Fault-Tolerant Control of a Blade-pitch WindTurbine With Inverter-fed Generator

V. Lesic, M. Vasak, N. PericFaculty of Electrical Engineering

and ComputingUniversity of Zagreb

Zagreb, Croatiae-mail: vinko.lesic@fer.hr

T. WolbankFaculty of Electrical Engineering

and Information TechnologyVienna University of Technology

Vienna, Austria

G. JoksimovicFaculty of Electrical Engineering

University of MontenegroPodgorica, Montenegro

Abstract—A fact is that wind energy is both green andexpensive energy. In order to increase its economic competence,wind turbine faults should be reduced and prevented. In windturbines faults most commonly occur in the gearbox and in thegenerator system components like power converter or generatorelectromechanical parts. This paper proposes a fault-tolerantcontrol strategy for variable-speed variable-pitch wind turbinesin case of identified and characterized generator electromechan-ical faults like broken rotor bar or winding inter-turn fault. Inparticular we propose an upgrade of the torque control loop withflux-angle-based torque modulation. Usage of pitch controllerin the low wind speed region is also proposed to intentionallyreduce power capture in order to avoid or to postpone the systemfault development. Presented fault-tolerant control techniques aredeveloped considering their easy implementation and installationin available control systems of existing wind turbines to extendtheir life cycle and energy production. Simulation results for thecase of 700 kW direct-drive wind turbine and the identified statorwinding fault are presented.

I. INTRODUCTION

Due to global warming and climate changes, renewableenergy sources and green energy have considerable impacton today’s economy. Wind energy is the fastest-growingrenewable energy source. Compared however with fossil fuelbased power systems, wind energy is considered to be a lowpower quality unreliable source with low conversion efficiency,which results in an expensive energy system. Therefore, themain goal is to develop effective and efficient renewableenergy systems and to achieve minimization of the cost andmaintenance of the corresponding installation at the same time.

To keep the efficiency of energy conversion processes inwind turbines at or near their optimum values all systemcomponents have to be continuously monitored. If there issome kind of fault detected in the system, wind turbinestoday have a safety protocol which rotates its blades at 90◦

pitch angle and halts the turbine rotation by reducing theaerodynamic torque to zero and behaving as an aerodynamicbreak. Energy production therefore also drops to zero.

Many of these faults can be detected through a monitoringsystem long before they become fully developed and triggerthe shut-down protocol. Once noticed, the development of thefault should be slowed down by a fault-tolerant control system

that extends the life and operation time of expensive turbinecomponents and sustains the energy production.

Focus of this paper is, therefore, to research and developa fault-tolerant extension of the wind turbine control systemfor the case of generator electromechanical faults, which arebesides gearbox and power converters faults the most commonin wind turbine systems [1]. In case of identified faults, itadapts control actions through a fast control loop for flux-angle-based modulation of the generator torque, and througha slow control loop that ensures the generator placement at apoint of its speed-torque plane where it is possible to:

• enable the fast loop to perform correctly,• protect the generator and other wind turbine components

by stopping the fault further development,• keep the electrical energy production optimal under emer-

gency circumstances.

This paper is organized as follows. Wind turbine electricalsubsystem with different generator types is described in Sec-tion II. Some of the basic control strategies for a variable-speedvariable-pitch wind turbine are presented in Section III alongwith its normal operating maps. In Section IV, a fault-tolerantapproach and control algorithm is proposed and described toenable wind turbine operation in emergency state. Section Vprovides MATLAB/Simulink simulation results obtained withthe proposed fault-tolerant control startegy.

II. ELECTRICAL SUBSYSTEM

Wind turbine in principle consists of a three-blade aerody-namic system mounted on a hub, of a nacelle and of a tower.Inside the nacelle there is a drivetrain with optional gearboxand electrical subsystem with a generator and an electronicconverter. There are several types of generators used in windturbines: doubly-fed induction generator (DFIG) with a woundrotor connected to the grid through slip rings and electronicconverter (EC), squirrel-cage induction generator (SCIG) withan EC connected to the stator (Fig. 1) and a direct-drivesynchronous generator (SG) coupled to the grid through an ECand with rotor slip-rings for the excitation voltage. A lot ofeffort is currently put into developing large-scale synchronousgenerators with permanent magnets.

