrsquos angularvelocity sensor

(3) If the residual of the generatorrsquos angular velocityremains within the threshold level but the residual ofthe pitch system passes the threshold level a fault hasoccurred in the pitch system

In order to evaluate performance of the FDS togetherwith the proposed algorithm various faults were introducedto the WECS for duration of 300 s according to Table 4In this case the residual signals are shown in Figure 9 Inthis figure a value of 1 means occurrence of a fault and avalue of zeromeans that the corresponding element functionsproperly As it can be seen from the results performance ofthe designed FDS is very good togetherwith theminimal falsefault detections In this figure there are very few false alarmswhich are significant and desirable To reduce the numberof false detections the threshold level can be increased inorder to avoid false alarms due to noises disturbances anduncertainties However an increase in the threshold level willbe followed by the sensitivity reduction of the FDS Alwaysa compromise should be considered to reduce the numberof false alarms and to achieve the desired sensitivity when aconstant threshold is utilized


0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)

Figure 8 The residual signals for occurrence of three types of faults (a) the residual signal of the generatorrsquos angular velocity sensor and (b)the residual signal of the pitch system of the blade 1

0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)

Figure 9 The residual signals under occurrence of the faults specified in Table 4 (a) the residual signal of the generatorrsquos angular velocitysensor and (b) the residual signal of the pitch system of the blade 1

5 The Robustness Issue

Since there are disturbances uncertainties andmeasurementnoises in practical systems decision making can be sensitiveto them The mentioned factors cause the robustness issueto be so important in FDSs The robustness problem inFDSs is to minimize the number of false alarms and tomaximize its sensitivity simultaneously As it is describedin [20] robustness of FDSs can be acquired by two generalmethods

(1) active methods in which the robustness issue is con-sidered from the beginning of the design procedureof the FDS so that it is not sensitive to disturbancesuncertainties and measurement noises Generallythese approaches utilize unknown input observersrobust parity equations and linear parameter varyingobservers [30ndash32]

(2) passive methods in which the robustness issue isachieved in the decision making component of theFDS In these approaches robustness is obtained byan adaptive threshold As it is stated in [20] thepassive method has an advantage over the active onesince the desired robustness can be acquired in spiteof uncertain parameters of the model

To avoid false alarms in passive approaches the valueof the constant thresholds should be selected large enoughbecause of unmodeled dynamics disturbances uncertaintiesandmeasurement noises On the other hand a large value forthe constant threshold causes the sensitivity degradation ofthe FDS As it is mentioned earlier when a constant thresholdis utilized a compromise should be considered to reduce thenumber of false alarms and to attain the desired sensitivityTherefore it is suggested to use the adaptive threshold Inthe adaptive threshold the value of the threshold varies intime according to the obtained information from the residualsignal In this paper to achieve the robustness of the FDS theproposed adaptive threshold in [20] is utilized This adaptivethreshold is described by the following equations

119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)

where ](119896) and 119898(119896) are the variance and mean value of theresidual signal for the past 119899 samples respectively and 120578 isthe momentum parameter which is considered close to 1Furthermore the significance level 120574 relates to probability ofexceeding the residual signal from a random value 119905

120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old

ResidualAdaptive threshold

20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)

Figure 10 Residual evaluation by the adaptive threshold during occurrence of three categories of faults in the pitch system (a) the residualand adaptive threshold and (b) decision making by means of the adaptive threshold

Table 5 The number of false and missed alarms

Threshold type Number offalse alarms Number of missed alarms

Constant 8 382Adaptive 5 57

N(0 1) The following equation describes the significancelevel [20]

120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)

To investigate performance of the defined adaptivethreshold the residual signal in Figure 7 was consideredagain and the adaptive threshold was calculated In thiscase the simulation result is shown in Figure 10 As it isobvious from the obtained result the adaptive threshold indi-cates the satisfactory behaviors Additionally the number offalse and missed alarms for both the adaptive and constantthresholds is calculated and results are gathered in Table 5The statistical analysis confirms that the performance of theadaptive threshold (Figure 10) is considerably better than theconstant threshold (Figure 7) By using the adaptive thre-shold the number of both false and missed alarms is reducedsignificantly

Furthermore to study the efficiency of the presented FDSthe integrated test which is presented inTable 4 is performedagain To compare the performance of the FDS togetherwith the adaptive threshold and the FDS together with theconstant threshold three indices are utilized These indicesare the number of false and missed alarms and detectiontime 119905detect Table 6 shows the obtained results in this caseIt is noteworthy that in Table 6 the number of false alarms iscalculated for whole residual signal however the number ofmissed alarm is calculated for each type of fault separatelySimulation results verify the validity of the proposed FDSThe presented FDS together with the adaptive thresholdhas good sensitivity and the number of its missed alarms

is appropriate Likewise its detection time is very low andfavorable

6 Conclusion

In this paper an FDS was proposed for the WECS Thedynamicmodel of theWECSwas a comprehensive onewhichcontained both the electrical andmechanical parts Detectionof faults was performed in such a way that two neural modelswere used to emulate the normal system behaviorsTheywerethen placed in parallel with the system and fault detectionwas acquired by comparing their outputs The designed FDScan detect faults in the generatorrsquos angular velocity sensor thepitch sensors and actuators The FDS employed the dynamicRNN and the ARS method was used to train the networkThis kind of dynamic neural networks presented very highability to estimate both the generatorrsquos angular velocity andpitch angle In order to attain the robustness it was suggestedto use an adaptive threshold because the constant thresholdwas so sensitive tomeasurement noises and disturbancesThesimulation results for different operation conditions verifythat the proposed FDS operates fast precisely and accuratelyand detects the faults appropriately and its false and missedalarms are very low

