Vibration-based structural health monitoring of wind turbines

      VIBRATION-BASED STRUCTURAL HEALTH MONITORING OF WIND TURBINES Gustavo Miguel Cameira da Silva Oliveira A dissertation presented to the Faculty of Engineering of the University of Porto for the degree of Doctor of Civil Engineering Supervisors: Álvaro Cunha (Full professor); Filipe Magalhães (Assistant professor); Elsa Caetano (Associate professor) April 2016 Vibration-Based Structural Health Monitoring of Wind Turbines 9 To my parents Vibration-Based Structural Health Monitoring of Wind Turbines 4 Vibration-Based Structural Health Monitoring of Wind Turbines 9 ABSTRACT Wind power is one of the most attractive and reliable options for renewable and clean energy. In the last years, the installed capacity for exploitation of wind energy has consistently increased worldwide. Alongside, the technological evolutions of this sector have been based on the development of multiMW systems with increasingly larger structures elements, such as support structures and rotor blades. These wind turbines present considerable advantages considering the power production; however, they also represent several structural challenges: these wind turbines have become increasingly flexible structures, prone to resonance phenomena and to rapid wear. In that sense, the structural integrity and proper operation of large wind turbines is a concern for owners and operators, specially in turbines installed offshore. Monitoring systems capable of evaluating the condition of structural elements such as foundation, tower and blades, are seen as a suitable response to address this problem. Among the several techniques available, vibration-based systems reveal a great potential for structural monitoring. Therefore, this thesis is focused on the development and implementation of a vibration-based dynamic monitoring system for wind turbines. This system is based on Operational Modal Analysis tools, capable of accurately estimate the modal properties of wind turbine structures from their dynamic response. The efficiency of these tools in the modal identification of wind turbines was validated with the analysis of vibrational data collected during a short period from onshore (Izar Bonus 1.3MW/62) and offshore (Vestas V90-3.0MW) models. Afterwards, a vibration-based monitoring system was implemented on a 2.0 MW Senvion MM82 wind turbine allowing the collection of data during more than one year. Throughout this program, the system was defined with two main purposes: detection of structural anomalies (based on the continuous estimation and statistical analysis of the variations of the modal properties) and fatigue assessment (based on a reduced number of installed sensors). The program was complemented with the analysis of alternative solutions for optimization of the number of installed sensors. The usefulness of the system was tested with different damage scenarios. It was concluded that the monitoring system is capable of detecting small damages in the support structure of both onshore and offshore wind turbines. The tools developed for fatigue evaluation using the estimated modal responses showed promising results but a complete validation of their accuracy need further research. Vibration-Based Structural Health Monitoring of Wind Turbines Vibration-Based Structural Health Monitoring of Wind Turbines 9 RESUMO Energia eólica é uma das mais atrativas e fiáveis opções para energia renovável e limpa. Nos últimos anos, a capacidade instalada para aproveitamento do recurso eólico tem crescido de forma consistente em todo o mundo. Ao mesmo tempo, a evolução tecnológica do sector tem sido baseada no desenvolvimento de sistemas com múltiplos MW, recorrendo a elementos estruturais de dimensões cada vez maiores, tais como estruturas de suporte e pás. Estas torres eólicas apresentam vantagens consideráveis do ponto de vista da produção; no entanto, representam também diversos desafios estruturais: estes aerogeradores tornaram-se estruturas cada vez mais flexíveis, propensos a fenómenos de ressonância e a um desgaste rápido. Nesse sentido, a integridade estrutural e a correta operação de modernas torres eólicas é uma preocupação para donos e operadores, especialmente em turbinas instaladas em offshore. Sistemas de monitorização capazes de avaliar a condição de elementos estruturais, tais como fundação, torre e pás, são vistos como uma resposta adequada para lidar com este problema. De entre as várias técnicas disponíveis, sistemas baseados na análise de vibrações revelam um grande potencial para monitorização estrutural. Assim, esta tese foca-se no desenvolvimento e implementação de um sistema de monitorização dinâmico baseado na análise de vibrações para torres eólicas. Este sistema é baseado em ferramentas de Análise Modal Operacional, capazes de estimar com precisão as propriedades modais das estruturas de aerogeradores a partir da sua resposta dinâmica. A eficácia destas ferramentas na identificação modal de torres eólicas foi validada com a análise de dados de vibração colhidos durante um curto período de tempo para uma torre instalada em terra (Izar Bonus 1.3MW/62) e uma outra em offshore (Vestas V90-3.0MW). Posteriormente, um sistema de monitorização foi implementado numa torre eólica Senvion MM82, permitindo a recolha de dados duranta mais de um ano. Ao longo deste programa, o sistema foi definido com dois objetivos principais: deteção de anomalias estruturais (baseado na estimativa contínua e análise estatística das variações das propriedades modais) e avaliação da condição de fadiga (com base num reduzido número de sensores instalados). O programa foi complementado com a análise de soluções alternativas para otimização do número de sensores instalados. A utilidade do sistema foi testada com diferentes cenários de dano. Foi concluído que o sistema de monitorização é capaz de detetar danos reduzidos na estrutura de suporte de torres instaladas em terra e em offshore. As ferramentas desenvolvidas para avaliação de fadiga, através de estimativas de respostas modais, mostraram resultados promissores, no entanto uma validação completa da sua precisão requere desenvolvimentos adicionais. Vibration-Based Structural Health Monitoring of Wind Turbines Vibration-Based Structural Health Monitoring of Wind Turbines 19 ACKNOWLEDGEMENTS This thesis would not be possible without the help and support of several people. Here I present my sincere gratitude: o to Prof. Álvaro Cunha, my advisor, for challenging me with such an interesting topic, for all the support given during this period and for his care to ensure all the conditions and means for the proper development of this thesis; o to Prof. Filipe Magalhães, my co-advisor, for all the support, for the endless hours he received me in his office and for the patience and sympathy to clarify unscheduled problems; o to Prof. Elsa Caetano, my co-advisor, for her support whenever needed and for the opportunity to cooperate on interesting projects; o to Eng. José Carlos Matos, Eng. Miguel Marques and Eng. Silvina Guimarães from INEGI, for the opportunity to work within the Rotor Blade Extension project; o to Prof. Christof Devriendt and Doctor Wout Weijtjens from OWI-Lab, for the interesting conversations about modal identification and for the opportunity to use the data of the Vestas V90-3.0MW wind turbine; o to Eng. José Saraiva from Senvion and to Eng. Carlos Cardoso and Eng. Frederick Saborano from Cavalum, for all the support given within the study of the Senvion MM82 wind turbine; o to Prof. Álvaro Rodrigues and Prof. Fernando Marques da Silva, for the interesting suggestions and conversations that helped improve this thesis; o to my work colleagues and friends Nuno, Joana(s), Celeste, Berawi, Sandro, Fernando, Aires, Ana, André, Ricardo and Sérgio, for the fun that was working in our H304; o to my parents and brother, to whom I owe who I am; o to Paulina, for putting up with my bad mood and, even thus, always cheer me up; o to Fundação para Ciência e Tecnologia, for the financial support through the PhD fellowship SFRH/BD/79328/2011. Vibration-Based Structural Health Monitoring of Wind Turbines 22 3.1.1.3 Tower ..................................................................................................................................... 62 3.1.1.4 Transition Piece .................................................................................................................... 64 3.1.1.5 Foundation ............................................................................................................................ 64 3.1.1.6 Monitoring and Control System ........................................................................................ 72 3.1.2 Costs Breakthrough ...................................................................................................................... 72 3.1.3 Wind Turbine Components Reliability ..................................................................................... 76 3.2 Wind Turbine Performance ............................................................................................................. 80 3.2.1 Rotor Power Characteristics (Physics) ....................................................................................... 80 3.2.2 Axial Momentum Theory (The Actuator Disc) ........................................................................ 80 3.2.3 Angular Momentum Theory ....................................................................................................... 85 3.2.4 Blade Element Theory .................................................................................................................. 88 3.2.5 Blade Element Momentum .......................................................................................................... 90 3.2.6 Control Strategies of Wind Turbines ......................................................................................... 92 3.2.6.1 Stall Control .......................................................................................................................... 92 3.2.6.2 Pitch Control ......................................................................................................................... 93 3.2.6.3 Rotor Speed Control ............................................................................................................ 94 3.3 Final Considerations ......................................................................................................................... 96 4. STRUCTURAL BEHAVIOUR OF WIND TURBINES .................................................................. 97 4.1 Structural Dynamics ......................................................................................................................... 97 4.1.1 Dynamic Characterization of the Tower ................................................................................... 98 4.1.2 Dynamic Characterization of the Rotor ..................................................................................... 99 4.2 Foundation Soil Stiffness ................................................................................................................105 4.3 Tower-Rotor Dynamic Coupling ..................................................................................................110 4.4 Definition of Tower Stiffness .........................................................................................................111 4.5 Damping ...........................................................................................................................................113 4.5.1 Structural Damping ....................................................................................................................114 4.5.2 Aerodynamic Damping ..............................................................................................................114 4.5.3 Tower Dampers ...........................................................................................................................116 4.5.4 Soil Damping ...............................................................................................................................116 4.5.5 Hydrodynamic Damping ...........................................................................................................117 4.6 Cyclic Vibration Loads ...................................................................................................................118 4.7 Numerical Model of a Wind Turbine ...........................................................................................121 4.8 Final Considerations .......................................................................................................................125 Vibration-Based Structural Health Monitoring of Wind Turbines 23 5. OPERATIONAL MODAL ANALYSIS OF WIND TURBINE S ....................................................127 5.1 Introduction to Operational Modal Analysis .............................................................................. 127 5.2 Application of OMA to Wind Turbines ...................................................................................... 129 5.3 Particularities of OMA Application to Wind Turbines ............................................................. 133 5.4 Output-only Stochastic Identification Methods ......................................................................... 136 5.4.1 Algorithms Based on Identification of State-Space Models ................................................. 136 5.4.1.1 State-Space model .............................................................................................................. 136 5.4.1.2 SSI-COV algorithm ........................................................................................................... 137 5.4.1.3 Kalman filter ....................................................................................................................... 143 5.4.1.4 SSI-DATA algorithm ......................................................................................................... 143 5.4.2 p-LSCF ......................................................................................................................................... 148 5.4.2.1 Half-Spectrum .................................................................................................................... 148 5.4.2.2 Right Matrix-Fraction Description .................................................................................. 149 5.4.2.3 p-LSCF algorithm .............................................................................................................. 151 5.5 Modal Response Estimation .......................................................................................................... 157 5.5.1 Forward Innovation Model ....................................................................................................... 157 5.5.2 Application to the Stochastic Identification Algorithms ...................................................... 158 5.5.2.1 Application to the SSI-DATA algorithm ........................................................................ 158 5.5.2.2 Application to the SSI-COV algorithm ........................................................................... 160 5.5.2.3 Application to the p-LSCF algorithm .............................................................................. 160 5.5.3 Quantification of the Modal Contributions ............................................................................ 164 5.6 Auxiliary Tools to Overcome OMA Violations .......................................................................... 167 5.6.1 Coordinate Transformation - Nacelle Rotation ..................................................................... 167 5.6.2 Coordinate Transformation - Rotor Rotation ........................................................................ 168 5.6.3 Periodic Nature of the Excitation Forces ................................................................................. 170 5.6.3.1 Kurtosis-based Methods ................................................................................................... 171 5.6.3.2 Cepstral Method ................................................................................................................. 172 5.6.3.3 Time Synchronous Averaging .......................................................................................... 173 5.7 Automated Operational Modal Analysis ..................................................................................... 175 5.7.1 Implemented Hierarchical Cluster Analysis ........................................................................... 176 5.8 Case Study – Izar Bonus 1.3MW/62 ............................................................................................. 179 5.8.1 Introduction ................................................................................................................................ 179 5.8.2 Description of the Wind Turbine ............................................................................................. 179 5.8.3 Measurement System ................................................................................................................. 181 Vibration-Based Structural Health Monitoring of Wind Turbines 24 5.8.3.1 Measurement System Based on Fibre Bragg Grating Sensors ......................................181 5.8.3.2 Measurement System Based on Accelerometers ............................................................181 5.8.4 Analysis before the installation of the RBE .............................................................................184 5.8.4.1 Analysis of fibre Bragg grating sensors measurements .................................................184 5.8.4.2 Analysis of accelerometers measurements ......................................................................189 5.8.5 Analysis after the installation of the RBE ................................................................................198 5.8.5.1 Analysis of the fibre Bragg grating sensors measurements ..........................................198 5.8.6 Conclusions .................................................................................................................................201 5.9 Case Study – Vestas V90-3.0MW ..................................................................................................202 5.9.1 Introduction .................................................................................................................................202 5.9.2 Wind Turbine Description ........................................................................................................202 5.9.3 Monitoring System Description ................................................................................................204 5.9.4 Acceleration Data Sets ................................................................................................................204 5.9.5 Modal Results ..............................................................................................................................208 5.9.6 Conclusions .................................................................................................................................216 6. FATIGUE ASSESSMENT OF WIND TURBINES ........................................................................ 217 6.1 Introduction to Fatigue Problems in Wind Turbines ................................................................217 6.2 Fatigue Design Loads ......................................................................................................................218 6.3 Application to Wind Turbine Support Structures ......................................................................222 6.3.1 Main Structural Details ..............................................................................................................222 6.3.2 Fatigue Analysis According to Standards/ Guidelines ...........................................................223 6.4 Fatigue Assessment Using Accelerometers ..................................................................................225 6.4.1 Proposed Procedure for Fatigue Assessment ..........................................................................228 6.4.1.1 Estimation of the Quasi-Static and Dynamic Stresses Contributions to Fatigue ......233 6.4.2 Virtual Sensors ............................................................................................................................240 6.5 Final Considerations .......................................................................................................................243 7. STRUCTURAL MONITORING OF WIND TURBINES ............................................................. 245 7.1 Introduction to Structural Monitoring of Wind Turbines ........................................................245 7.1.1 Condition Monitoring of Wind Turbines ...............................................................................248 7.1.2 SHM of Wind Turbines .............................................................................................................249 7.2 Vibration-Based SHM System .......................................................................................................252 7.2.1 Damage Detection ......................................................................................................................252 7.2.1.1 Removing of Environmental and Operational Effects on Natural Frequencies ........252 Vibration-Based Structural Health Monitoring of Wind Turbines 25 7.2.1.2 Damage detection .............................................................................................................. 257 7.2.2 Fatigue Monitoring ..................................................................................................................... 259 7.2.2.1 Estimation of the Remaining Lifetime ............................................................................ 261 7.2.3 Overview of the Dynamic Monitoring System Main Steps ................................................... 262 7.3 Case Study – Senvion MM82 ......................................................................................................... 265 7.3.1 Introduction ................................................................................................................................ 265 7.3.2 Wind Turbine Description and Numerical Models ............................................................... 265 7.3.3 Operating Conditions ................................................................................................................ 270 7.3.4 Monitoring System Description ............................................................................................... 273 7.3.5 Preliminary Results ..................................................................................................................... 275 7.3.6 Continuous Characterization of the Dynamic Properties ..................................................... 281 7.3.6.1 Dynamic Characterization of the Wind turbine ............................................................ 281 7.3.6.2 Automated Identification of the Modal Parameters ..................................................... 288 7.3.6.3 Damping Estimation from Free Decay Responses ........................................................ 298 7.3.6.4 Participation of the Vibration Modes/ Harmonics to the Measured Dynamic Response .............................................................................................................................................. 303 7.3.6.5 Removal of Operational and Environmental Effects .................................................... 307 7.3.6.6 Damage Detection ............................................................................................................. 316 7.3.7 Fatigue Assessment Results ....................................................................................................... 322 7.3.8 Optimization of the Monitoring System ................................................................................. 332 7.3.8.1 Layout 1 (+74.988 m level) ............................................................................................... 333 7.3.8.2 Layout 2 (+48.392 m level) ............................................................................................... 340 7.3.8.3 Layout 3 (+74.988 m and +48.392 m levels) ................................................................... 345 7.3.9 Conclusions ................................................................................................................................. 350 8. CONCLUSIONS AND FUTURE RESEARCH ..............................................................................353 8.1 Conclusions ...................................................................................................................................... 353 8.2 Future Research ............................................................................................................................... 356 Appendix A - MODEL RESPONSE ESTIMATION - VALIDATION ..............................................357 A.1. Introduction ..................................................................................................................................... 357 A.2. Numerical Simulation .................................................................................................................... 358 Appendix B - IZAR BONUS 1.3MW/62 WIND TURBINE – MODE SHAPES ...............................363 B.1. Introduction ..................................................................................................................................... 363 B.2. Analysis of Accelerometers Measurements ................................................................................. 363 Vibration-Based Structural Health Monitoring of Wind Turbines 26 B.3. Analysis of Fibre Bragg Grating Sensors Measurements (After RBE) .....................................368 REFERENC ES ..................................................................................................................................... 371 Chapter 1 21 1 INTRODUCTION 1.1 RESEARCH CONTEXT The electricity sector has undergone profound changes in the last years. The awareness for the environmental conservation, in particular to the greenhouse effect, alongside with the desire of higher energy independence by importing countries on fossil fuels, has led to the investment in the exploitation of renewable energy sources. In fact, renewable sources are in the focus of current energy policies. Almost all major world economies have developed studies and programs to introduce more clean energy into their energy mix. In particular, The European Union has been implementing a program with challenging objectives for 2020, known as “20-20-20” targets (Commission of the European Communities, 2008). Among them, it was defined a 20 % share of renewable energies in overall European Union energy consumption by 2020 (European Commission, 2013), including a target of 34 % of the electricity demand supplied by renewable sources (European Commission, 2015c). Subsequent programs for 2030 (European Commission, 2015a) and 2050 (European Commission, 2015b) are already under development. In Portugal, until a few decades ago, the hydroelectric production represented almost the whole renewable contribution to the energy mix. From the 1990s, wind energy began to arouse some interest and the initial wind farms were installed. In the next decade, large investments in the implementation of wind turbines were made, which increased the importance of this source in the national electricity mix. Successively, wind power has gained importance in the national panorama, recently achieving power production numbers close (or even higher) to the hydropower generation. Currently, Portugal has been presenting very good results in the introduction of energy from renewable sources in its electrical system. The results obtained in 2015 are very good indicators: 50 % of the electrical energy demand was supplied from renewable sources, with wind power accounting for 22 % (Portuguese Renewable Energy Association (APREN), 2015). This value confirms the importance of this source in the national electric system. Apart from these aspects, two additional perspectives may promote (once again) the installation of new wind turbines in Portugal (Government of Portugal, 2015). The first one is related to the future prospects from the national government of achieving a share of 40 % of the gross final consumption of energy from renewable sources by 2030, including a strong participation of wind power for electric power demand. The second perspective is related to the future possibility of establishment of European electric power interconnections. This possibility is related to the export of energy produced by renewable sources to countries with difficulties to meet the targets agreed with the European Introduction 22 Commission. This interconnection, which could achieve 15 % of the total installed capacity by 2030, would lead to a considerable boost of implementation of new wind power plants. Alongside, an important portion of the installed wind power capacity in Portugal is achieving its design lifetime, with repowering operations being expected in the next years. Given this policy background, it is consensually accepted that wind power is a key element in the present and future electric energy strategy. New wind turbines are expected to be installed in the next few years with power outputs considerably higher than the nowadays common values, mainly due to cost aspects. In addition, offshore locations are becoming very attractive to install turbines due to their higher production yields. Three significant difficulties will be faced by this new wind turbine models: o The increase of the wind turbines dimension, particularly the increase of the height of tower and blades length, will turn the wind turbine into more flexible structural systems. Consequently, the study of the dynamic characteristics of the structure will be of major importance in order to avoid resonance problems and rapid wear of the components; o The installation of wind turbines in offshore locations is still shrouded in some uncertainty concerning the real wear suffered by the structures. On the other hand, the costs associated with offshore wind turbines are still high, which demand for optimization in their design; o Apart from reducing the cost of installation of the wind power plants (CAPEX), the reduction of the costs over the period of its operation (OPEX) also represents an important vector for competitiveness. A crucial aspect to lower this cost is the optimization of the maintenance strategy. Considering the high power outputs of new models, the downtime of a single wind turbine may represent a significant income loss. In that sense, several monitoring system are being developed to remotely assess the condition of several components of the wind turbine, allowing to optimize the maintenance interventions according to expected loss of production during downtime, availability of replacing components and meteorological conditions (in the case of offshore wind farms or onshore wind farms in mountains). These facts address the new challenges that, from a structural point of view, will concern the owners of wind farms. In that sense, a real-time monitoring system capable of assessing the structural integrity of the support structure of wind turbines (including tower and foundation) can be a very useful tool to aid decision-making. With a monitoring system, the wind farm owner can analyse the structural health of the wind turbines in remote locations and adapt the maintenance strategy according to the received data. In short, in possession of this information, the owner could maximize the investment. In order to be effective, a monitoring system installed at a wind turbine support structure should be able to answer two important questions: o Is the structure damaged? o How is the fatigue condition of the structure? Is the structure able to fulfil its period of life? Or should the structure be disassembled before (or after) this period? To meet these two aspects, different modules need to be integrated into one vibration-based structural health monitoring (SHM) system: a structural anomalies detection monitoring system and a fatigue monitoring system. The structural anomalies detection monitoring system is a tool with the aim of detecting damage. It can be based on the continuous tracking of the modal properties of the structure. For this purpose, Chapter 1 23 tools already tested on civil engineering structures can be used in wind turbines in order to extract the monitored features. These tools, from a branch of the experimental modal analysis field named as Operational Modal Analysis (OMA), permit to identify the modal characteristics of structures during the various operating conditions of the turbines. Thus, considering that damage is usually associated with stiffness reductions, the natural frequencies of the various vibration modes can be used as damage indicators. The study of the evolution and variation of these indicators indirectly evidence the existence of damage in the structure. The second module comprises the fatigue analysis of the structure. Fatigue assessment is a key point in wind turbines, since these structures are mainly subjected to dynamic loads. Thereby, this module permits to assess the evolution of the wear of the wind turbine support structure over time. This information can then be compared with the estimated lifetime of the structure in order to validate the suitability of this period. Introduction 24 1.2 OBJECTIVES AND MAIN CONTRIBUTIONS The main goal of this thesis consists on the development of a complete vibration-based monitoring system capable of delivering useful results to assess the integrity of the wind turbine support structure. To achieve this goal, this thesis addresses the following objectives: o Implementation of output-only modal identification algorithms in the context of wind turbines and development of strategies for continuous identification of the modal properties of these structures; o Development of a monitoring system to identify structural changes in the support structure of wind turbines based on the identified modal properties; o Development of a methodology to estimate the fatigue damage at the support structure of wind turbines based on a small number of sensors; o Integration of the two components (damage identification and estimation of the fatigue wear) of the vibration-based dynamic monitoring system in a single software package, demonstrating with full-scale applications the usefulness of the system in the management of wind farms. It is expected that the outcomes presented in this thesis may represent a step forward in the development of global systems to monitor the most important components of wind turbines. In that sense, the main contributions of this thesis are the following: o Synthesis of the major technical progresses of wind turbines and current state of evolution (Chapter 2); o Description of the main components of a wind turbine, with a main focus on the different types of support structure, including costs breakthrough and reliability (Chapter 3); o Description of the main characteristics related to the dynamic behaviour of wind turbine structures (Chapter 4); o Analysis of the implications of the application of output-only modal identification algorithms to vibration signals from wind turbines (sections 5.3 and 5.7); o Adaptation of the post-processing tool originally developed to the SSI-DATA algorithm to decompose the vibration signals into modal responses to be used together with the SSI-COV and p-LSCF algorithms (section 5.5.2); o Application of the developed algorithms to data sets recorded on the blades and tower of a Izar Bonus 1.3MW/62 wind turbine using two different measurement systems: based on fibre Bragg grating sensors and accelerometers (section 5.8); o Application of the developed algorithms to data sets collected during a short period on the support structure of an offshore Vestas V90-3.0MW wind turbine; o Development of a strategy to estimate the fatigue state along the support structure of a wind turbine based on a reduced number of sensors (section 6.4.1); o Creation of a vibration-based dynamic monitoring system, specially designed to meet the requirements of a wind turbine, able to perform, in a first module, the online automatic Chapter 1 25 identification of the modal parameters under all operating conditions, to remove the influence of operational and environmental effects and to compute indices permitting to detect the presence of small structural anomalies; and, in the second module, estimate the fatigue conditions along the support structure of a wind turbine (section 7.2); o Conception, assembly and operation of a monitoring system on a Senvion MM82 wind turbine for a period of one year, where the developed routines were tested, demonstrating the ability of the system to detect the occurrence of small damages (section 7.3); o Optimization analysis concerning the ability (and loss of accuracy) of the dynamic monitoring system to operate with a reduced number of installed sensors (section 7.3.8). From Windmills 32 Figure 2.8 During the Germany. T fuel power created wit h RAW prog r ambition o f remarkable This rotor w from the d i yawing wit h However, t h some of the Apart from energy, alt h from 1948 program, t h design, alth o Also in Fra n time. The 3 Vadot turb i During the Hutter, wh o 2006), con d diameter W power outp to the Modern W a – Smith wind t 1930s and 1 T his develop m (Hau, 2006 h renowned s r am, the pr o f building la characteris t w ould have a i rect drive t y h the rotor. T h e war prev e e se character i m Denmark a h ough in a s m to the earl y h e EnfieldA ough associ a n ce, there w a 0.1 m rotor i ne are exam post-war pe r o had alread y d ucted some W -34 wind tu r ut of 100 k W W ind Turbines a ) urbines (Hau, 2 940s, much m ent was u n ). For this p s cientists, te c o ject led by rge machin e t ics like a 13 a power out p y pe. The de s T he concept e nted its con s i stics are stil l a nd USA, ot h m all scale. I n y 1960s (Sp e A ndreau win d a ted with lo w a s some int e diameter, 8 0 ples of proj e r iod in Ger m y been disti n experiment a r bine with a n W at a wind s 2 006): a) 50 k W theoretical a n dertaken b y p urpose, th e c hnicians a n the enginee r e s to reduce 0 m rotor d p ut of 10 M W igned tower was impro v s truction (H l not widely i h er regions a n the Unite d e ra, 1994). A d turbine pr o w efficiency ( H rest in the d 0 0 kW BestR cts from thi s m any, Ulrich n guished on a l tests duri n n AC synch r p eed of 8 m / W model with s t tower a nd design a c y the Germa n e “Reichsarb n d industrial s r Franz Kle i the cost of e d iameter wit h W at a tip sp e r was a guye d v ed from 19 3 au, 2006). It i mplemente d a lso showed d Kingdom, t A mong som oject stands Hau, 2006)) . d evelopment R omani tur b s time (Hau, Hutter was previous pa n g the 1950s r onous gene r / s (Figure 2. 