978-1-4244-9311-1/11/$26.00 ©2011 IEEE 2097

1 : ns

SCIG

DC

AC

AC

DC

<

<

<

Fig. 1. Stator-controlled squirrel cage induction generator.

Fault-tolerant control proposed in this paper can be appliedto any of listed wind turbine electrical subsystems, assumingthat the generator tracks the given torque reference with certaindynamics. In the following we thus consider the generatortorque tracking system as a first-order lag system.

Every type of generator has its own way of speed controland it can be used to shift operating points in the generatorx-axis of speed-torque plane. By using pitch control of a windturbine aerodynamic torque can be also displaced in the y-axis.This gives the control system the ability to move the operatingpoint with two degrees of freedom in the speed-torque plane.

III. CONTROL OBJECTIVES

Taking into consideration both physical and economic con-straints, the optimum point to which the wind power capturewill rise is chosen, which determines the wind turbine ratedpower (full line in Figure 2). Thus, operating map of theturbine is parted into a low wind speed region (region I), whereall the available wind power is fully captured and high windspeed region (region II) where the power output is maintainedconstant while reducing the aerodynamic torque to the ratedvalue and keeping generator speed at the rated value.

The ability of a wind turbine to capture wind energy isexpressed through a power coefficient CP which is defined asthe ratio of extracted power Pr to wind power PV :

CP =PrPV

. (1)

The maximum value of CP , known as Betz limit, is CPmax =1627 = 0.593. It defines the maximum theoretical capability ofwind power capture. The real power coefficient of moderncommercial wind turbines reaches values of about 0.48 [2].Power coefficient data is usually given as a function of thetip-speed-ratio λ and pitch angle β (Fig. 3). Turbine powerand torque are given by [3]

Vm i n Vm axVN

V (m / s)

Pow

er

PN

I I I

PNB

VBmaxVNB

Fig. 2. Ideal power curve with maximum PN and power curve due todeveloped fault with maximum PNB .

CPmax

30

150

0.5

β λ

0

0

a)

30

15

0

0.08

0

0β λ

b)

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.02

0.04

0.06

0.08

λ

λoptλBopt

CP max

CPB max

CP

CQ

CP

CQ

CQB

CPB

c)

Fig. 3. Power a) and torque b) coefficients for an exemplary 700kW variable-pitch turbine. Fig. c) is for optimal β0 in low wind speed region (CP , CQ)and for β = 10◦ (CPB , CQB).

Pr = CP (λ, β)PV =1

2ρR2πCP (λ, β)V 3, (2)

Tr =Prω

=1

2ρR3πCQ(λ, β)V 2, (3)

where CQ = CP /λ, ρ, R, V and ω are torque coefficient,air density, radius of aerodynamic disk, wind speed and theangular speed of blades, respectively, and λ = ωR

V .

A. Variable-speed control

Since the goal is to maximize the output power in low windspeed region, wind turbine must operate in the area wherethe power coefficient CP is at its maximum value (or nearit). This is achieved by maintaining λ and β on the valuesthat ensure CP = CPmax [2]-[6], see Fig. 3. To achieve theoperating point in which λ is optimal, the generator torqueand consequently the aerodynamic torque is determined by

Tgref =1

2λ3optn3s

ρπR5CPmaxω2g = Kλω

2g , (4)

where ns is the gearbox ratio. This way the wind turbineoperating points in low wind speed region are located at themaximum output power curve, called CPmax locus (BC pathon Fig. 5). This Tgref = Kλω

2g torque controller (Fig. 4) can

be easily realized using a simple look-up table.

