Fault-tolerant Control of Permanent Magnet SynchronousGenerator in Wind Turbines

Vinko Lešic, Mario VašakUniversity of Zagreb, Faculty of Electrical

Engineering and Computingvinko.lesic@fer.hr, mario.vasak@fer.hr

Goran Stojcic, Thomas M. Wolbank,Vienna University of Technology, Faculty of

Electrical Engineering and Information Technologygoran.stojcic@tuwien.ac.at,

thomas.wolbank@tuwien.ac.at

Abstract:Increase of wind turbine availability is one of the

main goals in wind energy research trends. The paperconcerns with avoiding wind turbine shut-down undergenerator stator insulation degradation. We propose afault-tolerant control that modulates the machine mag-netic flux and reallocates the electrical stress from faultyto healthy generator stator parts, and extracts the max-imum available power in the faulty operation under astrict condition of stopping further fault propagation. Thealgorithm is set for the case of 700 kW wind turbine withdirect-drive permanent magnet synchronous generatorbut can be applied for any other type of generator aswell. Proposed method is suitable for a wide rangeof generator operation and fault conditions, from earlystage of fault-development to inter-turn short circuit. Themethod is also conceived as a modular extension tothe conventional wind turbine control system. Simulationresults are obtained and possible wind turbine operatingarea under different stage of fault is mapped.

1. IntroductionIncrease by 18% in 2010 of direct-drive wind tur-

bine (WT) concepts and announcements of new 7-8MW WTs [1] makes it evident that permanent magnetsynchronous generator (PMSG) is the future trend inwind energy. However, some of the previous gearboxproblems will be transferred to the generator, whichalready has a fault frequency about 10 times greaterthan equivalent-power industrial machines [2]. Raisingconcerns for generator availability are to be expectedand a lot of effort is currently put into development ofnew diagnostic methods. Motivated by this we proposea fault-tolerant control (FTC) for generator electrome-chanical faults.

With the goal of increasing the total efficiency ofwind energy extraction and market competence, FTC forincrease of WT availability emerged as a promising areaof research. Different strategies are proposed, mostlybased on redundancies of sensors and electronic com-ponents, and control algorithm is used to evaluate thetrustworthiness of each [3]. Focus here is on generator

electromechanical faults, which are besides gearboxand power converters faults the most common in windturbine systems [2].

About 30% to 40% of electric machine faults arerelated to stator insulation [2], [4]–[7]. Some of the mostcommon causes are moisture in the insulation, windingoverheating or vibrations [8]. Modern voltage-sourceinverters also introduce additional voltage stress on theinter-turn insulation caused by the steep-fronted voltagesurge.

Built on available diagnostic methods, we isolate thefault and reallocate the generator stress such that thefault propagation is stopped and the generator is operat-ing safely in the fault presence. Specifically, we considerstator winding faults such as insulation degradationthat will evidently cause inter-turn (within the samephase), phase-to-phase (between two different phases)or phase-to-ground short circuits. Researches in publicdomain [4]–[7] show that emergence of this kind of faultsoccurs gradually and can be detected on-line beforethey are fully developed to catastrophic proportions.This gives an opportunity for an autonomous reactionof the control algorithm to protect the generator andenable the safe operation under occurred fault until thescheduled maintenance takes place. The FTC is usedto modulate generator electromechanical variables ina way that the main cause of rapid fault spreadingis removed but also that maximum possible powerproduction in the faulty conditions is maintained.

In our recent work, we proposed FTC of squirrel-cage induction generator for rotor-cage defect [9] andstator inter-turn short circuit [10]. Here we make acontribution to the PMSG with specific distinctions ofsynchronous operation and permanent magnetic fluxbut also extend the FTC possibilities for early insulationdegradation stage of fault development. The methodcan be applied to any variable-speed variable-pitch windturbine, regardless of the generator type.