9 eel lattice tow e c tivity in th e n Reich with eitsgemeins c s . Among th e i nhenz, in 1 9 e nergy prod u h a three or ed of 5 and t d tubular st e 3 8 to 1942 a n is interestin d in comme r some inter e t here was a w e different d out from t h . of experim e b ine and the 2006). the main na pers on the t . His studies r ator (Gasch 9 ) (Johnson, b) e r; b) 70 kW m o wind energ y the aim of a c haft Wind k e projects de v 9 37, stands o u ction. This four-bladed t he generato r e el tower, w i n d was read y g to note th a r cial wind tu r e st in the ex p w ind energy d esigns dev e h e others du e ntal wind t u 35 m rotor d m e in the fi e t heory of wi n culminated and Twele, 2 2001). This t o del with conc y field was h a self-sufficie n k raft” (RA W e veloped un d out, reflecti n wind turbi n d downwind r would hav e i th the upp e y for constr u a t, even now r bines p loitation o f program r u e loped duri n e to its inn o u rbines duri n d iameter, 1. 0 e ld of wind p i nd turbines in the 34 m 2012) with a t urbine, ere c rete h eld in n cy in W ) was d er the n g the n e had rotor. e been e r part u ction. a days, f wind u nning n g the o vative n g this 0 MW p ower. (Hau, m rotor a rated c ted in 1957 , supp o cons t (Ha u 3.6). T like t aero d 2006 ) spee d desi g aero d One o (Fig u betw e syste m with (Ma n (Lun d Alth o such caus e avoi d turbi n failu r less c char a Bran d , had a tw o o rted by g u t ruction. Fo r u , 2006) and T he solutio n t he one use d d ynamically ) . The pitch m d of rotation g n philosop h d ynamics. Figure 2.9 – o f most inn o u re 2.10), de s e en 1958 a n m (Johnson , an inductio n n well, McG o d sager, Fra n o ugh these c h as the pow e e d flow sepa r d ing the ne e n e was equ i r e (Gasch an c omplex, fr o a cteristics a n d strup et al . o -bladed, do w u y wires (J o r this reaso n they were a n found for t h d in the S m damped by m m echanism o of the roto r h y, relying o n W-34 wind tu r o vative and r s igned by Jo h n d 1967 (Lu n , 2001). The n generator ( o wan et al., 2 n dsen et al., h aracteristic e r control t h r ation unde r e d for pitch i pped with t d Twele, 20 1 o m a mech a n d innovatio n . , 2004). Th w nwind rot o o hnson, 20 0 n , the blade s a erodynamic h is connecti o m ith-Putnam m echanicall y o f the blades r (Vargo, 19 7 n the reduc t bine (Hau, 200 r eliable win d h annes Jull a n dsager, Fr a Gedser win ( rather than 2 010) achie v 1980). Th e s were not s o h rough aero d r strong win d control, lik urnable bla d 1 2). Compar a nical point n s led to a p e e Gedser w i or with a s i 0 1). One o f s were mad e c ally refined, o n was anot h wind turbi n y coupling t h s changed th e 7 4). This wi n t ion of the s 0 6) d turbines b u a nd located i a ndsen et al . n d turbine h a the more c o v ing a powe r e tower had o impressiv e d ynamic st a d conditions , k e the Smid t d e tips whi c r ed to the S m of vie w ( V eriod of ope i nd turbine i mple hollo w f Hutter’s m e of an adv a being conn h er innovati o n e, the teet e h e teetering e ir angles at h n d turbine is s tructure w e Figure 2. 1 u ilt during t h i n Denmark . , 1980), co n a d a 24 m d o nventional, a r output of a height o f e , this wind t a ll: its blade s , acting as a t h wind tur b h were acti v m ith-Putna m V estergaard, ration with o was decom m w pipe tow e m ain priorit i a nced glassf ected to a t e o n: instead o e ring move m angle to the h igher wind considered e ight and o n 1 0 – Gedser wi n h is time was t . This wind t n nected to t h i ameter, thr e a t that time, 200 kW at a f 24 m and urbine had s s had an ae r c ompletely p b ine. For ae v ated by ce n wind turbi n Brandstrup o ut major m a m issioned i n e r with 22 m i es was the f ibre compo s e etering hu b o f a more co m m ents of th e blade-pitch speed to ke e as an exam p n the optimi n d turbine (Ha u the Gedser w t urbine was h e Danish p e e-bladed, u synchrono u a wind spe e was made s ome major r odynamic d p assive pow e e rodynamic b n trifugal for c n e, the Geds e et al., 200 4 a intenance ( V n 1967 and Chapter 2 3 3 m of heigh t lightweigh t s ite materia l b (see Figur e m plex desig n e rotor wer e angle (Hau , e p a constan t p le of a thir d zation of it s u , 2006) w ind turbin e in operatio n p ublic powe r u pwind roto r u s generator ) e d of 15 m/ s of concrete . innovations , d esign whic h e r limitation , b raking, th e c es at a gri d e r was muc h 4 ). All thes e V estergaard , it was late r 3 t t l e n e , t d s e n r r ) s . , h , e d h e , r From Windmills to the Modern Wind Turbines 34 refurbished in the mid-1970s at the request of NASA for measurements, in the framework of an American program (Hau, 2006). Although Hutter and Juuls’ projects were considered a success, the wind turbine projects in general were not yet reliable, with numerous problems and faults to be dealt with (Hau, 2006). Besides these reasons, the extremely low prices of primary fuels after the World War II, along with the increased investments in nuclear energy, demonstrated that the wind generated electricity was too expensive to compete with other sources (Gasch and Twele, 2012). Due to this, the wind energy industry suffered another breakdown during the 1960s. 2.1.1.3 The Modern Wind Turbine Concept In the late 1960s - beginning of 1970s, the awareness of dependency on the oil exporting countries started to take place. The oil crisis in 1973 and 1979 confirmed this misgiving, having led to supply problems and an increase in the oil prices in the western economies. With the aim of reducing this situation, national programs for the development of renewable energy sources were created. In the USA, the Federal Wind Energy Program began in 1972 (Ramler and Donovan, 1979). The National Aeronautics and Space Administrator (NASA) was selected to manage the technology development and initial deployment of large wind turbines in the Lewis Research Center. This project represents one of the most extensive development program in the wind energy field, in which several variations of structural configurations and mechanisms were tested. The first wind turbine developed and built by this program was the NASA/DOE Mod-0 in 1975. This wind turbine was a two-bladed, 38 m rotor diameter with a power output of 100 kW at a wind speed of 8 m/s (Ramler and Donovan, 1979). This turbine had a 30 m high tower. The Mod-0 wind turbine was extensively tested with a large number of modifications along its operation life: with a teeter and rigid hub, different blade materials, with pitch and stall control, with stiff and more flexible supporting towers, different kinds of generators, among others (Spera, 1994) (Figure 2.11). The turbine operated, in most of the time, as a downwind rotor, although the upwind solution had also been tested, as well as a one-bladed rotor solution (Corrigan and Ernsworth, 1986). One of the most noticeable characteristic of this wind turbine was the influence of the tower in the blade vibration when the rotor was downwind, one important dynamic characteristic of this type of turbines. The Mod-0 was dismantled in 1987 (Spera, 1994). The s this m (Spe r (200 betw e wind be s u (Spe r The M (the l This m steel meg a face d to it s Don o mou n peri o avoi d tech n and t disas s s econd deve l m odel was t r a, 1994). T h kW) (Ram l e en 1977 an d conditions. u ccessfully i n r a, 1994). Th M OD-1 proj l argest ever b model had a truss desig n a watt sized w d some prob l s heavy, co m o van, 1979). n ted blades, o d of life (S p d these probl n ical and ec o t elevision in t s emble of th e l opment of t t o study, id e h is model w a l er and Do n d 1980. Eac h From this p r n tegrated in t e MOD-0A p ect entered i b uilt (Spera, a rated powe r n and was 4 w ind turbine l ems. It was t m plex and l a The effect becoming c l p era, 1994). ems but, du e o nomic pro b t erference ( C e wind turbi n Figure 2.11 t he NASA/ D e ntify and s o a s basically a n ovan, 1979 h location r e r oject, it was t o the norm a p roject ende d n service in 1 1994)) with r of 2.0 MW 4 2.7 m hig h in the worl d t oo heavy a n a rge full sp a of the towe r l ear that thi s A new mo d e to funding b lems, there C ollins, Shalt n e (Johnson , 1 – MOD-0 win d D OE progra m o lve technic a a version of 9 ). Four pr o e presented a proven tha t a l operation d in 1982 (S p 1979. The w i two steel bl at a wind sp h . This win d d (Collins, S h n d, consequ e a n pitch co n r on the bl a s design phil d el, MOD-1 A issues, it wa were also s o t ens et al., 1 9 , 2001). d turbine varia t m was the M o a l and oper a the Mod-0 w o totypes we r different sc e , while not y s of a utilit y p era, 1994). i nd turbine h ades (Raml e eed of 14.6 m d turbine w h altens et al. , e ntly, too ex p n trolled blad a des created osophy wo u A , was desi g s not built ( C o me compla i 9 82). The M O t ions o d-0A wind a tional utilit y w ith a large r e built for e nario both et cost-effec t y , producing h ad a 61 m d i r and Dono v m /s (Johnso n w as consider e 1982). Ho w p ensive, mai n e s and to i t high impul s l d not be su i g ned with s o C ollins, Shal t nts from lo c O D-1 projec t turbine. Th e y interconn e r gearbox a n four differ e for grid int e t ive, wind t u g high-qualit y d iameter do w v an, 1979) ( F n , 2001). Th e r ed the first w ever, the M O nly due to i t t s bedplate ( sive loads t o itable for a 2 o me solutio n t ens et al., 1 9 c al residents t ended in 1 Chapter 2 3 5 e purpose o f e ction issue s n d generato r nt location s e gration an d u rbines coul d y AC powe r w nwind roto r F igure 2.12) . e tower had a operationa l O D-1 mode l t s stiff tower , ( Ramler an d o the rigidl y 2 0 - 30 year s n s aiming t o 9 82). Beside s about nois e 9 88 with th e 5 f s r s d d r r . a l l , d y s o s e e From Windmills 36 The next it e al., 1983) ( F the previou to as a sec o turbine wa s turbine wa s 2.5 MW at a Three of th e o Th e po w bla d o Th e use d In t bla d o Th e of t h This desig n MOD-1 de s 1979). Three MO D disposition interferenc e were also b economic s t group of la r to the Modern W e ration of th e F igure 2.13). s NASA/D O o nd generat i s a design e v s a two-blad e a wind spee d e major mo d e power co n w er control o d e span; e tower desi g d in previou t his design, t d es. For this e load reduc t h e rotor. n approach p s ign (which D -2 machin e of the th r e s between l a b uilt for util i t udies show e r ge wind tur b W ind Turbines Figure 2 e NASA pro g This projec O E projects ( M i on machin e v olution of t e d, upwind r d of 12.3 m/s d ifications fr o n trol. Instea d o f the wind g n philosop h s projects. It he natural f r reason this d t ion. The ro t p ermitted t o was smalle r e s were built r ee wind t u a rge turbin e i ty compani e e d that the c b ines could o 2 .12 – MOD-1 w g ram started t was desig n M OD-0, M O e (Ramler a n t he propose d r otor with a d and used a s o m the MO D d of the hea v turbine was h y. The desi g consisted i n r equency of t d esign is call e t or was desi g o save weig h r ), the MO D and tested i n u rbines was s in downw i e s. The MO o sts were sti l o perate in a t w ind turbine ( W in 1977 wit h n ed as a seq u O D-0A and M n d Donovan d design fo r d iameter of 9 s ynchronou s D -1 design w v y and com p handled th r g ned tower w n a 61 m hig h t he tower is l e d “soft-soft ” g ned to allo w h t and, cons e D -2 was aro u n a cluster i n defined i n i nd (wake e f D-2 machi n i ll not comp e t otally auto m W ikipedia, 200 9 h the MOD2 u ence of the M OD-1) an d , 1979). Th e r the MOD9 1.4 m. Thi s s generator ( G w ere (Ramler p lex full-sp a r ough the pi w as conside r h steel tower l ower than t h ” (see 3.3.4); w teeter of u p e quently, re d u nd 10 % l i n 1980 in Go n order to f fects) (Sper a n es suffered e titive. How e m atic and un a 9 ) 2 project (G o findings an d d , for that re a e project of 1A model. T s model had G ordon, An d and Donov a n pitch con t t ch of just t h r ably more f with a cylin d h e frequenc y p to 5 o in an d uce costs. C i ghter (Ram l odnoe Hills, study poss i a , 1994). T w some techn i e ver, this pr o a ttended mo o rdon, Andr d developm e ason, it is re the MOD-2 T he MOD-2 a power out d rews et al., a n, 1979): t rol of the b h e outer 30 f lexible than d rical shell d y of rotation n d out of the C omparing t l er and Do n , Washingto n ible aerody n w o other ma c i cal proble m o ject proved o de (Spera, 1 9 ews et e nts of ferred wind wind p ut of 1983). b lades, % the those d esign. of the plane t o the n ovan, n . The n amic c hines m s and that a 9 94). The t proj e stop p once The M roto r The p wind com m turbi n The M turbi n a par t shell inno v to 17 Alon g in wi NAS A Ame r turbi n to o p (Fig u steel the m MW t hird gener a e cts: MOD3 p ed in an ini t again, to de v M OD-5A de r with two b l p ower outp u conditions m ercial succ e n e would re p MOD-5B, d n e followed t t ial span pit c and had a r v ation of th e .3 rpm). Figure 2.13 – M g side with t h nd energy t o A for proje c r ican and o t n es (design a p erate. This m u re 2.15). It h shell tower f m ost powerf u MOD-2. a tion of hori z 3 , MOD-4, M t ial phase) ( S v elop cost c o sign, develo p l ades and th e u t of this m a (Johnson, 2 0 e ss from Ge p resent, for n d eveloped b y t he design c o c h control o f r ated powe r e model was t M OD-2 wind t u h e NASA/D O o operate wi t c t managem t her Swedis h a ted as “syst e m achine wa s h ad two fibe r f ollowed a “ s u l ever mad e z ontal-axis w M OD-5A a n S pera, 1994). o mpetitive, l a p ed by Gene e hub was p l a chine was 7 . 0 01). Howe v n eral Electr i n owadays st a y Boeing fo r o ncept of th e f the blades ( S of 3.2 M W t he ability o f u rbines (Wikip e O E, the Dep a t h its hydroe e nt and tec h h ) was select e m verificati o s a horizont a r glass blades s oft-soft” de s e , with a po w w ind turbin e n d MOD-5 B . The main g a rge wind tu r e ral Electric C laced 76 m a . 2 MW with v er, this ma c i c which wit a te-of-art, o n r NASA/D O e MOD-2 m a Spera, 1995) W and a rot o f its turbine t e dia, 2009) a rtment of t h e lectric turbi n h nical supp o t ed to desig n o ns units” - a l axis wind t mounted o n s ign with 80 w er output o e s from the B (although g oal of the M r bines (Bald w C ompany fo r a bove the g r a rotor rot a c hine was n o h drew from n e of the mo s O E, was buil t a chine: a tw o . The turbin e o r diameter t o operate s u Fi g h e Interior o n es (Spera, 1 o rt and a j o n , fabricate a SVUs). In 1 t urbine with n a teetered h m of height . o f 4.0 MW. NASA/DO E the MODOD-5 progr a w in and Ken r NASA/DO ound (Bald w a tion of 13 o o t built due the project. s t powerful p t in 1987 ( S o -bladed, up w e was suppo r o f 97.5 m ( F u ccessfully a t g ure 2.14 – MO o f the USA ( D 995). For th i o int-venture a nd install t w 982, the W T a 79.2 m di a h ub with full - This wind t T he second E program i n 3 and MO D am, started i n nard, 1985). O E, had a 12 2 w in and Ke n o r 17 rpm, d e to low pers p . Neverthele s p rojects. S pera, 1995 ) w ind, teeter e r ted by a cyl i F igure 2.14) t variable sp e O D-5B (Wikiped D OI) was al s is reason, th of two co m w o megawa t T S-4 wind t u ameter, do w - blade pitch t urbine was, SVU install e Chapter 2 3 7 n cluded fou r D -4 project s i n 1980, was , 2 m diamete r n nard, 1985) . e pending o n p ectives of a s s, this win d . This win d e d rotor wit h i ndrical stee l . The majo r e ed (from 1 3 ia, 2009) s o intereste d e DOI aske d m panies (on e t t scale win d u rbine bega n w nwind roto r control. Th e at that time , e d was a 2. 5 7 r s , r . n a d d h l r 3 d d e d n r e , 5 From Windmills 38 During the the researc h Darrieus d e Éole VAW T was the firs t of 4.0 MW, the rated p o encouragin g concept fiel to the Modern W F 1970s, ther e h efforts w e e sign. Amon g T . The instal l t megawattc operating a t o wer was lo w g and the C a d was also p e Figure 2.1 6 W ind Turbines F igure 2.15 – W e was also s o e re towards g others (s m l ation of thi s c lass Darrie u t variable sp e w ered to 2.5 M a nadian pro g e rformed in a) 6 – Éole VAWT: W TS-4 wind tur b o me relevant the vertica l m all) turbine s s turbine wa s u s turbine, w i e ed (Figure 2 M W. The e x g ram was te the USA in t a) general vie w b ine (Wikipedi a t research in l axis wind s , the Natio n s complete i n w ith a 64 m d i 2 .16). Howe v x perience gai e rminated ( H t he Sandia N w (Wikipedia, 2 a , 2009; Schwe r wind powe r turbines ( V n al Research n 1987 in Q u i ameter and v er, to ensur e n ed and the H au, 2006). S N ational Lab o 2 005); b) illustr a r in, 2010) r outside th e V AWT), sp e Council (N R u ebec, Cana d with an ori g e the longev i results achi e S ome resear c o ratories in A b) a tion (Spera, 1 9 e USA. In C a e cifically wi t R C) develop e d a (Spera, 19 g inal power o i ty of the m a e ved were n o c h in the D a A lbuquerqu e 9 94) a nada, t h the e d the 94). It o utput chine, o t very a rrieus . In E u prog r “that creat i Geds turbi n (Inte r with turbi n a full Prev i Anot Ener g The 2 of th Age n rails o need Magl the s a of 3. 0 towe r u rope, some r ams during t it should b e i ng particul a er wind tur b n es with 40 r national E n steel blade s n es had a di f -span pitch c i ously in 197 Figure 2 t her Nordic c g y Source D e 2 .0 MW, 75 e cylindrica l n cy (IEA), 1 9 on the side o for a large c arp wind tu r a me consort i 0 MW with a r with a heig Governme n this period. e possible to g a r problems b ine was re fu m diamete n ergy Agenc y s pars and b o f ferent pow e c ontrol. The s 5, a 2.0 MW 2 .17 – Nibe A w c ountry wit h e velopment w m diameter l concrete t o 9 84). This t u o f the towe r c rane (Spera, r bine in 198 i um that bui l a 78 m dia m ht of 80 m ( n ts from No r In Denmar k g enerate 10 % in the publ i fu rbished fo r r were buil t y (IEA), 19 8 o th had a c o e r control m e s e wind turb i wind turbi n w ind turbine h important w as founde d WTS-75 Na o wer had it s u rbine had a r , for raising 1994). The s 2 (Internati o l t the WTS4 m eter, two-bl a Internation a r dic and Ce n k , an ambiti o % of the Dan i c power gri r a joint stu d t in Nibe, w 8 4). These w o ncrete tow e e chanism: o n ines operate d n e was built i n developme n d in 1975 an d a sudden win d s first rotati a n unusual fe or lowerin g second larg e o nal Energy 4 for the NA a ded, down w a l Energy Ag n tral Europe a o us progra m ish power re d ” (Hau, 2 0 d y with NA S w hich had t h w ind turbin e e r (Spera, 1 9 n e had a tip - d for 15 yea r n Tvind, De n Fi g n ts was Swe d d two large w d turbine wi t on in 1983 fe ature: a ca r g major com p e wind turbi n Agency (IE A SA/DOI pro w ind rotor ( F ency (IEA), a n countries m started in 1 q uirement f r 0 06). For th i S A. Further m h eir first rot a s had a thr e 94) (Figure - controlled r r s. n mark (Hau , g ure 2.18 – T vi n d en. The Na t w ind turbine s t h two blad e (Figure 2.1 9 r riage assem b p onents. Th i n e erected i n A ), 1984). T h gram. The W F igure 2.20) . 1 984). also develo p 1 974. The m r om wind en i s purpose, t m ore, two 6 3 ation in 19 7 e e-bladed, u 2.17). Each r otor while t h , 2006) (Fig u n d wind turbin e t ional Swedi s s were built e s on a rigid 9 ) (Internati b ly mounte d is feature el i n S w eden wa s h is machine W TS-3 had a . It also had Chapter 2 3 9 p ed researc h ain goal wa s ergy withou t t he 200 k W 3 0 kW win d 7 9 and 198 0 pwind roto r of the win d h e other ha d u re 2.18). e s h Board fo r ( Hau, 2006) . hub upwin d onal Energ y d on vertica l i minated th e s the WTS3 was built b y rated powe r a “soft-soft ” 9 h s t W d 0 r d d r . d y l e 3 y r ” From Windmills 40 Fi g The Germ a (Internatio n turbine, w h ever built ( F a 100 m tal l full-span pi t operation a problems, i (Internatio n smaller ma c diameter r o F i to the Modern W g ure 2.19 – Na s a n state s u n al Energy A h ich was ass e F igure 2.21). l steel tower s t ch control. T a lthough it w i ncluding f a n al Energy A c hines oper a o tor (Figure 2 i gure 2.21 – Gr W ind Turbines s udden wind t u u bsidized pr A gency (IE A e mbled in 1 9 It had a 100 s tabilized b y T he Growia n w as not wel l a tigue in m A gency (IEA a ted satisfac t 2 .22) (Spera, owian wind tu u rbine o gram on A ), 1984). T 9 82 (Thiele, m diameter y several guy n machine w succeed. A d ajor compo ), 1989). De t orily (such 1994). r bine the develo p T he most e m 1984). This w , two-blade d cables (Sper w as also the f i d ditionally, nents whic h spite of the as the 370 k Figure 2.20 p ment of w m blematic p r w ind turbin e d , downwind a , 1994). Th e i rst wind tu r the Growia n h conducte d low success k W Monopt Figure 2.22 – M – Maglarp win d w ind energy r oject was t h e was, at th a rotor which e carbon-fila b ine to atte m n wind turb i d to its dis a of the Gro w e ros with a M onopteros w d turbine started in h e Growian a t time, the l h was suppor t a ment blades m pt variable - i ne suffered a ssemble in w ian project, one-bladed, w ind turbine 1974 wind l argest t ed by had a - speed other 1987 some 48 m Chapter 2 41 The large wind turbines developed during the 1970s and 1980s failed, in general, one of their main purposes: to produce energy at a competitive price. They were not as reliable as expected, with short life periods due to several failures. In (Johnson, 2001), it is referred the fact that smaller turbines (in the 100 kW range) could be built at lower costs and with better performance than the larges turbines as one of the reasons to the end of the American program. In fact, the seek for larger and powerful wind turbines underestimated the difficulty of building reliable machines of this size. The Growian wind turbine is an example in which the size of the turbine is too large for the time in which it was built. On the other hand, for the first time in the history of the wind energy, there was a consistent experimental and theoretical knowledge of wind turbines. This knowledge was fundamental for the beginning of the commercial market of wind turbines as it is known today. In hindsight, it is possible to evidence three distinct groups of approaches on the structural and control level over the evolutionary history of wind turbines (Thresher and Dodge, 1998): o Turbines designed to withstand high wind loads. These models were considerably robust, with low rated power and were optimized for reliability. An example of this philosophy was the Gedser wind turbine; o Turbines designed to be compliant and shed loads. These models were optimized for performance. Their design had an important concern with the reduction of weight and with the optimization of the aerodynamic profile of the blades. An example of this design concept was the W-34 wind turbine; o Turbines designed to manage loads mechanically and/ or electrically. These turbines were optimized for control, with several mechanical and electrical innovations (such as hinged blade connections and variable speed generators). An example of this concept was the SmithPutnam turbine. The first approach was indubitably the most durable and reliable. However, the increase of knowledge in the industry has led to less conservative designs, with the aim of weight reduction (to reduce cost) and control (to optimize the production). Thus, a joint of the second and third approaches is currently the main driver of the design concepts. An illustration of the principal projects held during this period of development is shown in Figure 2.23. The evolution of the dimension of the wind turbines is notorious. From Windmills to the Modern Wind Turbines 48 In the future, another major change may take place for the offshore turbines. The continuous increasing of rotor diameters may lead to a definition of the blade design by a deflection limit in upwind rotors, instead of a load limit criterion (Butterfield, Musial et al., 2007). This is due to the increased levels of strength and flexibility achieved in blades. For this reason, downwind rotors may be an option for future offshore wind turbines because, contrary to the upwind solution, the blades deflect away from the tower. The downwind solution was abandoned in the past due to vibrations and noise problems (Butterfield, Musial et al., 2007) with the blades passing through the tower shadow. Nevertheless, for large distances from the shore, noise disturbances are not a problem. Some other perspectives for future developments of wind turbines are presented in (European Commission, 2011). In the report of the UpWind program, some considerations are made for the design of a giant 20 MW wind turbine. Although the program was not exclusively for the offshore market, the dimensions of the turbines under analysis make them suitable for the implementation at offshore locations. Among other considerations, some important aspects are referred for the feasibility of turbines with this dimension: o Reduction of the magnitude of fatigue loads. For this, advanced rotor control strategies are required (the concept of “smart turbine” is introduced); o Implementation of control systems for detection and evaluation of upcoming wind loads (gusts or vortex) with the aim of load alleviation (such as LIDAR systems mounted at the nacelle); o Individual pitch control of each blade; o Application of materials with lower mass to strength ratio; o Introduction of monitoring technologies to assess the structural integrity of the system; o Due to transportation issues, the blades might have to be splitted into two pieces since the rotor of the studied 20 MW wind turbine has a diameter of 252 m. For this reason, this joint might be an important focus of attention; o The need for optimization of the offshore substructure (foundation and transition piece). The offshore substructure is another important topic for the future of offshore wind turbines. Nowadays there is a large variety of commercially implemented, tested and concept designs (see Chapter 3). The future trend, as stated earlier, is to increase the distance from the shore. In this situation, due to a larger water depth, floating structures seem to be the most suitable option. Until today, a few number of experimental projects have been deployed. For the next years, many floating wind turbine projects are schedule to start in several countries (Main(e) International Consulting LLC, 2012). Chapter 2 49 2.2 BRIEF MARKET ANALYSIS 2.2.1 THE START OF THE DANISH AND AMERICAN MARKET The wind energy market gained relevance in the second half of the 20th century (Hau, 2006). In Denmark in the early 1980s, some small manufacturers of agricultural machines entered in the market with simple wind turbines with power outputs around 30 - 75 kW (Hau, 2006; Gasch and Twele, 2012). These machines followed the Juul’s concept with a three-bladed, stall-regulated, upwind rotor working at a fixed speed with an induction generator (Burton, Sharpe et al., 2001). This market was initially sustained by an appropriate feed-in tariff set by the government (Gasch and Twele, 2012). A consequence of the development of the Danish market was the creation of a certificate by the Wind Turbine Test Station in Risø to attest the maturity and safety of the wind turbines. On the other hand, the American market was created mainly due to politic measures. Consecutive measures took by the Senate that culminated in the Public Utilities Regulatory Policy Act (PURPA) in 1978 (Hau, 2006), conducted to a favourable situation of subsidies for wind energy investments. The state which provided the best incentives, and which also had good wind conditions, was California (Manwell, McGowan et al., 2010). Thus, the first wind farms were built there between 1979 and 1980. Due to economic viability, these wind farms were constituted by 100 or more turbines (Johnson, 2001). These small wind turbines, with power outputs up to 100 kW, were initially manufactured by American companies. However, the initial operation of these wind turbines was characterized by several difficulties due to the technological immaturity of the models (Manwell, McGowan et al., 2010). Sometime later, Danish wind turbines entered in the American market and became more successfully than native companies, mainly due to their larger experience. After the initial problems, the number of wind farms increased very quickly around 1981, with an installed capacity over 1500 MW (Johnson, 2001). However, in the years between 1986 and 1987, the economic situation changed in California (Hau, 2006). The conjugation of the expiration of the tax credits for the investors, alongside with the lower supply tariffs offered by the utilities, led to a slowdown (and, sometime later, to the stagnation) of the growth of wind farms (Hau, 2006). In the rest of Europe, the wind energy market started in the 1990s with a support scheme mainly based in feed-in tariffs for wind power generation (Ackermann and Söder, 2002). 2.2.2 ONSHORE WIND TURBINE MARKET The analysis of the evolution of the wind energy market and its current situation is a clear way to attest the success of this industry in the last 15 years. In this section, a brief market analysis is made for the entire market (onshore together with offshore), since the latter still has a minor importance in terms of total installation numbers (around 2.4 % of the total installed capacity). Analysing the cumulative installed capacity in the world (Figure 2.28), it is possible to observe the consistent growth of the wind energy market, with a total installed capacity already exceeding the 350 GW. Qualitatively, it is also possible to observe that Europe and Asia are the leaders in the installed capacity. In fact, Asia became the region in the world with the largest installed wind park during 2014. The main driver of this situation is China, which has become the world leader in installed capacity when it surpassed the USA during 2010 (Global Wind Energy Council (GWEC), 2011). The top 10 countries with the largest cumulative installed capacity are presented in Figure 2.29. From Windmills to the Modern Wind Turbines 50 Figure 2.28 – Cumulative installed capacity (the share at the end of 2014 results is presented in brackets) (EWEA 2007, 2008, 2009, 2010, 2011b, 2012b, 2013c, 2014b, 2015b) (GWEC 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015) Figure 2.29 – Top 10 Countries in cumulative installed capacity in the end of 2014 (European Wind Energy Association (EWEA), 2015b; Global Wind Energy Council (GWEC), 2015) On the other hand, European investments stagnated during the last years which can be justified by the financial crisis installed in this continent (Figure 2.30). In the opposite side, China was responsible, during 2013 and 2014, by more than 45 % of the new installations (Figure 2.31). These recent investments led China to a position of market domination. 0 50000 100000 150000 200000 250000 300000 350000 400000 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Cummulative Installed Power [MW] Cumulative Installed Capacity Pacific Region [1.2 %] North America [21.1 %] Latin America & Caribbean [2.3 %] Europe [36.3 %] Asia [38.4 %] Africa & Middle East [0.7 %] China 31% USA 18% Germany 11% Spain 6% India 6% UK 3% Canada 3% France 2% Italy 2% Brazil 2% Restofthe world 16% Top10CumulativeCapacity(2014) Chapter 2 51 Figure 2.30 – Annual installed capacity (the share at the end of 2014 results is presented in brackets) (EWEA 2007, 2008, 2009, 2010, 2011b, 2012b, 2013c, 2014b, 2015b) (GWEC 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015) Figure 2.31 – Top 10 Countries in new installed capacity in the 2014 (European Wind Energy Association (EWEA), 2015b; Global Wind Energy Council (GWEC), 2015) In Portugal, large investments were done in wind energy since the first wind farm was commissioned at Madeira in 1986. Portugal is the 12th country in the world with largest installed power and the 8th in Europe with a cumulative installed capacity of 4 914 MW (European Wind Energy Association (EWEA), 2015b; Global Wind Energy Council (GWEC), 2015) (Figure 2.32). However, the investments have been declining in recent years. This situation may be explained by the financial crisis, by the minor incentives given by the Government and by some limits imposed for penetration in the national electrical system. 