Appendix

Parameters of the System

119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596

119892nom = 1958 radsNumber of blades = 3 119873

119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10

3Nms V119908cut-in = 4ms V

119908cut-off = 25ms120588 = 1225 kgm3 Number of poles = 4 119877

119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu


Table 6 Evaluation of the suggested FDS for the constant and adaptive thresholds

Fault type Number of false alarms Number of missed alarms 119905detect

Constant Adaptive Constant Adaptive Constant Adaptivef 1

29for all of thesamplesduring 300seconds


3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Blanke KMichel L Jan and SMarcelDiagnosis and Fault-Tolerant Control Springer 2006

[2] H C Cho J Knowles M S Fadali and K S Lee ldquoFault detec-tion and isolation of induction motors using recurrent neuralnetworks and dynamic bayesian modelingrdquo IEEE Transactionson Control Systems Technology vol 18 no 2 pp 430ndash437 2010

[3] K Rothenhagen and F W Fuchs ldquoDoubly fed induction gen-erator model-based sensor fault detection and control loopreconfigurationrdquo IEEE Transactions on Industrial Electronicsvol 56 no 10 pp 4229ndash4238 2009

[4] C Sloth T Esbensen and J Stoustrup ldquoRobust and fault-toler-ant linear parameter-varying control of wind turbinesrdquoMecha-tronics vol 21 no 4 pp 645ndash659 2011

[5] B Dolan Wind turbine modelling control and fault detection[PhD dissertation] Technical University of Denmark LyngbyDenmark 2010

[6] M A Kahyeh N Heraud I S Guelle and O Bennouna ldquoFaultdiagnosis of variable speed wind turbinerdquo in Proceedings ofthe 18th Mediterranean Conference on Control and Automation(MED rsquo10) pp 471ndash476 June 2010


[8] S Donders V Verdult and M Verhaegen ldquoFault detection andidentification for wind turbine systems a closed-loop analysisrdquoin Proceedings of the 2004 International Conference onNoise andVibration Engineering (ISMA rsquo04) pp 2619ndash2630 September2004

[9] AVerma andAKusiak ldquoFaultmonitoring ofwind turbine gen-erator brushes a data-mining approachrdquo Journal of Solar EnergyEngineering Transactions of the ASME vol 134 no 2 Article ID021001 2012

[10] A Kusiak and W Li ldquoThe prediction and diagnosis of windturbine faultsrdquo Renewable Energy vol 36 no 1 pp 16ndash23 2011

[11] M Entezami S Hillmansen P Weston and M Ph PapaeliasldquoFault detection and diagnosis within a wind turbine mechan-ical braking system using condition monitoringrdquo RenewableEnergy vol 47 pp 175ndash182 2012

[12] L Wenyi W Zhenfeng H Jiguang and W Guangfeng ldquoWindturbine fault diagnosismethod based on diagonal spectrum andclustering binary tree SVMrdquo Renewable Energy vol 50 pp 1ndash62013

[13] E Kamal and A Aitouche ldquoRobust fault tolerant control ofDFIG wind energy systems with unknown inputsrdquo RenewableEnergy vol 56 pp 2ndash15 2013

[14] S M Tabatabaeipour P F Odgaard T Bak and J StoustrupldquoFault detection of wind turbines with uncertain parametersa set-membership approachrdquo Energies vol 5 no 7 pp 2424ndash2448 2012

[15] Ozdemir Ahmet Arda Peter Seiler and J Gary Balas ldquoWindturbine fault detection using counter-based residual threshold-ingrdquo in Proceedings of IFAC World Congress pp 8289ndash82942011

[16] Z Hameed Y S Hong Y M Cho S H Ahn and C K SongldquoConditionmonitoring and fault detection ofwind turbines andrelated algorithms a reviewrdquo Renewable and Sustainable EnergyReviews vol 13 no 1 pp 1ndash39 2009

[17] P Caselitz and J Giebhardt ldquoAdvanced maintenance and repairfor offshore wind farms using fault prediction techniquesrdquo inProceedings of the World Wind Energy Conference 2002

[18] I Hwang S Kim Y Kim and C E Seah ldquoA survey of faultdetection isolation and reconfiguration methodsrdquo IEEE Tran-sactions on Control Systems Technology vol 18 no 3 pp 636ndash653 2010

[19] V Venkatasubramanian R Rengaswamy K Yin and S NKavuri ldquoA review of process fault detection and diagnosis partI quantitativemodel-basedmethodsrdquoComputers and ChemicalEngineering vol 27 no 3 pp 293ndash311 2003

[20] K Patan Artificial Neural Networks for the Modelling and FaultDiagnosis of Technical Processes vol 377 Springer 2008

[21] V Venkatasubramanian R Rengaswamy and S N Kavuri ldquoAreview of process fault detection and diagnosis part II quali-tative models and search strategiesrdquo Computers and ChemicalEngineering vol 27 no 3 pp 313ndash326 2003

[22] B Jiang Z Gao P Shi and Y Xu ldquoAdaptive fault-tolerant track-ing control of near-space vehicle using TakagiSugeno fuzzymodelsrdquo IEEE Transactions on Fuzzy Systems vol 18 no 5 pp1000ndash1007 2010