The paper presents conventional control algorithmsof wind turbine (Section 2.) and field-oriented con-trol (FOC) of PMSG (Section 3.). Fault-tolerant con-trol theory, developed algorithm, achievable PMSG andWT operation and an extension of conventional con-

trol structure are elaborated in Section 4. Simulationresults are presented in Section 5., performed on a2 MW PMSG with power and torque scaled to matchthe 700 kW direct-drive WT aerodynamics. Finally, theSection 6. provides conclusions.

2. Wind turbine control systemModern variable-speed variable-pitch wind turbines

operate in two different regions. One is so-called low-wind-speed region where torque control loop adjusts thegenerator torque to achieve the desired wind turbinerotational speed in order to make the power productionoptimal. The other region is high-wind-speed regionwhere the power output is maintained constant whilereducing the aerodynamic torque and keeping generatorspeed at the rated value. For this task a blade-pitchcontrol loop is responsible. Both control loops are shownin Fig. 1

The ability of a wind turbine to capture wind energyis expressed through a power coefficient CP which isdefined as the ratio of extracted power Pt to wind powerPV :

CP =PtPV

. (1)

The maximum value of CP , known as Betz limit, isCPmax = 16

27 = 0.593. It defines the maximum theo-retical capability of wind power capture. The real powercoefficient of modern commercial wind turbines reachesvalues of about 0.48 [11]. Power coefficient data isusually given as a function of the tip-speed-ratio λ andpitch angle β (Fig. 2). Turbine power and torque aregiven by [12]:

Pt = CP (λ, β)PV =1

2ρR2πCP (λ, β)V 3, (2)

Tt =Ptω

=1

2ρR3πCQ(λ, β)V 2, (3)

where CQ = CP /λ, ρ, R, V and ω are torque coefficient,air density, radius of the aerodynamic disk of a wind

TORQUEcontroller

GENERATOR & INVERTER

WIND

PITCH servo& controller

SPEEDcontroller

+-

Tg

*ω β*β

FOC +

Figure 1: Control system of a variable-speed variable-pitch wind turbine.

CPmax

30

150

0.5

β λ

0

0

a)

30

15

0

0.08

0

0β λ

b)

Figure 2: Power a) and torque b) coefficients for anexemplary 700 kW variable-pitch turbine.

turbine, wind speed and the angular speed of blades,respectively, and λ = ωR

V .Since the goal is to maximise the output power in

low-wind-speed region, wind turbine must operate suchthat the power coefficient CP is at its maximum value.This is achieved by maintaining λ = λopt and β = β0on values that ensure CP = CPmax. Therefore thegenerator torque and consequently the aerodynamictorque is determined by:

T ∗g =1

2λ3optρπR5CPmaxω

2 = Kλω2. (4)

Uppercase ’*’ denotes reference values. This way thewind turbine operating points in low wind speed regionare located at the maximum output power curve, calledCPmax locus. For more information about wind turbinemodeling and control system design see [11], [12].

3. Generator model and controlCommon approach in modeling and control of perma-

nent magnet synchronous machine is to use the math-ematical model represented in a two-phase (d,q) coor-dinate system that rotates with supply voltage speed ωeand is aligned with d-axis permanent magnet rotor flux(rotor flux vector ψr is set to constant ψr). The generalmodel is described with:

usd + ∆usd = Rsisd + Lsddisddt

, (5)

usq + ∆usq = Rsisq + Lsqdisqdt

. (6)

Variables usd,q are stator phase voltages in (d,q) coor-dinate system, isd,q are stator phase currents, Lsd andLsq are stator inductances in d and q axes. For the caseof non-salient machine (magnets are attached to therotor exterior), two inductances are equal, Lsd = Lsq.Parameter Rs is the stator resistance. Voltages ∆usdand ∆usq are called decoupling or correction voltages:

∆usd = Lsqωeisq, (7)

