DEVELOPMENT OF WIND TURBINE CONTROL ALGORITHMS FOR INDUSTRIAL USE
T.G. van Engelen, E.L. van der Hooft, P. Schaak
Energy research Centre of the Netherlands (ECN), Wind Energy
P.O. Box 1, NL-1755 ZG Petten, The Netherlands
Telephone: ++31 224 564141
Telefax: ++31 224 568214
email: [e-mail]
ABSTRACT: A tool has been developed for design of industry-ready control algorithms. These pertain to the prevailing
wind turbine type: variable speed, active pitch to vane. Main control objectives are rotor speed regulation, energy yield
optimisation and structural fatigue reduction. These objectives are satisfied through individually tunable control loops.
The split-up in loops for power control and damping of tower and drive-train resonance is allowed by the use of dedicated
filters. Time domain simulation results from the design tool show high-performance power regulation by feedforward of
the estimated wind speed and enhanced damping in sideward tower bending by generator torque control. The tool for
control design has been validated through extensive test runs with the authorised aerodynamic code PHATAS-IV.
Keywords: Control, Variable speed operation, Dynamic models.
1. INTRODUCTION
generator curve
generator speed
&!
curve
blade angle
The number of wind turbine manufacturers that apply pitch Ś
T
generator torque
T
full gen
control towards feathering position for power limitation is tower nodding
xnod
load
xnay tower naying
increasing considerably. Usually, pitch-to-vane control is
&! u tilt control
low pass
combined with variable speed operation, which is facilitat-
xnod
ed by commercially available fast switching components in
power electronics. Operation outside stall conditions and en- band
pass fore/aft tower "Śdamp
�0t
thrust control
hanced energy yield around and below nominal wind speed
+
are major drivers towards this concept. In comparison with
low
&!nom pass aero power Śset pitch Ś
Śfull
�3p
power reduction by stall, the axial blade and tower loading control actuator
+ _ +
is smaller and the aerodynamic behaviour is much better
very low
Tcurve Tset
electric power EM-torque
pass
Tgen
predictable. Especially at offshore siting the first feature is
servo
control
+
+
�v
being considered more important than ever because of the
w
band
shaft torsion
pass
extreme high reliability requirements.
torque control
�0d
+
"Tdamp
This situation raises the need for control algorithms for vari-
band
lateral tower +
pass
able speed pitch-to-vane wind turbines. For this reason, a
�0t torque control
xnay
design tool for such control algorithms has been developed
&!
at ECN [4]. This paper addresses the following topics of the
control tool:
Figure 1: Feedback loops for control of rotor speed, power,
" problem identification and approach;
tower bending and shaft distortion
" turbine modelling and design principles;
" time domain simulation results.
distortion damping are typical narrow band processes around
�0t and �0d, both (far) beyond �Vw (low- and band-pass
2. CONTROL PROBLEM AND APPROACH
filters in fig. 1). Furthermore, the frequency �3p applies
(<" 0.6-1.2 Hz). This is the center frequency of the effects
The main control loops concern the power production and
of rotationally sampled turbulence and tower shadow. For a
rotor speed behaviour. Besides, control loops can be added
3-bladed rotor, this is 3 times the rotational frequency (3p);
for compensation of resonances (active damping). The latter
for a 2-bladed rotor this �2p (2p), which does not differ much
loops are not allowed to significantly disturb the primary
from �3p as the rotor speed is considerably higher for a 2-
control functions. The resonances may appear in the rotor
blader. A suitable filter should eliminate these Bp-effects in
blades, the drive-train and the tower. In a multivariable
the pitch-actuator activity (B=2,3). However, an exception
design approach [1] the difference between all loops will not
can be made for the control loop on shaft distortion as this
exist any more. In the developed design tool, the different
loop can also be used for reduction of inertia loads caused
control loops (fig. 1) are designed separately.
by  Bp rotor acceleration .
Separate loop design is enabled because the frequency ranges
The control scheme in fig. 1 does not deal with resonance
of the phenomena to be controlled significantly differ, which
of rotor blades because it is limited to active damping on-
is illustrated in figure 1. The following typical frequencies
ly. Blade resonance is usually reduced by passive damper
exist:
devices ( mass spring damper systems).