B. Pitch control

Above designated rated wind speed, available wind poweris higher than the generator rated power and it rises rapidly

2098

ωref+-

ω

ω

βref β

Tgref Tg

PITCH servo& controller

SPEEDcontroller

TORQUEcontroller

GENERATOR & INVERTER

WINDWIND

TURBINEω

Fig. 4. Control system of a variable-speed variable-pitch wind turbine.

along with the wind speed (see (2)). Therefore, the task ofthe control system is to maintain output power of the windturbine constant. It can be done by reducing the aerodynamictorque and angular speed of blades by rotating them along theirlongitudinal axis (pitching). Consequently, power capturedfrom the wind is reduced.

Control system (Fig. 4) is usually designed in a cascadestructure with inner loop representing the servo drive positioncontrol of blades to the reference pitch angle βref defined bythe outer speed control loop. Outer loop controls the rotationalspeed of the wind turbine and sets it to the reference (rated)value. A PI or proportional-integral-derivative (PID) controllerwith gain-scheduling technique is often satisfactory for pitchcontrol.

C. Switching between torque and pitch control

Following the CPmax locus curve, wind turbine usuallyreaches its rated angular speed before it reaches its ratedtorque. It is then desirable to increase the torque and powerwithout any further speed increase. This is achieved by im-proving the torque control loop with a closed-loop controllerthat maintains the torque on its rated value (A1BC1D charac-teristic in Fig. 5). Usually smooth transition between the torquecontrol and pitch control operating regimes of the wind turbineis enforced by deviating from the optimal power curve onedges of the low wind speed region [4], characteristic ABCDin Fig. 5.

IV. FAULT-TOLERANT CONTROL

In previous sections some of the most common and reliablewind turbine control strategies are described. This sectionextends them to propose a fault-tolerant control approachdesigned to protect wind turbine components by disablinggenerator fault further development and to keep energy produc-tion optimal in emergency state. Common faults of an electricmachine are stator winding inter-turn short circuit, rotor bardefect in case of squirrel-cage induction machines and rotoreccentricity. These faults may lead to overheating or breakingof the defected component and thus possibly to a catastrophicfault. Consequently, it triggers the safety procedure and resultsin a wind turbine shut-down. Whole repair process requiresimmense amounts of money and the situation is even worsefor off-shore wind turbines. So, from this aspect, it is an

A A1

B

C1

C

4 m/s

6 m/s

8 m/s

10 m/s

12 m/s

14 m/s

16 m/s18 m/s

Increasingpitch

CPmax locus

Generator speed

Gen

erat

or to

rque

Torque characteristics for different wind speeds

D

Fig. 5. Control strategy of a variable-speed wind turbine [4].

interesting idea to reduce voltage or current stress on thefaulty part of the generator as it operates and to anticipatesuch fault-tolerant behavior in overall torque-speed control ofthe turbine. This way, the fault development will be evadedor postponed while at the same time it will be possible tooptimize the energy production in the non-healthy generatorstate. This increases wind turbine’s total energy output andconsequently its economic value.

In case of a machine fault (like damaged rotor bar orstator winding fault), magnetic flux of the machine only ona small part of its path as it moves along the circumferenceaffects the damaged component. That part of the magneticflux path is denoted with ∆θ = θ2 − θ1, see Fig. 6. Ourprimary goal is to reduce the electrical stress reflected throughthe generator torque in that angle span to the maximumallowed safety value Tgf . The value Tgf is determined basedon fault identification through machine fault monitoring andcharacterization techniques, together with flux angles θ1 andθ2 [7]. For the case of identified rotor bar damage a faultidentification procedure directly outputs the safety torque valueTgf together with the location (values θ1 and θ2) in therotor magnetic flux frame to reduce mechanical stress on thedamaged rotor bar. For the case of identified stator windinginter-turn fault, a fault identification procedure localizes thedamaged part in the stator magnetic flux frame and outputsthe maximum allowed machine flux time derivative on thedamaged part which can be transferred to the maximum safetytorque allowed with respect to the generator speed.

