Doubly Fed Induction Generator Model-Based Sensor … · Doubly Fed Induction Generator Model-Based...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009 4229

Doubly Fed Induction Generator Model-BasedSensor Fault Detection and Control

Loop ReconfigurationKai Rothenhagen, Student Member, IEEE, and Friedrich Wilhelm Fuchs, Senior Member, IEEE

Abstract—Fault tolerance is gaining interest as a means to in-crease the reliability and availability of distributed energy systems.In this paper, a voltage-oriented doubly fed induction generator,which is often used in wind turbines, is examined. Furthermore,current, voltage, and position sensor fault detection, isolation, andreconfiguration are presented. Machine operation is not inter-rupted. A bank of observers provides residuals for fault detec-tion and replacement signals for the reconfiguration. Control istemporarily switched from closed loop into open-loop to decouplethe drive from faulty sensor readings. During a short period ofopen-loop operation, the fault is isolated using parity equations.Replacement signals from observers are used to reconfigure thedrive and reenter closed-loop control. There are no large tran-sients in the current. Measurement results and stability analysisshow good results.

Index Terms—Doubly fed induction machine, fault-tolerantcontrol, observers, sensors.

I. INTRODUCTION

ENERGY production from renewable energy sources hasdeveloped at an extraordinary pace over the past decade,

contributing to an energy mix that is less reliant on carbondioxide emitting fuels. Wind power has garnered enormousinterest in the last decade and can now be considered a matureindustry. One of the main types of wind generators is the doublyfed induction generator (DFIG) [1], which is a wound rotorinduction generator that is controlled by an inverter at the rotor.

In the future, large offshore wind parks are expected tocontribute significantly to wind power production. However, theremote location and high investment costs for multimegawattwind turbines have created interest in more reliable, self-diagnosing, and even fault-tolerant wind turbines.

One possible cause for faults is sensor failure. The control ofelectrical drives requires sensors that measure current, voltage,speed, or position. To improve the reliability of the system, it isadvantageous to have a fault detection device. The logical nextstep after fault detection is system reconfiguration by replacing

Manuscript received December 21, 2007; revised January 5, 2009. Firstpublished February 3, 2009; current version published September 16, 2009.This work was supported by the Deutsche Forschungsgemeinschaft (GermanResearch Foundation).

The authors are with the Institute of Power Electronics and ElectricalDrives, Christian-Albrechts-University of Kiel, 24143 Kiel, Germany (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2009.2013683

the detected faulty sensor with an equivalent observed signal.This may enable fault-tolerant operation.

Generally, fault tolerance can also be achieved by imple-menting hardware redundancy, such as an extra sensor, at extracost. The proposed method requires only extra computationalpower. It is assumed that the cost of computational power willdecline in the future based on past trends.

Fault tolerance is an issue that has been addressed by manyauthors. A comprehensive introduction to this area can, forexample, be found in [2] and [3]. Due to the often very specificapplication and the wide range of methods applied, an all-encompassing description is beyond the scope of this paper.However, a short review shall be given. A thorough definitionof relevant terminology has been given in [4], including thefollowing:

1) fault: unpermitted deviation of at least one characteristicproperty or parameter of a system from its acceptable/usual/standard condition;

2) residual: fault indicator, based on deviation betweenmeasurements and model-equation-based computations;

3) fault detection: determination of faults present in a sys-tem and time of detection;

4) fault isolation: determination of type, location, and timeof detection of a fault; follows fault detection. This defin-ition should be amended with the term;

5) reconfiguration: rearrangement of the control structureof a system that enables continued operation in spite of afault.

Fault detection of electrical machines has earned some atten-tion. In [5], detection of increased rotor resistance is describedfor a DFIG. Parameter estimation [6] or signal-based methods[7] have been used for fault detection of squirrel cage inductionmachines. Artificial intelligence has also been researched forfault detection in induction machines [8]. Fault-tolerant controlof permanent magnet synchronous motor (PMSM) is presentedin [9] and [10], where actuator redundancy is used by imple-menting an extra inverter leg. Fault tolerance does not onlyapply to failures of the generator or its control but also to ridingthrough grid faults [11].

Work in the field of sensor fault tolerance is scarce. Sensorfault-tolerant control has been researched for traction [12],[13] and industry drives [14]. These works use model-basedmethods. Fuzzy methods are used [15] to reconfigure a drive.Sensor fault-tolerant control for electric vehicles has also beentreated [16], [17], [19], [39]. All cited approaches focus on

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4230 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009

Fig. 1. Rotor-controlled DFIG and employed sensors.

induction or PMSM machines. Work on fault-tolerant controlof DFIG has been presented [19]–[21].

