CONTROL DESIGN FOR TWO-BLADED WIND TURBINES CONTROL DESIGN FOR TWO-BLADED WIND TURBINES Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 29 september 2015 om 12:30 uur door Edwin VAN SOLINGEN ingenieur in de systeem- en regeltechniek geboren te Bernisse, Nederland. Dit proefschrift is goedgekeurd door de (co)promotoren: Prof. dr. ir. M. Verhaegen Dr. ir. J. W. van Wingerden Dr. ir. R. De Breuker Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. dr. ir. M. Verhaegen, Technische Universiteit Delft, promotor Dr. ir. J. W. van Wingerden, Technische Universiteit Delft, copromotor Dr. ir. R. De Breuker, Technische Universiteit Delft, copromotor Onafhankelijke leden: Prof. dr. ir. G. A. M. van Kuik, Technische Universiteit Delft Prof. dr. ir. D. M. van Solingen, Technische Universiteit Delft Prof. dr. M. Lovera, Politecnico di Milano Dr. ir. D.-P.Molenaar, Siemens Wind Power Prof. dr. ir. R. Babuška, Technische Universiteit Delft, reservelid This dissertation has been completed in partial fulfilment of the requirements of the Dutch Institute of Systems and Control (DISC) for graduate studies. This work was funded and supported by the Far and Large Offshore Wind (FLOW) pro- gram, no. P201101 − 016−TUD, “Integrated design of far large offshore wind turbines”. Copyright © 2015 by E. van Solingen All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Cover: Photograph of NedWind 1MW wind turbines at Windpark Eemmeerdijk, Flevoland, The Netherlands. Edited by Jeroen Zwijnenburg and Karin van Driel. ISBN 978-94-6259-828-7 ACKNOWLEDGEMENTS This thesis is most certainly not the result of four years of individual work. Many people were directly or indirectly involved and have contributed to the final result. I would like to thank them for their contributions in this place. First and above all I would like to thank my daily supervisor Jan-Willem van Winger- den for his supervision during the past years. Without his enthusiasm, ideas, and sugges- tions to solve one of the many problems encountered during research, this thesis would not have been here in its current form and at this time. The freedom to participate in conferences and events all over the world was gratefully appreciated. Besides being al- most always available for work related matters, he also provided great understanding and support with more personal matters. Jan-Willem, I believe I could not have wished for a better supervisor. Thanks!! I would also like to thank Michel Verhaegen for giving me the opportunity to do a PhD and Roeland De Breuker for his supervision and useful input during the research. The thesis is part of the Far and Large Offshore Wind (FLOW) research programme for which I would like to thank FLOW for making this research project available as well as providing the financial means for the project. In the last phase of the project, a case study was carried out together with the Dutch company 2-B Energy, which is the industrial partner of this PhD project. I appreciated working with Jan Beerens from 2-B Energy and I am sure that both 2-B Energy and my research have been positively affected by this cooperation. During my PhD I had the fortunate opportunities to do two measurement campaigns with the NREL CART2 wind turbine. I am thankful to Paul Fleming and Andy Scholbrock who did a great job during my visits in helping me to implement the controllers, collect- ing the data during windy days (when I already left), and providing me with the required details to understand and analyze the collected data. Also, the many activities outside of the measurement campaign in and around Boulder were greatly appreciated. Thanks Paul, Andy, and all others who have made my visits to NREL possible and very enjoyable! Furthermore, I had the opportunity to conduct a number of wind tunnel experi- ments. For these experiments a small-scale two-bladed wind turbine was designed and built by the department’s technicians. The small-scale turbine was extremely reliable and basically plug-and-play so that much time was saved for the actual experiments. This is to a great extent due to Kees, Simon, and Will. Unfortunately, the results of the experiments did not make it to the final thesis, however they did lead to some nice pub- lications. The working days at the university were (luckily) not only composed of work, but also with coffee breaks and later on foosball. I really enjoyed playing one of the many tense or not so tense games. The ‘almost’ 10-0 and 0-10 games, the ’tiebreaks’, and the most bizarre goals are unforgettable (as well as winning