" �Vw: rotor uniform turbulence (<"0.07 Hz);
" �0t: first tower bending mode (<"0.35 Hz);
3. MODELLING AND CONTROL SYNTHESIS
" �0d: first shaft distortion mode (<"2.5 Hz).
The next subsections deal with the turbine model for control
Aerodynamic and electric power control (thick-line blocks)
design and the synthesis principles of the identified loops.
concerns frequencies around �Vw . Tower bending and shaft
3.1 Model for control design expressions in the pitch angle. The approach is based on the
dynamic inflow modelling principle in [6] .
The control tool includes models for wind and wave influ-
ences and for the dynamic response of the wind turbine. The The stochastic wave simulation is based on water depth de-
model features are listed below and discussed afterwards. pendent power spectra of the wave velocity and the wave
acceleration. All these spectra are governed by the pow-
External influences:
er spectrum of the surface elevation through the linear wave
" stochastic wind and wave generation;
theory (Airy) [7]. Figure 3 shows for a water depth d of 20 m
" aerodynamics by BEM-theory;
the (fully) correlated horizontal wave speed and acceleration
" dynamic inflow effect of blade pitching;
signals on 55%, 65%, up to 95% of d above the sea bottom.
" hydrodynamics by Morison s equation.
A Pierson Moskowitz wave spectrum has been applied at an
average wind speed of 12 m/s.
Wind turbine system dynamics:
" first bending mode of tower (2 directions);
Afstand tot grond: 55% 65% 75% 85% 95% van waterdiepte van 20.0 m
0.6
" first distortion mode of drive-train;
0.4
" linear servo behaviour for generator torque; 0.2
0
" non-linear servo behaviour for pitch actuation;
-0.2
" delayed and quantisized measurements.
-0.4
-0.6
The stochastic wind simulation is based on a rotor-wide
-0.8
100 110 120 130 140 150 160 170 180 190 200
description of the effect of rotationally sampled wind turbu-
lence, tower shadow and wind shear. This approach is based
1
on the modelling principle in [3]. A wind signal is obtained
0.5
by inverse Fourier transform of  the rotor-wide power spec-
0
trum of the wind field as  sampled by the rotor blades. This
spectrum is derived from auto power spectra and coherence
-0.5
functions in accordance with IEC standards. Figure 2 shows
-1
100 110 120 130 140 150 160 170 180 190 200
a typical generated wind speed signal; the detailed lower
tijd [s]
file F:\tgengel\ctrltool\MODELS\PS\khv12d20.ps 08-Dec-2000
by F:\tgengel\ctrltool\MODELS\M\hydrload.m
graph visualises the effect of rotational sampling and tower
shadow on this signal (Bp-effects).
Figure 3: Realisation of wave speed and acceleration
wind signal for power and thrust coefficient data including turbulence and tower shadow
16 Note that the lower graph in fig. 3 shows the product of
14 mass coefficient Cm and wave acceleration a. This product
12 is the  force effective acceleration with wave diffraction
included as proposed by MacCamy and Fuchs [2]. If the
10
waves are perpendicular to the wind, Morison s equation for
8
the (lateral) wave force per unit tower length fhy on z m
6
0 50 100 150 200 250 300 350 400
below the sea surface is given by
11.5
2 eff
1
11 fhyz = �water � ĄDz � (�z - ćnyz ) +. . .
4
10.5
H
1
10 Cd � �water � Dz � (wz - �nyz ) � |wz - �nyz | ,
2
9.5
9
with tower diameter Dz, wave speed wz and force effective
8.5
eff
acceleration �z , naying speed �nyz and acceleration ćnyz .
8
100 102 104 106 108 110 112 114 116 118 120
H
time [s]
Realistic values for the drag coefficient Cd lay between 0.6
file F:\tgengel\verkoop\articles\ewec01\paper\fgvweff.ps 26-Jun-2001
and 1.2 [7].
Figure 2: Realisation of rotor-wide wind speed
Tower bending and drive-train dynamics are modelled by the
following set of mutually dependent differential equations
The rotor-wide wind speed Vw is fed through power and
(waves perpendicular to wind):
thrust coefficient data (Cp, Ct) for conversion to the aero-
dynamic torque Ta and axial force Fa (with nodding speed
mtćnd = -kt�nd - ctxnd + Fa cos �tilt ,
�nd; rotor blade radius Rb, tip speed ratio ):
Tnac
3
mtćny = -kt�ny - ctxny + + . . .
