Development of wind turbine control algorithms for industrial use

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: vanengelen@ecn.nl

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

The number of wind turbine manufacturers that apply pitch
control towards feathering position for power limitation is
increasing considerably. Usually, pitch-to-vane control is
combined with variable speed operation, which is facilitat-
ed by commercially available fast switching components in
power electronics. Operation outside stall conditions and en-
hanced energy yield around and below nominal wind speed
are major drivers towards this concept. In comparison with
power reduction by stall, the axial blade and tower loading
is smaller and the aerodynamic behaviour is much better
predictable. Especially at offshore siting the first feature is
being considered more important than ever because of the
extreme high reliability requirements.

This situation raises the need for control algorithms for vari-
able speed pitch-to-vane wind turbines. For this reason, a
design tool for such control algorithms has been developed
at ECN [4]. This paper addresses the following topics of the
control tool:

• problem identification and approach;

• turbine modelling and design principles;

• time domain simulation results.

2. CONTROL PROBLEM AND APPROACH

The main control loops concern the power production and
rotor speed behaviour. Besides, control loops can be added
for compensation of resonances (active damping). The latter
loops are not allowed to significantly disturb the primary
control functions. The resonances may appear in the rotor
blades, the drive-train and the tower.

In a multivariable

design approach [1] the difference between all loops will not
exist any more. In the developed design tool, the different
control loops (fig. 1) are designed separately.

Separate loop design is enabled because the frequency ranges
of the phenomena to be controlled significantly differ, which
is illustrated in figure 1. The following typical frequencies
exist:

• ω

: rotor uniform turbulence (

∼0.07 Hz);

• ω

: first tower bending mode (

∼0.35 Hz);

• ω

: first shaft distortion mode (

∼2.5 Hz).

Aerodynamic and electric power control (thick-line blocks)
concerns frequencies around

. Tower bending and shaft

full

Ω

nom

set

band

pass

band

pass

very low

pass

band

pass

nay

aero power

control

pitch

actuator

fore/aft tower

thrust control

lateral tower

torque control

electric power

control

shaft torsion

torque control

Ω

gen

generator speed

blade angle

generator torque

nay

tower nodding
tower naying

nod

tilt control

curve

generator curve

full
load

EM-torque

servo

Ω

low pass

damp

∆

∆Θ

damp

set

curve

low

pass

Ω

nod

gen

Figure 1: Feedback loops for control of rotor speed, power,
tower bending and shaft distortion

distortion damping are typical narrow band processes around
ω

0 t

and

, both (far) beyond

(low- and band-pass

filters in fig. 1). Furthermore, the frequency

applies

(

∼ 0.6−1.2 Hz). This is the center frequency of the effects

of rotationally sampled turbulence and tower shadow. For a
3-bladed rotor, this is 3 times the rotational frequency (3p);
for a 2-bladed rotor this

(2p), which does not differ much

from

as the rotor speed is considerably higher for a 2-

blader. A suitable filter should eliminate these

Bp-effects in

the pitch-actuator activity (

B=2,3). However, an exception

can be made for the control loop on shaft distortion as this
loop can also be used for reduction of inertia loads caused
by ‘

Bp rotor acceleration’.

The control scheme in fig. 1 does not deal with resonance
of rotor blades because it is limited to active damping on-
ly. Blade resonance is usually reduced by passive damper
devices (‘mass spring damper’ systems).

3. MODELLING AND CONTROL SYNTHESIS

The next subsections deal with the turbine model for control
design and the synthesis principles of the identified loops.

3.1 Model for control design

The control tool includes models for wind and wave influ-
ences and for the dynamic response of the wind turbine. The
model features are listed below and discussed afterwards.

External influences:

• stochastic wind and wave generation;

• aerodynamics by BEM-theory;

• dynamic inflow effect of blade pitching;

• hydrodynamics by Morison’s equation.

Wind turbine system dynamics:

• first bending mode of tower (2 directions);

• first distortion mode of drive-train;

• linear servo behaviour for generator torque;

• non-linear servo behaviour for pitch actuation;

• delayed and quantisized measurements.

The stochastic wind simulation is based on a rotor-wide
description of the effect of rotationally sampled wind turbu-
lence, tower shadow and wind shear. This approach is based
on the modelling principle in [3]. A wind signal is obtained
by inverse Fourier transform of ‘the rotor-wide’ power spec-
trum of the wind field as ‘sampled’ by the rotor blades. This
spectrum is derived from auto power spectra and coherence
functions in accordance with IEC standards. Figure 2 shows
a typical generated wind speed signal; the detailed lower
graph visualises the effect of rotational sampling and tower
shadow on this signal (

Bp-effects).

