Multi-disciplinary Optimization of Rotor Nacelle Assemblies for Offshore Wind Farms An Agile Systems Engineering Approach
Tanuj Tanmay
Multi-disciplinary Optimization of Rotor Nacelle Assemblies for Offshore Wind Farms An Agile Systems Engineering Approach
by
Tanuj Tanmay
in partial fulfillment of the requirements for the degree of Master of Science in Sustainable Energy Technology at Delft University of Technology
Student number: 4614844 Project duration: Nov 13, 2017 - Aug 13, 2018 Thesis committee: Prof.dr. Simon Watson TU Delft, Chairman Dr.ir. Michiel Zaaijer TU Delft, Supervisor Dr. Julie Teuwen TU Delft Sebastian Sanchez Perez- TU Delft Moreno
Keywords: systems engineering, multi-disciplinary optimization, offshore wind farms, rotor nacelle assembly
Cover photo: Siemens An electronic version of this thesis is available at http://repository.tudelft.nl/. Whatever you do will be insignificant, but it is very important that you do it. Mahatma Gandhi CONTENTS
Summary 5
Preface 7
Glossary 9
1 Introduction1 1.1 Overview...... 1 1.2 Problem statement...... 2 1.3 Scope...... 3 1.4 Research theme...... 3 1.4.1 Main objective...... 3 1.4.2 Research objective #1...... 4 1.4.3 Research objective #2...... 5 1.4.4 Research objective #3...... 5 1.5 Report organization...... 6
2 Systems Engineering of Offshore Wind Farms7 2.1 Background...... 7 2.1.1 Systems engineering...... 7 2.1.2 MDAO...... 8 2.1.3 Agility...... 8 2.2 System ontology...... 9 2.2.1 WINDOW...... 9 2.2.2 Coupling of RNA with WINDOW...... 12
3 Design Iteration #1 13 3.1 Use case...... 14 3.2 Literature survey...... 15 3.3 Development...... 16 3.3.1 Model assessment...... 16 3.3.2 Blade...... 17 3.3.3 Hub & Nacelle...... 24 3.3.4 Cost...... 30 3.3.5 Coupling the disciplines...... 31 3.4 Validation...... 33 3.5 Analysis...... 36
3 4 CONTENTS
4 Design Iteration #2 43 4.1 Use case...... 44 4.2 Literature survey...... 46 4.3 Development...... 48 4.3.1 Design scaling...... 48 4.3.2 Aerodynamic design...... 48 4.4 Validation...... 49 4.4.1 Response variables...... 49 4.4.2 Energy yield...... 50 4.4.3 Cost...... 53 4.4.4 Levelized cost...... 55 4.4.5 Error analysis...... 55 4.5 Analysis...... 58 4.5.1 Square farm layout...... 58 4.5.2 Rectangular farm layout...... 61 5 Design Iteration #3 65 5.1 Use case...... 66 5.2 Literature survey...... 68 5.3 Development...... 69 5.3.1 Model assessment...... 69 5.3.2 Model update...... 70 5.4 Validation...... 73 5.4.1 Error identification...... 73 5.4.2 Error analysis...... 74 5.5 Analysis...... 75 5.5.1 RNA Scaling with different configurations...... 75 5.5.2 Reliability study of different configurations...... 78 6 Concluding Remarks 81 6.1 Conclusion...... 81 6.2 Retrospection...... 84 6.3 Recommendation...... 84 Epilogue 85 A Appendix 87 A.1 Chapter 3...... 87 A.2 Chapter 4...... 91 A.3 Chapter 5...... 91 References 93 SUMMARY
The models with different fidelities for the siloed application of niche wind farm dis- ciplines - rotor aerodynamics, aeroelasticity or wake aerodynamics - are prevalent in literature. These models are often used sequentially while designing a wind farm that may lead to a sub-optimal design due to their agnosticism towards the inter-disciplinary influences. This paper demonstrates the multi-disciplinary optimization of rotor nacelle assemblies for offshore wind farms. The designs of three aspects of rotor nacelle assembly are addressed - rotor blade, power density and drive train configuration - that support the development of an open-source agile systems engineering framework and allow flex- ibility in their utility to various stakeholders of offshore wind farms.
The first research objective is to develop insight into the benefits of systems engineer- ing by studying the effect of system scope on the rotor design. The dissemination of knowl- edge on the utility of the tool in painting a bigger picture of an offshore wind farm among the wind energy researchers is intended. It is found that the siloed application or the op- timization of blade design in a limited system scope leads to a sub-optimal design at the wind farm level because they fail to capture the inter-disciplinary influences with the support structure, wake effect and cable topology. The LCOE of the wind farm is mini- mum when the system scope for the blade design is at the wind farm level.
The second research objective is to study the effect of the rotor radius and its rated power on the LCOE of the wind farm. The dissemination of knowledge on the utility of the tool in designing a wind turbine specific to a particular offshore site among the wind tur- bine/farm developers is intended. The disciplines outside the RNA respond non-linearly to the changes in the RNA size, which necessitates a systems engineering framework that captures such inter-disciplinary dynamics to find an optimal rotor size. It is found that a turbine with lower power density is optimal for a site with lower wind resource, and vice-versa. The position of the substation has a large influence on the cable topology and the farm layout.
The third research objective is to compare various drive train configurations and the effect of their reliability on the LCOE of the wind farm. The dissemination of knowledge on the utility of the tool to select an optimal drive train configuration for a given rotor among the wind turbine manufacturers is intended. The coupling of cost, efficiency and reliability of the drive train configurations to the offshore wind farm enables detailed comparison of such configurations at the wind farm level. The analysis leads Permanent Magnet Synchronous Generator with 1-stage gearbox to be the most favorable configu- ration. A higher reliability from Permanent Magnet Synchronous Generator with direct- drive is expected so that its levelized cost of energy breaks-even with that of the geared configurations.
5
PREFACE
The opportunity for research in form of a thesis in the masters programme was the pri- mary factor that lured me to TU Delft. The remarkable journey of this thesis was marked by the test of perseverance, the sense of gratification and the realization of the passion for wind energy. This journey would not have been possible without the help and sup- port of the people around me.
My utmost gratitude goes to Dr. Michiel Zaaijer and Sebastian Sanchez. Dr Zaaijer’s nimble remarks, words of wisdom, easy accessibility and meticulous feedback gave the necessary shape and direction to the thesis. Without the elegant framework built by our Chief Software Architect, Sebastian, and his help, it would not have been possible to ac- complish the goals of this project.
My gratitude extends to my friends and family whose support never let the stress of the thesis to creep into me. I would specially like to thank Steyn Verschoof for orientating me to the Dutch lifestyle.
The final credit goes to Ayn Rand’s The Fountainhead for being the fountainhead of my motivation and courage for the disruptive idea of pursuing this masters.
Tanuj Tanmay Delft, August 2018
7
GLOSSARY
Abbreviations
AEP Annual Energy Production
BEM Blade Element Momentum
CARB Compact-Aligning toroidal Roller Bearing
CFD Computational Fluid Dynamics
DFIG Doubly Fed Induction Generator
DTU Danmarks Tekniske Universitet
FEM Finite Element Method
FUSED Framework for Unified Systems Engineering and Design of Wind Plants
IEC International Electrotechnical Commission
IO Input-Output
LCOE Levelised Cost of Electricity
MDAO Multi-Disciplinary Analysis & Optimization
N5RT NREL 5 MW Offshore Reference Turbine
NREL National Renewable Energy Laboratory
O&M Operations and Maintenance
OWF Offshore Wind Farm
PMSG Permanent Magnet Synchronous Generator
RNA Rotor Nacelle Assembly
SE Systems Engineering
SRB Spherical Roller Bearing
TI Turbulence Intensity
UTS Ultimate Tensile Strength
WINDOW Windfarm Integrated Design and Optimization Workflow
9 10 PREFACE
WISDEM Wind-Plant Integrated System Design and Engineering Model
XDSM Extended Design Structure Matrix
Subscripts aer o aerodynamic bed bedplate cc cable cost conv converter decom decommissioning des design dt drive train edge edgewise elec electrical ew east to west direction f l ap flapwise gb gearbox gen generator gr av gravity hss high speed shaft l ss low speed shaft mb main bearing nor m normalized ns north to south direction oi other investments peg pegged points pl at nacelle platform re f NREL 5MW Reference Offshore Turbine r na rotor nacelle assembly ss support structure PREFACE 11
ts f transformer
Constants
3 ρair density of air [1.225 kg/m ]
g acceleration due to gravity [9.8 m/s2]
E Young’s modulus of blade material [36.23 GPa]
UTS UTS of blade material [400 MPa]
Symbols
α wind shear factor [-]
δti p tip deflection [m]
η efficiency [-]
γ safety factor [-]
κ capacity factor [-]
Λ availability of the wind farm [-]
λ tip speed ratio [-]
µ mass per unit length of the blade section [kg/m]
Ω rotor rotational speed [r ad/s]
Ψ shaft tilt angle [°]
σ stress [Pa]
τ thickness factor [-]
θ blade pitch angle [°]
Fhub~ force vector at the centre of the hub [N]
M~hub moment vector at the centre of the hub [Nm]
ζ rotor power density [kW /m2]
a annuity factor [-]
B number of blades [-]
C cost [e]
c chord length [m]
Cp power coefficient [-] 12 PREFACE
Cq torque coefficient [-]
Ct thrust coefficient [-]
D diameter [m]
dr length of the blade section [m]
E Young’s modulus [N/m2]
EI stiffness [Nm2]
fx force at the blade section normal to the plane of rotation [N/m]
fy force at the blade section tangential to the plane of rotation [N/m]
H height [m]
I area moment of inertia [m4]
L length [m]
M bending moment [Nm]
m mass [kg]
Np number of planets in each gearbox stage [-]
Nt number of turbines in the farm [-]
Pr ated machine rating [kW]
Qr otor rotor torque [Nm]
R radius [m]
r radial distance along the blade section [m]
rgb gearbox ratio [-]
t maximum blade thickness [m]
Tr otor rotor thrust [N]
U ambient wind speed [m/s] ∞ 1 INTRODUCTION
1.1. OVERVIEW The wind of change, of energy transition and sustainable future, is gaining strength; and so is the expectation from wind energy. Bloomberg predicts an influx of investments worth $3.3 trillion in building new wind power capacity over the period of 2017 to 2040, approximately a third of the global investment in new power generations [1]. However, the proliferation of wind energy conflicts with the concerns for land usage, noise and vi- sual impact. This has led to an increasing interest in offshore wind farms (OWF) as they alleviate such concerns. The global offshore wind installed capacity is expected to reach 114.9 GW in 2030, compared to a meagre amount of 17.6 GW in 2017 [2]. This surge in offshore wind capacity is conjugated with an expectation of 71% decline in its global benchmark levelised cost, in contrast to 47% decline in its onshore counterpart (Figure 1.1), mainly on the accounts of heuristic learning, economies of scale and increasing competition.
140
120 118 -71% 100
80
60
LCOE [$/MWh] LCOE 55 -47% 40 35 20 30
0 2018 2040 2018 2040 Offshore wind Onshore wind
Figure 1.1: Wind energy global benchmark LCOE [2]
1 2 1.I NTRODUCTION
The technological advancement of offshore wind energy should commensurate with 1 the expectations from the economists. The discovery of latent dynamics that lurk at the nexus of various disciplines constituting the broad domain of OWF is paramount for a steady ascent on the learning curve. An OWF comprises of myriad disciplines, such as: technical, social, economic and regulatory. Each discipline can further be broken down into several sub-disciplines, leading to a complex socio-technical system. The future success of OWF depends on efficiently capturing the interactions among various disci- plines while heeding to the security, affordability and reliability of the electricity grid, and ultimately being a financially lucrative venture to lure necessary investment.
