Multi-Disciplinary Optimization of Rotor Nacelle Assemblies for Offshore Wind Farms an Agile Systems Engineering Approach

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

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 disciplines - 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 flexibility in their utility to various stakeholders of offshore wind farms.

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 dissemination of knowledge 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 optimization 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 minimum 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 turbine/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 configuration. 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.

PREFACE

The opportunity for research in form of a thesis in the masters programme was the primary 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 support 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 accomplish 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

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

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 disciplines 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 agnosticism 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 research 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 available in literature with physics based models for the rotor, drive-train and support structure; 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 research 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 couples 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 development 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 using 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 design iterations to reach a milestone that is apportioned to meet the corresponding research 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 development 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 efficiency and the blade mass RNA maximization of the ratio of aerodynamic efficiency 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 development 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 optimized 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 conditions 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 effect 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 advantages 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 development 2 SYSTEMS ENGINEERINGOF OFFSHORE WIND FARMS

This chapter aims to throw light on the concept of systems engineering (SE) in wind energy and the effect of model choice on the use case. The terms frequently used in multidisciplinary 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 management 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 dynamics 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 interaction 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 computationally 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 controller 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 uncertainty 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 example, 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 aerodynamics. 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 engineering 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 introduced. 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 represents 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 advantage 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 aerodynamics 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 corresponding 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 spacing - that are controlled by the MDAO driver (rounded rectangle). The vertical line connected to each discipline represents the ﬂow of inputs, while the horizontal line represents the ﬂow of output.

The Layout discipline sets the coordinates of the turbines and the substation depending 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 coefficient (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 substation 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 components 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 coupled 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 researchers is intended.

This chapter is divided into ﬁve sections:

1. Use case - The underlying use case to study the ﬁrst research objective is formulated. 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 efficiency and the blade mass C RNA maximization of the ratio of aerodynamic efficiency 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 stability, operational reliability and power quality over its lifetime [8]. This design objective is thus a multi-disciplinary optimization that requires a coupled interaction among various 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 coupled 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 baseline 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 degradation 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 sections 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 designed use case. The aptness of the model is sensed by the sensitivity of the power output, 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 constituting components and to glean various tools and models for each component from literature. 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 module based on BEM for the blade aerodynamic design and scaling law for the blade structural 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 characterized 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.

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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 factor 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 perform the aerodynamic calculations: Blade Element Momentum (BEM) models, vortex models and CFD models. Due to its high computational speed and reasonably accurate 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 respectively. 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

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Figure 3.4: Sensitivity of bending moment with τ

τ = τ = τ = τ = τ = τ = τ = τ =

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# #

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

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 symbols and connections is provided in Appendix A.1. 3.3.D EVELOPMENT 25

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 bearing 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 bearing 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

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 provides 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 component of the rotor weight due to the shaft tilt; the force at the hub in the y-direction cancels 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 considered. 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

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"#" "#"

(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 responsible 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

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 misalignment 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 aerodynamic 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 industry 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 capital 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) converter. However, in this use case, a full scale converter is (inadvertently) used. The empirical 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 aerodynamic 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 dynamics, 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 connecting 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 discipline, 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 additional 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 maximum 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 bearing 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 function 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 sequentially, 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 performance 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 control 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 results 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 optimization 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 dissemination 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 formulated. 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 throughout 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 economical 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 distribution - 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 generator 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 related 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).

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, generator 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 discipline 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 design), 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 turbine and ∆U is the wind speed deﬁcit at that turbine.

To visualize the sensitivity of these response variables, the design variables are normalized 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

= =

(a) Wake loss (b) AEP

Figure 4.3: Sensitivity analysis of the energy yield and the wake loss

Rrotor = 63m, Prated = 5MW Rrotor = 63m, Prated = 5MW

Rrotor = 63m, Prated = 6MW Rrotor = 63m, Prated = 6MW Rrotor = 60m, Prated = 5MW Rrotor = 60m, Prated = 5MW

(a) Power coefﬁcient in the full load region (b) Thrust coefﬁcient in the full load region

Figure 4.4: Sensitivity analysis of Cp and Ct curves

An increase in Pr ated increases the Cp , and thus Ct , at all points in the full load region of the turbine, as seen in Figure 4.4. While an increase in Rr otor results in the wake effect of a turbine to be felt over a larger area. Both of these factors lead to higher overall farm losses (Figure 4.3a) with increasing Pr ated and Rr otor .