0 10000 20000 30000 40000 50000 60000 2006 2007 2008 2009 2010 2011 2012 2013 2014 NewInstalled Power [MW] Annual Installed Capacity Pacific Region [1.1 %] North America [14.3 %] Latin America & Caribbean [7.3 %] Europe [25.0 %] Asia [50.5 %] Africa & Middle East [1.8 %] China 45% Germany 10% USA 9% Brazil 5% India 5% Canada 4% UK 3% Sweden 2% France 2% Turkey 2% Restofthe world 13% Top10NewInstalledCapacity(2014) From Windmills to the Modern Wind Turbines 52 Figure 2.32 – Annual cumulative and installed capacity in Portugal (since 2005) (EWEA 2007, 2008, 2009, 2010, 2011b, 2012b, 2013c, 2014b, 2015b) Figure 2.33 shows the geographical distribution of wind farms in the continental territory of Portugal. As can be observed, the major part of wind farms is located in the north and centre of the country, mainly in interior highlands. Figure 2.33 – Installed wind farms in Portugal at the end of 2014 (Institute of Mechanical Engineering and Industrial Management (INEGI) and Portuguese Renewable Energy Association (APREN), 2015) 0 1.000 2.000 3.000 4.000 5.000 6.000 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Power output [MW] Cumulative and Installed Capacity in Portugal Cummulative installed Capacity Annual installed capacity Wind Total Farms Power Output [ [0.5 – 1.9] [2.0 – 9.9] [10.0 – 24.9] [25.0 – 49.9] >50 [ MW] ? Chapter 2 53 2.2.3 OFFSHORE WIND TURBINE MARKET Compared to the onshore market, offshore wind power is still in the beginning, with slightly less than 9 GW installed, corresponding to 2.4 % of the total installed capacity worldwide (Figure 2.34). At the end of 2014, there were only 17 countries in the world with offshore wind turbines installed. From these, the major part is from Europe. The implementation in this continent represents more than 90 % of the world installed capacity. Figure 2.34 – Annual cumulative capacity of offshore wind turbines .The share values in brackets are referred to the end of 2014 (EWEA 2011a, 2012a, 2013b, 2014a, 2015a) (GWEC 2012, 2013, 2014, 2015) In today’s market, the UK is clearly dominant with more than 50 % of the entire global capacity. The UK has been doing a large investment in the offshore market in the last years, as can be seen in Figure 2.35. Portugal has a small portion of the entire market with just one 2.0 MW experimental floating offshore wind turbine. Figure 2.35 – Annual installed capacity of offshore wind turbines (data from 2013 is only referred to European countries). The share values in brackets are referred to the end of 2012 (EWEA 2011a, 2012a, 2013b, 2014a, 2015a) (GWEC 2012, 2013, 2014, 2015) The dominance of the offshore market by the Northern countries of Europe is a clear evidence. For this fact, the water depth conditions present in these countries should be considered as an important driver. Analysing Table 2.1, it is evident the large portion of shallow waters present in the north of Europe, in opposition to the situation at the south regions, where the water depth increases rapidly 0 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 2009 2010 2011 2012 2013 2014 Annual Cumulative Power [MW] Annual Cumulative Power US [0.00 %] Korea [0.06 %] Portugal [0.06 %] Norway [0.02 %] Spain [0.06 %] Portugal [0.06 %] Norway [0.02 %] Ireland [0.29 %] Japan [0.57 %] Finland [0.57 %] Sweden [2.42 %] Belgium [8.13 %] Germany [11.98 %] China [7.51 %] Netherlands [2.82 %] Denmark [14.51 %] UK [51.32 %] 0 250 500 750 1000 1250 1500 1750 2000 2010 2011 2012 2013 2014 Annual Installed Power [MW] Anual Installed Power US [-] Korea [-] Portugal [-] Norway [-] Spain [-] Portugal [-] Norway [-] Ireland [-] Japan [-] Finland [0.01 %] Sweden [-] Belgium [8.76 %] Germany [32.84 %] China [7.89 %] Netherlands [-] Denmark [-] UK [50.51 %] From Windmills to the Modern Wind Turbines 54 with the distance from the coast. In addition, it is also possible to note the apparent good conditions for the USA to install offshore wind farms. However, in the last years, investments in this area were not considered a priority by this country. Table 2.1 – Percentage of water depths in different regions up to 100 km offshore (Henderson, 2003) Region Water Depth < 25 [m] 25 – 50 [m] 50 – 100 [m] 100 – 300 [m] North Europe 21 26 32 20 South Europe 16 11 23 49 Japan 22 9 18 51 USA 50 26 13 11 Chapter 2 55 2.3 FINAL CONSIDERATIONS This chapter described the evolution of wind turbines, since the first attempts to modern utility-scale models. In the same manner, the emergence and development of offshore turbines, from land-based models to especially designed models to be installed offshore, was covered. Apart from the efficiency in the exploitation of energy from the wind, two important aspects defined the success of some models over others: reliability and cost effectiveness. The second part of the chapter briefly introduced the wind energy market. It was attested the importance of this sector, with a consistent growth sustained by both consolidated and emergent markets. In addition, the potential growth of the offshore market, still in an early phase of deployment, was referred. This chapter is especially important to frame the scope of the present work. A monitoring system, able to detect structural damages at an early stage and perform an estimation of the fatigue condition of the support structure, represents an important tool to remotely control the condition of the wind turbine and, thus, its reliability. At the same time, this continuous assessing provides helpful information to timely prepare maintenance actions, as well as possible retrofitting needs, allowing to optimize the reduction of OPEX (cost over the period of operation – see Chapter 3). From Windmills to the Modern Wind Turbines 56 Chapter 3 57 3 BASICS OF WIND TURBINES 3.1 GENERAL LAYOUT 3.1.1 WIND TURBINE TYPOLOGY Historically, wind turbines can be defined according to several design configurations. Concerning conceptual design aspects, a major distinction is made according to the position of the axis of rotation of the wind rotor: the axis can be positioned vertically or horizontally. Vertical-axis wind turbines, such as the Savonius and Darrieus rotor (Figure 2.4 and 2.5), are rarely used in modern large wind turbines. Although this kind of turbines presents some advantages, some negative aspects such as the low tip-speed ratio, the inability to self-start and the difficulty to control the rotor speed (Hau, 2006) led to low interest in their development during the 1970s and 1980s. The horizontal-axis wind turbine is the most common solution. This type of wind turbines can be subdivided into two main groups considering the configuration of the rotor with respect to the wind flow direction: upwind and downwind rotors (being the latter almost not used nowadays). In this work, the main focus is oriented towards the horizontal-axis upwind turbines, the typical nowadays configuration. Notwithstanding, some considerations are made about other solutions. The layout of a nowadays common onshore and offshore wind turbine is shown in Figure 3.1. The represented offshore example refers to a monopile foundation solution (see section 3.1.1.5). In Figure 3.2 the terminology for the translational and rotational degrees of freedom of a wind turbine is introduced. A brief description of the main components of nowadays onshore and offshore wind turbines is presented in the following sections. Basics of Wind Turbines 64 3.1.1.4 Transition Piece The transition piece only exists in offshore wind turbines. It connects the foundation to the tower. This element is considered one of the most critical points of the structural integrity of offshore wind turbines. This element is grouted on the top of the foundation and, in this operation, any lack of verticality is corrected (Figure 3.9). The transition piece usually attaches a structure for boat landing, platforms, ladders and the j-tube (a metallic tube that guides the cables to the seabed). Although the transition piece is utilized in several types of foundations for offshore wind turbines, other offshore solutions may not need this element. Figure 3.9 – Grouted joint for the connection between the foundation (monopile) and the transition piece. In this situation, the verticality is corrected by the connection (Gasch and Twele, 2012) 3.1.1.5 Foundation The foundation is the component that best distinguishes onshore and offshore wind turbine structures. While onshore turbine foundations follow traditional in-land civil engineering solutions, offshore models have been progressively adopting solutions from oil and gas offshore industry. However, both onshore and offshore foundations have the same function: to ensure stability and drive the loads from the structure to the ground, which means, to prevent the structure from sinking due to gravitational loads, from sliding due to horizontal loads and from fall over due to base overturning moments. Besides this, it is important to bear in mind that the definition and implementation of the designed foundation will influence the dynamic behaviour of the entire structural. Onshore Solutions The foundations for onshore wind turbines employ well-known and controlled solutions. There are mainly two possibilities: slab foundations or pile foundations (Figure 3.10). tower base flange grounted joint monopile scour protection transition piece (includ. access platform, cable ducts, ladder, add-ons) submarine cable Chapter 3 65 a) b) Figure 3.10 – Examples of foundations for onshore wind turbines: a) slab foundation; b) pile foundation Slab foundations are used when the ground near the top is of good quality. They consist on reinforced concrete slabs which usually have a polygonal geometry (such as an octagonal shape) with a tapered or constant thickness. This kind of foundation resists to the overturning moment with the eccentricity of the reaction. The vertical and horizontal loads are resisted by the dispersion of the load through the foundation area and by the friction between the ground and the foundation, respectively. Pile foundations are used for weaker soils. They are constituted by a pile cap from which a certain number of piles are connected and extended until a good soil layer is reached. In this situation, the loads are absorbed by the soil through axial and lateral pile resistance against the soil. Once again, reinforced concrete is used in this solution. Offshore Solutions In contrast to onshore turbines, there is the need for diversified offshore solutions, depending on the water depth. In addition, these solutions are considered far more complex than for onshore. Offshore solutions for wind turbines can be divided in three categories: for shallow waters (up to 25 – 30 m), for transitional waters (from around 30 to around 60 m) and for deep waters (more than 60 m). The most appropriate solutions for each water depth are presented in Table 3.1. Basics of Wind T 66 Gravity-ba s (Figure 3.1 1 the require d loads. The c filled with Besides the This operat i This soluti o aerodynam i structure d u Gravity fo u farm in De n e.g. the Th o T urbines T Soluti o Gravityb Mono p T ripo Jack e T ripil Floati n s ed foundati o 1 ). It consist s d weight. T h c aisson is f a ballast. For need for he a i on ensures c o n is conside i c damping o u e to the dy n u ndations ar e n mark). Ho w o rnton Bank Figure 3.11 T able 3.1 – Off s o n b ased p ile d e t e n g o n is the sec s on a caisso n h erefore, a l a bricated on the operati o a vy machine r c ompaction red, with re g o f the rotor n amic loads ( e indicated f o w ever, there wind farm, i – Gravity-base s hore foundati o Shallow wate r (0 – 30 m) ✓ ✓ o nd most u s n (usually m a arge footpri land and th o n on the s i r y, another d and homog e g ard to the v i do not cont r ( see section 4 o r very shal l are exampl e i n Belgium ( T d foundation ( on solutions c o rs T ran s ( 3 s ed solution a de of concr i nt is used t o h en transpor t i te, heavy v e d isadvantage e nization of t ibrational c h r ibute in lar g 4 .5) (Hau, 2 0 l ow waters ( a e s of imple m T homsen, F o photo (Scots R o ncerning wat e s itional waters 3 0 – 60 m) ✓ ✓ ✓ for current o ete) which i s o absorb m o t ed to the si t e ssels are re is the neces s t he soil to pr h aracteristic s g e measure t 0 06). a round up t o m entation at d o rsberg et al. R enewables, 20 e r depth Deep w (+ 6 0 ✓ o ffshore wi n s filled with m o ments due t e, where it quired to s e s ary prepara t e vent uneve n , as “stiff”. F t o alleviate t h o 10 m – e. g d eeper wate r , 2007)). 11) and illustr a w aters 0 m) ✓ n d turbine p r m aterial to a c to environ m is submerg e e t the foun d tion of the s e n settling. F or this reas o h e response g . the Nyste d r s (around 2 a tion) ( S (S e Tower r ojects c hieve m ental e d and d ation. e abed. o n, the of the d wind 7 m – S eabed) e a Level) Mon o used drive In si t pene t outsi d insta l altho Cont their Mon o of ar o foun d A di f tech n tech n sinki n savi n ham m later a o pile found a solution in o n or drilled ( t uations in t ration. Sin c d e ladders a n l led on the t r ugh signific a rary to the g dynamic be h o pile found a o und 25 m t d ation was u f ferent appr o n ology alrea d n ology consi s n g of the b u n g in materi a m ering is a v a l stability a n a tion is ano t o ffshore win ( depending o which the m c e the press u n d the j-tub e r ansition pie a nt boulders g ravity-base d h aviour (Ha u a tions are us e t o 30 m is a u sed in the H Figure 3.1 2 o ach under d d y used in t h s ts of skirte d u cket into th a l (compare d v oided (Byr n n d the vertic a t her alterna t d turbines ( F o n soil quali t m onopile is u re introdu c e ) cannot b e ce. The pre v should be a v d solution, m u , 2006). e d in deeper consensual l orns Rev wi n 2 – Monopile f o d evelopment h e oil and g a d shallow fo u e soil due t o d to commo n e, Houlsby e a lity of the t o t ive solution F igure 3.12) . t y) into the s implement e c ed by the h e installed di v ious prepar a v oided on th m onopile fo u waters than l imit for the n d farm (in D o undation (ph o for the fou n a s industry ( u ndations, w h o the create d n monopiles e t al., 2002) . o wer (Tong, for shallo w . It consists o s eabed by m e e d by drivi n h ammers is rectly on th e a tion of the s e foundatio n u ndations a r gravity-bas e implement a D enmark). o to (LORC, 201 2 n dation of t u ( Figure 3.13 ) h ich inside w d pressure d i ), and a fast e . However, t 2 010). w waters and o n a free-sta n e ans of speci g, hydrauli c very high, e monopile. F eabed is not n area. r e considere d e d solutions. a tion of this f 2 b) and illustra u rbine tower s ) (Byrne, H o w ater is pu m i fferential. S u e r and simp l t here is som e d is, nowada y n ding steel p i al and heav y c hammers a appurtenan c For this rea s necessary f o d as “soft”, i However, a foundation. a tion) s is the suct i o ulsby et al. , m ped out, re s u ction buck e l er installati o e concern r e (Seab e (Sea Le v Tower Transition P i Chapter 3 6 7 y s, the mos t p ipe which i s y equipment . a re used fo r c es (such a s s on, they ar e o r monopile s i n respect o f water dept h This type o f i on bucket, a , 2002). Thi s ulting in th e e ts present a o n, in whic h e garding th e e d) v el) i ece 7 t s . r s e s f h f a s e a h e Basics of Wind T 68 This type implement e Dogger Ba n problems i n Water dep t turbines. B e demanding technologi e Tripod fou n concept wi t diverge fro m The tripod g in the legs, prearrange m high produ c legs is com p Tripod fou n has been al r T urbines of foundat i e d (in Fred e n k (UK) ( C n 2005 (Ener c t hs of aroun e yond this l i on material e s are under d n dation is o n t h a larger f m a single n o g eometry al l scour prote m ent is req u c tion expen d p lex and a p o n dations are r eady imple m i on is still e rikshavn, D C arbon Tru c on GmbH, Figure 3.13 – S d 25 m – 3 0 i mit, the ap p weight and o d evelopmen t n e of the alt e f ootprint (F i o de. These t h l ows this sol u ction is gen e u ired. On th e d iture) and d o tential focu s suitable for m ented on t h in an expe e nmark) (I b st, 2013)). H 2005). S uction bucke t 0 m are the p licability o f o n machine r t nowadays ( e rnatives for gure 3.14). T h ree points a r u tion to be l i e rally not n e e other han d d ifficult to t r s of fatigue p water depth h e Alpha Ve n e rimental p h b sen, Liinga a H owever a p t foundation ( p limit of cu r f the presen t r y for imple m ( for transitio transitional Tripods co n r e anchored i ght-weight a e eded (Ton g d , these str u r ansport (H a p roblems. h s up to aro u n tus wind fa r h ase. There a rd et al., 2 0 p roject was p hoto and illus t r rent comm o t ed solution s m entation. F o nal and dee p waters. It is n sist on a st r in the seabe d a nd “stiff”. S g , 2010). In a u ctures are c a u, 2006). Al u nd 50 m – 6 r m, in Germ a are alread y 0 05) and m o cancelled d t ration) o n commer c s becomes v e o r this reaso n p waters). an expansio r ucture wit h d . i nce the loa d a ddition, on l o mplex to b so, the mai n 0 m. This ki a ny (Bartsch y some ex a o re recently d ue to insta l c ial offshor e e ry expensi v n , new foun d o n of the mo n h three legs w d s are mainl y ly reduced s b uild (leadin n joint of th e i nd of found h , 2012). (Seabed) (Sea Level) Tower Transition Piece a mples at the l lation wind v e and d ation n opile w hich y axial s eabed g to a e three ations Anot an a p cons i Jack e mo m the n desir e piles This this t used is an t her alternat i p plication o f i sts on a trus e t foundatio n m ents. Altho u n ecessary we l e site where or with suct i type of stru c t echnology i s for implem e example of i Figure 3.1 4 i ve for transi f a common s tower with n s are lightw u gh they re p l dings. Its in s the structur e i on buckets ( c tures is no w s employed f e ntation of o i mplementa t 4 – T ripod foun t ional water design em p three or fo u w eight and e f p resent a no t s tallation pr o e is implem e ( LORC, 201 2 w adays ideal f or deeper w a o ffshore turb ion of wind t n dation (photo depths is th e p loyed by th e u r legs conne f ficient stru c t able reducti o cess is sim i e nted. The a n 2 a). l ized for wa t w aters on the ines in deep turbines on j (Wikipedia, 20 e jacket fou n e oil and ga s cted to each c tures, with a on of mater i lar to the tr i n choring of t t er depths u p oil and gas i er waters. T h j acket found 1 2) and illustra n dation (Fig u s industry f o other by br a a very good r i al (steel), t h pod. The ja c t he structur e p to around i ndustry, so i h e Beatrice w ations. a tion) u re 3.15). Th o r offshore s a cings. r esistance to h ey are expe c ket is trans p e is also real i 50 m – 60 m it can be als o w ind farm ( i ( S Tower Transition Piec Chapter 3 6 9 i s solution i s s tructures. I t overturnin g n sive due t o p orted to th e i zed throug h m . However , o potentiall y i n Germany ) (Seabed) S ea Level) e 9 s t g o e h , y ) Basics of Wind T 70 The tripile i consists on installed an This desig n installation pile needs t o The tripile implement e GmbH). T urbines Fi g i s other fou n a natural e v d connected n has the a d of the three o be hamme r solution is e d in the B A g ure 3.15 – Jac n dation tech n v olution fro m at the top b y d vantage of piles is of m r ed which is indicated f o A RD Offshor e ket foundatio n n ology instal l m the mono p y a transitio n increasing t m ajor import extremely n o r water de p e 1 wind far m n (photo (LOR C led nowada y p ile: instead n piece. t he stiffness ance and ne oisy (LORC , p ths up to m and in th e C , 2012a) and il l y s for mediu m of just one s of the mo n eds a rigoro u , 2012c). 50 m. This e Hooksiel w ustration) m water dep t s teel pile, th r n opile soluti o u s approach . technology w ind farm (B t h (Figure 3. ree monopi l on. Howev e . In additio n has alread y B ARD Engin e (S e (Sea L Tower Transition Pi e 16). It l es are e r, the n , each y been e ering e abed) L evel) e ce As r e indu s expe r feasi b Besi d a m a cond i The (But t o o o Alth o float i F e ferred in C h s try is the r imental pr o b ility of com m d es the possi b a ss-producti o i tions. Anot h design of f t erfield, Mus i o Ballast – create a r the stru c oil indu s o Moorin g lines un d o Buoyan c weighte d o ugh each d e i ng platform F igure 3.16 – Tr h apter 2, on e floating st r o jects under m ercial offs h b ility of intr o o n of struc t h er advanta g f loating str u i al et al., 200 – This kind o r ighting mo m c ture helps t o s try for man y g Lines - Pla t d er tension; c y – This las t d plane area f e scribed co n s usually pr e r ipile foundati o e of the tod a r ucture for developme n h ore wind tu o duction of w t ures since g e of floatin g u ctures foll o 5): o f solution u m ent and hi g o minimize t y years (Mus i t forms using t concept rel f or righting m n cept presen t e sent a hybr i o n (photo (BAR a y’s main fie l deep wate r n t, however t u rbines base d wind turbin e they can a g platforms i s o ws mainly u ses the we i g h inertial r e t he heave m o i al, Butterfie g this techno l l ies on a dis t m oment (B u t s a differen t i d system. C D Engineering l ds of devel o r depths. N t here is still d on floating e s at deep w chieve a hi s the possibi l three diff e i ght of balla s e sistance to p o tion. This s o ld et al., 200 4 l ogy achieve t ributed buo y u tterfield, M u t physical pr o mmonly, s o GmbH) and ill u o pment in t h N owadays, t h a long way foundations ater depths, g h indepen d ity of being t e rent conce p s t below a c e p itch and rol l o lution has b 4 ); stability thr o y ancy, achie v u sial et al., 2 0 i nciple to a c o lutions are ustration) h e offshore w h ere are a l of develop m s . floating co n d ence from t owed to the p ts to achi e entral buoy a l . The elong a b een used in o ugh the us e v ed throug h 0 05). c hieve stabil i designed b a ( Tower Chapter 3 71 w ind turbin e ready som e m ent for th e n cepts enabl e the seabe d i r location. e ve stabilit y a ncy tank t o a ted shape o f the offshor e e of moorin g the use of a i ty, in realit y sed on all o f (Seabed) ( Sea Level) e e e e d y o f e g a y f Basics of Wind Turbines 72 the three concepts, although generally relying on one primary source for stability (Butterfield, Musial et al., 2005). A representative design of each of the listed concepts is presented in Figure 3.17. a) b) c) Figure 3.17 – Floating solutions for offshore wind turbines(adapted from (Butterfield, Musial et al., 2005)): a) ballast; b) mooring lines; c) buoyancy 3.1.1.6 Monitoring and Control System Modern wind turbines are usually equipped with a monitoring and control system named SCADA (Supervisory Control and Data Acquisition system). This system consists of a microprocessor, together with several sensors, to control the operation and monitor the performance of the turbine. Under this system, several data is registered through sensors that record, among others: o Wind speed and direction; o Rotor speed; o Nacelle orientation; o Generator speed; o Pitch angle. With this data, the control system is responsible for operations like the start and stop of rotor rotation, emergency shut-down, adjustment of nacelle orientation and pitch angle. The system is also used to monitor the power production from a remote location, since it is usually connected through any means of communication (such as internet network). The information provided by the SCADA system can be also used to monitor the condition of several components (see Chapter 5). This data represents an important part in the architecture of the developed monitoring system (see Chapter 7). 3.1.2 COSTS BREAKTHROUGH The investment costs of wind farms are of paramount importance for the feasibility of wind energy. These costs are divided into capital costs (CAPEX - including all the costs for the implementation of the farm) and variable costs (OPEX - including all the costs over the period of its operation – e.g. operation and maintenance, land rental, insurance, among others). Tower (Sea Level) (Seabed) Mooring Lines (Sea Level) Tower Mooring Lines (Seabed) Tower (Sea Level) Mooring Lines (Seabed) Chapter 3 73 The NREL study present in (Tegen, Hand et al., 2012) describes some costs related to onshore models of U.S. wind projects during 2010. Figure 3.18 presents the principal results of this study, namely the capital cost share of the principal components of a wind turbine located in wind farm. These costs are grouped in larger groups, namely: o Turbine – comprises the wind turbine itself, which includes the tower, nacelle and rotor components (Blanco, 2009); o Balance of plant – including all the infrastructure except the turbine (foundations, buildings, roads, among others) (Department of Energy & Climate Change, 2010); o Installation and commissioning – including the installation and commissioning of the turbine and balance of plant (Department of Energy & Climate Change, 2010); o Development and consent – includes the multifaceted process of taking a wind farm from inception through to the point of financial close or commitment to build, depending on the contracting model, including several studies and contracts (Department of Energy & Climate Change, 2010). Basics of Wind Turbines 80 3.2 WIND TURBINE PERFORMANCE 3.2.1 ROTOR POWER CHARACTERISTICS (PHYSICS) The understating of the operation of a wind turbine has been continuously improved. The axial momentum theory, initially developed by Rankine in 1865 (Rankine, 1865), was the first explanation of power extraction at a rotor from a free-stream. In 1878, Froude originally developed the blade element theory, where he studied the effects of the flow on blades. Based on the axial momentum theory, Betz in 1920 (Betz, 1920) (and also, independently, Lanchester in 1915 and Joukowsky in 1920 (van Kuik, 2007)) calculated the maximum efficiency of an ideal wind turbine rotor, known as the Betz limit. Besides these initial works, other authors such as Glauert and Prandtl also contributed with subsequent developments (Burton, Sharpe et al., 2001). In this section, the combination of the axial momentum theory with the blade element theory is presented, which constitute the base of the nowadays procedure to analyze the wind turbine system aerodynamic performance. 3.2.2 AXIAL MOMENTUM THEORY (THE ACTUATOR DISC) The axial momentum theory (also known as the actuator disc theory) assumes that a stream tube passes through a disc, where the kinetic energy of the flow is extracted. In this theory, it is assumed that just the mass of air that passes through the disc is affected (Figure 3.26). The mass flow rate remains constant during the whole process. So, with the approach to the disc, the air stream slows down and, consequently, expands its cross section area (due to the principle of linear momentum). Figure 3.26 – The energy extracting stream tube of a wind turbine (adapted from (Burton, Sharpe et al., 2001)) This theory considers the following assumptions (Manwell, McGowan et al., 2010): o Homogenous, incompressible, steady state fluid flow; o No frictional drag; o An in-plane continuous disc (similar to an infinite number of blades); o Uniform thrust over the disc; o A non-rotating wake; o The static pressure far upstream and far downstream of the rotor is equal to the undisturbed ambient static pressure. A schematic illustration of the flow mechanism according to this theory is presented in Figure 3.27. Flow Direction Chapter 3 81 Figure 3.27 – Actuator disc with stream tube. Velocity and pressure development along the stream tube (adapted from (Tempel, 2006)) Considering the variation of linear momentum of the volume of air in the stream tube and the mass conservation principle, it is possible to calculate the axial thrust force of the rotor (), considering the variation of the cross section between 0 and ), represented in Figure 3.27: 󰇛..󰇜󰇛..󰇜 (3.1) with:  Axial thrust force of the rotor  Mass density of air ∗ wind velocity (in section *) ∗ Area of cross section (in section *) ∗ Section far ahead of the rotor ∗ Section far wake of the rotor F T U 0 Stream Tube Actuator Disk U W U 0 Stream Tube Axis Actuator Disc Velocity Velocity Pressure Pressure Axis Far Ahead Actuator Disc Far Wake Section 0 U0 p0 A0 Section W U W p W A w Section D,0 U D p D,0 A D Section D,W U D p D,W A D U D U 0 Basics of Wind Turbines 82 Since the flow is considered as in a steady state, it is possible to consider:  󰇗 󰇛..󰇜󰇛..󰇜 (3.2) with:  󰇗 Mass flow rate The thrust force can then be defined as:  󰇗 󰇛󰇜 (3.3) Applying the Bernoulli equation between the sections far ahead and in the vicinity ahead of the rotor (∗,), and between the vicinity of the rotor wake (∗,) and the far wake of the rotor, it becomes: 12..,12..,  (3.4) ,12.., 12..  with: ∗ Pressure (in section *) As exposed in Figure 3.27, the flow velocity is the same immediately before (section ,0) and after (section ,) the actuator disc and the pressure is identical far away of the rotor disc (ahead and after). So, defining the thrust force according to the variation of pressure on each vicinity of the disc: ,, (3.5) and introducing (3.4) in equation (3.5), one obtains: 12..󰇛 󰇜 (3.6) Chapter 3 83 From equation (3.6) and considering 󰇗󰇛..󰇜 in equation (3.3), it is possible to conclude that the velocity in the disc section is the average value of the upstream and downstream flow speed:  2 (3.7) Introducing the axial induction factor () as:   (3.8) it is possible to rewrite equation (3.7) as: 󰇛1󰇜 (3.9) 󰇛12.󰇜 As shown in the previous equations,  defines the degree of slowdown of the wind at the actuator disc. From equation (3.9), it is concluded that, in the extreme case, the induction factor can be  = 1/2. However, in this situation, the flow would cease and, thus, the flow mechanism would not be possible. Since the power output () is obtained as the rate of work done by the force at the actuator disc, it can be written as: .12....󰇟4.󰇛1󰇜󰇠 (3.10) where the term defined in the first square brackets represents the power that is present in the flux, while the second square brackets represents the efficiency of the power capturing. Considering equations (3.6) and (3.9), the thrust force is defined as: 12....4.󰇛1󰇜 (3.11) Basics of Wind Turbines 84 Usually, both  and  parameters are characterized by non-dimensional coefficients: the power coefficient () and the thrust coefficient (), respectively:  12....4.󰇛1󰇜 12...4.󰇛1󰇜 (3.12)  12....4.󰇛1󰇜 12....4.󰇛1󰇜 (3.13) In Figure 3.28 both coefficients are represented. As expected, the maximum values of the coefficients are attained for different values of  (as already referred, values of  greater than 1/2 are unrealistic). Figure 3.28 – Variation of  and  with the axial induction factor The calculation of the induction factor for the maximum values of the coefficients is obtained with: d d0→,16 27≅0.593,13 (3.14) d d0→,1,12 (3.15) While the results obtained for the thrust coefficient are not of too much importance (due to the fact that the maximum value is obtained for an unrealistic situation), the result of equation (3.14) represents an important achievement. The value of 16/27, named as Betz Limit, is considered the theoretical maximum limit for power extraction from the flow. This means that, no matter the efficiency of the machine, no wind turbine can extract more than 59.3 % of the kinetic energy of the wind. Obviously, this theory does not accurately characterize the real physical situation: the rotor is not composed by a uniform disc with only axial thrust acting on it and the wind does not continue as an undisturbed axial flow after passing through the rotor, among other things. To overcome these 00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 a (Induction factor) CP, C T (Dimensionless Amplitudes) C P C T Chapter 3 85 simplifications, the variation of angular momentum in the flow is considered in the theory presented in the next section. 3.2.3 ANGULAR MOMENTUM THEORY The angular momentum theory also studies the extraction of power from the wind flow. However, this theory, unlike the axial momentum theory, assumes the rotation of the rotor and, consequently, the creation of a rotational wake flow. This rotational wake flow has an opposite direction from the rotor rotation in reaction to the torque exerted by the flow on the rotor. An important difference from the axial momentum theory is that the energy extracted from the flow is lower. This is due to the energy employed in the rotor and wake rotation. It is assumed that the angular velocity of the rotor (Ω) is high when compared to the angular velocity of the wake flow (). Since the tangential speed of the rotor is not the same for all radial positions, annular rings of radius  and thickness d are considered, defining areas of 2...d (Figure 3.29). Figure 3.29 – Annular ring in the stream tube and decomposition of wake wind speed (adapted from (Manwell, McGowan et al., 2010)) As shown in Figure 3.29, the wake flow has an axial speed of 󰇛1󰇜 (like in the axial momentum theory) and a rotational speed of . Defining an angular induction factor as: ′  2.Ω (3.16) Axis dr r Ω ω.r RU 0 (1-a) Basics of Wind Turbines 86 the angular velocity of the wake flow can be written as: 2.Ω.′ (3.17) The torque of the annular stream is defined as the rate of change of angular momentum (due to the rotational speed): d.2...d.󰇛1󰇜.2.Ω.󰆒. 4.󰆒.󰇛1󰇜..Ω...d (3.18) with:  Torque on the actuator disc With the defined rotor torque, it is possible to calculate the power output due to it: dT.Ω (3.19) Defining the relationship between the tangential speed of the rotor at a radial distance  and the wind speed as the local speed ratio (or tip speed ratio, for the case of ): Ω.  Ω.  (3.20) The power output (3.19) for each ring of radius  and thickness d can be written as: d12...2...d.󰇟4.′󰇛1󰇜.󰇠 (3.21) Once again, the term defined in the first square brackets represents the power of the flux, while in the second square brackets, the efficiency of the capturing element is quantified (also known as blade element efficiency (Burton, Sharpe et al., 2001)). Chapter 3 87 As shown in (3.21), the power output extracted from the wind when the rotational wake is considered, depends not only on  and 󰆒, but also on the tip speed ratio. The power coefficient is defined by: dd 12...⇒8 ′󰇛1󰇜d   (3.22) Although the calculation of the integral in the equation (3.22) is not presented in this work (it can be consulted in (Manwell, McGowan et al., 2010)), it is important to note two things: o The power coefficient () depends on the tip speed ratio (λ); o The maximum power that can be extracted from the wind tends to the Betz Limit (16/27). Figure 3.30 illustrates the previous statements. Figure 3.30 – Evolution of  with λ according to angular momentum theory Considering the previous statements, it is possible to conclude that the evolution from rotors with fixed-speed to rotors with variable-speed was a major evolution step for the efficiency in energy harvesting. Whereas in a fixed-speed, the optimum tip-speed ratio is only achieved for a specific wind speed, with a variable-speed turbine, it is possible to have different optimum points of operation for each wind speed (Figure 3.31). 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 λ (Tip speed ratio) CP Betz limit Basics of Wind Turbines 88 Figure 3.31 – Power output as function of rotational speed for a fixedand variable-speed wind turbine for different wind speed classes (adapted from (Tempel, 2006)) Although the previous momentum theories already explain the power extraction from a wind flow, the problem is still not solvable yet due to unknown axial and angular induction factors ( and 󰆒). For this reason, an additional approach to this problem is needed: the blade element theory. 3.2.4 BLADE ELEMENT THEORY In this theory, the forces acting on the blades are expressed as a function of their shape and orientation. The following assumptions are adopted: o Each blade is divided into  elements along its longitudinal axis; o There is no radial flow (the aerodynamic interaction between elements is ignored); o The forces acting on the blades are determined only according their airfoil characteristics: lift () and drag () coefficients; o Three-dimensional effects are neglected. Figure 3.32 presents a different perspective of the rotor annular ring of the Figure 3.29. It also presents a detailed illustration of a blade, with an arbitrary airfoil and the wind and rotor velocities associated with one element (grey area). variable speed fixed speed 13 m/s 11 m/s 9 m/s 7 m/s 100 10 20 30 40 50 60 70 80 90 0 200 400 600 800 1000 0 1200 Rotational speed [RPM] P [kW] Chapter 3 89 Figure 3.32 – Rotor annular ring and detail of a blade element (adapted from (Burton, Sharpe et al., 2001)) As previously introduced, a blade element with a radius  and a radial width d is subjected to an axial wind speed of 󰇛1󰇜 and a rotational wind speed2 of Ω.󰆒 created by a rotor angular speed of Ω. Since tangential speeds are obtained from rotational speed multiplied by , the resultant relative velocity between the blade element and the wind is: 󰇟󰇛1󰇜󰇠󰇟Ω.󰇛1′󰇜󰇠 (3.23) An illustration of the relative velocity, its components and the associated lift () and drag () forces is presented in Figure 3.33 (where the chord of the airfoil is represented by ,  represents the pitch angle and  represents the angle of inflow). Figure 3.33 – Relative wind velocity applied to the airfoil and the subsequent lift and drag forces 2 The rotational speed of the blade element is obtained assuming a linear increase from 0 (at the far ahead location) to 2.Ω.′ (in the far wake location). δr r rΩ.r Ω.r.a’ Ω U0(1-a) U0(1-a) Ω.r(1+a’) URel FD FL α θ c Wind Direction Ф Basics of Wind Turbines 96 3.3 FINAL CONSIDERATIONS This chapter starts with the description of the main structural elements of wind turbines. A special focus is given to the support structure (tower and foundation – in onshore models; tower, transition piece and foundation – in offshore models). This element conditions, in a large extent, the modal properties and, consequently, the dynamic behaviour of wind turbines. The chapter continues with a depiction of the main costs related to a wind farm project for onshore and jacket-based offshore models. A high relative cost is found for the support structure and blades. Specially in the case of offshore installations, the foundation represents an important share of the overall cost. Also the reliability of the various elements of wind turbines is analysed. It is seen that accumulated experience demonstrated that the support structure in onshore wind turbines is not a commonly problematic element. However, the increase of the wind turbine dimensions, together with the installation of turbines in offshore harsh environments, is expected to introduce new problems. The evaluation of the reliability of the wind turbine components is a key aspect on the definition of the maintenance procedures, including new strategies based on data collected by installed monitoring systems. Lastly, a brief description of the wind turbine performance based on the axial momentum and blade element theories is introduced. This theoretical background represents a helpful insight for the comprehension and definition of the various operational conditions of a wind turbine. The variation of the conditions requires the definition of control strategies for the proper operation of the turbine. In that sense, simplified aerodynamic and rotor torque control strategies are included in this chapter. As will be seen in the following chapters, the variations imposed by the various regimes of operation of a wind turbine influence its modal properties. Chapter 4 97 4 STRUCTURAL BEHAVIOUR OF WIND TURBINES 4.1 STRUCTURAL DYNAMICS Wind turbine structures are highly dynamic systems. As illustrated in Figure 4.1, the normal operation of a wind turbine is a process in which different types of dynamic excitation take place. However, two main sources of excitation are evident: environmental conditions (wind loading and offshore conditions, if applicable) and the rotating machinery during operation, mainly the rotor. Figure 4.1 – Sources of dynamic excitations of an offshore wind turbine (for onshore turbines, tides, currents and waves are, obviously, not applicable) Waves Tides and Currents Wake effects Wind Structural Behaviour of Wind Turbines 98 Thus, an accurate description of the dynamic behaviour is extremely important in this context, otherwise resonance phenomena are very likely to occur due to several sources. A complete wind turbine structure can be idealized as an assembly of coupled multi degree-of-freedom mass-spring-damper systems. With this in mind, the structure is defined according to its mass, damping and stiffness properties (Clough and Penzien, 1995): . 󰇘 . 󰇗 .󰇛󰇜 (4.1) with:  Mass matrix  Damping matrix  Stiffness matrix  Displacement vector 󰇛󰇜 Excitation force Although the complete characterization of a wind turbine might be complex, simplifications for some components can be made for initial considerations. Within the scope of this thesis, the most important aspects related with the dynamic characterization of the tower, blades and the tower-blades coupling are presented. 