1.2. PROBLEM STATEMENT The division of labour in the wind energy sector has led to discrete development of niches. The models with different fidelities for the siloed application of these niches - rotor aerodynamics [3], aeroelasticity [4], gearbox design [5], wake models [6] or layout optimization [7] - are prevalent in literature. These models are often used sequentially while designing a wind farm that may lead to a sub-optimal design due to their agnosti- cism towards the inter-disciplinary influences [8].
A confluence of these well-researched niches in form of a Systems Engineering (SE) tool has a potential to capture the latent dynamics in an OWF. In such tools, the inter- disciplinary coupling of input-output, constraints and mutually competing elements in the objective function can be harnessed to realize the trade-offs in the system. The re- search focusing on these inter-disciplinary interactions is limited, but growing [9]. [10] and [11] have captured the interactions among blade aerodynamics, structural dynamics and control system to optimize the rotor design. [12] performed a holistic optimization of wind turbine by using high fidelity aero-servo-elastic model for the rotor design and 3D FEM for the tower design. An integrated analysis of OWF with high fidelity structural dynamics was done by [13]. [14] demonstrated the benefits of coupled optimization of support structures and farm layout over the standalone and sequential optimization of each discipline. These researches are still limited to sub-system levels, leaving enough room to further realize the trade-offs by up-scaling the system scope to the wind farm level.
DTU and NREL have been at the forefront of harnessing the power of multi-disciplinary optimization for wind farm design by developing state-of-the-art softwares like FUSED- Wind [15], WISDEM [16] and TOPFARM [17]. Although these tools are elegantly designed for the SE of the wind farms, they fall short on at least one of the key requirements:
• comprehensiveness - to integrate life-cycle assessment of every major discipline comprising a wind farm • physically precise - to have physics based models with reasonably precise results to enable better coupling of different disciplines • low computational cost - to enable quicker generation of results • agility - to allow the users to select their own model for any given discipline and execute the model for different case studies 1.3.S COPE 3
FUSED-Wind is a framework, rather than an analysis model, over which WISDEM is built. In this regard, FUSED-Wind supports agile workflow, but lacks comprehensive- 1 ness outside the scope of wind turbine. WISDEM is the most comprehensive tool avail- able in literature with physics based models for the rotor, drive-train and support struc- ture; however, it lacks agility that limits its usage to a fixed case study. TOPFARM uses high-fidelity models for the wind climate and rotor design, which leads the study on the optimization of farm layout to be computationally expensive. Hence, there is a need for a SE tool that bridges the shortfalls in the existing tools and meets the above requirements.
Considering the key requirements of an OWF SE framework, the Wind Energy re- search group at the Faculty of Aerospace Engineering, TU Delft has been developing a software - Windfarm Integrated Design and Optimization Workflow (WINDOW) - for the multi-disciplinary design analysis and the optimization of OWF. The software cou- ples the low-fidelity physics based models for different disciplines of the wind farm and performs a life cycle analysis to compute the LCOE. The feature of agility - its ability to tailor the workflow to suit a desired case study - makes this a unique framework. A brief overview of the software will be provided in Chapter2. However, in the current WIN- DOW setup, the coupling between Rotor-Nacelle-Assembly (RNA) and the rest of OWF is static. This is because the turbine parameters are held fixed which impedes the flexibility in designing the RNA components and studying their influence on the wind farm.
1.3. SCOPE In view of the problems posed in the previous section, this research aims to reinforce WINDOW with an improved physical representation of RNA, thus, allowing more inputs and outputs and enabling the capture of multi-disciplinary influences of various RNA configurations on the wind farm. In this regard, this project is limited to the modelling of the RNA and its coupling to the wind farm model.
1.4. RESEARCHTHEME In this section, the research theme of this project is discussed by elucidating the main objective, along with three discrete, but underpinning, research objectives. Since, the creation of knowledge entails creation of a new tool, each research objective contributes to the development process of the software, which necessitates apportioning of the de- velopment milestones.
1.4.1. MAINOBJECTIVE To address the problems and to meet the SE requirements, as discussed in Section 1.2, while being constrained by the scope of the project, as discussed in Section 1.3, the main objective of this report is to perform the multi-disciplinary optimization of rotor nacelle assemblies for offshore wind farms by comprehensively representing their components us- ing the models that are physically precise and computationally fast. There are various aspects of RNA that can be optimized in the context of OWF.The research objectives are designed to address three such aspects - blade design, power density and drive train con- figuration. 4 1.I NTRODUCTION
1 The approach for the project is based on the Agile Project Management technique, which involves iterations 1 or sprints to attain an objective by decomposing it into gran- ular sub-objectives or stories [18]. The software is developed incrementally through de- sign iterations to reach a milestone that is apportioned to meet the corresponding re- search objective. The open-source nature of the software seeks to aid future research in the SE of OWF by supporting agility, scalability and user-friendliness. The development milestones pertaining to the research objectives are listed in Figure 1.2.
•Milestone #1 - a comprehensive, low fidelity physics based RNA model coupled to the OWF model •Research Objective #1 - to develop insight into the benefits of system Design engineering by studying the effect of system scope on the rotor design Iteration #1
•Milestone #2 - support for turbine scaling in the OWF model •Research Objective #2 - to optimize the rotor diameter, power rating and, Design thus, the power density of the turbines in a given wind farm Iteration #2
•Milestone #3 - support for various drive train configurations in the RNA model •Research Objective #3 - to compare various drive train configurations and the Design effect of their reliability on the LCOE Iteration #3
Figure 1.2: Research objectives and their corresponding development milestones
1.4.2. RESEARCHOBJECTIVE #1 The first research objective is to develop insight into the benefits of system engineering by studying the effect of system scope on the rotor design. To accomplish this, the develop- ment milestone is to have a comprehensive, low fidelity physics based RNA model coupled to the OWF model.
In this regard, a rotor is designed - with design tip speed ratio, thickness factor 2, pitch angle, chord and twist distribution as design variables - with increasing system scope, as shown in Table 1.1.
1Iteration is an Agile Project Management term; not to be confused with numerical iteration 2a factor to uniformly scale the blade laminate thicknesses - skin, spars and shear webs. 1.4.R ESEARCHTHEME 5
System scope Objective function 1 Aerodynamics maximization of aerodynamic efficiency Blade maximization of the ratio of aerodynamic effi- ciency and the blade mass RNA maximization of the ratio of aerodynamic effi- ciency and the RNA mass Farm minimization of the wind farm LCOE
Table 1.1: Underlying cases for Research Objective #1
The OWF components outside the system scope are then designed sequentially in a farm with 25 turbines in a fixed square layout; thereafter, the LCOE for each scenario is calculated. It is expected that as the scope of the system increases, the inter-disciplinary couplings in the form of constraints and mutually competing elements in the objective function are better captured, which would lead to realization of trade-offs in the system and a subsequent decrease in the LCOE of the OWF.
1.4.3. RESEARCHOBJECTIVE #2 The second research objective is to optimize the rotor diameter, power rating and, thus, the power density of the turbines in a given wind farm. To accomplish this, the develop- ment milestone is to include the support for turbine scaling in the OWF model.
64 NREL 5MW Reference Turbines are considered in an OWF with a regular (square or rectangular) layout. The turbine’s rotor diameter, rated power and spacing are opti- mized to yield the minimum LCOE for two sites - one with high average wind speed, and the other with low average wind speed.
A rotor with higher diameter is preferable for a site with lower average wind condi- tions for the maximization of the AEP.However, a larger diameter leads to a higher RNA cost and a higher thrust which, in turn, translates to a higher support structure cost. Ad- ditionally, wider wake of the turbines with larger diameter necessitates larger spacing in the farm, which increases the cable cost. The SE model that couples such interactions is well equipped to address the optimization of the LCOE.
1.4.4. RESEARCHOBJECTIVE #3 The final research objective is to compare various drive train configurations and the ef- fect of their reliability on the LCOE. To accomplish this, the development milestone is to include the support for various drive train configurations in the RNA model.
The drive train configurations that will be compared, along-with their known advan- tages and disadvantages, are listed in Table 1.2. 6 1.I NTRODUCTION
1 Nomenclature Configuration Advantages Disadvantages DFIG-3S 3-stage gearbox with low generator cost, lower reliability of a Doubly Fed Induc- low converter cost, the gearbox and slip tion Generator high generator effi- rings, high grid com- ciency at full load pliance cost PMSG-1S 1-stage gearbox with low gearbox cost, higher generator a Permanent Mag- high generator ef- cost net Synchronous ficiency at partial Generator load, smooth grid operation PMSG-DD direct drive with a increased drive train large generator size Permanent Magnet efficiency and reli- and cost Synchronous Gener- ability, smooth grid ator operation
Table 1.2: Different drive train configurations for Research Objective #3
Due to the prevalence of DFIG-3S in the market, it is expected that it would be the most favorable configuration when its reliability is not taken into consideration. The PMSG-DD and PMSG-1S configurations are expected to exhibit higher reliability so as to yield the LCOE that is lower than or equal to that displayed by DFIG-3S.
1.5. REPORT ORGANIZATION The report sets off by laying the foundation on the concepts of systems engineering. Thereafter, each proceeding chapter deals with the development of the models towards their respective development milestone, and the study of the corresponding research objective. The content of each chapter is given below:
• Chapter 2 - overview of SE and ontology of WINDOW • Chapter 3, 4 and 5 - pertains to Design Iteration #1, #2 and #3 respectively. The organization of these chapters are as follows: – Use case - problem formulation for the corresponding Research Objective – Literature survey - survey on the pertinent researches – Development - development of the RNA model towards the respective Mile- stone – Validation - validation of the model thus developed – Analysis - study of the formulated problem • Chapter 6 - conclusion, retrospection and scope for future research and develop- ment 2 SYSTEMS ENGINEERINGOF OFFSHORE WIND FARMS
This chapter aims to throw light on the concept of systems engineering (SE) in wind en- ergy and the effect of model choice on the use case. The terms frequently used in multi- disciplinary optimization will be familiarized, which will form a foundation to meet the research objectives in the subsequent chapters. This chapter is divided into two parts: 1. Background - to acquaint the readers with SE 2. System ontology - to give an overview on the ontology of WINDOW, an OWF SE model
2.1. BACKGROUND Before delving into the implementation of SE, an overview of some definitions, concepts and terminologies (italicized) is necessary, which is done using an illustration.
2.1.1. SYSTEMSENGINEERING Systems engineering is an interdisciplinary approach that helps in the design and man- agement of a complex engineering system. There are various definitions associated with SE [19]; in a nutshell, it exhibits the following characteristics [9]: • holistic picture of the system behaviour over its full life cycle • coupling of the multi-disciplinary interactions in the system • integrated solution to all its stakeholders SE has garnered extensive application in the aircraft design [20] and of late its ben- efits are being realized in the wind energy sector. In Figure 2.1, a wind turbine rotor is taken as an example of a system, and the following use cases are used for the illustration: 1. Preliminary estimation of the rotor mass 2. Aero-servo-elasticity modelling for the controller design
7 8 2.S YSTEMS ENGINEERINGOF OFFSHORE WIND FARMS
DRIVER
AERODYNAMICS STRUCTURAL CONTROL SYSTEM 2 DYNAMICS
Steady Model Static Model Gain Scheduled PI Controller Model
Unsteady Model Dynamic Model
Use case 1: Preliminary design estimation of the rotor mass
Use case 2: Aero-servo-elasticity modelling for the controller design
Figure 2.1: Use case, workflow and driver for a use case illustrating rotor design
2.1.2. MDAO The most important aspect of SE is the Multidisciplinary Design Analysis and Optimiza- tion (MDAO). It provides a holistic tool to facilitate system level analysis by capturing inter-disciplinary interactions - both implicit and explicit. In Figure 2.1, with a rotor as the system, the two different use cases comprise of two different MDAO interactions. For the preliminary estimation of the rotor mass, as depicted in Use Case #1 (blue), only the coupling of aerodynamics and structural dynamics modules (blue boundary) with low fidelity models (blue arrows) is necessary. However, for the controller design of the rotor, as illustrated in Use Case #2 (yellow), the coupling of aerodynamics, structural dynam- ics and controller design modules (yellow boundary) using high fidelity models (yellow arrows) is required. The workflow is the coupling of the disciplines in the form of input- output interactions among the models (yellow and blue arrows). The driver regulates the flow of inputs and outputs for the optimization purpose. These characteristics of MDAO architecture are summarized in Table 2.1[21].