Additionally, both Pr ated and Rr otor affect the power curve of the turbine by chang- ing their Ur ated - an increase in Pr ated leads to an increase in Ur ated , while an increase in Rr otor leads to a decrease in Ur ated . As Ur ated increases, the turbine spends more time in the partial load region, where Ct is the highest and constant, resulting in higher wake losses. 52 4.D ESIGN ITERATION #2

τ =

τ = !

(a) Rated wind speed (b) Capacity factor 4 Figure 4.5: Sensitivity analysis of the rated wind speed and the farm capacity factor

Despite the increased wake losses, higher Pr ated and Rr otor increase the capability of a turbine unit to produce more power, resulting in an overall increase in AEP (Figure 4.3b). It can also be concluded from the ﬁgure that Rr otor has a larger effect on the AEP than Pr ated .

Dns

Dew

Directional Sampling of 90° Directional Sampling of 60°

(a) Wake loss in a rectangular farm layout (b) Effect of directional sampling

Figure 4.6: Effect of directional sampling in a rectangular farm layout

In a square layout, where Dew Dns , the uniform spacing is represented by Dew ns . = = A steady decline in the wake loss with increased Dew ns is logical (Figure 4.3). However, = the wake loss versus spacing curve is not smooth when a rectangular layout with different Dew and Dns is considered, as seen in Figure 4.6a. The curves for Dew and Dns are superimposed due to the directional symmetry imposed by the assumption of uniform wind rose. The occurrence of several local extremum is due to the discreteness in the wind directional sampling. This anomaly is explained in Figure 4.6b where 4 turbines are considered. 4.4.V ALIDATION 53

It can be seen that the directional sampling of 90° would lead to an overestimation of wake loss because at every angle of wind direction analysis, one of the turbines would lie in the wake; while such situation will not occur when the directional sampling of 60° is considered. These critical angles of analysis depend on the ratio of Dew and Dns , leading to the roughness in the response curve in the sensitivity analysis.

Since τ only affects the cross-sectional property of the blade, it has no inﬂuence over the wake losses and AEP.The capacity factor (κ) of the farm is given by: AEP κ (4.12) = 64 P 8760 × r ated × At a given Pr ated , κ is proportional to AEP,as seen in Figure 4.3b and 4.5b. However 4 the trend reverses for the Pr ated curve.

4.4.3. COST The sensitivity analyses of the cable cost, support structure cost, RNA cost and other investment costs are shown in Figure 4.7- 4.9. It should be noted that the RNA and support structure costs is aggregated for all the 64 turbines.

τ Dns Dew

" !

(a) Cable cost in a square farm layout (b) Cable cost in a rectangular farm layout

Figure 4.7: Sensitivity analysis of Ccc

The cable cost (Ccc ) depends on the cable type and its length. The cable type (from a given database) is determined by its capacity which is dictated by the number of turbines per cable (8 in this case) and the turbine’s Ir ated , as given by:

Pr ated Ir ated (4.13) = p3 V × r ated The cable layout, and thus its length, depends on the farm layout (Dew , Dns ). Both the cable type and its layout are optimized using Esau-Williams heuristic algorithm [26]. 54 4.D ESIGN ITERATION #2

(a) Reference farm layout (b) Support structure cost 4 Figure 4.8: Farm layout and sensitivity analysis of Css

τ Prated R rotor =

" !

(a) RNA capital cost (b) Other investments

Figure 4.9: Sensitivity analysis of RNA cost and other capital costs for the entire farm

In Figure 4.7a, the heuristic nature of the algorithm leads to the roughness in the sensitivity analysis of the cable cost with respect to Pr ated . In a square layout, the cable cost is seen to vary linearly with the spacing (Figure 4.7a), while the trend is discontinuous in a rectangular layout (Figure 4.7b). The switch in the cable layout occurs at the spacing of 945m in Figure 4.7b, when the spacing in one direction exceeds the spacing in the other direction (constant reference value of 945 m). Due to the positioning of the substation in the east of the farm, as shown in Figure 4.8a, the cabling cost is dominated by Dew after the switch in the cable layout 1.

