International Conference on Renewable Energies and Power Quality (ICREPQ’16)

Madrid (Spain), 4th to 6th May, 2016

Renewable Energy and Power Quality Journal (RE&PQJ)

ISSN 2172-038 X, No.14 May 2016

Variable structure strategy to avoid torque control saturationof a wind turbine in the presence of faults

C. Tutiven, Y. Vidal, L. Acho and J. Rodellar

Universitat Politecnica de Catalunya,Applied Mathematics-III (MA-3) Department, CoDAlab,

Comte d’Urgell, 187, 08036, Barcelona, Spain.Phone number:+0034934137309, e-mail:christian.tutiven@upc.edu, yolanda.vidal@upc.edu

leonardo.acho@upc.edu, jose.rodellar@upc.edu

Abstract. Every physical actuator is subject to saturation. It hasbeen well recognized that, when the actuator saturates, theper-formance of the closed-loop system (designed without consideringactuator saturation) may seriously deteriorate. In extreme cases, thesystem stability may even be lost. This paper proposes an avoidsaturation strategy for the torque controller of a wind turbine bench-mark model. The simulation results show that the proposed strategyhas a clear added value with respect to the baseline controller (well-accepted industrial controller) in the presence of faults.Anotheradvantage of the contributed method is that conservative boundsfor the actuator torque can be fixed in order to extend the servicelife of the wind turbine.

Key wordswind turbine, torque control, saturation, faults, fault de-

tection

1. IntroductionWind turbines (WT) have become an important source

of renewable power generation in the last years, with aconcurrent growth in demand for the expertise of engineersand researchers in the wind energy field. There are still manyunsolved challenges in expanding wind power, and there arenumerous open problems of interest to systems and controlresearchers. A major issue with wind turbines, specially thoselocated offshore, is the relatively high cost of maintenance[1]. Since the replacement of main components of a WT is adifficult and costly affair, improved maintenance procedurescan lead to essential cost reductions. Autonomous onlinefault detection algorithms allow early warnings of defectsto prevent major component failures [2]. Furthermore, sideeffects on other components can be reduced significantly.Many faults can be detected while the defective componentis still operational [2]. Thus necessary repair actions canbe planned in time and need not be taken immediately andthis fact is of special importance for off-shore plants wherebad conditions can prevent any repair actions. Therefore theimplementation of fault detection (FD) systems is crucial.

The past few years have seen a rapid growth in interestin wind turbine FD, [3]. So far, revising the literature,methods ranging from Kalman filters [4], observers [5],parity equations [6], dynamic weighting ensembles [7] and

fuzzy modeling and identification methods [8] have alreadybeen suggested as possible model-based techniques for faultdiagnosis of wind turbines.

For instance, in [9] and [10], besides of providing faultestimates, an active fault tolerant control approach is pro-posed. In [11] FD is based on the use of interval observersand unknown but bounded description of the noise.

In the presence of faults, if the torque controller requiresexcessive actuator action the closed-loop stability may belost due to the torque saturation. The main possible effectsofactuator saturation on a control system are poor performanceand/or instability to large disturbances [12]. As a result,their stability cannot be guaranteed. Saturation mitigationtechniques are using to avoid actuators saturation. For ex-ample, reference [13] presents the anti-windup technique.Direct approach to dealing with actuator saturation in windturbines are used in [14] where an anti-windup controller tominimize deH∞ norm of the closed-loop system is designed.The design of a compensation method, which is based onvariable structure systems to avoid both amplitude and rateinput saturation by means of an auxiliary loop is presentedin [15].

In this work, we propose a strategy to avoid torquesaturation and the consequent undesired effects, guaranteeingthe closed-loop operation of the control system. The pro-posed methodology is based on variable structure conceptsand reference signal conditioning ideas. Our contribution:anticipatory activation, in contrast to immediate activation.

The structure of the paper is the following. In Section2 the WT benchmark is recalled. In Section 3 the faulttolerant control used in the simulations is presented. Section4 presents the design of the proposed avoid saturationstrategy (ASS). The simulation results obtained with theproposed approach applied to the advanced WT benchmarkare summarized in Section 5. Concluding remarks are givenin Section 6.