To facilitate this MDAO architecture, an open-source platform developed by NASA Glenn Research Center called OpenMDAO is used in WINDOW. OpenMDAO enables easy decomposition of the system into sub-components, tight coupling of their inter- action and efficient numerical techniques to tackle the use cases [22].
2.1.3. AGILITY The essence of a SE framework lies in its agility to be executed for different use cases by various stakeholders.
Lower fidelity models, that capture lower amount of physics and are computation- ally cheaper, are preferred for preliminary design analysis, whereas high fidelity models should be used for a detailed and intricate design of the components. A high fidelity 2.2.S YSTEMONTOLOGY 9
Term Description Example
System number of disciplines that define Rotor comprising of aerodynam- scope the system ics, structural dynamics and con- troller design disciplines Model fi- the level of physical detail cap- Aerodynamics module comprises delity tured by the model of each disci- of a low fidelity steady-state model 2 pline and a high fidelity unsteady-state model Use case analysis of the system for a partic- preliminary estimation of the ro- ular objective tor mass Driver numerical method governing the optimization of the rotor mass and use case, for example - sensitiv- its performance ity analysis, optimization or un- certainty quantification Workflow the coupling of disciplines repre- coupling of the steady state aero- sented by the path of data-flow be- dynamic model with the static tween the driver and the models structural model
Table 2.1: MDAO terminology model may be essential to study a particular niche of the wind farm, but details of such model may be irrelevant and computationally hampering for other analyses. For exam- ple, high fidelity 3D CFD models are used to determine the aerodynamic loads and pres- sure distribution to perform the aeroacoustic analysis of the wind turbine [23]. However, the details captured by these models are irrelevant to the calculation of the wind farm’s LCOE, which can alternatively be captured by low fidelity BEM theory for rotor aero- dynamics. In this case, inclusion of both the models enables flexibility in performing multiple analyses - for an aeroacoustic engineer in reducing the noise and for a farm manager to determine the LCOE of the farm.
The selection of the model fidelity depends on the use case. In general, an engineer- ing model can be classified into one, or the combination, of the categories highlighted in Table 2.2. The selection criteria over which the suitability of a model to fit into the OpenMDAO framework is assessed is summarized in Table 2.3.
2.2. SYSTEMONTOLOGY In Section 1.3, the OWF model - Windfarm Integrated Design and Optimization Work- flow (WINDOW) - developed in the Wind Energy Research Group at TU Delft was intro- duced. Since the scope of this project is limited to the modelling of the RNA components, only a brief overview of WINDOW, its disciplines and their interactions are discussed.
2.2.1. WINDOW The interactions between multiple disciplines of a system can be lucidly captured using Extended Design Structure Matrix (XDSM) [24]. It should be noted that XDSM repre- sents a particular workflow for a given use case. The (simplified) XDSM of WINDOW, where the RNA is statically coupled, is shown in Figure 2.2, where the crosswind and 10 2.S YSTEMS ENGINEERINGOF OFFSHORE WIND FARMS
Model type Description
Physical based on the physics of the component and could be ana- models lytical or numerical in nature. They support larger number of inputs and outputs (IO), and thus are better equipped in capturing the inter-disciplinary influences. To simplify real 2 life scenario, several assumptions are made that reduce the model fidelity, leading to fewer IO, lower accuracy and lost inter-disciplinary interactions, but at a highly sought advan- tage of faster computation. Empirical the relationships between the model IO are established us- models ing experimental results and industry data. Although these models are physics agnostic, they are computationally fast and considerate to the learning curve of the given technology. Scaling mod- the properties of the component are scaled from a reference els component using scaling laws. Meta models these are the models based on the mathematical relationships between inputs and outputs of an underlying physical model. They serve as surrogates of high fidelity physical models that are computationally expensive to run.
Table 2.2: Types of engineering models
downwind spacing of the turbines in a farm with a rectangular layout is being optimized for the minimum LCOE. The detailed illustration of WINDOW and the workflows can be found in [25].
R , rotor R , m , Windrose, rotor rna Bathymetry U , T , P N , C Availability Power curve, rated rotor rated t rna Ryaw Ct curve
WINDOW Spacing
Water depth Turbine & Turbine Layout at each substation coordinates turbine coordinates
Turbulence Wake Intensity at AEP AEP Aerodynamics each turbine
Support C Structure ss
Cabling Ccc
C , C , Cost inv o&m Cdecom
Objective LCOE function value
Figure 2.2: XDSM of WINDOW with static RNA coupling 2.2.S YSTEMONTOLOGY 11
Criteria Description
Use case The model response should be sensitive to the design variables of the use case. For example, a steady state blade aerodynam- ics model is sufficient to calculate the static load on the blade, however, an unsteady state blade aerodynamics is necessary to calculate the dynamic load 2 IO The model should provide the inputs and outputs necessary for the inter-disciplinary coupling required for a given use case Accuracy The model results should not deviate significantly from the real life case Computational The model should be computationally fast to enable quick sys- speed tem level analysis Compatibility The model should be compatible with the environment and the framework
Table 2.3: Selection criteria of the models for SE
The green rectangular boxes in the diagonal represent the disciplines comprising the OWF system in WINDOW. The first row includes all the fixed parameters for the corre- sponding discipline while performing the given MDAO. The presence of necessary RNA parameters - mass (mr na), cost (Cr na), maximum thrust (Tr otor ), yaw radius (Ryaw ), rated wind speed (Ur ated ), power curve and thrust coefficient (Ct ) curve - in this row demonstrates the static coupling between RNA and WINDOW.
The second row comprises of the design variables - crosswind and downwind spac- ing - that are controlled by the MDAO driver (rounded rectangle). The vertical line con- nected to each discipline represents the flow of inputs, while the horizontal line repre- sents the flow of output.
The Layout discipline sets the coordinates of the turbines and the substation de- pending on the spacing provided by the driver. The water depth at each turbine and the substation is calculated using the bathymetry data of the site.
In the Wake Aerodynamics discipline, the wind is sampled into discrete speeds and directions using the windrose data. For each wind sampling, the power and thrust co- efficient (Ct ) curve of the turbine are interpolated, and the wake effect - in the form of wind speed deficit at each turbine due to every other turbine - is calculated. Thereafter, a wake merge model is used to calculate the overall wind speed deficit at each turbine, and thus the power output from each turbine for every wind sampling is computed. This power output is then integrated with the Weibull distribution of the site wind condition to determine the farm AEP.
The wake induced turbulence, water depth at each turbine, RNA mass (mr na), yaw radius (Ryaw ), rated wind speed (Ur ated ) and maximum rotor thrust (Tr otor ) are used to design the Support Structure. 12 2.S YSTEMS ENGINEERINGOF OFFSHORE WIND FARMS
The Cabling discipline determines the cable layout, length and cost (Ccc ) based on Esau-Williams heuristic algorithm [26] using the coordinates of the turbines and the sub- station as the inputs. It also selects an apt cable type from a database for a given capacity 2 (Pr ated ) of the turbine. The Cost model aggregates the cost of RNA, support structure and cabling for all the turbines (Nt ) along-with other investments costs. The O&M cost is scaled linearly with AEP. It then returns the capital expenditure (Cinv ), operating expenditure (Co&m) and the decommission (Cdecom) costs. Finally, the aggregation of AEP with these costs yields the LCOE of the OWF,which is sent back to the optimizer driver to generate a new set of design variables.
2.2.2. COUPLINGOF RNA WITH WINDOW To meet the objective of this report, as stated in Section 1.4.1, the coupling between RNA and WINDOW needs to be dynamic to allow the flexibility in designing the RNA compo- nents and studying their influence at the wind farm level. In this regard, the XDSM as illustrated in Figure 2.3 is sought.
Prated, Rrotor, Blade design, R , Bathymetry rotor R P N Availability Drive train Windrose rotor rated t design
WINDOW Spacing
Water depth Turbine & Turbine Layout at each substation coordinates turbine coordinates
Power curve, mrna, Urated, RNA Crna Ct curve Trotor, Ryaw
Turbulence Wake Intensity at AEP AEP Aerodynamics each turbine
Support C Structure ss
Cabling Ccc
C , C , Cost inv o&m Cdecom
Objective LCOE function value
Figure 2.3: XDSM of WINDOW with dynamic RNA coupling
It can be seen that the inclusion of RNA discipline grants the flexibility in designing the RNA with respect to its radius (Rr otor ), rated capacity (Pr ated ), blade design and drive train configurations. The interaction of RNA with Wake Aerodynamics, Support Structure and Cost disciplines are shown in grey boxes. 3 DESIGN ITERATION #1
The objective of this chapter is to develop insight into the benefits of system engineering by studying the effect of system scope on the rotor design. In this regard, the target milestone for the first design iteration is a comprehensive, low fidelity physics based RNA model cou- pled to the OWF model. A SE framework that enables integration of specialized tools for the MDAO of the offshore wind farms is introduced. The dissemination of knowledge on the utility of the tool in painting a bigger picture of an OWF among the wind energy re- searchers is intended.
This chapter is divided into five sections:
1. Use case - The underlying use case to study the first research objective is formu- lated. 2. Literature survey - A survey on similar researches is performed. 3. Development - The models for every component comprising the RNA are gleaned from literature. The rationale and ontology of the models adapted for this design iteration is elucidated. Furthermore, the sensitivity analyses of the model response with respect to their corresponding dependent variables are performed. Finally, the coupling of the models of all the disciplines to attain a complete RNA model is explained using the XDSM diagram. 4. Validation - The RNA model developed thereby is validated by the comparison of the model results against the known values of the NREL 5MW Reference Turbine and the Siemens SWT-2.3-108. 5. Analysis - The validated model is used to meet the first research objective - the effect of the blade designed with different system scopes on the LCOE of the wind farm.
13 14 3.D ESIGN ITERATION #1
3.1. USECASE The first research objective is to develop insight into the benefits of systems engineering by studying the effect of system scope on the rotor design.
The use case underlying this objective is to re-design the NREL 5MW Reference Tur- bine (N5RT) blade for different objective functions pertaining to varying system scopes, as shown in Table 3.1. The design variables for these optimization problems are de- 1,2,3 sign tip speed ratio (λdes ), thickness factor (τ), blade pitch angle (θ) and chord (cpeg ) 1,2,3 3 and twist (βpeg ) distribution at three blade junctions (referred in this report as pegged points). The description of these design variables is provided in Section 3.3.2.
The system scopes of Aerodynamics, Blade, RNA and Farm are referred here as Case A, B, C and D respectively.
Case System scope Objective function
A Aerodynamics maximization of aerodynamic efficiency B Blade maximization of the ratio of aerodynamic effi- ciency and the blade mass C RNA maximization of the ratio of aerodynamic effi- ciency and the RNA mass D Farm minimization of the wind farm LCOE
Table 3.1: Underlying cases for research objective #1 3.2.L ITERATURE SURVEY 15
3.2. LITERATURE SURVEY The requirements of low cost, long lasting and low service are the major challenges in the wind energy sector. In this regard, the design objective of a wind farm should be to maximize its energy production at the lowest possible cost while ensuring structural sta- bility, operational reliability and power quality over its lifetime [8]. This design objective is thus a multi-disciplinary optimization that requires a coupled interaction among var- ious disciplines constituting a wind farm.