∆usq = −Lsdωeisd − ψrωe, (8)

which ensure that the voltage value in one axis is not af-fected by the voltage in other. The rotor flux ψr is createdby permanent magnets and, for the purpose of controllerdesign, it is commonly assumed to be constant (in fact

it is dependent on the magnet temperature). The fluxperceived by stator is dependent on currents that flowthrough stator windings:

ψsd = Lsdisd + ψr, (9)

ψsq = Lsqisq, (10)

and affect the stator flux amplitude ψs =√ψ2sd + ψ2

sq.Machine electromagnetic torque is given by:

Tg =3

2p [ψrisq + (Lsd − Lsq)isdisq] , (11)

where p denotes the number of pole pairs. The torque iscontrolled only by q stator current component, whereasthe d component is set to zero in order to reachthe maximum possible torque range. The above-ratedspeed operation can be achieved by controlling the isdwith negative values.

A non-salient machine is considered in the sequeldue to simplicity reasons for deriving the fault-tolerantcontrol laws and stator inductance is set to Lsd = Lsq =Ls.

Machine model given by (5) and (6) is suitable forproportional-integral (PI) controller design. If integraltime constants TI = Ls/Rs and gain Kr are chosen,closed loop dynamics can be represented as a first-order lag system with transfer function:

isd(s)

i∗sd(s)=isq(s)

i∗sq(s)=

1

1 + τs, (12)

where τ is a time constant defined with τ = Ls

Kr.

Described conventional control method is called field-oriented control. For more information about machinemodeling and FOC please refer to [13].

4. Fault-tolerant controlThe new and intact insulation in healthy generator

conditions is negatively affected by the voltage deriva-tive that arises from the pulse-width modulation. How-ever, once degraded, the insulation has pronounced re-sistive character and is rapidly damaged further with thestator voltage amplitude [5], i.e., the voltage amplitudebecomes dominant to voltage derivative contributionin insulation degradation and is proportional to inter-turn currents through degraded insulation that result inlocal over-heating. Therefore, in order to stop the faultdevelopment, induced voltage in the generator statorwindings needs to be restricted and kept under somesafe value K obtained from the machine diagnostics.To this aim, the K restriction is to be imposed on statorflux time-derivative, which is the main contribution to theinduced stator voltage. In the three-phase coordinatesystem (a,b,c) stator voltage equation is defined with:

usx = isxRs +dψsxdt≈ dψsx

dt, (13)

where x denotes one of the phases. The goal forsuppressing the fault is formed as a restricted value offlux derivative: ∣∣∣∣dψsxdt

∣∣∣∣ ≤ K. (14)

The magnetic flux is generated with permanent mag-nets on the rotor and can be considered constant asdescribed before. However, the magnetic flux perceivedby stator windings from (9) and (10) can be reducedwith adequate stator currents such that permanent mag-net flux is dissipated in the air-gap instead of closingthrough stator coils. This feature is commonly used inthe above-rated-speed operation, known as the flux-weakening method. We utilize this possibility to form aFTC and to restrict the flux derivative.

Approach with globally weakened flux in the below-rated-speed operation can be used to avoid the faultpropagation, but it reduces the power production un-necessarily (Fig. 3). Theoretical maximum of powerproduction in faulty operation and boundary conditionfor fault suppressing is the case when flux derivativereaches the exact value of K:∣∣∣∣dψsxdt

∣∣∣∣ = K. (15)

Arising from this condition, the flux is modulated toobtain a triangular waveform with slope value of K suchthat its derivative is equal to fault restriction coefficient:

ψsa(t) = Kt, t ∈ [− π2ωe

, π2ωe

] + 2kπωe,

ψsa(t) = −Kt+Kπ, t ∈ [ π2ωe

, 3π2ωe

] + 2kπωe.