[23] H M Hasanien S M Muyeen and J Tamura ldquoSpeed controlof permanent magnet excitation transverse flux linear motor byusing adaptive neuro-fuzzy controllerrdquo Energy Conversion andManagement vol 51 no 12 pp 2762ndash2768 2010

[24] K Patan and T Parisini ldquoIdentification of neural dynamicmodels for fault detection and isolation the case of a real sugar


evaporation processrdquo Journal of Process Control vol 15 no 1 pp67ndash79 2005

[25] B Cannas G Celli M Marchesi and F Pilo ldquoNeural networksfor power system conditionmonitoring and protectionrdquoNeuro-computing vol 23 no 1ndash3 pp 111ndash123 1998

[26] I B Ciocoiu ldquoTime series analysis using RBF networks withFIRIIR synapsesrdquo Neurocomputing vol 20 no 1ndash3 pp 57ndash661998

[27] T G Barbounis and J B Theocharis ldquoLocally recurrent neuralnetworks for long-term wind speed and power predictionrdquoNeurocomputing vol 69 no 4ndash6 pp 466ndash496 2006

[28] T G Barbounis and J B Theocharis ldquoLocally recurrent neuralnetworks for wind speed prediction using spatial correlationrdquoInformation Sciences vol 177 no 24 pp 5775ndash5797 2007

[29] M Ayoubi ldquoFault dynamic neural structure and application toa turbo-chargerrdquo in Proceedings of the International Symposiumon Fault Detection Supervision and Safety for Technical Pro-cesses pp 618ndash623 1994

[30] L M Ho ldquoApplication of adaptive thresholds in robust faultdetection of an electro-mechanical single-wheel steering actua-torrdquo in Proceedings of the Fault Detection Supervision and Safetyof Technical Processes vol 8 no 1 pp 259ndash264 2012

[31] D Valh B Bratina and B Tovornik ldquoOn-line fault detectionand isolation using analytical redundancyrdquo ElectrotechnicalReview vol 73 no 5 pp 267ndash272 2006

[32] S Montes De Oca V Puig and J Blesa ldquoRobust fault detectionbased on adaptive threshold generation using interval LPVobserversrdquo International Journal of Adaptive Control and SignalProcessing vol 26 no 3 pp 258ndash283 2012

[33] F D Bianchi H de Battista and R J Mantz Wind TurbineControl Systems Springer 2007

[34] M O L Hansen Aerodynamics of Wind Turbines Earthscan2008

[35] A Junyent-Ferre O Gomis-Bellmunt A Sumper M Sala andM Mata ldquoModeling and control of the doubly fed inductiongenerator wind turbinerdquo Simulation Modelling Practice andTheory vol 18 no 9 pp 1365ndash1381 2010

[36] L Xu and P Cartwright ldquoDirect active and reactive powercontrol of DFIG for wind energy generationrdquo IEEE Transactionson Energy Conversion vol 21 no 3 pp 750ndash758 2006

[37] A A El-Sattar N H Saad andM Z S El-Dein ldquoDynamic res-ponse of doubly fed induction generator variable speed windturbine under faultrdquoElectric Power Systems Research vol 78 no7 pp 1240ndash1246 2008

[38] P C Krause O Wasynczuk and S D Sudhoff Analysis ofElectric Machinery IEEE Press 2002

[39] R Pena J C Clare and G M Asher ldquoDoubly fed inductiongenerator using back-to-back PWM converters and its appli-cation to variable-speed wind-energy generationrdquo IEE Proceed-ings-Electric PowerApplications vol 143 no 3 pp 231ndash241 1996

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Applied Computational Intelligence and Soft Computing

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



for pattern recognition purposes while recurrent ones areused to prepare dynamical model of a process Among neuralnetworks that have been used frequently in FDSs multilayerfeedforward neural networks (MFNNs) radial basis functionneural (RBFN) networks and globally and locally recurrentnetworks can be mentioned

In structure of recurrent neural networks dynamic neu-rons replace the standard ones In one type of dynamicneurons the dynamics are applied by introducing an IIR filterinto the neuron structure This network structure does nothave any global feedbacks In fact this network has a structurethat is somewhere in between a feedforward and a globallyrecurrent structure [20]The recurrent neural network with aneuron model using the IIR filter has been used successfullyfor modeling fault detection and time series prediction In[20 24] this kind of network was used for fault detectionof a sugar evaporation process Also in [20] applicationsfor fault detection by using the mentioned network werepresentedThis network was utilized to detect faults in a fluidcatalytic cracking and a DC motor In [2] this network wasused for fault detection and isolation of induction motorsIn [25] by using this network an FDS for protecting andmonitoring systems of power networks was designed in sucha way that reliability of the power grid has risen up In [26]by combining the RBFN and the neuron model with the IIRfilter a network was proposed and it was used to predict timeseries In [27 28] it was utilized to predict both the windspeed and power in wind farms Finally in [29] it was usedto detect faults of a turbocharger

In addition fault detection of theWECSs has attracted theattention of many researchers in recent years For instancein [4 7] using a linear model of mechanical parts of a windturbine (electrical parts were neglected) a fault-tolerant con-troller was presented by utilizing the linear parameter varyingcontrol which was replaced with the reference controller Inthese two researches the occurred faults were diagnosed andthen the controller was reconfigured In [5] fault detectionof a wind turbine was performed using the linear modelof the mechanical parts and only occurrence of a fault wasconsidered In [6] faults of the induction generator wereconsidered Also the linearmodel of themechanical parts wasused to detect two categories of faults using the Kalman-filterin [8] Utilizing the supervisory control and data acquisition(SCADA) in [9] the occurred faults in a wind turbine weredetected In [10] by using the data-mining approach bearingfaults were detected In [11] utilizing the real data obtainedfrom a condition monitoring system faults of the brakingsystem of a wind turbine were detected In [12] a faulttolerant controller was proposed using fuzzy observers In[14] utilizing the Set-Membership approach and a modelfor the mechanical parts various faults of a wind turbinewere detected Also in [15] numbers of faults were detectedusing amodel for themechanical parts and the counter-basedresidual thresholding method