The most vividly discussed inter-disciplinary interaction in the wind farm design is 3 aeroelasticity, which couples the blade aerodynamics with its structural dynamics. It is used by [27] to optimize the blade design for the maximum AEP at a fixed cost, whereas [28] uses it to minimize the cost of energy. PHATAS [29], FAST [30] and Bladed [31] with their linear beam model and HAWC2 [32] based on non-linear multi-body dynamics are the popular aeroelasticity tools. When the system scope includes the interaction of aeroelasticity with the controller, it is called aero-servo-elasticity. The benefits of cou- pled interactions by increasing the system scope in the integrated blade design has been studied by [33] and [34]. However, these models are computationally expensive and can hinder their application on the wind farm level. [35] used multilevel optimization with metamodels to make the computation quicker, however, the analysis was still limited to the wind turbine level.
Beyond the rotor design, the use of MDAO has been scarce in wind energy research, especially in the drive train domain. [36] performed an integrated analysis of rotor and tower design using MDAO, and found 2.3% reduction in the LCOE compared to the base- line NREL turbine. NREL’s has been developing a framework - WISDEM - to allow an integrated MDAO of various aspects of a wind farm. Some of the tools in the WISDEM framework include RotorSE for the blade design, DriveSE for the drive train design, Tow- erSE for the support structure design and TurbineCostsSE for the cost model [9].
DTU’s TOPFARM is another wind farm MDAO tool that synthesizes the models of the rotor, control system, gearbox, generator, wake effects and lifetime cost modelling into an economical objective function by performing aeroelastic simulation to calculate the AEP and fatigue degradation of the farm. The economical objective function is the financial balance of the wind farm operator resulting from the generated revenue from the sale of electricity and incurred investment, maintenance and component degrada- tion costs. Two stage fidelity - the first stage uses a low-fidelity stationary wake model, while the second stage uses a high fidelity dynamic wake meandering model - is used for quicker optimization convergence. Their analysis led to an improvement in the financial balance of 2.1 M€ on accounts of increased energy production and decreased electrical connection costs as compared to the baseline case of the Middelgrunden wind farm [17]. 16 3.D ESIGN ITERATION #1
3.3. DEVELOPMENT In this section, the RNA model necessary to study the first use case is developed. Firstly, the list of models assessed to fit into the RNA model is discussed. The subsequent sec- tions focus on the ontology of the adapted tools and the physical significance of their IO to study the influence of one discipline over another. The detailed formulation of the adapted tools is not treated in this chapter; however it can be found in the referenced sources.
3 3.3.1. MODELASSESSMENT The realization of the first research objective requires a RNA model that is apt for the de- signed use case. The aptness of the model is sensed by the sensitivity of the power out- put, mass and cost of the RNA on the blade design, and the generation of other outputs, like yaw diameter and thrust coefficient, that are necessary to couple the RNA model with other disciplines in WINDOW.
The foremost step towards a comprehensive RNA model is to identify all its constitut- ing components and to glean various tools and models for each component from litera- ture. Based on the scope of the tools evaluated to model the RNA components, the RNA is divided into three sub-systems: Blade, Hub & Nacelle and Cost. The categorization of the sub-systems is in the context of MDAO, and may not reflect a physical sub-system of the RNA (for example Cost). The list of the tools assessed for each sub-system and their performance against the selection criteria are summarized in Table 3.2.
Sub-system Tools Description Assessment
Blade RotorSE high fidelity rotor design mod- incompatible with [37] ule based on BEM for aerody- OpenMDAO v2 namics and FEM for structural dynamics QBlade high fidelity rotor design mod- high computational [38] ule based on BEM, Lifting Line time and Aero-elasticity AeroDyn quasi-steady aerodynamics comprehensive IO, [39] module based on BEM fast and accurate Ad Hoc custom built module with BEM comprehensive IO, and scaling laws fast and accurate Hub & Na- DriveSE comprehensive drive train comprehensive IO celle [40] module with physics based and computation- models for major load bearing ally fast components Cost WindPACT calibrated empirical model limited IO and based [41] with component wise cost on 2002 data breakdown
Table 3.2: RNA sub-systems and the assessed models 3.3.D EVELOPMENT 17
There are plethora of tools available for the blade design; but, the options are limited for a comprehensive physical and cost model for the rest of the RNA. AeroDyn, RotorSE and QBlade for the blade design, DriveSE for the hub & nacelle design, and WindPACT for the cost modelling of the RNA components are the tools assessed in this design iteration.
Based on the assessment criteria specified in Table 2.3, RotorSE and QBlade are dis- qualified due to their high fidelity and compatibility issues. A custom built Ad-hoc mod- ule based on BEM for the blade aerodynamic design and scaling law for the blade struc- tural design is adapted. To demonstrate agility, AeroDyn, which supports quasi-steady state blade aerodynamics due to wind shear and yaw misalignment, is also integrated to 3 the framework, but is not used in the analysis due to slightly higher computational time.
DriveSE for the hub & nacelle design and WindPACT for cost modelling are the other tools adapted for the first design iteration.
3.3.2. BLADE The blades are responsible for the conversion of power in the wind to the mechanical power in the rotating shaft. While doing so, the blades experience aerodynamic loads which result in their elastic deformation and the subsequent development of stress. A blade has to be designed to withstand the extreme deformation and the stress during its lifespan, whilst maintaining the highest aerodynamic performance at the lowest possible cost. This aspect of a blade is dictated by two disciplines - aerodynamics and structural dynamics.
Ucut in, Rrotor, Rhub, Rrotor, Rhub, − B, Rrotor, Ψ, Rrotor, Rrotor Ucut out, Airfoils B, U − Rhub Rhub ∞ Prated, ηdt
1,2,3 1,2,3 Blade cpeg , βpeg τ λ, θ λ, θ
dr(r), c(r), dr(r), c(r), Aerodynamic dr(r), c(r) β(r), A β(r), dr(r), c(r) design swept AirfoilID(r) AirfoilID(r)
t(r), µ(r), EI (r), Structural flap mblade EI (r), design edge Iflap(r), Iedge(r)
Aerodynamics C , C at partial load t p
Pelec(U), Power curve Urated Ct(U)
Aerodynamics T , Q f (r), f (r) rotor rotor at rated speed x y
Mflap(Rhub), σflap(r), Mechanics σedge(r), δtip
Figure 3.1: XDSM of the Blade sub-system for Use Case #1
The decomposition of the Blade sub-system in the Ad-hoc module into constituting 18 3.D ESIGN ITERATION #1
disciplines and their IO connections are explained using XDSM in Figure 3.1. The work- flow of the XDSM pertains to the use case formulated in Section 3.1. The symbols are explained in the following sub-sections and are also listed in the Glossary.
The Aerodynamic design and the Structural design disciplines pertain to the design of the surface and the cross-sectional properties of the blade respectively. The Aerody- namics at partial load discipline calculates the aerodynamic efficiency of the blade at a partial load condition of U 8 m/s. The Power curve discipline then calculates the ∞ = rated wind speed and interpolates the aerodynamic performance of the blade for a range 3 of wind speeds. The Aerodynamics at rated speed discipline calculates the aerodynamic load on the blade at the rated wind speed. The Mechanics discipline calculates the limit state of the blade at the rated wind condition.
In the following sub-sections, these disciplines will be described. It should be noted that Aerodynamics at partial load and Aerodynamics at rated speed are the same except the difference in the input U . ∞
3.3.2.1. AERODYNAMICDESIGN The aerodynamic design of the blade refers to the exterior blade surface that affects the flow field around it, and is responsible for the development of aerodynamic load that eventually leads to the rotation of the blade. The blade cross-section is an airfoil charac- terized by the chord length and the twist angle. In practice, the blades are also pre-coned or pre-bent to prevent the blade-tower impact; but they are not taken into consideration in this model.
1 1,2,3 This model takes the airfoil distribution , chord lengths (cpeg ) and the twist angles 1,2,3 (βpeg ) at three pegged blade sections as inputs to draw the aerodynamic profile. These three pegged blade sections for the chord and the twist distribution are listed in Table 3.3.
Pegged blade sections Sample input
Chord length root section, 70% and 90% [3.54, 3.05, 2.31] m of the blade length Twist angle transition section, 40% and [13.31, 9.00, 3.12] ° 70% of the blade length
Table 3.3: Pegged blade sections for chord and twist distribution
A linear profile is assumed between each pegged section. For the chord distribution, a linear profile connecting the pegged blade sections at 70% to 90% of the blade length until the transition section 2 is taken, while another linear profile from the transition
1Airfoil ID associated with a database of airfoils and their respective starting point along the blade 2The transition section is the blade section where the cross-section transitions from a circular or an elliptical shape to an airfoil shape. 3.3.D EVELOPMENT 19 section to the root chord is drawn. For the twist distribution, the twist angle at the tip is set to 0°. The twist angle for the circular blade sections near the root have no meaning due to their rotational symmetry. The rationale for the location of these pegged sections is to ease the manufacturing process and reduce the material close to the root without adversely affecting the aerodynamic efficiency [42].
With the input of the chord lengths and the twist angles of N5RT at these pegged points from Table 3.3, a comparison of the chord and the twist distribution between N5RT [43] and the profile generated using this module is shown in Figure 3.2. The red vertical lines represent the pegged section, while the cyan vertical line represents the 3 transition section.
!" #" $!" !" #"
! !
°
$!"
% !" % !"
Figure 3.2: Chord and twist distribution in the Ad-hoc module
The blade is divided from the root (where r R ) to the tip into 20 sections. The = hub swept area (Aswept ) of the rotor is given by:
A π(R2 R2 ) (3.1) swept = r otor − hub Other outputs of the model are the radial distance (r ), chord length (c(r )), twist angle (β(r )), length (dr ) and airfoil ID of each blade section.
3.3.2.2. STRUCTURALDESIGN The endurance of the blade to the aerodynamic load is governed by its structural design, which in turn is characterized by the cross-sectional stiffness and mass per unit length. The cross section of a wind turbine blade, with its internal profile is shown in Figure 3.3. The airfoil is supported internally using the shear webs and spar caps. Their dimensions and positions along with the thickness of the blade skin, the aerodynamic profile and the material of the blade complicate the cross-sectional analysis of the blade. Hence, to 20 3.D ESIGN ITERATION #1
ease the analysis, the structural design of the blade is carried out using scaling laws with respect to the N5RT.
An important parameter in the scaling law is the thickness factor (τ) which is a fac- tor to uniformly scale the laminate thicknesses - blade skin, shear web and spar caps. In other words, the laminate thicknesses scale linearly with the scaling factor, and then they are re-factored using τ. A uniform τ over the entire blade section is assumed. The blade is assumed to be characterized uniformly by glass fibre reinforced plastics with the 3 ultimate tensile strength (UTS) of 400 MPa and the Young’s Modulus (E) of 36.23 GPa [44].
Maximum Structural skin stress point
Flapwise axis Maximum stress point Shear web Spar cap Edgewise axis
Figure 3.3: Cross section of a blade
The mass of the blade (mbl ade ) is given by:
Z R mbl ade µ(r )dr (3.2) = Rhub
The computation of cross sectional properties of the blade is based on the scaling laws [45] as given by: c s (3.3) = cre f
t(r ) t (r ) s (3.4) = re f ×
µ(r ) µ (r ) s2 τ (3.5) = re f × ×
EI(r ) EI (r ) s4 τ (3.6) = re f × ×
EI(r ) I(r ) (3.7) = E The following assumptions are made in this law:
• The material of the blade is assumed to be the same as that of the reference turbine • The blade is aerodynamically similar to the reference turbine in terms of airfoil distribution • The laminate thicknesses are small compared to the airfoil thickness to justify the use of thin shell approximation 3.3.D EVELOPMENT 21
3.3.2.3. AERODYNAMICS The aerodynamics at the blade is responsible for the generation of load that is eventually translated into the rotation of the blade. There are various models in literature to per- form the aerodynamic calculations: Blade Element Momentum (BEM) models, vortex models and CFD models. Due to its high computational speed and reasonably accu- rate results, BEM has been a prominent model for rotor aerodynamics, and has been thoroughly discussed in literature [46]. The limitations in the original BEM model are overcome by the following corrections: • tangential induction factor to account for the rotation of the wind in the wake of 3 the turbine • Prandtl’s tip and root loss correction factor to account for a finite number of blades • Glauert correction factor for heavily loaded rotor The inflow conditions are assumed to be steady. The unsteady effects due to the yaw misalignment and wind shear are not modelled. Other unsteady effects such as the dynamic inflow at the rotor level 3 or the dynamic stall at the airfoil level 4 are also not taken into consideration in this module.