(16)

Generally, the stator flux is considered sine-wave (inthe fundamental-wave approaches, such as FOC) withamplitude |ψs|, angular frequency ωe and phase offsetϕx. The flux in phases x = a, b, c is represented with:

ψsx(t) = |ψs|(t) sin(ωet+ ϕx), (17)

and relation |ψs| =√ψ2sd + ψ2

sq holds.Following from (15) and (17), an appropriate flux

amplitude envelope is chosen to achieve the triangularwaveform (for phase a with ϕa = 0):

|ψs|(t) =Kωeωet

sin(ωet), (18)

Normal operation

Flux-weakening

Theoretical maximum with FTC

π

ψsn

θeElectrical angle, (rad)

ψs(

θ e )

Sta

tor

flux,

(

Wb)

Figure 3: Angle-dependent stator flux waveforms forhealthy generator and faulty generator with FTC.

Kωe

π2

π2

π

Kωe

θeElectrical angle, (rad)

|ψs|(

θ e )

Sta

tor

flux

ampl

itude

,

(W

b)

Figure 4: Electrical-angle-dependent stator flux ampli-tude modulation for FTC.

where ωet = θe is the electrical angle used for (d,q)transformations. The minimum absolute value is at an-gles ωet = 0, π, ..., and maximum at ωet = π/2, 3π/2...:

|ψs|(0) = Kωe,

|ψs|(π2

)= K

ωe

π2 .

(19)

The FTC is used to calculate stator currents thatmodulate the stator flux amplitude based on the instan-taneous flux position, with twice the frequency of thedesired waveform, as shown in Fig. 4. As the q-currentis responsible for maintaining the constant torque, thed-current from (9) is used to achieve corresponding|ψs|(t). Note that targeted flux amplitude is in fact a time-sequence of sinc functions, which ultimately results in atriangular waveform when multiplied with sine magneticflux distribution generated by permanent magnets rota-tion. With modulated stator flux amplitude, the stator fluxrate of change and consequently the induced voltage instator windings are restricted and the fault developmentis stopped or greatly delayed.

Proper values of isd are chosen to achieve the trian-gular form in Fig. 3 while taking into account: (i) |is|mustnot exceed predefined nominal value isn, (ii) desiredmachine torque and corresponding isq, (iii) the maxi-mum flux restriction (rated value ψsn) due to saturation.If the isd is set to a minimum allowed value, whichcorresponds to minimum value of stator flux ψs,min, theFTC is acting as a simple flux weakening. In order toachieve full rated current isn and thus the maximumpossible operating area of the faulty generator, isd is setto follow an equivalent trajectory as |ψs|(t). This allows

the isq modulation as a counterpart from is =√i2sd + i2sq

and thereby larger possible mean torque value. The isqmodulation also introduces additional torque oscillationsand undesirable increase of WT structural loads butextends the possible operation by about notable 40%more power as the simulations performed show.

For a time-variable flux amplitude envelope |ψs|(t),

the flux derivative for fault suppression is defined with:

dψsx(t)

dt=d|ψs|(t)dt

sin(ωet) + |ψs|(t)ωe cos(ωet) ≤ K,(20)

where the derivative of amplitude envelope from (18) is:

d|ψs|(t)dt

= Ksin(ωet)− ωet cos(ωet)

sin2(ωet). (21)

Note that two parts in (20) are related to sin and cos,which is in fact the restriction (14) presented in (d,q)rotating coordinate system. Both parts can be thereforeindividually considered for K restriction:

d|ψs|(t)dt ≤ K,

|ψs|(t)ωe ≤ K,(22)

and maximum boundary values follow:

d|ψs|(t)dt

sin(ωet) =

0, ωet = 0K, ωet = π

2

, (23)

|ψs|(t)ωe cos(ωet) =

K, ωet = 00, ωet = π

2

. (24)

On the other hand, the fastest achievable transientof isd is determined with inverter limitation. Consideringthe worst case scenario and a typical value of DC-linkvoltage Udc in wind turbines, even the maximum statorflux derivative at t = π

2ωeis achievable and this issue

is not explicitly treated in the derived FTC. The FTCalgorithm is given in the Algorithm 1.

