Journal of Wind Engineering and Industrial Aerodynamics, 27 (1988) 237-246
237
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
OPTIMAL CONTROL OF WIND POWER PLANTS
M. STEINBUCH 1,2, W.W. de BOER I, O.H. BOSORA 2, S.A.W.M. PETERS I, J. PLOEG 2
IN.V. KEMA, P.O. Box 9035, 6800 ET Arnhem (The Netherlands)
2Delft University of Technology, Mekelweg 2, 2628 CD Delft (The Netherlands)
SUMMARY
The control system design for a wind power plant is investigated. Both the
overall wind farm control and the individual wind turbine control effect the
wind farm dynamic performance.
For a wind turbine with a synchronous generator and rectifier/inverter
system a multivariable controller is designed. Using the optimal output
feedback method a compromise is found between speed, power fluctuations and
mechanical load. Nonlinear simulations show the superior performance compared
to a classical control design.
Preliminary results for the overall wind farm control show that the
compensation of aerodynamic interactions between the wind turbines for energy
maximisation is beneficial. Load control is even more important, especially in
combination with wind prediction models.
INTRODUCTION
Application of wind power plants coupled to the public grid reveals several
new aspects with respect
to load control
and power system dynamic behavior.
The major problems are the fluctuating nature of the energy output,
effectiveness,
and the life time of the wind turbines.
control design methodology,
it is possible
the cost
Using an appropriate
to use active control systems to
find a compromise between power fluctuations, energy generation and life time.
On behalf of the construction and operation of the Dutch National Wind Farm
at Sexbierum, a study is being performed on the control system design for wind
power plants. The aim of this research is to develop,
implement and evaluate
control strategies for wind power plants. This is worked out at two levels.
First
the
investigated.
control
system
Secondly,
design
for
the
individual
wind
the overall control design is analysed,
turbines
is
in order
to
account for aerodynamic and electric interactions between the individual wind
turbines.
Scope o f the paper
0
Because the overall power plant behavior depends heavlly on the performance
of each wind turbine system,
0167-6105/88/$03.50
the control system design for the wind turbines
© 1988 Elsevier Science Publishers B.V.
238
is discussed in part A first. Using a dynamic model an optimal multivariable
controller
has been designed.
With nonlinear simulations
the performance
is
shown, in comparison with a classical PID design.
The second part of the paper adresses the design approaches for wind farm
control. Preliminary results are shown.
A. WIND TURBINE CONTROL
Description of the system
The
system
under
investigation
is
a
three-bladed,
horizontal
axis wind
turbine with a rated power of 300 kW (see Fig. I). It has a relatively heavy
rotor
and
generator,
and
an
an
electrical
conversion
a controllable
inverter.
system
consisting
thyristor bridge rectifier,
Hence,
rotor
speed ~
of
a DC
is variable so
a
synchronous
(ripple)
that an
reactor
increase
in
energy output and a decrease in mechanical loads can be obtained. In addition,
the electrical power or direct current Idc must be controlled. The available
inputs
are:
delay
angle
Ur
of
the
rectifier,
field
voltage
uf
of
the
synchronous generator and pitch angle ~ of the blades.
ROTOR
GEAR
GENERATOR
RECTIFIER
INVERTER
GRtD
V
Fig. I.
wind turbine system with synchronous generator and DC Link.
Dynamic model
To
be
able
performance,
properly.
In
it
to
design
is
this
control
necessary
study,
to
systems
model
the
the aerodynamic
and
to
dynamics
part
evaluate
of
the
is modelled
the
wind
using
dynamic
turbine
a simple
nonlinear stationary model. The mechanical part is modelled by a first order
lag
(rotor
inertia),
and
second
order
dynamics
of
torsional
oscillations
resulting from a flexible element in the secondary shaft (tel. I).
The dynamics of the electrical conversion system are very important because
239
with these the wind turbine mechanics can be influenced very fast. A nonlinear
five-state
variable
model
has
been
build
to
describe
these
dynamics
(see
ref. 2).
From the complete nonlinear model,
linear models are obtained at several
operating conditions.