2. Reference wind turbineA complete description of the wind turbine model of the

FDI/FTC benchmark can be found in [3]. Hereafter, only

the generator-converter actuator model and the pitch actuatormodel will be shown, as the faults acting in the system affectthose subsystems.

The generator and converter dynamics can be modeled bya first-order transfer function [3], which is given by:

τg(s)

τg,r(s)=

αgc

s+ αgc

,

where τg is the real generator torque,τg,r is the torquereference to the generator (given by the controller), wherewe setαgc = 50 [16]. Additionally, the power produced bythe generator,Pe(t), can be modeled using [3]:

Pe(t) = ηgωg(t)τg(t),

where ηg is the efficiency of the generator andωg is thegenerator speed. In the numerical experiments,ηg = 0.98is used [3]. The hydraulic pitch system consists of threeidentical pitch actuators, which are modeled as a lineardifferential equation with time-dependent variables, actualpitch angleβi(t) and its reference angleβri(t). In principle,it is a piston servo-system, which can be expressed as asecond-order differential system [3]:

βi(s)

βri(s)=

ω2n

s2 + 2ζωns+ ω2n

, i = 1, 2, 3, (1)

whereωn andξ are the natural frequency and the dampingratio, respectively. For the fault-free case, the parametersξ =0.6 andωn = 11.11 rad/s are utilized. [3].

A. Baseline control strategy

This paper deals with the full load region of operation.The baseline torque and pitch controllers specifications aredescribed in the technical report [16] by the U.S. Departmentof Energy’s National Renewable Energy Laboratory (NREL).Here a brief review of these controllers is given as itsperformance will be used for comparison with the proposedtechniques.

In the full load region, the torque controller maintainsconstant the generator power; thus, the generator torque isinversely proportional to the filtered generator speed or,

τg,r(t) =Pref(t)

ωg(t), (2)

where Pref is the reference power (normally the nominalvalue is used) andωg is the filtered generator speed (see[16]). This controller will be referred to as the baselinetorque controller. As the generator may not be able tosupply the desired electromechanic torque depending onthe operating conditions and in the case of overshooting,the torque controller is saturated to a maximum of47.40KNm and a maximum rate limit of15 KNm/s; see [16].Therefore, if the torque controller required a fast and/orexcessive actuator action the closed-loop operation couldbelost because of these constraints, leading to large and longovershoots caused by windup and other undesired effects, oreven the control system instability.

To assist the torque controller with regulating the WTelectric power output, while avoiding significant loads andmaintaining the rotor speed within acceptable limits, a col-lective pitch controller is added to the rotor speed trackingerror. The collective blade pitch gain scheduling PI-controller(GSPI) is one of the first well-documented controllers, andit is used in the literature as a baseline controller to comparethe obtained results [17]. This controller was originallydeveloped by Jonkman for the standard land-based 5-MWturbine [16]. The GSPI control has the filtered generatorspeed,ωg(t), as the input and the pitch servo set-point,βri(t), as the output. That is,

βri(t)=Kp(γ)(ωg(t)− ωg,r) +Ki(γ)

∫ t

0

(ωg(τ) − ωg,r)dτ,

Kp > 0, Ki > 0,(3)

where ωg,r is the nominal generator speed (usually thenominal value is used) and the scheduling parameterγ istaken to be the previously measured collective blade pitchangle. As the three pitch angles are measured, the collectivepitch angle is obtained by averaging the measurements ofall pitch angles. The pitch angle actuators generally presenthard constraints on their amplitude and their speed response.Because of this, a pitch limit saturation to a maximum of45◦ and a pitch rate saturation of8◦/s are implemented (see[16]) to avoid pitch actuator damage.