This paper contributes to the model-based sensor fault-tolerant control of DFIGs.

This paper is organized as follows. An introduction, in-cluding an overview of fault detection and isolation (FDI) ofelectrical drives has been given in Section I. The concept andcontribution of the proposed scheme are described in Section II.The used control strategy is briefly shown in Section III; themodeling and observer design are described in Sections IV andV, respectively. Section VI gives the detailed information aboutthe FDI algorithms, while measurement results are given inSection VII. This paper and its contribution are summed up ina conclusion in Section VIII. An appendix and references areincluded.

II. CONTRIBUTION AND CONCEPT

This paper presents a model-based sensor fault-tolerant con-trol of a grid-connected closed-loop controlled DFIG. Fig. 1shows the drive’s sensors and control structure. The drive isfault tolerant toward faults in the rotor position, rotor current,stator current, and stator voltage sensors. The grid side con-verter is not covered.

The drive is equipped with FDI algorithms that detect, iso-late, and mitigate a fault in the aforementioned sensors. For thispurpose, a bank of observers consisting of five observers andone position estimator is used. The fault is detected and isolatedin real time without interruption of drive operation. After isola-tion, the control is reconfigured to a suitable replacement signalfor the faulty sensor, which is supplied by an observer. Faultdetection is usually possible within a few sampling intervals;fault isolation and reconfiguration are possible within 5 ms.

The proposed scheme has a unified strategy that is applied toall of the four considered sensors. For fault isolation, no thresh-olds are needed. Instead, various residuals are compared to eachother. This greatly reduces the complexity and thereby enhancestransferability and comprehensibility. Special care has beentaken to reduce the tuning requirements of the algorithms. Onlyfive parameters are needed to tune the FDI algorithms. Theimplemented machine model relies on a further five measurableparameters.

The proposed concept does not interfere with normal driveoperation: It is shown that the proposed scheme is tolerant to

harsh load steps. The drive is equipped with a rotor overcur-rent and overvoltage protection device for DFIG, which is acrowbar [43]. It is not triggered during the faults and theirreconfiguration. There are no large transients and only minordistortions during the fault and the following reconfigurationprocess. Thus, no harmful torque pulses are produced. Thecontrollers have a competitive bandwidth. Furthermore, thelaboratory experiments were carried out with full stator voltage(400 V) and half rated power (10 kW). Stability and robustnessanalyses were also performed.

III. CONTROL OF THE CONSIDERED GENERATOR

The DFIG is controlled by two cascaded control loops, asshown in Fig. 1: an inner rotor current control loop and an outerstator power control loop. The control is set in a stator voltage-oriented reference frame, which is widely used for DFIG [23].

The inner rotor current control loop has a fast rise timeof approximately 3 ms, while the stator power control loophas a rise time of 80 ms. The stator power control loop usesstator current and voltage measurements, and the rotor currentcontrol loop uses rotor current measurements; no decouplingis used. The dc link voltage is used to calculate the dutycycle of the pulsewidth modulated rotor side inverter, whilethe stator voltage and rotor position are needed to obtain thetransformation angle for the reference frame. A phase-lockedloop (PLL) is then used to generate the stator voltage angle fromthe voltage measurement. In this case, a dq-PLL [24] is used.

IV. MODELING AND OBSERVER DESIGN

A. Electrical State-Space Model

The model is derived from the voltage equations of the statorand rotor. It is assumed that the stator and rotor windingsare symmetrical and symmetrically fed. The saturation of theinductances, iron losses, skin effect, and bearing friction isneglected. The winding resistance is considered to be constant.

The general state-space model is given in (1), where A isthe system matrix and B is the input matrix. The stator androtor voltages are defined as inputs (2) in input vector u, andthe stator and rotor currents are the states (3) in state vector x ofthe model. The subscripts “S,” “R,” “d,” and “q” indicate statorand rotor quantities of direct and quadrature axes. The outputsare combined in vector y, with C being the output matrix

x = Ax + Bu y = Cx (1)

u = [USd USq URd URq ]T (2)

x = [ ISd ISq IRd IRq ]T. (3)

Induction machines have a nonlinear nature, since the backEMF depends on the rotational speed of the machine. This leadsto a system matrix A that depends on the rotational speed,which is a variable. Models like these have been introduced[25]–[27], [30] for squirrel cage machines. In order to facilitatethe observer design, the nonlinear matrix is split into a fullylinear part A0 and a part A1 that is linear with respect tothe states (e.g., currents) and also linear with respect to therotational speed (4). This representation is called bilinear [12].