4.1.1 DYNAMIC CHARACTERIZATION OF THE TOWER The tower structure of a wind turbine is a component for which a rigorous dynamic characterization is essential. However, simple geometric sections are usually used (namely, tubular sections) and a sufficiently accurate characterization of the material is also often achievable with simple methods (mainly for steel structures). Furthermore, the rotation of the rotor introduces small influence on the first natural frequency of the tower, which enables its calculation with the rotor at stand-still position with sufficient rigorous results. Taking this into account, a simple cantilevered column with distributed mass and a concentrated mass at the top (Figure 4.2) can be used for initial assessment of the natural frequency of the first tower bending mode. Figure 4.2 – Simplified structure for calculation of the natural frequency of the tower bending mode Chapter 4 99 With this configuration, approximate values of the tower first natural frequency can be obtained through:  , 2.  . . ,..  (4.2) with:   Tower first natural frequency , Constant value: 1.732 (Young and Buynas, 2002) or 1.7436 (Vugts, 2000), depending on literature sources , Constant value: 0.236 (Young and Buynas, 2002) or 0.227 (Vugts, 2000), depending on literature sources  Tower elastic modulus  Tower section inertia  Tower top mass (including nacelle, all the equipment in it and the rotor)  Tower mass per unit length  Tower height Figure 4.3 presents an illustration with the mode shape configuration of the first vibration mode for the fore-aft (1 FA) and side-side (1 SS) directions. Figure 4.3 – First tower vibration mode for fore-aft and side-side directions: undeformed (grey) and deformed (black) structure (adapted from (Skjoldan, 2011)) 4.1.2 DYNAMIC CHARACTERIZATION OF THE ROTOR The definition of the dynamic properties of the rotor blades presents a more complex nature than for the tower structure. Besides the material composition and geometry of the blades, it is important to realize that the dynamic behaviour of the rotor acts as a whole, which means that the stiffness of the shaft supporting bearings has a direct influence on the vibration modes. It is also important to understand that, when the wind turbine is operating (and the rotor is spinning), two particular effects take place which affect the dynamic behaviour of the structural system: gyroscopic and centrifugal stiffening effects. 1 FA 1 SS Structural Behaviour of Wind Turbines 100 The rotor modes of wind turbines can be divided into two groups: flapwise and edgewise (see Figure 3.2). For each order of these modes, three “sub-modes” need to be considered, namely, one symmetric and two asymmetric modes in each direction. These modes are presented in Figure 4.4. The symmetric mode is characterized by the deflection of the three blades in the same direction: o Flapwise modes: the blades deflect in the rotor out-of-plane direction (1 FS); o Edgewise modes: the blades deflect in the rotor plane direction (1 ES). On the other hand, the two asymmetric modes are defined accordingly to the direction of the motion of the blades: o Flapwise modes: tilt (1 FT) and yaw mode (1 FY); o Edgewise modes: horizontal (1 EH) and vertical mode (1 EV). Figure 4.4 – First order rotor modes (for low values of pitch angle): undeformed (grey) and deformed (black) structure (adapted from (Skjoldan, 2011)) These asymmetric modes are associated with translation and rotation of the rotor. This is the reason why the stiffness of the supporting elements of the rotor has an important role in these modes. When the wind turbine is under operation and the rotor is spinning, two particular effects need to be accounted for: gyroscope effects and centrifugal stiffening. These effects should be considered in the equation of motion (equation (4.1)) of the rotor as: . 󰇘 󰇛󰇜 󰇗 󰇛󰇜󰇛󰇜 (4.3) with:  Gyroscopic matrix  Geometric stiffness matrix 1 F Y1 F T 1 F S 1 E V 1 E H 1 ES Chapter 4 101 Gyroscope Effect The rotation of the rotor introduces a well-known characteristic in the context of rotor dynamics: the gyroscopic effect. This effect is due to the flexibility of supporting bearings of the rotor which leads to deviation of the rotating axis from the bearing centre line (Yoon, Lin et al., 2013). Essentially, when the rotor is rotating at the shaft axis, the motion in the two orthogonal axes is coupled. This is evident by the skew-symmetric nature of the gyroscopic matrix (Ewins, 2000; Yoon, Lin et al., 2013). Thus, under rotation, the rotor suffers two rotational movements: the rotation of the shaft itself; and a whirl rotation due to gyroscopic effects. There are two types of whirl rotation, namely, forward (when the rotation is in the same direction of the shaft) and backward (when the rotation is in the opposite direction). Figure 4.5 illustrates these two phenomena for two different situations: one where the rotor/ stator system is symmetric and another where the system is non-symmetric. a.1) a.2) b.1) b.2) Figure 4.5 – Motion of the rotor system (for a fixed reference) including the gyroscopic effect (the smaller trajectory represents the rotation of the shaft around itself, while the larger path indicates the whirl motion): a) represents a symmetric rotor system; b) represents a non-symmetric system; .1 represents the backward whirl mode; .2 represents the forward whirl movement (adapted from (Ewins, 2000)) The dynamic behaviour of wind turbine rotors is similar to what was described above. With the rotation of the rotor, the two asymmetric modes couple (the tilt with the yaw flapwise mode; and the horizontal with the vertical edgewise mode), resulting in the development of the whirl modes. The frequency of these whirl modes (backward – BW - and forward - FW) drift, from a fixed-frame reference, due to the rotor rotation. This situation is illustrated in Figure 4.6. As exposed in Figure 4.5, the forward and backward definition of the whirl modes refers to the rotation of the rotor centre of mass in the same or against the rotor direction, respectively (Skjoldan, 2011). ΩΩ ΩΩ Structural Behaviour of Wind Turbines 102 Figure 4.6 – Campbell diagram of fixed-frame natural frequencies (O) for the first 10 structural modes of a 600 kW threebladed wind turbine. Lines denote the centre frequencies of the rotor whirling modes given Ω added to the fixed-frame natural frequencies (adapted from (Hansen, 2007)) Figure 4.6 illustrates some important phenomena that should be considered when studying the dynamic behaviour of wind turbine rotors. When the rotor is stopped, modes 4 and 5 (first flapwise yaw and flapwise tilt modes) are very close. The difference between them is due to different elastic supports in the corresponding directions. Usually, the yaw mode is lower than the tilt mode because towers are stiffer in tilt than in yaw direction (Hansen, 2003). The 6th mode, the flapwise symmetric mode, is slightly higher than the asymmetric ones. This is justified by the fact that this mode, in which all the blades vibrate simultaneous in-phase, beholds also some fore-aft motion of the tower in out-of-phase (Hansen, 2003). When the rotor starts to operate, a change in the frequency value of the modes is evident. As highlighted in Figure 4.6, the pair of asymmetric modes starts to couple and became pairs of whirling modes. Thus, FW and BW modes start to drift, increasing and decreasing their frequency values, respectively, in an amount equal to the rotor speed (±Ω). This splitting phenomenon, identified considering a fixed reference of observation, is due to the gyroscopic effect. Modes 7 and 8 have a similar behaviour as the described for the 4th and 5th mode. These frequencies are also slightly different when the rotor is stopped due to different flexibilities of the rotor supports. When the rotor starts to spin, a similar splitting effect is noticeable. In the last two modes (2 flapwise FW and BW modes), the difference at parked situation of these two frequencies indicates an even greater difference in the requested flexibility of the support in both directions. Although the behaviour of these two modes is very similar to modes 4 and 5, it is important to refer that it is less pronounced due to the lower contribution of the gyroscopic reaction forces (Hansen, 2007). 0 1 2 3 4 0 5 10 15 20 25 -Ω +Ω -Ω +Ω 1 FY 1 FT 1 EV 1 EH 2 FY 2 FT Rotor speed [rpm] Natural frequency [Hz] 1. fixed-free drivetrain torsion 1. lateral tower bending 1. longitudinal tower bending 1. flapwise backward whirling 1. symmetric flapwise 1. flapwise forward whirling 1. edgewise backward whirling 2. flapwise backward whirling 1. edgewise forward whirling 2. flapwise forward whirling 1 FS Chapter 4 103 The evolution of the frequencies with the rotor speed usually leads to situations where two different modes stay very close to each other. In the presented situation, the 1st flapwise FW with the 1st symmetric mode and the 1st edgewise FW with the 2nd flapwise BW feature very close frequencies. In these situations, the vibrations modes interact with each other, presenting a mode shape with a mixed configuration. One last aspect should also be mentioned. If Figure 4.6 is observed carefully, it is possible to verify that the frequency of the 1 FS mode, which does not contain any gyroscopic effect, also increases with the rotor speed. This situation is also noticeable for the centre lines of the whirl modes (solid line) which imply that another effect is present that increases the value of the frequencies too. This phenomenon is called centrifugal stiffening. Centrifugal Stiffening Effect As introduced in the previous section, the centrifugal stiffening effect is responsible for the increase of the rotor modes frequencies with the rotor speed. As referred, this effect is very pronounced in the flapwise modes, being the responsible by the curved path of these frequencies in the Campbell diagram (Figure 4.6). This effect is justified by an increase in stiffness due to centrifugal forces acting on the rotating blades. This centrifugal stiffening is then defined by the additional tensile forces installed on the blades for a  position along the blade (Naguleswaran, 1994): 󰇛󰇜 ..Ω󰇛󰇜  d (4.4) with:  Centrifugal force  Density of the blade  Cross section area of the blade Ω Rotational frequency of the rotor  Blade length  Rotor hub radius  Position of the blade under consideration Alongside with the tensile force presented in the blade due to the centrifugal forces, the influence of the gravity (self-weight) can also be introduced. This effect, which is reflected by an axial force acting on the blade, depends on the position of the blade (Murtagh, Basu et al., 2005). Thus, the effect of the self-weight of the blade should be added or subtracted to its stiffness, either it is a tensile or a compressive force, respectively. However, it is referenced that this gravity effect is negligible when compared to the effect of the centrifugal stiffening (Arrigan, Pakrashi et al., 2011). Structural Behaviour of Wind Turbines 104 Several authors, among which (Naguleswaran, 1994) and (Yoo and Shin, 1998), studied the problem of determination of natural frequencies of simple beams rotating on a hub taking into account the centrifugal stiffening. However these studies focused on simple beams, with constant parameters along the length of the beams, which diverge substantially from a common wind turbine blade. More complex studies were developed for the specific case of the blades, e.g (Hansen, 2003), however they are outside the scope of this work. Nevertheless, a rough estimation of the increase of the natural frequency of a blade due to centrifugal stiffening is presented (Putter and Manor, 1978): ,  .Ω (4.5) with: , Angular frequency of a rotating blade  Angular frequency of a blade at stand-still position  Southwell coefficient: 1.73 (Madsen, Frandsen et al., 1984) Although this effect is important and should be considered when studying the dynamic behaviour of the rotor vibration modes, it is not very noticeable in edgewise modes. This is justified by the softening effect that is also introduced by the centrifugal forces on the linear stiffness of deflection in the rotor plane that almost cancels the stiffening effect (Hansen, 2007). Chapter 4 105 4.2 FOUNDATION SOIL STIFFNESS The consideration of the soil stiffness is an important aspect when trying to accurately simulate the behaviour of tall, slender structures. Thus, wind turbines are no exception. As an example, the guidelines of the Danish standard (Det Norske Veritas (DNV), 2002) refer a reduction between 0 % and 5 % up to a maximum of 20 %, when comparing a model with fixed boundary conditions and another with the consideration of the soil stiffness. A larger variation is presented by Hau (Hau, 2006) for an onshore wind turbine with a slab foundation (Figure 4.7). Figure 4.7 – Influence of the soil stiffness on the first natural bending frequency of a wind turbine tower (Hau, 2006) For the modelling of the soil stiffness, the recommendations defined in the DNV guidelines (Det Norske Veritas (DNV), 2002) are then presented. In order to introduce the effect of the soil, four foundation springs must be included: o Vertical spring stiffness - ; o Horizontal spring stiffness - ; o Rotational (rocking) spring stiffness - ; o Torsional spring stiffness - . It is important to note that soil behaves in a non-linear manner. But instead of using non-linear springs, it is common to model the springs according to the strain level of the soil and then using springs with linear behaviour. DNV (Det Norske Veritas (DNV), 2002) suggests three different levels of dynamic loading (and corresponding shear strains ): o From earthquakes: large shear strains up to 10-2 to 10-1; o From wind and ocean waves: moderate shear strains up to 10-2, typically 10-3; o From rotating machines: small shear strains, usually less than 10-5. Ground shear module E S 10 6 N/m 2 300 200 1000 1st Bending eigenfrequency [Hz] 0 0.1 0.2 0.3 0.4 0.5 ground shear module 106 N/m 2 - sand, loose, round 20 - 50 - sand, loose, sharp 40 - 80 - sand, med. dense, round 50 - 100 - sand, med. dense, sharp 80 - 150 - pebbles, without sand 100 - 200 - brash, sharp 150 - 300 m = 250 t H = 70 m t = 18 mm D = 5.0 m 12 m Structural Behaviour of Wind Turbines 112 Figure 4.12 – Campbell diagram of a 1.5 MW three-bladed rotor, variable-speed wind turbine (adapted from (Gasch and Twele, 2012)) Operating range 510 1520 25 Rotational speed in rpm 1 st Flapw. 1 st Edgewise bending 1 st Tower torsion 2 nd Flapwise bending 2 nd Tower bending Longitudinal Lateral 1 2 3 4 Natural and rotational frequenc y in Hz 1 2 3 4 5 6 7 8 9 0 0.1 0.2 0.3 0.4 0in Hz Operating range 510 1520 25 in rpm 1 st Tower bending 1 st Flapw. bending 1 st Edgewise bending 1 st Tower torsion 2 nd Flapw bending 2 nd Tower bending 1 2 3 4 Natural and rotational frequenc y in Hz 1 2 3 4 5 6 7 8 9 0 0.1 0.2 0.3 0.4 0in Hz Ω Ω Ω Ω Ω Ω Ω Ω Ω Chapter 4 113 4.5 DAMPING In the dynamic characterization of the wind turbine system, other important parameters that need to be determined, besides the value of the natural frequencies, are the damping coefficients. With the aim of illustrate the importance of these parameters on the supporting structure, a simple single degree of freedom (SDOF) structure, defined by its mass , stiffness  and damping , is presented in Figure 4.13 a). Its dynamic amplification factor (DAF – which represents the magnification the structure response suffers with the application of a dynamic load relative to the response to a static force) is defined by (Clough and Penzien, 1995):  1  󰇩1    󰇪2..     (4.10) with:   Applied load frequency  Natural frequency of the structure  Damping ratio of the structure In Figure 4.13 b), the DAF for a simple SDOF structure was calculated for two different values of damping ratios. As can be observed, the DAF value is highly dependent on the damping value. The value of the structural response in resonance is considerably higher for a structure with a damping ratio of 0.2 % (a common value for a wind turbine in an idling or parked situation) than for a structure with  = 4 % (a conservative value for a wind turbine under production). For this reason, it is easy to understand that, for structures subjected to dynamic excitations (such as wind turbines), their damping value is a key-factor to handle with the problem of fatigue. The damping of a wind turbine can be considered as linear sum of different damping sources: structural, aerodynamic, from devices, soil and hydrodynamic. From their nature, the last two are only referred to offshore wind turbines. a) b) Figure 4.13 – a) SDOF structure. b) DAF values for different damping ratios 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 -1 10 0 10 1 10 2 10 3 f load /f 1 DAF ξ = 0.2 % ξ = 4.0 % Structural Behaviour of Wind Turbines 114 4.5.1 STRUCTURAL DAMPING Structural damping is referred to the portion of damping that is intrinsic to the structure. It is due to the absorption of vibrations by internal friction and conversion into heat. Structural damping depends on the type of material (e.g. concrete or steel) and on the type of contacting surfaces (e.g. types of connections in the structure). Also, offshore wind turbines usually present a higher damping value than onshore models, mainly due to the grouted connection (TarpJohansen, Andersen et al., 2009) or higher complexity of the foundation. Thus, different tower concepts and connections lead to different damping values. Typical values of structural damping ratios are in the order of 0.2 % to 0.8 % (Det Norske Veritas (DNV), 2002; Tarp-Johansen, Andersen et al., 2009). 4.5.2 AERODYNAMIC DAMPING One of the most important components of damping is the aerodynamic contribution. Aerodynamic damping has its origin in the wind load acting on the rotor or, more accurately, in the interaction between the wind flow and the motion of the structure. This phenomenon, which occurs for flexible structures, can be a source of instability under certain situations. However, for the along-wind direction, it is favourable and should be accounted for during the design stage and the evaluation of structure integrity along its lifetime. This interaction between wind flow and wind turbines can be explained through the simple description presented in (Kuhn, 2001): “A motion of the tower top in the wind direction (…) results in a smaller angle of attack at the rotor blades [see Figure 3.33] because the apparent out-of-plane velocity component [U󰇛1a󰇜] is reduced by the tower top velocity. A smaller angle of attack corresponds, for attached flow conditions, to lower aerodynamic lift and drag forces [equations (3.24) and (3.25)] and to a reduction of the thrust force (…). Likewise a movement of the nacelle against the wind direction increases both the angle of attack and the thrust force. In both situations the alternation of the thrust is oriented opposite to the disturbing tower top motion and is experienced as aerodynamic damping. (…) For higher angles of attack, stall occurs and the dynamic damping is lower or may even become negative because the slope of the lift curve is reduced. Under such conditions aero-elastic instability can occur if insufficient damping exists.” For the purpose of illustration, Figure 4.14 presents the experimental results for lift and drag coefficients for the NACA 63-415 airfoil obtained in a wind tunnel by Bak et al (Bak, Fuglsang et al., 2000). As can be seen, the lift coefficient has an almost linear increase for the initial range of angle of attack. Then, the slope of the curve starts to decrease until a peak is reached. After this point, the variation of the lift coefficient with the angle of attack becomes negative. The values of drag coefficients for angle of attack of around 15º are considerable low. Chapter 4 115 Figure 4.14 – Variation of lift () and drag () coefficients with the angle of attack (adapted from (Bak, Fuglsang et al., 2000)) Garrad (Kuhn, 2001) presented a simple equation (4.11) for the calculation of the aerodynamic damping for a wind turbine support structure. It assumes that the wind turbine is operating under stationary rotor dynamics at a high tip speed ratio, where the inflow angle () is small and the drag forces are negligible compared to lift forces (Freris, 1990; Salzman and Tempel, 2005). ..Ω 8..  .d d.󰇛󰇜.d   (4.11) with:   Frequency of the first fore-aft vibration mode  Modal mass of the first fore-aft mode  Length of the blade  Airfoil chord From the previous equation, some important aspects should be highlighted. The aerodynamic damping is inversely proportional to the natural frequency (and modal mass of the structure). This mean that structures with different philosophies of tower stiffness design (as presented in section 4.4) will lead to very different values of aerodynamic damping. On the other hand, the increase of the rotational speed of rotor increases the value of this additional portion of damping. Some other important aspects should be also mentioned: o The aerodynamic damping is specially noted for the first bending mode of the tower in the rotor out-of-plane direction (the first fore-aft vibration mode). This is expected since the aerodynamic forces act mainly in this direction; o In the rotor plane direction (the side-side direction) the effect of the aerodynamic damping is expected to be negligible since there is a very low level of aerodynamic forces in this direction; o In idling or parked situations, the effect of aerodynamic damping is expected to vanish for both orthogonal directions. This situation is due to the fact that, in these situations, the blades are usually in a feathered position (with high angles of attack). Nevertheless, some effect could α[º] α[º] -0.5 0.0 0.5 1.0 1.5 2.0 -10 0 10 20 30 0.0 0.1 0.2 0.3 0.4 0.5 -10 0 10 20 30 C D C L Structural Behaviour of Wind Turbines 116 be noted for the side-side direction due to the opposition of the blade to the wind flow in this direction; o Variable and fix rotor speed turbines present different values for aerodynamic damping (Salzman and Tempel, 2005). Fix speed turbines operate at high tip speed ratios in low wind speeds and lower tip speed ratios at high wind speeds (due to the constant rotor speed). For these reasons, in low wind speed the angle of attack is small and, consequently, the flow is attached to the blade. When the wind speed is higher, the angle of attack increases which lead to higher angles of attack and some separation of the flow at the blade. In the case of variable speed rotors, since they operate with their blades close to stall under rated wind speed, there is some flow separation which leads to an aerodynamic damping below the optimal value. For the higher wind speed, the flow stays attached to the blade and the damping is higher. 4.5.3 TOWER DAMPERS One artificial method for additional introduction of damping in the support structure can be achieved with the installation of special devices, typically in the form of a mass pendulum. This technique is a widely implemented solution in tall structures. Ideally, it consists in the attachment of an additional mass, linked to the structure through a spring and a damper (Figure 4.15). The damper system is tuned according to the vibration mode which response is desired to be attenuated. Commonly, solutions consisting in a pendulum immersed in high viscous oil (Damgaard, Ibsen et al., 2013a), a tuned mass damper (Shirzadeh, Devriendt et al., 2013) or a liquid damper (Tarp-Johansen, Andersen et al., 2009) are used in wind turbines, usually installed offshore. The damping value introduced by these devices depends on the implemented damper system and on the tuning accuracy. In (Colwell and Basu, 2009), a numerical study about the efficiency of a tuned liquid column damper in an offshore monopile wind turbine is presented. Figure 4.15 – Idealized structural system with the damper system (index 2) attached to the main system (index 1) 4.5.4 SOIL DAMPING The operation of a wind turbine introduces vibrations at the ground level, causing cyclic motion of the surrounding foundation soil. In offshore wind turbine, the effect of the soil in the introduction of damping should be analysed. It is considered one of the most complex components of damping to be determined (Germanischer Lloyd (GL), 2005). Soil damping is formed by a combination of two parts: geometrical dissipation and material damping. Geometrical dissipation is due to wave propagation into the soil. However, it is referred that this effect is insignificant at frequencies below 1 Hz (Andersen, 2010). On the other hand, material damping is due to the internal friction of soil grains and should be accounted for. k 1 c 1 k 2 c 2 m 1 m 2 Chapter 4 117 The damping introduced by the soil is dependent on the type of soil and also, to some extent, on the type of foundation. Along with the inherent complexity of this phenomenon, it is comprehensible that there is a quite wide range of values between published works. Damping ratio values between 0.23 % and 1.00 % for monopile foundations are referred in (Tarp-Johansen, Andersen et al., 2009; Versteijlen, Metrikine et al., 2011; Damgaard, Ibsen et al., 2013a). Damgaard et al (Damgaard, Ibsen et al., 2013b) also studied the influence of soil damping in an offshore prototype wind turbine with a bucket foundation and found a value of 0.16 % for the damping ratio during power production. 4.5.5 HYDRODYNAMIC DAMPING In offshore wind turbines, there is also another component of damping, the hydrodynamic damping. This component is essentially constituted by two terms: one due to wave radiation and another due to hydrodynamic drag. In order to assess the relative importance of each term, the value of the KeuleganCarpenter number is usually analysed: .  (4.12) with:  Flow velocity amplitude  Wave period  Characteristic length (diameter of cylinder section for a pile) For small values of  (below 2 (Naess and Moan, 2012)), the radiation damping is dominant; while for high value of , the drag component prevails. Thus, the contribution of each damping term depends on the type and size of the foundation solution (and also on the sea conditions). Some authors refer the larger contribution of the radiation damping with respect to the viscous drag component for monopile wind turbine foundations (Tarp-Johansen, Andersen et al., 2009; Shirzadeh, Devriendt et al., 2013). Some typical values for the wave radiation component of the hydrodynamic damping are present in published works. Leblanc and Tarp Johansen (LeBlanc and Tarp-Johansen, 2011) present a value of 0.12 % for the damping ratio of an offshore wind turbine with a pile diameter of 4.7 m, with a water depth of 20 m and a natural frequency value of 0.3 Hz. Also in (Germanischer Lloyd (GL), 2005), the value of 0.11 % for damping ratio of a monopole wind turbine is presented. Likewise, Tarp-Johansen et al (Tarp-Johansen, Andersen et al., 2009) present a value of 0.22 %, following a numerical procedure. Besides the hydrodynamic effect of the pile, the presence of mooring lines in floating wind turbines also represents an important contribution to the damping of the system (Hall, Buckham et al., 2013). Structural Behaviour of Wind Turbines 118 4.6 CYCLIC VIBRATION LOADS As mentioned earlier, wind turbines are subjected to a large variety of dynamic loads (Manwell, McGowan et al., 2010). In this section, a special reference is made to cyclic loads. These loads hold a large importance when studying the response of the structure. With a dynamic monitoring system, it is expected to capture the resonance peaks of the structure in order to identify its natural frequencies. However, as cyclic loads are acting on the structure, some peaks will be present in the records that do not correspond to the dynamic properties of the structure. For this reason, there is the need for previous identification of these peaks. There are mainly three sources of this kind of loads: aerodynamic forces, mass unbalance or wave forces. In Figure 4.16, the frequency domain spectrum response (acceleration) at the top of a three-bladed, fixed-speed wind turbine (obtained in a numerical analysis) is presented. This turbine was subjected to a three-dimensional turbulent wind field. As can be seen, several peaks spaced by 3Ω (highlighted by the red dashed line) are easily detected. Figure 4.16 – Frequency domain spectrum of the acceleration of the top of the tower of a wind turbine due to turbulent wind inflow In the situation of the Figure 4.16, the cyclic loads are only due to aerodynamic forces of three types: o Rotational sampled turbulence spectrum: As already explained in section 4.3, for each revolution, each blade passes through a gust once. This will lead to an excitation of 1Ω for the blades and of .Ω for the structures that support the rotor (3Ω in the case of Figure 4.16); o Tower shadow: For an up-wind rotor, the presence of the tower disturbs the wind flow, retarding the wind speed. The decrease in the wind speed leads to a decrease of the force on the blade every time it passes in front of the tower, causing a cyclic excitation on the blade (and, consequently, on the tower). For down-wind rotors, the effect of the tower is more severe. The retardation of the flow is felt at larger distances and lead to strong excitations; o Vertical wind shear: The mean wind velocity increases with height (Figure 4.17). With today’s large rotor diameters, blades are long enough to experience a reasonable variation of wind speed from top to bottom position. Thus, blades will complete a cycle from the maximum to the minimum mean wind load in each rotor revolution. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 -6 10 -4 10 -2 10 0 Frquency [HZ] Amplitude Tower 1 st natural frequency Chapter 4 119 Figure 4.17 – Vertical wind shear Unbalanced rotors represent another source of cyclic loads. It leads to a rotating force that can excite lateral vibrations of the nacelle and tower (Gasch and Twele, 2012). As examples of causes of unbalanced rotors, manufacturing defects and accumulation of ice can be pointed out. In Figure 4.18, a comparison of the response between an unbalanced mass rotor and a balanced rotor is shown. The time history was obtained through a numerical analysis, where the unbalanced rotor was defined by an abnormal mass at the tip of one of the blades with the purpose of evidence the described phenomenon. As can be observed, the unbalance presented in the rotor introduced an excitation with a frequency of 1Ω in the support structure. Figure 4.18 – Time history of the tower top accelerations for a balance and unbalance mass rotor For offshore wind turbines, another source of excitation forces needs to be accounted for. Wave excitation acts on support structures in a wide range of frequencies, usually bellow the tower natural frequency (Tempel, 2006). Thus, time histories of the motion of an offshore tower will likely record these excitations, which need to be analysed and discharged when a dynamic continuous monitoring system is installed in a wind turbine. The usual wave excitation range of frequency is illustrated in Figure 4.19. As can be seen, the frequencies of excitation are not very well defined as are for aerodynamic forces. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 -4 10 -2 10 0 10 2 Frequency [Hz] Amplitude Balanced rotor Unbalanced rotor Structural Behaviour of Wind Turbines 120 Figure 4.19 – Range of frequencies of wave excitation on an offshore wind turbine (Tempel, 2006) Frequency [HZ] Ocurrence [%] 1Ω 3Ω f 1 100 80 60 40 20 0 0.20 0.4 0.6 0.8 1.0 1.2 Chapter 4 121 4.7 NUMERICAL MODEL OF A WIND TURBINE A numerical model of a wind turbine was developed with the HAWC2 software (Larsen and Hansen, 2007) in order to illustrate some of the methods presented throughout this thesis. HAWC2 is an aeroelastic code developed at Risø DTU and intended to calculate wind turbine response in the time domain. It uses a multibody formulation to model the wind turbine structure through beam elements, allowing to model each component of the wind turbine as an independent body. Each body is implemented in the model according to the finite-element theory. HAWC2 code allows simulating the structural response of wind turbines at onshore and offshore environments, subjected to hydrodynamic and aerodynamic loading. Since the main case study of this work is an onshore wind turbine, only aerodynamic loads were considered. The aerodynamic model implemented in the HAWC2 code is based on the blade element theory (briefly introduced in Chapter 3). The implemented model is extended to account for the dynamic and skew inflow, wind shear effect, the effect due to large deflections of the blades, tip loss effect and dynamic stall. In addition, the tower shadow effect, referred in section 4.6, is also included. The developed numerical model of the onshore wind turbine is based on the NREL 5MW reference wind turbine (Jonkman, Butterfield et al., 2009), which is available on (HAWC2 web site, 2013). This model was used as a basis for the numerical model described in the case study of the section 7.3. The NREL 5MW reference wind turbine is a conceptual model of a representative utility-scale wind turbine. It is a three-bladed, upwind rotor with a variable-speed turbine and with pitch control mechanism. The power curve and the relationship between the wind speed and the rotor speed of the NREL 5MW wind turbine is presented in Figure 4.20. The main dimensions of the model are presented in Figure 4.21, alongside with the position of the sensors considered to collect the accelerations of the structure. Figure 4.20 – Power curve (in blue) and relationship between rotor speed and wind speed (in red) of the NREL 5MW Figure 4.21 – Illustration of the numerical model of the NREL 5MW and position of the accelerometers The aeroelastic analysis was performed for a time length of 700 s, with a time step of 0.02 s. The first 100 s were disregarded to avoid transient responses from the start of operation of the turbine. 