Wind turbine operational optimization
considering revenue and fatigue objectives

A thesis accepted by the Faculty of Aerospace Engineering and Geodesy
of the University of Stuttgart in fulfillment of the requirements

for the degree of Doctor of Engineering Sciences (Dr.-Ing.)

by

Vasileios Pettas

born in Athens, Greece

Main referee: Prof. Dr. Po Wen Cheng
Co-referee: Prof. Dr. Carlo Luigi Bottasso

Date of defense: 23.01.2024

Stuttgart Wind Energy at the Institute of Aircraft Design
University of Stuttgart

2024





Contents

List of Figures v

List of Tables ix

Abbreviations xi

List of Symbols xiii

Abstract xv

Kurzfassung xvii

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research areas and research objectives . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis structure and organization . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Background 7
2.1 Background information and related research . . . . . . . . . . . . . . . . . . . 7
2.2 Definitions and metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Aeroelastic simulations and turbine definition . . . . . . . . . . . . . . . . . . 18
2.4 Wind turbine control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Introduction to surrogate modelling . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Controller design 35
3.1 Baseline controller design for the DTU 10 MW rwt . . . . . . . . . . . . . . . 35
3.2 Down-regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Power boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Individual blade control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Summary-Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4 Surrogate modelling and aero-servo-elastic analysis 53
4.1 Surrogate modelling methodology . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.1.1 Input and output variable space . . . . . . . . . . . . . . . . . . . . . . 54
4.1.2 Regression approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Uncertainty quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Aero-servo-elastic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.1 Discussion on tradeoffs and optimization potential . . . . . . . . . . . . 75
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78



iv Contents

5 Evaluation-optimization framework 81
5.1 Accumulation and evaluation framework . . . . . . . . . . . . . . . . . . . . . 81
5.2 Optimization problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3 Assumptions and considerations about the method . . . . . . . . . . . . . . . 92
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Data sets and definition of scenarios 97
6.1 Presentation and analysis of data sets . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Definition and discussion of optimization scenarios . . . . . . . . . . . . . . . . 107
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7 Optimization results and discussion 113
7.1 Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.1.1 Baseline reponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.2 Potential by applying IBC . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.1.3 Potential by applying down-regulation . . . . . . . . . . . . . . . . . . 125
7.1.4 Potential by applying selective shutdown . . . . . . . . . . . . . . . . . 128
7.1.5 Potential by applying power boosting . . . . . . . . . . . . . . . . . . . 131

7.2 Optimization under fixed prices . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.2.1 Fatigue damage minimization under fixed prices . . . . . . . . . . . . . 134
7.2.2 Revenue maximization under fixed prices . . . . . . . . . . . . . . . . . 146
7.2.3 Sensitivity to wind distribution uncertainty under fixed prices . . . . . 156

7.3 Optimization under fluctuating market prices . . . . . . . . . . . . . . . . . . 159
7.3.1 Fatigue damage minimization under fluctuating market prices . . . . . 159
7.3.2 Revenue maximization under fluctuating market prices . . . . . . . . . 170
7.3.3 Sensitivity to day ahead forecast uncertainty under fluctuating prices . 186
7.3.4 Sensitivity to forecast horizon length under fluctuating prices . . . . . . 189
7.3.5 Sensitivity to wind distribution uncertainty under fluctuating prices . . 192

7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

8 Conclusions 199
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.3 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . . . 204

Appendix 207
A.1 Code and data availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
A.2 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Bibliography 209



List of Figures

1.1 The different components of the present work building upon each other to
evaluate the research objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Overview of the components of the operational optimization method proposed
in this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Control regions of a wind turbine. . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Examlple maps of λ-θ-Cp and λ-θ-Ct . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Schematic representation of the different IPC schemes. . . . . . . . . . . . . . 29
2.4 Possible controller trajectories for generator torque and generator speed consid-

ering power boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1 λ-θ-Cp and λ-θ-Ct maps for the DTU 10 MW rwt used for the controller design 37
3.2 Effect of the torque-speed ramp on region 1.5. . . . . . . . . . . . . . . . . . . 38
3.3 Block diagram of the full controller and actuators . . . . . . . . . . . . . . . . 39
3.4 Steady state operational characteristics for the baseline controller . . . . . . . 39
3.5 The two trajectories considered for the derivation of down-regulation set points

along with the minimum Ct trajectory . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Steady state operational characteristics for the two down-regulation trajectories 42
3.7 Power boosting controller trajectories for generator torque and speed . . . . . 43
3.8 Steady state operational characteristics for the power boosting mode . . . . . 44
3.9 Identified linear model and FAST simulation response around 16 m/s with 5%

turbulence intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.10 Block diagram of the IBC controller . . . . . . . . . . . . . . . . . . . . . . . . 47
3.11 Filter design for the IBC loop . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.12 Indicative time series of the pitch angle of each blade along with the mean pitch

value for a simulation with mean wind speed 18 m/s . . . . . . . . . . . . . . . 49
3.13 Blade root flapwise moment and pitch rate PSD at 16 m/s . . . . . . . . . . . 50
3.14 Overview of the controller structure, including the switching between modes

cascaded in the decision-making loop . . . . . . . . . . . . . . . . . . . . . . . 51

4.1 Overview of the procedure to create, apply and validate a surrogate model. . . 54
4.2 Sampling of validation set based on the latin hypercube method . . . . . . . . 57
4.3 Box plots of the relative error and relative absolute error . . . . . . . . . . . . 60
4.4 Comparison between the surrogate response and the validation set per quantity

of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Relative error between the surrogate predictions and the validation dataset

sorted per input variable for blade loads . . . . . . . . . . . . . . . . . . . . . 63
4.6 Relative error between the surrogate predictions and the validation dataset

sorted per input variable for the tower bottom loads . . . . . . . . . . . . . . . 64



vi List of Figures

4.7 Relative error between the surrogate predictions and the validation dataset
sorted per input variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.8 Relative error between the surrogate predictions and the validation dataset
sorted per input variable for the low-speed shaft loads . . . . . . . . . . . . . . 65

4.9 Relative error between the surrogate predictions and the validation dataset
sorted per input variable for mean power and blade pitch travel. . . . . . . . . 66

4.10 GPR surrogate response for the tower bottom DELs. . . . . . . . . . . . . . . 67
4.11 GPR surrogate response for the tower top/nacelle loads. . . . . . . . . . . . . 69
4.12 GPR surrogate response for the blade root loads. . . . . . . . . . . . . . . . . 71
4.13 GPR surrogate response for the low-speed shaft loads. . . . . . . . . . . . . . . 73
4.14 GPR surrogate response for electric power, energy, and blade pitch travel. . . . 74

5.1 Overview of the accumulation process . . . . . . . . . . . . . . . . . . . . . . . 82
5.2 Example output of the framework applied to evaluate different operational

strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Schematic overview of the optimization process for all cases considered . . . . 89

6.1 Example time series of the data used . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Wind speed PDFs and CDFs, and TI distributions over wind speeds for all years

and locations considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 Fitted Weibull distributions for the wind speeds at both sites using all the

available data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.4 Electricity price PDFs and CDFs for all years and markets considered . . . . . 103
6.5 Percentage of time when the turbine: is not operating (upper), the mean wind

speed is above baseline rated (middle), the mean wind speed is above rated and
the price higher than the mean of the year (lower) for all years and sites. . . . 104

6.6 Bivariate probability of wind speed and electricity prices for all years and sites
considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.1 Contribution of wind speed and electricity prices bins to the total revenue for all
years and sites considered using the baseline control mode in fluctuating market
prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.2 Contribution of wind speed and electricity prices bins to the total revenue for
all years combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.3 Contribution of wind speed and electricity prices bins to the total accumulated
damage for the tower, nacelle, and low-speed shaft loads using the baseline
controller in fluctuating market prices . . . . . . . . . . . . . . . . . . . . . . . 119

7.4 Contribution of wind speed and prices bins to the total accumulated damage
for the blade loads using the baseline controller in fluctuating market prices . . 121

7.5 KPIs by applying the IBC loop per year and location considered . . . . . . . . 122
7.6 KPIs by applying the IBC for wind speeds above the threshold considering all

years for both locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.7 KPIs by operating the turbine constantly in different power levels below the

baseline for the whole period in both locations considered . . . . . . . . . . . . 126
7.8 KPIs by applying selective shut-down based on projected revenue thresholds. . 130
7.9 Expected relative increase in revenue compared to the baseline operation by

constantly applying different levels of power boosting under fluctuating prices 132



List of Figures vii

7.10 KPIs by applying constant power boosting for the whole period considered and
both locations under fixed prices . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.11 KPIs for revenue-neutral load minimization cases under fixed prices using both
trajectories for the whole period considered for both locations and different
maximum power levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.12 KPIs for revenue-neutral load minimization under fixed prices using both tra-
jectories per year and per location . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.13 Power level per wind speed bin resulting from revenue-neutral load minimization
for all locations and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.14 KPIs for load minimization cases including a revenue reduction cap of 5% for
the DE site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.15 KPIs for load minimization cases including a revenue reduction cap of 5% for
the DK site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.16 Power level per wind speed bin resulting from optimization using wind speed
distributions for load minimization with a revenue reduction cap of 5% for all
locations and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.17 KPIs for load-neutral revenue maximization cases under fixed prices using both
trajectories for the whole period considered for both locations and different
maximum power levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.18 KPIs for load neutral revenue maximization under fixed prices using both
trajectories per year and per location . . . . . . . . . . . . . . . . . . . . . . . 149

7.19 Power level per wind speed bin resulting from optimization for load-neutral
revenue maximization for all locations and trajectories . . . . . . . . . . . . . 150

7.20 KPIs for revenue maximization cases including a load increase cap of 5% cases
under fixed prices for the DE site . . . . . . . . . . . . . . . . . . . . . . . . . 152