ROTHENHAGEN AND FUCHS: GENERATOR SENSOR FAULT DETECTION AND CONTROL LOOP RECONFIGURATION 4231

The system matrices are explicitly given in (5), (6), and (7),where ωm is the mechanical rotor frequency, p is the number ofpole pairs, and ωA is the rotational frequency of the referenceframe. C is the unity matrix. Stator and rotor resistances andinductances are written as RS , RR, LS , and LR, respectively.M denotes mutual inductance; σ is defined by (8).

Using this system description, it is possible to easily convertthe system from stator fixed into a synchronous reference frameor any other, since the influence of the rotation is described byωA. Explicitly, a stator fixed system is using ωA = 0, while asystem oriented with the stator voltage uses the stator angularfrequency ωA = ωS = 2π50 s−1. Moreover, the nonlinear in-fluence of the rotor mechanical speed ωm is separated.

The derived state-space model is the basis for the observersthat are used to observe the stator current, rotor current, andstator voltage

x = A0x + A1pωmx + Bu y = Cx (4)

A0 =

⎡⎢⎢⎢⎣

− RS

σLSpωA

MRR

σLSLR0

−pωA − RS

σLS0 MRR

σLSLRMRS

σLRLS0 − RR

σLRpωA

0 MRS

σLRLS−pωA − RR

σLR

⎤⎥⎥⎥⎦ (5)

A1 =

⎡⎢⎢⎢⎣

0 M2

σLSLR0 M

σLS

− M2

σLSLR0 − M

σLS0

0 − MσLR

0 − 1σ

MσLR

0 1σ 0

⎤⎥⎥⎥⎦ (6)

B =

⎡⎢⎢⎣

1σLS

0 − MσLRLS

00 1

σLS0 − M

σLRLS

− MσLRLS

0 1σLR

00 − M

σLRLS0 1

σLR

⎤⎥⎥⎦ (7)

σ = 1 − M2L−1S L−1

R . (8)

B. Mechanical Model

The mechanical model of the DFIG contains two equations(9), which are the rotor position γ and the angular frequency ω.The equations contain inertia J and torque T . They are neededfor the speed observer design described later

γ = ω ω =1J

(TDFIG − TLoad). (9)

C. Stator Flux Model

Apart from the state-space model, a steady state stator fluxmodel is derived [38]. It is used for the estimation of therotor position [28]. The equations are based on (10) and (11),assuming steady stator voltage, and result in (12), and arenot explained here to maintain brevity. They are also used forthe calculation of parity equations, which are needed for faultisolation, as explained later in Section VI

ΨS =∫

(US − RSIS)dt = −jUS

ωS+ j

RSIS

ωS(10)

ΨS =LSIS + MIR (11)

ISRd = − LS

MISSd IS

Rq = −LS

MISSq −

1ωSM

USSd. (12)

Fig. 2. Block diagram of a linear Luenberger state observer.

V. OBSERVER DESIGN

A. Design of Luenberger Current Observers

In the presented state-space model, the stator and rotorcurrents of the DFIG are the states. The Luenberger state ob-server is therefore suitable to observe the generator’s currents.Luenberger state observers are a mature technology and arewell researched [29]. They contain two parts: a feedforwardmodel and error feedback.

The feedforward model of the system carries out the mainpart of state observation. A well-designed feedforward modelwill give a good representation of the system’s states using theinputs. For nonideal representations, a sole feedforward modelwill drift from the observed system due to unmodeled systemdynamics, uncertain parameters, and disturbances.

The error feedback ensures that the observed states do notdrift from the real ones. The error between observed states x andmeasured states x is used to correct the observed states, muchlike a controller, regulating the error to zero. The error dynam-ics of the observer are defined by placing the eigenvalues ofmatrix (A-LC) using the feedback matrix L [30]. The standardLuenberger observer is given in (13) and is shown in Fig. 2.

The observer error dynamics should be designed to be fasterthan the system that is to be observed [30]. Usually, poleplacement algorithms, such as Ackermann’s equation, are usedto calculate L. In the case of a bilinear system, like the DFIG,the eigenvalues are defined by A0 + A1ωm − LC. The errordynamics are thus a function of the rotational speed [12],[13], [25], [32]. All four states are measurable for DFIG. Itis therefore possible to compensate for the nonlinearity bysubstituting L = L0 + L1ωm and setting L1 := A1C−1, if Chas full rank and is therefore invertible

˙x = Ax + Bu + LC(x − x) (13)

CSCO =

⎡⎢⎣

0 0 0 00 0 0 00 0 1 00 0 0 1

⎤⎥⎦

CRCO =

⎡⎢⎣

1 0 0 00 1 0 00 0 0 00 0 0 0

⎤⎥⎦ . (14)



Fig. 3. Deviation of stator and rotor current residuals normalized to therespective measured currents as a function of mutual inductance parameter.