100

150

200

250

300

350

400

wind signal for power and thrust coefficient data including turbulence and tower shadow

[m/s]

100

102

104

106

108

110

112

114

116

118

120

8.5

9.5

10.5

11.5

[m/s]

time [s]

file F:\tgengel\verkoop\articles\ewec01\paper\fgvweff.ps 26−Jun−2001

Figure 2: Realisation of rotor-wide wind speed

The rotor-wide wind speed

is fed through power and

thrust coefficient data (

) for conversion to the aero-

dynamic torque

and axial force

(with nodding speed

˙x

; rotor blade radius

, tip speed ratio

λ):

(θ

, λ)/λ ·

1
2

ρπR

3
b

· (V

− ˙x

)

(θ

, λ) ·

1
2

ρπR

2
b

· (V

− ˙x

)

The pitch angle value

as used in aerodynamic conversion

is obtained from the ‘physical’ pitch angle value

having

led through a so called lead-lag filter. This filter

models the dynamic inflow effect of pitching through the
following differential equation:

(θ

) + θ

= τ

+ θ

The time constants

and

depend on the operating

conditions. The actual values are obtained from polynomial

expressions in the pitch angle. The approach is based on the
dynamic inflow modelling principle in [6] .

The stochastic wave simulation is based on water depth de-
pendent power spectra of the wave velocity and the wave
acceleration. All these spectra are governed by the pow-
er spectrum of the surface elevation through the linear wave
theory (Airy) [7]. Figure 3 shows for a water depth

d of 20 m

the (fully) correlated horizontal wave speed and acceleration
signals on 55%, 65%, up to 95% of

d above the sea bottom.

A Pierson Moskowitz wave spectrum has been applied at an
average wind speed of 12 m/s.

100

110

120

130

140

150

160

170

180

190

200

−0.8

−0.6

−0.4

−0.2

0.2

0.4

0.6

golf

[m/s] bij 12.0m/s

Afstand tot grond: 55% 65% 75% 85% 95% van waterdiepte van 20.0 m

100

110

120

130

140

150

160

170

180

190

200

−1

−0.5

0.5

⋅

golf

[m/s

] bij 12.0m/s

tijd [s]

file F:\tgengel\ctrltool\MODELS\PS\khv12d20.ps 08−Dec−2000

by F:\tgengel\ctrltool\MODELS\M\hydrload.m

Figure 3: Realisation of wave speed and acceleration

Note that the lower graph in fig. 3 shows the product of
mass coefficient

and wave acceleration

a. This product

is the ‘force effective’ acceleration with wave diffraction
included as proposed by MacCamy and Fuchs [2]. If the
waves are perpendicular to the wind, Morison’s equation for
the (lateral) wave force per unit tower length

z m

below the sea surface is given by

water

1
4

πD

2
z

· ( ˙w

eﬀ
z

− ¨x

) + . . .

1
2

water

· D

· (w

− ˙x

) · |w

− ˙x

| ,

with tower diameter

, wave speed

and force effective

acceleration

eﬀ
z

, naying speed

˙x

and acceleration

Realistic values for the drag coefficient

lay between 0.6

and 1.2 [7].

Tower bending and drive-train dynamics are modelled by the
following set of mutually dependent differential equations
(waves perpendicular to wind):

−k

˙x

− c

+ F

cos θ

tilt

−k

˙x

− c

3
2

nac

+ . . .

F(f

)dz ,

·J

· ¨γ = −c

· γ − k

· ˙γ + . . .

· (T

− T

) +

· T

· ˙Ω

−c

· γ − k

· ˙γ + T

− T

The shaft distortion speed

˙γ is the difference between ro-

tor speed

Ω

and ‘slow shaft level’ generator speed

Ω

(gearbox transmission ratio

and

are correspond-

ing moments of inertia;

and

are the shaft stiffness and

damping constant for the 1

distortion mode with natural

damping rate

(

∼ 0.005). Tower mass m

and damping

and stiffness constant

and

are the tower top equivalent

parameters for the 1

st bending mode with natural damping

rate

(

∼ 0.005).

The integral of function

F in the hydrodynamic force dis-

tribution

yields the tower top equivalent hydrodynamic

load. Function

F caters for the shape of the 1

bending

mode and the distance

−(d−z) between the tower top

and

. The loss torque

is modelled by a constant and

a rotor speed dependent term. The sideward tower bend-
ing torque

nac

approximately equals the (slow shaft level)

generator torque

The servo behaviour of the generator torque is modelled by
2

order dynamics with cut-off frequency

and damping

rate

. The pitch servo model includes both 2

order

dynamics (

) and a delay

that depends on sign

reverse in pitching speed setting and on the thrust force.