3.3.2.4. POWER CURVE This discipline returns the aerodynamic power (Paer o(U)), electrical power (Pelec (U)) and thrust coefficient (Ct (U)) over a specified range of wind speeds. The wind speeds from 0 to 30 m/s in a step size of 1 m/s are considered.
With the aerodynamic efficiency (Cp,max ) from the Aerodynamics discipline executed at the partial load condition as an input and a constant drive train efficiency (ηdt ) of 95%, the rated wind speed (Ur ated ) is given by: ³ P ´ 1 U r ated 3 (3.8) r ated = 1 2 Cp,max ρair Aswept ηdt The power and thrust coefficient curves are determined using: 1 3 Cp,max ρair Aswept U if Ucut in U Ur ated − ≤ < 2 Paer o(U) Pr ated (3.9) = if Ur ated U Ucut out ηdt ≤ < − 0 if U Ucut in,U Ucut out < − ≥ − P (U) P (U) η (3.10) elec = aer o × dt Ct,max if Ucut in U Ur ated − ≤ < C (U) (3.11) t 4a(1 a) if Ur ated U Ucut out = − ≤ < − 0 if U Ucut in,U Ucut out < − ≥ − 3time delay in the load experienced by the blade due to a change in the inflow condition 4non-linear aerodynamic effect at high angles of attack 22 3.D ESIGN ITERATION #1
The thrust coefficient at full load condition in Equation 3.11 depends on the overall rotor axial induction factor (a), which can be calculated using the quadratic equation given by:
2 Pr ated Cp 4a(1 a) if Ur ated U Ucut out (3.12) = − = 1 3 ≤ < − 2 ρair Aswept U ηdt
3.3.2.5. MECHANICS The aerodynamic load at each blade section translates to the deformation of the blade 3 and build up of stress. The limit states of the blade - maximum stress, fatigue damage and the maximum tip deflection - in a relevant load case have to be considered as design constraints in the multi-disciplinary analysis of the wind turbine.
In this module, the calculation is simplified by making the following assumptions:
• The loads are static in nature with a dynamic amplification factor of 1.0 • The blade is assumed to be infinitely rigid, implying an immediate translation of aerodynamic loads into stress at each blade section
1D linear Euler-Bernoulli beam model with an assumption of small deflection is used to perform the calculations, as given by:
Z R µ ¶ M f l ap (x0) fx (x00) µ(x00) g sin(Ψ) (x00 x0)dx00 (3.13) = x0 + × × −
Z R Medge (x0) fy (x00)(x00 x0)dx00 (3.14) = x0 −
Z R µ ¶ Mgr av (x0) µ(x00) g cos(Ψ) (x00 x0)dx00 (3.15) = x0 × × −
M f l ap (x0) 0.5 t(x0) σf l ap (x0) × × (3.16) = I f l ap (x0) ³ ´ M (x0) M (x0) 0.75 c(x0) edge + gr av × × σedge (x0) (3.17) = Iedge (x0)
R x Z ³Z M f l ap (x0) ´ δti p dx0 dx (3.18) = Rhub Rhub EI f l ap (x0) Since the positions of the neutral axes in the flapwise and the edgewise directions are difficult to determine, they are assumed to be at the positions as shown in Figure 3.3. The points of maximum stress are approximated to lie at a distance of 50% of the section thickness and 75% of the chord length from the flapwise and edgewise neutral axes re- spectively. Due to the static nature of the input blade loading, fatigue damage cannot be calculated. 3.3.D EVELOPMENT 23
The sensitivity of the moment and stress due to the aerodynamic force and gravity force along the blade span of N5RT at the rated wind condition with respect to τ are shown in Figure 3.4 and 3.5. The sensitivity of tip deflection with respect to τ is shown in Figure 3.6.
τ = τ = τ = τ = τ = τ = τ = τ = 3
!
" "
Figure 3.4: Sensitivity of bending moment with τ
τ = τ = τ = τ = τ = τ = τ = τ =
" !
# #
Figure 3.5: Sensitivity of stress with τ
The flapwise bending moment due to the aerodynamic force and edgewise bending moment due to the gravity force are highest at the blade root, and zero at the tip. Due to a higher stiffness at the blade root to meet the tip deflection constraint, the stress at the blade root is lower. The aerodynamic force and moment do not depend on the laminate 24 3.D ESIGN ITERATION #1
3
Figure 3.6: Sensitivity of δti p with τ
thicknesses, hence overlapping curves for different τ in Figure 3.4(L) can be seen. As the blade’s mass per unit length (µ) increases linearly with τ, the moment due to gravity increases (Equation 3.15); however, at the same time, I scales linearly with τ (Equation 3.6), leading to the insensitivity of gravity stress with respect to τ (Equation 3.17).
The δti p is inversely proportional to EI f l ap (Equation 3.18), which scales linearly with τ, hence we see a similar inverse relationship between δti p and τ.
3.3.3. HUB &NACELLE The hub and nacelle are the carrier of aerodynamic loads generated by the blades. The torque loads are converted into power, while the non torque loads due to the rotor thrust, wind shear, gyroscopic load due to the yaw misalignment etc have to be transmitted to the tower with the aid of hub and nacelle components. NREL’s DriveSE is used to comprehensively model the components comprising this sub-system. In this section, a basic overview of the DriveSE model that is pertinent to this use case is provided. The detailed validation of DriveSE against higher fidelity Finite Element Analysis model can be found in its documentation [40].
3.3.3.1. DRIVESE The physical components of DriveSE are shown in Figure 3.7, and can be classified into three categories :
• major load bearing components that are physically modelled: Gearbox, LSS and Mainframe • major load bearing components that are parametrically (combination of physical and empirical models) formulated: Hub and Yaw • non-load bearing components that are empirically modelled: HSS, Generator, Trans- former and Converter
The constituting disciplines of the Hub & Nacelle sub-system based on DriveSE and their IO connections are summarized in Figure 3.8. The detailed explanation of the sym- bols and connections is provided in Appendix A.1. 3.3.D EVELOPMENT 25
3
Figure 3.7: Schematic of a wind turbine drive train [47]
B, Rrotor, Prated, Rrotor, Rrotor, rgb, Np Rrotor, rgb Prated, Rrotor Prated Prated, Rrotor Dtower, Rrotor Rhub,Ψ Loverhang,Ψ
1 cpeg, mblade, Hub & Nacelle Trotor, Qrotor, Qrotor Qrotor Mflap(Rhub)
mpitch, F~ , M~ , F~ , M~ , mspinner, Hub hub hub hub hub m m mhub, mrotor rotor rotor
mgb Gearbox mgb, Lgb mgb, Lgb
up mlss, mmb, up Llss, mlss, down LSS Rlss up down mmb mmb, mmb
mhss HSS Lhss, mhss
mgen Generator Lgen mgen, Lgen
Transformer & mtsf , mconv, mtsf , mconv Converter Ltsf
mbed, mplat, Mainframe mhvac, mcover
myaw Yaw
Figure 3.8: XDSM of the Hub & Nacelle sub-system for Use Case #1
To facilitate the transmission of non-torque loads to the tower, the drive train can take different configurations [48]. Two such configurations that are used in this chapter are:
• 3-point suspension - The two torque arms of the gearbox and a single main bear- ing form the three contact points for the transmission of the loads to the tower. The downwind main bearing is integrated into the low speed side of the gearbox as the planetary carrier bearing. • 4-point suspension - In addition to the above three contact points, a second bear- ing is used in the downwind side of the main shaft (Figure 3.9) to reduce the non- torque load on the low speed side of the gearbox, which may otherwise dislodge the teeth of the planetary gear [49]. 26 3.D ESIGN ITERATION #1
3
Figure 3.9: Force diagram of a 4-point suspension system [48]
3.3.3.2. HUB In DriveSE, the hub assembly comprises of a hub, a pitch system and a spinner. The hub acts as a connection point of the rotor blades to the main shaft of the drive train, thereby transmitting all the loads generated by the blade. The pitch system allows for the pitch control of the turbine in the full load region. It comprises of pitch motors and bearing, which can alternatively be a part of the blades. The spinner or nose cone pro- vides weather protection to the hub and reduces the drag force. They are typically made up of glass fiber. The rigid design of the hub with respect to the main shaft makes this model unsuitable for the analysis of 2-bladed rotor.
The calculation of the force and the moment at the hub center in the coordinate system as specified in Figure 3.9 is added to the Hub discipline of DriveSE to enable its integration to the Blade sub-system. The equations for the calculation are given by:
m B m m m m (3.19) r otor = × bl ade + hub + pi tch + spinner
F T m g sin(Ψ) (3.20) hub,x = r otor + r otor × × F 0 hub,y = F m g cos(Ψ) hub,z = − r otor × ×
M Q (3.21) hub,x = r otor M 0 hub,y = M 0 hub,z = The force in the x-direction comprises majorly of the rotor thrust force and the com- ponent of the rotor weight due to the shaft tilt; the force at the hub in the y-direction can- cels off due to an assumption of symmetrical blades; while the z-component of the force 3.3.D EVELOPMENT 27 at the hub is primarily due to the rotor weight. The drag force on the hub is not consid- ered. The moment due to wind shear in the y-direction and gyroscopic load due to yaw misalignment in the z-direction are considered to be 0. Again, due to the assumption of symmetrical blades, the moment due to gravity at the hub in the y-direction cancels off.
The sensitivities of the mass of the hub assembly to the influencing inputs - moment at the blade root and length of root chord - are shown in Figure 3.10. It should be noted that the variation in the length of root chord, as shown in Figure 3.10b, also leads to variation in the moment at the blade root. 3
!"$"% " " " " !"$"% " " # # " " # !!% # !!%
& !! & !!
" #" " #"
(a) Sensitivity of hub mass to flapwise moment (b) Sensitivity of hub mass to the length of root at the blade root chord
Figure 3.10: Sensitivity of hub mass to the model inputs
3.3.3.3. GEARBOX DriveSE includes a physical model of a 3-stage gearbox. Due to the high load in the first stage of the gearbox, a planetary gear is fixed, while the last stage is set to a parallel gear due to its simple and reliable design. The second stage comprises of a planetary gear. The gearbox is designed for the torque that is 1.5 times the rated Qr otor .
The gearbox mass is sensitive to only one input - torque - that is pertinent in this use case, which is shown in Figure 3.11. It is seen that their relationship is linear.
3.3.3.4. LOWSPEEDSHAFT The main shaft or the low speed shaft (LSS) helps in the transmission of the torque to the generator via the gearbox. The LSS, in conjugation with the main bearings, are responsi- ble for the transfer of non-torque loads to the tower via the bedplate and the yaw drive.
In DriveSE, the LSS, the main bearing and an additional downwind main bearing in the case of 4-point suspension system are designed simultaneously. N5RT uses a Compact-aligning toroidal roller bearing (CARB) type for the main bearing, while a Spher- ical roller bearing (SRB) type for the second bearing. The sensitivity analysis of LSS mass with respect to influencing input parameters is shown in Figure 3.12. 28 3.D ESIGN ITERATION #1
3
Figure 3.11: Sensitivity of gearbox mass to torque
Figure 3.12: Sensitivity of LSS mass to aerodynamic load
In Figure 3.12, it can be seen that the LSS design is sensitive to My and Mz , which are assumed to be zero in Equation 3.21 because the effect of wind shear and yaw misalign- ment are not modelled in the aerodynamics discipline. This may lead to an inadequate design and an underestimation of the mass of the load bearing components. DriveSE provides a provision to correct for this input deficiency using empirical corrections, as given by [40]:
M 59.7 m (0.004 R 0.9642) (3.22) y = × r otor × × r otor + M 53.8 m (0.004 R 0.9642) z = × r otor × × r otor +
3.3.3.5. HIGHSPEEDSHAFT The high-speed shaft (HSS) of the drivetrain connects the output side of the gearbox to the generator. In DriveSE, this discipline includes a mechanical brake, which is located 3.3.D EVELOPMENT 29 on the high speed shaft because the low torque allows the brake to be less bulky. Like the gearbox, the HSS is also designed for the torque that is 1.5 times the rated Qr otor .