The system is observable with only two measured states, ascan be easily derived using the observability criterion. There-fore, neither rotor nor stator currents need to be measured for afunctional observer.

Two current observers are designed: a stator current observer(SCO) and a rotor current observer (RCO). The SCO uses rotorcurrent measurement for feedback. Its output matrix is CSCO,as shown in (14). The RCO uses stator current measurement.Its output matrix is CRCO. Both observers need the stator androtor voltages as inputs.

Since matrices CSCO and CRCO are not invertible, the ob-server dynamics are speed dependent. Work-arounds includethe use of precalculated error feedback matrices [25] or fuzzy-like blending between numerous fixed speed matrices [27]. Inthis paper, fixed eigenvalues are designed for a rotational speedof ωm = 2π50 s−1, which is the synchronous speed of themachine.

B. Stability and Robustness of the Current Observer

The accuracy of a Luenberger observer depends on the cor-rectness of the anticipated parameters. Parameter dependenceof flux observers for induction has been treated, e.g., [41]and [42]. Parameter mismatch leads to an inaccurate forwardmodel. To a certain extent, parameter mismatch is neutralizedby the observer feedback. The residuals that are not fed backwill not be directly corrected, however, and may suffer fromsteady state deviation. Regarding the presented fault detectionand the reconfiguration, these residuals need to be sufficientlysmall. The most influential parameter of the model is the mutualinductance.

In a laboratory experiment, the observers’ mutual inductanceis varied from the best found value of 51 mH. The magnitudeof the residuals is normalized to the respective magnitude of theactual stator or rotor current, as shown in Fig. 3. The deviationof the stator current residual is plotted for the SCO, and the rotorcurrent residual is plotted for the RCO. It is found to be quitelarge in terms of numbers, in the range of 11% to 13% for theRCO and in the range of 15% to 17% for the SCO. This is due

Fig. 4. Observed and measured rotor and stator currents [all 50 A/div].(Ch.1) Observed rotor current. (Ch.2) Measured rotor current. (Ch.3) Observedstator current. (Ch.4) Measured rotor current. Horizontal axis [10 ms/div].Machine operated at 1300 r/min, 10-kW stator power, and 277-V statorvoltage.

Fig. 5. Discrete Luenberger state observer eigenvalues as a function ofrotational speed.

to small phase shifts and harmonics that have a large influenceon the calculated residual. The observers still deliver a goodapproximation of the stator and rotor currents. The observedand measured currents are plotted by oscilloscope, as seen inFig. 4, using a digital-to-analog converter.

Next, to the mutual inductance, the influence of the rotationalspeed is of high importance to the observer. The observers’eigenvalues are placed using the synchronous speed. Theymove with variable rotor speed. It is shown that the observerstays stable for all relevant rotor speeds by the root locus as afunction of ωm shown in Fig. 5.

The observer is discretized using a first order Taylor–Rowapproximation for a sampling time of 200 μs. A voltage syn-chronous reference frame is most suitable for DFIG modelaccuracy in discrete systems [33]. DFIG is typically operatedwithin a 30% range around the synchronous speed—in thiscase, from 1000 to 2000 rounds per minute.



C. Design of Voltage Observer

Unlike state observers, input observers have not drawn somuch attention, particularly in electrical machine applications.

In the model derived in (4), the stator and rotor voltages func-tion as inputs to the system. The stator voltages are observed,and the rotor voltages are considered to be known.

Two strategies for input observation have been investigated[34]. It is necessary to split the input matrix B (7) into twomatrices BSV and BRV (15), which represent the input matrixfor the stator and rotor voltages, respectively. The input vectoris split into known inputs u and unknown inputs ν (16).

One possible method uses an unknown input state observer[35]–[37], [40]. This type of observer is decoupled from spec-ified inputs—in this case, the unknown stator voltage. It there-fore does not need them to observe the system’s states.

Using rotor voltage and current measurements, the decoupledinput, e.g., the stator voltage, may be calculated. Completecompensation of the rotor speed dependent nonlinearity ispossible [34]. This approach is not used in this paper

BSV =

⎡⎢⎢⎣

1σLS

00 1

σLS

− MσLRLS

00 − M

σLRLS

⎤⎥⎥⎦

BRV =

⎡⎢⎢⎣− M

σLRLS0

0 − MσLRLS

1σLR

00 1

σLR

⎤⎥⎥⎦ (15)

u = [URd URq ]T v = [USd USq ]T

(16)[xv

]︸︷︷︸

x∗

=[

A BSV

0 0

]︸︷︷︸

A∗

[xv

]︸︷︷︸

x∗

+[

BRV

0

]︸︷︷︸

B∗

u y = [ C 0 ]︸︷︷︸C∗

[xv

]

(17)

e= (A∗0−L∗

0C∗) (x∗−x∗)+(A∗

1−L∗1C

∗) pωm (x∗−x∗)= (A∗

0−L∗0C

∗) e. (18)

Instead, a disturbance observer is used [34]. The stator volt-age that is to be observed is treated as an unknown disturbanceto the system. The system matrix is extended to sixth order bytwo extra states v (16), representing the stator voltages (17).