the first official DCSC table foosball tournament with Shuai). I also enjoyed playing soccer, beach volleyball, ’game nights’, v vi ACKNOWLEDGEMENTS and more. Sachin, Ivo, Pieter, Gijs, Hans, Elisabeth, Subramanya, Bart, Kim, Mernout, Noortje, Max, Sjoerd, Reinier, Laurens, Patricio, Dieky, Ruxandra, Baptiste, Paolo, Dean, Yasin, Hildo, Jan-Maarten, Renshi, Jacopo, Sadegh, Ana, Arne, Yue, Le, Yashar, Moham- mad (x2), Esmaeil, Vahab, and everyone who expected his or her name in this list but could not find it.. thanks for these nice times! Conferences would not have been so nice without Maxime, Pim, Antonio, Lars, Thijs, Etana, and Joost, Tom, Bram, and Frank from TU Eindhoven. Marieke, Kitty, Esther, Saskia, and Heleen, thanks for the support with the many administrative matters and for always being in the mood for joking around. I also thank MSc students Rishabh, Jelle, Sandor, and Sebastiaan. It was really nice working with you and your results have provided me with many new insights and better understanding of many aspects. A special thanks also goes to Sachin for proofreading many of my articles and to Jeroen Zwijnenburg and Karin van Driel for designing the thesis cover. Outside of work I had great times with Tom, Ferry, Arjen, Liona, Sabrina, ’De Krant’, and ’MiXX’. Thanks for your interest in my work, your support, and the many enjoyable moments during parties, nights out, holidays, etc. I also had a great time with Yu Hu, with whom I shared a house for a couple of years during my PhD. I would also like to thank my parents, brother, and sister for their support and for always being there. Finally, I thank Yvonne for her love, for her patience whenever I was at home but my thoughts were still at work, and for her support and understanding throughout the last two years. Edwin van Solingen Delft, September 2015 CONTENTS 1 Introduction 1 1.1 Cost of wind energy ............................. 2 1.2 Renewed interest in two-bladed wind turbines ............... 4 1.3 Control of wind turbines .......................... 11 1.4 Structured control for wind turbines .................... 15 1.5 Thesis goal and outline ........................... 16 2 Linear individual pitch control design for two-bladed wind turbines 19 2.1 Introduction ................................ 20 2.2 Conventional Individual Pitch Control ................... 22 2.2.1 Multi-Blade Coordinate transformation ............... 23 2.2.2 Individual Pitch Control ....................... 24 2.2.3 MBC for three-bladed rotors ..................... 25 2.2.4 MBC for two-bladed rotors...................... 26 2.3 Linear Individual Pitch Control ....................... 29 2.4 Controller design for IPC .......................... 31 2.4.1 Simulation environment and two-bladed wind turbine ....... 32 2.4.2 Baseline controller .......................... 33 2.4.3 Obtaining a model for IPC design .................. 33 2.4.4 Structured H∞ control design for Linear IPC............. 35 2.4.5 Conventional IPC design....................... 40 2.5 Results ................................... 43 2.6 Conclusions................................. 46 3 Field testing of linear individual pitch control on the NREL CART2 51 3.1 Introduction ................................ 51 3.2 NREL CART2 wind turbine and control system ............... 54 3.3 IPC methods ................................ 55 3.3.1 Conventional IPC .......................... 55 3.3.2 Linear IPC .............................. 56 3.4 Control design ............................... 57 3.4.1 System identification ........................ 58 3.4.2 Conventional IPC design....................... 59 3.4.3 Linear IPC design .......................... 59 3.4.4 Gain-scheduling Linear IPC ..................... 60 3.5 Results ................................... 62 3.5.1 Below-rated Linear IPC ....................... 62 3.5.2 Single dataset results......................... 63 3.5.3 Binned datasets results........................ 67 vii viii CONTENTS 3.6 Conclusions................................. 69 4 Control design for two-bladed downwind free-yaw wind turbines 73 4.1 Introduction ................................ 73 4.2 Wind turbine description .......................... 77 4.3 Control system description ......................... 79 4.4 Yaw control design ............................. 81 4.4.1 Obtaining a yaw model ....................... 82 4.4.2 Yaw control strategies ........................ 84 4.4.3 Yaw controller tuning ........................ 87 4.4.4 Yaw-damping-by-IPC ........................ 88 4.5 Results