As it is obvious in researches that have been performedso far either a small number of faults have been studied orthe WECS has not been modeled completely or the linearmodels have been used to design the FDS It is obvious thatusing the more accurate nonlinear model will lead us to the

results which are closer to the real ones Another importantissue is robustness of the proposed scheme Robustnesscan be achieved either by active approaches or by passiveones [20] Active approaches consider the desired robustnessfrom the beginning of the design procedure [30ndash32] whilepassive approaches utilize adaptive thresholds architecturein decision making block to achieve the desired robustness[20] In this paper by utilizing a comprehensive nonlinearmodel of the WECS an FDS is suggested which has thecapability to detect faults in the generatorrsquos angular velocitysensor pitch sensors and pitch actuatorsThe presented FDSis composed of the dynamic neural network with the IIRfilter as the dynamic neuronmodel Additionally an adaptivethreshold is employed to achieve the anticipated robustnessThe proposed FDS can be utilized to detect the faults in otherparts of the WECS

The structure of this paper is organized as followsdynamic model of the WECS is presented in Section 2 InSection 3 the RNN with the IIR filter as neuron model isintroduced Section 4 presents the design procedure of theFDS In Section 5 the robustness of the proposed FDS isinvestigated

2 Dynamic Model of the WECS

The block diagram of the considered model in this paperis shown in Figure 1 In this figure the yaw mechanismis neglected and wind speed is the exogenous input Theaerodynamic torque of the turbinersquos rotor119879

119903(119905) is transferred

to the generator through the drive train The drive trainincludes a high speed shaft a low speed shaft and a gearboxThe induction generator converts the mechanical energy tothe electrical one and is connected to the power grid Aninterface is used for calculation of the active and reactivegenerated power The grid model includes a local loadtransformers transmission lines and the infinite-bus at theend Converters a dc link rotor and grid side controllers aremodeled in this study

Equations for modeling of the mechanical parts of theWECS are as follows [4 33ndash36]

V119908(119905) = V

119908(119905) + V

119908119904(119905) + V

119905119904(119905) + V

119905119906(119905) (1)

where in (1) which is related to the modeling of the windV119908(119905) is the wind speed including the tower shadow wind

shear and turbulence components In this equation V119908(119905) is

the mean wind speed V119908119904(119905) is the wind shear component

V119905119904(119905) is the wind speed tower shadow component and V

119905119906(119905)

is the wind speed turbulence component Consider

119875119903(119905) = 05120588119860V3

119903(119905) 119862119901(120582 (119905) 120573 (119905))

119879119903(119905) =

119875119903(119905)

120596119903(119905)

=1

120596119903(119905)

05120588119860V3119903(119905) 119862119901(120582 (119905) 120573 (119905))

(2)

Equations (2) are used to model wind turbinersquos aerody-namic where 119875

119903(119905) is the captured power by the turbinersquos

rotor 120573(119905) is the pitch angle 120582(119905) is the tip-speed ratio119862119901(120582(119905) 120573(119905)) is the power coefficient 119860 is the rotor swept

area V119903(119905) is the rotor effective wind speed 120588 is the air


Wind model

Aerodynamics

Pitch system

Tower


Interface


DC link and grid

side converter


Grid model


r(t)

120573(t)

Ft(t)

Tr(t)

120596r(t)

120573ref (t)

120596g(t)

Tg(t)

Qlowastg(t)

Plowastg (t)

Qg(t)

Pg(t)

Vlowastdqr

Vdqr

idqs

Vdqs

idqr

Vdqg

Vlowastdqg

Vdc

Vlowastdc

ilowastqg

Vabc Iabc


minus

+vw(t) v v

w(t)Σ





119862119901(120582(119905) 120573(119905)) and 119862



119865119905(119905) = 05120588119860V2

119903(119905) 119862119905(120582 (119905) 120573 (119905)) (3)




119903is the







Consider

119869119903119903= 119879119903minus 119870119889119905120579120575minus 119861119889119905

120579120575

119869119892119873119892119892= minus119879119892119873119892+ 119870119889119905120579120575+ 119861119889119905

120579120575

120579120575= 120596119903minus

120596119892

119873119892

(4)




119905is the tower


119905(119905) is



119872119905119905(119905) = 119865

119905ℎ(119905) minus 119861

119905119905(119905) minus 119870

119905119909119905(119905) (5)

V119903(119905) = V

119908(119905) minus

119905(119905) (6)



120573 (119905) = minus2120577120596119899

120573 (119905) minus 1205962

119899120573 (119905) + 120596

2

119899120573ref (119905) (7)


119881119902119904= 119877119904119894119902119904+

119889

119889119905120593119902119904+ 120596119904120593119889119904

119881119889119904

= 119877119904119894119889119904+

119889

119889119905120593119889119904minus 120596119904120593119902119904

119881119902119903= 119877119903119894119902119903+

119889

119889119905120593119902119903+ (120596119904minus 120596119903) 120593119889119903