Calculating an error feedback matrix L∗0 for the new system

matrices A∗ and C∗, these states converge to the stator voltage.Compensation of the rotor speed dependence is possible usingL∗

1 [34] by choosing A∗1 − L∗

1C∗ to be zero, as shown in (18).

The disturbance observer requires the disturbance to be asteady signal [30]. Therefore, a synchronous reference frameneeds to be chosen to satisfy this criterion.

D. Design of Rotor Position Estimator

There are various ways to estimate the rotor position ofvariable-speed drives. Stator-fed machines commonly rely ona flux estimator using terminal voltage and current to derive anangle for reference frame transformation; this method is alsocalled the “back EMF method.” Methods based on the back

Fig. 6. Events during detection, isolation, and reconfiguration of a sensorfault.

EMF have problems with low rotor speeds and are not usableat zero speed, since there is no coupling between stator androtor. Transferring this problem to the wound rotor inductionmachine, the difficult point is the synchronous speed, wherethe stator flux and the rotor rotate synchronously and the drivebehaves almost like a synchronous machine. DFIGs are meantto be used in a speed region around the synchronous speed.For this reason, back EMF-based methods are not suitable.A method to estimate the rotor position has been describedvery comprehensively and thoroughly [28]. It is therefore onlybriefly sketched in this paper.

The first rotor current in stator voltage synchronous refer-ence frame is calculated from (12). Then, it is compared tothe measured rotor current, which is by nature in the rotorfixed reference frame. Since the rotor current is known in tworeference frames, the angle between these two frames can becalculated, which directly leads to the estimated rotor position.

E. Design of Speed Observer

Both rotor position sensor and estimator provide an anglesignal. Deriving the rotor speed by differentiation may causeproblems due to noise. Another way is to use an observer basedon (9) to reconstruct the rotor speed, as described by (19). Theobserver error is the deviation between observed and measured(or estimated) rotor angles. Two of these observers are used:One uses the rotor position sensor as input, and the other oneuses the rotor position estimator. Stator power control is used,which could be extended to a speed control loop. The obtainedspeed signal is used as input to the bilinear observers of (4)and (17). Speed observers also play an important part in faultisolation, as described in Section VI[ ˙γ

˙ω

]=

[0 10 0

] [γω

]+

[L1

L2

](γ − γ) . (19)

VI. BANK OF OBSERVERS FOR FDI

The fault-tolerant control scheme is realized in three steps:fault detection, fault isolation, and reconfiguration. A bank ofobservers is used for three purposes: to provide residuals for thefault detection, to provide information for the fault isolation,and to provide replacements to the sensor readings for thereconfiguration. Fig. 6 shows the whole process.

A. Bank of Observers

A bank of observers is implemented, as shown in Fig. 7.Five observers and one estimator are used. They use machine



Fig. 7. Bank of observers, FDI unit, and control.

TABLE IEMPLOYED OBSERVERS AND REPLACED MEASUREMENTS

terminal and rotor position measurements as inputs, as ex-plained by Table I. For each measurement, there is one observeror estimator to provide a replacement signal. Instead of thepulsed rotor voltage, the rotor voltage reference is used

RS,SCO,abs =

√(ISα − ISα(SCO)

)2

+(ISβ − ISβ(SCO)

)2

(20)

RR,RCO,abs =

√(IRα − IRα(RCO)

)2

+(IRβ − IRβ(RCO)

)2

.

(21)

B. Fault Detection

Fault detection is the first step of the fault-tolerant scheme.A fault is detected when any of the residuals (20) or (21)cross a predefined threshold, where α and β indicate statorfixed natural reference frames. This threshold is derived fromexperience but may be calculated depending on the actualcurrents [31]. It is still unknown which sensor has failed. Afterfault detection, the control system is switched to open-loopoperation to decouple it from the sensor measurements. Thefault isolation process is started. A counter named fault detectis set to 5 ms, which also serves as a signal to switch to open-loop. It counts down and is active while larger than zero. Should

the residuals (20) or (21) cross the threshold again before afault is isolated, the counter is refreshed to 5 ms. The residualsthemselves are not useful in isolating the fault. Usually, allresiduals are affected by any fault. All observers except one usethe faulty signal as inputs and therefore show a wrong output,thus generating a residual. The one observer that does not usethe faulty signal as input calculates proper outputs, which arethen compared to the faulty measurement, also leading to aresidual.