7.21 KPIs for revenue maximization cases including a load increase cap of 5% cases
under fixed prices for the DK site . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.22 Power level per wind speed bin resulting from optimization using wind speed
distributions for revenue maximization with a load increase cap of 5% for all
locations and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.23 Resulting Weibull wind speed distributions by varying the originally derived
coefficients by ±10% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.24 Results of optimization cases compared to baseline operation under fixed prices
using the modified Weibull distributions . . . . . . . . . . . . . . . . . . . . . 157

7.25 KPIs for revenue-neutral load minimization cases under fluctuating prices using
both trajectories for the entire period considered for both locations and different
maximum power levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

7.26 KPIs for revenue-neutral load minimization under fluctuating prices using both
down-regulation trajectories per year . . . . . . . . . . . . . . . . . . . . . . . 162

7.27 Relative differences of revenue, energy, and fatigue damage for the TBMy and
BRMz loads to the baseline per wind speed-price bin for the DK 2019 data
considering the revenue-neutral load minimization scenario under fluctuating
prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

7.28 KPIs for load minimization cases including a revenue reduction cap of 5% under
fluctuating prices for the DE site . . . . . . . . . . . . . . . . . . . . . . . . . 166



viii List of Figures

7.29 KPIs for load minimization cases including a revenue reduction cap of 5% under
fluctuating prices for the DK site . . . . . . . . . . . . . . . . . . . . . . . . . 167

7.30 KPIs for load minimization cases including a revenue reduction cap of 5% under
fluctuating prices for the DE2022 dataset . . . . . . . . . . . . . . . . . . . . . 169

7.31 KPIs for load-neutral revenue maximization cases under fluctuating prices using
both trajectories for the entire period considered for both locations and different
maximum power levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.32 KPIs for load-neutral revenue maximization under fluctuating prices using both
trajectories per year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

7.33 Relative differences of revenue, energy, and fatigue damage for the TBMy and
BRMz loads to the baseline per wind speed-price bin for the DK 2015 data
considering load-neutral revenue maximization under fluctuating prices . . . . 176

7.34 Relative differences of revenue, energy, and fatigue damage for the TBMy and
BRMz loads to the baseline per wind speed-price bin for the DE 2018 data
considering load-neutral revenue maximization under fluctuating prices . . . . 178

7.35 Relative differences of revenue, energy, and fatigue damage for the TBMy and
BRMz loads to the baseline per wind speed-price bin for the DE 2022 data
considering load-neutral revenue maximization under fluctuating prices . . . . 179

7.36 KPIs for revenue maximization with a load increase cap under fluctuating prices
using both trajectories for the DE site . . . . . . . . . . . . . . . . . . . . . . 181

7.37 KPIs for revenue maximization with a load increase cap under fluctuating prices
using both trajectories for the DE2022 dataset . . . . . . . . . . . . . . . . . . 183

7.38 KPIs for revenue maximization with a load increase cap under fluctuating prices
using both trajectories for the DK site . . . . . . . . . . . . . . . . . . . . . . 185

7.39 Example time series of wind speed, TI, and electricity prices with the added
uncertainty from the DK2015 dataset . . . . . . . . . . . . . . . . . . . . . . . 187

7.40 Comparison of results of load neutral cumulative revenue maximization based
on DA forecasts under fluctuating prices with and without uncertainty in the
forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

7.41 Comparison of results for revenue-neutral cumulative fatigue damage minimiza-
tion based on DA forecasts under fluctuating prices with and without uncertainty
in the forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.42 Results of optimization cases compared to baseline operation in fluctuating
prices using varying forecast horizon lengths. . . . . . . . . . . . . . . . . . . . 190

7.43 KPIs of revenue maximization cases under fluctuating prices using the modified
Weibull distributions representing the uncertainty in wind speed distribution
estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193



List of Tables

2.1 Metrics definitions, abbreviations and units . . . . . . . . . . . . . . . . . . . . 17
2.2 DTU 10 MW rwt design parameters . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Natural frequencies of the DTU 10 MW rwt . . . . . . . . . . . . . . . . . . . 19

3.1 Pitch actuator and generator speed filter modelling parameters . . . . . . . . . 36
3.2 Design characteristics of the baseline controller . . . . . . . . . . . . . . . . . . 37

4.1 Variables and parameters for the simulations used to create the training set . . 56
4.2 Kernel functions and basis functions used in GPR for the different quantities of

interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Evaluation metrics of the GPR and spline-based surrogate models compared to

the validation set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Qualitative summary of DELs’ sensitivity to the controller modes and wind

conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.1 Instantaneous and cumulative quantities included in the output of the evaluation
framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.2 Hyperparameters used for the GA and PSO algorithms as implemented in the
Matlab optimization toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.1 Overview of datasets used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.1 Absolute performance metrics for the baseline operation for all periods and sites
considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.2 Relative increase in blade pitch travel by applying IBC and percentage of time
IBC is active for various activation thresholds considering all years for both
locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124





Abbreviations

AEP Annual energy production
BRIp In-plane blade root moment
BRMx Edgewise blade root moment
BRMy Flapwise blade root moment
BRMz Blade root torsion
BROop Out-of-plane blade root moment
BS Band stop
CapEx Capital expentditure
CDF Cumulative distribution function
CfD Contract for differences
CorRES Correlations in renewable energy sources
CPC Collective pitch control
DA Day-ahead
DE Germany
DEL Damage equivalent load
DK Denmark
DOE Design of experiment
DoF Degree of freedom
DTU Technical university of Denmark
FAST Fatigue, Aerodynamics, Structures, and Turbulence
GA Genetic algortihm
GPR Gaussian process reggression
HP High pass
IBC Individual blade control
IEC International Electrotechnical Commission
IPC Individual pitch control
KPI Key performance indicator
LCOE Levelized cost of energy
LHM Latin hypercube method
LP Low pass
LSSMy Low-speed shaft moment around y-axis
LSSMz Low-speed shaft moment around z-axis
LSSTq Low-speed shaft torque
LTI Linear time-invariant
LU Luxemburg
MAE Mean absolute error



xii Abbreviations

ME Mean error
MedAE Median absolute error
ND Non-dimensional
NEWA New European wind atlas
NREL National Renewable Energy Laboratory
O&M Operations and maintenance
OpEx Operating expenses
PDF Probability density function
PI Proportional integral
PID Proportional integral derivative
PitchTr Blade pitch travel
PPA Power purchase agreement
PSD Power spectral density
PSO Particle swarm optimization
Rev Revenue
rwt Reference wind turbine
SCADA Supervisory control and data acquisition
SISO Single input single output
std Standard deviation
SWE Stuttgart Wind Energy
TBMx Fore-aft tower bottom moment
TBMy Side-side tower bottom moment
TBMz Tower bottom torsion
TI Turbulence intensity
TKE Turbulence kinetic energy
TSR Tip speed ratio
TTMx Tower top roll moment
TTMy Tower top pitch moment
TTMz Tower top yaw moment
VAF Variance accounted for
VSPR Variable speed pitch regulated
WF Wind farm
wsp Wind speed
WT Wind turbine



List of Symbols

Greek letters
α Wind shear power law coefficient
∆ Difference
κ Torque controller gain
λ Tip speed ratio
µ() Mean function of Gaussian process
ωrot Rotational speed of the rotor
ωg Rotational speed of the generator
ωg,rat Rated rotational speed of the generator
ωg,1.5,max Maximum rotational speed of the generator in control region 1.5
ωg,1.5,min Minimum rotational speed of the generator in control region 1.5
ωNS Natural frequency of the mechanical system for controller design
ωN Natural frequency of the notch filter
ρ Density
σ2 Variance
θ Blade pitch angle
θfine Blade pitch angle for control region 2
ξ Damping ratio

Roman letters

A Weibull distribution shape parameter
Arot Rotor area
B Number of bins
c Material/cross-section constant
Cp Power coefficient
cpen Constant defining the gain of the penalty term
Ct Thrust coefficient
D Damage
e Error
F () Objective function



xiv List of Symbols

g Gravitational acceleration constant
gi() Evaluation function for threshold exceedance of objectives
iGB Gear box ratio
J Moment of inertia
k Weibull distribution scale parameter
K() Covariance kernel matrix
k() Covariance function of Gaussian process
KP Proportional gain
KI Integral gain
li Lower bound
m Wöhler exponent
Ma Aerodynamic torque
Mg Generator torque
Mg,max15 Maximum generator torque in control region 1.5
Mg,rat Rated generator torque
Mloss mechanical torque loss in the drive train
N Number of stress cycles
Ncrit Critical number of stress cycles for failure
Neq Equivalent number of stress cycles for the derivation of DEL
P Power
Prat Rated power
Q Quantity
Qdepth Notch filter parameter regulating the depth
Qwidth Notch filter parameter regulating the width
R Radius
R2 Coefficient of determination
S Load range
T Thrust force
Th Forecast horizon duration
t time
u Wind speed
ui Upper bound
w Weight
x Input
X Input variable space
y Output



Abstract

Wind energy holds significant importance in achieving the energy transition towards a sus-
tainable, carbon-free energy future. The core technology has matured over the last decades,
resulting in a substantial increase in installed capacity. While these advancements have led to
considerable cost reductions, they have also brought about reductions in mechanisms supporting
the economic viability of wind energy projects. Additionally, wind energy is required to play a
more substantial role in supporting the electrical network, traditionally done by conventional
generation technologies. However, wind energy differs fundamentally from these technologies in
terms of cost allocation through the project’s lifecycle and the ability to forecast and regulate
energy production. These factors have given rise to new challenges for wind energy research,
expanding its focus on topics such as enhancing grid integration, increasing profitability, and
better utilization of existing farms through lifetime extension.

