IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009
4229
Doubly Fed Induction Generator Model-Based
Sensor Fault Detection and Control
Loop Reconfiguration
Kai Rothenhagen, Student Member, IEEE, and Friedrich Wilhelm Fuchs, Senior Member, IEEE
Abstract—Fault tolerance is gaining interest as a means to increase 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, and
reconfiguration are presented. Machine operation is not interrupted. A bank of observers provides residuals for fault detection and replacement signals for the reconfiguration. Control is
temporarily switched from closed loop into open-loop to decouple
the drive from faulty sensor readings. During a short period of
open-loop operation, the fault is isolated using parity equations.
Replacement signals from observers are used to reconfigure the
drive and reenter closed-loop control. There are no large transients in the current. Measurement results and stability analysis
show good results.
Index Terms—Doubly fed induction machine, fault-tolerant
control, observers, sensors.
I. I NTRODUCTION
E
NERGY production from renewable energy sources has
developed at an extraordinary pace over the past decade,
contributing to an energy mix that is less reliant on carbon
dioxide emitting fuels. Wind power has garnered enormous
interest in the last decade and can now be considered a mature
industry. One of the main types of wind generators is the doubly
fed induction generator (DFIG) [1], which is a wound rotor
induction generator that is controlled by an inverter at the rotor.
In the future, large offshore wind parks are expected to
contribute significantly to wind power production. However, the
remote location and high investment costs for multimegawatt
wind turbines have created interest in more reliable, selfdiagnosing, and even fault-tolerant wind turbines.
One possible cause for faults is sensor failure. The control of
electrical drives requires sensors that measure current, voltage,
speed, or position. To improve the reliability of the system, it is
advantageous to have a fault detection device. The logical next
step after fault detection is system reconfiguration by replacing
Manuscript received December 21, 2007; revised January 5, 2009. First
published February 3, 2009; current version published September 16, 2009.
This work was supported by the Deutsche Forschungsgemeinschaft (German
Research Foundation).
The authors are with the Institute of Power Electronics and Electrical
Drives, Christian-Albrechts-University of Kiel, 24143 Kiel, Germany (e-mail:
kro@tf.uni-kiel.de; fwf@tf.uni-kiel.de).
Color versions of one or more of the figures in this paper are available online
at 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 implementing hardware redundancy, such as an extra sensor, at extra
cost. The proposed method requires only extra computational
power. It is assumed that the cost of computational power will
decline in the future based on past trends.
Fault tolerance is an issue that has been addressed by many
authors. A comprehensive introduction to this area can, for
example, be found in [2] and [3]. Due to the often very specific
application and the wide range of methods applied, an allencompassing description is beyond the scope of this paper.
However, a short review shall be given. A thorough definition
of relevant terminology has been given in [4], including the
following:
1) fault: unpermitted deviation of at least one characteristic
property or parameter of a system from its acceptable/
usual/standard condition;
2) residual: fault indicator, based on deviation between
measurements and model-equation-based computations;
3) fault detection: determination of faults present in a system and time of detection;
4) fault isolation: determination of type, location, and time
of detection of a fault; follows fault detection. This definition should be amended with the term;
5) reconfiguration: rearrangement of the control structure
of a system that enables continued operation in spite of a
fault.
Fault detection of electrical machines has earned some attention. In [5], detection of increased rotor resistance is described
for a DFIG. Parameter estimation [6] or signal-based methods
[7] have been used for fault detection of squirrel cage induction
machines. Artificial intelligence has also been researched for
fault detection in induction machines [8]. Fault-tolerant control
of permanent magnet synchronous motor (PMSM) is presented
in [9] and [10], where actuator redundancy is used by implementing an extra inverter leg. Fault tolerance does not only
apply to failures of the generator or its control but also to riding
through grid faults [11].
Work in the field of sensor fault tolerance is scarce. Sensor
fault-tolerant control has been researched for traction [12],
[13] and industry drives [14]. These works use model-based
methods. Fuzzy methods are used [15] to reconfigure a drive.