Due to the unforeseeable nature of faults, it cannot be ex-cluded that the described conditions of (20) and (21) for faultdetection may be fulfilled by faults other than those treated here,such as an inverter fault, a grid fault, or others.

Usually, such a fault would be met by switching the systemoff after overcurrent detection, for instance, by a fuse. Antici-pating a false positive detection of a sensor fault, the presentedalgorithm would either try to reconfigure or do nothing at all,depending on the outcome of the fault isolation.

Due to the possibly incorrect isolation, the fault would not bemitigated. As a result, the conventional fault detection wouldswitch the system off, as would have happened in the firstplace. The fault isolation could be supplemented to includeother faults, so that proper action can be taken.

C. Open-Loop Operation

Faulty measurements cause serious malfunction when theyenter the control loops. For this reason, the rotor voltage ref-erence d- and q-components, the rotor position angle, and therotor angular frequency are stored at each interval. After faultdetection, the rotor voltage reference is kept constant, and therotor position is extrapolated using the rotor angular frequency.The rotor current and stator power control loops are set tostandby to prevent integrator saturation. Open-loop operation isactive for 5 ms, while fault detect is larger than zero. If duringthis time the condition for fault detection is met again, the open-loop time is extended. Open-loop operation ends after a fault isisolated or if the open-loop time has expired.

It is understood that an open-loop control has inherent disad-vantages, since there is no possibility to react to load changesand the like. However, using a voltage reference value that hasbeen obtained from past steady state operation is better thancalculating a new voltage reference from faulty sensor readings.

D. Fault Isolation of the Mechanical Sensor

The sensors and their observers are split into two groups: onefor rotor position fault isolation and one for fault isolation of theother electrical sensors.

Two speed observers are located in group one. The first onetracks the rotor position sensor signal; the other one follows theestimated rotor position. Faults in any of the electrical sensorslead to a sudden false rotor position estimation.

For any fault, one observer will follow a faulty signal andthus will have larger control feedback activity. This is used todecide whether the fault has happened in the mechanical orelectrical sensors. No threshold is needed; instead, the controlefforts of the two observers are compared to each other, andthe larger one marks the faulty group, either a mechanical or



Fig. 8. Fault isolation of rotor position sensor; corresponds to Fig. 14.

electrical sensor fault. In order to be reliable, any result has tobe steady for a defined period of time—in this case, 4 ms. If,at this point, the rotor position sensor is isolated as faulty, faultisolation is finished, and reconfiguration is started.

For demonstration, the fault isolation corresponding to thereconfiguration of the rotor position sensor in Fig. 14 is shownin Fig. 8. The counters are only evaluated while fault detect isnonzero. Before that, they have random values.

E. Fault Isolation of Electrical Sensors

The electrical sensor observers are located in group two.They are checked for faults by calculating parity equationsfor each observer. The idea behind this is that any observerthat is using false measurements in its feedback path is forcedto follow this wrong measurement, so that the observer errordeclines to zero.

If it does so, the states no longer represent the observedsystem because a control effort through the feedback path hastaken place. In this case, the observed states violate the parityof the steady state system defined by (12)√(

Ls

MISd,SCO− Usd

ωsM−IRd,SCO

)2

+(

Ls

MISq,SCO−IRq,SCO

)2

(22)√(Ls

MISd,RCO− Usd

ωsM−IRd,RCO

)2

+(

Ls

MISq,RCO−IRq,RCO

)2

(23)√(Ls

MISd,SVO−Usd,SVO

ωsM−IRd,SVO

)2

+(

Ls

MISq,SVO−IRq,SVO

)2.

(24)

For each observer, a new parity residual is calculated. In detail,the SCO uses its stator and rotor current observation and themeasured d-component of the stator voltage (22). The RCOuses (23), and the stator voltage observer uses (24). These parityequations serve as a cross-check for whether the observer still

Fig. 9. Fault isolation of stator current sensor, corresponding to Fig. 13.

delivers plausible outputs. The parity equations do not needextra parameters. The observers’ parameters are taken.

To better detect peaklike increases of the parity equation, itsmaximum is kept. This enables detection of fast increases ofthe parity equations. The obtained value is decreased at eachsampling step by a forgetting factor, which, in this case, is 0.97.