The objective of this thesis is to support these goals by introducing a methodology for the
management of long-term operational objectives, in terms of revenue and fatigue loading, based
on adaptive control considering wind conditions and electricity prices. Currently, wind turbines
produce power according to the wind conditions, operating in a single mode for most of their
operational life. However, wind turbines have the capability to adjust their power output.
They can operate in down-regulation, producing lower power than the baseline mode, which
also decreases structural loading. Moreover, they can operate in power-boosting mode, which
allows for exceeding the baseline power level at higher wind speeds with a tradeoff in structural
loading. Additionally, modern turbines are capable of individually adjusting the pitch angle of
each blade, enabling individual pitch control (IPC), which can reduce structural loading with
the penalty of increased pitch actuator usage. These functionalities require mainly software
modifications and can be applied to most machines, allowing for switching between modes
according to an external decision-maker. The active management of power output and fatigue
loading over time (e.g, in hourly intervals) according to wind conditions and electricity prices
enables operational strategies for optimizing long-term objectives. Fatigue consumption and
revenue generation can be effectively redistributed over time and conditions in an optimal
manner, providing additional flexibility to both wind farm owners and grid operators.

Exploring this research objective requires a multidisciplinary approach encompassing aspects
of controller design, surrogate modeling, and optimization. As a first step, a multi-mode



xvi Abstract

controller is synthesized, allowing adjustment of the power level between 50% and 130% of the
baseline level and the optional application of an IPC loop. Two configurations are considered
to assess the impact of the choice of down-regulation trajectory on structural load reduction.
The IPC loop is based on an individual blade control (IBC) approach involving an independent
controller for each blade.

In the next step, a data-driven surrogate model is created based on mid-fidelity aeroelastic
simulations. Two regression approaches are considered: a spline-based interpolation and a
Gaussian process regression (GPR). The two methods performed very similarly with low
uncertainty in their predictions, possibly due to the dense factorial sampling considered.

The surrogate model is utilized to develop an evaluation-optimization framework for long-
term operational strategies. As a monitoring tool, it resembles a digital twin, enabling the
tracking of fatigue consumption across all components, revenue accumulation, and other metrics
potentially useful for condition monitoring purposes based on input time series of wind and
prices. Two optimization approaches are developed within this framework. The first employs
as input the mean wind distribution, aiming to optimize the controller mode per wind speed,
thereby creating a long-term operational schedule according to wind conditions. The second
approach leverages forecasts of wind speeds and electricity prices to assign the optimal control
mode per time step within the designated horizon.

The proposed method is evaluated using two multi-year datasets, each representing distinct
boundary conditions with regard to wind and price dynamics. Two optimization scenarios
are considered, reflecting potential business cases: revenue maximization with a constraint on
fatigue damage accumulation and fatigue damage minimization with constraints on cumulative
revenue. This methodology is employed to assess the applicability and performance of the
proposed operational approach for different objectives, considering both fixed and fluctuating
market prices. Furthermore, it investigates the impact of controller design, optimization
approach, and boundary conditions on the optimization outcomes.

The results indicate that the method is able to concurrently optimize the revenue and fatigue
loads in the long term. The two optimization approaches exhibited differences in terms of
improvements achieved and the distribution of fatigue and revenue. Fatigue reduction was
possible across all wind turbine components, suggesting that it can enable lifetime extension for
the entire system while maintaining profitability. Revenue maximization cases showed higher
dependency on the optimization approach and the maximum power boosting level considered.
For the forecast-based optimization, the length of the horizon considered proved to be critical.
For all cases, the most influential factor determining the extent of improvement was found to
be the boundary wind and market dynamics. Overall, this thesis demonstrates that there is
potential for optimizing long-term objectives using adaptive control, and it is worth exploring
it further to address current research challenges in wind energy.



Kurzfassung

Die Windenergie ist von großer Bedeutung für die Energiewende. Technologische Weiter-
entwicklungen und Skalierungseffekte beim Ausbau haben zu Kostensenkungen geführt, die
wiederum die Reduktion staatlicher Subventionen nach sich gezogen haben. Zudem muss die
Windenergie durch die Reduktion konventioneller Kraftwerke eine größere Rolle bei der Unter-
stützung des Stromnetzes spielen. Dabei unterscheidet sich die Windenergie grundlegend von
konventionellen Kraftwerken, in Bezug auf die Kostenzuweisung über den Lebenszyklus sowie
die Fähigkeit zur Vorhersage und Regulierung der Energieerzeugung. Diese Faktoren haben zu
neuen Herausforderungen für die Windenergieforschung geführt, etwa die Verbesserung der
Netzintegration, die Steigerung der Rentabilität und die bessere Nutzung bestehender Anlagen
durch Verlängerung der Lebensdauer.

Diese Arbeit soll einen Beitrag zur Umsetzung dieser Ziele leisten. Konkret wird eine adaptive
Anlagensteuerung für langfristige Betriebsziele in Bezug auf Einnahmen und Ermüdungslasten
eingeführt, wobei Windbedingungen und Strompreise berücksichtigt werden. Gegenwärtig
hängt die Stromproduktion hauptsächlich von den Windverhältnissen ab und die Anlagen
werden überwiegend in einem einzigen Modus betrieben. Windenergieanlagen können jedoch
ihre Leistungsabgabe anpassen. Sie können gedrosselt betrieben werden, meist verbunden mit
geringeren strukturellen Lasten. Alternativ können sie gezielt über Nennleistung betrieben
werden, was jedoch oft mit höheren strukturellen Lasten verbunden ist. Darüber hinaus
erlauben moderne Anlagen eine blattindividuelle Anstellwinkelsteuerung (IPC), die strukturelle
Lasten verringern kann, wobei jedoch die Stellmotoren stärker beansprucht werden. Diese
Funktionen erfordern in erster Linie Softwareanpassungen und können auf den meisten Anlagen
angewandt werden, so dass die Umschaltung zwischen den Modi in Abhängigkeit von einer
externen Entscheidungsinstanz möglich ist. Das aktive Management der Leistungsabgabe und
der Ermüdungslasten im Zeitverlauf (z. B. in stündlichen Intervallen), abhängig von Windbe-
dingungen und Strompreisen, ermöglicht Betriebsstrategien zur Optimierung langfristiger Ziele.
Die Energieabgabe ins Netz und die Erträge können über die Zeit optimal umverteilt werden,
was Windparkbesitzern und Netzbetreibern zusätzliche Flexibilität bietet.

Die Umsetzung dieses Forschungsziels erfordert einen multidisziplinären Ansatz, der Aspekte
des Reglerentwurfs, der Surrogat-Modellierung und der Optimierung umfasst. In einem ersten
Schritt wird ein Regler mit mehreren Betriebsmodi entwickelt, der eine Anpassung der Leistung



xviii Kurzfassung

zwischen 50% und 130% der Leistung des Normalbetriebs und die optionale Anwendung einer
IPC-Schleife ermöglicht. Es werden zwei Konfigurationen betrachtet, um die Auswirkungen
der Wahl der Drosselungstrajektorie auf die strukturelle Lastreduzierung zu bewerten. Die
IPC-Schleife basiert auf einem Ansatz der Einzelblattsteuerung (IBC), mit unabhängigen
Reglern für jedes Blatt.

Im nächsten Schritt wird ein datengetriebenes Surrogate-Modell erstellt, basierend auf
aeroelastischen Simulationen. Dabei werden zwei Regressionsansätze untersucht, die ähnliche
Vorhersageergebnisse liefern. Das Surrogat-Modell wird zur Entwicklung eines Bewertungs- und
Optimierungsansatzes für langfristige Betriebsstrategien herangezogen. Ähnlich einem digitalen
Zwilling erlaubt das Surrogat-Modell, den zeitlichen Verlauf von Anlagenzuständen, etwa Ermü-
dungsfortschritt oder finanzielle Erträge, bei verschiedenen Wind- und Preiszeitreihen effizient
abzuschätzen und die Betriebsstrategie zu optimieren. In dieser Arbeit werden zwei Opti-
mierungsansätze untersucht. Der erste verwendet die mittlere Windverteilung und optimiert den
Reglermodus pro Windgeschwindigkeit, um so einen langfristigen Betriebsplan entsprechend
den Windbedingungen zu erstellen. Der zweite Ansatz nutzt Windgeschwindigkeits- und
Strompreisprognosen, um den optimalen Modus für jeden Zeitschritt innerhalb eines fest-
gelegten Zeithorizonts zu bestimmen.

Die vorgeschlagene Methode wird anhand von zwei mehrjährigen Datensätzen evaluiert, die
jeweils unterschiedliche Randbedingungen in Bezug auf die Wind- und Preisdynamik darstellen.
Es werden zwei Optimierungsszenarien betrachtet (potenzielle Geschäftsfälle): Maximierung
der Erträge bei beschränkten Ermüdungslasten sowie Minimierung der Ermüdungslasten
bei beschränkten Ertragsverlusten. Für diese Szenarien werden die Anwendbarkeit und
Leistungsfähigkeit der entwickelten Methode bewertet, wobei sowohl feste als auch variable
Marktpreise berücksichtigt werden. Darüber hinaus wird der Einfluss des Reglerentwurfs, des
Optimierungsansatzes und der Randbedingungen auf die Optimierungsergebnisse untersucht.

Die Ergebnisse zeigen, dass die Methode, gleichzeitig Ertrag und die Ermüdungslasten
langfristig optimieren kann. Die beiden Optimierungsansätze unterschieden sich in den erzielten
Verbesserungen und der Verteilung von Ermüdungslasten und Ertrag. Die Ermüdungslasten
aller Komponenten der Windenergieanlage konnten reduziert werden, was nahelegt, dass eine
Lebensdauerverlängerung des Gesamtsystems bei Erhalt der Rentabilität möglich ist. Für die
Ertragsmaximierung zeigt sich eine stärkere Abhängigkeit vom Optimierungsansatz und der
betrachteten maximalen Leistungserhöhung. Bei der prognosebasierten Optimierung erwies
sich die Länge des betrachteten Horizonts als kritisch. In allen Fällen beeinflusst die Wind-
und Preisdynamik das Verbesserungspotential am meisten. Insgesamt weist die Arbeit nach,
dass eine adaptive Steuerung Optimierungspotential für langfristige Betriebsziele hat und sich
ihre weitere Erforschung für das Voranbringen der Energiewende lohnt.



