ECN-RX--04-125
TORQUE CONTROL FOR VARIABLE
SPEED WIND TURBINES
P. Schaak
T.G. van Engelen
This paper has been presented at the European Wind Energy Conference,
London, 22-25 November, 2004
NOVEMBER 2004
Torque Control for Variable Speed Wind Turbines
Pieter Schaak, Tim G. van Engelen
Energy research Centre of the Netherlands, ECN Wind Energy
P.O. Box 1, 1755 ZG Petten, The Netherlands
telephone: +31 224 56 4278, fax: +31 224 56 8214
e-mail: schaak@ecn.nl, web: www.ecn.nl
Abstract: An advanced generator control algorithm has been developed and implemented in ECN’s control
design tool for wind turbines. For wind speeds above nominal the algorithm limits power and rotor speed to the
common bounds of constant power control in variable speed turbines, while the electromagnetic torque varies
half as much as found in literature. Simultaneously production dips at above nominal wind speeds are avoided.
The algorithm has been examined by the aero-elastic wind turbine code Phatas. Application on a commercial
wind turbine is in preparation.
Keywords: control, converter, generator, power, torque, variable speed, wind turbine.
1. Introduction
For wind speeds above the nominal wind speed,
conventional generator control algorithms of
variable speed turbines result in production dips.
Some currently applied turbines still suffer from
this undesired phenomenon, although literature
offers a solution since at least one decade.
This paper explains how the algorithm that has been
implemented in ECN’s control design tool prevents
for the production dips and why our algorithm
excels on torque behaviour. Simulations at wind
speeds above the nominal wind speed show that our
algorithm reduces torque variations by 50%,
compared to the algorithms found in literature.
2. Literature
In variable speed wind turbines a relatively fast
servo controller sets the electromagnetic generator
torque on the basis of rotor speed measurements. A
conventional speed-torque relation is shown in
figure 1 [5].
Ω
conventional characteristic
nom
1.2
P
nom
T
1
nom
full load
torque
0.8
transition
0.6
0.4
aerodynamic efficiency of the turbine by aiming the
optimum Lambda, i.e the optimum tip speed ratio.
The full load curve describes the speed-torque
combinations that result in nominal generator
power. As a consequence of operational restrictions
those 2 curves usually cannot be applied up to the
operating point that they have in common.
Therefore the transition cu rve has been introduced.
Applying a minimum rotor speed as well completes
the figure.
During full load operation a blade pitch controller
strives to maintain a desired rotor speed that lies on
or a little above the nominal rotor speed. When the
rotor speed deviates from the desired rotor speed,
due to raising or falling winds, the blades are
pitched to overcome this deviation. For falling
wind, this is maintained until the power that is
extracted from the wind no longer can be increased
by pitching the blades. Then the rotor will
decelerate and the generator torque will be
controlled on the basis of the transition curve of
figure 1.
Of course blade pitching does not follow wind
speed changes instantaneously. So during full load
operation the rotor speed fluctuates around the
desired rotor speed and, despite pitching the blades,
the transition curve of figure 1 also then becomes
applicable sometimes. The rotor speed, the torque
and thus the power decrease below nominal and a
production dip during full load operation has arisen.
This still occurs on some nowadays turbines [7].
0.2
optimum Lambda
0
0
0.2
0.4
0.6
0.8
rotor speed
1
1.2
1.4
file e:\schaak\ctrltool\report\convchar.ps 24-Apr-2003
by e:\schaak\ctrltool\m\rappfigs.m
1.6
Figure 1: Conventional speed-torque relation,
normalised on nominal operation.
This relation is based on the partly dashed curves
for optimum Lambda and full load control. The
optimum Lambda curve aims to maximise the
As long as blade pitching can be used to increase
the rotor speed, a too low rotor speed will be
cancelled out by blade pitching, almost regardless
the speed-torque relation that is applied. So the
production dips will be prevented by applying the
dashed part of the nominal power curve instead of
the transition curve, in the case that blade pitching
lags behind a falling wind [1,2].