119881119889119903

= 119877119903119894119889119903+

119889

119889119905120593119889119903minus (120596119904minus 120596119903) 120593119902119903

(8)


119904and 119877



119903is the




axis fluxes and 120593119889119903



120593119902119904= 119871119904119894119902119904+ 119871119898119894119902119903

120593119889119904

= 119871119904119894119889119904+ 119871119898119894119889119903

120593119902119903= 119871119903119894119902119903+ 119871119898119894119902119904

120593119889119903

= 119871119903119894119889119903+ 119871119898119894119889119904

(9)



119903=



119879119890= 15119901 (120593

119889119904119894119902119904minus 120593119902119904119894119889119904) (10)





119889

119889119905120596119892=

1

2119867(119879119890minus 119865120596119892minus 119879119892)

119889

119889119905120579119892= 120596119892

(11)


119892and 119871

119892are





power of the GSC

119881119889119892

= 119877119892119894119889119892

+ 119871119892

119889

119889119905119894119889119892

minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881119902119892

= 119877119892119894119902119892

+ 119871119892

119889

119889119905119894119902119892

+ 120596119904119871119892119894119889119892

+ 119881119902119904

119875119892=

3

2(119881119889119904119868119889119892

+ 119881119902119904119868119902119892)

119889119881119889119888

119889119905=

119875

119881119889119888119862

=

119875119903minus 119875119892

119881119889119888119862

=

119875119890minus 119875119904minus 119875119892

119881119889119888119862

(12)


119881lowast

119889119903= 1205901198711199031198811015840

119889119903+ 119877119903119894119889119903minus 119904120596119904120590119871119903119894119902119903minus 119904120596119904(119871119898

119871119904

)120593119902119904

119881lowast

119902119903= 1205901198711199031198811015840

119902119903+ 119877119903119894119902119903+ 119904120596119904120590119871119903119894119889119903+ 119904120596119904(119871119898

119871119904

)120593119889119904

(13)


1015840




119889119903and 119894lowast


1198811015840

119889119903=

119889119894119889119903

119889119905= 1198701198751

(119894lowast

119889119903minus 119894119889119903) + 1198701198681int (119894lowast

119889119903minus 119894119889119903) 119889119905

1198811015840

119902119903=

119889119894119902119903

119889119905= 1198701198751

(119894lowast

119902119903minus 119894119902119903) + 1198701198681int (119894lowast

119902119903minus 119894119902119903) 119889119905

(14)




119881lowast

119889119892= 119877119892119894119889119892

+ 1198711198921198811015840

119889119892minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881lowast

119902119892= 119877119892119894119902119892

+ 1198711198921198811015840

119902119892+ 120596119904119871119892119894119889119892

+ 119881119902119904

(15)




1198811015840

119889119892=

119889119894119889119892

119889119905= 1198701198752

(119894lowast

119889119892minus 119894119889119892) + 1198701198682int(119894lowast

119889119892minus 119894119889119892) 119889119905

1198811015840

119902119892=

119889119894119902119892

119889119905= 1198701198752

(119894lowast

119902119892minus 119894119902119892) + 1198701198682int (119894lowast

119902119892minus 119894119902119892) 119889119905

(16)





120593 (119896) =

119899

sum

119894=1

119908119894119906119894(119896) (17)


119894 119894 = 1 2 119903 and 119887

119894


u1(k)

u2(k)

un(k)

W1

W2

Wn

sum(k) z(k)IIR

g1

g2

120590() y(k)

middotmiddotmiddot

120593



119911 (119896) =

119903

sum

119894=0

119887119894120593 (119896 minus 119894) minus

119903

sum

119894=1

119886119894119911 (119896 minus 119894) (18)


119910 (119896) = 120590 (1198922(119911 (119896) minus 119892

1)) (19)



120579lowast

= min120579isinC

119869 (120579) (20)



119869 (119897 120579) =1

2

119873

sum

119896=1

(119910119889(119896) minus 119910 (119896 120579))

2

(21)



0 1205791 120579




120579119896+1

= 120579119896+ 119903119896 (22)


119896


119896+1is


) is smaller than 119869(120579119896)

otherwise 120579119896+1








119896should have


4 FDS Scheme



nected to the WECS








0


119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)


end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end


119896 = 1 120579119896= 120579best 119894 = 119894best



Breakelse 120579


end


120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end




120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)





119891AIC = log (119869) + 2119870

119873 (25)





119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Wind model

Aerodynamics

Pitch system

Tower


Interface


DC link and grid

side converter


Grid model


r(t)

120573(t)

Ft(t)

Tr(t)

120596r(t)

120573ref (t)

120596g(t)

Tg(t)

Qlowastg(t)

Plowastg (t)

Qg(t)

Pg(t)

Vlowastdqr

Vdqr

idqs

Vdqs

idqr

Vdqg

Vlowastdqg

Vdc

Vlowastdc

ilowastqg

Vabc Iabc


minus

+vw(t) v v

w(t)Σ





119862119901(120582(119905) 120573(119905)) and 119862



119865119905(119905) = 05120588119860V2

119903(119905) 119862119905(120582 (119905) 120573 (119905)) (3)




119903is the







Consider

119869119903119903= 119879119903minus 119870119889119905120579120575minus 119861119889119905

120579120575

119869119892119873119892119892= minus119879119892119873119892+ 119870119889119905120579120575+ 119861119889119905

120579120575

120579120575= 120596119903minus

120596119892

119873119892

(4)