3.3.3.6. GENERATOR The generator converts the mechanical torque to the electrical power. In DriveSE, it is assumed to be a high speed Doubly Fed Induction Generator (DFIG).
3.3.3.7. TRANSFORMER &CONVERTER The phase voltage in the DFIG generator is limited to 5000 V. Hence, it requires to be stepped up for the collector system’s medium voltage level. DriveSE allows the position- 3 ing of the transformer inside the nacelle. The converter improves the power quality of the electricity in accordance to the grid requirements.
3.3.3.8. MAINFRAME The mainframe comprises of the bedplate, crane and other platforms required for facili- tating operation and maintenance. It is connected to the tower through the yaw bearing. The drive train and the nacelle components are protected against weather using a cover which is usually made of glass-fiber [46]. The sensitivity analysis of bedplate mass with respect to influencing input parameters is shown in Figure 3.13.
Figure 3.13: Sensitivity of bedplate mass to aerodynamic load
Similar to the LSS, the bedplate design is sensitive to the moment due to wind shear (My ) and the gravity load (Fz ). Again, an empirical correction of My (Equation 3.22) is done to determine an adequate bedplate design.
3.3.3.9. YAWDRIVE Yaw drive is used to align the rotor to the wind direction, to ensure maximum aerody- namic efficiency and fatigue life of the blades. The yaw system comprises of several yaw 30 3.D ESIGN ITERATION #1
motors and a friction plate bearing. In DriveSE, the number of yaw motors and their weights are determined based on knowledge based engineering.
3.3.4. COST A cost model from WindPACT based on the empirical relationship derived from 2002 in- dustry data is used to determine the cost of all the components discussed earlier. The detailed formulation of the model can be found in [41]. The cost constitutes of the cap- ital expenses and excludes the assembly costs, overheads and profits. The costs are in 3 USD, which is converted to EUR using the exchange rate of EUR/USD = 1.23 [50], for the integration of RNA to WINDOW.
Since the original model is insensitive to the component mass, WindPACT results are calibrated to meet the requirements of the first use case. This is done by calculating re f 5 re f the mass of each component (mi ) of the N5RT using DriveSE, and their cost (Ci ) using WindPACT, and then calibrating the cost of these components using the following equation:
re f C C m i (3.23) i = i × re f mi re f re f re f C f (R ,P ) i = r otor r ated
The XDSM of the Cost sub-system is shown in Figure 3.14.
ref ref mi , Ci
Cost mi
th Ci i component
Figure 3.14: XDSM of the Cost sub-system
The DFIG generator only requires a partial scale (upto 30% of machine rating) con- verter. However, in this use case, a full scale converter is (inadvertently) used. The em- pirical model of the converter cost is given by:
C 79 P (3.24) conv = × r ated
, where Pr ated is in kW. Due to a large converter cost, this leads to an inflation in the RNA cost. However, as the Pr ated is held constant in this use case, implying the converter cost to remain fixed, this error has no influence on the optimal solution.
5i Blade, Hub, Gearbox, LSS, Bearings, HSS, Generator, Transformer & Converter, Mainframe and Yaw ∈ 3.3.D EVELOPMENT 31
3.3.5. COUPLINGTHEDISCIPLINES So far the Blade, Hub & Nacelle and Cost sub-systems were discussed separately. To get a complete picture of the RNA model, its XDSM is presented in Figure 3.15.
B, Rrotor, B, Rrotor, Rhub, Ψ, U , Rhub, Ψ, rgb, ∞ ref ref ref ηdt, Ucut in, Np, Prated, m , C δ , γ, UTS − i i tip Ucut out, Loverhang, − Prated, Airfoils Dtower
c1,2,3, β1,2,3, τ, RNA peg peg c1 λ, θ peg 3
mblade, Trotor, Paero(U), σflap(r), Blade Qrotor, mblade mblade, Cp Ct(U) σedge(r), δtip Mflap(Rhub)
mrna Hub & Nacelle mi mi
Crna Cost Ci
Constraint Constraint value
Objective Objective value function
Figure 3.15: XDSM of the RNA model for Use Case #1
In Figure 3.15, τ is shown as a design variable; however, for a given value of other design variables, τ can take only one value that satisfies the constraints, while for other values of τ, the overall feasibility of the MDAO may not be maintained; although every individual discipline always satisfy their equations. This MDAO architecture is called In- dividual Design Feasible (IDF). Here, τ is not essentially a design variable, but acts as a promoted surrogate variable [51].
Multi-disciplinary Design Feasible (MDF) is an alternative architecture where such surrogate variables are handled through iterations using Gauss-Siedel or Newton-based methods to ensure the overall feasibility of the MDAO framework for every value of the design variables. In this RNA model, IDF is taken as a preferred architecture due to its faster convergence rate in a gradient based optimization [52].
The Aerodynamics discipline in the Blade sub-system calculates the steady aerody- namic load at the normal power production operation of the turbine. However, IEC recommends different design load cases - that include turbulence modelling, unsteady aerodynamic effects, aero-elastic effects, coupling of vibration modes in structural dy- namics, control system behavior - to test the limits of the wind turbine components [53]. Due to this limitation in the Ad-hoc module, a safety factor of 1.5 is used while connect- ing the aerodynamic loads from the Blade sub-system to the Hub & Nacelle sub-system. In this regard, the LSS and Mainframe disciplines receive M~hub and Fhub~ that have been amplified by a factor of 1.5. 32 3.D ESIGN ITERATION #1
The component-wise mass distribution of N5RT is shown in Figure 3.16.
Mainframe Gearbox Hub Blades LSS Generator Transformer Main Bearing 3 Yaw Drive Converter Second Bearing HSS
Figure 3.16: N5RT RNA mass breakdown
It can be seen that the mainframe is the bulkiest component, because it is the major load bearing component, transmitting the aerodynamic and gravity forces from the rotor and the drive train to the tower. The collective mass of the hub and the blades (rotor) is higher than that of the bedplate. In the drive train, gearbox is the heaviest, followed by the LSS. 3.4.V ALIDATION 33
3.4. VALIDATION In this section, the coupling of various sub-systems in the RNA model is validated.
With a complete picture of the RNA model, it is executed for two different offshore wind turbines - NREL 5 MW reference turbine (N5RT) and Siemens SWT-2.3-108. The NREL turbine is chosen because its inputs [43] and outputs [54], generated from FAST simulation, are well documented in literature. However, since the DriveSE and Wind- PACT tools used in this RNA model are also developed by NREL, their result could be bi- ased towards N5RT. Therefore, Siemens SWT-2.3-108, having a different drive train con- 3 figuration, is also used for the validation.
The primary inputs (Pr ated , Rr otor , λ, rgb and Ψ) and outputs (mr otor , mnacelle and power curve) are taken from the Siemens website [55], while the other unknown inputs are scaled from N5RT. The inputs for both the turbines are listed in Table 3.4. The result and the corresponding error from the RNA model are listed in Table 3.5. Their electrical power curves are also compared in Figure 3.17.
Inputs SWT-2.3-108 NREL-5.0-126
Pr ated [kW] 2300 5000
Rr otor [m] 54 63
Rhub [m] 1.28 1.50 Ψ [°] 6 5
λdes [-] 7.4 7.6 Airfoil Same as N5RT Same as N5RT
cpeg [m] [3.04, 2.58, 1.98] [3.54, 3.01, 2.31]
βpeg [°] [13.31, 9.00, 3.12] [13.31, 9.00, 3.12] Main bearing SRB CARB Second bearing - SRB Transformer False True
rgb [-] 91 96.76
Np [-] [3, 3, 1] [3, 3, 1]
ηdt [-] 95% 95%
Ucut in [m/s] 3 3 − Ucut out [m/s] 25 25 − Dtower [m] 3.24 3.78
Table 3.4: Inputs for the validation 34 3.D ESIGN ITERATION #1
SWT-2.3-108 NREL-5.0-126 Output Unit Website Model Error FAST Model Error data result data result
Cp,max [-] 0.507 0.5029 -0.81% 0.488 0.5037 +3.22%
δti p [m] - 5.98 7.5 6.99 -6.8%
M f l ap (Rhub) [MNm] - 4.79 13.0 10.58 -18.61%
mr otor [ton] 60 53.32 -11.13% 110 103.0 -6.36% 3 mnacelle [ton] 82 90.34 +10.17% 240 224.16 -6.6% Table 3.5: Outputs of the validation
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(a) Power curve of SWT-2.3-108 (b) Power curve of N5RT
Figure 3.17: Validation of the Blade sub-system
Blades Blades Gearbox Gearbox Converter Converter Hub Hub Generator Generator Transformer Transformer Mainframe Mainframe Other Other
(a) N5RT RNA cost breakdown (b) REpower 5 MW RNA cost breakdown [56]
Figure 3.18: Validation of the Cost sub-system 3.4.V ALIDATION 35
For both the turbines, the mr otor and mnacelle from the RNA model are within an acceptable error range for a low-fidelity preliminary design and analysis model. The maximum tip deflection (δti p ) and the flapwise moment at the blade root (M f l ap (Rhub)) are underestimated in this model because the calculations are done with an assumption of steady aerodynamics.
The Cp,max and the power curve are similar for both the turbines, except the cut-in wind speed region for SWT-2.3-108. This is because in reality there is a limitation on the minimum rotational speed of the rotor that prevents the operational tip speed ratio to 3 be lower than the design tip speed ratio, thus reducing the Cp . It should be noted that due to the scale of the axes in Figure 3.17, the differences are not clearly noticeable.
In Figure 3.18, the component-wise cost distribution of N5RT is compared against the cost distribution of its equivalent real offshore turbine - REpower 5 MW.
In both the turbines, the cost is dominated by the rotor blades, while the gearbox, converter and the generator are the more expensive components of the drive train in the descending order. The noticeable differences in the breakdown of costs of N5RT and REpower exemplifies the inherent differences associated with the cost models, which are due to the empirical nature of the model, price volatility and inflation. 36 3.D ESIGN ITERATION #1
3.5. ANALYSIS The use case for the first research objective was framed in Section 3.1. The development of RNA model was discussed in Section 3.3. The model was validated in Section 3.4. Af- ter the RNA model is developed and validated, it is coupled to the WINDOW model. The coupling between the RNA and WINDOW was discussed in Chapter 2.2.2. This leads to the final step of analyzing the first research objective.
The use case underlying this objective is to re-design N5RT blade for different objec- 3 tive functions pertaining to varying system scopes, as defined as:
³ ´ MAX C Case A, System scope: Aerodynamics p ³ Cp ´ MAX Case B, System scope: Blade Objective Function: mbl ade ³ C ´ MAX p Case C, System scope: RNA mr na ³ ´ MIN LCOE Case D, System scope: Farm (3.25)
The design variables for these optimization problems are design tip speed ratio (λdes ), 1,2,3 1,2,3 thickness factor (τ), blade pitch angle (θ) and chord (cpeg ) and twist (βpeg ) distribution at the three pegged points. The bounds and initial values of the design variables for the optimization problem are listed in Table 3.6.