3. Fault-tolerant control

The fault tolerant control (FTC) law based on a controlplus disturbance estimator in the time discrete domain pro-posed in [18] is briefly recalled in this section. The controlobjective is the tracking of the reference signalβri(t) (givenby the baseline pitch controller; see Equation (3) and its cor-responding velocity, even in the case of pitch actuator fault.That is, the objective is to ensure the asymptotic convergenceof the tracking error vector to zero. To achieve the slidingmode, the control law with disturbance compensator [19] isas follows:

u[k] = −d[k] +(

cT b)

−1[cT

(

βri [k]

βri [k]

)

− cTAx[k] + qs[k]

− ηsgn(s[k])],(4)

d[k] = d[k − 1] + (cT b)−1g[s[k]− qs[k − 1]

+ ηsgn(s[k − 1])],(5)

where the notation [k] is used for these discrete time signals,and 0 ≤ q ≤ 1, 0 < g < 1, andη > 0 and beingd[k] thefault estimator or also called the disturbance estimator. In thenumerical simulations:q = g = 1/2 and η = 100. As canbe seen in Equation (4), the proposed discrete controller foractive FTC is dependent on a fault estimate,d[k], provided

by the fault diagnosis system. The error vector is defined as:

e[k] = (e1[k], e2[k])T= (βi[k]− βri [k], βi[k]− βri [k])

T ,(6)

ands[k] = cT e[k]. (7)

The pitch controller used by the FTC strategy is the baselineGSPI controller, see Section 2-A. On the other hand, the usedtorque controller is the chattering control proposed in [20],which is recalled here to be

τc(t) =−1

ωg(t)[τg,r(t)(aωg(t) + ˙ωg(t))− aPref(t)

+Kαsgn(Pe(t)− Pref(t))],

(8)

wherePref is the reference power andPe is the electricalpower considered here (only for the control design) to bedescribed as [21]

Pe(t) = τg,r(t)ωg(t), (9)

whereτg,r(t) is the torque control andωg(t) is the filteredgenerator speed. In the numerical simulations the valuesa = 1 andKα = 1.5 · 105 have been used and a first orderapproximation of ˙ωg(t) is computed. This torque controlleris saturated to a maximum of47.40 KNm and a maximumgenerator torque rate saturation of15 KNm/s, similarly tothe baseline one.

4. Design of the Avoid Saturation Strategy(ASS)

In the presence of faults, the torque controller might besaturated. This section describes the design of an avoid sat-uration strategy (ASS) based in a commutation law. Its mainobjective is to readjust the reference power (Pref) and thereference generator speed (ωg,r) to avoid saturation and theconsequent undesired effects, guaranteeing the closed-loopoperation of the control system. Control torque bounds areadded: the superior torque (τs) and the inferior torque (τi).These two values are chosen using the difference between themaximum mechanical torque (τmax) and the nominal torque(τn),

τdif = τmax− τn = 47.40KNm − 40.68KNm

= 6.72KNm,

andh =

τdif

a; a > 0. (10)

Different values ofa were tested and found that the ASShad better performance whena = 6, so h = 1.12KNm andthe proposed control bounds are:

τs = τn + h = 40.68KNm+1.12KNm = 41.80KNm, (11)

and

τi = τn − h = 40.68KNm− 1.12KNm = 39.55KNm. (12)

Fig. 1 illustrates the behavior of the ASS. When the controltorque (τg,r) is greater thanτs, the ASS commutesPref tothe minimum power (Pmin) and whenτg,r is lower thanτi, the ASS commutesPref to the maximum power (Pmax),otherwise,Pref is equal to the nominal power (Pn).

0

0

τmax

τs

τn

τi

Pref(MW)

Pmax

Pn

Pmin

τc(Nm)

t(s)

t(s)

Fig. 1. Avoid saturation strategy.

The value ofPmax and the value of the maximum generatorspeed (ωg,max) are established by using the simple rule ofthree to calculateωg,max,

τmax

τn=

ωg,max

ωg,n

; ωg,max = 143.22rads. (13)

With τmax andωg,max, we calculatePmax,

Pmax = τmaxωg,max; Pmax = 6.78MW. (14)

To calculate the value ofPmin and the value of theminimum generator speed (ωg,min), first we calculate thedifference betweenτn andτdif ,

τmin = τn − τdif = 33.95KNm. (15)

To calculateωg,min, we use again the rule of three,

τmin

τn=

ωg,min

ωg,n

; ωg,min = 102, 59rads. (16)

With τmin andωg,min, we calculatePmin,

Pmin = τminωg,min; Pmin = 3.48MW. (17)

So the ASS is responsible for performing the switching ofPref andωg,r, by the following implemented commutationlaw:

Pref(t) =

Pmax, if τg,r(t) < τi,

Pmin, if τg,r(t) > τs,

Pn, otherwise,

ωg,r(t) =

ωg,max, if τg,r(t) < τi,

ωg,min, if τg,r(t) > τs,

ωg,n, otherwise.