Instead of torque reduction in the whole rotational period asa reaction to the fault, a fast control loop is proposed to reducetorque only in the ∆θ section of the flux rotation path. Flux inthe air-gap, and consequently torque, is therefore modulated,based on the machine flux angular position with respect to the

θoff θ1 θ2 θonπ

Flux linkage angle (rad)

Gen

erat

or to

rque

(N

m)

Δθ

Tg_nonf

Tgf

Fig. 6. Torque modulation due to a fault condition.

2099

θ* θ1 θ2

Gen

erat

or to

rque

(N

m)

π

Δθ

Flux linkage angle (rad)

Tg*

Tgf

Fig. 7. Torque modulation due to a fault condition when Tg nonf cannotbe restored.

damaged part. In case of e.g. induction generators, this methodis applied using a field-oriented control (FOC) technique.

Torque modulation is shown in Fig. 6. When the flux inangle θ approaches the angle span ∆θ, the torque is reduced tothe maximum allowed value Tgf defined with a fault conditionand, possibly, current generator speed. After the flux passes it,torque is restored to the right selected value Tg nonf . The valueof Tg nonf is determined such that the average machine torqueis maintained on the optimal level, taking into account themachine constraints. Procedure is then periodically executed,with electrical angle period equal π, since the flux influencesthe faulty part with its north and south pole in each turn. Due tothe finite bandwidth of the torque control loop, it is necessaryto start reducing the torque prior to reaching the flux angleθ1, while the torque is restored to the value Tg nonf at theelectrical angle θon after passing θ2.

Torque transitions between steady-state operating areas aresimplified and presented as linear characteristics that corre-spond to maximum available torque decrease/increase ratedetermined by maximum possible currents decrease/increaserates, i.e. by the power converter DC link constraints. Con-sidering more realistic torque changes which would be amix of linear and exponential functions can be also handledbut is in the following presentation omitted to facilitate themathematical treatment of the proposed method. Fig. 6 alsoshows that reducing the torque takes less time than restoring it.This is due to the back-electromotive force which opposes thecurrent and thereby aggravates torque restoration. Availabletorque rates for generator torque decrease and increase aredenoted with Tg−(ωg) and Tg+(ωg), respectively.

In the following we derive the fault-tolerant control strategyfor the synchronous machine stator fault due to stator windinginter-turn fault, but similar strategy can be also derived for afaulty asynchronous machine, either for the rotor bar defector for the inter-turn winding fault on the stator. For easiermathematical treatment we assume constant value of Tgf , al-though for this type of fault there exists an inverse-proportionalrelation between Tgf and electrical speed. Since the generatorelectrical speed in case of synchronous machine is defined as

ωe = pωg =∆θ

∆t(5)

and duration of the torque decrease transient as

∆toff =Tg nonf − Tgf

Tg−(ωg), (6)

by combining these two relations the following is obtained:

θ1 − θoffpωg

=Tg nonf − Tgf

Tg−(ωg). (7)

Finally, θoff can be derived from (7):

θoff = θ1 − pωgTg nonf − Tgf

Tg−(ωg). (8)

In the same way, θon is obtained as

θon = θ2 + pωgTg nonf − Tgf

Tg+(ωg). (9)

If the torque value Tg nonf can be restored at some angle,then

θon − θoff 6 π. (10)

Putting (8) and (9) into (10), the following is obtained forcondition (10):

pωg(Tg nonf−Tgf )

[1

Tg+(ωg)+

1

Tg−(ωg)

]6 π−∆θ. (11)

Because of large inertia of the whole drivetrain, generatorand blade system, these torque oscillations are barely notice-able on the speed transient, such that the speed is affected bythe mean torque value:

Tav =1

π

π∫0

Tgdθ. (12)

Mean value of the generator torque from Fig. 6 is then givenby

Tav = Tg nonfπ − (θon − θoff )

π+Tgf + Tg nonf

2·

·θ1 − θoffπ

+ Tgfθ2 − θ1π

+Tgf + Tg nonf

2

θon − θ2π

. (13)

Equation (10) (or (11)) is not satisfied if the speed ωg islarge enough (or if there is a large rotor path under faultinfluence). In that case the torque modulation is given withFig. 7 and peak torque T ∗

g is attained at angle θ∗:

θ2 − π + pωgT ∗g − Tgf

Tg+(ωg)= θ1 − pωg

T ∗g − Tgf

Tg−(ωg). (14)

Values T ∗g and θ∗ can be expressed as:

T ∗g = Tgf +

π − ∆θ

pωg

(1

Tg+(ωg)+ 1

Tg−(ωg)

) , (15)

θ∗ = θ1 −π − ∆θ

1 +Tg−(ωg)

Tg+(ωg)

. (16)

Mean value of the generator torque from Fig. 7 (i.e. in casewhen (10) is not satisfied) is now given by

Tav = Tgfθ2 − θ1π

+Tgf + T ∗

g

2

θ∗ + π − θ2π

+

+Tgf + T ∗

g

2

θ1 − θ∗

π. (17)

2100

Concludingly, if (11) is fulfilled, the resulting average torqueis given with (13); if not, then the resulting average torqueis given with (17). On the boundary, i.e. for equality in(10) or (11), both (13) and (17) give the same torque Tav ,such that Tav(ωg) is continuous. The maximum availabletorque Tg nonf is the nominal generator torque Tgn. ReplacingTg nonf in (13) with the nominal generator torque Tgn givesthe maximum available average torque under fault character-ized with ∆θ and Tgf . Replacing Tg nonf with Tgn in (11)will result in speed ω∗

g up to which it is possible to restore thenominal torque in the generator in case of the considered fault.Above ω∗

g , (17) holds for the average torque. Fig. 8 showsan exemplary graph of available speed-torque points undermachine fault, where the upper limit is based on relations (11),(13) and (17) with Tg nonf = Tgn. Dashed area denotes allavailable average generator torque values that can be achievedfor certain generator speed.

From Fig. 8 it follows that up to the speed ωg1 it is possibleto control the wind turbine in the faulty case without sacri-ficing power production. However, from that speed onwardsit will be necessary to use blades pitching in order to limitthe aerodynamic torque (e.g., CPB and CQB in Fig. 3) and tokeep the power production below optimal in order to suppressthe fault from spreading. The speed control loop is modifiedsuch that instead of reference ωn the reference ω1 (in caseof gearbox, ω1 = ωg1/ns) is selected. This activates pitchcontrol once the right edge of the feasible-under-fault optimaltorque characteristics is reached. The optimal power point onTav(ωg), which is always on the upper edge of the dashed area,may deviate from this point and thus further improvementsin power production outside the point (ωg1, Tav (ωg1)) maybe obtained by using maximum power tracking control alongthe curve of maximum Tav in the speed span [ωg1, ωgn]. Theinterventions in classical wind turbine control that ensure fault-tolerant control are given in Fig. 9. Algorithms of the slow andthe fast fault-tolerant control loops are given in the sequel.

1) Fault-tolerant control algorithm, slow loop:

I. Compute Tg nonf from (8), (9) and (13) such thatTav(ωg) = T

′

gref ; if Tg nonf > Tgn, set Tg nonf = Tgn;

0 10 20 300

50

100

150

200

250Tgn

Tgf

Tav

Tgopt

ωg1ωg*

Speed (rpm)

Ge

ne

rato

r to

rqu

e (

kNm

) Healthy machine

Faulty machine

ωgn

Fig. 8. Available torque-speed generator operating points under fault condi-tion (shaded area). Full line is the achievable part of the wind turbine torque-speed curve under faulty condition. Dash-dot line is the healthy machine curve.

TORQUEcontroller

GENERATOR & INVERTER

WIND

FAULT-TOLERANT control

ωref

ω

ω

β

Tg

WINDTURBINE

ω

Tgref'

βref PITCH servo& controller

SPEEDcontroller

ωg

Tgref

θ

+-

FASTloop

SLOWloop

Fault detection and characterization

Tgref'

ωg

Tg_nonfTgref

TgfTgf θ1,θ2

θ

ωref

a)

b)

θstart

θend

Fig. 9. a) Control system of wind turbine with fault-tolerant control strategy.b) Enlarged fault-tolerant control block.