Controller design
The
requirements
which
turbine systems depend on
can
be
load conditions maximisation of
strategy.
However,
in
stated
on
the
dynamic
behavior
the type of operating condition.
this
energy output
paper
we
restrict
results
the
of
wind
E.g. at partial
in a variable
analysis
to
speed
full
load
conditions only. At full load (v > 12 m/s) rotor speed and power have to be
constant.
Nevertheless,
fluctuations
provided
that
this
in these variables are tolerated
certain
extent
control
system design must offer a compromise,
results
in
lower
mechanical
to a
loads.
despite restrictions
The
in the
input variables such as the bounded rate of change of the pitch angle of the
blades.
In
summary,
measured
the
outputs
(w,
wind
Idc)
turbine
and
a
has
set
three
of
inputs
conflicting
(~,
ar,
uf),
requirements
two
stated
above. This makes the problem very suitable to be treated as an optimisation
problem. A powerful method, which can handle multiple input/output systems in
a natural way,
is the linear quadratic optimal control method (e.g. ref. 3).
The requirements are stated in the form of an integral performance index:
(l)
J : ~ (ql~2 + q2I~c + ... + r182 + r2u~ + ...) dt
o
The control
problem is now reduced to finding the weighting factors qi and
r i. and to calculate the controller C which minimises J.
The first results were obtained using state-feedback, and were presented in
ref. 4. Here the results are shown for a implementable controller, obtained
using
robust
output
feedback.
More
details on
the design
can
be found in
ref. 5.
Results
The
dynamic
behavior
of
the wind
turbine system
is simulated using the
complete nonlinear model. The optimal multlvariable controller is compared to
a classical PID design, which is based on a slngle-lnput slngle-output (siso)
approach. As a test case, a large wind gust is used (fig. 2).
240
\
\
windspeed
o
8.00
0.00
t8,O
TIME
Z4,0
~..0
5
40.0
I. Optimal controller
2. Siso-controller
2
rotor speed
z
2
0.00
8.00
16,0
TIME
~2.,0
Z+P.O
5
1
4"0.0
7
electrical power
N
8
0.~
8.~
15.0
TIME
5
24.0
~2.0
40.0
Fig. 2. Wind gust response of the wind turbine with
(i) and with the siso-controller (2).
the optimal controller
241
In fig. 2 the responses of the rotor speed and of the electrical power are
shown.
Both
rotor
speed
fluctuations
the optimal
very
controller
well
(=
I%
(I) and the siso-design
deviation).
However,
(2) control
the
differ enormously between both controllers.
power
the
output
The siso--design (2)
results in a 80 kW variation, while the optimal multivariable
controller
(I)
gives a 3 kW (1%) fluctuation. Obviously, these variations are also present in
the torques, which makes the optimal controller design even more preferable.
The
reason
for
the
difference
between
the
controllers
is
that
the
multivariable controller compensates for the internal interactions in the wind
turbine system,
and uses the three inputs in the most efficient way. This can
be illustrated with the behavior of the pitch angle (fig. 3). It is seen from
the figure
pitch
angle
variations,
that
the optimal
then
the
siso
controller
controller
(I) acts a fraction earlier
(2)
does.
This
leads
to
on the
less
power
despite the restriction in the rate of change of the pitch angle
(d~/dt < 5°/s).
o
"o
o
8
0,00
8.00
[6.0
TIME
5
24.0
~.0
4.0
Fig. 3. Behaviour of the blade pitch angle at a wind gust: with (I) optimal
controller, (2) siso-controller.
Conclusions and further remarks on wind turbine control
The
design
approach
results
shown,
can
used
be
indicate
to
obtain
leads systematically
fluctuations and mechanical
that
a
a multivariable
superior
wind
optimal
turbine
control
system
performance.
This
to a proper compromise between power and speed
loads. The design methodology is straightforward,
and as simple as slso-controllers to Implement in digital computer systems.