Chapter 1

Introduction

1.1 Motivation

Wind energy has emerged as a prominent renewable energy source, playing a pivotal role in
the energy transition required for protecting the environment and mitigating climate change.
Its higher energy density, compared to other renewable sources, and its versatility in terms of
suitable locations, both onshore and offshore, have fueled significant technological advancements
and widespread deployment in recent decades.

As a result, wind energy has now matured into a reliable technology, bringing about new
demands and expectations. In its earlier stages, wind energy relied heavily on subsidies due to
the relatively high costs associated with developing the technology at its infant stages. Addi-
tionally, there were minimal requirements placed on supporting the electrical grid. Currently,
the landscape has evolved. Subsidies are diminishing or disappearing altogether, putting wind
energy projects in direct competition with conventional energy sources. This shift necessitates
a focus on cost reduction and revenue enhancement in order to maintain the profitability of
wind energy and sustain its growth. Moreover, wind energy producers are required to play a
more substantial role in grid stability by providing flexibility and ancillary services.

Thus, the objectives in wind energy research expand from the earlier objectives of optimizing
the wind turbine itself by increasing the power output and reducing manufacturing costs to
broader ones. These include objectives such as improving the operation to the wind farm
level, increasing flexibility in power production and reducing forecasting uncertainty for better
grid integration, extending the lifetime to more efficiently utilize already installed plants,
increasing revenue and reducing maintenance costs to maintain profitability and attractiveness



2 Chapter 1 Introduction

of investment, leveraging digitalization and computational power to further improve the
performance and reduce costs, reducing environmental impacts, and improving the circularity
of the various components among others.

This work aligns with these evolving objectives in wind energy research. It aims to propose an
operational management approach that allows for flexible wind turbine operation, focusing on
optimizing long-term revenue and fatigue objectives. By utilizing existing control technologies,
this approach offers an added degree of freedom for stakeholders, contributing to the broader
goals of improving wind energy efficiency and profitability as well as grid integration.

In the current operational paradigm, wind turbines operate during their entire operational
lifetime in one control mode, with the power output being dictated by the wind conditions.
The only exception to this is when grid operators may require wind farms to curtail power
production or shut down entirely for reasons related to grid stability or congestion. Modern
wind farm flow control concepts have also employed the concept of down-regulation to mitigate
the wake effects downstream of a wind turbine, aiming to enhance the overall performance of
the entire wind farm. Furthermore, retrofit packages offered as add-ons exist in the market,
offering the possibility to strategically boost the power output beyond baseline levels in specific
wind conditions in order to increase power production. Moreover, control technologies focusing
on structural load reductions to potentially reduce manufacturing costs, such as individual
pitch control, have been developed and extensively tested in the field, but are scarcely employed
in commercial wind turbines due to a lack of clear financial benefits.

The proposed operational management integrates these established control technologies
and utilizes them within a novel framework for managing the revenue and fatigue damage
accumulation over time in order to optimize long-term operational objectives. Taking into
account the wind and pricing boundary conditions, energy production and structural fatigue
budget can be distributed over conditions and over time more efficiently compared to the
current monolithic operational approach. This new approach can enable pursuing various
objectives such as maximizing revenue to enhance profitability, extending the operational
lifetime, and enabling efficient participation in additional markets such as intraday or balancing
electricity markets.

1.2 Research areas and research objectives

The present dissertation focuses on the method development and proof of concept of an opera-
tional management approach aiming to concurrently optimize the fatigue damage accumulation
and revenue generation of a wind turbine during its entire operational lifetime. This task
requires a multidisciplinary approach involving the research areas of controller design, surrogate
modeling, and mathematical optimization. The different components of the method are built



1.2 Research areas and research objectives 3

on top of each other in a modular manner, as illustrated in figure 1.1.

At its core, this method involves designing a wind turbine controller capable of adjusting
the power output of the wind turbine as well as employing an individual pitch control loop
according to the external commands of the decision maker. Furthermore, using an aeroelastic
simulator, a large dataset of simulations is created to capture the wind turbine’s response
under varying wind conditions for all control modes. This dataset serves as the foundation for
creating a data-driven surrogate model able to predict the turbine’s response for the entire
spectrum of expected conditions quickly and accurately without the need to perform expensive
aeroelastic simulations.

Based on this surrogate model, a numerical framework is developed to track the accumulation
of key metrics over time. This framework takes into account the input wind conditions,
electricity price, and the selected control mode for each time step. An optimization framework
is developed around the accumulation framework. The objective is to determine the optimal
control mode to assign to each time block, ultimately optimizing cumulative revenue and
fatigue objectives by the end of the designated time period.

The potential of the proposed operational approach is evaluated within different scenarios,
considering various combinations of revenue and fatigue objectives, that are relevant to practical
business cases. These scenarios are realistically evaluated using two historical datasets with
distinct wind and price dynamics.

These tools enable the assessment of the efficacy and performance of the proposed operational
management method for different objectives and investigate the influence of the controller
design, optimization approach, and boundary conditions on the optimization outcomes. This
is the overarching research objective of the present work. An overview of the different steps
and methods followed to achieve this is provided in figure 1.2.

The specific research objectives are summarized in the following list:

• Controller design
Develop a simple and robust wind turbine controller featuring multiple modes, utilizing
already applied methods that do not require additional sensors or actuators. Explore
diverse controller design approaches to derive down-regulation and power-boosting set
points in combination with individual pitch control. Identify the impact of controller
design choices on the aeroelastic response of the turbine regarding power production,
fatigue loading, and blade pitch actuator usage, as well as the overall optimization
outcomes.

• Surrogate modeling
Create an efficient surrogate model tailored for the application, encompassing the struc-
turals loads for all major components of the system, power production, and other



4 Chapter 1 Introduction

relevant metrics. Evaluate different methods for creating the surrogate model in terms of
uncertainty quantification, complexity, and computational cost.

• Optimization
Develop and evaluate an optimization framework that incorporates various optimization
approaches that are able to utilize wind speeds, in terms of mean long-term distributions
or forecasts, and electricity price forecasts to optimize long-term revenue and fatigue
objectives under constant or fluctuating market prices by adapting the control mode of
the wind turbine.

• Overall
Evaluate the feasibility of managing revenue and fatigue damage accumulation across
all major components of a wind turbine, by adapting the power level of the turbine and
selectively applying individual pitch control based on an optimization framework used
for decision-making. Quantify the expected optimization performance and its sensitivity
to different combinations of objectives under different pricing mechanisms, controller
configurations, optimization approaches, wind conditions, and market dynamics. Evaluate
the impact of input uncertainty on the optimization’s performance.

Figure 1.1: The different components of the present work building upon each other to evaluate the
research objective

1.3 Thesis structure and organization

Given the multidisciplinary nature of this work, the thesis chapters are structured to consolidate
all relevant information related to each discrete topic within the respective chapter. Each
chapter also includes a critical discussion of the methods utilized, potential alternatives, and
suggestions for further research on the topic.

Chapter 2 compiles all the background information and knowledge essential to comprehend
the methods and scope of the rest of the work. It presents background information on
energy pricing mechanisms, revenue streams for wind turbines, and related research aimed at
optimizing systems in directions similar to the work discussed here. Additionally, it introduces



1.3 Thesis structure and organization 5

fundamental concepts in wind energy used throughout the thesis, and it offers a summary of
the state of the art in the topics of controller design and surrogate modeling. Finally, this
chapter introduces the models, software, and metrics used throughout the thesis.

Chapter 3 encompasses all aspects related to the controller’s design. It introduces the
controller synthesis for the baseline operation of a reference wind turbine. Subsequently, the
baseline controller is expanded to incorporate additional modes that enable down-regulation,
power boosting, and individual pitch control. The rationale behind the tuning and design
choices is explained, and their implications are thoroughly discussed. Lastly, the chapter
explains the combination and switching between these modes.

Chapter 4 focuses on the development of surrogate models for all controller modes based
on mid-fidelity aeroelastic simulations. The design of experiment approach is motivated, and
two methods for creating the surrogate model based on the simulated dataset are introduced.
The two models are compared and discussed in terms of complexity, computational costs, and
performance. Based on the surrogate model, a comprehensive aero-servo-elastic analysis of the
response of the wind turbine under the full range of conditions is performed. This analysis
compares various controller design choices and derives insights regarding their potential impact
on the optimization.

Chapter 5 introduces the evaluation-optimization framework. Based on the surrogate
model, a data-driven digital twin of the wind turbine is developed. This evaluation framework
tracks the instantaneous and cumulative response of the turbine in terms of fatigue damage,
energy production, revenue, and other metrics. The chapter also delves into the development of
the optimization framework, built upon the evaluation framework, with its primary objective
being the long-term management of the wind turbine’s fatigue and revenue. The assumptions
considered, the formulation of the objective functions, and the choice of optimization algorithms
are presented and critically discussed.

Chapter 6 provides an overview of the historical datasets, spanning several years, employed
to assess the proposed methods. Two locations, each characterized by distinct wind conditions
and electricity market dynamics, are considered in order to evaluate the proposed method
under varying boundary conditions. The datasets are analyzed, and the attributes relevant to
the proposed method are discussed. Furthermore, the optimization scenarios considered for
the evaluation of the proof of concept are introduced and critically discussed, focusing on their
potential application within real-world business cases.

Chapter 7 consolidates the components of this study, presenting optimization results.
Initially, the potential of each control mode is individually analyzed, establishing optimization
bounds stemming from controller design and dataset-specific boundary conditions. Subsequently,
results for various scenarios are individually and comparatively discussed, with a differentiation
based on pricing mechanisms: fixed prices and fluctuating market prices. The performance



6 Chapter 1 Introduction

of the methods, as well as the influence of factors such as controller design, optimization
approach, wind and market boundary conditions, are critically discussed. Additionally, the
chapter includes uncertainty analyses to assess the sensitivity of the optimization outcomes to
input uncertainty.

Chapter 8 concludes the study by summarizing the main findings, offering high-level
conclusions about the operational optimization method, and suggesting further research on the
topic. For detailed comments and recommendations related to the various research topics and
technical implementations, readers are referred to the respective sections within the relevant
chapters.