Design Initial Value Lower Bound Upper Bound Variable
λdes 7.6 5 12 c [3.04, 2.58, 1.98] 0.75 Initial Value 1.25 Initial Value peg × × β [13.31, 9.00, 3.12] 0.5 Initial Value 1.5 Initial Value peg × × θ 0.0 -5.0 5.0 τ 1.0 0.5 1.5
Table 3.6: Design variables for Use Case #1
Although the effect of blade pitch angle can be compensated by the twist angle, the inclusion of θ as design variable is necessary because the twist angle at the blade tip is set to zero in the Aerodynamic Design discipline. The chord lengths are allowed to vary within the range of 25% of their original values, and not higher due to the manufactur- ± ing and transportation constraints. Since at values of τ lower than 0.5, the buckling of the blade could emerge as a governing actor, which is not modelled in Blade Mechanics, a lower bound of 0.5 on τ is imposed.
The optimization problem is subject to two constraints: maximum tip deflection and 3.5.A NALYSIS 37 maximum stress along the blade cross sections, as given by:
δti p re f 1 Maximum tip deflection margin (δmar gin) δ Constraints: ti p = (3.26) γ σmax f l ap 1 Maximum stress margin (σ ) UTS ≤ mar gin
The stress along the blade section (σf l ap (r )) is received from the Mechanics disci- pline, and then the maximum is determined and a safety factor (γ) is applied to calculate its margin with respect to the Ultimate Tensile Strength (UTS) of the blade material (dis- 3 cussed in Section 3.3.2). As shown in Figure 3.5, the maximum stress may not be at the blade root, and the cross section at which the blade experiences the maximum stress is not relevant. The load factor, material factor and consequence of failure factor are taken from IEC guidelines for Class IIB turbines [53], which are listed in Table 3.7. An addi- tional safety factor of 1.5 is taken to account for the steady aerodynamics assumption (as discussed in Section 3.3.5).
Criteria Description Value
Unsteady due to steady state assumption 1.5 factor Load factor due to uncertainties in load 1.35 Material fac- due to variation in material properties 1.2 tor Consequence effect of a failure on the overall turbine 1.0 of failure Overall γ 2.43 = Table 3.7: Safety factor for the ultimate stress limit of the blade
Since the objective function of Case A is the aerodynamic efficiency of the blade, that is insensitive to τ, the optimizer may yield a blade design that is stiffer than necessary. This would lead to unfair comparison between Case A and the other cases. Hence, the tip deflection constraint is implemented as an equality constraint. The constraint of maxi- mum tip speed is not taken into consideration. Other input parameters are the same as that of the N5RT (Table 3.4).
A gradient based sequential (least-square) quadratic programming algorithm, SLSQP, is used for the optimization. The sensitivity analyses of the mass of the major load bear- ing components with respect to their influencing variables in Figures 3.10, 3.11, 3.12 and 3.13 demonstrate (partially) that the response curve with respect to the chosen design variables is smooth. It is also known that the variation in Cp with respect to the given design variables is smooth. Hence, the optimization problem is apt for gradient based 4 optimizer. A convergence tolerance of 10− is used. The design variables, objective func- tion and the constraints are normalized using min-max scaling to make the process of gradient descent quicker and to prevent it from getting dominated by a particular design 38 3.D ESIGN ITERATION #1
variable [57].
For each case of the system scope, once the blade has been designed, the disciplines outside the corresponding system scope in the WINDOW model are executed sequen- tially, and the LCOE for each scenario is calculated. The wind farm is assumed to have 5 5 wind turbines in a square layout having an equal downwind and crosswind spacing × of 7.5D, as shown in Figure 3.19. The wind rose is assumed to be uniform and a constant water depth of 20m is considered. 3
Figure 3.19: Farm layout for Use Case #1
C C The results are listed in Table 3.8. The LCOE, p and p have been normalized mbl ade mr na with respect to their corresponding Case A values. The tip deflection constraint is the only active constraint, whereas the maximum stress margin is safely retained during the optimization. The difference in the blade profile for all the cases is shown in Figure 3.20. The variation in the mass and cost of relevant components are shown in Figure 3.21.
Parameter Unit A: Aerody- B: C: D: Farm namics Blade RNA
Design λdes [-] 7.74 6.73 8.60 7.69 variables τ [-] 0.93 0.5 0.5 0.5 θ [°] -0.52 3.52 3.49 3.45
Objective Cp [-] 0.5104 0.4890 0.4952 0.4943 C functions p [-] 1.00 1.60 1.52 1.57 mbl ade C p [-] 1.00 1.15 1.21 1.19 mr na LCOE [-] 1.00 0.9363 0.9552 0.9346
Constraints δmar gin [-] 1.0 1.0 1.0 1.0
σmar gin [-] 0.86 0.78 0.85 0.88
Others Ct [-] 0.8553 0.7348 0.8280 0.7665
η f ar m [-] 0.8302 0.8588 0.8371 0.8518
Table 3.8: Results of Use Case #1 3.5.A NALYSIS 39
!" #" $!" !" #" %! %!
$!" 3
& !" & !"
Figure 3.20: Variation in chord and twist distribution with different system scopes
250 3.1
3 200 2.9
2.8 150 2.7
Mass [ton] Mass 100 2.6 Cost [Million EUR] EUR] [Million Cost 2.5 50 2.4
0 2.3 Rotor Gearbox Nacelle RNA Support structure
Aerodynamics Blade RNA Farm Aerodynamics Blade RNA Farm
(a) Mass variation (b) Cost variation
Figure 3.21: Variation in the component mass and cost with different system scopes
The LCOE is highest when the blade is designed for the maximum aerodynamic per- formance in Case A, that is, when the system scope is limited to the aerodynamics level. 6 It can be seen that an individual turbine has the highest Cp as well as the highest Ct . This translates into higher wake losses and a lower wind farm efficiency (η f ar m). Addi- tionally, the mass (Figure 3.21a) and the cost of the rotor is maximum, along with the cost of the support structure (Figure 3.21b) that is dictated by the rotor thrust.
In Case B, when the system scope increases to the blade level, the optimizer tries to minimize the blade mass while withholding the tip deflection constraint. As discussed in Section 3.3.2.5, δti p is influenced by flapwise moment, which in turn depends on the
6 All references to Cp and Ct in this chapter denote the maximum value of the respective coefficients, that is, at the partial load condition 40 3.D ESIGN ITERATION #1
fx , aerodynamic force acting on the blade section in the direction perpendicular to the plane of rotation. This fx is essentially the thrust force (Tr otor ) when integrated over the entire rotor. The tip deflection is controlled using the stiffness (EI) of the blade. The con- trol of the optimizer over the blade stiffness and the blade mass are intertwined. Hence Tr otor is the dominating factor driving the optimization in this case. The intertwining of the mass and the stiffness properties of the blade are given by:
µ s2 τ (3.27) 3 ∝ × EI s4 τ ∝ × Since the stiffness is more sensitive to the changes in chord length than that in τ, the chord length becomes longer (Figure 3.20), while τ is brought down to its lower bound to minimize the blade mass. Due to the longer chord, λdes reduces so as to retain the optimal blade solidity for the maximum Cp . Since Pr ated is held constant, low λdes re- sults in high Qr otor , which translates into higher gearbox mass (Figure 3.11 and 3.21a). With a lighter blade and heavier gearbox, the overall nacelle mass reduces only slightly, but the cost is decreased significantly (compared to Case A) because the blade is more expensive component than the gearbox (Figure 3.21b). The minimization of Tr otor leads to a significant improvement in the support structure cost and wake losses, although this is not explicitly in the interest of the optimizer.
In Case C, at the RNA level, the objective is to maximize the Cp while keeping the mr na to a minimum. The extra components in Hub & Nacelle means the minimization of blade mass is no longer necessary. The sensitivity of the nacelle mass to Qr otor and Tr otor is shown in Figure 3.22.
Figure 3.22: Sensitivity of nacelle mass with Qr otor and Tr otor
It can be seen that the nacelle mass is not sensitive to Tr otor , but is quite sensitive to Qr otor . Since the nacelle constitutes over 65% percent of the RNA mass, the optimizer favors reduction in the nacelle mass by reducing Qr otor than the reduction in blade mass 3.5.A NALYSIS 41
by reducing Tr otor . Hence, Qr otor becomes the dominating factor driving the optimiza- tion of this case.
Cp From Equation 3.18, it can be inferred that the tip deflection is proportional to EI . However, since the Cp in this case has increased as compared to Case B, to meet the tip deflection constraint, the chord length increases (Figure 3.20). Although this leads to a slight increase in the rotor mass, an appreciable decrease in the nacelle mass leads to a decrease in the overall RNA mass as compared to Case B (Figure 3.21a).
C From Table 3.8, it can be seen that although the p is the maximum in this case, 3 mr na this doesn’t necessarily translate into a minimum LCOE. The higher LCOE in Case C as compared to Case B is contrary to the expected result from this use case as discussed in Section 1.4.2. This is because the dominating factor of Tr otor in Case B that led to lower support structure cost and wake losses is taken over by Qr otor .
The inter-disciplinary influences missed in the Cases A, B and C are captured when the system scope increases to the wind farm level in Case D. The LCOE in this case is quite close to that of Case B, which could be because the optimizer might be stuck in a local minimum due to the roughness in the response curve at the wind farm level. How- ever, in view of this use case, this is not a deterrent in demonstrating that the best result is obtained when the system scope is at the wind farm level.
This leads to a conclusion that the blade design that respects the inter-disciplinary influences over every aspects of the wind farm, as in Case D, yields a better LCOE than any other case. Increasing the system scope for the blade design may not necessarily lead to a better wind farm LCOE, as seen in Case C. This is because the influence of thrust dominates at the blade (Case B) and the farm level (Case D), while the influence of torque dominates at the drive train or the RNA level (Case C).
4 DESIGN ITERATION #2
The objective of this chapter is to optimize the rotor diameter, power rating and, thus, the power density of the turbines in a given wind farm. To accomplish this, the development milestone is to include the support for turbine scaling in the OWF model. The dissem- ination of knowledge on the utility of the tool in designing a wind turbine specific to a particular offshore site among the wind turbine and wind farm developers is intended.
This chapter is divided into five sections:
1. Use case - The underlying use case to study the second research objective is for- mulated. 2. Literature survey - A survey on similar researches is performed. 3. Development - The required updates in the MDAO workflow is explained. 4. Validation - The coupling of the updated RNA model to WINDOW is validated by performing sensitivity analyses of pertinent response variables with respect to the design variables of this use case. 5. Analysis - The validated model is used to meet the second research objective - to study the effect of variation in the power density of a rotor on the LCOE of the wind farm.
43 44 4.D ESIGN ITERATION #2
4.1. USECASE The objective of this use case is to study the effect of the rotor radius and its rated power - or the power density (ζ) in general - on the LCOE of the wind farm. The power density (ζ) is given by: Pr ated ζ (4.1) = Aswept The scope of this use case lies at the intersection of the RNA scaling and the wind farm layout optimization. Since both these domains are diverse and involve numerous degrees of freedom, a full optimization could be computationally very expensive; hence, a simplified case with reasonable assumptions is presented.
At the RNA level, the rotor Cp,max and Ct,max are held constant by scaling the blade 4 design from NREL 5 MW Reference Turbine (N5RT). The design tip speed ratio, shaft tilt angle, gearbox ratio and drive-train efficiency are taken from Table 3.4. The cut-in and cut-out wind speeds are also assumed to be constant.
At the wind farm level, the site is considered to have a uniform wind rose, which nullifies the significance of the farm layout angle. A fixed Weibull shape factor k 2.11 = is taken, while the analysis is performed at different scale factors of a 8.15 & 9.0m/s = taken at the hub height. The farm is assumed to consist of 8 8 turbines in a square or a × rectangular layout without any area constraint. A uniform water depth of 20m through- out the farm is considered. Furthermore, in the calculation of the farm AEP,Jensen wake model with the directional sampling of 10° and the speed sampling of 1m/s is used. The wind farm availability of 98% is taken. These assumptions are summarized in Table 4.1.