Sensor fault-tolerant control for electric vehicles has also been
treated [16], [17], [19], [39]. All cited approaches focus on
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009
harsh load steps. The drive is equipped with a rotor overcurrent and overvoltage protection device for DFIG, which is a
crowbar [43]. It is not triggered during the faults and their
reconfiguration. There are no large transients and only minor
distortions during the fault and the following reconfiguration
process. Thus, no harmful torque pulses are produced. The
controllers have a competitive bandwidth. Furthermore, the
laboratory experiments were carried out with full stator voltage
(400 V) and half rated power (10 kW). Stability and robustness
analyses were also performed.
III. C ONTROL OF THE C ONSIDERED G ENERATOR
Fig. 1. Rotor-controlled DFIG and employed sensors.
induction or PMSM machines. Work on fault-tolerant control
of DFIG has been presented [19]–[21].
This paper contributes to the model-based sensor faulttolerant control of DFIGs.
This paper is organized as follows. An introduction, including an overview of fault detection and isolation (FDI) of
electrical drives has been given in Section I. The concept and
contribution of the proposed scheme are described in Section II.
The used control strategy is briefly shown in Section III; the
modeling and observer design are described in Sections IV and
V, respectively. Section VI gives the detailed information about
the FDI algorithms, while measurement results are given in
Section VII. This paper and its contribution are summed up in
a conclusion in Section VIII. An appendix and references are
included.
II. C ONTRIBUTION AND C ONCEPT
This paper presents a model-based sensor fault-tolerant control of a grid-connected closed-loop controlled DFIG. Fig. 1
shows the drive’s sensors and control structure. The drive is
fault tolerant toward faults in the rotor position, rotor current,
stator current, and stator voltage sensors. The grid side converter is not covered.
The drive is equipped with FDI algorithms that detect, isolate, and mitigate a fault in the aforementioned sensors. For this
purpose, a bank of observers consisting of five observers and
one position estimator is used. The fault is detected and isolated
in real time without interruption of drive operation. After isolation, the control is reconfigured to a suitable replacement signal
for the faulty sensor, which is supplied by an observer. Fault
detection 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 to
all of the four considered sensors. For fault isolation, no thresholds are needed. Instead, various residuals are compared to each
other. This greatly reduces the complexity and thereby enhances
transferability and comprehensibility. Special care has been
taken to reduce the tuning requirements of the algorithms. Only
five parameters are needed to tune the FDI algorithms. The
implemented machine model relies on a further five measurable
parameters.
The proposed concept does not interfere with normal drive
operation: It is shown that the proposed scheme is tolerant to
The DFIG is controlled by two cascaded control loops, as
shown in Fig. 1: an inner rotor current control loop and an outer
stator power control loop. The control is set in a stator voltageoriented reference frame, which is widely used for DFIG [23].
The inner rotor current control loop has a fast rise time
of approximately 3 ms, while the stator power control loop
has a rise time of 80 ms. The stator power control loop uses
stator current and voltage measurements, and the rotor current
control loop uses rotor current measurements; no decoupling
is used. The dc link voltage is used to calculate the duty
cycle of the pulsewidth modulated rotor side inverter, while
the stator voltage and rotor position are needed to obtain the
transformation angle for the reference frame. A phase-locked
loop (PLL) is then used to generate the stator voltage angle from
the voltage measurement. In this case, a dq-PLL [24] is used.
IV. M ODELING AND O BSERVER D ESIGN
A. Electrical State-Space Model
The model is derived from the voltage equations of the stator
and rotor. It is assumed that the stator and rotor windings
are symmetrical and symmetrically fed. The saturation of the
inductances, iron losses, skin effect, and bearing friction is
neglected. The winding resistance is considered to be constant.
The general state-space model is given in (1), where A is
the system matrix and B is the input matrix. The stator and
rotor voltages are defined as inputs (2) in input vector u, and
the stator and rotor currents are the states (3) in state vector x of
the model. The subscripts “S,” “R,” “d,” and “q” indicate stator
and rotor quantities of direct and quadrature axes. The outputs
are combined in vector y, with C being the output matrix
ẋ = Ax + Bu
u = [ USd
x = [ ISd
y = Cx
USq
ISq
URd
IRd
(1)
T
URq ]
T
IRq ] .