2
3 Lt
1
Ta = Cp(�ac, )/ � �ĄRb � (Vw - �nd)2 ,

2
d
2
1
F(fhyz )dz ,
Fa = Ct(�ac, ) � �ĄRb � (Vw - �nd)2 .
2
0
Jr�Jg
� ł = -cd � ł - kd � ł + . . .
� Ł
The pitch angle value �ac as used in aerodynamic conversion
Jr+Jg
is obtained from the  physical pitch angle value �ph by Jg
Jr
� (Ta - T ) + � Te ,
Jr+Jg Jr+Jg
having �ph led through a so called lead-lag filter. This filter
Ł
models the dynamic inflow effect of pitching through the
Jr � &!r = -cd � ł - kd � ł + Ta - T .
Ł
following differential equation:
The shaft distortion speed ł is the difference between ro-
Ł

d d
tor speed &!r and  slow shaft level generator speed &!g/igb
�iDI � (�ac) +�ac = �dDI � �ph + �ph .
dt dt
(gearbox transmission ratio igb). Jr and Jg are correspond-
The time constants �iDI and �dDI depend on the operating ing moments of inertia; cd and kd are the shaft stiffness and
conditions. The actual values are obtained from polynomial damping constant for the 1st distortion mode with natural
golf
v
[m/s] bij 12.0m/s
2
m
golf
C
�"
a
[m/s ] bij 12.0m/s
[m/s]
[m/s]
meas
Ś
damping rate �d (<" 0.005). Tower mass mt and damping
and stiffness constant kt and ct are the tower top equivalent
partial load
LPF
pitch setting
&!3pfilt
r
parameters for the 1st bending mode with natural damping
Ś3pfilt
nom
rate �t (<" 0.005).
&!
r setpoint
scheduling
adaptation
The integral of function F in the hydrodynamic force dis-
ref part
&!r
Ś
set
tribution fhyz yields the tower top equivalent hydrodynamic Ś
PD LL
+ +
- +
load. Function F caters for the shape of the 1st bending
+
full switch limitation
inactivity zone
&!3pfilt feedback dynamic inflow Ś
r
compensation force
mode and the distance Lt - (d-z) between the tower top
Ś
meas
&!
r
forced speed full / partial
and fhyz . The loss torque T is modelled by a constant and
D
limitation load selector
a rotor speed dependent term. The sideward tower bend-
`feedforward'
est
ing torque Tnac approximately equals the (slow shaft level) Ta 3pfilt
&!3pfilt
&!r
r
+
J d/dt LPF
&!
P/
generator torque Te.
+
low-pass
The servo behaviour of the generator torque is modelled by 3pfilt
meas
Pe
Pe
Te
LPF
2nd order dynamics with cut-off frequency �sv and damping
Te
torq
rate �sv . The pitch servo model includes both 2nd order
&!
r
VLPF
Ł Ł Ł
� � �
dynamics (�sv, �sv) and a delay �d that depends on sign
set
very low-pass
Te
full
reverse in pitching speed setting and on the thrust force. load
torque/speed curve
Control tool modules. The models listed above have been
Figure 4: Feedback structure for power control
implemented in MATLAB program modules for numeric
integration in time domain simulations. They also have been
included in linearised form (transfer functions) in program
for &!ref- &!3pfilt as much as allowed in more favourable
r r
modules for frequency domain based controller synthesis.
est
operating conditions and by fitting the D-gain for Ta on
the inverted power coefficient data (gain scheduling).
3.2 Power control and resonance damping
Next to models for wind, waves and wind turbine system
The feedback gains for tower and drive-train damping are
dynamics, the control tool incorporates feedback structures.
derived from isolated analysis of the governing equations for
These pertain to aerodynamic and electric power control and
the 1st bending and distortion mode. The tower loops include
to damping of resonance in the tower and drive-train. The
narrow band-pass filters with nearly zero phase shift around
features are listed below and discussed afterwards.
the tower eigenfrequency �0t. Additionaly, sharp band-
stop filters reduce the peaks around the mBp-frequencies
Aerodynamic and electric power control:
(m = 1, 2) in the nodding signal. The drive-train loop
" rotational speed feedback with setpoint adaptation;
includes a high-pass filter and a Kalman filter for estimation
" non-linear feedforward of estimated wind speed;
of the shaft distortion from the generator speed.