Control tool modules. The models listed above have been
implemented in MATLAB program modules for numeric
integration in time domain simulations. They also have been
included in linearised form (transfer functions) in program
modules for frequency domain based controller synthesis.

3.2 Power control and resonance damping
Next to models for wind, waves and wind turbine system
dynamics, the control tool incorporates feedback structures.
These pertain to aerodynamic and electric power control and
to damping of resonance in the tower and drive-train. The
features are listed below and discussed afterwards.

Aerodynamic and electric power control:

• rotational speed feedback with setpoint adaptation;

• non-linear feedforward of estimated wind speed;

• dynamic inflow compensation;

• inactivity zone and filtering of Bp-effects;

• scheduling of control parameters;

• forced rotational speed limitation;

• partial load pitch setting;

• smooth transients between partial and full load;

• low-pass effectuation of torque/speed curve.

Tower bending and drive-train distortion damping

• nodding acceleration feedback to pitch speed;

• naying speed feedback to generator torque;

• narrow band-pass filter in tower loops;

• shaft distortion speed feedback to generator torque;

• Kalman filter in drive-train loop;

• maximum level in control effort.

Figure 4 visualises the feedback structure for aerodynam-
ic and electric power control.

The proportional differ-

ential (PD) feedback of the filtered rotational speed error
Ω

ref
r

−Ω

3pﬁlt
r

is the core of the aerodynamic control loop;

it is the usual approach to control the inertia based rotor
dynamics. The differential (D) ‘feedforward’ of the estimat-
ed aerodynamic torque

est

effectuates pseudo wind speed

feedforward towards the pitch angle that belongs to the actual
wind speed. The lead-lag filter for dynamic inflow compen-
sation (LL) implements the inverse of the dynamic inflow
model equation in

§3.1.

The control gains in the feedback and ‘feedforward’ loop
are derived with Nyquist analysis in worst case operating
conditions (industry-adopted stability assessment). High-
performance control is obtained by enlarging the PD-gains

scheduling

inactivity zone

setpoint

adaptation

feedback

switch

limitation

partial load

pitch setting

Ω

ref
r

part

full

meas

Ω

nom

set

LPF

3pfilt

dynamic inflow

compensation

`feedforward'

forced speed

limitation

d/dt

LPF

low-pass

full / partial

load selector

Ω

3pfilt

Ω

meas

VLPF

very low-pass

Ω

3pfilt

Ω

torq

Ω

LPF

meas

est

3pfilt

full
load

torque/speed curve

set

force

Ω

3pfilt

Ω

3pfilt

Figure 4: Feedback structure for power control

for

Ω

ref
r

− Ω

3pﬁlt
r

as much as allowed in more favourable

operating conditions and by fitting the D-gain for

est

the inverted power coefficient data (gain scheduling).

The feedback gains for tower and drive-train damping are
derived from isolated analysis of the governing equations for
the 1

bending and distortion mode. The tower loops include

narrow band-pass filters with nearly zero phase shift around
the tower eigenfrequency

. Additionaly, sharp band-

stop filters reduce the peaks around the

mBp-frequencies

(

m = 1, 2) in the nodding signal. The drive-train loop

includes a high-pass filter and a Kalman filter for estimation
of the shaft distortion from the generator speed.

The servo systems for the actuators behave ideal in the tower

loops (

), whereas in the drive-train loop

the actuator bandwidth is sufficiently large (

≥2ω

The filtered tower signals and estimated distortion speed

(

bp
nd

˙x

bp
ny

, ˆ

˙γ

) are fed back to damping contributions in

pitch speed and torque setting:

∆ ˙θ

r
nd

· ¨x

bp
nd

∆T

−K

· ˙x

bp
ny

∆T

−K

· ˆ˙γ

The relevant parts of the bending and distortion equations
are then approximated by (

∂F

∂θ

< 0):

∼ −k

˙x

− c

− |

∂F

∂θ

| · K

· ˙x

∼ −k

˙x

− c

−

3
2

· ˙x

·J

· ¨γ ∼ −c

· γ − k

· ˙γ −

· K

· ˆ˙γ

This yields the following enhanced damping rates:

∼

∂Fa

∂θ

|·K

√

∼

3
2

√

∼

/(J

)

·K

√

/(J

)

·c

The feedback gains

and

are tuned in non-

linear time domain simulations. The achievable damping

rate in realistic wind conditions is constrained by the allowed
level of (harmonic) control effort and stability requirements.
The nodding gain

is scheduled in a similar way as the

PD-gains for the rotational speed error.