Algorithm 1 Fault-tolerant control for PMSG1. Obtain corresponding mean value of q-current,

isq,mean from (4) and (11) with torque reference T ∗gand current speed ω; obtain corresponding meanvalue of d-current, isd,mean from isq,mean and isn;

2. Obtain ψs,min from (19); if obtained ψs,min ≥ ψsn forcurrent ω, no FTC is needed: set i∗sd = 0, ω∗ = ωnand go to Step 8, otherwise continue on Step 3;

3. Calculate minimum value of d-current, isd,min fromψs,min; calculate mean value of stator flux, ψs,meanfrom isq,mean using (9) and (10);

4. If calculated ψs,mean < ψs,min, apply flux weakening:set i∗sd = isd,mean, i∗sq = isq,mean, ω∗ = ωC and go toStep 8, otherwise continue on Step 5;

5. Find maximum value for the modulation ψs,max from(18) with ψs,min and ψs,mean;

6. Obtain current value of |ψs|(t) with ψs,min andψs,max from (18), aligned with stator flux angle fromarctan(ψsq/ψsd);

7. Determine current references i∗sd and i∗sq with isn andobtained |ψs|(t); set ω∗ = ωC ;

8. Pass calculated i∗sd and i∗sq to FOC; pass ω∗ to pitchcontroller;

9. Initialization: Set ωC = ωn and execute steps 1–5 until ψs,max ≤ k

ωe

π2 from (19). Decrease ωC by

small value εω at each iteration; set ω∗ equal to theobtained ωC at the last iteration.

Step 9 needs to be performed only once per certainK, steps 1–5 once per modulation period and steps 6–8 at each sample time instant (or only step 8 if no fluxmodulation is required). The algorithm requires fairlylow computer resources with summations, divisions,sine and square root calculations. It can be even moresimplified by using look-up tables, such as e.g. ωC(K)or slightly more complex i∗sd(K,ωe, θe) for θe ∈ 0, π2 .

Using the described method, an exemplary graphof available speed-torque points under machine faultis shown in Fig. 5. Normal operation of the healthygenerator is bounded with rated machine torque Tgnand rated speed ωn and pitch control is responsibleto keep the operating point between boundaries. Thecurve denoted with Optimum power represents optimaloperating points of wind turbine at which the power fac-tor coefficient Cp and power production is at maximumvalue, (4). The flux weakening is applied between ’A’and ’B’ points and flux modulation between ’B’ and ’C’.The closer the WT operation is to point ’C’, the moreexpressed are the torque oscillations. In the faulty state,optimum power production can be followed to the edgeof possible generator operating area and blade pitchingis used to keep the WT at new rated point denoted with’C’. For the case of diagnosed fault, shaded area de-notes all available generator torque values that can beachieved for certain generator speed. Generator torquedenoted with Tf is the largest available torque that canbe achieved under fault condition, wherein the meantorque value is considered for the flux modulation part.Interventions in classical variable-speed variable-pitchwind turbine control that ensure fault-tolerant operationare given in Fig. 6 (red blocks).

Desired generator torque reference T ∗g , dictated bythe wind turbine torque control loop (4), determines ad-equate mean value of isq. Remaining part of the currentis the maximum allowed value of isd, which determines

Tgn

Optimum power

ωn

Tf (ω)

A

Speed (rpm)

Ge

ne

rato

r to

rqu

e (

kNm

)

WT operating area for K = 600 Wb/s

Flux weakening

Flux modulation

0 5 10 15 20 25 30 350

50

100

150

200

250

C

B

Figure 5: WT operating area for healthy generator caseand faulty with K = 600 Wb/s (value of K = 1070 Wb/scorresponds to the healthy generator).