119905is the tower


119905(119905) is



119872119905119905(119905) = 119865

119905ℎ(119905) minus 119861

119905119905(119905) minus 119870

119905119909119905(119905) (5)

V119903(119905) = V

119908(119905) minus

119905(119905) (6)



120573 (119905) = minus2120577120596119899

120573 (119905) minus 1205962

119899120573 (119905) + 120596

2

119899120573ref (119905) (7)


119881119902119904= 119877119904119894119902119904+

119889

119889119905120593119902119904+ 120596119904120593119889119904

119881119889119904

= 119877119904119894119889119904+

119889

119889119905120593119889119904minus 120596119904120593119902119904

119881119902119903= 119877119903119894119902119903+

119889

119889119905120593119902119903+ (120596119904minus 120596119903) 120593119889119903

119881119889119903

= 119877119903119894119889119903+

119889

119889119905120593119889119903minus (120596119904minus 120596119903) 120593119902119903

(8)


119904and 119877



119903is the




axis fluxes and 120593119889119903



120593119902119904= 119871119904119894119902119904+ 119871119898119894119902119903

120593119889119904

= 119871119904119894119889119904+ 119871119898119894119889119903

120593119902119903= 119871119903119894119902119903+ 119871119898119894119902119904

120593119889119903

= 119871119903119894119889119903+ 119871119898119894119889119904

(9)



119903=



119879119890= 15119901 (120593

119889119904119894119902119904minus 120593119902119904119894119889119904) (10)





119889

119889119905120596119892=

1

2119867(119879119890minus 119865120596119892minus 119879119892)

119889

119889119905120579119892= 120596119892

(11)


119892and 119871

119892are





power of the GSC

119881119889119892

= 119877119892119894119889119892

+ 119871119892

119889

119889119905119894119889119892

minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881119902119892

= 119877119892119894119902119892

+ 119871119892

119889

119889119905119894119902119892

+ 120596119904119871119892119894119889119892

+ 119881119902119904

119875119892=

3

2(119881119889119904119868119889119892

+ 119881119902119904119868119902119892)

119889119881119889119888

119889119905=

119875

119881119889119888119862

=

119875119903minus 119875119892

119881119889119888119862

=

119875119890minus 119875119904minus 119875119892

119881119889119888119862

(12)


119881lowast

119889119903= 1205901198711199031198811015840

119889119903+ 119877119903119894119889119903minus 119904120596119904120590119871119903119894119902119903minus 119904120596119904(119871119898

119871119904

)120593119902119904

119881lowast

119902119903= 1205901198711199031198811015840

119902119903+ 119877119903119894119902119903+ 119904120596119904120590119871119903119894119889119903+ 119904120596119904(119871119898

119871119904

)120593119889119904

(13)


1015840




119889119903and 119894lowast


1198811015840

119889119903=

119889119894119889119903

119889119905= 1198701198751

(119894lowast

119889119903minus 119894119889119903) + 1198701198681int (119894lowast

119889119903minus 119894119889119903) 119889119905

1198811015840

119902119903=

119889119894119902119903

119889119905= 1198701198751

(119894lowast

119902119903minus 119894119902119903) + 1198701198681int (119894lowast

119902119903minus 119894119902119903) 119889119905

(14)




119881lowast

119889119892= 119877119892119894119889119892

+ 1198711198921198811015840

119889119892minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881lowast

119902119892= 119877119892119894119902119892

+ 1198711198921198811015840

119902119892+ 120596119904119871119892119894119889119892

+ 119881119902119904

(15)




1198811015840

119889119892=

119889119894119889119892

119889119905= 1198701198752

(119894lowast

119889119892minus 119894119889119892) + 1198701198682int(119894lowast

119889119892minus 119894119889119892) 119889119905

1198811015840

119902119892=

119889119894119902119892

119889119905= 1198701198752

(119894lowast

119902119892minus 119894119902119892) + 1198701198682int (119894lowast

119902119892minus 119894119902119892) 119889119905

(16)





120593 (119896) =

119899

sum

119894=1

119908119894119906119894(119896) (17)


119894 119894 = 1 2 119903 and 119887

119894


u1(k)

u2(k)

un(k)

W1

W2

Wn

sum(k) z(k)IIR

g1

g2

120590() y(k)

middotmiddotmiddot

120593



119911 (119896) =

119903

sum

119894=0

119887119894120593 (119896 minus 119894) minus

119903

sum

119894=1

119886119894119911 (119896 minus 119894) (18)


119910 (119896) = 120590 (1198922(119911 (119896) minus 119892

1)) (19)



120579lowast

= min120579isinC

119869 (120579) (20)



119869 (119897 120579) =1

2

119873

sum

119896=1

(119910119889(119896) minus 119910 (119896 120579))

2

(21)



0 1205791 120579




120579119896+1

= 120579119896+ 119903119896 (22)


119896


119896+1is


) is smaller than 119869(120579119896)

otherwise 120579119896+1








119896should have


4 FDS Scheme



nected to the WECS








0


119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)


end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end


119896 = 1 120579119896= 120579best 119894 = 119894best



Breakelse 120579


end


120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end




120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)





119891AIC = log (119869) + 2119870

119873 (25)





119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




axis fluxes and 120593119889119903



120593119902119904= 119871119904119894119902119904+ 119871119898119894119902119903

120593119889119904

= 119871119904119894119889119904+ 119871119898119894119889119903

120593119902119903= 119871119903119894119902119903+ 119871119898119894119902119904

120593119889119903

= 119871119903119894119889119903+ 119871119898119894119889119904

(9)