The support structure cost (Css ) is inﬂuenced largely by the maximum rotor thrust (Tr otor ) and slightly by the tower top mass (mr na). Since, the blade design is held constant, the maximum rotor Ct (or Ct in the partial load region) doesn’t change, however

1The domain of the spacing in Figure 4.7b is expanded to 1800 m to demonstrate this effect 4.4.V ALIDATION 55

due to an increase in Ur ated at increasing Pr ated , its effect is reﬂected in a higher Tr otor and support structure cost (Figure 4.8b). Although the Ur ated decreases with increasing R , since T R2 , the support structure cost increases, which is ampliﬁed r otor r otor ∝ r otor due to an increase in mr na. Since the water depth of 20 m is assumed throughout the farm, Css does not vary with the spacing.

Since the blade is the most expensive component of the RNA (Figure 3.18a), which is inﬂuenced by Rr otor and τ, their effects in the sensitivity analysis of RNA capital cost is more pronounced than the effect of Pr ated (Figure 4.9a). Other investments (Coi ) include the procurement and installation costs, which is moderately sensitive to Pr ated and Rr otor (Figure 4.9b). 4.4.4. LEVELIZEDCOST 4 The superimposition of all the factors studied in this section results in the sensitivity analysis of the farm LCOE with respect to all the design variables.

Dns

Dew ] ] kWh c cEUR

[ [

tor

Prated

Dew = ns !

(a) Sensitivity analysis of LCOE in a square (b) Sensitivity analysis of LCOE in a rectangular layout layout

Figure 4.10: Sensitivity analysis of LCOE

It can be seen that the response curve is quite smooth for the square layout (Figure 4.10a), except few bumps with respect to Pr ated and Rr otor , while it becomes rougher in the case of a rectangular layout (Figure 4.10b).

4.4.5. ERROR ANALYSIS There are two inadvertent assumptions in the model - zero wind shear and full scale converter - that require further analysis.

4.4.5.1. EFFECT OF ZERO WIND SHEAR The Weibull scale factor a 9m/s at the hub height of 90 m is considered in this use case. = Due to the zero wind shear assumption, the difference in the inﬂow wind condition at 56 4.D ESIGN ITERATION #2

different hub heights is ignored. This presents an undue advantage to the turbines with lower hub heights and undue disadvantage to the turbines at higher hub heights. The effect of this assumption can be studied by the following equations:

µ ¶α re f H U(H ) U(H ) hub (4.14) hub = hub re f Hhub a(H ) U(H ) hub hub (4.15) re f ∝ re f a(Hhub) U(Hhub) The sensitivity of the LCOE with respect to a, keeping everything else constant, is shown in Figure 4.11. 4

"a!"!

Figure 4.11: Sensitivity analysis of LCOE with respect to Weibull a at Hhub

In the domain of the scaling analysis, where Rr otor varies from 50 m to 90 m and Hhub varies from 77 m to 117 m (Equation 4.6), it can be found out that a varies from 8.85 m/s to 9.25 m/s, using Equation 4.14 with the offshore wind shear factor α 0.11. = From Figure 4.11, it can be seen that this would yield an error of 4%. Since the error ± varies linearly with a, the corrected LCOE can be written as:

µ a(H ) ¶ LCOE LCOE k 1 hub (4.16) cor r ≈ model + 2 × − re f a(Hhub) µ ¶ ³ Rr otor ´α LCOE LCOE k0 1 ⇒ cor r ≈ model + 2 × − re f Rr otor ³ ´α 1 ∂(LCOEmodel ) ∂(LCOEcor r ) Rr otor − k0 α 2 re f ⇒ ∂Rr otor ≈ ∂Rr otor + × Rr otor

, where k ,k0 0 2 2 >

∂(LCOEcor r ) The correct optimal R is at the point where reaches zero. Since k0 is r otor ∂Rr otor 2 greater than zero, at that point, ∂(LCOEmodel ) is also greater than zero, implying LCOE ∂Rr otor model 4.4.V ALIDATION 57 has already started increasing after reaching a minimum. This implies that the assumption of zero wind shear leads to an underestimation of Rr otor . This inference is coher- ent with the fact that this model provides undue advantage to turbines with lower hub height.