TORQUEcontroller

GENERATOR-&-INVERTER

WIND

PITCH-servo&-controller

SPEEDcontroller

+-

*isq

*isd Tg

*ω β*β

K

is

FOC-+FAULT-TOLERANTcontrol

Fault-DETECTION&-characterisation

isd,isq,θe

Figure 6: Control system of wind turbine with fault-tolerant control strategy.

the maximum possible reduction of stator flux ψsd. Thisfeature is also dependent on the generator type, sizeand permanent magnet flux since the stator flux canonly be reduced to the minimum value of ψs,min =−Lsdisn+ψr, as follows from (9). This is one limit for theWT operating area with FTC and corresponding productof |ψs|(t)ωe – the other is WT speed and the minimummeaningful cost effectiveness of available power, bothof which are related to the stage of fault development.However, megawatt class WTs offer very wide area ofoperation depending on the value of K, as presentedin Fig. 7.

If there is a short-circuit between turns of the samephase, permanent magnets and variable magnetic fluxinduce voltage in the shorted turn and, due to verysmall resistance, cause very high current that developsthe fault rapidly. By constraining the flux derivative, thecurrent in shorted turn is restricted as well. Therefore,the proposed method works both for the insulationdegradation and inter-turn short circuit cases and canbe applied to any stage of the fault development. Thestage of fault is dictated only by the coefficient K, whichusually falls in the interval (10% ÷ 100%) of the ratedproduct ωenψsn (see Fig. 7).

200400

600800

1000

0

5

10

15

20

25

30

0

50

100

150

200

250

Speed (rpm)

Ge

ne

rato

r to

rqu

e (

kNm

)

K (Wb/s)

Figure 7: WT operating area for different stages of faultdevelopment, expressed through the K coefficient.

5. Simulation resultsThis section provides simulation results for a 700 kW

MATLAB/Simulink variable-speed variable-pitch WTmodel with a 2 MW PMSG. The focus is on elec-tric variables, which are related to a 2 MW generatorbut parameters and transients are comparative to anymegawatt-class wind turbine. On the other hand, theaerodynamic model differs significantly for various typesand sizes of WTs and therefore the generator is scaledto match the torque and power of a 700 kW machine.Simulations are performed on an ideal PMSG modelpresented in Section 3 with the goal of observing electri-cal transients and possibilities for stator flux modulationand FTC. Inverter dynamics are therefore neglected dueto minor influence on the observed problem. Generatorand aerodynamic parameters are given in tables 1and 2.

Table 1: Generator parameters used in simulations.

Description Parameter ValueRated power Pn 2 MWRated frequency fn 12.64 HzNumber of pole pairs p 32Stator resistance Rs 0.01 ΩStator inductance in d-axis Lsd 3 mHStator inductance in q-axis Lsq 3 mHPermanent magnets flux ψr 12.9 Wb

Table 2: Wind turbine parameters used in simulations.

Description Parameter ValueRated power Ptn 700 kWMaximum power factor CPmax 0.47Blades disc radius R 25 mOptimum tip-speed-ratio λopt 7.4Rated speed ωn 29 rpmRated torque Tt 230.5 kNmTotal moment of inertia Jt 780 000 kgm2

Simulations are performed for the case of K =600 Wb/s and faulty phase a. Figure 8 shows the d-current component responsible for flux modulation. Dueto reduced tracking capability of PI controllers used inFOC, a time lag occurs between the reference andresponse of the isd. The lag causes unsymmetrical fluxderivative and results in overshoot of the imposed limit,as shown in Fig. 9 (dash-dot line, denoted as PIs).Simple solution for the problem is to set K to a lowervalue to ensure redundancy.

Here we apply simple predictive controller from [14]to overcome the problem. Triangular flux waveform ispresented in Fig. 10 and its derivative never exceedsthe limit K, as shown in Fig. 9. Drops of flux derivativeat peak values can be removed by including antici-pated rapid stator flux angle changes in the predictivecontroller. Figure 9 also shows comparison with phasevoltage (dashed line), where the approximation (13) is

35.1 35.15 35.2 35.2535.1 35.15 35.2 35.25

−1200

−1100

−1000

−900

−1200

−1100

−1000

−900

−800

−1300

i (A)sd

Time (s)

i (A)sd

Time (s)a) b)

Figure 8: Direct current component isd for case of: a)conventional PI control, b) predictive control. Dashed isthe reference value.