The inevitable leaving of full load operation is
announced when blade pitching no longer can
increase the rotor speed. Only then the full load
curve should be left. In figure 1 the operational
point will be at the left side of the conventional
transition curve then and torque control must be
adapted to the conventional speed-torque relation
gradually.
speed ±6%. The restriction of torque and power are
thus defined by nominal ±6% as well, for
respectively constant power and const ant torque.
Proportionally equal ranges for torque and power
define the mixed version curve. Those ranges cover
full load options
1.15
Ω
nom
constant power
mixed version
constant torque
Remark that the torque control that prevents for
production dips also allows to move the
conventional transition curve a little to the right,
because it can connect to the full load curve above
the at full load desired rotor speed now. Further the
transition could be realised by constant speed servo
control as well and sometimes full load operation is
realised by a horizontal constant torque curve [1,2].
P
1.1
nom
torque
1.05
1
Tn o m
0.95
0.9
3. Novel views on full load torque control
During full load operation pitching the blades
controls the rotor speed. The torque and power
behaviour follows via the speed-torque relation.
Applying a different but also proper speed-torque
relation barely influences the rotor speed. That
means that the full load curve always should lie
somewhere in the shaded area of figure 2, because
outside this area either the applicable power or the
applicable torque range is enlarged without
obtaining a profit in change.
Ω
area to optimise
P
nom
nom
1.2
T
1
nom
full load
torque
0.8
transition
0.6
0.4
0.2
0.85
0.85
0.9
0.95
1
rotor speed
Figure 3: Full load curves.
approximately nominal ±3%.
1.05
1.1
1.15
file e:\schaak\ctrltool\report\FullLoadOpts.ps 24-Apr-2003
by e:\schaak\ctrltool\m\rappfigs.m
Applying the constant torque curve will result in
really constant generator torques, because the
torque controller defines the generator torque.
Applying the constant power curve will not result in
a really constant generator power (or: product of
torque and rotor speed), because the generator
torque is realised on the basis of the rotor speed
while suffering from delay and phase shift.
Normalised to their nominal values the power
fluctuations appear to be about half as large as the
torque fluctuations. If the mixed version curve is
applied the power fluctuations appear to be barely
larger than for the constant power curve, while the
torque fluctuations by definition become half as
large. This is confirmed by the simulation results
for a representative multi-MW wind turbine in full
load operation (figure 4).
optimum Lambda
upper:const.
const.
middle:
mixed
version
upper:
T T middle:
middle
course
bottom:bottom:
const. Pconst. P
0.2
0.4
0.6
0.8
rotor speed
1
1.2
1.4
1.6
1.2
file e:\schaak\ctrltool\report\optchararea.ps 24-Apr-2003
by e:\schaak\ctrltool\m\rappfigs.m
Figure 2: Optimisation area for full load curves.
Ω r / Ωnom
0
0
1
0.8
100
200
300
400
500
600
700
200
300
400
500
600
700
200
300
400
500
600
700
200
300
500
600
700
Te / Tnom
1.2
1
0.8
100
1.2
Pe / Pnom
The full load curve is positioned within the shaded
area on the basis of restrictions for generator torque
and power. As a side effect less steep falling curves
slightly stabilises the pitch controlled process, but
that is of no practical importance.
1
0.8
100
30
Θ [o]
Figure 3 shows three possible full load curves:
constant power, constant torque and a mixed
version. In all cases the desired rotor speed is the
nominal rotor speed. All three curves limit
generator torque and power to their appearance at
the outer limits of the rotor speed range that almost
completely covers full load operation. This range
depends on the turbine and its pitch control
algorithm. In figure 3 this range covers the nominal
20
10
0
100
400
t [s]
file e:\schaak\ctrltool\report\sim3full.ps 24-Apr-2003
by e:\schaak\ctrltool\m\KarSftSims.m
Figure 4: Simulation results for a representative
multi-MW wind turbine controlled conform the
constant torque, constant power and mixed version
curve.