(2)
(3)
Induction machines have a nonlinear nature, since the back
EMF depends on the rotational speed of the machine. This leads
to 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 facilitate
the observer design, the nonlinear matrix is split into a fully
linear part A0 and a part A1 that is linear with respect to
the states (e.g., currents) and also linear with respect to the
rotational speed (4). This representation is called bilinear [12].
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ROTHENHAGEN AND FUCHS: GENERATOR SENSOR FAULT DETECTION AND CONTROL LOOP RECONFIGURATION
The system matrices are explicitly given in (5), (6), and (7),
where ωm is the mechanical rotor frequency, p is the number of
pole pairs, and ωA is the rotational frequency of the reference
frame. C is the unity matrix. Stator and rotor resistances and
inductances 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 convert
the system from stator fixed into a synchronous reference frame
or any other, since the influence of the rotation is described by
ωA . Explicitly, a stator fixed system is using ωA = 0, while a
system oriented with the stator voltage uses the stator angular
frequency ωA = ωS = 2π50 s−1 . Moreover, the nonlinear influence of the rotor mechanical speed ωm is separated.
The derived state-space model is the basis for the observers
that are used to observe the stator current, rotor current, and
stator voltage
y = Cx
ẋ = A0 x + A1 pωm x + Bu
⎡ RS
⎤
M RR
− σLS
pωA
0
σLS LR
⎢ −pω
RS
M RR ⎥
− σL
0
A
⎢
σLS LR ⎥
S
A0 = ⎢ M RS
⎥
RR
⎣ σLR LS
0
− σLR
pωA ⎦
M RS
RR
0
−pωA − σL
σLR LS
R⎤
⎡
M2
M
0
0
σLS LR
σLS
2
⎢
⎥
M
0
− σL
0 ⎥
⎢− M
S
A1 = ⎢ σLS LR
⎥
M
⎣
0
− σL
0
− σ1 ⎦
R
M
1
0
0
σ
R
⎤
⎡ σL
1
M
0
− σLR LS
0
σLS
1
⎥
⎢
0
0
− σLM
σLS
R LS ⎥
B=⎢
1
⎦
⎣− M
0
0
σLR LS
σLR
M
1
0
− σLR LS
0
σLR
2 −1 −1
σ = 1 − M LS LR .
(4)
(5)
(6)
(7)
(8)
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 needed
for the speed observer design described later
ω̇ =
1
(TDFIG − TLoad ).
J
Fig. 2. Block diagram of a linear Luenberger state observer.
V. O BSERVER D ESIGN
A. Design of Luenberger Current Observers
B. Mechanical Model
γ̇ = ω
4231
(9)
C. Stator Flux Model
Apart from the state-space model, a steady state stator flux
model is derived [38]. It is used for the estimation of the
rotor position [28]. The equations are based on (10) and (11),
assuming steady stator voltage, and result in (12), and are
not explained here to maintain brevity. They are also used for
the calculation of parity equations, which are needed for fault
isolation, as explained later in Section VI
US
RS IS
ΨS = (US − RS IS )dt = −j
+j
(10)
ωS
ωS
(11)
ΨS = LS IS + M IR
LS S
LS S
1
S
S
S
I
U . (12)
IRq = − ISq −
IRd = −
M Sd
M
ωS M Sd
In the presented state-space model, the stator and rotor
currents of the DFIG are the states. The Luenberger state observer is therefore suitable to observe the generator’s currents.
Luenberger state observers are a mature technology and are
well researched [29]. They contain two parts: a feedforward
model and error feedback.
The feedforward model of the system carries out the main
part of state observation. A well-designed feedforward model
will give a good representation of the system’s states using the
inputs. For nonideal representations, a sole feedforward model
will drift from the observed system due to unmodeled system
dynamics, uncertain parameters, and disturbances.
The error feedback ensures that the observed states do not
drift from the real ones. The error between observed states x̂ and
measured states x is used to correct the observed states, much
like a controller, regulating the error to zero. The error dynamics of the observer are defined by placing the eigenvalues of
matrix (A-LC) using the feedback matrix L [30]. The standard
Luenberger observer is given in (13) and is shown in Fig. 2.