−800

−400

0

400

800

35.08 35.12 35.16 35.2 35.24

Faulty phase Voltage

PIs

Figure 9: Stator flux derivative in phase coordinates.Dashed is the phase voltage in the targeted (faulty)phase.

−15

−10

−5

0

5

10

15

Time (s)

Stator flux in phases a,b,c (Wb)

35.08 35.12 35.16 35.2 35.24

Figure 10: Stator flux in phase coordinates.

justified. Targeted flux magnitude modulation is shownin Fig. 11.

The generator electromechanical fault is reflectedin stator voltages and currents (Fig. 12), and therebyas periodical changes in power production, which arefurther on rectified to DC-link, then inverted back andfiltered by grid-side converter. The DC-link capacitoralso acts as a power buffer that smoothes the powerproduction oscillations.

Mechanical variables of WT for the case of normal

9.2

9.6

10

10.4

Time (s)

Stator flux magnitude (Wb)

35.08 35.12 35.16 35.2 35.24

Figure 11: Stator flux amplitude envelope modulation,|ψs|(t).

35.08 35.12 35.16 35.2 35.24−1500

−1000

−500

0

500

1000

1500

Time (s)

Stator currents in phases a,b,c (A)

Figure 12: Stator phase currents.

8

9

10Wind speed profile (m/s)

32 33 34 35 36 3723

23.5

24

Generator speed (rpm)

200

400

600Generator torque (kNm)

Time (s)35.08 35.12 35.16 35.2 35.24

32 33 34 35 36 37

Figure 13: Wind speed and WT operating point.

turbulent wind and applied FTC are shown in Fig. 13.Torque oscillations due to applied isd and isq currentsmodulation are evident, but because of very large mo-ment of inertia of WT rotor disc, the effect is barelynoticeable in WT speed. The mean value of torque

is kept on the same value as for the case of healthygenerator and given operating point, which makes thegenerator behave identically from the outer WT controlloops perspective, only with reduced operating range.

Depending on the diagnostic method sensitivity, theFTC can achieve a wide scope of generator operation,from inter-turn short circuit and from about 30% to al-most intact power production, i.e., it can be applied per-manently or only temporarily for avoiding the wind tur-bine shut-down and power production opportunity costsuntil the next scheduled repair. The FTC is designed asan extension of conventional WT control and algorithminputs are stator flux derivative constraint imposed bythe machine monitoring subsystem, speed and currentsmeasurements, i.e., only already available sensors arerequired for the implementation. It is important to pointout that FTC keeps the operation below rated valuesof generator variables – they are just shaped andreallocated properly to achieve fault-tolerant operation.This relaxes increased generator iron losses due to non-sine waveforms and increased harmonic compositioncaused by FTC, as well as torque oscillations influenceon structural loads.

6. Conclusions

Results show that generator insulation faults can bestopped from spreading with proper modulation of mag-netic flux perceived by stator and safe operation in thepresence of the fault can be achieved. We further showhow power production can be safely maximized in thefaulty conditions. Added market value of proposed con-trol algorithms lays in the fact that they are conceivedas cheap, efficient and modular software upgrades tothe existing classical generator control algorithms andwhole wind turbine control strategy, without any me-chanical interventions. The nature of upgrades allowsthe fault-tolerant control to be easily incorporated in newconcepts, but also in already available and working windturbines with various types of generators. Moreover, themethod can be applied for any inverter-fed AC electricmachine, regardless of size and application.

Acknowledgement

The research leading to these results has re-ceived funding from the European Community’s Sev-enth Framework Programme under grant agree-ment no 285939 (ACROSS), from the "Centre ofExcellence for Structural Health" (CEEStructHealth)supported by the European Union under contractIPA2007/HR/16IPO/001-040513, and from the Republicof Croatia Proof of Concept Grant Fund for Researchersthrough project "Proof of Concept for Wind TurbineGenerator Fault-tolerant Control" (PoC-WTGFTC), grantno PoC5_1_108.