119903=



119879119890= 15119901 (120593

119889119904119894119902119904minus 120593119902119904119894119889119904) (10)





119889

119889119905120596119892=

1

2119867(119879119890minus 119865120596119892minus 119879119892)

119889

119889119905120579119892= 120596119892

(11)


119892and 119871

119892are





power of the GSC

119881119889119892

= 119877119892119894119889119892

+ 119871119892

119889

119889119905119894119889119892

minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881119902119892

= 119877119892119894119902119892

+ 119871119892

119889

119889119905119894119902119892

+ 120596119904119871119892119894119889119892

+ 119881119902119904

119875119892=

3

2(119881119889119904119868119889119892

+ 119881119902119904119868119902119892)

119889119881119889119888

119889119905=

119875

119881119889119888119862

=

119875119903minus 119875119892

119881119889119888119862

=

119875119890minus 119875119904minus 119875119892

119881119889119888119862

(12)


119881lowast

119889119903= 1205901198711199031198811015840

119889119903+ 119877119903119894119889119903minus 119904120596119904120590119871119903119894119902119903minus 119904120596119904(119871119898

119871119904

)120593119902119904

119881lowast

119902119903= 1205901198711199031198811015840

119902119903+ 119877119903119894119902119903+ 119904120596119904120590119871119903119894119889119903+ 119904120596119904(119871119898

119871119904

)120593119889119904

(13)


1015840




119889119903and 119894lowast


1198811015840

119889119903=

119889119894119889119903

119889119905= 1198701198751

(119894lowast

119889119903minus 119894119889119903) + 1198701198681int (119894lowast

119889119903minus 119894119889119903) 119889119905

1198811015840

119902119903=

119889119894119902119903

119889119905= 1198701198751

(119894lowast

119902119903minus 119894119902119903) + 1198701198681int (119894lowast

119902119903minus 119894119902119903) 119889119905

(14)




119881lowast

119889119892= 119877119892119894119889119892

+ 1198711198921198811015840

119889119892minus 120596119904119871119892119894119902119892

+ 119881119889119904

119881lowast

119902119892= 119877119892119894119902119892

+ 1198711198921198811015840

119902119892+ 120596119904119871119892119894119889119892

+ 119881119902119904

(15)




1198811015840

119889119892=

119889119894119889119892

119889119905= 1198701198752

(119894lowast

119889119892minus 119894119889119892) + 1198701198682int(119894lowast

119889119892minus 119894119889119892) 119889119905

1198811015840

119902119892=

119889119894119902119892

119889119905= 1198701198752

(119894lowast

119902119892minus 119894119902119892) + 1198701198682int (119894lowast

119902119892minus 119894119902119892) 119889119905

(16)





120593 (119896) =

119899

sum

119894=1

119908119894119906119894(119896) (17)


119894 119894 = 1 2 119903 and 119887

119894


u1(k)

u2(k)

un(k)

W1

W2

Wn

sum(k) z(k)IIR

g1

g2

120590() y(k)

middotmiddotmiddot

120593



119911 (119896) =

119903

sum

119894=0

119887119894120593 (119896 minus 119894) minus

119903

sum

119894=1

119886119894119911 (119896 minus 119894) (18)


119910 (119896) = 120590 (1198922(119911 (119896) minus 119892

1)) (19)



120579lowast

= min120579isinC

119869 (120579) (20)



119869 (119897 120579) =1

2

119873

sum

119896=1

(119910119889(119896) minus 119910 (119896 120579))

2

(21)



0 1205791 120579




120579119896+1

= 120579119896+ 119903119896 (22)


119896


119896+1is


) is smaller than 119869(120579119896)

otherwise 120579119896+1








119896should have


4 FDS Scheme



nected to the WECS








0


119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)


end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end


119896 = 1 120579119896= 120579best 119894 = 119894best



Breakelse 120579


end


120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end




120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)





119891AIC = log (119869) + 2119870

119873 (25)





119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




u1(k)

u2(k)

un(k)

W1

W2

Wn

sum(k) z(k)IIR

g1

g2

120590() y(k)

middotmiddotmiddot

120593



119911 (119896) =

119903

sum

119894=0

119887119894120593 (119896 minus 119894) minus

119903

sum

119894=1

119886119894119911 (119896 minus 119894) (18)


119910 (119896) = 120590 (1198922(119911 (119896) minus 119892

1)) (19)



120579lowast

= min120579isinC

119869 (120579) (20)



119869 (119897 120579) =1

2

119873

sum

119896=1

(119910119889(119896) minus 119910 (119896 120579))

2

(21)



0 1205791 120579




120579119896+1

= 120579119896+ 119903119896 (22)


119896


119896+1is


) is smaller than 119869(120579119896)

otherwise 120579119896+1








119896should have


4 FDS Scheme



nected to the WECS








0


119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)


end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end


119896 = 1 120579119896= 120579best 119894 = 119894best



Breakelse 120579


end


120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end




120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)





119891AIC = log (119869) + 2119870

119873 (25)





119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







0


119894 = 1 119896 = 1 120579119896= 1205790

while (119894 lt 5)while (119896 le 100119894)


end119894 = 119894 + 1 119896 = 1 120579

119896= 1205790

end


119896 = 1 120579119896= 120579best 119894 = 119894best



Breakelse 120579


end


120592119894= 10minus119894

1205920 1205791015840119896= 120579119896+ 119903119896

if (119869(1205791015840119896) le 119869(120579

119896))