242
B. WIND FARM CONTROL
Introduction
The control design for an individual wind turbine is focussed at an optimal
performance for a solitary wind turbine.
control
system
interaction
is
not
is not
farm control
necessarily
taken
But for a group of wind turbines this
optimal.
into account
to enhance
example
in the design
could reduce unfavourable
also be needed
For
interactions.
controllability
of
the
aerodynamic
the control.
A wind
A wind
farm control
can
or quality of the power output of
the farm.
This part presents a study which investigates
farm control.
First
concepts
theoretically
are
an overview will
the potentialities
of a wind
be given from the literature,
next some
investigated
for
the
Experimental
Wind
Farm
in
Friesland.
Literature
In
the
turbines
USA
penetration
surveys
were
published
level of wind turbines
modifications
and/or
some
into the utility grid (e.g. refs.
have
to
be
made
on
the
6-8).
aspect
of
A conclusion
fitting
wind
Is that if the
is above 5% of the area energy production,
in
the
normal
in the operation of the wind turbines
utility
operating
procedures
(refs. 6-7). A wind farm control
can be of great importance for this latter aspect,
In
ref.
control
its
8 such
strategy
capacity,
a control
is proposed.
and prescribes
the
load
and
It
is a part
how to operate
the
ramping
a wind
capability
of
of
a sophisticated
farm as a function of
the regulating
units.
Three control regimes are specified for the operation of wind turbines. A wind
farm control
fast
power
compensate
by
sending
is involved
changes.
In
in one of these regimes and its purpose is to smooth
this
way
the
regulating
the fluctuations of the wind turbines.
power
setpoints
to
the
wind
units
have
enough
time
to
The fluctuations are reduced
turbines
(load
control).
For
the
determination of these power setpoints wind velocity prediction is used.
In ref.
9 a practical
experience
wind farm at the Hawaii island,
has
implemented
control
systems
is described
of a wind
farm control.
A
consisting of 15 wind turbines of 600 kW each,
on
two
levels:
I, a control
system
for
the
individual wind turbine and 2.an overall control for the wind farm.
The purpose
of
the control
systems
is to operate
the wind
farm as a single
operating unit. The overall wind farm control has two modes:
I. the control
sends a setpoint
to each wind turbine and it does not monitor
or readjust the setpoints after sending
2. the control does performance
these actions,
so that
the output of the wind
243
farm is controlled actively (i.e. closed loop).
In ref.
9 it is concluded
that
following the first operation o£ the farm,
expectations are high for a trouble free integration into the utility grid.
From the above it can be concluded that load control, consisting of sending
power setpoints to the wind turbines is important, especially with large wind
turbine penetration.
Little or no attention is paid to reducing small power
variations due to turbulence with a wind farm control. Similarly there is no
attention
paid
in
reducing
the
aerodynamic
interaction
with
a
wind
farm
control for maximising energy generation.
The potentiality of load control as well as wind farm control for the last
mentioned objectives will be considered
in the next sections.
This will be
done with respect to the Experimental Wind Farm.
Load control
The planned increase of wind turbines in the Netherlands makes it sensible to
pay attention to load control.
To achieve load control it is necessary to control the energy output of the
wind farm on a scheduled but realisable value, even at wind speeds less than
rated. This implies that operation with pitch angle control is needed.
For scheduling a power setpoint wind power or velocity prediction is needed
(ref.
8)
To
predict
wind
power
Measurement Grid can be used.
the
information
of
the
Sap-National
Wind
A first step in developing a wind prediction
method is given in ref. I0.
Minimisinq power variations due to turbulence
Simulations showed that the influence of the control of the individual wind
turbines is large upon the wind farm power fluctuations (ref. 11). For example
in
fig.
4
the
~max = I m/s 2)
farm output
passing
in
a
is given
worst
for a strong
case
direction
gust
through
(v = 13 ~
the
19 m/s,
Experimental
Wind Farm. The wind turbines are controlled using a siso-controller which is
compared to the optimal controller from part A.
This
shows
controlled
that
the
wind
siso-controlled
power
turbines
wind
fluctuation
are
turbines.
of
the wind
very
small
Responses
on
farm with
(20 kW)
wind
noise
the optimal
compared
showed
to
the
the
same
influence of the type of control system.