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 Wind speed [m/s] Power Output [kW] 0 5 10 15 20 25 0 3 6 9 12 Rotor speed [rpm] + 0.000 + 30.000 + 60.000 + 87.600 S1 S2 S3 126 m 90 m Operational Modal Analysis of Wind Turbines 128 Nevertheless, OMA presents some disadvantages inherent to its concept (Magalhães and Cunha, 2011): o Although the excitation is assumed to be of broad band nature, the frequency content may not cover the whole spectrum of interest, mainly in the case of structures with high natural frequencies. Also, if the excitation does not correspond to a flat distribution of energy along the frequency spectrum, some misidentification might occur; o The modal mass is not estimated. OMA has been widely used in the last years in several engineering domains. In civil engineering, this technique has been applied in diverse structures. Bridges (Cunha, Caetano et al., 2001), (Caetano, Magalhães et al., 2007), (Brownjohn, Magalhães et al., 2010), dams (Rodrigues, 2004)) and buildings ((Ventura, Finn et al., 2003), (Shi, Shan et al., 2012), (Gentile and Saisi, 2007) are among the most commons examples of structures tested with OMA methodology. In mechanical engineering, OMA is also applied in different structures, such as helicopters (Peeters, Cornelius et al., 2007), (Ameri, Grappasonni et al., 2013), aircrafts (Mevel, Benveniste et al., 2006), (Hermans and Auweraer, 1999) or vehicles (Goursat, Döhler et al., 2010), (Hermans and Auweraer, 1999). Chapter 5 129 5.2 APPLICATION OF OMA TO WIND TURBINES The dynamic behaviour of wind turbines is a major concern, as exposed in the previous chapters. Thus, an experimental dynamic characterization of the system became a required tool in order to prevent possible resonance effects. Wind turbine presents three important particularities that highlight the importance of application of OMA in these structures: o Considering the typology and size of wind turbines, it is easy to understand the difficulty in providing means to adequately excite these structures; o Wind turbines are located in windy locations. Thus, wind can be used as an ambient source of excitation (with a broadband spectrum); o It is important to adequately identify the modal characteristics of the structural system, both in parked and in real operation conditions, since rotor operation can introduce important variations in these properties. Therefore, it is not surprising that modal identification of wind turbines played an important role in the development of OMA. The first formalized modal testing of blades and turbines began in the late 1970s (Carne and James Iii, 2010). In 1982, (Carne, Lobitz et al., 1982) developed a finite element procedure to be applied to vertical-axis wind turbines. In order to validate the procedure, an input-output test was performed in a 2 m height, research vertical axis wind turbine at parked condition and at different operating speeds. In the parked test, the excitation was achieved through a traditional impact hammer and accelerometers were used as sensors. For the tests realized under operation, it is referred that there were some difficulties in exciting the structure (Carne and James Iii, 2010). The solution adopted consisted on a pretensioned cable attached between the tower and one blade. When the cable was suddenly released, it created a broad-brand step-relaxation excitation (Carne and Nord, 1983). In this test, accelerometers were also used, alongside with strain gauges. The identified modal parameters consisted in frequency values, damping ratios and mode shapes, and the correlation obtained between numerical and experimental results was very good. However, the procedure for the step-relaxation technique was very time-consuming because, every time a new test was performed, the turbine had to be brought to parked condition. Later in 1986, Carne et al performed a modal test of the 110 m height Éole VAWT in parked conditions (machine introduced in Chapter 2) (Carne, Lauffer et al., 1988). Since it was extraordinary higher than the 2 m height VAWT previously tested, a different approach was followed in this test: a traditional input-output test, where the excitation consisted in two forces of 45 kN and 135 kN applied on one blade and on the tower, respectively; and a second test in which the wind turbine was only subjected to wind loading and only the structural response was recorded. The later consisted in one of the first ambient vibration tests in which a full modal analysis was performed, including mode shapes, frequencies, and damping values (Carne and James Iii, 2010). In this test, four separate setups of response measurements were recorded, with four reference channels repeated in every setup. Then, autoand cross-spectral densities were computed in order to extract the modal properties of the Éole turbine. The obtained results showed a very good correlation between the two experimental tests Operational Modal Analysis of Wind Turbines 130 (Carne, Lauffer et al., 1988), evidencing the advantages of ambient vibration tests (considerably faster and more practical) with regard to forced vibration tests. The success achieved with the previous application led to the development of a new identification method named Natural Excitation Technique (NExT) (James, Carne et al., 1993). This technique was further validated and used in numerical (FloWind Corporation 19 m VAWT) and experimental tests, both in parked - FloWind Corporation 19 m VAWT - and in operation – DOE/ Sandia 34 m VAWT - situations (James, Carne et al., 1993). Reference should also be made to the application of NExT to a rotating 100 kW horizontal axis wind turbine (James, 1994). After these initial tests, other authors have also performed some modal identification analysis on wind turbine structures. Molenaar (Molenaar, 2003) performed an experimental modal test on a 750 kW horizontal axis wind turbine, under parked conditions, in order to compare the results with a numerical model. For the test, the wind turbine was excited through the step-relaxation technique by applying a static load on the tower top and the structural response was measured with 19 accelerometers mounted both on tower and blades. In (Osgood, Bir et al., 2010), continuing earlier works (Osgood, 2001), a parked 600 kW three-bladed horizontal axis wind turbine was experimentally tested following both forced and ambient vibration test procedures. For the forced vibration test, two independent hydraulic actuators were used, which excited the structure at the top in both orthogonal directions. The turbine was heavily instrumented with accelerometers, totalling 75 channels distributed in the tower, rotor and drive train. A very good correlation was obtained with the two tests (although it was possible to detect additional modes in the forced vibration test). (Hansen, Thomsen et al., 2006) explored different excitation techniques for wind turbine testing. Experimental results obtained with two different types of harmonic excitation were confronted with the results from an ambient vibration test. The harmonic excitation was induced by blade pitch angle variation and by electrical torque variation. However, it was concluded that the excitation of wind turbines with these techniques presents some problems, namely: o The excitation of high-frequency and highly damped modes is not technically possible due to limitation of the blade pitch actuators; o The excited structure vibrations are not pure modal vibrations and the estimated damping is therefore not the actual modal damping. Since it is not possible to isolate the desired modes, the estimation of damping for modes with close frequencies will result in considerable errors. In the opposite way, the authors (Hansen, Thomsen et al., 2006) concluded that the results obtained with the adopted output-only tool confirmed its suitability for identifying closely-spaced modes. Griffith et al (Griffith, Mayes et al., 2010) conducted a modal identification test on a small 60 kW VAWT under parked conditions. As in the above references, an ambient vibration and forced vibration (excitation from an impact force, from step-relaxation and from human random excitation) were performed and both accelerometers and strain gauges were used. The results revealed good agreement between all the tests. Chauhan et al (Chauhan, Tcherniak et al., 2011) and Carcangiu et al (Carcangiu, Tcherniak et al., 2012) experimentally studied a 3 MW, 100 m diameter wind turbine. In this work, OMA techniques were applied in order to extract the main vibration modes of the tower and rotor. For that purpose, Chapter 5 131 several accelerometers were placed on the tower, nacelle, gearbox and generator. Several vibration modes were identified and presented for different rotor speed regimes. A numerical aeroelastic model was also developed and the results obtained were correlated with the experimental ones. Ozbek et al (Ozbek, Rixen et al., 2010; Ozbek and Rixen, 2012) monitored the dynamic response of a 2.5 MW HAWT using conventional instrumentation (strain gauges) and optical measurement systems (laser interferometry and photogrammetry). The wind turbine was tested under parked (both with strain gauges and laser interferometry) and rotating (both with strain gauges and photogrammetry) conditions. Although good results were achieved, two important drawbacks associated with the use of optical measurement systems are referred: laser interferometry is not suitable for rotating conditions testing; and the available camera systems used for the photogrammetry testing had a reduced memory, allowing to record only small measurement segments. Also Marinone et al (Marinone, Cloutier et al., 2014) performed both experimental and operational modal analysis on two 225 kW wind turbines, in parked condition. A very complete instrumentation was used, with 80 accelerometers installed on the blades, hub, nacelle and tower and 6 seismic accelerometers installed at the foundation. The authors of the study were able to identify 18 vibration modes in the 0 – 15 Hz frequency range and the correlation between the results from the EMA and OMA was very good. Apart from the entire wind turbine structure testing, blades properties are important features that need to be identified (Yang and Sun, 2013). (Thomsen, Petersen et al., 2000) tried to identify damping of edgewise blade modes of a 600 kW wind turbine under operation. For that purpose, the authors installed eccentric rotating masses in the nacelle to excite the desired modes. Modal identification tests are also often conducted under laboratory conditions (Griffith, Smith et al., 2006; Griffith and Carne, 2010; White, Adams et al., 2010). Yang and Allen (Yang and Allen, 2012) also performed a modal analysis on a small wind turbine blade based on a laser scanning technique. The test was performed under parked conditions and the authors accomplished to identify some vibration modes (frequencies and mode shapes). Another important field of application of OMA techniques on wind turbines is in offshore situations, since different foundation designs lead to different structural behaviours (section 3.1.1.5). Moreover, the contribution of the different types of damping is also difficult to predict (see section 4.5). Thus, the extraction of the modal parameters under operating conditions reveals as an essential tool for the correct comprehension of the dynamic behaviour of these structures. Some work in this area has already been published. In (Devriendt, Magalhães et al., 2014), the modal identification of a 3.0 MW offshore wind turbine with monopile foundation is introduced. This study analyses the acceleration data recorded during 2 weeks (under non-operating conditions). The modal results obtained were then confronted with collected environmental data, such as tidal level and wind speed. This wind turbine is also study in section 5.9 of the present work. In (Shirzadeh, Devriendt et al., 2013), the same wind turbine is experimentally tested. The main goal of the test was to calculate the damping value of the fundamental fore-aft (FA) vibration mode. For this purpose, both ambient and rotor-stop tests were performed. Rotor-stop tests (sometimes named “overspeed stop tests”) are a type of forced vibration test, in which the turbine is operating at a normal situation until a sudden pitch-out of the blades (Figure 5.1). In this procedure the wind turbine is highly excited by the sudden absence of aerodynamic loads on the blades. Furthermore, the Operational Modal Analysis of Wind Turbines 132 aerodynamic damping contribution from the rotor almost does not interfere in the decay response of the structure, since the blades are pitched-out. The authors were able to identify the first pair of vibration modes (in FA and SS directions) and the obtained value of the damping in the FA direction was similar in both ambient and forced vibration tests. An aeroelastic model was also developed, in which the two tests were simulated with good results. a) b) Figure 5.1 – Example of fore-aft acceleration a) and blade pitch variation b) on a rotor-stop test (adapted from (Damgaard, Ibsen et al., 2013)) In (Damgaard, Ibsen et al., 2013) the dynamic characteristics of offshore wind turbines with monopile foundations are also studied. In this study, the value of damping of the fundamental mode for the sideside direction was investigated. Once again, ambient vibration and rotor stop tests were performed with the aim of extracting frequency and damping values for this vibration mode. In the analysis of the results, some considerations are also made concerning the damping introduced by the soil. Like the previous authors, (Versteijlen, Metrikine et al., 2011) studied the damping effect present in an offshore wind turbine located in the Burbo Banks wind farm. 12 rotor stop tests were realized in order to assess the influence of the soil. In (Ibsen and Liingaard, 2006), a different type of offshore wind turbine is studied. A 3 MW wind turbine with a prototype suction caisson foundation is tested in three different conditions: idling; without blades; and without blades and nacelle. For the test, 15 accelerometers were installed along the tower, and the structure was subjected to ambient excitation. The experimental results were compared with a numerical model of the structure. Fore-Aft Acceleration [m/s 2 ] -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 0 10 20 30 40 50 60 70 80 90 Blades Pitch [°] Time [s] Time [s] 20 40 60 80 100 120 020 40 60 80 100 120 0 Chapter 5 133 5.3 PARTICULARITIES OF OMA APPLICATION TO WIND TURBINES In the previous section, the main modal identification tests performed on wind turbines were presented. Although some refer to wind turbines under operation, there is an important part that only discusses the modal properties of the structure under parked or idling condition. This might seems a contradiction to one of the main advantages of OMA techniques – the ability to extract the modal characteristics under real operating conditions - but there is one main reason for that: the application of OMA to wind turbines under operation violates some of its basic assumptions (Tcherniak, Chauhan et al., 2010a; Ozbek, Meng et al., 2013). There are mainly four assumptions for the applicability of OMA (Tcherniak, Chauhan et al., 2010a): o The structure does not vary in time; o The forces should have broadband frequency spectra; o The forces have to be uncorrelated; o The forces have to be distributed over the entire structure. When in operation, wind turbines can be idealized as a set of connected substructures with rotations with respect to each other: the tower is fixed, the nacelle rotates on the top of the tower and the rotor spins relative to the nacelle. This is an obvious case of violation of the time invariance assumption of the structure. Addressing the previous assumptions related to the input force, it is correct to assume that the wind, as exciting force, would validate all the conditions listed. This is the reason why OMA works in a straightforward way for wind turbines under parked situations: the structure is fixed (there is no relative movement between substructures) and the acting wind is the only excitation force. However, when the rotor is operating, the spectrum of the forces acting on the rotor changes from a flat spectrum to one with several peaks (as explained in Chapter 4). Tcherniak et al (Tcherniak, Chauhan et al., 2010a) presents an analytical study in which evidences the violation of the temporal and spatial randomly distributed nature of the excitation forces, due to the effect of the operating rotor. The authors studied the temporal auto-correlation at different blade radius. The main results are presented in Figure 5.2. Figure 5.2 – Normalized power spectral density of the temporal auto-correlation functions computed for points on the same blade (for different radii cases) (adapted from (Tcherniak, Chauhan et al., 2010a)) 0.001 0.01 0.1 1p 2p 3p 4p 1 10 -2 10 -1 10 0 10 1 10 2 Power density spectra r = 0 r = 26.42m r = 54.40m Frequency [Hz] Operational Modal Analysis of Wind Turbines 134 As can be seen, the power spectral density functions (for radii higher than 0) are not flat as in a common wind spectrum (Kármán, 1948). Moving from the centre of the rotor to the blade tip, peaks with a frequency equal to the frequency of rotation of the rotor (and its harmonics) become more pronounced. This is motivated by the same phenomena exposed in Chapter 4: o Every time a blade passes through a region with a determined wind speed (gust), the action on the blade is somehow “similar” to the prior passage (considering the gust is long enough) – this fact justifies the existence of the peaks; o With the increase of radius of the point on the blade, the ratio between tangential speed of the point and the mean wind speed increases – this fact justifies the increase of the peaks with the increase of the radius of the point. This is the reason why the second assumption presented earlier is violated. On the other hand, the results obtained for the point with  = 0, since it is stationary, do not present any peak. This is the reason why this assumption is not violated under parked conditions. The third assumption of OMA (spatial non-correlation of the input excitation) was also investigated in (Tcherniak, Chauhan et al., 2010a). For this study, the authors computed the coherence () between the wind speed fluctuations at different points ( and ) on the same and different blades:  |󰇛󰇜| 󰇛󰇜.󰇛󰇜 (5.1) with:   Coherence  Autoor cross-spectrum of wind turbulence at points i and j (respectively, if ij and ij ) The results presented in (Tcherniak, Chauhan et al., 2010a) for points with different radii are shown in Figure 5.3. It is once again evident that several peaks are presented at rotor frequency (and its harmonics), leading to the violation of the third OMA assumption. Figure 5.3 – Coherence functions for 2 points under different study scenarios (adapted from (Tcherniak, Chauhan et al., 2010a)) 0 1p 2p 3p 4p 1 6p 7p 8p 9p 2 11p 2.5 0 0.2 0.4 0.6 0.8 1 Frequency [Hz] Coherence γ 2 AB γ 2 AB (r A = 26.42m , r B = 54.40m , same blade) γ 2 AB (r A = 26.42m , r B = 54.40m , diff. blades ) γ 2 AB (r A = 26.42m , r B = 26.42m , diff. blades ) γ 2 AB (r A = 54.40m , r B = 54.40m , diff. blades ) Chapter 5 135 One important observation that should be noted is the wide shape of the peaks in Figure 5.3 (and also noted in Figure 5.2). This situation, in which the peaks have “thick tails”, leads to the spread of the assumption violation for a quite wide frequency band around the harmonics. Contrary to a situation with narrow peaks, in which the signal is only “polluted” in a very narrow band of frequency around the harmonic, Figure 5.3 highlights the fact that the band between harmonics in which the coherence is approximately 0 is very narrow. This fact may increase the difficulty in applying OMA to wind turbines. The last assumption, in which is referred that the forces have to be distributed over the entire structure, is almost fully fulfilled. Although the top of the supporting structure is subjected to a considerable higher loading when in operation (due to the rotor), the remaining part is also excited by the wind. Hence, this assumption does not introduce any additional concern in the modal analysis of wind turbines. In spite of these difficulties, it is still possible to apply OMA to operating wind turbines. Section 5.4 describes the modal identification algorithms used in this work. Some possible solutions to overcome the problem of the assumptions violation are presented in section 5.6. Operational Modal Analysis of Wind Turbines 136 5.4 OUTPUT-ONLY STOCHASTIC IDENTIFICATION METHODS In this section, an overview of the output-only algorithms implemented in Matlab (MathWorks, 2012) and used in this work is presented. 5.4.1 ALGORITHMS BASED ON IDENTIFICATION OF STATE-SPACE MODELS This section introduces two different time-domain, parametric modal identification algorithms: the SSI-COV and the SSI-DATA. They both aim to identify a state-space model of the structural system from the measured signals (in this case, accelerations). For a better understanding of the methods, some considerations about state-space models and Kalman filters are also presented in this section. 5.4.1.1 State-Space model A stochastic state-space model is an alternative time domain formulation of a dynamic system. In its discrete version, a stochastic state-space model is characterized by (Juang, 1994): .. (5.2) .. with:  State vector (which contains the displacement and velocity vectors of the system)  Output vector (which contains the measured output values)  Input vector  State matrix  Input matrix  Output matrix  Direct transmission matrix  Vector containing noise due to disturbances and modelling inaccuracies  Vectors containing noise due to sensor inaccuracy Among all the elements previously presented, a special reference should be made to the  matrix since it characterizes the structural system (it is possible to extract the modal properties of the system from its eigenvalues and eigenvectors). This is the reason why the main goal of these algorithms is to estimate this matrix. Chapter 5 137 In situations in which the inputs are unknown, as is the case of OMA, the terms related to  can be grouped together with the noise terms. In this situation, equation (5.2) can be rewritten as: . (5.3) . The state-space model from equation (5.2) can also be defined in a modal basis. Considering a special case of similarity transformation: Ψ., (5.4) with: Ψ Matrix with eigenvectors of  in each column , Modal state vector at  instant it is possible to define the modal state-space model: ,Λ.,Ψ. (5.5) ., with: Λ Modal state matrix (ΛΨ..Ψ)  Modal output matrix (.Ψ) One important property of the modal state-space model is that, due to the diagonal structure of the Λ matrix, it is possible to decouple the contribution of each vibration mode to the response of the structure. In the same way, the  matrix contains the observable components of the mode shapes in each column, in accordance with the eigenvalues from the Λ matrix. Due to these characteristics, it is possible to reduce the order of the state-space model in order to consider only the desired modes. This property will be applied and discussed in section 5.5.2.3. 5.4.1.2 SSI-COV algorithm The COVariance driven Stochastic Subspace Identification method is a time-domain, parametric method that identifies a stochastic state-space model from the output covariance matrix (or correlation, since the mean value of the signals is assumed to be zero). The algorithm presented in this work was developed and described in (Peeters, 2000). Operational Modal Analysis of Wind Turbines 144 The version of SSI-DATA algorithm implemented in this work is presented in (Peeters, 2000), which in turn is based on (Overschee and Moor, 1996). The SSI-DATA algorithm starts with the organization of the data in an Hankel matrix: 1 √           …     …  … … … …    …    …    …  … … … … . . … .         󰇩|  |.󰇪󰇩 󰇪↕↕. . "" "" (5.21) with: 2.1 Total number of data points (per channel)  Number of outputs sensors  Number of reference outputs  Parameters of the method to be defined by the analyst It is common to divide the Hankel matrix into a past reference and a future part, the upper and lower part of the matrix, respectively. Considering this division, the projection operation can then be defined as: / 󰇡󰇢 (5.22) The definition of the  is a very important aspect of the algorithm. In fact, the SSI-DATA algorithm relies on fact that the  can be factorized as product of the extended observability matrix  and the Kalman filter state sequence : .  . … ..󰇟     …   󰇠 (5.23) The most computational efficiency way to calculate  is through the application of the 1 factorization to the Hankel matrix: 󰇩 󰇪. (5.24) 1 In a  factorization, the  is an orthonormal matrix (..) and  is a lower triangular matrix. Chapter 5 145 Omitting the columns filled only with zeros in the  matrix, the  and  matrices can be organized as follow: . 󰇛1󰇜 ↔ ↔ ↔ ↔ ↔ .   󰇛1󰇜↕↕↕↕ 0 0 0   0 0    0     .              ↕↕↕↕.   󰇛1󰇜 (5.25) Computing the singular value decomposition of , the following factorization is obtained: ..󰇟󰇠.󰇣0 0 0󰇤.󰇩 󰇪.. (5.26) From the factorization process,  and  can be calculated according to: ./ (5.27)   . (5.28) On the other hand, the projection of future row spaces into past row spaces can be expressed with the help of the  and  submatrices:   . (5.29) After the estimation of , it is necessary to compute the state sequence :    .  (5.30) The extended observability matrix  is obtained after deleting the last  rows of , while   is given by:  󰇟 󰇠.󰇩 󰇪 (5.31) Operational Modal Analysis of Wind Turbines 146 At this point, the system matrices can be estimated through the application of the system of equations from the state-space model (see equation (5.3)):  |󰇣󰇤.    (5.32) where the | matrix can be defined resorting, once again, to the  and  submatrices: |  0   .󰇯  󰇰 (5.33) Once all matrices all calculated, equation (5.32) can be used to estimate matrices  and . Since it is an overdetermined problem, it can be solved through: 󰇣󰇤󰇩   |󰇪.   (5.34) Once state-space matrices  and  are obtained, the modal properties of the structural system can be calculated with the already presented equations (5.13) to (5.16). An important property of the SSI-DATA algorithm is that it allows to recover the noise covariance matrices ,  and  from the state-space model equations:    .󰇟󰇠 (5.35) Like in the case of the SSI-COV, it is common to calculate the state-state matrices ( and ) for different orders. Then a similar strategy is followed, where the results from the different orders are compared in order to identify the stable poles. Example The simulated acceleration time series from the NREL 5MW wind turbine were used to illustrate the SSIDATA algorithm. For this analysis, three sensors were considered as reference and a value of  = 80 was used. The stabilization criteria defined in the SSI-COV example were also used in this example. The obtained stabilization diagram is presented in Figure 5.7. The damping values of the stable poles are shown in Figure 5.8. Chapter 5 147 Figure 5.7 – Stabilization diagram obtained with the SSI-DATA method (average spectra at the background) Figure 5.8 – Modal damping ratio estimates for the stable poles The values of natural frequencies and damping ratios of the two founded vibration modes are shown in Table 5.2. The values are very similar to those previously obtained with the SSI-COV algorithm. Once again, the contribution of the aerodynamic damping is noticeable for the 1st vibration mode. Table 5.2 – Modal properties: SSI-DATA results vs reference results SSI-DATA results Reference results Mode Natural frequency [Hz] Damping ratio [%] Natural frequency [Hz] Damping ratio [%] 1 0.332 6.85 0.333 0.24 2 2.625 1.98 2.686 1.91 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 Frequency [Hz] Model Order 3Ω 6Ω 9Ω 12Ω All poles Stable Freq. Stable Damp. MAC Stabilization diagram 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 Frequency [Hz] Damping ratio [%] Stabilization Frequency - Damping Operational Modal Analysis of Wind Turbines 148 5.4.2 P-LSCF The third and last identification method covered in this work is the poly-reference Least Squares Complex Frequency Domain method (p-LSCF), also known as Polymax. This is a parametric, frequency-domain method which was initially developed in order to identify the modal characteristics of a system from its frequency response functions (Guillaume, Verboven et al., 2003; Peeters, Auweraera et al., 2004). Later, the previously developed methodology was adapted by (Peeters and Auweraer, 2005) to work based on the output half-spectrum functions, an output-only version of this method. In this work, only this last version is presented. 5.4.2.1 Half-Spectrum Prior to the application of the p-LSCF routine, the half spectrum matrix should be estimated. Considering the input excitation as white noise, the input spectrum () is constant and not dependent on frequency, and the output spectrum is obtained by: 󰇛󰇜󰇛󰇜..󰇛󰇜 (5.36) Considering the modal decomposition of the frequency response function (Heylen, Lammens et al., 2007), 󰇛󰇜. .∗. .∗   (5.37) with:  Number of vibration modes in the frequency range under analysis  Observable components of mode shape   Modal participation factor of mode   System poles (,∗..  1.) it is possible to define the output spectrum as a summation of the contribution of structural vibration modes (Peeters, 2000): 󰇛󰇜. .∗. .∗. .∗. .∗   (5.38) with:  Operational reference vector of mode  Chapter 5 149 As can be observed, the previous equation has four poles for each mode which impose the use of models with twice the order of the system defined by equation (5.37). For this reason, the positive (or half) spectrum is usually used: Since the frequency response function (5.37) and the half spectrum (5.39) present similar modal decomposition, they both can be parameterized in exactly the same way (Peeters and Auweraer, 2005). In this work, the Correlogram approach, restricted to the positive time lags of the correlation function, is used for the estimation of the half spectrum: 󰇛0󰇜 2󰇛.Δ󰇜...   (5.40) with:  Number of time lags to analyse With the Correlogram approach, an exponential window should be applied to the correlations before the use of equation (5.40). This window is important mainly for two reasons: to reduce the effect of leakage and to reduce the influence of the higher time lags, which have a larger variance (Peeters and Auweraer, 2005). The used exponential window follows the equation: .., for 1 (5.41) with:  Decay rate of the window The application of the exponential window leads to biased values of damping for the computed poles. For this reason, the damping values should be corrected according to (Cauberghe, 2004):   (5.42) 5.4.2.2 Right Matrix-Fraction Description The p-LSCF method uses a mathematical representation of the dynamic system called right matrixfraction description (RMFD). The RMFD is used to model linear time-invariant systems, 󰇛󰇜. .∗. .∗   (5.39) Operational Modal Analysis of Wind Turbines 150 parameterizing the transfer function as a right division of two polynomial matrices  and  (Reynders, 2009): 󰇛󰇜.󰇛󰇜 (5.43) 󰇛󰇜   ..󰇯   .󰇰 with: ,  Polynomial matrices ,  Model order of the  and  matrices, respectively  Complex variable For the implemented version of the p-LSCF method, it is of great importance to refer the conversion from a RMRD model to a state-space model (Reynders, 2009). Assuming that matrices  and  have the same order () and that the degree of the polynomial with the determinant of 󰇛s󰇜 is equal to. (where  refers to the number of structure inputs), the matrices , ,  and  from the statespace model are obtained through (the subscript ∗ is dropped for simplification): . . … ..  0 … 0 0 ⋮ ⋱ … ⋮ ⋮ 0 0 …  0  (5.44)  0 .. … .. . with:  State matrix (of order )  Input matrix (of order )  Identity matrix Chapter 5 151 5.4.2.3 p-LSCF algorithm The p-LSCF method models the half spectrum matrix using a right matrix-fraction description (RMFD) in the discrete-time frequency domain, the z-domain (Magalhães, 2010). This is achieved through the use of matrices  and . Considering both matrices as polynomials of the same order , they are defined as: .󰇛󰇜󰇯....   󰇰.󰇯....   󰇰 (5.45) Bearing in mind that these matrices contain the modal parameters of the dynamic system, the main goal of this method involves the calculation of  and  that reduce the approximation error associated to equation (5.45). The nonlinear least squares problem can be simplified to a linear problem according to (Guillaume, Verboven et al., 2003): 󰇯....   󰇰.󰇯....   󰇰 (5.46) Considering the polynomial basis functions evaluated at each frequency (ω) organized in one row with (1) components: ΩΩ Ω … Ω󰇟... ... … ...󰇠 (5.47) equation (5.46) can be re-written as: Ω.       ⋮      Ω.Ω.… Ω..  ⋮  (5.48) with:  Line of the ,  or  matrix (which varies from 1 to the number of measured outputs - ) Operational Modal Analysis of Wind Turbines 152 Introducing the following definitions:   ⋮  (5.49)        ⋮      , with 1,2,…, (5.50) equation (5.48) can be written in a more compact form: 󰇛,󰇜󰇟󰇠.󰇣 󰇤 (5.51) where: 󰇯Ω󰇛󰇜 ⋮ Ω󰇡󰇢󰇰 (5.52)  󰇡Ω󰇛󰇜…Ω󰇛󰇜󰇢⊗ 󰆹 󰇛󰇜 … Ω󰇡󰇢…Ω󰇡󰇢⊗ 󰆹 󰇡󰇢, with 1,2,…, (5.53) with: ⊗ Kronecker product operator ,  Limits of the frequency range under analysis Expanding equation (5.51) with all the parameters from matrices α and β, one obtains: 0 … 0  0 … 0  ⋮ ⋮ ⋱ ⋮ ⋮ 0 0 … .       ⋮       . (5.54) Chapter 5 153 The solution for the identification problem can be solved through .0. However, this is very computationally demanding. For this reason, a different approach is usually followed. It consists on determining the model parameters through a linear least squares cost function obtained by adding all the squared elements of the matrix  evaluated at each discretized frequency: ,.,∗       (5.55) with:  Number of reference outputs From equations (5.52) and (5.53), (5.55) can be written as: 󰇛,󰇜󰇝󰇛,󰇜.󰇛,󰇜󰇞   . .󰇣 󰇤   .; .; . (5.56) with: 󰇛∗󰇜 Trace of the matrix * Thus, the minimum of the cost function is obtained with: 󰇛,󰇜 2󰇛..󰇜0 (5.57) 󰇛,󰇜  2..   0 (5.58) Eliminating the unknowns , the size of the system of equations can be reduced: 2󰇛..󰇜0⇔..   (5.59) Then, the α matrix is obtained through: 2..0⇔.0   (5.60) Structural Monitoring of Wind Turbines 256 The coefficient  is a ratio of variances that aims to quantify the proportion of variance of  “explained” by the selected predictor variables (it varies from 1 to 0, where 1 holds to situations where the adjust passes through all data points – a “perfect adjust” -, while 0 corresponds to a total independence between response and predictor variables). After the assessment of the residual errors is complete and the results are accepted, the model is ready to predict future values of the response variable () based only on the predictors not considered for its definition ():   . 󰆹 (7.9) At this point, the model is capable of predicting natural frequencies (the response variable), based on the environmental effects (the predictor variables) from the same period. Thus, observed and forecasted values can be compared. Since errors () from this difference are inevitable, the definition of a range in which the errors are acceptable is required. In that sense, if the errors  are considered as normally distributed, a confidence interval of 100󰇛1α󰇜 % is given by (Johnson and Wichern, 2002):   󰇡2󰇢.  󰇟1󰇛.󰇜.󰇠  󰇛󰇜 (7.10) with: 󰇡2󰇢 The upper 100󰇛1󰇜th percentile of a t-distribution with n-p-1 degrees The previous equation set a range 󰇠󰇛󰇜;󰇛󰇜󰇟 with a defined confidence level in which the new values of response variable should lay in. If the previously referred considerations about the construction of the matrix  are met (first column of  is filled with ones and the elements of the other columns are normalized), the confidence interval can be written as (Magalhães, 2010): 󰇛󰇜  .  󰇛󰇜   (7.11) with:  New response variable value (which was not considered for the definition of ) The previous equation can be interpreted in the context of the monitoring situation under study. Once the training period for the definition of matrix 󰆹 is complete, predictions of the frequency values () from the subsequent periods can be computed. These predictions will be formulated considering the entire set of environmental effects covered during the training period. For this reason, predicted frequencies will present variations that are interpreted as normal, i.e., this variations do not refer to any kind of damage since the training period is assumed to have occurred during a healthy stage of the structure. When comparing the predicted and real values of the natural frequencies from the Chapter 7 257 subsequent periods, their difference should be evaluated. If it is abnormally high (i.e., the value is outside the confidence interval defined in equation (7.11)), the variation cannot be explained by the environmental effects considered during the training period, and an abnormal condition affecting the structure, such as damage, may be present. The generalization of the presented method is easily performed for several dependent variables (frequency values of several vibration modes). This can be achieved by formulating the previous methodology as many times as response variables or through the matrix equation: . (7.12) with:  Matrix with n observations of the m dependent variables  Matrix with the n values of the p predictors variables (p environmental effects)  Matrix with weight parameters of the p predictor variables  Matrix with the values of the random error One last property from these models should also be referred: Multivariate Linear Regression Models are not valid for extrapolations. For that reason, a period of training with a wide range of values from the environmental effects should be used. Dynamic Regression Models An extension of the previous approach is given by the Dynamic Regression Models. In the previous section, it was shown that a Multivariate Regression Model, in order to predict a response value at a time instant , uses the observations of the predictor variables at the same  time instant – it is then considered a static model. On the other hand, a Dynamic Regression Model considers that observations of predictor variables at previous time instants also influence the foreseen of the dependent variables. This consideration is very useful when dealing with response variables with a large inertia to variations of predictors. The implementation of Dynamic Regression Models follows the same procedure as the Multivariate Models. The only change in the methodology is the introduction of additional predictors consisting of “past” observations of the independent variables. 7.2.1.2 Damage detection The described statistical techniques allow estimating a variable (the residual error) which can be used as an indicator of abnormal conditions (usually damage) of a monitored wind turbine structure. However, since it is desired that the monitoring system operates in an autonomous way, an automatic procedure to identify situations of damage is required. A general procedure to control the residual error from the frequency values of several vibration modes is obtained with the application of control charts. Control charts, one of the simplest techniques of Structural Monitoring of Wind Turbines 258 statistical process control, are used to evaluate if one or more variables are kept within predefined limits, which indicates that the process is occurring without abnormalities. For this reason, control charts are a very suitable technique to monitor possible frequency deviations due to damage. A typical control chart is presented in Figure 7.4. It consists of a graphical display, with horizontal development (usually associated with time), in which observations are plotted. There are also some control parameters: a centre line, which represents the average value of the quality characteristic under study; an upper (UCL) and lower control line (LCL) defining an interval in which the observations are considered “in-control”. If an observation has a value considered as abnormal, it falls outside this interval and is considered as “out-of-control”. Figure 7.4 – Control chart A common control chart to assess the evolution of a single variable is the Shewhart -chart. In the process control, the points (in the plot) under control represent a single observation or the mean of a group of observation (subsample). For a -chart, the definition of the upper and lower control lines is given by (Montgomery, 2009):    .    . (7.13) with:   Mean value from all observations  Standard deviation. When each point represent one single observation,  is the standard deviation from all observations; if each point represents the mean of a subsample with  elements,  is given by the quotient between the standard deviation from all observations and √   “Distance” between the control lines and the centre line. If 3 is defined in a distribution considered as normal, the control limits correspond to a confidence level of 99.7 % When dealing with a situation with more than one variable (like  vibration modes), it is required a slightly evolution from a univariate technique (such as the -chart) to a multivariate technique. A similar technique of the Shewhart -chart for monitoring more than one parameter is the  control Upper control limit Center line Lower control limit Sample quality characteristic Sample number or time Out-of-control Out-of-control Chapter 7 259 chart. The  control chart is a simple tool to detect deviations in the characteristics under evaluation. Although very similar to -charts,  control charts present two distinct characteristics: the vertical axis does not represent the quality characteristic under evaluation, but a statistic test named ; and the LCL is always zero. This multivariate statistical parameter control can be also applied to individual observations or subgrouped data (subsamples). When every observation is checked (i.e. each point of the plot represents one observation), the - statistic and the UCL are computed according to (Montgomery, 2009):  1.