" dynamic inflow compensation;
The servo systems for the actuators behave ideal in the tower
" inactivity zone and filtering of Bp-effects;
Ł
� Te
" scheduling of control parameters;
loops (�sv �0t, �sv �0t), whereas in the drive-train loop
Te
" forced rotational speed limitation;
the actuator bandwidth is sufficiently large (�sv e" 2�0d).
" partial load pitch setting;
The filtered tower signals and estimated distortion speed
" smooth transients between partial and full load;
Ćhp)
(ćbp, �bp, ł are fed back to damping contributions in
Ł
ny
nd
" low-pass effectuation of torque/speed curve.
pitch speed and torque setting:
Tower bending and drive-train distortion damping
r
Ł
"�nd = Knd � ćbp ,
nd
" nodding acceleration feedback to pitch speed;
r
"Tny = -Kny � �bp ,
ny
" naying speed feedback to generator torque;
r
" narrow band-pass filter in tower loops;
Ćhp
"Ttr = -Ktr � ł .
Ł
" shaft distortion speed feedback to generator torque;
" Kalman filter in drive-train loop; The relevant parts of the bending and distortion equations
are then approximated by ("Fa < 0):
" maximum level in control effort.
"�
"Fa
Figure 4 visualises the feedback structure for aerodynam-
mtćnd <" -kt�nd - ctxnd -| | � Knd � �nd ,
"�
ic and electric power control. The proportional differ-
Kny
3
mtćny <" -kt�ny - ctxny - � �ny ,
ential (PD) feedback of the filtered rotational speed error 2
Lt
&!ref- &!3pfilt is the core of the aerodynamic control loop;
r r Jr�Jg
Jr
Ćhp
� ł <" -cd � ł - kd � ł - � Ktr � ł .
� Ł Ł
Jr+Jg Jr+Jg
it is the usual approach to control the inertia based rotor
dynamics. The differential (D)  feedforward of the estimat-
This yields the following enhanced damping rates:
est
ed aerodynamic torque Ta effectuates pseudo wind speed
"Fa
feedforward towards the pitch angle that belongs to the actual kt+| |�Knd
"�
"
�tnd <" ,
2 mtct
wind speed. The lead-lag filter for dynamic inflow compen-
3
sation (LL) implements the inverse of the dynamic inflow kt+ Kny/Lt
2
"
�tny <" ,
2 mtct
model equation in ż3.1.
kd+Jr/(Jr+Jg)�Ktr
"
�d <" .
The control gains in the feedback and  feedforward loop
2 JrJg /(Jr+Jg)�cd
are derived with Nyquist analysis in worst case operating
conditions (industry-adopted stability assessment). High- The feedback gains Knd, Kny and Ktr are tuned in non-
performance control is obtained by enlarging the PD-gains linear time domain simulations. The achievable damping
+
Effect naying damping (all filters included); dotted: bF = 1, solid: bF = 15
25
rate in realistic wind conditions is constrained by the allowed
20
level of (harmonic) control effort and stability requirements.
The nodding gain Knd is scheduled in a similar way as the
15
PD-gains for the rotational speed error.
0 50 100 150 200 250 300 350 400
2000
Control tool modules. The feedback structures listed above
have been implemented in MATLAB program modules for
1500
time domain simulation: the MATLAB edition of the con-
1000
trol algorithms. The algorithms are also available in the
0 50 100 150 200 250 300 350 400
programming languages C and Fortran for straightforward
0.1
incorporation in process computers and aerodynamic codes.