120579119896+1

= 1205791015840

119896

else 120579119896+1

= 120579119896

endif (119869(1205791015840

119896) le 119869(120579best))

120579best = 1205791015840

119896

119894best = 119894end




120596119892= ℎ1(119881119908 120596119903) (23)

120573123

= ℎ2(119881119908 120596119903) (24)





119891AIC = log (119869) + 2119870

119873 (25)





119891FPE =119869 (1 + (119870119873))

(1 minus (119870119873)) (26)






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 00282 00296 minus35148 00126 00129 minus43491N2241

(1) 33 00379 00405 minus32068 00200 00207 minus38790N2251

(1) 41 00258 00286 minus35554 00151 00157 minus41521N2261

(1) 49 00521 00575 minus28566 00573 00602 minus28105N2271

(1) 57 00406 00455 minus30900 00664 00703 minus26551N2231

(1) 31 00268 00285 minus35574 00134 00138 minus42815N2241

(1) 41 00417 00453 minus30953 00424 00442 minus31196N2251

(1) 51 00378 00419 minus31734 00409 00430 minus31456N2261

(1) 61 00349 00394 minus32333 00327 00348 minus33594N2271

(1) 71 00795 00917 minus23900 00850 00913 minus23941N32321

(2-2) 50 01286 01421 minus19510 00365 00384 minus32604N32421

(2-2) 61 00902 01019 minus22837 00767 00815 minus25069N32431

(2-2) 73 01135 01314 minus20300 00141 00152 minus41886


119898



ing set1198732231






119892and the







020 40 60 80 100

0

5

Time (s)

Erro

r (ra

ds)

minus5







119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119869 119891FPE 119891AIC 119869 119891FPE 119891AIC

N2231

(1) 25 02447 02583 minus13536 02510 02574 minus13573N2241

(1) 33 01023 01099 minus22083 01471 01520 minus18836N2251

(1) 41 00394 00431 minus31451 00821 00855 minus24588N2261

(1) 49 00422 00465 minus30673 00964 01012 minus22902N2271

(1) 57 00509 00561 minus28799 01150 01208 minus21138N2231

(1) 31 00304 00325 minus34261 00793 00818 minus25035N2241

(1) 41 00781 00854 minus24609 01078 01123 minus21865N2251

(1) 51 00471 00526 minus29450 01037 01091 minus22153N2261

(1) 61 00348 00384 minus32601 00873 00917 minus23894N2271

(1) 71 00457 00527 minus29437 00782 00936 minus23686N32321

(2-2) 50 00641 00714 minus26390 00952 01001 minus23018N32421

(2-2) 61 00373 00426 minus31566 00849 00902 minus24053N32431

(2-2) 73 00282 00325 minus34103 01012 01089 minus22177



119899(f 2) 80 120


119899(f 8) 265 290

0 20 40 60 80 100

04

Time (s)

minus4

Resid

ual o

fwg



0 20 40 60 80 100

04

Time (s)

Resid

ual

minus4




Thus the 1198732




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 20 40 60 80 100

0

1

Time (s)

Erro

r (de

g)

minus1


0 20 40 60 80 100

0

1

03

Time (s)

minus03

minus1

Resid

ual o

f1205731







119899were










0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

5

10

15

20 40 60 80 100Time (s)

0minus5

Resid

ual o

fwg

(a)

0

2

4

6

8

20 40 60 80 100Time (s)

0minus4

minus2

Resid

ual o

f1205731

(b)


0

1

0 50 100 150 200 250 300Time (s)

Faul

t in

the g

ener

ator

rsquos an

gula

r vel

ocity

sens

or

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

0 50 100 150 200 250 300Time (s)

(b)







119879 (119896) = 119905120574] (119896) plusmn 119898 (119896)

] (119896) = 120578] (119896) + (1 minus 120578) ] (119896 minus 1)

119898 (119896) = 120578119898 (119896) + (1 minus 120578)119898 (119896 minus 1)

(27)


120574 with


0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

1

Resid

ual a

nd ad

aptiv

e th

resh

old


20 40 60 80 100Time (s)

0minus1

(a)

0

1

Faul

t in

the p

itch

syste

mof

the b

lade

1

20 40 60 80 100Time (s)

0

(b)






120574 = 119875(

1003816100381610038161003816100381610038161003816

119903 minus 119898

]

1003816100381610038161003816100381610038161003816gt 119905120574) (28)




6 Conclusion


Appendix


119875 = 2MW 119881119899= 690 v 119891

119899= 60Hz 120596


119892= 85 119870

119889119905= 10383 times 10

8 119861119889119905

=

10383 times 106 ℎ = 60m 119877 = 3056m 119869

119903= 87 times 10

6 kgm2119869119892= 150 kgm2 119872

119905= 250 times 10

3 kg 119870119905= 555 times 10

6Nm119861119905= 298 times 10



119904= 00069314 pu

119877119903= 000906 pu 119871

119897119904= 008083 pu 119871

119897119903= 009934 pu

119871119898

= 329 pu 119881119889119888nom = 1200 v 119862 = 10000 times 10

minus6 F119877119892= 00015 pu 119871

119892= 015 pu







3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









3 2 02 005f 2 348 74 03 04f 3 3 3 025 01f 4 235 41 15 06f 5 3 1 02 02f 6 3 2 01 01f 7 79 11 01 03f 8 245 39 05 035



References

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Robust Fault Detection of Wind Energy ...downloads.hindawi.com/journals/cin/2014/580972.pdf · Robust Fault Detection of Wind Energy Conversion Systems Based on Dynamic