4.4.5.2. EFFECT OF FULL SCALE CONVERTER In Section 3.3.4, it was highlighted that the cost of a full scale converter is assumed in the configuration with DFIG generator, however only 30% partial scale converter is necessary. Although this assumption did not have any influence in the previous use case, it may affect the result of this use case. The sensitivity analysis of AEP with respect to Pr ated along-with a linear fit is shown in Figure 4.12.

Prated

Figure 4.12: Sensitivity analysis of AEP with respect to Pr ated

Since, it can be deduced that AEP is linearly related to Pr ated with the y-intercept of zero, the corrected LCOE can be written as:

∆Cconv LCOEcor r LCOE k3 (4.17) ≈ model − × AEP Pr ated LCOEcor r LCOE k0 ⇒ ≈ model − 3 × AEP LCOE LCOE k00 ⇒ cor r ≈ model − 3

, where k ,k0 ,k00 0 and ∆C is the difference between the cost of a full scale con- 3 3 3 > conv verter and a partial scale converter at a given Pr ated .

Hence, similar to the previous use case, the error in the converter cost modelling has no effect on the optimal solution. 58 4.D ESIGN ITERATION #2

4.5. ANALYSIS The use case for the second research objective was framed in Section 4.1, which led to an update in the MDAO workﬂow, as discussed in Section 4.3. The response curve with respect to each design variable for this use case was validated in Section 4.4. This leads to the ﬁnal step of analyzing the second research objective.

The analysis for the square farm layout and the rectangular farm layout are separated. This segregation is done because of the complexity of the response curve and the computational cost associated with the optimization in the rectangular layout. In this regard, a simpliﬁed case of the square layout is dealt with a brute force analysis to get an indication of the variation in the optimized LCOE with Rr otor , Pr ated and Weibull scale factor a. Subsequently, the analysis is expanded to obtain an optimal power density and 4 spacing in the rectangular layout using a gradient-free COBYLA optimizer. The result is compared against the corresponding result from the analysis of the square layout.

The cases to be analyzed are listed in Table 4.3.

Case Layout Description

1 Square Brute force analysis of Optimized LCOE vs Rr otor at P 4MW and a 9m/s r ated = = 2 Square Brute force analysis of Optimized LCOE vs Rr otor at P 5MW and a 9m/s r ated = = 3 Square Brute force analysis of Optimized LCOE vs Rr otor at P 6MW and a 9m/s r ated = = 4 Square Brute force analysis of Optimized LCOE vs Rr otor at P 5MW and a 8.15m/s r ated = = 5 Rectangle COBYLA optimization of LCOE a 8.15m/s = 6 Rectangle COBYLA optimization of LCOE a 9m/s = Table 4.3: Cases to be analyzed for Research Objective #2

4.5.1. SQUARE FARM LAYOUT As discussed in Section 4.4, for the square layout, the spacing in the east-west direction and the north-south direction are the same, and is represented by Dew ns . Hence, the = design variables are reduced to Pr ated , Rr otor , τ and Dew ns . Since the response curves = with respect to these design variables are relatively smooth, the optimization problem is apt to be tackled by gradient based optimizer. However, more insights can be derived by studying the variation in the optimized LCOE for a range of Rr otor and Pr ated , rather than by analyzing one optimized solution. Since this would require solving multiple optimization problems for a set of Rr otor and Pr ated , the analysis would be constrained by the long convergence time associated with an optimizer; hence, a brute force approach is chosen. 4.5.A NALYSIS 59

The brute force, or an exhaustive search is an approach where the optimization is done by evaluating the function over a discrete range of design variables. This is an apt approach when the search space is sufﬁciently small and other algorithms are relatively slow.

While optimizing for the minimum LCOE for a given Rr otor and Pr ated , since τ is a surrogate variable, its value is determined through Gauss-Seidel iteration with a toler- 4 ance of 10− , as given by:

δti p (τi ) τi 1 τi (4.18) + = × re f Rr otor δti p re f × Rr otor τ 1 0 = 4 The domain of other design variables for the analysis is listed in Table 4.4.