The first three plots from above show the rotor
speed, generator torque and generator power, all
normalised on their nominal values. The last plot
shows the blade pitch angle in degrees. Per plot we
see the results for the constant torque, mixed
version and constant power curve. The mixed
version results are plotted ‘in the middle’, without
any offset. For the sake of visualisation the constant
torque and constant power results are plotted 10%
too high respectively too low, or, in the case of the
blade angle, 10° too high and too low.
We conclude that a mixed version curve will result
in very well turbine behaviour. Turbines behave
similar to constant power control, though the torque
varies half as much. As a consequence of
restrictions for torque and power other mixed
version curves than the one presented here could
become attractive as well. Even when the generator
torque is not allowed to exceed nominal, a mixed
version might improve turbine behaviour [11].
When the full load curve does not equal the
nominal power curve and both the desired speed
and desired torque equal their nominal values, nonlinearity’s will result in an average generator power
that does not match the nominal power. This can be
solved easily by adapting the full load curve to the
observed product of speed and torque. This has also
been applicable for figure 4, resulting in a full load
curve just below the initial curve of figure 3.
4. Generator control design
Now we will design a generator controller for a
representative model of a multi-MW wind turbine.
Starting-points are a rotor speed controller by blade
pitching and a conventional generator controller
that already have been designed by ECN’s control
design tool [3,4,6,9,10]. From the model with the
operation appears to equal the nominal rotor speed
±6%, similar to the examples of paragraph 3.
We will change the generator controller on the basis
of the knowledge from the former paragraphs. First
the full load curve is adapted to the mixed version
curve of figure 3. Then the default transition curve,
as it is when the turbine starts up, is moved to
slightly higher rotor speeds. Now it joins the full
load curve at the rotor speed where pitching starts
when coming from below nominal production. See
figure 5 for the situation that has arisen.
From turbine start -up the optimum-Lambda and
default transition curve are applicable until the rotor
speed exceeds the value where blade pitching starts
and full load becomes applicable. Then the full load
curve remains applicable until pitching the blades
cannot cancel out a too low rotor speed anymore.
At that moment a transition to optimum -Lambda
must become applicable again, but the current
speed-torque combination will not lie on the default
transition curve. Therefore we define a temporary
transition curve that joins the full load curve at the
current operating point. Every next controller
calculation step the temporary transition curve is
shifted a little in the direction of the default
turbine
start up
transition
=
default
apply optimum
Lambda and
transition curve
pitch control
active?
no
small transition
shift backt(until
default)
no
apply transition
from current
working point
yes
analysed full load control options
1.1
P
Ω
nom
apply full load
curve
constant power
mixed version
constant torque
nom
T
1
nom
0.9
pitch control
active?
torque
0.8
0.7
yes
transition
0.6
Figure 6: Diagram to determine the state of the
generator torque controller.
transition curve, until both transition curves
coincide. This process is summarised in figure 6.
0.5
0.4
0.3
0.2
optimum Lambda
0.1
0.6
0.7
0.8
0.9
rotor speed
1
1.1
1.2
file e:\schaak\ctrltool\report\complete3.ps 24-Apr-2003
by e:\schaak\ctrltool\m\rappfigs.m
Figure 5: Generator torque control with the default
transition curve; the ‘mixed version’ full load curve
has been applicable.
premature generator controller, the rotor speed
range that almost completely will cover full load
To guarantee that the average generator power
matches the nominal power during full load
operation, the torque is scheduled adaptively. This
will result in slightly lower actual torque settings
for rotor speeds in the range of nominal ±6%.
5. Simulation results
Using ECN’s control design tool for wind turbines
we performed some simulations for the turbine and
the controller that has been designed in paragraph 4.
During the simulations the temporary transition
curve was realised as the default transition curve,
but shifted to lower rotor speeds (i.e. to the left in
figure 5) and enlarged to remain connected to the
other curves. Its junction to the optimum -Lambda
curve is shifted to the left as much as its junction
with the full load curve. So the temporary transition
curve becomes slightly steeper as it is shifted to the
left. Furthermore the full load curve is defined
differently for rotor speeds below 0.93 times
nominal. There the speed-torque relation is defined
conform a temporary transition that joins the full
load curve at 0.93 times the nominal rotor speed.