Control tool modules. The feedback structures listed above
have been implemented in MATLAB program modules for
time domain simulation: the MATLAB edition of the con-
trol algorithms. The algorithms are also available in the
programming languages C and Fortran for straightforward
incorporation in process computers and aerodynamic codes.

Besides, interactive program modules have been developed
for parametrising the filters and gains of the linear parts in
the control loops; these modules include the linearised wind
turbine system dynamics. For overall stability and robust-
ness assessment, program modules have been developed for
Nyquist analyses of the open loop transfer function. This
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
speed measurement feedback path to the PD-action.

4. SIMULATION RESULTS

The results plotted below apply to a typcial multi-MW (off-
shore) wind turbine.

They have been obtained from the

simulation stage in the design tool. Validation runs with the
aerodynamic computer code PHATAS [5] (control algorithm
included) yielded equal behaviour.

400

450

500

550

600

650

pitch angle

[dg]

400

450

500

550

600

650

−4

−2

pitching speed

[dg/s]

time [s]

400

450

500

550

600

650

rotor effective wind speed (gray); estimated windspeed; rated wind speed (dashed)

[m/s]

400

450

500

550

600

650

aerodynamic power (gray); electric power

[MW]

400

450

500

550

600

650

rotor speed (gray); rotor speed setpoint; rated rotor speed (dashed)

[rpm]

Figure 5: Aerodynamic and electric power control with wind
speed estimator

5. CONCLUSIONS

A design tool has been developed for control algorithms for
variable speed wind turbines. The by nature multivariable
control problem is split-up into physically interpretable con-
trol loops that are individually parametrised. These loops
pertain to aerodynamic and electric power control and to

100

150

200

250

300

350

400

Effect naying damping (all filters included); dotted: b

= 1, solid: b

= 15

Ω

rel

[rpm]

100

150

200

250

300

350

400

1000

1500

2000

[kNm]

100

150

200

250

300

350

400

−0.1

−0.05

0.05

0.1

[m/s]

time [s]

file E:\schaak\TowDamp\SCOPE\PS\scnyeff.ps 01−Feb−2001
by E:\schaak\TowDamp\SCOPE\M\slnywtrs.m

Figure 6: Lateral tower resonance at waves perpendicular
to the wind (lower graph: naying acceleration [m/s

]; dash:

without damping)

damping of tower bending and drive-train distortion. Spe-
cial features are (i) dedicated filter design, (ii) wind speed
estimation in power control and (iii) shaft distortion estima-
tion by Kalman filtering.

The algorithms with the implemented control loops are clear
in implementation and operation, and are on-site tunable
by well-educated operators. The C- or Fortran-coded algo-
rithms can be incorporated in process computers and aero-
dynamic codes with very minor effort.

The approach as implemented in the tool has been exensively
validated by non-linear time domain simulations with the
authorised aerodynamic code PHATAS [5].

ACKNOWLEDGEMENT

Koert Lindenburg (ECN) is acknowlegded for his contribu-
tion to dealing with the impact of dynamic inflow on power
control and for the many validation runs with PHATAS. Jan
Pierik (ECN) is acknowlegded for his contributions to elec-
tric system modelling and desk top publishing.

REFERENCES

[1] P.M.M. Bongers; Modeling and Identification of flexi-
ble wind Turbines and a Factorizational Approach to Robust
Control, PhD thesis, ISBN 90-370-0100-9, Delft Universi-
ty of Technology, fac. of Mech. Eng., the Netherlands, 1994.
[2] S.K. Chakrabarti; Hydrodynamics of Offshore Structures,
Computational Mechanics Publications Southampton, 1987.
[3] J.B. Dragt; Atmospheric Turbulence Characteristics in
the Rotating Frame of Reference of a WECS Rotor. Pp 274-
278 in proc. ECWEC Conf. Madrid, Spain, 1990.
[4] T.G. van Engelen, E.L. van der Hooft and P. Schaak;
Ontwerpgereedschappen voor de Regeling van Windturbines
(in Dutch), Technical report, ECN Wind Energy, Petten, the
Netherlands, Draft, June, 2001.
[5] C. Lindenburg and J.G. Schepers; PHATAS-IV Aeroe-
lastic Modelling, Program for Horizontal Axis Wind turbine
Analysis and Simulation, version IV, ECN Wind Energy,
Petten, the Netherlands.
[6] H. Snel, J.G. Schepers; Joint Investigation of Dynam-
ic Inflow Effects and Implementation of an Engineering
Method. Technical Report ECN-C-94-107, ECN Wind En-
ergy, Petten, the Netherlands, April, 1995.
[7] J.F. Wilson; Dynamics of Offshore Structures. John
Wiley & Sons, 1984.

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