The block diagram of Fig. 2 shows the connectionsbetween the fault tolerant control (FTC) system presentedin [18], with the added ASS.

ASS

Torque Control

&

Generator

Pitch ControlFDI &

FTC

Rate Limiter

Saturator

Actuator

FAST

Filter

Rate LimiterSaturator

Pg(t)

τg,r(t)

u(t)

βi(t)

βi(t)

βi(t)

βi[k]

βi[k]

d[k]

βg,r [k]

u[k]βg,r(t)

ωg(t)

ωg(t)Pref(t)

ωg,r(t)

Fig. 2. Block diagram of the fault tolerant control with the avoid saturation strategy(FTC+ASS) closed loop system.

5. Simulation resultsThe results compare the performance of the contributed

FTC+ASS technique under different faulty scenarios withrespect to the baseline torque controller recalled in Section2-A. The wind turbine simulator software FAST is usedfor simulations. The results compare the performance of thecontributed FTC+ASS under different faulty scenarios withrespect to the baseline control under the same faults.

The response of the generator velocity and electrical powerare analyzed in terms of the normalized integral absoluteerror through the following performance indices:

Jω(t) =∫ t

0 |ωg(τ) − ωg,n|dτ ,

Jp(t) =∫ t

0 |Pg(τ) − Pn|dτ .

A. Offset in generator speed sensor (F1)

A faulty sensor can reduce turbine availability, especiallyif the sensor measurement is required for control. As dis-cussed in [22], sensor failures can be difficult to diagnose.

Here, an offset fault in the generator speed sensor isstudied. We selected an offset value of15% of ωg,n that isequal to18, 43 rad

s . This fault, (F1), is active all the time.

It can be seen from Fig. 3 that the system behavior(electrical power and generator speed) with the FTC+ASSis stable even when an offset fault exists in the generatorspeed sensor. On the other hand, the baseline system becomesunstable after a while when this type of fault exists.

As can be observed in Fig. 4 the proposed strategy avoidsoverloadingτg,r, protecting it from saturation and maintain-ing its values within the configured limits (τs andτi). Alsothe commutation of the nominal generator speed helps the

0 200 400 600 800

0

1000

2000

3000

4000

5000

6000

7000

8000

time (s)

Pe

(k

W)

Pn

Baseline

FTC+ASS

0 200 400 600 8000

500

1000

1500

2000

2500

time (s)

ωg (

rpm

)

ωg,n

BaselineFTC+ASS

Fig. 3. Generated power (top) and generator speed (bottom) in case ofoffset fault (F1).

0 200 400 600 800

0

10

20

30

40

time (s)

τc (

kN

·m)

τmax

τs

τi

Baseline

FTC+ASS

0 50 100 150 200 250 30038

39

40

41

42

43

44

45

time (s)

τc (

kN

·m)

Fig. 4. Torque control in case of offset fault (F1).

blades pitch angles not to saturate as shown in the Fig. 5.On the other hand, the baseline system becomes unstable,because of the saturation of torque and pitch controllers.

B. Pitch actuator faults

Blade pitch systems faults are studied as they have thehighest failure rate in WT [17]. Some types of fault (highair content in oil (F2), pump wear (F3), and hydraulicleakage (F4)) may change the dynamics of the pitch systemby varying the damping ratio (ζ) and natural frequencies(ωn) from their nominal values to their faulty values inEquation (1). The parameters for the pitch system underdifferent conditions are given in [3].