No threshold is needed, since only the magnitudes of all threeparity equation sets are compared to each other. The smallestis searched for, since the observer that still delivers plausibleobservations is decoupled and therefore least affected.

In order to obtain reliable unambiguous fault isolation, theresult needs to be constant for a predefined period of time. Thisis realized by software counters. There is a counter for eachparity equation. The smallest result is found, and the respectivecounter is increased. All other counters are reset to zero. Ifany counter reaches the predefined necessary time threshold of4 ms, as in the mechanical fault isolation, the respective fault isconsidered isolated. If no counter reaches this value before theopen-loop period is over, no fault is isolated. This may be thecase when noise leads to wrong fault detection. This mechanismtherefore effectively suppresses false alarms.

For demonstration, the fault isolation corresponding to thereconfiguration of the rotor current sensor in Fig. 13 is shownin Fig. 9. The rotor current parity equation (23) is smallest,because this observer is decoupled from the faulty sensor.

F. Reconfiguration

After fault isolation, the control scheme is reconfigured usingobserver replacement for the faulty sensor. In the case of a rotorposition sensor fault, the estimated position is used. In the caseof a rotor current sensor fault, the observed rotor currents areused for rotor current control. For a stator current sensor fault,the observed currents are used for stator power calculation,which, in return, is used for power control. Finally, for a statorvoltage sensor fault, the observed voltage is used for powercalculation and to determine the stator voltage angle by PLL. Inall cases, switching from open-loop to reconfigured closed-loopoperation is difficult, which means that there is no blending ofthe values.



Fig. 10. Step of the rotor current reference. (Ch.1) Stator voltage [200 V/div].(Ch.2) Stator current [50 A/div]. (Ch.3) Rotor current [50 A/div]. (Ch.4) Faultdetect flag. Horizontal axis [100 ms/div].

G. Tuning Effort

An important property of any algorithm is low tuning effort.The scheme should work with as little tuning as possible. Thefault detection step needs two parameters, e.g., the thresholdsfor the residuals. The calculation of parity equation resultsrequires one parameter, which is the forgetting factor. Thefault isolation step needs one parameter, which is informationregarding how long the result should be unambiguous before afault is considered as isolated. The open-loop mechanism re-quires one parameter, which is the time of open-loop operation.This time should be only a little longer than the time neededfor fault isolation. A total of five parameters are needed for FDIand reconfiguration.

The current and voltage observers and the rotor positionestimator need the five physical machine parameters, which aremeasurable. The parity equation parameters are equivalent tothe observers’ parameters. The five observers need eigenvaluesas design parameters. The determination of these eigenvalues,from the experience of the authors, is uncritical as long as theyare stable. In total, five parameters need to be tuned.

VII. MEASUREMENT RESULTS

The described fault-tolerant control is implemented on alaboratory test setup. It is controlled by a dSPACE DS10062800-MHz processor at a sampling rate of 200 μs. Machineparameters are RS = 113 mΩ, RR = 110 mΩ, LS = LR =46.8 mH, and M = 45.8 mH. Nominal DFIG power is 22 kWat a stator voltage of 400 V. All measurements are taken at10-kW stator power, 1300 r/min rotational speed, and 400-Vstator voltage. Electrical sensor faults are caused by physicallyunplugging the sensor. A position sensor fault is caused bysetting the reading to zero, using software. The concept is unaf-fected by reference steps. The reconfiguration of all consideredsensors is proved.

A. Step Response

The fault-tolerant control scheme is not affected by referencesteps. Fig. 10 shows a step in the rotor current d and q compo-

Fig. 11. Stator current sensor reconfiguration. (Ch.1) Measured stator current[50 A/div]. (Ch.2) Externally measured stator current [50 A/div]. (Ch.3) Rotorcurrent [50 A/div]. (Ch.4) Fault detect flag. Horizontal axis [10 ms/div].

Fig. 12. Rotor current sensor reconfiguration. (Ch.1) Measured rotor current[50 A/div]. (Ch.2) Externally measured rotor current [50 A/div]. (Ch.3) Statorcurrent [50 A/div]. (Ch.4) Fault detect flag. Horizontal axis [20 ms/div].

nents of 15 A for 200 ms. The steps in the two componentsare overlapping by 100 ms. During this experiment, the powercontrol loop is disabled. The DFIG is operated at approximately10-kW stator power, 1300 r/min, and 400-V stator voltagebefore steps are demanded. No fault is detected during thesteps. Stator and rotor currents and rotor voltage are shown. Thefault detect flag is not triggered, although the fault detection isactive. The presented load changes are greater than typical loadchanges would be.