Controller design

• Baseline controller
• Down-regulation
• Power boosting
• Individual blade control

Surrogate model

Aeroelastic 
simulations

Training set

Splines, GPR

Surrogate

Control mode
Wind speed 

TI

DEL
Energy

Other metrics

Accumulation framework

Digital twin

Wind
Prices

Control mode

Operational optimization

Optimizer Optimizer

OR

Considering 
Fixed electricity prices
Fluctuating market prices

Optimize hourly
Power level
IBC activation
Selective shutdown

Based on
Wind speed distributions
Wind and price forecasts

To achieve long-term objectives on
Revenue 
Fatigue damage 

𝑡𝑛𝑜𝑤𝑡0

R
ev

e
n

u
e

𝑡𝑛𝑜𝑤𝑡0

D
am

ag
e

 p
e

r 
co

m
p

o
n

e
n

t

𝑡𝑒𝑛𝑑

𝑡𝑒𝑛𝑑

Baseline
Optimized

Figure 1.2: Overview of the components of the operational optimization method proposed in this
work



Chapter 2

Background

This chapter provides background information related to the work done in the thesis. Related
research and an overview of the state of the art are provided to explain the motivation and
context of the research topics involved. Moreover, definitions of quantities, metrics, aeroelastic
simulations, and the turbine model used throughout the rest of the thesis are introduced.

2.1 Background information and related research

In this section, background information on topics related to the proposed operational man-
agement approach to provide an understanding of the context and the motivation. Moreover,
related research is discussed in relation to optimization objectives for wind farm operation and
the general direction of this work. More specific discussion on the state-of-the-art regarding
the technical approaches in controller design, surrogate modeling, etc., can be found in the
relevant sections.

The goal of the electricity markets is to ensure efficient balancing between the generation,
consumption, distribution, and pricing of electricity. Most markets can be divided into two
main segments: the day-ahead (DA) or spot market and the intraday market. Within the
DA market, projected consumption is estimated on an hourly basis for the following day.
Subsequently, considering the hourly forecasts of renewable energy generation, conventional
power producers participate in bidding, operating within the established regulatory framework,
by specifying prices and trading volumes. Employing the merit order principle, the lowest bids
are accepted with the aim of economically optimizing the electricity supply based on lower
marginal costs. This process establishes DA prices for all market participants and determines



8 Chapter 2 Background

which power plants will be designated to deliver the required energy. To address short-term
fluctuations in production or demand throughout the day, electricity is actively traded in the
intraday market. The intraday market features shorter trading intervals, often extending to
just a few minutes, enabling rapid adaptation to changing conditions. Moreover, additional
markets exist offering grid balancing services and other ancillary services delivered by flexibility
providers.

Within this market model, the pricing mechanism for wind energy producers varies. In its
initial stages, wind farm operators received governmental subsidies to offset the high costs
associated with wind energy. These subsidies were typically provided in the form of a fixed
electricity price guaranteed for a specified number of years or energy production volume. This
approach aimed to safeguard the economic viability of wind projects, especially considering
the volatility in market prices and wind conditions. Such agreements are often structured as
power purchase agreements (PPAs), ensuring a fixed price or employing mechanisms such as
two-way contracts for differences (CfDs).

As wind energy technology has matured, cost reductions have become achievable, leading to
a decrease in the reliance on subsidies. However, subsidies remain integral to the sustainability
of wind energy projects. The newer subsidy schemes involve pricing mechanisms such as
constant or sliding premium tariffs, which entail an additional premium on top of the DA prices
and other financial instruments such as green certificates. Moreover, wind energy producers
are typically not involved in the intraday or secondary markets. This trend has spurred efforts
to enhance profitability in order to ensure the continuing expansion of wind energy capacity as
the subsidizing mechanisms diminish.

In contrast to conventional fuel-based electricity generation, wind energy requires a high
upfront capital investment and has low marginal costs. Moreover, production cannot be flexibly
regulated to meet demand or precisely forecasted. Additionally, wind farms are frequently
located in remote areas, posing additional challenges on the transmission grid, which can
lead to curtailment requests by the grid operator to avoid local grid congestion. These facts
highlight the challenges in grid integration and expansion of wind energy while maintaining
profitability and attractiveness of investment.

As the fundamental technology involved in wind energy generation has matured and wind
energy penetration in the mix has increased significantly, research objectives have evolved
to adapt to these new requirements. In addition to the traditional objectives of decreasing
manufacturing costs and increasing power production, wind energy systems have to be optimized,
taking into account objectives such as grid integration, overall profitability, market structures,
environmental impact, etc.

In [1], a detailed overview of the challenges of large-scale integration of renewables to the
current market structures and pricing mechanisms is provided. The need for change in pricing



2.1 Background information and related research 9

mechanisms to capacity-based support schemes in order to support grid integration and ensure
profitability is highlighted. In the same direction, [2] discusses the issues of the current structure
and recommends potential adaptations in the market structures to accommodate wind energy,
such as the consideration of probabilistic bids, the introduction of alternative business models,
and leveraging digitalization and artificial intelligence to explore more efficient market clearing
mechanisms. [3] examines the potential profitability of turbines without subsidies in Germany
through simulations of the present and future electricity systems. The need to look into
revenue metrics instead of solely relying on levelized cost of energy (LCOE) and the importance
of emission prices in order to maintain the profitability of wind farms is highlighted. [4]
explores the cost reductions achieved in wind energy due to technological advancements and
examines their impact on pricing mechanisms and overall profitability. The repercussions of
this downward price trend are discussed in [5], shedding light on the uncertainties associated
with future revenues and their implications on the realization and final investment decisions
for offshore wind projects secured through auctions.

Through the analysis of the challenges of increasing renewables penetration in the Irish
electricity market, [6] underscores the necessity and potential benefits, for all stakeholders,
of transforming the markets from cost-based to value-based able to reward and incentivize
flexible and reliable capacity. Additionally, [7] presents findings from a simulation study that
explores potential approaches for wind energy producers to participate in balancing markets.
The study suggests that such participation can offer both technical and economic advantages to
the system and the producers. The study presented in [8] focused on the possible participation
of wind in reserve and ancillary markets. The findings indicate that greater participation of
wind energy in these markets can be beneficial for the power system and play a crucial role in
maintaining the profitability of wind farms, especially as subsidies diminish.

Additionally, as the amount of installed wind capacity with relatively modern machines has
increased, the topic of end-of-life decision-making has emerged. Lifetime extension, under the
appropriate conditions, can lead to better use of material, accelerating the energy transition as
well as increased profitability for the producers. As discussed in [9], decision-making depends
on both technical and financial aspects, while novel operational approaches are required to
effectively manage structural loads while maintaining profitability.

Echoing these challenges, research focusing on the design and operation of wind turbines
and wind farms is adapting its goals. [10] introduces new value-based metrics for renewables,
expanding beyond annual energy production (AEP) and LCOE, aiming to better capture the
time-varying value of wind energy in electricity markets. In [11], these metrics are utilized
within wind farm design optimization, showing how different monetary objectives influence the
optimal technical design. Furthermore, [12] delves into the potential and associated technical
and legislative challenges of leveraging wind farm control to enable efficient participation in



10 Chapter 2 Background

various electricity markets and ancillary services. The study highlights the importance of price-
driven operation and structural load management as crucial enabling factors. [13] identifies
the current prospects and grand challenges in the field of wind farm control. It emphasizes the
necessity of designing and optimizing wind farms and relevant control strategies with a holistic
approach, considering value-based objectives, structural load management, and non-economic
objectives like environmental impact. Aligned with these objectives, [14] demonstrates the
potential of designing wind turbines taking into account the environmental and societal impact,
specifically in terms of generated and displaced greenhouse gas emissions across the entire
lifecycle. The findings suggest that significant improvements in environmental and societal
objectives can be achieved with a relatively small tradeoff in profitability. Furthermore, [15]
explores the benefits of low specific power wind turbine designs on the value of wind energy.
Trading maximum power output for higher production in lower wind speeds is shown to have
benefits for both farm operators and the grid in terms of revenue, forecasting uncertainty, and
reduced balancing and grid costs.

Focusing more on revenue objectives, several approaches have been explored in the litera-
ture. From a trading perspective, optimization methods have been proposed that can utilize
probabilistic wind generation forecasts to optimize dispatching strategies while participating in
both DA and balancing markets [16, 17]. In [17], a trading framework for optimal decision-
making is developed to concurrently optimize trading financial products and participating
in the day-ahead and intraday electricity markets in the short term. The findings suggest
that revenues can be increased within specific risk and uncertainty levels compared to passive
participation in the DA market. Furthermore, [18] introduces a profit maximization approach
tailored for wind energy producers involved in both DA and reserve markets. This approach
involves actively down-regulating the farm’s output and optimally trading reserves in the
reserve market, ultimately leading to increased expected revenue.

Moreover, revenue maximization has been considered in literature with respect to the
operational strategy and control of wind farms. [19] suggests capacity over-installation combined
with constant down-regulation to maximize profit, considering the DA market. This strategy
involves increasing the wind farm’s output at lower wind speeds, and its effectiveness depends
on pricing mechanisms and the correlation between wind speeds and prices. In a similar
approach, [20] suggests and experimentally evaluates the constant down-regulation of a wind
farm by 10% to provide up-regulation reserves in the secondary frequency reserve market. The
results demonstrate that this approach is technically feasible and can lead to increased revenue
compared to operating the farm at full capacity while participating only in the DA market.
The feasibility of this approach depends on the farm’s ability to respond accurately and rapidly
to up-regulation requests.

The planning of the downtime allocated for preventive maintenance, dictated by the op-



2.1 Background information and related research 11

erations and maintenance (O&M) schedule, based on expected revenue is suggested in [21].
The study demonstrates that revenue can be increased when monetary-based availability
objectives are considered compared to time-based or production-based approaches. Moreover,
[22] introduces an operational concept for wind turbines that combines structural fatigue
life estimation with revenue maximization strategies. This concept considers participation in
both the DA and intraday markets, factoring in forecasts and balancing costs. The findings
demonstrate the potential to improve profitability, emphasizing the importance of managing
the lifetime of wind turbines. Notably, the framework is conceptually similar to the approach
presented here, although the publication focuses solely on financial considerations, omitting
the lifetime management aspect.