0.05
0
Besides, interactive program modules have been developed -0.05
-0.1
for parametrising the filters and gains of the linear parts in
0 50 100 150 200 250 300 350 400
the control loops; these modules include the linearised wind time [s]
file E:\schaak\TowDamp\SCOPE\PS\scnyeff.ps 01-Feb-2001
by E:\schaak\TowDamp\SCOPE\M\slnywtrs.m
turbine system dynamics. For overall stability and robust-
Figure 6: Lateral tower resonance at waves perpendicular
ness assessment, program modules have been developed for
to the wind (lower graph: naying acceleration [m/s2]; dash:
Nyquist analyses of the open loop transfer function. This
without damping)
transfer function is obtained by linearisation of the integrat-
ed model of the control loops and the wind turbine, with the
main feedback path cut through, that is to say the rotational
damping of tower bending and drive-train distortion. Spe-
speed measurement feedback path to the PD-action.
cial features are (i) dedicated filter design, (ii) wind speed
estimation in power control and (iii) shaft distortion estima-
4. SIMULATION RESULTS
tion by Kalman filtering.
The results plotted below apply to a typcial multi-MW (off-
The algorithms with the implemented control loops are clear
shore) wind turbine. They have been obtained from the
in implementation and operation, and are on-site tunable
simulation stage in the design tool. Validation runs with the
by well-educated operators. The C- or Fortran-coded algo-
aerodynamic computer code PHATAS [5] (control algorithm
rithms can be incorporated in process computers and aero-
included) yielded equal behaviour.
dynamic codes with very minor effort.
rotor effective wind speed (gray); estimated windspeed; rated wind speed (dashed)
The approach as implemented in the tool has been exensively
20
validated by non-linear time domain simulations with the
15 authorised aerodynamic code PHATAS [5].
10
ACKNOWLEDGEMENT
400 450 500 550 600 650
aerodynamic power (gray); electric power
5
Koert Lindenburg (ECN) is acknowlegded for his contribu-
4
tion to dealing with the impact of dynamic inflow on power
3
control and for the many validation runs with PHATAS. Jan
2
Pierik (ECN) is acknowlegded for his contributions to elec-
1
400 450 500 550 600 650
tric system modelling and desk top publishing.
rotor speed (gray); rotor speed setpoint; rated rotor speed (dashed)
18
16
REFERENCES
14
[1] P.M.M. Bongers; Modeling and Identification of flexi-
12
ble wind Turbines and a Factorizational Approach to Robust
10
400 450 500 550 600 650
Control, PhD thesis, ISBN 90-370-0100-9, Delft Universi-
pitch angle
ty of Technology, fac. of Mech. Eng., the Netherlands, 1994.
15
[2] S.K. Chakrabarti; Hydrodynamics of Offshore Structures,
10
Computational Mechanics Publications Southampton, 1987.
5
[3] J.B. Dragt; Atmospheric Turbulence Characteristics in
0
400 450 500 550 600 650
pitching speed
the Rotating Frame of Reference of a WECS Rotor. Pp 274-
4
278 in proc. ECWEC Conf. Madrid, Spain, 1990.
2
[4] T.G. van Engelen, E.L. van der Hooft and P. Schaak;
0
Ontwerpgereedschappen voor de Regeling van Windturbines
-2
-4
(in Dutch), Technical report, ECN Wind Energy, Petten, the
400 450 500 550 600 650
time [s]
Netherlands, Draft, June, 2001.
Figure 5: Aerodynamic and electric power control with wind
[5] C. Lindenburg and J.G. Schepers; PHATAS-IV Aeroe-
speed estimator
lastic Modelling, Program for Horizontal Axis Wind turbine
Analysis and Simulation, version IV, ECN Wind Energy,
Petten, the Netherlands.
5. CONCLUSIONS [6] H. Snel, J.G. Schepers; Joint Investigation of Dynam-
ic Inflow Effects and Implementation of an Engineering
A design tool has been developed for control algorithms for
Method. Technical Report ECN-C-94-107, ECN Wind En-
variable speed wind turbines. The by nature multivariable
ergy, Petten, the Netherlands, April, 1995.
control problem is split-up into physically interpretable con-
[7] J.F. Wilson; Dynamics of Offshore Structures. John
trol loops that are individually parametrised. These loops
Wiley & Sons, 1984.
pertain to aerodynamic and electric power control and to
rel
r
&!
[rpm]
e
T [kNm]
ny
a
[m/s]
[m/s]
[MW]
[rpm]
[dg]
[dg/s]