The observer error dynamics should be designed to be faster
than the system that is to be observed [30]. Usually, pole
placement algorithms, such as Ackermann’s equation, are used
to calculate L. In the case of a bilinear system, like the DFIG,
the eigenvalues are defined by A0 + A1 ωm − LC. The error
dynamics are thus a function of the rotational speed [12],
[13], [25], [32]. All four states are measurable for DFIG. It
is therefore possible to compensate for the nonlinearity by
substituting L = L0 + L1 ωm and setting L1 := A1 C−1 , if C
has full rank and is therefore invertible
x̂˙ = Ax̂ + Bu + LC(x̂ − x)
⎡
⎤
0 0 0 0
⎢0 0 0 0⎥
CSCO = ⎣
⎦
0 0 1 0
0 0 0 1
⎡
⎤
1 0 0 0
⎢0 1 0 0⎥
CRCO = ⎣
⎦.
0 0 0 0
0 0 0 0
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(13)
(14)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009
Fig. 3. Deviation of stator and rotor current residuals normalized to the
respective measured currents as a function of mutual inductance parameter.
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) Observed
stator current. (Ch.4) Measured rotor current. Horizontal axis [10 ms/div].
Machine operated at 1300 r/min, 10-kW stator power, and 277-V stator
voltage.
The system is observable with only two measured states, as
can be easily derived using the observability criterion. Therefore, neither rotor nor stator currents need to be measured for a
functional observer.
Two current observers are designed: a stator current observer
(SCO) and a rotor current observer (RCO). The SCO uses rotor
current 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 and
rotor voltages as inputs.
Since matrices CSCO and CRCO are not invertible, the observer dynamics are speed dependent. Work-arounds include
the use of precalculated error feedback matrices [25] or fuzzylike blending between numerous fixed speed matrices [27]. In
this paper, fixed eigenvalues are designed for a rotational speed
of ωm = 2π50 s−1 , which is the synchronous speed of the
machine.
B. Stability and Robustness of the Current Observer
The accuracy of a Luenberger observer depends on the correctness of the anticipated parameters. Parameter dependence
of flux observers for induction has been treated, e.g., [41]
and [42]. Parameter mismatch leads to an inaccurate forward
model. To a certain extent, parameter mismatch is neutralized
by the observer feedback. The residuals that are not fed back
will not be directly corrected, however, and may suffer from
steady state deviation. Regarding the presented fault detection
and the reconfiguration, these residuals need to be sufficiently
small. The most influential parameter of the model is the mutual
inductance.
In a laboratory experiment, the observers’ mutual inductance
is varied from the best found value of 51 mH. The magnitude
of the residuals is normalized to the respective magnitude of the
actual stator or rotor current, as shown in Fig. 3. The deviation
of the stator current residual is plotted for the SCO, and the rotor
current residual is plotted for the RCO. It is found to be quite
large in terms of numbers, in the range of 11% to 13% for the
RCO and in the range of 15% to 17% for the SCO. This is due
Fig. 5. Discrete Luenberger state observer eigenvalues as a function of
rotational speed.
to small phase shifts and harmonics that have a large influence
on the calculated residual. The observers still deliver a good
approximation of the stator and rotor currents. The observed
and measured currents are plotted by oscilloscope, as seen in
Fig. 4, using a digital-to-analog converter.
Next, to the mutual inductance, the influence of the rotational
speed is of high importance to the observer. The observers’
eigenvalues are placed using the synchronous speed. They
move with variable rotor speed. It is shown that the observer
stays stable for all relevant rotor speeds by the root locus as a
function of ωm shown in Fig. 5.
The observer is discretized using a first order Taylor–Row
approximation for a sampling time of 200 μs. A voltage synchronous reference frame is most suitable for DFIG model
accuracy in discrete systems [33]. DFIG is typically operated
within a 30% range around the synchronous speed—in this
case, from 1000 to 2000 rounds per minute.
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ROTHENHAGEN AND FUCHS: GENERATOR SENSOR FAULT DETECTION AND CONTROL LOOP RECONFIGURATION
4233
C. Design of Voltage Observer
Unlike state observers, input observers have not drawn so
much attention, particularly in electrical machine applications.