Design Variable Domain

Pr ated [kW] {4000, 5000, 6000}

Rr otor [m] {50, 52.5, 55, ..., 90}

Dew ns [m] {5D, 5.5D, 6D, ..., 15D} = Table 4.4: Domain of the design variables for the brute force analysis

The variation in the optimized LCOE with Rr otor at different values of Pr ated and a ﬁxed value of Weibull scale factor a 9m/s (Case 1, 2 and 3) is presented in Figure 4.13. = Each point on the curve on the left represents the optimized spacing whose normalized value is shown on the right. The optimal points are indicated with the dotted vertical lines.

Prated = 4MW, a = 9m/s Prated = 4MW, a = 9m/s Prated = 5MW, a = 9m/s Prated = 5MW, a = 9m/s

Prated = 6MW, a = 9m/s Prated = 6MW, a = 9m/s

] kWh

cEUR

[

! !

Figure 4.13: Optimized LCOE and spacing vs Rr otor at a 9m/s in a square layout = 60 4.D ESIGN ITERATION #2

The variation in the optimized LCOE with Rr otor at different values of Weibull scale factor and a ﬁxed value of P 5MW (Case 2 and 4) is presented in Figure 4.14. The r ated = result is analyzed by studying the variation in cost and AEP at different points in the graph. This analysis is presented in Figure 4.15.

Prated = 5.0MW, a = 8.15m/s Prated = 5.0MW, a = 8.15m/s Prated = 5.0MW, a = 9m/s Prated = 5.0MW, a = 9m/s

] kWh cEUR [ 4

! !

Figure 4.14: Optimized LCOE vs Rr otor at P 5MW in a square layout r ated =

900 1400 900 1400

800 1200 800 1200 700 700 1000 1000 600 600 500 800 500 800 400 600 400 600 AEP [GWh] AEP [GWh]

Cost [M-EUR] Cost 300 [M-EUR] Cost 300 400 400 200 200 100 200 100 200 0 0 0 0 R = 100m R = 130m R = 150m P = 4 MW P = 5 MW P = 6 MW

Other investments RNA Support structure Other investments RNA Support structure Cable CAPEX AEP Cable CAPEX AEP

(a) Comparison of the optimal AEP and costs at (b) Comparison of the optimal AEP and costs for different Rr otor at P 5MW and a 9m/s Case 1, 2 and 3 at the stated P r ated = = r ated Figure 4.15: Comparing the gradients of AEP and cost

In Figure 4.13, it can be seen that at a very low value of Rr otor , the (normalized) optimized spacing as well as the optimized LCOE are high. This is because the low AEP from that conﬁguration is not able to compensate for the incurred capital costs. As Rr otor increases, the AEP increases at a faster rate than the capital costs leading to a decline in the LCOE. This trend continues until the optimal point after which the increase in the 4.5.A NALYSIS 61 capital cost surpasses the gain in AEP.The explains the shape of the curve in Figure 4.13 and 4.14, which is seconded in Figure 4.15a, where the gradient of the AEP curve reduces after reaching the optimal diameter, while that of the total costs remains the same.

An inference that can be drawn from Figure 4.14 is that a high wind resource site, the optimal power density (ζ 380W /m2) is higher than that at a low wind resource site ≈ (ζ 280W /m2). ≈

4.5.2. RECTANGULAR FARM LAYOUT As the search space increases in the rectangular layout of the farm due to the separation of Dew and Dns as design variables, brute force is not suitable to analyze this use case. Also due to the roughness of the response curve in this case, a gradient based optimizer may not be an ideal candidate. Hence, the SLSQP - Sequential Least SQuare Program- 4 ming, a gradient based algorithm used in the previous use case is not used. Instead, a gradient-free optimizer COBYLA - Constrained Optimization BY Linear Approximation, which approximates the non-linear problem to a simplex, linear programming problem is used [68].