The profit of the mixed version curve compared to
the other full load curves has been shown in figure
4 already, in which the average wind speed matched
1.6 times the nominal wind speed. Figure 7 shows
simulation results at the same wind speed, but now
applying the mixed version curve is compared to
conventional generator control.
windspeed: 1.6*nominal
control: conventional
Ω r / Ωnom
1.1
1
Te / Tnom
0.9
100
200
300
400
500
600
0.8
0.6
Pe / Pnom
200
300
400
500
600
700
100
200
300
200
300
400
500
600
700
500
600
700
o
o
Θ [ ] and dΘ/dt(:) [ /s]
0.6
30
20
10
0
100
400
t [s]
file e:\schaak\ctrltool\report\simConvVw3.ps 24-Apr-2003
by e:\schaak\ctrltool\m\KarSftSims.m
windspeed: 1.6*nominal
control: proposed
1.1
Ωr / Ω nom
The first 2 advantages together increase the yearly
production by about 1.5%. We also observe 3 minor
drawbacks:
1
0.8
1
0.9
100
T e / Tnom
1. Production dips have been eliminated:
realised by extending the full load curve for
rotor speeds below nominal.
2. Nominal power is reached earlier:
as a consequence of applying the transition
closer to optimum-Lambda.
3. When the production dips of the conventional
situation are excepted, the generator torque still
varies significantly less during full load
operation:
realised by applying the mixed version curve
that covers a narrower torque range.
4. During full load operation the average rotor
speed is lower:
because in the conventional situation a raised
desired rotor speed has been applied to reduce
production dips.
700
1
100
The first three plots from above sho w the rotor
speed, generator torque and generator power, all
normalised on their nominal values. The fourth plot
shows the blade pitch angle in degrees and the
blade pitch speed in degrees per second (around 0).
We also simulated at other wind speeds [11]. Those
simulations are not shown here. Only a summary of
the observations is given. When we replace a
conventional generator control algorithm by the
proposed algorithm we observe the following
advantages:
200
300
400
500
600
700
200
300
400
500
600
700
200
300
400
500
600
700
200
300
500
600
700
1
1. During full load operation the maximum
generator torque has been increased by 3%:
caused by applying the extended full load
curve above the nominal torque.
2. During full load operation the rotor speed varies
slightly more:
caused by applying the extended full load
curve that covers a broader rotor speed range.
3. Switching from full to partial load behaviour
comes through more expressively in the generator
torque:
caused by postponing the switching moment.
0.8
0.6
Pe / Pnom
100
1
0.8
Θ [o] and dΘ /dt(:) [o/s]
0.6
100
30
20
6. Verification and prospective
Using models of commercial wind turbines, the
outstanding performance of the mixed version
curve has been confirmed by the aero-elastic wind
turbine code Phatas as well [8]. The first
implementation on a turbine is planned for 2005.
10
0
100
400
t [s]
file e:\schaak\ctrltool\report\simPropVw3.ps 24-Apr-2003
by e:\schaak\ctrltool\m\KarSftSims.m
Figure 7: Simulation results for a representative
multi-MW wind turbine controlled conventionally
(upper plots) and conform the mixed version curve.
7. Results and conclusions
ECN’s control design tool for wind turbines has
been equipped with a modern generator control
algorithm. Compared to the algorithms found in
literature our algorithm reduces electromagnetic
torque variations of variable speed wind turbines by
50%, while achieving constant power behaviour.
The algorithm meets the state of the art of
preventing for production dips and has been
examined by the aero-elastic wind turbine code
Phatas. A wind turbine manufacturer is preparing
the application of the algorithm on a commercial
turbine.
Acknowledgement
The authors like to thank the Netherlands Agency
for Energy and Environment Novem for funding a
part of this research (contract 2020 -01-12-10-003).
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Wind
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