Considering research focusing more on the technical aspects of wind farm flow control, only
a few publications can be found considering revenue and prices. This shows a gap that needs to
be bridged between the research focused on technical implementation at the wind farm/turbine
level and research focusing on bidding/dispatching strategies and other finance-oriented topics
related to wind energy. On one hand, research focused on the economics of wind energy
can benefit by considering more in-depth the technical capabilities and limitations of the
current wind energy technology, while more technical research can better focus its objectives
on addressing issues that can potentially have a major impact on the value of wind energy.

In [23], the potential of wind farm flow control to optimize revenue considering the DA
prices was explored in a comparative study where different modeling and control approaches
were evaluated with the same price and wind data representing current and future market
scenarios. The results highlighted that revenue increases can be achieved, with the extent of
the increase dependent on market conditions. Moreover, it was shown that revenue and energy
increases are not necessarily proportional and that the wind and market dynamics exert a high
influence on the magnitude of the revenue increase. Additionally, the study emphasized the
need for models and frameworks that can consider both revenue and loads in wind farm control
optimization, as most of the existing tool chains focus solely on power and neglect structural
load considerations. The work presented in [24] explored the potential increase in revenue for
wind farms operating within the DA markets by applying wake steering. The study considered
historical data across various areas in the US. The expected increase in revenue was found
between 0.8% and 1.7%, slightly higher than the expected increase in energy production.

Apart from the value-related objectives, the management of fatigue consumption is the
second area of focus in this work. In the context of wind farm control research, the focus
has been more on maximizing power production and providing ancillary services, while the
topic of fatigue loading is less prominent [25, 26]. There have been fewer published studies,
such as [27, 28, 29, 30], that focus on optimizing both power production and fatigue loading
simultaneously. These studies typically employ a surrogate model to simulate the loading



12 Chapter 2 Background

of each turbine, utilizing single-turbine aeroelastic simulations and flow models of varying
fidelity to account for flow interactions within the farm. The control strategies are derived
from multi-objective optimization methods, employing both closed- and open-loop wind farm
control approaches.

The optimization of both loads and power in wind farm control has been somewhat limited in
the past. However, this approach has gained prominence in recent years due to its significance
in achieving comprehensive system optimization. The integration of value-based objectives,
including fatigue accumulation objectives, in wind farm control optimization and evaluating
long-term operational strategies are important topics that can enable the holistic assessment
of the impact of the control methods and, thus, enable wider industry adoption. The method
proposed in this work, focusing on a single turbine, contributes to this direction by suggesting
multi-objective optimization approaches for cumulative fatigue and revenue objectives, as well
as a methodology suitable for the evaluation of the long-term impact of such methods.

Traditionally, research focused on individual wind turbines has concentrated on load reduction
and power optimization, primarily oriented towards wind turbine design improvements and
potential cost reductions. However, the long-term impact of implementing these strategies
on fatigue and revenue, and consequently in topics such as grid integration, profitability,
lifetime extension, etc., has not been extensively examined. Leveraging digital twins and
condition-monitoring systems for monitoring component fatigue consumption, in combination
with adaptive control strategies, can lead to reduced maintenance costs and extended lifetime
for the entire turbine or of specific sub-components [31, 9]. To this end, methods implemented
on the turbine controller level adapting the controller in real-time have been suggested, as
shown for example in [32, 33]. These methods involve the use of real-time load measurements or
model-based estimators to internally calculate and accumulate fatigue damage. Subsequently,
through a predefined logic, such as targeting a specific damage accumulation level or utilizing
model predictive control with a short-term prediction horizon, the control mode continuously
adjusts to achieve fatigue reductions while balancing trade-offs with other objectives like power
output and actuator usage. Additionally, adaptive control approaches, taking into account
both fatigue and power, considering inputs such as the turbulence level [34] or based on load
thresholds [35] can be found in the literature.

These approaches align with the research objectives of this work but differ fundamentally in
terms of approach and evaluation methodology. In the present work, the controller mode is
adapted in a quasi-static manner, with adjustments made for each consecutive hourly time block
based on commands from an external decision-maker responsible for assigning the controller
mode to the turbine with the aim of optimizing long-term objectives. Moreover, the results
in this work are evaluated in terms of cumulative metrics for the fatigue loading of all major
components, revenue, and other metrics over multiple years of operation while also considering



2.1 Background information and related research 13

the effect of the pricing mechanisms.

In the context of operational management for long-term objectives, literature on the perspec-
tive discussed in the present work is rather limited. In [36], a method for selective shut-down
of a wind turbine according to the projected revenue threshold is introduced. This approach
considers a simplified model for fatigue damage, which is used to estimate potential lifetime
extensions by the application of the method. Assuming operation with a fixed subsidy for an
initial period and operation in the DA market for the lifetime extension period, the findings
suggest that there is potential to increase the overall profitability. The selective shut-down
approach is also considered in the present work as a fatigue reduction method in combination
with down-regulation and individual pitch control. Additionally, in [37], a reliability-based
method for fatigue management of a single turbine is presented, focusing on the blade loads.
This approach involves down-regulation and power boosting while optimizing power levels
using model predictive control. The power level is optimized for consecutive time blocks based
on wind forecast horizons of a few days with the objectives of reducing fatigue damage and
increasing energy production. The findings suggest significant reductions in blade fatigue
damage, while potential increases in energy are not explicitly reported. Moreover, [38] out-
lines an operational strategy for targeting fatigue damage accumulation levels of a specific
component of a single wind turbine within a wind farm while minimizing the trade-off in
energy production. This approach utilizes down-regulation and optimizes power levels based
on site-specific mean wind speed distributions. The potential economic benefits of the method
are evaluated by considering the lifetime extension of the turbine under the assumption that
the damage reductions at the tower represent the entire turbine and that fixed prices will also
be valid during the extension period. These recent studies align with the research direction of
the present work, underscoring the significance and potential for addressing current research
challenges related to long-term operational strategies for wind turbines.

Overall, the literature review and discussions in this section underscore the necessity for
operational strategies capable of concurrently managing revenue and fatigue loading in wind
turbines over time. This work aims to introduce and evaluate such a methodology for a
single turbine based on adaptive control, encompassing down-regulation, power boosting, and
individual pitch control. The goal is to assess the method on a technical level, analyzing the
tradeoffs between revenue and fatigue accumulation on the entire system under various wind
and market conditions. As a foundation, the proof of concept and the example optimization
scenarios detailed in this work lay the groundwork for leveraging the method in a broader
context, aligning with the diverse research areas discussed in this section.



14 Chapter 2 Background

2.2 Definitions and metrics

In this section, definitions of quantities and metrics used throughout the thesis are provided to
facilitate the understanding.

Basic definitions

The electrical or aerodynamic power of a wind turbine (P) can be correlated to the wind speed
using the dimensionless power coefficient (Cp) power coefficient as shown in equation 2.1.

P =
1

2
ρArotv

3Cp ⇒ Cp =
2P

ρArotv3
(2.1)

Where ρ is the density of air, Arot is the swept area of the rotor, and v is the uniform,
incoming horizontal wind speed.

The aerodynamic thrust force, defined as the axial force applied by the wind on the rotor of
a wind turbine, can be correlated to the wind speed using the dimensionless thrust coefficient
(Ct) using equation 2.2.

T =
1

2
ρArotv

2Ct ⇒ Ct =
2T

ρArotv2
(2.2)

The tip speed ratio (TSR or λ) is a dimensionless parameter defined by the ratio of the
translational speed at the tip of the blade to the mean horizontal wind speed. It is useful as it
correlates the rotor’s rotational speed to the horizontal mean wind speed and provides insights
into the performance and efficiency of a rotor. It is used in the aerodynamic and controller
design of wind turbines. TSR can be calculated using equation 2.3.

TSR = λ =
ωrotR

v
(2.3)

Where ωrot is the rotational speed of the rotor, and R is the rotor’s radius.

The Weibull distribution is a widely used probability distribution in wind energy due to its
ability to accurately model long-term wind speed distributions. It is employed to represent the
wind speed frequency distribution at a specific location using historical measurement data. The
distribution’s versatility makes it suitable for various wind conditions encountered in different
regions. The Weibull distribution is characterized by two parameters: the shape parameter (k)
and the scale parameter (A). The shape parameter determines the skewness and coefficient
of variation of the distribution. The scale parameter influences the distribution’s spread and
height, and is closely correlated to the mean wind speed. The probability density function
(PDF) of the Weibull distribution is expressed as defined in equation 2.4



2.2 Definitions and metrics 15

f(v; k,A) =
k

A

( v
A

)k−1

e−(v/A)k (2.4)

where v is the wind speed, k is the shape parameter, and A is the scale parameter.

Structural fatigue calculations

To evaluate the structural reliability of wind turbines under the impact of stochastic cyclic
loading, the concept of fatigue damage is used. Fatigue damage (D) and damage equivalent
loads (DELs) serve as metrics for quantifying the fatigue impact of load series on a component.
Using these, the structural strength required for each component in order to avoid structural
failure due to fatigue, for a predefined lifetime duration, can be calculated. Moreover, they
enable the comparison of different designs in terms of their impact on fatigue accumulation
and, therefore, predicted structural lifetime. As the management of fatigue accumulation is
one of the main focuses of this work, the topic is briefly introduced here.

The fatigue performance of a material is typically characterized by the S-N curve. The S-N
curve shows the number of cycles (N) for various load ranges (S) a material can endure before
failing. Points below the curve indicate the ‘safe’ region, while above, failure occurs. The curve
itself represents the critical value. In its logarithmic form, it can be assumed linear with a
slope equal to −1/m where m is referred to as the Wöhler exponent (m). Based on this, the
maximum allowed cycles for each load range are calculated using equation 2.5.