In the model derived in (4), the stator and rotor voltages function 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 two
matrices BSV and BRV (15), which represent the input matrix
for the stator and rotor voltages, respectively. The input vector
is 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 specified inputs—in this case, the unknown stator voltage. It therefore does not need them to observe the system’s states.
Using rotor voltage and current measurements, the decoupled
input, e.g., the stator voltage, may be calculated. Complete
compensation of the rotor speed dependent nonlinearity is
possible [34]. This approach is not used in this paper
⎡
⎢
BSV =⎢
⎣
⎡
⎢
BRV =⎢
⎣
1
σLS
0
− σLM
R LS
0
1
σLR
0
− σLM
R LS
0
− σLM
R LS
0
0
u = [ URd
⎥
⎥
⎦
1
σLS
0
− σLM
R LS
⎤
0
URq ]T
⎤
⎥
⎥
⎦
1
σLR
A∗
x∗
Events during detection, isolation, and reconfiguration of a sensor
EMF have problems with low rotor speeds and are not usable
at zero speed, since there is no coupling between stator and
rotor. Transferring this problem to the wound rotor induction
machine, the difficult point is the synchronous speed, where
the stator flux and the rotor rotate synchronously and the drive
behaves almost like a synchronous machine. DFIGs are meant
to 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 described
very comprehensively and thoroughly [28]. It is therefore only
briefly sketched in this paper.
The first rotor current in stator voltage synchronous reference frame is calculated from (12). Then, it is compared to
the measured rotor current, which is by nature in the rotor
fixed reference frame. Since the rotor current is known in two
reference frames, the angle between these two frames can be
calculated, which directly leads to the estimated rotor position.
E. Design of Speed Observer
USq ]T
(16)
x
y = [C 0]
v
v = [ USd
ẋ
A BSV
B
x
=
+ RV u
v̇
v
0 0
0
ẋ∗
(15)
Fig. 6.
fault.
B∗
C∗
(17)
ė = (A∗0 −L∗0 C∗ ) (x̂∗ −x∗ )+(A∗1 −L∗1 C∗ ) pωm (x̂∗ −x∗ )
= (A∗0 −L∗0 C∗ ) e.
(18)
Instead, a disturbance observer is used [34]. The stator voltage that is to be observed is treated as an unknown disturbance
to the system. The system matrix is extended to sixth order by
two 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 using
L∗1 [34] by choosing A∗1 − L∗1 C∗ to be zero, as shown in (18).
The disturbance observer requires the disturbance to be a
steady signal [30]. Therefore, a synchronous reference frame
needs to be chosen to satisfy this criterion.
D. Design of Rotor Position Estimator
There are various ways to estimate the rotor position of
variable-speed drives. Stator-fed machines commonly rely on
a flux estimator using terminal voltage and current to derive an
angle for reference frame transformation; this method is also
called the “back EMF method.” Methods based on the back
Both rotor position sensor and estimator provide an angle
signal. Deriving the rotor speed by differentiation may cause
problems due to noise. Another way is to use an observer based
on (9) to reconstruct the rotor speed, as described by (19). The
observer 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 one
uses the rotor position estimator. Stator power control is used,
which could be extended to a speed control loop. The obtained
speed signal is used as input to the bilinear observers of (4)
and (17). Speed observers also play an important part in fault
isolation, as described in Section VI
0 1
γ̂
L1
γ̂˙
(γ̂ − γ) .
(19)
=
+
L2
ω̂˙
0 0
ω̂
VI. B ANK OF O BSERVERS FOR FDI
The fault-tolerant control scheme is realized in three steps:
fault detection, fault isolation, and reconfiguration. A bank of
observers is used for three purposes: to provide residuals for the
fault detection, to provide information for the fault isolation,
and to provide replacements to the sensor readings for the
reconfiguration. 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
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the residuals (20) or (21) cross the threshold again before a
fault is isolated, the counter is refreshed to 5 ms. The residuals
themselves are not useful in isolating the fault. Usually, all
residuals are affected by any fault. All observers except one use
the faulty signal as inputs and therefore show a wrong output,
thus generating a residual. The one observer that does not use
the faulty signal as input calculates proper outputs, which are
then compared to the faulty measurement, also leading to a
residual.