󰇛   󰇜..󰇛   󰇜 󰇛1󰇜. 3 .,󰇛󰇜 (7.14) with:  Number of observations collected during the reference period  Individual observation (vector with  components)  Covariance matrix ,󰇛󰇜  percentage point of the  distribution with  and  degrees of freedom If, instead of checking all the observations, subsamples with  observations are verified, the - statistic and the UCL are computed according to (Montgomery, 2009): .󰇛     󰇜..󰇛     󰇜 .󰇛1󰇜.󰇛1󰇜 .1.,.󰇛󰇜 (7.15) with:   Subgroup average   Process average  Number of groups collected during the reference period 7.2.2 FATIGUE MONITORING Wind turbines are structures predominantly subjected to dynamic loads throughout their period of life. In that sense, the continuous assessment of the fatigue condition of structural components can anticipate a fatal damage. Although failures from fatigue damage are also not expected to occur (if the structural design is correct), there is a large uncertainty about the real loading condition that the wind turbines will face. Thereby, the conditions considered during the design stage might not correctly recreate the actual conditions, leading to an over or underestimation of the components life. For these reasons, the implementation of a fatigue monitoring system can be an important advantage for the management of wind farms. Structural Monitoring of Wind Turbines 260 Support structures, as seen in Chapter 3, are a fundamental component of wind turbines that cannot fail at any circumstance, otherwise the whole system is jeopardized. Furthermore, their design is usually very conservative with respect to fatigue, which may lead to real fatigue life considerably higher than 20 years (the usually considered expected fatigue lifetime). Thus, the implementation of a fatigue monitoring system for assessment of the real solicitation of the support structure can introduce several advantages. If the monitoring system indicates that damage is not present in the structure, the fatigue monitoring system can be extremely useful in the following aspects: o Estimation of the evolution of real fatigue condition of the support structure and its suitability with the expected lifetime (usually 20 years); o Since an estimation of the real condition of fatigue damage is known, the results of the fatigue monitoring system could be an essential element for a decision about extending the lifespan of the structure, leading to a higher profitability of the investment; o Possibility of repowering or overpowering of the system, while keeping the support structure. If the fatigue monitoring system indicates a considerable margin of safety at the end of the period of life initially stipulated, together with a situation of non-damage detection by the dynamic monitoring system, one of these two options could be considered. For that purpose, a careful inspection of the structure would have to be carried out on-site. However, the results obtained with both components of the monitoring system, could provide a factual evidence of the overall good condition and low level of structural loading during the first period of life. The decision about repowering and overpowering could greatly reduce the cost of tower + foundation portion, which contributes with 18 % and 23 % of the capital cost for onshore and offshore installations, respectively (see section 3.1.2). The description of fatigue monitoring systems and publication of results from long periods of data acquisition is not very common in literature. In the context of the HISTWIN project (Veljkovic, Heistermann et al., 2012), a 2.1 MW wind turbine tower was monitored with strain rosettes, among other sensors. Results from two periods of 139 and 159 days for the most unfavourable structural detail lead to the conclusion of a considerable overdesign of the fatigue strength. Another work considering the problem of fatigue in the support structure of a wind turbine is reported in (Pollino and Huckelbridge, 2012). A 100 kW wind turbine was monitored with strain gauges during approximately one year. The authors studied the principal structural details of the tower and also concluded that the fatigue life of these elements were significantly higher than 20 years. An interesting study is described by Thies et al (Thies, Johanning et al., 2014) about the fatigue damage assessment of the mooring lines of an offshore floating marine energy converter. This equipment, that also comprises a 1.2 m diameter wind turbine, was monitored with load cells to measure the tension forces in the mooring system. Outside the scope of wind turbine support structures, there is a greater range of studies about the assessment of fatigue and prediction of the remaining period of life on steel structures. As an example, Ye et al (Ye, Ni et al., 2012) presented a study about a long-term monitoring data of dynamic strain on a steel bridge (the Tsing Ma Bridge). Chapter 7 261 7.2.2.1 Estimation of the Remaining Lifetime The results of fatigue damage of the support structure obtained during a representative time period may be used to estimate the remaining fatigue life of the structure. A direct way of doing this is considering the monitored period as representative of the whole period of life. In that case, the estimated accumulated damage at the end of the design fatigue life of the structural detail is obtained as: 󰇟󰇠 . (7.16) with: T Design fatigue life (usually 20 years)  Period of time which was considered for fatigue monitoring  Accumulated damage throughout the monitored period However, this extrapolation assumes that the monitored period is representative of the loading scenarios from the whole period of operation of the wind turbine. Considering that the monitored period may not be representative of the environmental loading along the estimated period of life, a more complex approach should be followed. An alternative approach can be obtained if the information about the environmental data is recorded. In that case, loading scenarios should be defined according to the simultaneous occurrence of the various environmental parameters. Important parameters such as mean wind speed, turbulence intensity and wind direction should be considered. Also, the significant wave height and peak period should be included for offshore installations. The variability of the parameters is usually reduced into bins with a representative magnitude in order to ease the computation of probability. Figure 7.5 shows part of the scatter diagram from the OWEZ site, where the probability of occurrence of loading scenarios with a mean wind speed of 10 m/s combined with various wave conditions is shown. In this figure, the wave loading condition is defined by the significant wave height  (introduced in section 6.2) and the mean zero-crossing period  (instead of the peak period ). This period is referred to the mean value of the zero up-crossings of a point at the sea surface (Tempel, 2006). Structural Monitoring of Wind Turbines 262 Figure 7.5 – Part of scatter diagram corresponding to the mean wind speed of 10 m/s (the values represent the probability of occurrence of the loading scenarios) (Tempel, 2006) Once a representative probability of occurrence of the environmental loading scenarios is obtained, the accumulated damage at the end of the design fatigue life of the structural detail can be estimated according to: 󰇟󰇠 .󰇛,,…󰇜.   (7.17) with: T Design fatigue life (usually 20 years)  Period of time which was considered for fatigue monitoring  Probability of occurrence of the load scenario   Accumulated damage of load scenario  during the monitoring period () The monitoring period of the structure (which might be much shorter than the monitoring period of the loading conditions) should include all the important load conditions for the quantification of D. 7.2.3 OVERVIEW OF THE DYNAMIC MONITORING SYSTEM MAIN STEPS At this point, all the important aspects of the dynamic monitoring system were already introduced. This section briefly summarizes the chain of processes throughout the developed system. The chart with the chain of procedures is presented in Figure 7.6. The processing starts with the acquisition of the 10 min. acceleration time series and data from environmental and operational conditions. Initially, the acceleration signals are decimated and a coordinate transformation is applied to these signals according to the yaw angle recorded by the SCADA system, in order to orientate the signals according to the FA and SS direction. After this preprocessing, the module related to structural damage detection starts with the automated modal analysis. The first step is referred to the application of the output-only identification algorithms 6 5.5 5 4.5 4 3.5 Hs 3 2.5 0.000038 0.000038 2 0.000342 0.000342 1.5 0.017727 0.001674 0.019401 1 0.003918 0.089550 0.093468 0.5 0.048009 0.004831 0.052840 0 0.000266 0.000038 0.000304 0 1 2 3 4 5 6 7 0.166394 0.166394 Vw = 10m/s Tz Chapter 7 263 (SSI-COV, SSI-DATA and p-LSCF) to the acceleration signals. These algorithms were introduced in section 5.4. The results obtained are then analysed through a cluster analysis (section 5.7.1), in which the poles with similar modal properties are gathered into the same clusters. Lastly, these clusters are compared with reference modal properties (frequency values and mode shapes) of the vibration modes intended to be tracked in order to separate the clusters referred to these modes from the other ones. These reference properties are defined during a training period prior to the automated processing. Once they are defined, these properties are saved in a database, being used in every processing cycle. From the moment the modal tracking is complete, it is necessary to remove the influence of the operational and environmental effects on the frequency values of the identified modes. In that sense, multivariate linear regression models have to be defined during a representative period (again, prior to the automated process). Once these models are set, they are applied to the identified frequency values in order to reduce their variability. This process was presented in section 7.2.1.1. The last step of the module is referred to the assessment of important deviations of the frequency values (damage detection). The implemented procedure, based on control charts, was introduced in section 7.2.1.2. A caveat should be made at this level that, if subsamples with more than one observation are used, the damage detection step is only processed after the required number of observations is achieved. The module related to the fatigue assessment of the wind turbine support structure starts after the application of the output-only identification algorithms to the acceleration signals. At this point, it is necessary to select an order of the state-space model. This selection should take into consideration the order with the highest number of identified modes with important contribution to the support structure motion. For that reason, the results from the modal tracking represent an important information. Furthermore, the selected order should contain poles related to the low order harmonics (when the turbine is operating). Thus, the data from the SCADA system is also important at this point. Once the state-space model order is selected, it is possible to define the forward-innovation model. With the transformation of the model into the modal basis, it is thus possible to obtain the modal state vector, essential information to estimate the acceleration at unmeasured locations (this procedure was presented in section 5.5). At this point, a detailed estimation of the mode shapes along the height of the support structure is required to estimate the acceleration time series at every location. Two options are available: o If the number of installed sensors at the structure is enough to estimate the mode shapes of the most important modes along the height of the support structure, an interpolation of the experimentally found mode shapes can be used. This methodology was referred in section 6.4.1; o On the other hand, if a reduced number of sensors is used, reference support structure mode shapes of the important modes should be used. In addition, operational deflection shapes of the harmonics should also be used for situations under operation. Both mode shapes and operational deflection shapes must be defined after a period of training and should consider the different operating conditions of the wind turbine. This procedure was described in section 6.4.2. Structural Monitoring of Wind Turbines 264 With the possibility of estimate the acceleration time series at every position of the wind turbine support structure, the fatigue damage of the structure is assessed with the procedure proposed in section 6.4.1. During this process, the stiffness matrix of the support structure is required and should be previously calculated according to the mechanical properties of the support structure. Lastly, the fatigue damage estimations from the 10 min. time series should be continuously summed in order to obtain a cumulative damage of the support structure. Once representative damage accumulation events from the various environmental loading scenarios are recorded, it is possible to perform an estimation of the damage condition at the end of the designed fatigue life and, thus, predict the real lifetime of the structure. This procedure was introduced in section 7.2.2.1. Figure 7.6 – Chain of events included in the dynamic monitoring system (the dashed box is only referred to situations in which a reduced number of sensors is used) Automated Modal Analysis Fatigue Assessment Acceleration Data SCADA Data Signal Decimation Coordinate Transformation Modal Identication Cluster Analysis Modal Tracking Definition of the State-Space Model Definition of the Forward-Innovation Model Fatigue Damage Removal Operational/ Environmental Conditions Damage Detection Accumulated Damage/ Lifetime Prediction Reference Modal Properties Multivariate Regression Model Reference Mode Shapes/ Operational Deflection Shapes Stiffness Matrix Mode Shape/ Operational Deflection Shape Estimation Database Database 7.3 7.3.1 This healt h stud y The g at wi n o o o o o o o 7.3.2 The S the T C ASE S TU D I NTROD U section intr o h monitorin y was perfor m g oal of this s t n d turbines. o Installati o o Impleme n o Full com p environ m o Identific a o Assessm e damages; o Fatigue a s o Study a b number o W IND T U S envion M M T orrão wind f D Y – S ENVI O U CTION o duces the m g methodol o m ed for this w t udy was to d The work c o o n of the m o n tation of t h p rehension o m ental condi t a tion of the m e nt of the ca s sessment o f b out the fea o f sensors. U RBINE D ESC M 82 is a 2.0 M f arm, in the n O N MM82 m ain results o o gy to a 2.0 M w ind turbin e d emonstrate o ntemplated o nitoring eq u h e structural h o f the dyna m t ions; m ain vibrati o p ability of t h f the wind tu s ibility of t h R IPTION AN D M W onshore n orth of Por t Figure 7.7 – o btained wit h M W Senvio n e . e the suitabil i several step s u ipment; h ealth moni t m ic behavio u o n modes; h e impleme n u rbine suppo r h e impleme D N UMERIC A wind turbi n tugal (Figur e – Location of t h h the applica t n MM82 wi n i ty of dyna m s : t oring tools i u r of the wi n n ted dynam i r t structure; ntation of m A L M ODELS n e. This win d e 7.7). h e Torrão wind t ion of the v i n d turbine. I n ic monitori n i n an autom a n d turbine i n i c monitorin m onitoring d turbine sta r farm i bration-bas e n that sense, n g systems t o a ted way; n different o p n g system to systems wi t r ted operati n Chapter 7 26 5 e d structura l a long-ter m o be installe d p erating an d detect smal l t h a smalle r n g in 2007 a t 5 l m d d l r t Structural Monitoring of Wind Turbines 272 a) b) Figure 7.13 – Pitch angle vs rotor speed: a) all regimes; b) only operating regimes The illustration of evolution of the blades pitch angle actuator with the wind speed (Figure 7.14) is helpful to understand the pitch mechanism in Region 4 and 5. In this figure, the start of the actuator around 11 m/s is clearly visible. From the observation of Figure 7.14 b), it is also possible to attest that the increase rate of the pitch angle with the wind speed is lower in Region 5 than in Region 4. a) b) Figure 7.14 – Pitch angle vs wind speed: a) all regimes; b) only operating regimes The analysis of the recorded SCADA data also permitted to conclude that the main wind incidence direction is around 110º. It is concluded, from the wind rose of Figure 7.15, that the higher wind speed regimes are also obtained for this direction. 0 5 10 15 0 20 40 60 80 100 Rotor speed [rpm] Pitch angle [º] 8 10 12 14 16 0 5 10 15 20 25 Rotor speed [rpm] Pitch angle [º] 0 5 10 15 20 25 0 20 40 60 80 100 Pitch angle [º] Wind speed [m/s] 0 5 10 15 20 25 Wind speed [m/s] Region 1 Reg. 2 Region 3 Reg. 4 Region 5 0 5 10 15 20 25 Pitch angle [º] Chapter 7 273 Figure 7.15 – Wind rose histogram of mean wind speed Figure 7.16 – Local orography on the wind turbine site The local orography at the wind turbine site is represented in simplified form in Figure 7.16. In this figure, the origin of the referential represents the wind turbine location. It is interesting to note that at the direction of 110º, the terrain presents an apparent depression. 7.3.4 MONITORING SYSTEM DESCRIPTION The implemented monitoring system is based on a central acquisition system to which all sensors are connected. It is composed by 9 uni-axial accelerometers distributed along the tower height and at the foundation level, according to the scheme presented in Figure 7.17. All the accelerometers were fixed to the tower through fixing clamps on the tower flanges. The central acquisition system is located at the first platform, around +20.000 m. All the equipment is placed inside the wind turbine. With the considered instrumentation layout, the acceleration on both horizontal directions at three different tower sections is measured. In addition, the pair of sensors S5 and S7 enables the characterization of motion associated with torsion modes. a) b) Figure 7.17 – Position of the accelerometers at the different levels of the wind turbine: a) front view; b) top view of the instrumented sections 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14 14 - 16 16 - 18 18 - 20 20 - 22 22 - 24 5% 10% 15% WEST EAST SOUTH NORTH Wind speed [m/s]: 0º 90º 180º 270º N EW S 110º + 0.000 + 21.772 + 48.392 + 74.988 + 0.000 + 21.772 + 48.392 + 74.988 S1 S2 S1 S2 S3 S3 S4 S4 S5 S5 S6 S7 S6 S7 S8 S9 S9 S8 Structural Moni t 274 The install e This accele r The measu r The central composed b the connec t converter. T The CR-5P of 50 Hz. T SCADA sy s Figure 7.1 t oring of Wind T u e d sensors a r ometer pre s r ing range v a l acquisition b y a digitize r t ion of up t T he internal unit was co T he length o f s tem to com p 8 – Accelerom u rbines a re force bal a s ents a dyn a a ries from േ 0 system is c o r (C R -5PA D o 9 uni-axi a computer c o nfigured to f the time se r p ute the me a a) c) eters installed a a nce accele r a mic range o 0 .1g to 4.0g. o mposed by 24) and an i a l accelero m o ntrols the r e r ecord 10 m r ies was dec i a n values of t h at: a) tower fla a cquisition syst r ometers, m o o f 140 dB, w i a C R -5P un i nternal co m m eters and is e cording op e m in. accelera t i ded in orde he monitor e nge; b) top to w t em with the C R o del CMG5 i th a freque n i t from Geo S m puter (C R - 5 equipped w e rations. t ion time se r r to match t h d paramete r w er flange; an d R -5P unit 5 S from Gu r n cy band fr o S IG (Figure 5 PRHDx). T h w ith a 24-bi t ies with a fr e h e 10 min. p s. b) d) c) foundation r alp (Figure o m DC to 1 0 7.18). This u h e digitizer a t analog-tod r equency sa m p eriod used b flange. d) Cen t 7.18). 0 0 Hz. u nit is a llows d igital m pling b y the t ral Chapter 7 275 The dynamic monitoring system is complemented by the SCADA system of the wind turbine. This system records the mean, maximum and minimum value from 10 min. period of several operational and environmental parameters. Among them, some were important for the context of this structural health monitoring project: o Wind speed and direction; o Rotor speed; o Yaw angle; o Blades pitch angle; o Outdoor temperature. Since it was not possible to connect the central acquisition system to an external GPS antenna, the data recorded by the CR-5P was manually synchronized to the SCADA data. This operation was tuned using the date information of startup and shut-down events of the turbine recorded by the SCADA data, which were correlated to events of sudden increase or decrease of the tower vibration levels. The dynamic monitoring system was installed at the wind turbine on the 22th of July of 2013. Unfortunately, problems related to electrical power supply of the central acquisition system prevented a continuous operation. Moreover, it was only possible to have access to the equipment during maintenance periods, which annulled the possibility to make rapid interventions once the problems were noticed. For that reason, it was not possible to avoid some periods with a low rate of recorded setups (or even inactivity of the system). A total number of 37 685 data sets were collected during this period. The percentage of recorded setups for each month between 22/07/2013 and 21/07/2014 is evidenced in Table 7.3. Table 7.3 – Percentage of recorded setups between 22/07/2013 and 21/07/2014 Year 2013 2014 Month 7 8 9 10 11 12 1 2 3 4 5 6 7 Recorded Setups [%] 100 100 63 0 23 89 89 100 100 94 67 59 53 7.3.5 PRELIMINARY RESULTS The processing of the continuously collected data comprehends an initial task of filtering and resampling to reduce the sampling frequency to 25 Hz. After this step, a coordinate transformation is applied to the acceleration time series measured at the tower in order to obtain signals that are always aligned with the FA and SS directions. Examples of the different excitation conditions that the wind turbine is subjected to are illustrated in Figures 7.19 to 7.21. Figure 7.19 shows the acceleration time series of the recorded setup with the highest observed mean wind speed (23.3 m/s). On the other hand, Figures 7.20 and 7.21 present two situations of sudden increase and decrease of the vibration level related to a situation of startup and shutdown of the rotor, respectively. Structural Monitoring of Wind Turbines 276 Figure 7.19 – Acceleration time series from a setup with the highest observed mean wind speed (23.3 m/s) Figure 7.20 – Acceleration time series during a startup event Figure 7.21 – Acceleration time series during a shutdown event The variation of the vibration levels during the monitored period is shown in Figures 7.22 and 7.23 for, respectively, the RMS and maxima values from each recorded 10 min. time series. The maximum acceleration recorded in FA direction was 3.73 m/s2 while in the SS direction was 3.10 m/s2. As expected, the vibration levels at the foundation are considerably lower than in the tower. Figure 7.22 – Time evolution of the RMS values of the acceleration time series collected during the monitored period 0 200 400 600 -2 -1 0 1 2 time [s] Acc. [m/s 2 ] 10/02/2014 00:50 0 200 400 60 0 -0.8 -0.4 0 0.4 0.8 time [s] Acc. [m/s2] 31/07/2013 12:40 0 200 400 60 0 -0.4 -0.2 0 0.2 0.4 time [s] Acc. [m/s2] 24/07/2013 04:40 0 0.5 1 1.5 2 x 10 4 0 0.2 0.4 0.6 Index Acc. [m/s 2] RMS +74.988 FA +74.988 SS +48.392 FA +48.392 FA +48.392 SS +21.772 FA +21.772 SS 0 0.5 1 1.5 2 x 10 4 0 2.5 5 x 10 -3 Index Acc. [m/s 2] RMS Found. 6 Found. 7 Chapter 7 277 Figure 7.23 – Time evolution of the maxima values of the acceleration time series collected during the monitored period It is interesting to observe that the higher values of acceleration do not occur at the tower top but at +48.392 m level. This is a common situation when the turbine is operating (the majority of the time). However, when the turbine is parked or idling, the highest vibration levels were recorded by the top sensors (+ 74.988 m). This behaviour was also noticed in the analysis of the offshore Vestas V90 wind turbine (section 5.9). Figure 7.24 shows the RMS values of acceleration in the FA direction for operating and non-operating situations. It can be seen that, when the turbine is operating, the acceleration level at the +48.392 m height is clearly higher than at the other two levels. Indeed, the vibration levels at the top (+ 74.988 m) and +21.772 m are similar. On the other hand, when the turbine is not operating, the level of vibration usually increases from the lowest part to the top of the tower structure. Nevertheless, the vibration at the +48.392 m sometimes exceeds the value from the top sensor. The causes for this behaviour will be further analysed in section 7.3.6.4. a) b) Figure 7.24 – Time evolution of the RMS values of the acceleration time series during: a) operating conditions and; b) parked or idling conditions 00.5 1 1.5 2 x 10 4 0 1 2 3 4 Index Acc. [m/s 2] Maxima +74.988 FA +74.988 SS +48.392 FA +48.392 FA +48.392 SS +21.772 FA +21.772 SS 0.5 1 1.5 2 x 10 4 0 0.01 0.02 0.03 Index Acc. [m/s 2] Maxima Found. 6 Found. 7 4000 4100 4200 4300 4400 4500 0 0.1 0.2 0.3 0.4 0.5 Index Acc. [m/s 2] Operation +74.988 FA +48.392 FA +21.772 FA 1250 1300 1350 1400 1450 1500 1550 1600 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Index Acc. [m/s 2] Parked/ Idling +74.988 FA +48.392 FA +21.772 FA Structural Monitoring of Wind Turbines 278 The wind excitation is, naturally, the main driver of wind turbine vibration. Figure 7.25 presents the time evolution of the RMS values at the +74.988 m level in the FA direction and of the wind speed. As expected, there is a clear coherence between acceleration level and wind speed. The relationship between the RMS values of acceleration and the wind speed is also illustrated in Figure 7.26. From the figure, it seems that the acceleration continuous increases with the increase of the wind speed. Figure 7.25 – RMS values of acceleration of the +74.988 m sensor in the FA direction vs the wind speed Figure 7.26 – Correlation of the RMS values of the sensors in the FA direction with the wind speed The variation of the vibration amplitude with the yaw angle is an important analysis to check the directions with greater wear of the support structure. As expected, the vibration level is highly dependent on the rotor orientation (which is conditioned by the wind direction). Figure 7.27 presents the RMS values of the acceleration in FA direction according to the yaw angle. As can be seen, this figure is coherent with the main wind directions illustrated in the wind rose of Figure 7.15. Figure 7.27 – RMS values of the acceleration in the FA direction according to the yaw angle Figure 7.27 clearly indicates the directions according to which the structure vibrates with the highest levels. However, as the wind speed is not evenly distributed across all the directions (as shown in Figure 7.15), it is not possible to make any consideration about the heterogeneity of the support structure just with this observation. 88008600 9000 9200 9400 9600 0 0.05 0.1 0.15 0.25 0.2 Acc. [m/s 2 ] 0 20 25 15 10 5 Wind speed [m/s] Index 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 Wind speed [m/s] Acc. [m/s 2 ] +74.988 FA +48.392 FA +21.772 FA 0 40 80 120 160 200 240 280 320 360 0 0.1 0.2 0.3 0.4 0.5 0.6 Yaw angle [º] Acc RMS [m/s2] +74.988 FA +48.392 FA +21.772 FA Chapter 7 279 In order to compare the vibration amplitude for different angles of nacelle orientation, only the recorded setups from a narrow range of wind speeds, under operating conditions, were selected. With this consideration, it can be assumed that the wind excitation is roughly similar across all directions. Still, differences can exist in terms of wind turbulence. Figure 7.28 presents the box plots obtained for the RMS values of acceleration in the FA direction for the top sensor considering only setups when the turbine was operating and the wind speed was between 6 and 7 m/s. For the analysis, the yaw angles were grouped in 18 ranges of 20º, from 0º to 360º. In this figure, the line connects the median value of each group, while the edges of the box represent the 25th and 75th percentiles. The whiskers were extended to the most extreme points not considered as outliers. In the background, the data considered for the analysis is plotted in light grey. This figure clearly indicates that, for roughly similar wind conditions, the structure presents higher vibration levels for the ranges 100º – 140º and 180º – 240º than for remain directions. The first range coincides with the main direction of the wind. Figure 7.28 – Box plots of the RMS values of acceleration of the top sensor in the FA direction according to the yaw angle, considering setups when the turbine was operating and the wind speed was in the 6 – 7 m/s range Figure 7.29 – Median values of the RMS values of acceleration of the top sensor in the FA direction according to the yaw angle, considering setups when the turbine was operating and several wind speed ranges This analysis is further extended to ranges of wind speed whose number of recorded setups is representative of all yaw sectors. For that reason, ranges with the largest wind speeds were not considered since they mainly occur in a few yaw sectors. Figure 7.29 presents the results obtained with this analysis, considering wind speed ranges between 3 and 8 m/s. In this figure, only the median values are shown. The results obtained are in line with the conclusion already introduced for Figure 7.28. It is interesting to note that, for example, the highest values obtained with the wind speed range 4 – 5 m/s are similar to the values obtained for the 7 - 8 m/s in the 300º - 360º region. From this analysis, it seems that the foundation is less stiff along the directions that are more excited by the wind. However, it should be noticed that this analysis should have taken into account the turbulence of the wind flow, which also influences the dynamic excitation of the support structure. Since this information is not provided by the SCADA system, it is not possible to confirm the presented considerations. It is also interesting to assess the evolution of RMS values of acceleration with the rotor speed (Figure 7.30). As expected, the vibration levels tend to increase with the increase of the rotor speed. 360200 240 280 320 0 0.05 0.1 0.15 0.2 Acc. [m/s 2 ] Wind speed: 6 - 7 m/s 0 40 80 120 160 Yaw angle [º] 0 40 80 120 160 200 240 280 320 360 0 0.02 0.04 0.06 0.08 0.1 0.12 Yaw angle [º] Acc. [m/s 2] 3 - 4 4 - 5 5 - 6 6 - 7 7 - 8 Wind speed [m/s:] Structural Monitoring of Wind Turbines 280 Figure 7.30 – RMS values of acceleration vs the rotor speed The colour map presented in Figure 7.31 illustrates the frequency content of the acceleration signals during a period of one month. This figure is a top view of the first singular value spectra of the spectrum matrices obtained from each recorded setup. The regions with the hotter colours represent the highest energy. Two vertical alignments with high energy are clearly visible around 0.35 Hz and 2.80 Hz (indicated by arrows). These frequency values are coherent with the results obtained for the first and second pairs of tower bending modes of the numerical models described in section 7.3.2. Albeit with less energy, two additional alignments are also visible around 1.30 Hz and 1.80 Hz (also indicated by arrows). In the same figure, the rotor speed frequencies from the 1Ω, 3Ω and 6Ω harmonics are represented by dashed lines. As expected, the excitation introduced by the rotor rotation is visible, mainly for the 3Ω harmonic. In a small scale, the 6Ω harmonic is also detected and seems to cross the 1.30 Hz alignment several times. The 1Ω harmonic alignment is very tenuous and is only visible in a few setups. Figure 7.31 – Colour map with the variation of the signals frequency content during the 15/02/2014 and 15/03/2014 0 2 4 6 8 10 12 14 16 0 0.1 0.2 0.3 0.4 0.5 0.6 Rotor speed [rpm] Acc. [m/s 2 ] +74.988 FA +48.392 FA +21.772 FA 0 0.5 1 1.5 22.5 3 3.5 4 4.5 5 Frequency [Hz] Time 1Ω 3Ω 6Ω Chapter 7 281 7.3.6 CONTINUOUS CHARACTERIZATION OF THE DYNAMIC PROPERTIES The design of a dynamic monitoring system requires the previous knowledge of the wind turbine modal properties. In that sense, the results obtained with an ambient vibration test (Oliveira, Magalhães et al., 2013) and with the analysis of initial recorded data were used to characterize the dynamic properties of the wind turbine. This initial characterization was used to tune the dynamic monitoring system to detect possible damage situations. 7.3.6.1 Dynamic Characterization of the Wind turbine As presented in section 7.3.3, wind turbines are time-varying structures subjected to different operating conditions. As example, Figure 7.32 presents the averaged normalized power spectrum density of two different setups, one referring to a non-operating situation and another referred to an operating condition. The shape of the spectra are considerable distinct. The most distinguished feature is the appearance of peaks at the harmonics frequencies in the operating setup. These peaks are due to the external excitation caused by the tower shadow effect. From the figure, it is also visible a small peak around 1Ω. As expected, this peak is considerable smaller than the ones associated with other harmonics. Besides the harmonic peaks, other interesting characteristics are also evident. The two peaks around 1.10 Hz and the peak at 2.30 Hz, clearly identified under non-operating conditions, are practically not visible in the operating setup. Furthermore, the peaks from the non-operating conditions spectrum at 1.30 and 1.80 Hz seem to move to slightly higher frequency values. Figure 7.32 – ANPSD of two different setups: under non-operating conditions (rotor speed = 0 rpm; wind speed = 1.9 m/s) and operating conditions (rotor speed = 16.4 rpm; wind speed = 10.7 m/s). The vertical dashed lines indicate the frequency values of the rotor speed and its harmonics It is thus important to perform a preliminary analysis of the properties of the most relevant vibration modes and their variation throughout the various operating conditions. In that sense, the recorded setups were initially processed with the modal identification algorithms introduced in section 5.4. Then, an automatic interpretation of the produced stabilization diagrams was performed by the algorithm based on the hierarchical clustering presented in section 5.7.1. The same datasets used to plot the ANPSD in Figure 7.32 are used to illustrate this preliminary analysis. The methodology is similar to the one described in section 5.9 for the case study related to the Vestas V90. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 -6 10 -4 10 -2 10 0 Amplitude Frequency [Hz] Non-operating Operating 1Ω 3Ω 6Ω 9Ω 12Ω 15Ω 18Ω Structural Monitoring of Wind Turbines 288 7.3.6.2 Automated Identification of the Modal Parameters Three output-only modal identification algorithms were used to perform an automated analysis of the modal parameters of the wind turbine: SSI-COV, SSI-DATA and p-LSCF. Once the reference modal properties of the vibration modes intended to be tracked were defined, it was possible to perform the identification in a completely automated way. The strategy introduced in previous sections was followed. For each identification algorithm, a pole is classified as stable in a stabilization diagram if it respects the limits presented in Table 7.5 for variations between models of consecutive orders. Once the stable poles are identified, the hierarchical cluster algorithm is applied. For this process, a maximum distance of 0.02 was defined for a single linkage criterion. Table 7.5 – Stable pole criteria for models of consecutive orders Modal parameter Maximum allowed variation Frequency Δ  ≤ 1 % Damping Δ ≤ 5 % Mode Shape MAC ≥ 0.97 From the obtained clusters, only the ones with a number of poles higher than 6 were considered. Then, for each reference mode, the clusters presenting an average natural frequency that did not differ more than a predefined percentage value (10 % to 20 % depending on the mode type) from the reference natural frequency value were selected. From those, it is selected the one that presents the average mode shape with the highest correlation with the reference mode shape (evaluated with the MAC coefficient). Modes with MACs lower than 0.80 are not considered. The stated parameters were tried on several initial datasets and proved to deliver good and coherent results. Figure 7.41 shows the Campbell diagram after the tracking (comparison of the cluster properties with the reference properties of the vibration modes intended to be monitored). It can be seen that, in this particular application, this simple tracking procedure was adequate to eliminate the influence of the harmonics in the modes under analysis. For that reason, it was not necessary to use the methods presented in section 5.6.3. Chapter 7 289 Figure 7.41 – Campbell diagram with the tracked vibration modes (p-LSCF algorithm) Naturally, it was also necessary to define the input parameters for each modal identification algorithm. Initial datasets were used to tune these parameters. The SSI-COV algorithm requires two input parameters: the  number of points of the correlation function and the maximum order of the model. It was decided to adopt correlation functions of 128 points and a maximum order of 70. Table 7.6 presents the main statistics related to the performance of this algorithm in the automated identification of the 9 considered vibration modes. A success rate above 60 % is consistently obtained, except for the 3 FA/3 SS, 3 SS* and 4 FA modes. Also, the 1 FA mode shows a considerably lower success rate than its pair. This fact is probably due to the high values of damping of this mode which hinders the identification of this mode by the algorithms. For the 3 FA/3 SS mode, the low success rate is explained by the fact that this mode presents an unusual behaviour, which tends to change its main direction of vibration according to the nacelle orientation. Thus, since a minimum MAC value for the modal tracking was defined, only a small portion of the clusters identified in the frequency range of this mode were considered. On the other hand, the low value obtained for the identification of the 3 SS* and 4 FA modes are mainly related to non-operating conditions (Regimes 1 and 2) and to the Regime 5. In these three regimes, the success rate was considerably low. From the analysis of Table 7.6, it is interesting to check that within the first pair of tower bending modes, the 1 SS mode presents a much smaller dispersion of its natural frequency than the 1 FA mode. Again, the high values of damping of the 1 FA mode may have influenced the quality of the detection of this mode. 0 2 4 6 8 10 12 14 16 18 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Campbel Diagram RPM Frequency [Hz] 1 FA 1 SS 1 SS* 2 SS* 2 FA 2 SS 3 SS* 3 FA/SS 4 FA Structural Monitoring of Wind Turbines 290 Table 7.6 – Statistics related to the results obtained with the SSI-COV algorithm Mode Success Rate [%]   [Hz]   [Hz]  .. 