N = cS−m (2.5)

c is a constant correlated to the exact material properties and the shape of the considered
cross-section. This is usually not known, and only the manufacturer can provide exact values.
When the objective is solely to compare fatigue loads for the same design, c=1 can be assumed,
as it is done in the present work. However, for actual design purposes, more information is
required.

Damage is a simplified metric to quantify the contribution of a combined loading spectrum,
encompassing multiple load ranges and cycles, to structural fatigue accumulation until failure
is reached. This simplification, based on Miner’s rule [39], involves the linear addition of the
different contributions, in terms of cycles counted per stress range, to determine the total
accumulated damage as expressed by equation 2.6.

D =

i=j∑
i=1

Ni

Ncrit,i

=

i=j∑
i=1

Ni

cS−m
i

=

i=j∑
i=1

NiS
m
i (2.6)

Where j is the total amount of binned load ranges, Si is the mean value of the ith load



16 Chapter 2 Background

range bin, and Ni is the number of cycles counted for this load range. These two values
can be calculated directly from the signal’s loading time series, produced by measurement or
simulations, using the rainflow-counting algorithm [40].

By definition, avoiding failure means that D≤1, which is the goal when designing components.
Since the material constant c for each component is unknown, the absolute value of damage
cannot be calculated. Consequently, it can only be calculated relatively compared to a reference
case. Hence, for the rest of this work, the total cumulative damage calculated for the baseline
case over the specified time period will be normalized to 1. This is a conservative assumption
implying that the baseline operation consumes the entire damage budget.

DEL is a commonly used metric allowing the comparison of the effects of different dynamic
loads for a specific time duration while removing the dependency on c explained earlier. The
idea behind DEL is to define an equivalent load range so that when it is applied for a specific
number of cycles Neq, it results in the same damage as the total load spectrum. DELs can be
calculated using equation 2.7.

Deq = D ⇒ Neq

cS−m
eq

=

i=j∑
i=1

NiS
m
i ⇒ Seq = DEL =

(
i=j∑
i=1

Ni

Neq

Sm
i

)1/m

(2.7)

The value of DEL is independent of the simulation length and needs to be used cautiously.
While it is effective for comparing different loading cases, DELs cannot be added linearly, e.g.,
the DEL from two different simulations cannot be added to calculate the total DEL. The
value of Neq can be arbitrarily chosen. In this work, the 1 Hz equivalent load is used. Thus,
Neq is equal to the duration of the signal in seconds. Based on the previous definitions, the
transformation between DEL and D can be derived as shown in equation 2.8.

DEL =

(
D

Neq

)1/m

⇒ D = DELmNeq (2.8)

It should be noted that within this approach, the mean of the load cycle is not considered,
only the range. This is a simplified approach used to compare fatigue load levels and evaluate
the influence of a proposed method comparatively. Nevertheless, it is important to be considered
in real-world applications as it has been demonstrated to have a high influence on the resulting
fatigue damage distribution [41, 42].

Metrics and KPIs definitions

From a fatigue evaluation perspective, the aim of this work is to assess fatigue loading across
all major wind turbine components. Thus, all the major components are considered, including
the tower, nacelle, blades, and low-speed shaft. The DEL is calculated from the aeroelastic



2.2 Definitions and metrics 17

simulations and used in the surrogate model. Within the developed accumulation framework,
the DEL predictions provided by the surrogate are translated to damage and added linearly
to track the fatigue accumulation of each component over time. The set of metrics defined is
presented in table 2.1. Additional metrics, such as generator speed std, tip-tower clearance,
etc., have been recorded from the aeroelastic simulations and are included in the surrogate
model but not used within the scope of this work. The complete set of metrics is included in
the publicly available repositories (see appendix A.1).

Table 2.1: Metrics definitions, abbreviations and units

Abbrev. Quantity Metric Unit Wöhler
BRMx Edgewise blade root moment DEL/D kNm/ND 10
BRMy Flapwise blade root moment DEL/D kNm/ND 10
BRMz Blade root torsion DEL/D kNm/ND 10
BROop Out of plane blade root moment DEL/D kNm/ND 10
BRIp In plane blade root moment DEL/D kNm/ND 10
TBMx Fore-aft tower bottom moment DEL/D kNm/ND 4
TBMy Side-side tower bottom moment DEL/D kNm/ND 4
TBMz Tower bottom torsion DEL/D kNm/ND 4
TTMx Tower top roll moment DEL/D kNm/ND 4
TTMy Tower top pitch moment DEL/D kNm/ND 4
TTMz Tower top yaw moment DEL/D kNm/ND 4
LSSMy Low-speed shaft moment around y-axis DEL/D kNm/ND 4
LSSMz Low-speed shaft moment around z-axis DEL/D kNm/ND 4
LSSTq Low-speed shaft torque DEL/D kNm/ND 4
Energy Energy

∫ tend

to
Pel dt kWh -

PitchTr Pitch travel
∑tend−1

to
|θt+1 − θt| deg -

The energy output is used to accumulate energy production over time and also calculate the
instantaneous and cumulative revenue by multiplying it with the electricity price. Furthermore,
pitch travel is used as a metric to track the pitch actuator usage in order to assess the impact
of different strategies, and especially the individual pitch control loop, on the pitch system.

The key performance indicators (KPIs) utilized to evaluate the optimization results in
chapter 7 include the relative differences in cumulative damage per load, cumulative energy,
cumulative revenue, and cumulative pitch travel. The relative differences for all quantities are
calculated compared to the baseline operation for a specified period using equation 2.9.

∆Q = 100
Qnew −Qbase

Qbase

[%] (2.9)

Moreover, two additional KPIs are introduced to evaluate the impact of the different



18 Chapter 2 Background

optimization approaches. The first, denoted as IBC%, indicates the percentage of time the
individual blade control (IBC) loop is active. It is calculated by dividing the amount of time
steps the IBC loop was active by the total amount of time steps where the wind turbine was
operational (not shut down). Since in the baseline operation, IBC is not considered, the values
reported are absolute values.

The second additional KPI, denoted as Shut%, quantifies the percentage of time that the
wind turbine is intentionally shut down based on the optimization strategy. This metric
evaluates the frequency of selective shutdowns requested by each optimization approach. It
is defined as the difference in shutdown time between the optimized and the baseline case,
divided by the total amount of time the turbine remained operational in the baseline case.

2.3 Aeroelastic simulations and turbine definition

The aeroelastic simulations required for this work were performed with the mid-fidelity, open-
source tool FAST v8.16.00 [43, 44] provided by the National Renewable Energy Laboratory
(NREL). All degrees of freedom available in the structural module ElastoDyn were enabled
besides the YawDOF option, as the nacelle yaw is maintained constant throughout the
simulations. In the aerodynamics module AeroDyn v14.04, the Beddoes dynamic stall model
was activated. Additionally, the equilibrium induction-factor model, along with the Prandtl
corrections for tip-loss and hub-loss calculations. Moreover, the tower shadow model was
deactivated. The settings regarding the turbine configuration and the various modules used in
FAST were kept consistent for all simulations.

The FAST software was compiled as an S-function and integrated within a Matlab/Simulink
framework. The controller and actuators were designed in Matlab and connected to the
S-function within the aforementioned simulation framework. More details on this can be found
in section 3.1. Additionally, pre- and post-processing tools were also developed in Matlab for
the present work.

The open-source software Turbsim v2.0.0 [45], provided by NREL, was used for generating
the numerical wind fields. The grid dimensions were set to 180 by 180 meters with 31 grid
points along each dimension. The time step of the wind fields was set to 0.125s. The turbulence
model used was the International Electrotechnical Commission (IEC) Kaimal model by enabling
the IECKAI option along with the IEC normal turbulence model and the default surface
roughness length options in Turbsim. The power law model was used for the wind shear. All
settings were kept constant for all wind fields generated. The only exceptions are the mean
wind speed at the hub height and the turbulence intensity (TI), as discussed in section 4.1.1.

The DTU 10 MW reference wind turbine (rwt) [46] was chosen as a representative of a



2.3 Aeroelastic simulations and turbine definition 19

modern multi-MW machine resembling the current generation of offshore wind turbines. The
turbine is considered in an onshore configuration to reduce computational costs. The main
design characteristics are presented in table 2.2. More information on the turbine model and
its implementation in FAST can be found in [46, 47]. The system’s main natural frequencies
are presented in table 2.3

Table 2.2: DTU 10 MW rwt design parameters

Turbine Parameters Value
Rotor radius 89.2 m
Hub Height 119 m
Gearbox ratio 1:50
Rated rotor speed 9.6 rpm
Rated generator speed 480 rpm
Cut in generator speed 275 rpm
Rated generator torque 2.1602E5 Nm
Rated power 10 MW
Electrical efficiency of generator 94%
Mechanical efficiency of gearbox 100%
Power losses from converter 220 kW

Although the proposed operational optimization and the size of the chosen turbine are
more relevant for offshore applications, the choice to use the onshore version was motivated to
reduce the computational time by excluding hydrodynamics. In a practical implementation,
hydrodynamics and offshore foundations should be included. However, the response of the
system, in terms of the metrics considered in this work, is not expected to differ substantially
in a fixed bottom offshore configuration as the hydrodynamic loads mainly affect the substruc-
ture. Consequently, this choice is not expected to affect the optimization outcomes and the
applicability of the method considered in this work.

Table 2.3: Natural frequencies of the DTU 10 MW rwt

Mode Natural Frequency Hz
1st Tower 0.26
1st edgewise blade 0.93
1st flapwise blade 0.61
2nd flapwise blade 1.74



20 Chapter 2 Background

2.4 Wind turbine control

The wind turbine’s control system encompasses several functions, including supervisory control,
closed-loop operational control, and the safety system [48, 49, 50]. It relies on sensors to
measure essential quantities like blade pitch angle, rotor speed, generator torque, and more.
Actuators, such as the generator torque actuator, blade pitch actuators, and the mechanical
brake, are employed to execute desired actions according to the logic programmed in the local
wind turbine controller software.