Due to the unforeseeable nature of faults, it cannot be excluded that the described conditions of (20) and (21) for fault
detection 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 system
off after overcurrent detection, for instance, by a fuse. Anticipating a false positive detection of a sensor fault, the presented
algorithm 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 be
mitigated. As a result, the conventional fault detection would
switch the system off, as would have happened in the first
place. The fault isolation could be supplemented to include
other faults, so that proper action can be taken.
Fig. 7. Bank of observers, FDI unit, and control.
TABLE I
EMPLOYED OBSERVERS AND REPLACED MEASUREMENTS
C. Open-Loop Operation
terminal and rotor position measurements as inputs, as explained by Table I. For each measurement, there is one observer
or estimator to provide a replacement signal. Instead of the
pulsed rotor voltage, the rotor voltage reference is used
2 2
ISα − IˆSα(SCO) + ISβ − IˆSβ(SCO)
RS,SCO,abs =
RR,RCO,abs =
IRα − IˆRα(RCO)
2
+ IRβ
(20)
2
− IˆRβ(RCO) .
(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 stator
fixed natural reference frames. This threshold is derived from
experience but may be calculated depending on the actual
currents [31]. It is still unknown which sensor has failed. After
fault detection, the control system is switched to open-loop
operation to decouple it from the sensor measurements. The
fault isolation process is started. A counter named fault detect
is set to 5 ms, which also serves as a signal to switch to openloop. It counts down and is active while larger than zero. Should
Faulty measurements cause serious malfunction when they
enter the control loops. For this reason, the rotor voltage reference d- and q-components, the rotor position angle, and the
rotor angular frequency are stored at each interval. After fault
detection, the rotor voltage reference is kept constant, and the
rotor position is extrapolated using the rotor angular frequency.
The rotor current and stator power control loops are set to
standby to prevent integrator saturation. Open-loop operation is
active for 5 ms, while fault detect is larger than zero. If during
this time the condition for fault detection is met again, the openloop time is extended. Open-loop operation ends after a fault is
isolated or if the open-loop time has expired.
It is understood that an open-loop control has inherent disadvantages, since there is no possibility to react to load changes
and the like. However, using a voltage reference value that has
been obtained from past steady state operation is better than
calculating 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: one
for rotor position fault isolation and one for fault isolation of the
other electrical sensors.
Two speed observers are located in group one. The first one
tracks the rotor position sensor signal; the other one follows the
estimated rotor position. Faults in any of the electrical sensors
lead to a sudden false rotor position estimation.
For any fault, one observer will follow a faulty signal and
thus will have larger control feedback activity. This is used to
decide whether the fault has happened in the mechanical or
electrical sensors. No threshold is needed; instead, the control
efforts of the two observers are compared to each other, and
the larger one marks the faulty group, either a mechanical or
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ROTHENHAGEN AND FUCHS: GENERATOR SENSOR FAULT DETECTION AND CONTROL LOOP RECONFIGURATION
Fig. 8.
Fault isolation of rotor position sensor; corresponds to Fig. 14.
electrical sensor fault. In order to be reliable, any result has to
be steady for a defined period of time—in this case, 4 ms. If,
at this point, the rotor position sensor is isolated as faulty, fault
isolation is finished, and reconfiguration is started.
For demonstration, the fault isolation corresponding to the
reconfiguration of the rotor position sensor in Fig. 14 is shown
in Fig. 8. The counters are only evaluated while fault detect is
nonzero. 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 equations
for each observer. The idea behind this is that any observer
that is using false measurements in its feedback path is forced
to follow this wrong measurement, so that the observer error
declines to zero.
If it does so, the states no longer represent the observed
system because a control effort through the feedback path has
taken place. In this case, the observed states violate the parity
of the steady state system defined by (12)
2 2
Ls
Ls
Usd
ISd,SCO −
−IRd,SCO +
ISq,SCO −IRq,SCO
M
ωs M
M
(22)
2 2
Ls
Ls
Usd
ISd,RCO −
−IRd,RCO +
ISq,RCO −IRq,RCO
M
ωs M
M
(23)
2 2
Ls
Ls
Usd,SVO
ISd,SVO −
−IRd,SVO +
ISq,SVO −IRq,SVO .