References[1] Renewable Energy Policy Network for the 21st Cen-

tury (REN21), “Renewables 2013”, Global statusreport, 2013.

[2] Z. Daneshi-Far, G. A. Capolino, H. Henao, “Reviewof Failures and Condition Monitoring in Wind Tur-bine Generators”, XIX International Conference onElectrical Machines - ICEM 2010, 2010.

[3] P. F. Odgaard, J. Stoustrup, M. Kinnaert. “Fault-Tolerant Control of Wind Turbines: A BenchmarkModel”, IEEE Transactions on Control SystemsTechnology, vol. 21, no. 4, pp. 1168–1182, 2013.

[4] G. Stojicic, G. Joksimovic, M. Vašak, N. Peric, T. M.Wolbank, “Increasing Sensitivity of Stator WindingShort Circuit Fault Indicator in Inverter Fed Induc-tion Machines”, 15th International Power Electronicsand Motion Control Conference, EPE-PEMC ECCEEurope 2012, pp. DS2a.10-1–7, 2012.

[5] J. Yang, J. Cho, S. B. Lee, J. Yoo, H. D. Kim. “AnAdvanced Stator Winding Insulation Quality Assess-ment Technique for Inverter-Fed Machines”, IEEETransactions on Industry Applications, vol. 44, no. 2,pp. 555–564, 2008.

[6] P. Nussbaumer, A. Mitteregger, T. M. Wolbank: “On-line Detection of Insulation Degradation in InverterFed Drive Systems Based on High Frequency Cur-rent Sampling”, 37th Annual Conference on IEEE In-dustrial Electronics Society, IECON 2011, pp. 1954–1959, 2011.

[7] T. Boileau, N. Leboeuf, B. Nahid-Mobarakeh,F. Meibody-Tabar: “Synchronous Demodulation ofControl Voltages for Stator Interturn Fault Detection

in PMSM”, IEEE Transactions on Power Electronics,vol. 28, no. 12, pp. 5647–5654, 2013.

[8] A. H. Bonnet and C. Yung, “Increased efficiency ver-sus increased reliability”, IEEE Industry ApplicationsMagazine, vol.14, no.1, pp. 29-36, 2008.

[9] V. Lešic, M. Vašak, N. Peric, T. M. Wolbank, G.Joksimovic. “Fault-tolerant Control of a Wind Turbinewith a Squirrel-cage Induction Generator and RotorBar Defects”, Automatika, vol. 54, no. 3, pp. 316–328, 2013.

[10] V. Lešic, M. Vašak, N. Peric, G. Joksimovic, T. M.Wolbank. “Fault-tolerant Control of a Wind Turbinewith Generator Stator Inter-turn Faults”, Automatika,vol. 54, no. 1, pp. 89–102, 2013.

[11] L. Y. Pao and K. E. Johnson, "Control of WindTurbines: Approaches, Challenges, and Recent De-velopments", IEEE Control Systems Magazine vol.31, no. 2, pp. 44-62, 2011.

[12] F. D. Bianchi, H. De Battista and R. J. Mantz,Wind Turbine Control Systems - Principles, Mod-elling and Gain Scheduling Design., London,England: Springer, ISBN 1-84628-492-9, 2007.

[13] M. P. Kazmierkowski, F. Blaabjerg and R. Krishnan,Control in Power Electronics - Selected Problems,San Diego, California: Academic Press, An imprintof Elsevier Science, ISBN 0-12-402772-5, 2002.

[14] V. Lešic, M. Vašak, N. Peric, G. Joksimovic, T.M. Wolbank. “Optimal Flux Magnitude Tracking withApplication to Fault-tolerant Control of Wind TurbineGenerators”, Proceedings of the European ControlConference, ECC 2013, pp. 466–471, 2013.