The optimization problem for this use case is given by:   ³ ´ MIN LCOE Objective function   re f  δ R ti p × r otor Optimization Problem: δmar gin re f 1 Tip deflection constraint = δ Rr otor ≤  ti p ×   D ,D 12 R Spacing constraint ew ns ≥ × r otor Since COBYLA cannot handle the equality constraints, the tip deflection is handled as an inequality constraint. It should be noted that a lower bound on the tip deflection constraint is not necessary because this constraint can be independently handled by varying τ, whose contribution to LCOE is minimum when the value of δmar gin is 1.

Since, Jensen wake model is used to calculate the wake losses in the farm, which is valid only for the far wake region that commence at around 6D [69], a space constraint is imposed. The constraint of the maximum stress along the rotor blade is not imposed because of three main reasons: 1. as discussed in Section 3.5, it is not an active constraint 2. an upscaling of the rotor doesn’t affect the stress due to the aerodynamic forces [45], however there could be some minor changes due to its inverse proportional- ity to τ and a shift in Ur ated 3. COBYLA’s linear approximation depends on the values of the objective function and the constraints, hence, an additional constraint may affect its computational speed Before using COBYLA for the analysis of the rectangular farm layout, it is validated by comparing it with the result of the brute force approach. In this regard, the optimization problem stated above is executed for a square farm layout at P 5MW and r ated = 62 4.D ESIGN ITERATION #2

6 a 9m/s with the design variables listed in Table 4.5. A tolerance of 10− is used for the = convergence. The results of the brute force approach and COBYLA are contrasted in Ta- ble 4.6.

Design Variable Initial Value Lower Bound Upper Bound

Rr otor [m] 63.0 50.4 88.2 τ [-] 1.0 0.5 1.5

Dew ns [m] 945.0 472.5 2835.0 = Table 4.5: Design variables to validate COBYLA at P 5MW and a 9m/s in a square layout r ated = = 4 Parameter Brute force COBYLA

Rr otor [m] 65.0 64.05 τ [-] 0.9596 0.9883

Dew ns [m] 9.5 D 10.01 D = LCOE [ce/kWh] 7.8370 7.8068

δmar gin [-] 1.0 1.0

Table 4.6: Result of the COBYLA validation at P 5MW and a 9m/s in a square layout r ated = =

It is seen that COBYLA yields a better solution than the brute force approach, which is because the design variables in the brute force analysis take discrete values, while COBYLA enables them to be continuous within the speciﬁed bounds. It can be concluded that COBYLA serves as a fair candidate for the study of this use case in a rectangular farm layout. However, the caveat in this comparison is that the validation of COBYLA is done at a relatively smooth response curve, while it is being used in a case with a more complex response curve. However, this should not be a deterrent in the scope of this use case.

Design Variable Initial Value Lower Bound Upper Bound

Pr ated [kW] 5000 3000 6000

Rr otor [m] 63.0 50.4 88.2 τ [-] 1.0 0.5 1.5

Dew [m] 945.0 472.5 2835.0

Dns [m] 945.0 472.5 2835.0

Table 4.7: Design variables for the optimization of Pr ated and Rr otor in a rectangular layout

The optimization problem is executed with the design variables listed in Table 4.7 for 4.5.A NALYSIS 63 two cases - ﬁrst at a 8.15m/s (Case 5) and second at a 9m/s (Case 6). The results are = = contrasted in Table 4.8.

Parameter Case 5 Case 6

a [m/s] 8.15 9.0

Design Pr ated [kW ] 3452.3 3652.0

Variables Rr otor [m] 61.2 57.8 τ [ ] 0.8122 0.9076 − Dew [m] 6.87D 6.32D

Dns [m] 21.11D 19.21D Response ζ [W /m2] 293.9 347.5 4 Variables Ur ated [m/s] 10.00 10.57 AEP [GWh] 729.9 828.1 κ [ ] 0.3771 0.4044 − 6 Cr na [10 e] 148.5 141.4 6 Css [10 e] 151.6 145.0 6 Ccc [10 e] 51.0 44.1 6 Coi [10 e] 162.1 161.6 LCOE [ce/kWh] 8.6762 7.6011

Table 4.8: Optimal solutions at different scale factors in a rectangular layout

From the Table 4.8, it can be seen that an improvement in the LCOE is observed when the optimization search space in the wind turbine design for a given site is expanded by separating Dew and Dns and extending the domain of Pr ated . A major change in the optimal result can be seen in the spacing, which gets dominated by Dns , where the effect on Ccc is minimally felt, as discussed in Section 4.4.3. The optimizer tries to minimize Dew to reduce Ccc , while it tries to maximize Dns to reduce the wake loss.