M
ωs M
M
(24)
For each observer, a new parity residual is calculated. In detail,
the SCO uses its stator and rotor current observation and the
measured d-component of the stator voltage (22). The RCO
uses (23), and the stator voltage observer uses (24). These parity
equations serve as a cross-check for whether the observer still
4235
Fig. 9. Fault isolation of stator current sensor, corresponding to Fig. 13.
delivers plausible outputs. The parity equations do not need
extra parameters. The observers’ parameters are taken.
To better detect peaklike increases of the parity equation, its
maximum is kept. This enables detection of fast increases of
the parity equations. The obtained value is decreased at each
sampling step by a forgetting factor, which, in this case, is 0.97.
No threshold is needed, since only the magnitudes of all three
parity equation sets are compared to each other. The smallest
is searched for, since the observer that still delivers plausible
observations is decoupled and therefore least affected.
In order to obtain reliable unambiguous fault isolation, the
result needs to be constant for a predefined period of time. This
is realized by software counters. There is a counter for each
parity equation. The smallest result is found, and the respective
counter is increased. All other counters are reset to zero. If
any counter reaches the predefined necessary time threshold of
4 ms, as in the mechanical fault isolation, the respective fault is
considered isolated. If no counter reaches this value before the
open-loop period is over, no fault is isolated. This may be the
case when noise leads to wrong fault detection. This mechanism
therefore effectively suppresses false alarms.
For demonstration, the fault isolation corresponding to the
reconfiguration of the rotor current sensor in Fig. 13 is shown
in 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 using
observer replacement for the faulty sensor. In the case of a rotor
position sensor fault, the estimated position is used. In the case
of a rotor current sensor fault, the observed rotor currents are
used 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 stator
voltage sensor fault, the observed voltage is used for power
calculation and to determine the stator voltage angle by PLL. In
all cases, switching from open-loop to reconfigured closed-loop
operation is difficult, which means that there is no blending of
the values.
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4236
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009
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) Fault
detect flag. Horizontal axis [100 ms/div].
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) Rotor
current [50 A/div]. (Ch.4) Fault detect flag. Horizontal axis [10 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. The
fault detection step needs two parameters, e.g., the thresholds
for the residuals. The calculation of parity equation results
requires one parameter, which is the forgetting factor. The
fault isolation step needs one parameter, which is information
regarding how long the result should be unambiguous before a
fault is considered as isolated. The open-loop mechanism requires one parameter, which is the time of open-loop operation.
This time should be only a little longer than the time needed
for fault isolation. A total of five parameters are needed for FDI
and reconfiguration.
The current and voltage observers and the rotor position
estimator need the five physical machine parameters, which are
measurable. The parity equation parameters are equivalent to
the observers’ parameters. The five observers need eigenvalues
as design parameters. The determination of these eigenvalues,
from the experience of the authors, is uncritical as long as they
are stable. In total, five parameters need to be tuned.
VII. M EASUREMENT R ESULTS
The described fault-tolerant control is implemented on a
laboratory test setup. It is controlled by a dSPACE DS1006
2800-MHz processor at a sampling rate of 200 μs. Machine
parameters are RS = 113 mΩ, RR = 110 mΩ, LS = LR =
46.8 mH, and M = 45.8 mH. Nominal DFIG power is 22 kW
at a stator voltage of 400 V. All measurements are taken at
10-kW stator power, 1300 r/min rotational speed, and 400-V
stator voltage. Electrical sensor faults are caused by physically
unplugging the sensor. A position sensor fault is caused by
setting the reading to zero, using software. The concept is unaffected by reference steps. The reconfiguration of all considered
sensors is proved.
A. Step Response
The fault-tolerant control scheme is not affected by reference
steps. Fig. 10 shows a step in the rotor current d and q compo-
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) Stator
current [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 components
are overlapping by 100 ms. During this experiment, the power
control loop is disabled. The DFIG is operated at approximately
10-kW stator power, 1300 r/min, and 400-V stator voltage
before steps are demanded. No fault is detected during the
steps. Stator and rotor currents and rotor voltage are shown. The
fault detect flag is not triggered, although the fault detection is
active. The presented load changes are greater than typical load
changes would be.