II. If (11) is fulfilled set θstart = θoff mod π else computeθ∗ from (16) and set θstart = θ∗ mod π and Tg nonf =Tgn; set θend = θ2;

III. Compute ωg1 as a speed coordinate of the intersectionpoint of Tav(ωg) and of the normal wind turbine torquecontroller characteristics, compute ω1 = ωg1/ns and setωref = ω1.

2) Fault-tolerant control algorithm, fast loop:I. On the positive edge of logical condition θ > θend setTgref = Tg nonf . On the positive edge of the logicalcondition θ > θstart set Tgref = Tgf .

V. SIMULATION RESULTS

This section provides simulation results for a 700 kWMATLAB/Simulink variable-speed variable-pitch wind turbinemodel. The direct-drive 60-pole synchronous generator torquecontrol system is modelled as a first-order lag system with timeconstant τgen = 0.02 s. Turbine parameters are: CPmax =0.4745, R = 25 m, λopt = 7.4, ωn = 29 rpm and Tgn = 230.5kNm. Fault is simulated between flux angles θ1 = π

2 andθ2 = π

2 + π5 , with Tgf = 0.5 Tgn and presented fault-tolerant

control algorithm is applied. Results in Fig. 10 show how thewind turbine behaves in healthy and faulty condition for alinear change of wind speed through the entire wind turbineoperating area.

Fig. 11 shows the fault-tolerant control system reaction tothe fault that is identified in t = 35 s for the case when theaverage generator torque under fault Tav(ωg) can be equal tothe required torque T

′

gref for the incurred speed ωg , i.e. theoptimum speed-torque point is in the dashed area of Fig. 8 forthe occurred fault.

Fig. 12 shows the fault-tolerant control system reaction tothe fault identified in t = 35 s for the case when the incurredhealthy machine speed-torque operating point falls out of the

2101

0 50 100 150 200 250 300 350 4000

10

20

0 50 100 150 200 250 300 350 4000

400

800healthy

0 50 100 150 200 250 300 350 400

0

10

20 healthy

Power (kW)

Time (s)

Wind speed (m/s)

Time (s)Pitch angle (degrees)

Time (s)

Fig. 10. Wind turbine output power and pitch angle for healthy and faultyconditions.

34.8 34.9 35 35.1 35.2

115

120

125

34.8 34.9 35 35.1 35.2

22.6

22.62

Rotor speed (rpm)

Time (s)

Generator torque (kNm)

Time (s)

Fig. 11. Generator torque modulation and wind turbine speed when theoperating point of healthy machine is feasible under fault. Fault occurs at35 s.

dashed area of Fig. 8. In this case blade pitching is used inthe faulty condition to bring the speed-torque operating pointinto (ωg1, Tav(ωg1)).

VI. CONCLUSIONS

In this paper we propose a fault-tolerant control schemefor blade-pitch wind turbines with an inverter-fed generator.We focus on generator faults that can be well characterizedwith machine flux path areas where the generator torqueshould be limited to prevent fault propagation and with themaximum safety torque value in that path areas. We propose asimple extension of the classical two-loop control structure ofblade-pitch wind turbines which ensures that the fault is fullyrespected in operation and that power delivery under fault isdeteriorated as less as possible compared to healthy machineconditions.

ACKNOWLEDGEMENT

This work has been supported by the European Commissionand the Republic of Croatia under grant FP7-SEE-ERA.netPLUS ERA 80/01.

34.8 34.85 34.9 34.95 35 35.05 35.1 35.15 35.2100

150

200

250

20 25 30 35 40 45 5024

26

28

30Rotor speed (rpm)

Time (s)

Generator torque (kNm)

Time (s)

20 25 30 35 40 45 50100

150

200

250

Fig. 12. Generator torque modulation and wind turbine speed when theoperating point of healthy machine is not feasible under fault. Fault occurs at35 s.

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