As discussed in the analysis of the square layout farm, Rr otor is higher and ζ is lower in case of the low wind site (Case 5), as compared to the high wind site (Case 6).

The optimal Pr ated is observed at around 3.5 MW for both the sites. This is contrary to the current market trend where the shift is towards higher machine rating. This could be because larger turbines in terms of machine rating can be lucrative when it leads to lower number of turbines (in a farm with a fixed capacity) which translates to lower operation and maintenance cost. However, in this use case, the number of turbines is held fixed, and hence this inter-disciplinary influence is not captured.

5 DESIGN ITERATION #3

The objective of this chapter is to compare various drive train configurations and the effect of their reliability on the LCOE of the wind farm. In this regard, the target milestone for the third design iteration is to have a RNA model in an agile SE framework that supports these drive train configurations. 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.

This chapter is divided into ﬁve sections:

1. Use case - The use case that enables the study of the third research question is presented 2. Literature survey - A survey on similar research papers is performed 3. Development - The required updates in the drive train model is explained 4. Validation - The errors in the model and their effect on the result are assessed 5. Analysis - The model is then used to meet the third research objective

65 66 5.D ESIGN ITERATION #3

5.1. USECASE The objective of this use case is to compare various drive train conﬁgurations and to study the effect of their reliability on the LCOE of the wind farm. The drive train conﬁgurations that are compared, along with their main advantages and disadvantages are summarized in Table 5.1.

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 5 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 5.1: Different drive train conﬁgurations for Research Objective #3

The inﬂuence of the drive train conﬁguration on the LCOE is captured in the following parameters:

1. Mass - The tower top mass influences the support structure design 2. Cost - The RNA constitutes approximately 30% of the overall investment cost (Fig- ure 4.2), of which over 35% is due to the drive train components (Figure 3.18a) 3. Drive train efficiency - The conversion efficiency of the gearbox, generator and converter determines the fraction of aerodynamic power from the rotor that is converted to electricity 4. Reliability - The reliability of the drive train components of the RNA has a large consequence on the availability of the wind farm, which in turn affects the AEP

The reliability modelling of the drive train configurations is a complex topic that requires either a high fidelity model of the gearbox and generator or an extensive data-set for heuristic modelling. Hence, the reliability modelling of drive train is not in the scope of this use case. However, its effect is studied through the wind farm availability. The availability (Λ) of the wind farm is a function of the reliability of the drive train configuration of the turbines, along-with the reliability of other components like blades, inter- array cables and the substation. It should be noted that a production-based availability 5.1.U SECASE 67 is used in WINDOW, which is given by:

AEPactual Λ (5.1) = AEPexpected

The analysis of this use case is divided into two parts:

1. the effect of scaling the NREL 5MW Reference Turbine (N5RT) rotor at a constant power density (ζ) with different drive train conﬁgurations on the LCOE of the wind farm 2. the required level of availability expected from PMSG-DD at which its LCOE breaks- even with that of DFIG-3S

The rotor and the wind farm description are the same as in Section 4.1. Due to the empirical nature of the O&M model, which scales linearly with the AEP,the difference in the O&M cost associated with different drive train conﬁgurations is not captured.

A square farm layout is considered in a site with the Weibull scale factor of a 9m/s = at the hub height of 90m. The wind shear effect on the inﬂow wind condition at different 5 hub heights is (inadvertently) ignored. As discussed in Section 4.4.5.1, the consequence of this assumption is that the correct Rr otor will be higher than that predicted by this model. 68 5.D ESIGN ITERATION #3

5.2. LITERATURE SURVEY The drive train is a critical component of a wind turbine that dictates its electrical conversion efﬁciency, capital cost and reliability. There are various drive train conﬁgurations that favor some of these factors while they compromise on the others. With over 80% of the market share [70], the current wind turbine market is dominated by 3-stage gearbox with Doubly Fed Induction Generators, primarily due to their lower weight and capital cost. However, the mire of their unreliability and higher O&M implications inhibit their application for offshore purposes.