The supervisory control loop is the higher-level layer, responsible for switching operational
states and ensuring safe operation, managing the overall operation of the system. Some of its
main functions include [48]:

• Managing standby operations, such as idling, locked rotor, nacelle yaw orientation, and
cable unwinding

• Verifying the execution of the current operational objective and identifying faults

• Initiating the start-up process when conditions meet the requirements

• Initiating the shut-down procedure, whether normal or emergency, in response to fault de-
tection, alarm triggers (e.g., overspeeding or high temperatures), or when wind conditions
fall outside the operational range

The closed-loop operational control is responsible for the operation of the turbine, including
normal operation, start-up and shut-down maneuvers. For modern multi-MW horizontal axis
wind turbines with variable speed and pitch regulation (VSPR), the basic control loop has
as inputs the (usually low passed) generator/rotor rotational speed, generator torque, blade
pitch angle, nacelle yaw orientation, and wind direction. Additional inputs, such as tower
top acceleration, hub height wind speed, load measurements in various locations, etc., can be
integrated into secondary control loops aimed at reducing loads or enhancing power production.
The outputs of the controller are the generator torque, blade pitch angle, and nacelle yaw
angle. The generator, blade pitch motor, and nacelle yaw motor are the actuators responsible
for converting these commands to mechanical work.

In normal operation, the closed-loop control is responsible for maximizing power extraction
until the design power level. When this is reached, in order to limit structural loads and noise
emissions, the controller focuses on keeping the power output constant and the rotor speed
and generator torque within a design envelope by engaging the blade pitch system.

This work focuses only on the closed-loop control of the turbine in normal operation,
excluding the start-up and shutdown maneuvers. Thus, in the following, more details will
be given on these topics as they are relevant to the controller design in this work. More
information on the rest of the controller’s functionality can be found in [48].



2.4 Wind turbine control 21

The control regions of a VSPR wind turbine are shown in figure 2.1. The graphs illustrate
how power, generator speed, and Cp relate to the different wind speeds and control regions.
Moreover, the characteristic of the generator (torque vs. rotational speed) is shown for the
different control regions.

Figure 2.1: Control regions of a wind turbine. Left: Power, generator speed and Cp as a function of
wind speed (figure modified from [51]) Right: Example of generator torque vs generator speed for the

different control regions (figure modified from [52])

Ideally, a wind turbine would produce power proportional to the cube of the wind speed at
every wind speed. Due to technical constraints, this is only possible for a limited range of wind
speeds in Region 2. In Region 1, the wind speed is too low; hence, the aerodynamic torque
is not able to match the minimum torque of the electrical generator, or it might not even be
enough to overcome the rotor’s inertia. In this region, the turbine is not producing electricity,
and the rotor is either locked or idling.

The minimum wind speed at which the turbine can produce electrical power is called the
cut-in wind speed, which denotes the lower limit of control region 1.5. In order to extract the
maximum possible power from the wind, a specific rotor rotational speed (ωrot), is necessary,
determined by the aerodynamic design of the rotor to attain the designated TSR value
associated with the maximum possible power Cp. In region 1.5, the optimal TSR can not be
achieved, leading to sub-optimal power extraction with a reduced Cp. This occurs because
the rotational speed has to be higher than the optimal in order to avoid resonance between
the 3P (third harmonic of ωrot) frequency of the rotor and the tower’s first natural frequency.
This is due to the common "stiff-stiff" design of steel wind turbine towers. Another reason for
the minimum rotor speed requirement could be the minimum rotational speed allowed by the
electrical generator.



22 Chapter 2 Background

In region 1.5, the controller’s objective is to keep rotational speed above the minimum and
ensure a controlled trajectory towards the optimal TSR (λopt) as wind speed increases while
minimizing Cp reduction and structural loading. The blade pitch angle typically remains
constant at the fine pitch value, which is determined by aerodynamic design considerations.
The regulation of the rotational speed is achieved by manipulating the generator torque. Two
common approaches are employed for controlling the generator torque in this region. The first
uses a linear ramp for the torque forcing the rotor speed on a prescribed trajectory [43, 53, 51]
as shown in figure 2.1. The second employs a PI loop [54, 53, 55] that sets the rotational speed
to the minimum value of region 2 where λopt is achieved. This PI loop is active until generator
torque reaches the minimum value of region 2, effectively creating a vertical trajectory on the
torque-speed graph. Both methods have advantages, with the PI loop being able to keep rotor
speed closer to λopt leading to higher energy capture, but on the other hand, the switching
between the regions and the decoupling with the PI loop for region 2.5 needs careful handling.
In this work, the linear ramp method is used for simplicity.

When design λopt is reached, control region 2 starts. Here, the generator torque is controlled
so that optimal torque is provided for each rotor rotational speed in order to maintain λopt and
thus optimal power extraction. In this region, the controller varies only the generator torque,
and the aerodynamically optimal blade pitch angle θ is kept constant. It can be derived that
for a given target λopt and Cp,opt, optimal power output and, consequently, optimal generator
torque is proportional to the square of the rotational speed:

Mg =
0.5ρπR5iGBCp,opt

λ3
opt

ω2
rot −Mloss ⇒ Mg = κω2

g −Mloss, Mg ∈ (Mg,max15 Mg,rat] (2.10)

Where iGB is the gear box ratio, so that ωrot = ωgiGB. Mg,rat is the generator torque at rated
power, Mg,max15 is the maximum generator torque in region 1.5 and Mloss is the mechanical
torque loss in the drive train.

More advanced techniques have also been suggested in the literature [56, 55, 57] using an
estimator that is able to track the rotor effective wind speed and subsequently λ so that a PI
loop for the generator torque can be designed to directly track the optimal TSR leading to
higher energy capture. In this work, the κω2 strategy is chosen for control region 2.

Region 2.5 is the transition region between regions 2 and 3. It is worth noting that this
region is important for the wind turbine loads as the turbine is operating in maximum thrust
while switching control objectives and engaging blade pitching. The generator torque and the
rotational speed of the rotor have upper limits according to manufacturer specifications and
noise emission legislation (often defined as tip speed restrictions), respectively. Region 2.5 is
the region in which one of these limits is reached while power has not reached the rated value.



2.4 Wind turbine control 23

The behavior of each turbine depends on the specific aerodynamic design and upper speed and
torque design limits. Region 2.5 can go from almost non-existent to spanning over a range of
wind speeds of 3 m/s. It is more common, especially as rotors grow larger, that ωrat is reached
first.

In region 2.5, two control approaches are commonly implemented. The simpler one is using
a torque-speed linear ramp to drive the generator torque to the rated values as shown in figure
2.1). In this case, the control design variables are the choice of the torque and speed value of
the first point of the ramp [43, 48]. To prevent interference between the pitch controller and
speed regulation and ensure smooth transitions, various strategies can be implemented. These
strategies may include imposing limits on the minimum pitch angle and setting a torque limit
slightly above the rated value, after which pitching is activated.

The second approach includes a PI loop that will create a vertical line in the speed-torque
map [58, 55, 53, 54]. In this method, the set point for the PI controller is the rated rotational
speed ωrat, and it is activated when the ωrat is reached. In order to clearly separate the two PI
loops (region 1.5 and 2.5) and the region 2 torque controller, saturation limits are applied to
the output torque. Moreover, the switching of the set point is activated based on a fixed torque
value close to the middle of region 2 between ωmin and ωrat. This leads to a smooth transition
since, until either limit is reached, the torque controller’s output is saturated. In order to make
sure that the pitch and torque controllers do not overlap in this region, various approaches can
be found in the literature. In [54], a switching logic based on a hard switch that allows the
pitch controller to start being active when the commanded value is slightly higher than the
minimum along with an anti-windup term for the integrator referencing the power is used. In
another approach [58, 55], known as the set point smoother, two tunable gains are used as
weights on the difference of current pitch angle to the minimum and the difference of current
rotational speed to rated to produce an offset to the set point of each controller. This ensures
that in regions 2 and 3, only one controller is active for speed regulation while the other is
saturated. In both cases, there are no tuning rules for the parameters, and it is usually done
iteratively.

In region 3, Prat, ωrat, and Mg,rat have been reached. The controller’s objective is to keep
ωrat constant for every wind speed until cut-off using the blade pitch system to regulate the
rotational speed. In regards to the torque controller, two modes are used. Constant power,
where the torque is commanded based on the current speed Mg = Prat/ωg and constant torque
where Mg = Mg,rat. The most common approach for the pitch controller is a feedback PI loop
with the setpoint being the rated rotational speed ωrat and saturation limits [θfine θmax].

An additional anti-windup term on the integrator is typically implemented. This ensures that
after a period of operation in below-rated conditions where the pitch controller is saturated, the
integral term will not increase indefinitely. This mechanism ensures a rapid response from the



24 Chapter 2 Background

pitch controller when the turbine transitions to rated conditions. It also aids in the decoupling
of the pitch and torque controllers concerning speed regulation. The anti-wind up can be
implemented by feeding the saturated commanded pitch values (which has to be θcom > θfine)
for the calculation of the integral error or setting hard limits on the integral error. Various
tuning methods exist for the pitch controller in region 3, with the most common being the
closed-loop shaping method. As this method is used in this work for the gain tuning of the
collective pitch PI loop, it is briefly introduced here.

The scope of the PI blade pitch controller is to minimize the error of the rotational speed of
the generator compared to the set point. The error is defined as:

e(t) = ωg(t)− ωg,rat (2.11)

The commanded pitch angle value from a PI scheme will have the form:

θcom,ti = KP eti−1
+KI

∫ t

t0

e dt (2.12)

Or equally

θcom,ti = KP eti−1
+

KP

TI

∫ t

t0

edt where TI =
KP

KI

and KP , KI , TI → f(θti−1
) (2.13)

The proportional (KP ) and integral (KI) gains can be calculated with the closed loop
shaping method. This simple method is based on a linearized single-DOF representation of the
drivetrain dynamics. Combining the single-DoF linear model (linearized for each wind speed)
with the PI leads to a second-order linear model, which can have the desired dyn