1 SS 81.2 0.354 0.002 0.005 1 FA 67.4 0.355 0.007 0.020 1 SS* 63.4 1.325 0.051 0.039 2 SS* 78.3 1.791 0.060 0.034 2 FA 75.8 2.792 0.024 0.009 2 SS 83.7 2.828 0.030 0.011 3 FA/ 3SS 9.1 3.673 0.042 0.011 3 SS* 29.5 3.782 0.043 0.011 4 FA 38.3 4.236 0.072 0.017 The second time domain identification algorithm used was the SSI-DATA. For this algorithm, two parameters were defined: the number of  blocks of the Hankel matrix and the maximum order of the model. After initial tuning, it was concluded that  = 70 blocks, together with a maximum model order of 70 led to the best results. The main statistics about the automated modal identification with the SSI-DATA are introduced in Table 7.7. The results are in line with the ones obtained with the SSI-COV. On the identification of the 4 FA mode, a considerably increase was obtained. Table 7.7 – Statistics related to the results obtained with the SSI-Data algorithm Mode Success Rate [%]   [Hz]   [Hz]  .. 1 SS 84.7 0.355 0.002 0.006 1 FA 67.4 0.358 0.008 0.022 1 SS* 84.9 1.330 0.050 0.038 2 SS* 89.8 1.793 0.057 0.032 2 FA 74.0 2.789 0.024 0.009 2 SS 60.2 2.829 0.030 0.011 3 FA/ 3SS 14.9 3.690 0.039 0.011 3 SS* 44.9 3.789 0.047 0.012 4 FA 82.3 4.266 0.079 0.019 The last identification algorithm used in the dynamic monitoring system was the p-LSCF. Positive time lags of the correlation with 1024 points were used to calculate the spectra. An exponential window with a factor of 0.1 was also used. A maximum model order of 40 was considered. The obtained results show that this algorithm provided much higher success rates for the modes not so successfully identified with the other two algorithms. Chapter 7 291 Table 7.8 – Statistics related to the results obtained with the p-LSCF algorithm Mode Success Rate [%]   [Hz]   [Hz]  .. 1 SS 80.8 0.354 0.002 0.006 1 FA 64.7 0.354 0.007 0.019 1 SS* 87.4 1.330 0.049 0.037 2 SS* 85.5 1.793 0.058 0.032 2 FA 80.1 2.796 0.017 0.006 2 SS 85.5 2.831 0.026 0.009 3 FA/ 3SS 43.2 3.700 0.030 0.008 3 SS* 67.8 3.809 0.058 0.015 4 FA 95.1 4.276 0.081 0.019 Once the modal parameters are identified, it is possible to analyse the variation of the parameters with the operational and environmental factors. Figure 7.42 characterizes the evolution of the natural frequencies of the 9 monitored vibration modes along the monitoring period. The variability of the frequency values is evident. Figure 7.42 – Variation of the of the monitored natural frequencies Figure 7.43 a) shows a zoom of the frequency variation of 1 FA and 1 SS vibration modes along the recorded setups. It is visible that the variability of the 1 FA mode is much higher than of the 1 SS, which is in agreement with the results presented in Tables 7.6 to 7.8. Figure 7.43 b) evidences the variation of the natural frequencies of the 1 SS* and 2 SS* modes, mainly due to their dependence on the rotor speed. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time Frequency [Hz] Structural Monitoring of Wind Turbines 292 a) b) Figure 7.43 – Zoom of the natural frequencies along the recorded setups: a) 1 FA and 1 SS; b) 1 SS* and 2 SS* In order to better understand the behaviour of the modal parameters of the 9 tracked modes, Figure 7.44 shows the variation of the natural frequencies for each operating regime. This graphic evidences the suitability of defining different Regimes for modal tracking. For example, the variation of the frequency values of the modes 1 SS* and 2 SS* is notorious. Apart from these modes, also the 2nd pair of tower bending modes shows a different behaviour when the turbine starts operating, with a better separation of the two modes. Figure 7.44 – Variation of the natural frequency, for each operating regime, of the monitored vibration modes Figure 7.45 a) presents a closer look of the first pair of tower bending modes. It is interesting to note that the variability of the 1 FA mode is smaller than the 1 SS mode for non-operating conditions. Once the turbine starts operating, the dispersion of the frequency values from this mode greatly increases. On the other hand, the variability of the 1 SS mode is kept almost constant throughout the different operating regimes. These facts reinforce the idea that the high values of damping of the 1 FA mode, during operating conditions, may have influenced the accuracy of the detection of this mode. Figure 7.45 b) evidences the better separation of the 2nd pair of tower bending modes under operating conditions. 00.5 11.5 2 x 10 4 0.32 0.34 0.36 0.38 0.4 Index Frequency [Hz] 00.5 11.5 2 x 10 4 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Index Frequency [Hz] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Frequency [Hz] Regime 1 Regime 2 Regime 3 Regime 4 Regime 5 Chapter 7 293 a) b) Figure 7.45 – Variation of the natural frequency, for each operating regime, of: a) 1 FA and 1 SS; 2 FA and 2 SS The results obtained with the identification of the natural frequencies and damping ratios of 9 monitored vibration modes with the p-LSCF algorithm are shown in Tables 7.9 and 7.10 for each regime. Table 7.9 – Results obtained for each operating regime: natural frequencies Mode 1 2 3 4 5   [Hz]   [Hz]   [Hz]   [Hz]   [Hz]   [Hz]   [Hz]   [Hz]   [Hz]   [Hz] 1 SS 0.353 0.003 0.353 0.003 0.354 0.002 0.355 0.001 0.355 0.002 1 FA 0.352 0.001 0.352 0.001 0.355 0.004 0.357 0.006 0.349 0.006 1 SS* 1.258 0.011 1.277 0.011 1.400 0.020 1.362 0.033 1.294 0.018 2 SS* 1.625 0.011 1.812 0.017 1.729 0.025 1.793 0.045 1.844 0.013 2 FA 2.767 0.012 2.784 0.013 2.781 0.022 2.799 0.015 2.796 0.014 2 SS 2.792 0.020 2.790 0.021 2.819 0.022 2.842 0.016 2.841 0.012 3 FA/ 3SS - - 3.659 0.042 3.664 0.038 3.702 0.028 3.702 0.026 3 SS* 3.668 0.050 3.683 0.055 3.748 0.053 3.812 0.036 3.870 0.018 4 FA 4.107 0.033 4.167 0.046 4.253 0.068 4.301 0.040 4.349 0.048 0.32 0.34 0.36 0.38 0.4 Frequency [Hz] Reg. 1 Reg. 2 Reg. 3 Reg. 4 Reg. 5 2.65 2.7 2.75 2.8 2.85 2.9 2.95 Frequency [Hz] Reg. 1 Reg. 2 Reg. 3 Reg. 4 Reg. 5 Structural Monitoring of Wind Turbines 294 Table 7.10 – Results obtained for each operating regime: damping ratios 1 2 3 4 5 Mode ߦ௠௘௔௡ [%] ߦ௦௧ௗ [Hz] ߦ௠௘௔௡ [%] ߦ௦௧ௗ [Hz] ߦ௠௘௔௡ [%] ߦ௦௧ௗ [Hz] ߦ௠௘௔௡ [%] ߦ௦௧ௗ [Hz] ߦ௠௘௔௡ [%] ߦ௦௧ௗ [Hz] 1 SS 0.974 0.631 0.733 0.438 0.707 0.590 0.630 0.394 1.096 0.548 1 FA 0.351 0.482 0.213 0.356 1.490 1.128 3.659 1.390 7.868 2.169 1 SS* 0.502 0.207 0.646 0.316 0.845 0.232 0.932 0.236 0.860 0.152 2 SS* 0.543 0.261 0.746 0.297 0.746 0.271 0.916 0.247 1.113 0.211 2 FA 0.175 0.100 0.195 0.120 0.624 0.231 0.884 0.320 1.291 0.284 2 SS 0.301 0.127 0.254 0.167 0.344 0.162 0.451 0.225 0.662 0.181 3 FA/ 3SS - - 0.778 0.275 1.013 0.350 1.395 0.427 1.820 0.407 3 SS* 0.572 0.230 0.551 0.228 0.660 0.224 0.719 0.149 0.888 0.232 4 FA 0.476 0.170 0.457 0.178 1.079 0.433 1.598 0.374 1.566 0.467 The evolution of the 1 SS* and 2 SS* modes with the rotor speed is illustrated in Figure 7.46. This figure resembles the typical behaviour the of rotor whirling modes. It is visible that, when the turbine is consistently rotating (for rotor speed higher than 8.7 rpm), the 1 SS* and 2 SS* modes have a similar behaviour with, respectively, a backward and a forward whirling mode. Considering that, when in operation, these modes are detected by tower motion in the SS direction, i. e., in the direction of the rotor plane, these two modes are most likely related to edgewise vibration modes. From the three configurations of first order edgewise modes shown in Figure 4.4, only asymmetrical modes create a reaction force at the rotor and, thus, are capable of inducing a detectable tower motion. For these reasons, it expected that 1 SS* and 2 SS* modes are in fact the first backward and forward edgewise modes, respectively. A regression model for each vibration mode is also presented in Figure 7.46 in dashed lines. These regression models were adjusted to the frequency values obtained for the two modes during events regarding Regime 4. Regime 5 was not considered for the definition of the models because this regime implies the variation of the blades pitch angle which introduces changes in the behaviour. The intercept of the regression models with the origin (rpm=0) gives an approximation of the frequency values of these two modes under parked conditions and with a pitch angle around 0º. Values of 1.526 Hz and 1.558 Hz were obtained for, respectively, the backward and forward mode. However, this configuration does not occur in the monitored wind turbine. When under parked conditions, the blades are usually oriented with a pitch angle between 72º and 90º, changing the direction of vibration of the edgewise modes from in-plane rotor motion (when in operation) to out-of-plane (when in nonoperation conditions). Consequently, the support conditions of the blades are also changed with this transition. Due to these reasons, modes vibrating at the referred frequencies were not detected. It was then investigated if, during events from Regime 1 and 2, there were modes with natural frequencies next to these frequencies and with a tower mode shape similar to the ones from the 1 SS* and 2 SS* modes but vibrating in the FA direction (as referred, during non-operating conditions, the edgewise modes vibrate out of the plane rotor). The cluster referred to the found vibration modes during Regime 1 and 2 are shown in Figure 7.46 in lighter colours. It is seen that, while for the 1 SS* mode, the identified modes have natural frequencies close to each other during Regime 1 and 2 (݂ ≈ 1.26 Hz), the same does not happen for the 2 SS* (݂ = 1.63 Hz and ݂ = 1.81 Hz for, respectively, Regime 1 and 2). In Chapter 7 295 fact, the identified clusters for the 2 SS* mode present a considerably change in the natural frequency between Regime 1 and 2. Unfortunately, this situation could only be deeper investigated if instrumentation at the blades would be available. Even though, the referred clusters for Regime 1 and 2 were considered for monitoring purposes. Figure 7.46 – Evolution of the frequency values of the 1 SS* and 2 SS* with the rotor speed Likewise, although on a smaller scale, the natural frequencies of the second pair of tower bending modes (2 FA and 2 SS) also shows an increasing trend with the operating regimes. On the other hand, the 1 FA and 2 SS modes do not have a very distinct trend over the regimes, as shown in Figure 7.47 a) b) Figure 7.47 – Median (and box plots) of the frequency values: a) 1 FA mode; b) 1 SS mode 0 2 4 6 8 10 12 14 16 1 1.2 1.4 1.6 1.8 2 Rotor speed [rpm] Frequency [Hz] 1 SS* 2 SS* 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Rotor speed [RPM] Frequency [Hz] 0.34 0.345 0.35 0.355 0.36 0.365 0.37 12345678910111213141516 Rotor speed [rpm] Frequency [Hz] 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 12 2 34 4 56 6 78 8 910 10 1112 12 1314 14 1516 16 1718 18 1920 20 21 Wind speed [m/s] Frequency [Hz] 0.34 0.345 0.35 0.355 0.36 0.365 0.37 123456789 111315171921 Wind speed [m/s] Frequency [Hz] Structural Monitoring of Wind Turbines 296 Globally, the damping ratio of the FA modes increases with the increase of the wind speed (which usually implies a higher rotor speed). This is mostly due to the contribution of the aerodynamic component of damping. As expected, this increase of the damping values is not notorious in the SS modes due to the lower opposition to the wind flow in this direction. It is however noticed that the damping of SS modes increases in Regime 5. This is probably due to the aerodynamic change introduced by the increase of the blades pitch angle. The analysis of the evolution of the damping of the two pairs of bending modes illustrates the complex dynamics of a wind turbine. For non-operating conditions (Regimes 1 and 2), the damping values of the SS modes are higher than for the FA modes. This situation is due to the deviation of the rotor from the main wind direction and to the high pitch value of the blades. Under these conditions, the blades present a larger opposition to the wind flow in the SS direction, leading to the appearance of aerodynamic damping in this direction. Once the turbine starts operating, the rotor is orientated to the main wind direction and the blades pitch angle is set to its minimum value. These conditions, together with the higher wind speed, lead to the increase of the aerodynamic damping in the FA modes and the almost vanishing of this contribution in the SS modes. Since the aerodynamic damping component increases with the increase of the wind speed, the damping values of the 1 FA and 2 FA modes are consistently growing over the operating regimes. This effect is more noticeable for modes with large modal amplitude at the tower top, where the wind force is higher. For this reason, the 1 FA mode presents higher values than the 2 FA (whose modal amplitude at the top is very small). The top plots of Figure 7.48 illustrate the evolution of the damping ratio of the 1 FA and 1 SS vibration modes with the rotor speed. The increase of the damping values of the 1 FA mode when the turbine starts operating is evident. It is also noted that the damping increases when reaching the final part of the rotor speed range. Notwithstanding, these figures only shows the evolution of damping until the wind rated speed is achieved (around 13 m/s). For that reason, the lower graphic of Figure 7.48 presents the evolution of the damping of the 1 FA mode with the wind speed. The shape of the adjusted line clearly shows a drop in the damping value around 15 – 17 m/s. This situation is consequence of the increase of the pitch angle in Regime 5 which reduces the thrust force at the tower top and, consequently, reduces the rotor blades opposition to the wind flow in the FA direction. On the other hand, the adjusted line for the damping values of the 1 SS mode only shows small variations over the different operating conditions, with a reduction when the turbine starts operating and an increasing when reaching its rated speed. Chapter 7 297 a) b) Figure 7.48 – Median (and box plots) of the damping ratios: a) 1 FA mode; b) 1 SS mode The situation illustrated in Figures 7.36 and 7.37, about the possible change of mode shape orientation of the 2 SS mode for high wind speed conditions, was further investigated during the modal tracking. In that sense, an additional reference “mode” named 2 SS(/FA), based on the 2 SS mode but with an orientation between the FA and the SS direction, was considered. As results, it was possible to confirm that this “mode” was identified on setups in which the 2 SS was missing. Considering the number of setups in which the 2 SS(/FA) “mode” was tracked, the success rate of the 2 SS increases from 67.1 % to 85.5 % (with the p-LSCF algorithm). a) b) Figure 7.49 – a) Evolution of the 2 FA and 2 SS modes with the wind speed. b) Evolution of the 2 FA, 2 SS and the 2 SS/(FA) 0 2.5 5 7.5 10 12.5 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Rotor speed [m/s] Damping [%] 0 1 2 3 4 5 6 7 12345678910111213141516 Rotor speed [RPM] Damping [%] 0 2.5 5 7.5 10 12.5 15 12 2 34 4 56 6 78 8 910 10 1112 12 1314 14 1516 16 1718 18 1920 20 21 Wind speed [m/s] Damping [%] 0 1 2 3 4 5 6 7 12 2 34 4 56 6 78 8 910 10 11 12 12 13 14 14 1516 16 1718 18 19 20 20 21 Wind speed [m/s] Damping [%] 5 10 15 20 25 2.75 2.8 2.85 2.9 Wind speed [m/s] Frequency [Hz] 2 SS 2 FA 5 10 15 20 25 2.75 2.8 2.85 2.9 Wind speed [m/s] Frequency [Hz] 2 SS 2 FA 2 SS(/FA) Structural Monitoring of Wind Turbines 304 forward innovation model. While in the example of section 5.5, a manual selection was performed based on the observation of the stabilization diagram, an automated strategy for choosing the best model order is required as part of a monitoring system. The implemented strategy is thus based on the selection of the order with the highest number of stable poles whose clusters were chosen during the tracking procedure. When the turbine is operating (Regimes 4 and 5), cluster referred to the harmonics were also considered in the selection of the model order. For a cluster to be considered as representative of the stationary response due the harmonic excitation, its frequency value has to be within a range of 10 % of the multiples of the mean rotor speed from the setup under analysis. In cases in which there is more than one cluster meeting this condition, the cluster containing the higher number of poles is chosen. If this cluster has more poles than a pre-defined minimum number, it is defined as representative of the wind turbine response due to the harmonic excitation. In this application, a minimum number of 6 poles was defined. The 1Ω, 3Ω and 6Ω harmonics were considered in this analysis, although the first was only identified in 5.6 % of the operating setups. Figure 7.59 characterizes the RMS values of the modal contributions associated with the modes vibrating in the FA direction, alongside with the harmonics, at the +74.988 m level. It is visible that the dynamic motion is dominated mainly by the 3Ω harmonic and the 1 FA mode. As expected, the acceleration response in 1Ω harmonic frequency represents a very low level. It is also interesting to note that the 1 FA mode (and also the 6Ω harmonic) present a different behaviour from the other responses, do not continuously increasing with the increase of the rotor speed (or wind speed). It is observable that, when the turbine starts operating, there is a steep increase on the values from the 1 FA mode, which tend to disappear when the turbine reaches the 10 rpm. This increase in the modal acceleration response of the 1 FA is probably due to the excitation of this mode by the 3Ω harmonic. Considering Figure 7.35, it is possible to attest that the 3Ω harmonic is close to the 1 FA mode at rotor speeds between 8.7 and 10 rpm which can lead to the excitation of this mode and, consequently, to the increase of the vibration amplitudes. A similar situation seems to occur with 6Ω harmonic response. For wind speed around 3 m/s (corresponding to the start of the turbine), an increase of the acceleration levels is also visible in Figure 7.59 b). This situation is probably justified by the interaction between this harmonic and the non-tracked FA mode with a frequency around 0.80 Hz (Figure 7.35). a) b) Figure 7.59 – RMS values from the modal and stationary responses in the FA direction at level +74.988 m with: a) rotor speed; b) wind speed 0 2 4 6 8 10 12 14 16 1 7 0 0.05 0.1 0.15 0.2 0.25 0.3 Sensor: 1 (+74.988 m) Rotor speed [rpm] Acc. [m/s 2 ] 0 5 10 15 20 25 0 0.05 0.1 0.15 0.2 0.25 0.3 Wind speed [m/s] Acc.[m/s 2 ] +74.988 m 3Ω 6Ω 1Ω 1 FA 2 FA 4 FA Chapter 7 305 Once the recorded acceleration time series are decomposed into modal (and stationary) responses, it is possible to use the procedure introduced in section 5.5.3 to quantify the relative contribution of each responses to the measured signal. Likewise in the example from section 5.5.3, the acceleration responses due to the harmonic excitation were also considered in this analysis. This analysis is helpful to better understand the changes in the dynamic behaviour of the wind turbine structure over the different conditions. Figure 7.60 shows the evolution of the relative modal contribution of the FA modes and 1Ω, 3Ω and 6Ω harmonics to the measured acceleration at the tower top sensor with the wind speed. The median values (from each range of 0.5 m/s of wind speed) from the biggest contributors responses (1 FA mode, 3Ω and 6Ω harmonics) are represented by the lines in light colour. For low wind speed conditions (non-operating scenarios), the dynamic behaviour at the tower top is clearly dominated by the 1 FA mode, with participations of almost 100 % in certain setups. Once the turbine starts operating, the response is partially dominated by the 3Ω harmonic and by the 1 FA mode, whose participation is still representative mainly due to the excitation of this mode by the 3Ω harmonic, as previously explained. From the moment this effect vanishes, it is observed that the acceleration is practically dominated by the 3Ω harmonic. From this point, the participation of this harmonic and the 1 FA mode tend to converge to a participation of 30 % each with the increase of the wind speed. The participation of the 6Ω harmonic is only relevant when the turbine starts its operation, decreasing from this point to participation levels below 5 % with the increase of the wind speed. Figure 7.60 – Variation of the participation of the modal and stationary responses in the measured acceleration in the FA direction at level +74.988 m with wind speed The analysis presented to the sensor at the tower top was also performed at the +48.392 m level in the FA direction. The results are presented in Figure 7.61. The acceleration, in the FA direction, is dominated by the 2 FA mode with RMS values clearly higher than the ones presented in Figure 7.59 for the 1 FA mode. This result is probably justified by the excitation introduced by the blade rotation (due to the tower shadow effect) at the level +48.392 m, corresponding to the maximum modal amplitude of the 2 FA mode. Anyway, the dynamic displacements would be expected to be higher at the tower top than at +48.392 m due to the lowest natural frequency of the 1 FA when compared to the 2 FA mode. This is confirmed later in section 7.3.7. 0 5 10 15 20 25 0 0.25 0.5 0.75 1 Wind speed [m/s] Participation +74.988 m 3Ω 6Ω 1Ω 1 FA 2 FA 4 FA Structural Monitoring of Wind Turbines 306 a) b) Figure 7.61 – RMS values from the modal and stationary responses in the FA direction at level +48.392 m with: a) rotor speed; b) wind speed The quantification of the contribution of the modal and stationary responses to the measured acceleration time series was also assessed. The results are shown in Figure 7.62. In this figure, besides the modes considered in Figure 7.60, the stationary response due to the 9Ω harmonic was also included. However, it is important to note that around a rotor speed of 14 rpm, this harmonic crosses the potential untracked FA vibration mode, identified with a frequency of around 2.30 Hz (Figure 7.35). Since this potential mode was not considered during the tracking procedure, the automated algorithm developed to identify clusters related to the harmonics cannot distinguish, for this region of the Campbell diagram, a cluster representative of the 9Ω harmonic from one representative of this mode. Thus, it is possible that clusters referred in Figure 7.62 as due to the 9Ω harmonic are actually representative of this potential mode. The results presented in Figure 7.62 clearly show that, under low wind speed conditions (nonoperating regimes), the acceleration is dominated by the 1 FA mode. Some sparse points from the 1 FA with high modal contribution are also visible for high wind speeds but these are referred to setups with no power production. When the rotor starts operating, the contribution of the 1 FA drops drastically, keeping low for every wind speed condition. As expected, the acceleration is dominated by the 2 FA mode while the remaining the modes and harmonics are kept low during all operating conditions. Notwithstanding, it is observed that, for wind speeds around 7 and 13 m/s, the relative contribution of the 2 FA decreases slightly. This region coincides with the increase of the contribution of the 9Ω harmonic. This increase is due to the cross of this harmonic with the referred potential vibration mode with frequency of 2.30 Hz, leading to a possible interaction or resonance of this mode. For wind speeds higher than 13 m/s, the relative contribution of the 2 FA increases to levels similar to the ones obtained to winds speed below 7 m/s and the contribution of the 9Ω harmonic drops, meaning that this effect was reduced. 0 2 4 6 8 10 12 14 16 0 0.2 0.4 0.6 0.8 1 Rotor speed [rpm] Acc.[m/s 2 ] +48.392 m 3Ω 6Ω 1Ω 1 FA 2 FA 4 FA 0 5 10 15 20 25 0 0.2 0.4 0.6 0.8 1 Wind speed [m/s] Acc.[m/s 2 ] +48.392 m 3Ω 6Ω 1Ω 1 FA 2 FA 4 FA Chapter 7 307 Figure 7.62 – Variation of the participation of the modal and stationary responses in the measured acceleration in the FA direction at level +48.392 m with wind speed 7.3.6.5 Removal of Operational and Environmental Effects The characterization of the influence of the operational and environmental factors on the modal properties of the tracked vibration modes is an important step to remove a significant part of their variability. As these effects may introduce variations on the modal parameters with higher amplitudes than the damage itself, the removal of the influence of these effects is crucial to detect small damages at an early stage. Wind turbines are equipped with sensors measuring several operational and environmental conditions. This data is usually accessed through the SCADA system, as is the case of the Senvion MM82 wind turbine. Some of the results obtained with this data were used to illustrate the operating conditions of the turbine in section 7.3.3. For that reason, the application of methods to remove the influence of the effects that take into account measurements of the predictors (input-output methods) represents a suitable option to be applied to wind turbines. The definition of the regression models is usually performed considering a period of data large enough to include all the important variations of the predictors. In that sense, a period of one year is usually used to define the regression model (Magalhães, Cunha et al., 2012). This model is then used to evaluate the possible occurrence of damage in the following years. Since it was only possible to acquire acceleration data corresponding to a period of about one year, a slightly different strategy was followed in this work. Thus, the whole data was split into two different periods, consisting each one in data from intercalary days. With this strategy, both periods contain results within a period of one year, but from different days. Period 1 was then used to define a suitable multivariate regression model, while Period 2 was used to assess the existence of damage. The influence of some operational factors on the modal properties was already presented throughout section 7.3.6.2. As example, the effect of the rotor speed on the frequency values of the modes, namely for the 1 SS* and 2 SS*, was shown. The changes on the behaviour of the natural frequencies with the different operating regimes were also presented in Figure 7.44. The variability shown between regimes evidences the effect that different factors have on the wind turbine. For that reason, a different multivariate linear regression model was established for each operating regime, reflecting the different 0 5 10 15 20 25 0 0.25 0.5 0.75 1 Wind speed [m/s] Participation +48.392 m 3Ω 6Ω 1Ω 1 FA 2 FA 4 FA 9Ω Structural Monitoring of Wind Turbines 308 conditions. The operational and environmental factors recorded by the SCADA system and considered in this analysis were: o Wind speed (w. s.); o Outdoor temperature (temp.); o Rotor speed (r. s.); o Blade pitch angle (pitch). The operating regime 1 is characterized by values of blades pitch angle (around 90º) with small variations, during non-production setups. Thus, the considered predictors influencing the most the variability of the frequency values are the temperature and, in a small scale, the wind speed. These expected results are confirmed by the obtained correlation coefficients (computed according to equation (7.4)) and presented in Table 7.12. This coefficient permits to highlight the modes whose natural frequencies are more (linearly) influenced by the factors under study. Figures 7.65 and 7.66 show two examples of the correlation between natural frequency and the wind speed and temperature for two different modes, respectively. Table 7.12 – Correlation coefficients between natural frequencies and operational/ environmental factors (Regime 1) w. s. temp. r. s. pitch 1 SS 0.12 -0.23 0.08 0.08 1 FA 0.38 -0.28 0.34 -0.03 1 SS* -0.49 -0.36 -0.44 0.09 2 SS* 0.19 -0.57 0.01 0.46 2 FA 0.25 -0.64 0.15 -0.02 2 SS -0.13 -0.43 -0.13 -0.08 3 SS* 0.29 -0.70 0.21 -0.11 4 FA -0.36 -0.49 -0.35 -0.01 Figure 7.63 – Natural frequency of 1 SS* mode (Regime 1) vs wind speed Figure 7.64 – Natural frequency of 2 FA mode (Regime 1) vs temperature 0 5 10 15 20 25 1.2 1.22 1.24 1.26 1.28 1.3 Wind speed [m/s] Frequency [Hz] Linear fit 1 SS* 0 5 10 15 20 25 30 35 2.7 2.725 2.75 2.775 2.8 2.825 2.852.85 Temperature [ºC] Frequency [Hz] Linear fit 2 FA Chapter 7 309 Regime 2 is similar to Regime 1 to the extent that they are both referred to non-production setups, in which the blades pitch angles is kept almost constant (although at lower values in Regime 2). Thus, it is comprehensible that the predictors with the highest correlation with the natural frequencies are again the wind speed and the temperature, as seen in the results of Table 7.13. Table 7.13 – Correlation coefficients between natural frequencies and operational/ environmental factors (Regime 2) w. s. temp. r. s. pitch 1 SS 0.27 -0.28 0.33 -0.06 1 FA -0.11 -0.64 0.01 0.03 1 SS* -0.45 -0.36 -0.39 0.06 2 SS* -0.19 -0.39 -0.13 -0.03 2 FA -0.06 -0.57 0.03 0.03 2 SS -0.18 -0.36 -0.09 -0.05 3 SS* -0.12 -0.35 0.04 -0.12 4 FA -0.07 -0.31 -0.01 -0.15 The correlation coefficients obtained between natural frequencies from Regime 3 and operational/ environmental factors are shown in Table 7.14. Operating regime 3 corresponds to transition situation in which the turbine changes from parked/ idling configuration to operating conditions, or vice-versa. For that reason, both the rotor speed and pitch angle show important changes during these setups. However, apart from some modes (such as 1 SS*, 2 SS* and 4 FA modes), these changes do not seem to have an important influence on the frequency values. Table 7.14 – Correlation coefficients between natural frequencies and operational/ environmental factors (Regime 3) w. s. temp. r. s. pitch 1 SS -0.09 -0.33 -0.08 -0.01 1 FA 0.03 -0.19 0.22 -0.23 1 SS* -0.70 -0.37 0.09 -0.23 2 SS* 0.56 -0.26 -0.01 0.19 2 FA 0.02 -0.38 -0.02 0.00 2 SS -0.03 -0.31 0.25 -0.22 3 SS* 0.25 -0.12 0.05 0.02 4 FA 0.17 -0.20 0.32 -0.23 The number of identified setups regarded to Regime 4 is considerably higher than for the first 3 regimes. This fact permitted to obtain a better characterization of the variations of the natural frequencies for this regime. The results obtain for the correlation analysis are presented in Table 7.15. Structural Monitoring of Wind Turbines 310 Table 7.15 – Correlation coefficients between natural frequencies and operational/ environmental factors (Regime 4) w. s. temp. r. s. pitch 1 SS 0.22 -0.50 0.27 0.08 1 FA -0.40 0.02 -0.39 -0.14 1 SS* -0.93 0.15 -0.95 -0.26 2 SS* 0.91 -0.42 0.97 0.15 2 FA 0.44 -0.51 0.51 0.05 2 SS 0.23 -0.54 0.34 -0.05 3 SS* 0.84 -0.53 0.88 0.15 4 FA 0.41 -0.55 0.48 0.10 Both the rotor speed and wind speed (which are themselves correlated) present interesting high values of correlation with the frequencies. As expected, the pitch angle does not represent an interesting source for explanation of the frequencies variability, since its value is practically constant during this Regime. On the other hand, the temperature presents important linear relationship with the frequencies, which are confirmed by visual observation of the results. The evolution of the frequency values of the 2 FA mode with the temperature is illustrated in Figure 7.65. The highest correlation values are obtained with the rotor speed. Due to the nature of the whirl modes, this fact is especially important for the 1 SS* and 2 SS* modes. This phenomenon is illustrated for the 2 SS* mode in Figure 7.66. Although slightly lower than with the rotor speed, the correlation coefficients obtained with the wind speed are also relevant. However, this fact is mainly related to the relation between the wind speed and the rotor speed than to physical relations between the wind and the natural frequencies. Figure 7.65 – Natural frequency of 3 SS* mode (Regime 4) vs temperature Figure 7.66 – Natural frequency of 2 SS* mode (Regime 4) vs rotor speed Finally, Regime 5 is related to production setups with the strongest wind speed conditions. It is characterized by an increase of the blades pitch angle with the wind speed in order to control the rotor speed. This Regime is then commanded by the pitch angle, which in turn is defined according to the wind speed. The relation between the pitch angle and the wind speed was already introduced in Figure 7.14. Again, the 1 SS* and 2 SS* present a large variability of their frequency values due to operational 0 5 10 15 20 25 30 35 3.65 3.7 3.75 3.8 3.85 3.9 3.95 Temperature [”C] Frequency [Hz] Linear fit 2 FA 9 10 11 12 13 14 15 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 Rotor speed [m/s] Frequency [Hz] Linear fit 2 SS* Chapter 7 311 factors. The variation introduced by the pitch angle in the frequency values of the 1 SS* mode is shown in Figure 7.67. Also the temperature seems to be an important predictor of the natural frequency of the 1 SS mode. This relationship is illustrated in Figure 7.68. Table 7.16 – Correlation coefficients between natural frequencies and operational/ environmental factors (Regime 5) w. s. temp. r. s. pitch 1 SS -0.02 -0.47 0.00 -0.01 1 FA -0.31 -0.27 -0.34 -0.34 1 SS* -0.91 -0.19 -0.68 -0.92 2 SS* -0.68 -0.32 -0.42 -0.67 2 FA -0.22 -0.56 -0.26 -0.22 2 SS -0.06 -0.57 -0.05 -0.04 3 SS* -0.22 -0.47 -0.01 -0.19 4 FA 0.42 -0.11 0.33 0.43 Figure 7.67 – Natural frequency of 1 SS* mode (Regime 5) vs blades pitch angle Figure 7.68 – Natural frequency of 1 SS* mode (Regime 5) vs temperature Once the influence of the predictors was analysed for each regime, two alternative regression models were considered: SM1 and SM2. SM1 only considers the predictors with important physical relations with the natural frequencies. For that reason, even predictors with high correlation coefficients (such as wind speed in Regime 4 and 5) were not considered, since the coefficient value is not related to a physical relation with this predictor but to a correlation between other predictors, as previously referred. The predictors considered for this model are presented in Table 7.17. On the other hand, the SM2 model considers all predictors, aiming to define a general regression model with potential application without any previous analysis (Table 7.17). -5 0 5 10 15 20 25 1.22 1.24 1.26 1.28 1.3 1.32 1.34 Pitch angle [º] Frequency [Hz] Linear fit 1 SS* 0 5 10 15 20 25 30 0.34 0.345 0.35 0.355 0.36 0.365 0.37 Temperature [ºC] Frequency [Hz] Linear fit 1 SS Structural Monitoring of Wind Turbines 312 Table 7.17 – Considered predictors for regression models SM1 and SM2 SM 1 Regime SM 2 Regime Predictors 1 2 3 4 5 Predictors 1 2 3 4 5 w. s. x x x w. s. x x x x x temp. x x x x x temp. x x x x x r. s. x r. s. x x x x x pitch x pitch x x x x x The suitability of both models to produce forecasts was quantified through the computation of the coefficient of determination , presented in equation (7.8). For its calculation, the Period 2 of data was used to assess the quality of the forecasts (as previously referred, this period of data was not considered in the construction of the regression models). The results obtained for the two models are very similar (Table 7.18). In that sense, the SM 2 was chosen since it considers all predictors, making its use more general to be implemented in any wind turbine in any regime. It is observed from Table 7.18 that the modes related to rotor motion (1 SS*, 2 SS* and 3 SS*) present the highest values of . The good quality of the predictions of these modes is justified by the fact that the variability of these modes is mostly driven by the rotor speed, which is a known predictor. On the other hand, the 1st tower bending modes (1 SS and 1 FA) presents the lower coefficients of