During the course of implementing the system it became apparent that proper scaling of the input variables was necessary in our case. Without it numerical errors would force the system to behave in an improper way.
The use of such future wind speed measuring device as LIDAR might improve systems behaviour during the stochastic wind turbulence simulation if the re-sults would be fed into the disturbance trajectory or have been used for the gain scheduling algorithm. Although wind estimates obtained with the kalman filter weren’t used for this (gain scheduling) purpose it seams that with proper fine tuning using them in this fashion would be possible.
11.3 Implementation 113
The control performance during the stochastic wind turbulence simulation raises significantly with the increase of sampling frequency what have been concluded during simulation’s preparation (not documented here). This is due to the fact that in this case controller has the chance to react faster to the wind speed changes.
It was noticed that during the simulations that would involve soft constraints ac-tivation the algorithm would significantly slow down while attempting to obtain proper solution by violating output constraints. Specialized algorithms might address this issue and their use is recommended.
114 Conclusions
Appendix A
FAST Linearization setup
The main FAST configuration files that are of importance in the linearization process are:
• *.fst file - the main FAST configuration file. It will be referred to as [.FST]
file
• * Linear.dat - the main linearization module configuration file. It will be referred to as [.DAT] file
Below the following notation will be used:
”.DAT//MODEL LINEARIZATION//(NAzimStep)” will refer to [NAzimStep]
parameter in the [MODEL LINEARIZATION] section of the [.DAT] file.
As pointed out in section2.2the way in which wind turbine is being controller is strictly connected to the current wind speed. Furthermore, due to the re-strictions introduced by it’s (wind turbine’s) designers, four different operation modes are distinguished. Which of them is currently active depends also on the speed of the wind at the given instant. This emphasizes the necessity of having multiple linear models constructed around different wind speed operation points in order to be able to achieve good control.
Keeping in mind different control approaches in each region, described in section
116 Appendix A
2.2, we will set FAST parameters differently for each mode of operation. Those parameters will include:
• .FST//TURBINE CONTROL//(BlPitch(1) through BlPitch(3)) - repre-sents the initial or fixed pitch of blades 1 through 3.
• .FST//INITIAL CONDITIONS//(RotSpeed) - represents the initial or fixed rotor speed
• .DAT//PERIODIC STEADY STATE SOLUTION//(TrimCase) - repre-sents the control strategy for the model. It’s possible settings are:
– 1 - find nacelle yaw (not useful in our case since it is assumed that there is no yaw control)
– 2 - find generator torque while the blade pitch is kept constant – 3 - find collective blade pitch while the generator torque is kept
con-stant
The main tool for obtaining proper values of those parameters is theCp curve.
We use it for calculating the border wind speeds (v1...v4) for the operation modes, optimum blade pitch (θopt) that would give maximum power coefficient Cp (provided that tip speed ratio would be optimal as well) and rotor speed that would give optimum tip speed ratio (see (2.1)) for the given wind speed.
Control strategy represented by the [TrimCase] parameter will be chosen based on the region characteristics outlined in2.2.
Guidelines for setting those parameters for the purpose of linearization are sum-marized in TableA.1.
FAST Linearization setup 117
Region I (low): v1...v2
Ωrmin limit reached parameter value
BlPitch(1) optimal pitchθopt
BlPitch(2) optimal pitchθopt
BlPitch(3) optimal pitchθopt
RotSpeed lower limit for rotors speed Ωrmin
TrimCase 2
Region II (mid): v2...v3
no limits reached parameter value
BlPitch(1) optimal pitchθopt
BlPitch(2) optimal pitchθopt
BlPitch(3) optimal pitchθopt
RotSpeed calculated with the use ofCp curve TrimCase 2
Region III (mid): v3...v4
Ωrmax limit reached parameter value
BlPitch(1) optimal pitchθopt
BlPitch(2) optimal pitchθopt
BlPitch(3) optimal pitchθopt
RotSpeed upper limit for rotors speed Ωrmax
TrimCase 2
Region IV (mid): v4...
Ωrmax andPemax limits reached parameter value
BlPitch(1) doesn’t matter BlPitch(2) doesn’t matter BlPitch(3) doesn’t matter
RotSpeed upper limit for rotors speed Ωrmax
TrimCase 3
Table A.1: Guidelines for choosing values of the key parameters of the FAST linearization module for different operation modes.
118
Bibliography
[1] International Energy Agency. World energy outlook 2010.
[2] F.D. Bianchi, Hern´an De Battista, and R.J. Mantz. Wind Turbine Con-trol Systems. Principles,Modelling and Gain Scheduling Design. Springer-Verlag, 2007.
[3] F. Borrelli, M. Morari, and U. Maedera. Linear offset-free model predictive control. Automatica, 45, 2009.
[4] T. Burton, D. Sharpe, N. Jenkins, and E. Bossanyi.Wind energy handbook.
John Wiley & Sons Ltd, 2001.
[5] E. Hendricks, O. Jannerup, and P.H. Sørensen. Linear Systems Control.
Deterministic and Stochastic Methods. Springer-Verlag, 2008.
[6] L.C. Henriksen. Model predictive control of a wind turbine. Master’s thesis, Technical University of Denmark, 2007.
[7] L.C. Henriksen. Model Predictive Control of Wind Turbines. PhD thesis, Technical University of Denmark, 2010.
[8] L. Jespersen and M.W. Krogen. Model predictive lidar control of wind turbines for load mitigation. Master’s thesis, Aalborg University, 2010.
[9] B.J. Jonkman. Turbsim user’s guide: Version 1.50. Technical report, NREL, 2009.
[10] J.M. Jonkman and M.L.Jr. Buhl. Fast user’s guide. Technical report, NREL, 2005.
120 BIBLIOGRAPHY
[11] J.M. Jonkman, S. Butterfield, W. Musial, and G. Scott. Definition of a 5-mw reference wind turbine for offshore system development. Technical report, NREL, 2009.
[12] Lecture notes for model predictive control course (02619) on dtu, 2010.
[13] J.M. Maciejowski.Predictive Control with Constraints. Prentice Hall, 2002.
[14] T.S. Mogensen and A.J. Larsen. Individuel pitchregulering af vindmølle.
Master’s thesis, Technical University of Denmark, 2006.
[15] J. Nocedal and S.J Wright.Numerical Optimization. Springer-Verlag, 2006.
[16] J.B. Rawlings and G. Pannocchia. Disturbance models for offset-free model-predictive control. AIChE Journal, 49(2), 2003.
[17] J.A. Rossiter.Model-Based Predictive Control. A Practical Approach. CRC Press, 2004.
[18] K. Selvam, S. Kanev, J. W. van Wingerden, T. van Engelen, and Verhae-gen. Feedback-feedforward individual pitch control for wind turbine load reduction.International Journal of Robust and Nonlinear Control, 19, 2009.
[19] Kasper Zinck Østergaard, Jakob Stoustrup, and Per Brath. Linear param-eter varying control of wind turbines covering both partial load and full load conditions. International Journal of Robust and Nonlinear Control, 19, 2009.
[20] P. Østergaard. Pitchregulering af en vindmølle. Master’s thesis, Technical University of Denmark, 1994.
[21] S.C. Thomsen. Nonlinear control of a wind turbine. Master’s thesis, Tech-nical University of Denmark, 2006.
[22] L. Wang. Model Predictive Control. System Design and Implementation Using MATLAB. Springer-Verlag, 2009.
[23] A.D. Wright and L.J. Fingersh. Advanced control design for wind turbines.
part i: Control design, implementation, and initial tests. Technical report, NREL, 2008.