Parameter Assumption
RNA 64 turbines with their blade design scaled from N5RT Wind rose Uniform with shape factor, k 2.11, and scale factors = of a 8.15 & 9.0m/s are considered = Bathymetry Fixed water depth of 20 m Farm layout rectangular layout with 8 8 turbines and 1 substation × without any constraint Wake model Jensen wake model with the directional sampling of 10° and the speed sampling of 1m/s Electrical in- 8 turbines per cable, grid 60 km, harbour 40 km, on- frastructure shore transport distance 100 km, collection voltage 66 kV, transmission voltage 220 kV
Table 4.1: Parameters for Use Case #2
Although the economies of scale associated with the manufacturing process and the 4.1.U SECASE 45 transportation and manufacturing issues with the larger blades are important factors in the upscaling of the wind turbines, they are not in the scope of this study.
It should be highlighted that the Weibull scale factor a is at the hub height of 90m and during the analysis of this use case, it is not scaled with the varying hub height. The effect of this error on this use case is equivalent to the assumption of taking zero wind shear factor. The implication of this error is discussed in Section 4.4.5.1.
With these assumptions, the influence of rated power, rotor radius and Weibull scale factor on the LCOE of the wind farm are studied for two different cases: a square farm layout and a rectangular farm layout. In this regard, the design variables for this use case are:
1. rotor radius (Rr otor ) 4 2. rated power (Pr ated ) 3. thickness factor (τ) 4. turbine spacing in the north-south direction (Dns ) 5. turbine spacing in the east-west direction (Dew )
In a uniform wind rose, there is no distinction between downwind and crosswind spacing, hence the naming convention of east-west and north-south spacing are used.
As discussed in Section 3.3.5, τ is not essentially a degree of freedom, but a surrogate variable, and it can only take a particular value for a given Pr ated and Rr otor to meet the tip deflection constraint. 46 4.D ESIGN ITERATION #2
4.2. LITERATURE SURVEY The market share of larger turbines has been on a steady rise in the offshore wind energy sector. Only 18% of the installed turbines between 2001-2005 were above 3 MW of rated capacity, while their proportion rose to 96% in 2011-2016. As high wind resource sites are becoming scarce, an upscaling of the turbines is necessary to maximize the econom- ical extraction of wind energy [58]. The extracting of energy from a turbine is dictated by its power curve - rated power and rated wind speed - and the site’s Weibull wind dis- tribution - scale and shape factors. If the rated wind speed is too high, the turbine will rarely be operating at the rated condition, and the cost of building strong blades, tower and drive train will not be justified. On the other hand, if the rated wind speed is too low, the required rotor size would be too high, leading to an excessive investment cost [59].
4 The rated wind speed (Ur ated ) is dependent on the turbine’s aerodynamic efficiency (Cp ), rated power (Pr ated ) and rotor radius (Rr otor ), as discussed earlier in Equation 3.8, while the site’s wind resources depend on the hub height (Hhub) and Weibull shape (k) and scale (a) factors at the reference height. In the upscaling of the turbines, the blade design, or Cp in other words, doesn’t play as important role as Pr ated and Rr otor [60].
The upscaling of the wind turbines is theoretically governed by the square-cube law, which says that the energy yield from a turbine scales with the square of the diameter, while its mass - and subsequently the cost - scales with the cube of the diameter. Ac- cording to this law there is an optimal point where the increase in the cost supersedes the gain in the energy yield from the turbine. However, this is a simplistic argument that assumes a constant rated wind speed and power density and ignores the effect of wind shear in granting higher wind speed at higher heights. In reality, this law has been cir- cumvented by improving the design and power density of the turbine, bringing down the factor with which the blade mass scales with its diameter to 2.3, instead of the theoretical value of 3 [61].
The power density of the turbine is the ratio of its rated power and swept area. The swept area is related to the size of the rotor (Rr otor ) while the Pr ated is related to the gen- erator capacity. The selection of a turbine from a list of turbines with different Pr ated and Rr otor for a given site in India was done by [62] using the maximum capacity factor as the selection criteria. Similar analyses on optimizing the relative size of the rotor and the generator were done by [63] and [64]. However, capacity factor (κ) is not a suitable in- dicator of assessing the optimal wind turbine sizing. This is because κ would approach unity when a very large rotor is chosen in comparison to the generator, which is not a rational choice from an economics point of view. Hence, the study of AEP - which is re- lated to κ - in conjugation with a cost model, in form of LCOE, is essential to determine an optimal rotor and generator sizing.
In this regard, the optimization of the relative rotor and generator size of a standalone turbine at various cost constraints was done by [65]. It was observed that a variation in the rotor size with respect to the generator size has a large impact on the levelized cost depending on the site. This observation is seconded in the industry data; for example, 4.2.L ITERATURE SURVEY 47
Vestas offers 2 MW turbines in six different diameters, apt for different sites, while GE offers 100m rotor for various machine ratings ranging from 1.6 MW to 2.85 MW (Figure 4.1).
4
Figure 4.1: Variation in the rotor size and the machine rating [58]
At the wind farm level, [66] used turbine sizing parameters - rotor diameter, gener- ator capacity and hub height - as well as their spacing in a rectangular farm layout as design variables to minimize the levelized cost of the farm. An AEP model derived from empirical array efficiency data and turbine capital cost model derived from [41] were used. The optimization results revealed an optimal configuration where κ is well below unity.
An aeroelastic model with simulated turbulence and a wind farm cost model was used by [60] to optimize the rotor diameter for the minimum cost of energy in a farm comprising of 5 7 turbines with a uniform wind distribution. A gradient based opti- × mizer was used with hub height, rotor speed, rotor diameter and rated power as design variables. The results showed 11% increase in the optimal rotor diameter for an offshore site leading to 28% increase in AEP,16% increase in the investment cost, and an overall reduction of 16% in the cost of energy.
[67] performed a similar analysis on a wind farm with a fixed capacity by varying the rated capacity and the diameter of each turbine. The RNA cost, support structure cost and electrical infrastructure costs were determined empirically and wake losses were not considered. It was found that for a 500 MW farm, the optimal capacity of a turbine lies in 10-13 MW range, while that for a 100 MW farm lies in the range of 5-7 MW. The optimal solution was due to the opposing effects of the turbine and support structure costs on one hand and the O&M costs on the other. Since the wake loss was not modelled, the effect of turbine upscaling on the spacing and cable cost was not captured. 48 4.D ESIGN ITERATION #2
4.3. DEVELOPMENT 1,2,3 The nature of the use case discussed in Chapter3 necessitated the use of λdes , τ, θ, cpeg 1,2,3 and βpeg as design variables while keeping the Rr otor and Pr ated fixed. However, since the objective of this chapter is to study the effect of Rr otor and Pr ated on the wind farm LCOE, the workflow has to be tailored to suit the need of the use case. In this regard, the necessary updates are analyzed and the corresponding changes are discussed.
4.3.1. DESIGNSCALING A Design scaling discipline is introduced in the Blade sub-system to scale all the lengths - Rhub, Loverhang , Dtower and Hhub - with Rr otor using N5RT as the reference. In the previous use case, these parameters were fixed inputs to the RNA model. The scaling of 4 Hhub, which is used for the support structure design, is done differently as compared to the other parameters, to allow a fixed clearance of 27m between the blade tip and the mean sea level. The scaling of various length parameters are given by:
Rr otor s (4.2) = re f Rr otor re f R R s (4.3) hub = hub ×
re f L L s (4.4) overhang = overhang ×
re f D D s (4.5) tower = tower ×
H 27 R (4.6) hub = + r otor
4.3.2. AERODYNAMICDESIGN In view of agility as a development goal of this project, a new model for the Aerodynamic design discipline is developed to suit this use case. In the previous use case, this disci- pline took the chord and twist angles at pegged nodes to design the aerodynamic profile of the blade. However, in this use case, these profiles are scaled from N5RT using the following equations: r r¯ (4.7) = Rr otor
c(r¯) c (r¯) s (4.8) = re f ×
β(r¯) β (r¯) (4.9) = re f The updated XDSM for the workflow pertaining to this use case is shown in the Ap- pendix A.2. 4.4.V ALIDATION 49
4.4. VALIDATION Since the development for this use case only required a change in the workflow of the MDAO, rather than any change in the individual disciplines (except Aerodynamic de- sign), the validation done in Section 3.4 still holds true. The purpose of the validation in this section is to ensure that the RNA and WINDOW coupling captures the necessary inter-disciplinary dynamics for this use case. This is done by performing the sensitivity analyses of the important response parameters of the farm with respect to the design variables discussed in Section 4.1, and assessing the results in contrast to the physical expectations. Finally, the effects of (inadvertent) errors due to assumption of zero wind shear and full scale converter on the result are analyzed.
4.4.1. RESPONSEVARIABLES The primary response variable of the sensitivity analysis is the LCOE of the farm, which, 4 in a simplified form, can be thought of as a ratio of the total cost and the farm AEP. In this regard, an overview of the associated response variables - cost and AEP - that will be validated in this section is provided below.
The primary drivers of the total cost associated with the changes in Pr ated and Rr otor are the RNA cost, support structure cost, cabling cost, and other investments in the form of procurement, installation and project management costs. Since the O&M cost is scaled empirically using a linear relationship with AEP in WINDOW, it constitutes a fixed value in the LCOE, and hence it is not an influencing parameter in this use case, as given by:
Cinv a Co&m LCOE + × (4.10) ≈ AEP a × Cinv k1 AEP LCOE + × ⇒ ≈ AEP a × Cinv LCOE k0 ⇒ ≈ AEP a + 1 ×
, where a is the annuity factor and k ,k0 0. 1 1 > The cost breakdown of a sample wind farm - with the inputs from Table 4.1 - is shown in Figure 4.2.
The farm AEP depends on the AEP of the individual turbines, which is dictated by the turbine’s power curve, and the site’s Weibull wind distribution, as discussed in Sec- tion 4.2. The power curve can be adapted to the site’s wind condition by varying the turbine’s Pr ated and Ur ated (which can be controlled using Rr otor ). The farm’s AEP is further influenced by the wake loss which depends on the rotor diameter , the spacing between the turbines and the thrust coefficient, as shown below:
³ ´ ³ ´ 2 ∆U p kwake x − 1 1 Ct 1 (4.11) U = − − × + Rr otor ∞ 50 4.D ESIGN ITERATION #2
Other investments RNA capital Support structure Cabling
Figure 4.2: Investment cost breakdown of a sample farm 4
where, kwake of 0.04 is the wake decay coefficient, x is the downwind spacing of the tur- bine and ∆U is the wind speed deficit at that turbine.
To visualize the sensitivity of these response variables, the design variables are nor- malized using min-max scaling. The minimum value (normalized value of 0) and the maximum value (normalized value of 1) of each design variables are listed in Table 4.2. While performing the sensitivity analysis with respect to one variable, other variables are kept constant at their respective reference value (normalized value of 0.5).
It should be noted that the analysis for the rectangular farm layout (Dew and Dns are independent) and the square farm layout (Dew ns ) are separated. The Weibull factors = k 2.11 and a 9.0m/s at the hub height are used for the analysis, while the other fixed = = parameters are summarized in Table 4.1.
Design Variable Reference Minimum Maximum Value Value Value
Pr ated [kW] 5000 4000 6000
Rr otor [m] 63 50.5 75.5 τ [-] 1 0.5 1.5
Dew [m] 945 630 1260
Dns [m] 945 630 1260
Table 4.2: Min-max scaling of the design variables for the sensitivity analysis
4.4.2. ENERGYYIELD The sensitivity analyses of the wake loss and AEP with respect to all the design variables are shown in Figure 4.3. The Cp and Ct curves in the full load region of various turbines are shown in Figure 4.4. The sensitivity analyses of rated wind speed and the farm ca- 4.4.V ALIDATION 51 pacity factor are shown in Figure 4.5.
τ τ