determination of all modes, showing that their variability is less dependent on the considered operational/ environmental effects. One possible cause to the low coefficients obtained for some modes might be related to the potential influence of asymmetric soil conditions on the natural frequency values, which could be considered by using the yaw angle as predictor in the regression model. However, it was decided not to use this predictor in order to assess the accuracy of the monitoring system to detect foundation asymmetries (see section 7.3.6.6). Notwithstanding, in situations in which the installation of the monitoring system is performed at an early stage of the turbine operation, the consideration of the yaw angle in the model would increase the accuracy of the system to detect abnormal structural changes. Table 7.18 – Coefficients of determination obtained with the regression models Modes SM 1 SM 2 1 SS 0.295 0.297 1 FA 0.377 0.391 1 SS* 0.965 0.967 2 SS* 0.950 0.952 2 FA 0.458 0.458 2 SS 0.706 0.719 3 SS* 0.860 0.864 4 FA 0.777 0.780 Chapter 7 313 Although steel structures do not usually present a significant thermal inertia, concrete structures do. Considering the importance of the support conditions (i. e. concrete foundation) in the definition of the dynamic properties of wind turbines, alternative dynamic models were also analysed in order to assess the influence of temperature records from previous time instants on the structure (see section 7.2.1.1). In that sense, 5 dynamic models were considered. These models consider all the predictors from the SM 2 model (including the temperature at the instant under consideration), along with the temperature records referred to different time delays of 3, 6, 12, 18 and 24 hours. For each dynamic model referred to a temperature measurement from a previous time instant, the temperatures from the more recent time instants were also considered. This means that, for a dynamic model considering temperature record with a delay of 12 hours, the temperature measurements from the current time instant and from time delays of 3, 6 and 12 hours were considered. The results obtained are shown in Table 7.19. In this table, the dynamic models are identified by the largest time delay considered. It can be seen that, although some improvements are noticed for the 1 FA and 3 SS* modes, smaller values were obtained for the 2nd pair of tower bending modes. Since the 2 FA and 2 SS modes are very sensitive to structural changes in the foundation condition and, consequently, represent important features to assess the existence of damage, the static model SM 2 was considered to be adequate to eliminate the environmental and operational effects on the frequency values. Table 7.19 – Coefficients of determination obtained with the dynamic models (the largest time delay considered for each model is indicated within parenthesis) Modes DM 1 (3 hours) DM 2 (6 hours) DM 3 (12 hours) DM 4 (18 hours) DM 5 (24 hours) 1 SS 0.296 0.293 0.292 0.284 0.299 1 FA 0.396 0.399 0.392 0.388 0.391 1 SS* 0.966 0.967 0.966 0.964 0.965 2 SS* 0.949 0.949 0.951 0.947 0.947 2 FA 0.450 0.445 0.436 0.440 0.428 2 SS 0.716 0.713 0.721 0.707 0.710 3 SS* 0.866 0.866 0.864 0.871 0.875 4 FA 0.775 0.774 0.771 0.767 0.770 In order to illustrate the quality of the SM 2 model, Figure 7.69 presents the predicted values of natural frequency of the 1 SS* and 4 FA modes for some data sets from Period 2, alongside with the identified values of these modes with the monitoring system. The accuracy of the prediction obtained with this model is clearly visible in this figure. Structural Monitoring of Wind Turbines 320 The presence of damage at just one (or two) blades leads to an anisotropic rotor. In that sense, the identification of such damage would be more easily detected through the identification of the 1Ω harmonic (as illustrated in Figure 4.18) or through the identification of phenomena such as the ones described in (Ramírez, Tcherniak et al., 2015), where a clear distinction in the singular values spectrum of the structure is identified between an isotropic and an anisotropic rotor. Therefore, the damage scenario D3 is referred to a similar deterioration of three blades, which may be caused by continuous wear of the blades due to operation. The stiffness of the three blades was decreased in 15 % over a length of 2 m, corresponding to 5 % of the total length of the blade. The damage was located at around 33 % in chord length from the blade root, which is said to be the location more prone to damage (Ciang, Lee et al., 2008). The imposed variation of stiffness led to a decrease of -0.65 % of the 1 SS* and 2 SS* rotor vibration modes. It was also noticed that the imposed stiffness variation was not significantly reflected in the other modes. For that reason, only the rotor modes 1 SS* and 2 SS* were used to detect this damage scenario. The variation of the natural frequencies of the vibration modes with the considered damage scenarios is resumed in Table 7.21. It is considered that the damage from each scenario occurred at the middle of Period 2. The artificial damage is thus introduced in the detected frequencies from the second part of Period 2 by reducing their values according to the values presented in Table 7.21. Table 7.21 – Variation of the natural frequencies of the modes associated with the damage scenarios Δ  [%] Modes D1 D2 D3 1 SS -0.20 -0.50 0.00 1 FA -0.20 -0.50 0.00 1 SS* 0.00 0.00 -0.65 2 SS* 0.00 0.00 -0.65 2 FA -0.40 -0.24 0.00 2 SS -0.40 -0.24 0.00 3 SS* 0.00 0.00 - 4 FA - - - The methodology followed to assess the presence of damage in the wind turbine is based on the use of  control charts, already introduced in section 7.2.2. This multivariate technique allows assessing the evolution of several vibration modes in the same chart. For the construction of these control charts, the residual error was used. As referred, the residual error is the difference between the identified frequency value of a vibration mode and its predicted value according to the defined SM 2 regression model, as illustrated in Figure 7.69. The control charts obtained for an undamaged situation and the three damage scenarios are presented in Figure 7.76. In their construction, groups with 36 observations were considered (corresponding to a quarter of a day). It is seen that the damages are clearly detected in all situations. However, a different upper limit control of the chart from the one defined in equation (7.15) was used due to the large number of false alarms obtained with this limit. This situation is most likely due to the fact that Chapter 7 321 features considered do not respect all the assumptions adopted for the definition of the limits (Magalhães, Cunha et al., 2012). To overcome this limitation, a different limit was imposed. This limit is defined by considering that 95 % of the values from the training period are considered within the safety region. Figure 7.76 –  control charts associated with a scenario where no damage is present and with the three defined damage scenarios This is a very relevant result, since it demonstrates that quite small damages in the foundation (and, although with less accuracy, in the blades) can be detected with the developed monitoring methodology. In the case of scenario D1, it is relevant to note that the identified damage (0.075) is considerably smaller than the recommended design value of 1.30 (Det Norske Veritas (DNV), 2011). It should be further referred that a longer monitoring period would even permit the detection of smaller frequency variations due to a better and more complete regression model and due to the possibility of using more observations to compute the  control chart, leading to more robust results. 0 50 100 150 200 250 300 Time T 2 Undamaged scenario 0 50 100 150 200 250 300 D1 Time T2 0 50 100 150 200 250 300 D2 Time T 2 0 50 100 150 200 250 300 D3 Time T2 Structural Monitoring of Wind Turbines 322 7.3.7 FATIGUE ASSESSMENT RESULTS The characterization of the fatigue condition of the wind turbine support structure was performed according to the procedure introduced in section 6.4.1. Unfortunately, it was not possible to install, during the period of this thesis, additional sensors to quantify the quasi-static motion of the tower. Consequently, this work is only focused on the estimation of the dynamic component of fatigue damage. The procedure is illustrated with 10 min. acceleration time series recorded during a period of strong wind conditions, with a mean wind speed of 20.9 m/s and maximum (instantaneous) speed of 35.9 m/s. During this period, the turbine operated at its rated rotor speed (around 16.5 rpm) and the blades pitch angle varied between 11.1º and 27.9º, in order to control the rotor torque. The acceleration time series collected by the dynamic monitoring system in the FA direction are presented in Figure 7.77. Figure 7.77 – Acceleration time series in the FA direction Prior to the integration process, the acceleration time series were multiplied by a time window with the aim of softening the start and end of the time series as discussed in section 6.4.1.1. These initial and last parts are then disregarded in the integrated displacement time series. After an initial analysis of several setups, it was considered that the disregarded of the initial and last 30 seconds would guarantee a safety margin to avoid transient errors. For the double integration process, the filter introduced in section 6.4.1.1 (Figure 6.12) was used. The constants of the filter ( and ) were set to only consider the dynamic component of the displacements. A good solution to tune these two parameters would be possible with the temporary use of instrumentation to measure the stress condition of the tower at an arbitrary condition. Since it is possible to estimate the stress condition at any position of the support structure with the presented methodology, the results obtained with the temporary instrumentation would be compared with the ones estimated with the accelerometers in order to tune the parameters. Since it was not possible to install this instrumentation, a compromise between the amplification of possible low frequency errors and the loss of relevant dynamic component information was studied with the help of numerical tests performed with the HAWC2 code (Larsen and Hansen, 2007). As result, the constants f and f were defined as, respectively, 0.10 Hz and 0.15 Hz. In that sense, the analysis described in this section regarding the fatigue assessment of the Senvion MM82 wind turbine is focused on the validation of the 0 100 200 300 400 500 60 0 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Time [s] Acceleration [m/s 2 ] +74.988 +48.392 +21.772 Chapter 7 323 developed procedure considering only the dynamic component of the fatigue, and not on the estimation of the real fatigue condition of the structure. Figure 7.78 shows the obtained displacements at the measurement levels in the FA direction. As expected, the displacements are higher at the top, in opposition to what was obtained with the acceleration time series (Figure 7.77). This result was expected since the displacements are mainly driven by the 1st pair of tower bending modes. In this figure, the transient initial and last parts are indicated by the vertical dashed lines and correspond to the referred 30 seconds in each part. Figure 7.78 – Dynamic displacement time series in FA direction (the vertical dashed lines indicate the disregarded initial and last part) Once the dynamic displacements along the turbine support structure are obtained, it is possible to estimate the dynamic component of the stress condition at any level of the tower. As an example, the bending stress at one point of the tower section at the foundation level was computed using the procedure based on the SSI-DATA identification algorithm described in section 6.4.1.1. The result is presented in Figure 7.79. Figure 7.79 – Estimated dynamic bending stress at the foundation level due to motion in the FA direction (the vertical dashed lines indicate the disregarded initial and last part) 0 100 200 300 400 500 600 -0.1 -0.05 0 0.05 0.1 0.15 Time [s] Displacements [m] +74.988 +48.392 +21.772 0 100 200 300 400 500 60 0 -40 -30 -20 -10 0 10 20 30 40 Time [s] Bending stress [MPa] Structural Monitoring of Wind Turbines 324 Lastly, the load cycles are counted with the Rainflow algorithm. The histogram with the number of bending stress cycles associated with different stress amplitudes is shown in Figure 7.80. The damage due to fatigue can then be assessed with the S-N curve defined for the detail under analysis. Figure 7.80 – Histogram with the number of bending stress cycles Considering that sensors installed at the tower structure are capable of detecting the motion in both orthogonal directions, the stress due to bending in the SS direction can also be computed with this methodology. With the stress condition computed in both FA and SS directions, it is thus possible to estimate the bending stress condition at any point of the tower cross section. Initially, the bending moment vectors in the FA and SS directions are reoriented according to the original SCADA referential (N-S, E-W). This coordinate rotation, illustrated in Figure 7.81, depends on the yaw angle. Figure 7.81 – Coordinate rotation from FA-SS referential to NS-EW referential Figure 7.82 – Calculation of the bending stress at a generic point P 0 10 20 30 40 50 60 70 80 0 50 100 150 200 250 300 350 Nº cycles Bending stress [MPa] N E S W MN-S ME-W MFA MSS FA direction SS direction N E S W β M N-S M E-W R.sin(β) σ P,N-S R.cos(β) σ P, E-W P Chapter 7 325 After defining the moment vectors in the original SCADA referential, it is then possible to estimate the stress condition at any point of the support structure cross section. This operation is illustrated in Figure 7.82 for a generic point . The stress condition at the point  is then defined according to: 󰇟.sin󰇛󰇜󰇠 󰇟.cos󰇛󰇜󰇠  (7.18) with:  Area moment of inertia of the cross section  Radius of the cross section A discretization of the cross section in 18 sectors was considered in order to assess the fatigue condition at the foundation level. The detail 71 from Eurocode 3 (European Comitee for Standardization (CEN), 2005) was used to study the welding-on flange connection between the tower and the foundation (Sørensen and Sørensen, 2011). The S-N curve corresponding to this detail was already introduced in Figure 6.7. Alongside with the bending stress estimation, it is also of utmost importance to have confidence on the obtained results. Since the procedure estimates the acceleration time series as a sum of vibration modes/ harmonics, it is necessary to evaluate if the estimations do not underestimate the motion of the structure (due to a badly defined state-space model) or, on the other hand, overestimate the importance of some frequency content (due to numerical residues). In that sense, the residual error ∆ from the forward innovation model (equation (5.80)) can be used to assess the quality of the estimated acceleration time series. However, in the context of stress estimation, in which a double integration is performed to estimate the displacement time series, the use of residual error as the only quality control parameter is not sufficient. Figure 7.83 shows an example of an estimated acceleration time series obtained from the forward innovation model, using all the 7 installed sensors. The residual error ∆ obtained is low (2 %), indicating that the estimation is good. The good agreement between the two signals is visually verified. Structural Monitoring of Wind Turbines 326 Figure 7.83 – Measured and estimated acceleration time series at the level +21.772 in the SS direction, considering all sensors as input for the forward innovation model (the right hand side figure shows a zoom of the time segment identified in the left hand side figure by the dashed lines) However, looking at these results in the frequency domain, important errors in the lowest part of the frequency range are observed. Figure 7.84 shows the power spectral density of the measured and estimated acceleration time series illustrated in Figure 7.83 (the spectrum is averaged with segments of 1024 points in order to facilitate the explaination). From this figure, it is possible to attest that, although a good estimation is obtained around important resonance peaks (namely the 1st and 2nd tower bending modes, as well as the 3Ω and 6Ω harmonics), there is an erroneous increase of the amplitude of several peaks in the low part of the spectrum. Since the response is clearly dominated by the 2nd bending mode, these errors are almost imperceptible in time domain, as evidenced in Figure 7.83. This is the reason why the error ∆ is low. Figure 7.84 – Measured and estimated acceleration time series (in frequency domain) at the level +21.772 in the SS direction, considering all sensors as input for the forward innovation model The main problem related to the bad estimation of the lower part of the spectrum occurs during the integration process to estimate the displacement time series. As referred in section 6.4.1.1, during this operation, the amplitude of vibrations related to the low frequencies is increased. Consequently, the displacement time series obtained from the measured and estimated acceleration will lead to considerably different results. Figure 7.85 illustrates the displacement time series obtained from the 0 100 200 300 400 500 60 0 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Time [s] Acc. [m/s 2 ] Measured Estimated 325 330 335 340 345 35 0 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Time [s] Acc. [m/s 2 ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10-10 10-8 10-6 10-4 Frequency [Hz] Amplitude Measured Estimated Chapter 7 327 measured and estimated acceleration signals represented in Figure 7.83. The erroneous majoration of the displacements obtained from the estimated signals is evident. Under these circunstancies, the estimation of the stress condition would naturally lead to erroneous results. Figure 7.85 – Displacement time series obtained with the double integration process based on the measured and estimated acceleration signals Due to possible occurrence of situations such as the one described, an additional quality index of the estimation is required to assess the adjustment in the lowest part of the spectrum. An index ∆ based on the relative difference of the energy countained in the lowest part of the frequency range of the estimated and measured acceleration signals was chosen. This index is defined as the ratio between the area defined by the difference of the spectra of the estimated and measured acceleration and the area defined by the spectrum of the measured acceleration signal (dark grey area in Figure 7.86). Only the frequency range between  and  is considered to compute this index. In the present work, these values were defined as 0.10 Hz (equal to ) and 0.35 Hz, in order to evaluate the adjustment of the signal for the frequency range below the 1st tower bending mode. Figure 7.86 – Definition of the area between the spectra of the estimated and measured acceleration signals and the area from the measured signal The results obtained for the quality indices using data sets collected during one year of monitoring were initially assessed. It was observed that the quality index ∆ is not very restrictive. Figure 7.87 a) 0 100 200 300 400 500 60 0 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 -3 Time [s] Disp. [m] Measured Estimated 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 10 -10 10 -8 10 -6 10 -4 Frequency [Hz] Amplitude Measured Estimated f 1 f 2 Structural Monitoring of Wind Turbines 328 shows the evolution of percentage of selected 10 min. time series events with the value adopted for ∆ considering the results obtained with the three tested modal identification algorithms. It is seen that for the method based on the SSI-DATA algorithm almost all events are considered for an admissible level of 0.15. For the other algorithms, it is visible that the estimations are apparently not so good. a) b) Figure 7.87 – Percentage of considered events with the evolution of: a) ∆ index; b) ∆ index The values computed for the second quality index ∆, referred to the quality of the adjust on the lowest frequency range of the spectrum, were also initially assessed. The percentage of events considered with the evolution of the ∆ index is presented in Figure 7.87 b). It was concluded that most results contain an increase of the energy in the frequency range considered for this index (0.1 – 0.35 Hz). It was thus noticed that the biggest problem associated with the bad estimation of this part of the spectrum is related to the unrealistic increase of the computed stress levels of the structure. It is interesting to note that the quality of the results provided by the alternative identification methods is inverse to the quantified by the index ∆. Nevertheless the difference is not very large. Based on this preliminary analysis of the quality indices, a strategy was defined to accurately disregard bad estimations of the fatigue damage. In that sense, it was decided to use the ∆ index to identify and dismiss events in which the defined forward innovation model was clearly not capable to estimate the acceleration time series as a sum of contributions of vibration modes/ harmonics. A value of ∆ = 0.20 was thus chosen, since it considers almost all events and, at the same time, imposes a limit that guarantees the quality of the estimates. The maximum admissible value of the ∆ was defined to admit a maximum error ∆ = 0.90. With this value, a rate of considered events of more than 90 % was achieved when the combination of the best estimations obtained from the three algorithms is computed. At this point, the fatigue damage estimation from the recorded acceleration time series can be computed. Figure 7.88 shows the evolution of accumulated damage calculated with the SSI-DATA algorithm at the welding-on flanged connection between the tower and the foundation using the S-N curve from the GL standard. From this figure, two periods of time with a rapid increase of damage are noticed. The first period corresponds to events occurred during November 2013, while the second occurs in February 2014. It is interesting to note that these two periods correspond to two long periods of consecutive data sets with high mean wind speeds. 0 0.1 0.2 0.3 0.4 0 .5 0 20 40 60 80 100 Percentage of considered events [%] Quality index Δ e SSI-DATA SSI-COV p-LSCF 0 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 Quality index Δ freq Percentage of considered events [%] SSI-DATA SSI-COV p-LSCF Chapter 7 329 It is also interesting to confirm that the most damaged sectors are the 100º-120º (and its symmetric 280º-300º) which is in accordance with the main wind direction of the wind (around 110º, see Figure 7.15). Figure 7.88 – Time history of the accumulated damage at the foundation level (with S/N curve from GL standard) using the methodology based on the SSI-DATA algorithm A direct extrapolation of the accumulated damage to the expected life of the wind turbine (20 years) can be performed according to equation (7.16). The results obtained with the three methods are presented in Table 7.22. As expected, the values obtained with the S-N curve from the EC3 code are slightly lower due to the consideration of the threshold referred in section 6.3.2 (Figure 6.7). Table 7.22 – Direct extrapolated accumulated damage at the end of the design life SSI-DATA SSI-COV p-LSCF GL 0.0420 0.0422 0.0213 EC3 0.0319 0.0339 0.0195 Success rate [%] 76.8 64.0 46.7 The results obtained present very low values of accumulated damage. Nevertheless, some important aspects should be highlighted. Firstly, it should be noted that the estimated damage is only referred to the dynamic component of the bending stress. Large loading cycles from the quasi-static frequency regime, which might have important contributions to the fatigue damage of the structure are not considered in these results. Two additional causes for this low accumulated damage should be also referred. The location of the Senvion MM82 wind turbine is considered a low-turbulence site, which means that high amplitude stress variations are not expected to occur frequently. This aspect has a direct impact on the estimation of the fatigue life of the analysed structural detail, since it only depends on the measured amplitude of the stress cycles and not on the mean stress level. In addition, technical problems occurred at the beginning of October, preventing the operation of the dynamic monitoring system during this month and almost the entire month of November. Thus, considering the detected high rate of damage during the end of November, it is very likely the occurrence of important events 0 1 2 3 4 5 6 7 8 x 10 -4 Accumulated Damage [0º-20º]/[180º-200º] [20º-40º]/[200º-220º] [40º-60º]/[220º-240º] [60º-80º]/[240º-260º] [80º-100º]/[260º-280º] [100º-120º]/[280º-300º] [120º-140º]/[300º-320º] [140º-160º]/[320º-340º] [160º-180º]/[340º-360]º Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2013 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Time Structural Monitoring of Wind Turbines 336 Figure 7.92 –  control charts associated with a scenario where no damage is present and with the three defined damage scenarios (Layout 1) Fatigue Results The estimation of fatigue damage using a single level of measurement is an interesting application for the methodology introduced with the virtual sensors in section 6.4.2. With this methodology, it is possible to estimate the response of the wind turbine support structure at any point of the structure, using only a (“well positioned”) single reference measurement point. In the case of the Layout 1, this reference point is the top measurement level. However, as was previously referred, this measurement position cannot be considered as “well positioned” since it coincides with a level of very low modal amplitude of an important vibration mode. Thus, it is not possible to accurately estimate the mode shape of this mode. In that sense, it was decided to despise all vibration modes and harmonics with a frequency value higher than 2 Hz. With this imposition, not only the second pair of bending modes is disregarded, but also some integer multiples of the harmonics are avoided since their operational deflection shapes also present a very low modal amplitude at the top of the tower. The importance of the second pair of tower bending modes in the context of the dynamic behaviour of the wind turbine structure was already described in section 7.3.6.4. It is thus expected that, using this sensor layout, the estimation of the acceleration at the middle and lower part of the tower will be underestimated. Figure 7.93 illustrates this problem, using the acceleration time series collected by the S8 and S9 sensors during a production period (rotor speed = 12.4 rpm). The acceleration signals were then processed by the methodology based on the p-LSCF algorithm. The top figures compare the 0 50 100 150 200 250 300 Undamaged scenario Time T2 0 50 100 150 200 250 D1* / D2 Time T 2 0 50 100 150 200 250 D3 Time T2 Chapter 7 337 original signal recorded by the sensor in the FA direction with the estimated signal as a sum of modes/ harmonics at the measured level in time and frequency domain. On the other hand, the plots at the middle and bottom of Figure 7.93 are referred to the estimations of the acceleration at unmeasured levels. Taking advantage of the non-used sensors (at levels +21.722 m and +48.392 m), the estimated acceleration time series at unmeasured locations are compared with the real measured time series. Figure 7.93 – Original and estimated acceleration time series at the measured level (+74.988 m) and unmeasured levels (+48.392 m and +21.772 m) in the FA direction The observation of the plots in Figure 7.93 clearly shows that, as expected, the disregard of the energy contribution from the spectrum for frequency values higher than 2 Hz leads to an important underestimation of the acceleration at the lowest 2/3 of the tower. Nevertheless, it is seen that, for the 0 100 200 300 400 500 60 0 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Time [s] Acc. [m/s 2 ] +74.988 (FA) - measured Original Estimated 0 0.5 1 1.5 2 2.5 3 3.5 4 4 .5 10 -3 10 -2 10 -1 10 0 10 1 10 2 +74.988 (FA) - measured Frequency [Hz] Amplitude Original Estimated 0 100 200 300 400 500 60 0 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Time [s] Acc. [m/s 2 ] +48.392 (FA) - unmeasured Original Estimated 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 10-3 10-2 10-1 100 101 102 Frequency [Hz] Amplitude +48.392 (FA) - unmeasured Original Estimated 0 100 200 300 400 500 60 0 -0.1 -0.05 0 0.05 0.1 Time [s] Acc. [m/s 2 ] +21.772 (FA) - unmeasured Original Estimated 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 10 -4 10 -2 10 0 10 2 +21.772 (FA) - unmeasured Frequency [Hz] Amplitude Original Estimated Structural Monitoring of Wind Turbines 338 considered frequency range, the agreement between the estimated and the real acceleration signal is quite good. Even the contribution of the 3Ω harmonic (represented by the large peak around 0.62 Hz), which requires the estimation of its operational deflection shape, shows a good agreement. The processing for fatigue damage estimation was then applied to the estimated acceleration signals. In order to illustrate the quality of the results obtained with this layout configuration, the dynamic component of the bending stress from a 10 min. period acceleration event at the foundation level was computed. The results were compared with the stress estimation obtained with the methodology based on the SSI-DATA considering the three levels of measurement, since it is considered the most accurate of the implemented procedures. The bending stress computed with the two procedures is shown in Figure 7.94. It is visible that the bending stress is underestimated mostly due to the non-consideration of the energy of the spectrum for frequency values higher than 2 Hz. Computing the damage associated with the two estimations (using the S-N curve from the GL standard), it is concluded that the value obtained with the procedure based on the p-LSCF with Layout 1 is 3.2 times lower than the value achieved with the SSI-DATA methodology using all sensors. Figure 7.94 – Estimated dynamic bending stress at the foundation level due to motion in the FA direction (the vertical dashed lines indicate the disregarded initial and last part) The same quality indices introduced in section 7.3.7 (∆ and ∆) were used to despise erroneous estimations of fatigue damage. Naturally, these indices are only referred to the results associated with the considered S8 and S9 sensors. Figure 7.95 illustrates the evolution of percentage of acceleration events with the increase of the indices. Comparing these results with the ones presented in Figure 7.87, it is visible with the index ∆ that the errors associated with the quality of estimation of the acceleration time series are higher. Qualitatively, it is seen that the procedure based on the SSI-DATA algorithm shows the best results, followed by the SSI-COV and, lastly, the p-LSCF, just like when all sensors were used. In relation to the index ∆, the p-LSCF algorithm shows, again, the best results. However, with this sensor layout solution, the difference to the other methods is higher than when all sensors are used. 0 100 200 300 400 500 600 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Time [s] Bending stress [MPa] SSI-DATA (all sensors p-LSCF (Layout 1) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Frequency [Hz] Amplitude SSI-DATA (all sensors p-LSCF (Layout 1) Chapter 7 339 a) b) Figure 7.95 – Percentage of considered events with Layout 1 with the evolution of: a) ∆ index; b) ∆ index As referred in section 7.3.7, the comparison of the direct extrapolated damage obtained with each methodology does not lead to a correct estimation of the quality of the results since it compares estimations of damage from different events. It is visible in the probability density function of Figure 7.96 a) that the considered events for each methodology differ considerably from each other. a) b) Figure 7.96 – Probability density function of wind speed (in the sector 100º-120º) recorded by the SCADA system and from the data considered for fatigue estimation with Layout 1 with: a) the thee algorithms; b) best estimations from the thee algorithms Thus, the estimated damage obtained with each methodology was compared with the damage estimated with the SSI-DATA using all sensors (considered the reference methodology) for the same events. The deviations obtained with the three methodologies are presented in Table 7.27. 0 0.1 0.2 0.3 0.4 0 .5 0 20 40 60 80 100 Quality index Δe Percentage of considered events [%] SSI-DATA SSI-COV p-LSCF 0 1 2 3 4 0 20 40 60 80 100 Quality index Δfreq Percentage of considered events [%] SSI-DATA SSI-COV p-LSCF 0 5 10 15 20 25 0 5 10 15 20 Wind speed [m/s] Percentage of occurrence [%] 1 year SSI-DATA SSI-COV p-LSCF 0 5 10 15 20 25 0 2 4 6 8 10 12 Wind speed [m/s] Percentage of occurrence [%] 1 year Layout 1 Structural Monitoring of Wind Turbines 340 Table 7.27 – Deviation of accumulated damage of coincident events between results with Layout 1 and the methodology based on SSI-DATA algorithm using all sensors SSI-DATA (All sensors) SSI-DATA SSI-COV p-LSCF GL - -67.4 % -69.3 -41.2 % EC3 - -68.9 % -71.1 -42.0 % Success rate [%] 76.8 60.7 37.4 26.7 From the results, it is evident that the damage estimations with Layout 1 were not very good. The damage obtained with the three methodologies is clearly underestimated. Also the success rate achieved is low, with only one methodology (based on the SSI-DATA) showing a rate higher than 50 %. Lastly, the fatigue damage using the best estimations from the three algorithms was computed. With this estimation, the distribution of considered wind speed events is close to the distribution obtained with the SCADA data (Figure 7.96 b)). The results are introduced in Table 7.28, where they are compared to the ones obtained with the best estimation using all sensors. Again, the values are considerably underestimated. Table 7.28 – Estimation of accumulated damage at the end of design life considering an adjusted extrapolation according to the PDF of the wind speed using the best estimations from the three algorithms All sensors Layout 1 Error GL 0.0371 0.015 -57.8 % EC3 0.0283 0.013 -52.4 % Success rate [%] 91.0 79.4 - 7.3.8.2 Layout 2 (+48.392 m level) Layout 2 represents an optimization of Layout 1. While the use of the top level as single level of measurement showed that it is not possible to consider the 2nd pair of bending modes, Layout 2 optimizes the selection of the single level of measurement. It was decided to use the measurement level at around 2/3 of the tower height (+48.392 m), since it (theoretically) enables the identification of all the important vibration modes. Looking to Figure 7.40, it is visible that none mode shape presents a reduced modal amplitude at this level. Modal Tracking and Damage Detection The same procedure described in section 7.3.6.2 was followed using the acceleration data collected by sensors S6 and S7 (at level +48.392 m). Just like in the case of Layout 1, a minimum MAC value of 0.50 was imposed during the modal tracking in order to distinguish between FA and SS modes. The Campbell diagram defined by the results obtained with the modal tracking procedure based on the pLSCF algorithm is presented in Figure 7.97. From this figure, it is visible the good quality of the identification of the second pair of tower bending modes, confirming the suitability of the measurement location. On the other hand, it is visible that the 15Ω harmonic hinders the identification Chapter 7 341 of the 3 SS* mode. In fact, some clusters referred to this harmonic are misidentified as being from this mode. As for the other vibration modes, no further erroneous modal identifications were detected. Figure 7.97 – Campbell diagram with the tracked vibration modes with Layout 2 (p-LSCF algorithm) The success rate in the identification of the 9 vibration modes is summarized in Table 7.29. It is concluded that the results are good for the 1 SS, 1 SS*, 2 SS*, 2 FA and 2 SS modes, with high rates of success in the tracking process. On the other hand, the identification of the 1 FA presents a very low success rate, especially for the p-LSCF. Table 7.29 – Success rate and coefficient of variation obtained with the identification algorithms (with Layout 2) Mode SSI-COV SSI-DATA p-LSCF Success Rate [%]  .. Success Rate [%]  .. Success Rate [%]  .. 1 SS 90.0 0.005 94.8 0.005 64.6 0.005 1 FA 46.0 0.018 61.0 0.019 18.6 0.016 1 SS* 48.7 0.040 84.7 0.037 29.6 0.034 2 SS* 84.6 0.031 93.4 0.031 72.5 0.029 2 FA 90.6 0.009 92.1 0.009 90.3 0.006 2 SS 73.5 0.012 83.3 0.011 72.8 0.010 3 FA/ 3SS 7.2 0.017 12.2 0.016 18.4 0.016 3 SS* 55.2 0.019 61.6 0.021 63.9 0.018 4 FA 30.6 0.018 76.2 0.018 96.2 0.018 After the modal tracking, the environmental and operational effects were removed from the frequency values, using a multivariate analysis (similar to the procedure described in section 7.3.6.5). Thus, using the frequency values as damage indicators, the three damage scenarios presented in section 7.3.6.6 (considering the dynamic monitoring system with three levels of measurement) were tested (see Table 7.21). 0 2 4 6 8 10 12 14 16 18 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Rotor Speed [RPM] Frequency [Hz] Campbel Diagram 1 FA 1 SS 1 SS* 2 SS* 2 FA 2 SS 3 SS* 3 FA/SS 4 FA [Document text truncated for crawler view.]