B. Reconfiguration of Sensors
A complete fault detection, isolation, and reconfiguration are
shown for all four sensor types in Figs. 11–14. For each sensor,
the measured value that is seen by the control is displayed on the
oscilloscope via a DA converter in channel 1. For comparison,
this regarded signal is externally measured by a current or
voltage probe, shown in channel 2. The external measurement
of the rotor position is not possible; thus, rotor current is shown
in Fig. 14. For each reconfiguration, another signal next to the
signal of interest is shown in channel 3 to prove continued
operation.
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ROTHENHAGEN AND FUCHS: GENERATOR SENSOR FAULT DETECTION AND CONTROL LOOP RECONFIGURATION
4237
Faults are detected and isolated in real time without interruption of drive operation. After isolation, the control is
reconfigured to a replacement signal supplied by an observer.
Fault detection takes place within a few sampling steps; fault
isolation and reconfiguration are possible within 5 to 10 ms.
The proposed scheme has a unified strategy that is applied to
all of the four considered sensors to reduce the complexity,
thereby enhancing transferability and comprehensibility. Only
five parameters are needed to tune the detection and isolation
algorithm.
Laboratory measurements were given and show fast and
reliable performance under realistic conditions. The proposed
scheme is tolerant to harsh load steps and does not produce
torque pulses.
Fig. 13. Stator voltage sensor reconfiguration. (Ch.1) Measured stator voltage [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 the
open-loop operation.
Faults are detected almost instantly, within a few steps.
Faults are isolated and reconfigured within 5 to 10 ms. During
fault isolation, some small distortions can be seen in the rotor
current. They are due to the open-loop operation.
VIII. C ONCLUSION
The sensor fault-tolerant control of DFIG drives has been
presented. All commonly used sensors were covered. Possible
applications include offshore wind farms or large variablespeed hydrogenerators.
The presented drive is tolerant toward faults in the rotor
position, rotor current, stator current, and stator voltage sensors.
The drive is equipped with a bank of observers to implement
FDI algorithms. A stability analysis of the applied observers
was included.
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Kai Rothenhagen (S’07) was born in Kiel,
Germany, in 1977. He received the Dipl.Ing. degree in electrical engineering from ChristianAlbrechts-University of Kiel, Kiel, in 2003.
From 2004 to 2008, he was a Graduate Research
Assistant with the Institute of Power Electronics and
Electrical Drives, Christian-Albrechts-University of
Kiel. His primary research interests include fault detection and fault-tolerant control of electrical drives.
Mr. Rothenhagen received the 2003 Technical
Faculty’s Best Diploma Award and the Prof. Werner
Petersen Prize in 2004.
Friedrich Wilhelm Fuchs (M’96–SM’01) was
born in Minden, Germany, in 1948. He received
the Dipl.Ing. and Ph.D. degrees from RheinischWestfälische Technische Hochschule Aachen University, Aachen, Germany, in 1975 and 1982,
respectively.
In 1975, he carried out research work at the University of Aachen, Aachen, mainly on ac drives for
battery-powered electric vehicles. Between 1982 and
1991, he was the Group Manager in the field of
power electronics and electrical drives at a mediumsized company. In 1991, he was with the Converter Division (currently
Converteam), AEG, Berlin, Germany. There, he was the Managing Director
for 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-AlbrechtsUniversity of Kiel, Kiel, Germany, as a Full Professor, where he is the Head
of the Institute for Power Electronics and Electrical Drives, which he and his
team have built up. His institute is a member of the Cewind Competence Center
of Wind Energy, Schleswig-Holstein, Germany, and the Competence Center
for Power Electronics, Schleswig-Holstein. His research interests are power
semiconductor applications, converters and their control, and variable-speed
drives. There is special focus on application to renewable energy, particularly
wind energy, on state-space and nonlinear control, as well as on diagnosis and
fault-tolerant drives. He has authored or coauthored more than 80 papers.
Dr. Fuchs is the Convener and International Speaker of the German standardization committee K331 (TC22) for power electronics and is a member of the
Association of German Electrical and Electronics Engineers and the European
Power Electronics Association.
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