The simulations
indicate
that using an optimal
individual control system
design for uprated wind speeds (full load conditions), it is hardly necessary
to develop an overall farm control for this purpose.
244
However,
power
the operation
fluctuations,
farm control
due
could
at wind
speeds
to the strategy
be desirable
to reduce
to a strong gust. This can be done using
pitch angle. However,
downrated
(partial
to maximise
load)
show more
the power output.
A wind
fast wind farm power excursions
due
load control with acting on the blade
some wind power will then be spilled.
5.90
r'
5.85
5.80
4J
5.75
4J
o
5.70
r..
5.65
5.60
5.55
10
20
30
Time
40
50
60
(s)
Fig. 4.
Simulations of the wind farm output when a wind gust (v=13~19 m/s)
is passing in a worst case wind direction through the Experimental Wind Farm.
The wind turbines are siso (--) and optimal (- - -) controlled.
Maxlmising energy capture
After
there
finding
is
a
turbines
down
keeping
the
rated.
tip
power coefficient
P
r
a good trade off between power variations
possibility
in
For
speed
maximising
an
individual
ratio
k
energy
wind
(= ~R/v)
capture
turbine,
optimal.
and spilled energy
for
a
energy
With
group
of
is maximised
this
strategy
(p = s p e c i f i c
a
mass o f
solitary
necessarily
eqn.
(2)
wind
farm
wind
(2)
the a i r ,
the best strategy
wind
A = rotor
turbine
the rotor power
the
by
the
C (l) and thus the rotor power P is maximal:
p
r
= ~.C ( k ) . p . A . v 3
p
For
wind
speed
this
is
for wind
is strongly
near
wind
a r e a , v = average wind speed)
the
best
turbines
grouped
influenced
turbines
strategy,
but
this
together.
by the wind speed
in a wake,
depends
is
not
As shown in
(v3).
on
the
In a
tip
245
speed ratio of the up wind turbines. If these tip speed ratios are reduced,
C
of these up wind turbines are also reduced, but the wind speeds in their
P
wakes are higher. This is of benefit for the energy capture of the wind
turbines
down
wind.
This
can
be
reformulated
as
finding
tip speed
ratios
k i so that
n
3
Pfarm(kl ...... k n) = ~ Y,.Cp(kl). P.A.vi(ki_ I, kl_ 2 ..... )
i=l
is
maximal
(n=number
of
WT's,
i=index
of
ie
(3)
WT,
vi(ki_ I,
ki_ 2 .... )
= wind speed near i th WT as a function of k's from the up wind WT's).
For
example:
kopt-l,
a wind
2nd
array
farm
by
can
be chosen
kopt-~
and
to operate
3rd
array
the up wind
by
lop t .
A
array
wind
by
farm
control can send these values to the wind turbines as a function of the wind
direction.
With
a
simulation
program,
"Milly"
(ref.
12),
such
a
strategy
is
investigated for the Experimental Wind Farm. The program Milly calculates the
wind
speeds
approach
as
a
to find
function
k i,
of
k.
showed minor
Simulations,
effects
for
using
a
trial
and
error
the Experimental Wind
Farm.
But when other types of wind turbines were used a slight increase was shown
(max. 4%, ref.
II). Therefore,
the favourable effect of this new strategy is
proved to exist, but needs further research.
Conclusions wind farm control
Especially
important.
when
wind
power
penetration
is
increasing,
load
control
is
It is unnecessary to reduce power fluctuations due to turbulence
with a wind farm control, if the individual wind turbines are equipped with a
good
control
(uprated).
Finally,
a
farm
control
strategy
downrated
can
(slightly) increase the overall energy capture.
In
a
next
phase
wind
farm
controls
are
further
investigated
for
the
Experimental Wind Farm based upon the results shown.
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1
2
M. Steinbuch and F. Melting, Analysis and simulation of a wind turbine with
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M. Steinbuch, Dynamic modelling and analysis of a wind turbine with
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3
H. Kwakernaak
and
R. Sivan,
Linear
optimal
control
systems,
Wiley
Interscience, New York, 1972.
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