B. Reconfiguration of Sensors

A complete fault detection, isolation, and reconfiguration areshown for all four sensor types in Figs. 11–14. For each sensor,the measured value that is seen by the control is displayed on theoscilloscope via a DA converter in channel 1. For comparison,this regarded signal is externally measured by a current orvoltage probe, shown in channel 2. The external measurementof the rotor position is not possible; thus, rotor current is shownin Fig. 14. For each reconfiguration, another signal next to thesignal of interest is shown in channel 3 to prove continuedoperation.



Fig. 13. Stator voltage sensor reconfiguration. (Ch.1) Measured stator volt-age [200 V/div]. (Ch.2) Externally measured stator voltage [200 V/div].(Ch.3) Rotor current [50 A/div]. (Ch.4) Fault detect flag. Horizontal axis[10 ms/div].

Fig. 14. Rotor position sensor reconfiguration. (Ch.1) Measured rotor position[0, . . . , 2π]. (Ch.2) Rotor current [50 A/div]. (Ch.3) Stator current [50 A/div].(Ch.4) Fault detect flag.

The measurement is triggered by the fault detection signal,displayed in channel 4. This signal also shows the length of theopen-loop operation.

Faults are detected almost instantly, within a few steps.Faults are isolated and reconfigured within 5 to 10 ms. Duringfault isolation, some small distortions can be seen in the rotorcurrent. They are due to the open-loop operation.

VIII. CONCLUSION

The sensor fault-tolerant control of DFIG drives has beenpresented. All commonly used sensors were covered. Possibleapplications include offshore wind farms or large variable-speed hydrogenerators.

The presented drive is tolerant toward faults in the rotorposition, rotor current, stator current, and stator voltage sensors.

The drive is equipped with a bank of observers to implementFDI algorithms. A stability analysis of the applied observerswas included.

Faults are detected and isolated in real time without in-terruption of drive operation. After isolation, the control isreconfigured to a replacement signal supplied by an observer.Fault detection takes place within a few sampling steps; faultisolation and reconfiguration are possible within 5 to 10 ms.The proposed scheme has a unified strategy that is applied toall of the four considered sensors to reduce the complexity,thereby enhancing transferability and comprehensibility. Onlyfive parameters are needed to tune the detection and isolationalgorithm.

Laboratory measurements were given and show fast andreliable performance under realistic conditions. The proposedscheme is tolerant to harsh load steps and does not producetorque pulses.

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Kai Rothenhagen (S’07) was born in Kiel,Germany, in 1977. He received the Dipl.Ing. de-gree in electrical engineering from Christian-Albrechts-University of Kiel, Kiel, in 2003.

From 2004 to 2008, he was a Graduate ResearchAssistant with the Institute of Power Electronics andElectrical Drives, Christian-Albrechts-University ofKiel. His primary research interests include fault de-tection and fault-tolerant control of electrical drives.

Mr. Rothenhagen received the 2003 TechnicalFaculty’s Best Diploma Award and the Prof. Werner

Petersen Prize in 2004.

Friedrich Wilhelm Fuchs (M’96–SM’01) wasborn in Minden, Germany, in 1948. He receivedthe Dipl.Ing. and Ph.D. degrees from Rheinisch-Westfälische Technische Hochschule Aachen Uni-versity, Aachen, Germany, in 1975 and 1982,respectively.

In 1975, he carried out research work at the Uni-versity of Aachen, Aachen, mainly on ac drives forbattery-powered electric vehicles. Between 1982 and1991, he was the Group Manager in the field ofpower electronics and electrical drives at a medium-

sized company. In 1991, he was with the Converter Division (currentlyConverteam), AEG, Berlin, Germany. There, he was the Managing Directorfor research, design, and development of the complete range of drive products,drive systems, and high-power supplies from 5 kVA to 50 MVA. In 1996,he joined the newly founded Faculty of Engineering, Christian-Albrechts-University of Kiel, Kiel, Germany, as a Full Professor, where he is the Headof the Institute for Power Electronics and Electrical Drives, which he and histeam have built up. His institute is a member of the Cewind Competence Centerof Wind Energy, Schleswig-Holstein, Germany, and the Competence Centerfor Power Electronics, Schleswig-Holstein. His research interests are powersemiconductor applications, converters and their control, and variable-speeddrives. There is special focus on application to renewable energy, particularlywind energy, on state-space and nonlinear control, as well as on diagnosis andfault-tolerant drives. He has authored or coauthored more than 80 papers.

Dr. Fuchs is the Convener and International Speaker of the German standard-ization committee K331 (TC22) for power electronics and is a member of theAssociation of German Electrical and Electronics Engineers and the EuropeanPower Electronics Association.


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