In the simulations, the faults are introduced only in thethird pitch actuator (thusβ1 and β2 are always fault-free)in the following way. From 0s to 100s, it is fault free (FF).From 100s a 101s, a fault due to high air content in oil (F2)is linearly introduced. From 101s a 201s, F2 is fully active.From 201s a 202s, F2 is linearly eliminated. From 202s to302s, it is fault free. From 302s a 322s, a fault due to pump

0 200 400 600 8000

10

20

30

40

time (s)

β 1 (de

g)

BaselineFTC+ASS

0 200 400 600 8000

10

20

30

40

time (s)

β 3 (de

g)

BaselineFTC+ASS

Fig. 5. Pitch angle variation ofβ1 (top) andβ3 (bottom) in case of offsetfault (F1).

wear (F3) is linearly introduced. From 322s a 422s, F3 isfully active. From 422s a 442s, F3 is linearly eliminated.From 442s to 542s, it is fault free. From 542s a 562s, a faultdue to hydraulic leakage (F4) is linearly introduced. From562s a 662s, F4 is fully active. From 662s a 682s, F4 islinearly eliminated. From 682s to 800s, it is fault free.

Fig. 6. Computation of the continuos residual signalr(t). Note that theSimulink R© dead zone block is used (start of dead zone value equal to 0and end of dead zone value equal to 2000.

The three types of faults are detected by the disturbanceestimatord given in Equation 5. To finally setup the faultdetection and isolation strategy, the proposed residual signalr(t), is computed as described in Fig. 6 and its results areshown in Fig. 7. This residual signal is close to zero whenthe system is fault free. On the other hand, it is significantlyaffected when a fault appears, and it allows to isolate thetype of fault (among the three studied pitch actuator faults).

It can be seen from Figures 8 (top) and 9 (top) that theFTC+ASS has a better performance of the electrical powerand generator speed regulation compared to the baselinecontrol. The performance indicesJp andJω corroborate thisstatement, see Fig. 8 (bottom) and 9 (bottom).

As can be observed in Fig. 10, the proposed strategy has abetter torque control performance than the baseline control,maintaining its values within the configured limits (τs andτi).

Fig. 11 (top) shows that the first pitch angle (β1), which

0 200 400 600 8000

0.5

1

1.5

2

x 104

time (s)

FTC+ASS

r

100 150 200 250 300 350 400 4500

100

200

300

400

500

time (s)

Fig. 7. Proposed residual signal in case of pitch actuator faults (F2, F3and F4).

0 200 400 600 800

4500

5000

5500

6000

time (s)P

e (

kW

)

Pn

Baseline

FTC+ASS

0 200 400 600 8000

2

4

6

8

10

12

14

16

x 104

time (s)

J P

BaselineFTC+ASS

Fig. 8. Generated power (top) andJp index (bottom) in case of pitchactuator faults (F2, F3 and F4).

is always fault-free, has a slightly different behavior withthe FTC+ASS than with the baseline control. This is dueto the fact that the fault is introduced in the third pitchactuator (β3) as can be seen in the Fig. 11 (bottom). Althoughhigher oscillations are present in the FTC+ASS, the pitchcontrol signal is regulated within the authorized variationdomain. That is, none of the variations exceed the mechanicallimitations of the pitch actuator.

6. ConclusionsAn avoid saturation strategy based on reference adaptation

ideas and variable structure concepts is proposed to avoid theamplitude saturation of the torque controller in a 5MW windturbine. The main objective is to reduce the actuator activityand avoid the instability of the system. On the other hand,the residual signal detects in short time the appearance ofthe faults in the pitch actuator. Moreover, according to theexperimental results, the overall closed-loop system is robustagainst the studied faults.

0 200 400 600 800

1000

1100

1200

1300

1400

1500

time (s)

ωg (

rpm

)

ωg,n

BaselineFTC+ASS

0 200 400 600 8000

1

2

3

4

5x 10

4

time (s)

J w

BaselineFTC+ASS

Fig. 9. Generator speed (top) andJω index (bottom) in case of pitchactuator faults (F2, F3 and F4).

0 200 400 600 800

0

10

20

30

40

time (s)

τc (

kN

·m)

τmax

τs

τi

Baseline

FTC+ASS

0 50 100 150 200 250 30034

36

38

40

42

44

46

48

time (s)

τc (

kN

·m)

Fig. 10. Torque control in case of pitch actuator faults (F2,F3 and F4).

AcknowledgmentsThis work has been partially funded by the Spanish

Ministry of Economy and Competitiveness through the re-search projects DPI2014-58427-C2-1-R, DPI2015-64170-R,and by the Catalonia Government through the researchproject 2014SGR859.

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β 1 (de

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BaselineFTC+ASS

0 200 400 600 8000

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