The advantages of Permanent Magnet Synchronous Generator (PMSG) over Doubly Fed Induction Generator (DFIG) are qualitatively discussed in [71]. Although the capital cost of PMSG is higher, its higher efﬁciency and lower grid connection costs may yield lower levelized cost of energy. The higher reliability of PMSG is reﬂected in its lower (time-based) unavailability of 1.98 days/year (0.5%) compared to 2.36 days/year (0.6%) for DFIG.

5 There are a few low fidelity physical models of wind turbine drive trains that exist in literature to aid the comparison of various configurations. An approximate estimate of the mass, cost and efficiency of the generators, gearbox and converter using simple analytical equations have been presented in [72]. NREL’s GeneratorSE [73] provides a low fidelity physics based sizing tool for various types of generators used in variable speed wind turbines - including DFIG and PMSG. It uses an optimization algorithm to design the key generator design parameters, such as airgap radius, stator core length, yoke height and stator slot height, subject to various electromagnetic, structural and thermal constraints.

Comparisons between various drive train conﬁgurations are made in [74] and [72]. In both of their analyses, PMSG-1S conﬁguration is deemed to be a promising solution because it alleviates the primary disadvantages of DFIG-3S and PMSG-DD - reliability in the former and large generator size in the latter.

A scaling analysis of PMSG-1S and PMSG-DD is performed in [75]. The levelized cost of PMSG-1S was found to be lower than PMSG-DD at all scaling factors. At Pr ated greater than 3 MW, PMSG-DD may impose manufacturing and transportation constraints. In case of PMSG-1S, the largest improvement in the levelized cost appears at around Pr ated of 5 MW. It is also acknowledged that the uncertainty in the price of generator components affects the result. 5.3.D EVELOPMENT 69

5.3. DEVELOPMENT The drive train model for the previous use cases was adapted from DriveSE, which only supported the 3-stage gearbox with DFIG conﬁguration. For the purpose of this use case, the model is adapted to support other conﬁgurations.

5.3.1. MODELASSESSMENT Based on the scope of the tools evaluated to model the RNA components, the RNA is divided into four sub-systems: Blade, Hub, Drive Train and Cost. The models for Blade, Hub and Cost are retained from the previous RNA model, while for the Drive Train, the models are gleaned from literature and are assessed for their suitability in the Open- MDAO framework. The list of the tools assessed for each sub-system and their performance against the selection criteria are summarized in Table 5.2. The assessment criteria were speciﬁed in Table 2.3.

Sub-system Tools Description Assessment Blade Ad Hoc See Table 3.2 5 Hub DriveSE See Table 3.2 Drive Train GeneratorSE comprehensive physical incompatible with [73] model for PMSG and DFIG OpenMDAO v2 Polinder et al low ﬁdelity physical model comprehensive IO [72] for the gearbox, the genera- with loss modelling tor and the converter WindPACT empirical model for differ- limited IO [41] ent conﬁgurations Cost WindPACT See Table 3.2

Table 5.2: RNA sub-systems and the assessed models

NREL’s GeneratorSE is the most comprehensive low-ﬁdelity generator design tool found in the literature. However, due to its incompatibility with OpenMDAO v2, it could not be on-boarded to the RNA framework for this use case. For the deﬁned use case, the required output from the Drive Train sub-system are the mass and cost of each component. Hence, a detailed physical model presented by GeneratorSE and Polinder et al are not strictly necessary. These outputs can alternatively be provided by a much simpler empirical model given by WindPACT. Although an empirical cost model is agnostic to design constraints during upscaling of the turbines, they are considerate to the learning curve of the technology.

Apart from the gearbox, generator and converter, the RNA also consists of the main shaft, bearings and mainframe. Although a physical model for these components for DFIG-3S conﬁguration was discussed in Section 3.3.3.1, similar comprehensive models for PMSG-1S and PMSG-DD could not be found in literature. In view of a fair comparison between all the three drive train conﬁgurations, only gearbox, generator and converter are taken into account, while the contribution of other components are neglected. The effect of this assumption on the LCOE of DFIG-3S is analyzed in Section 5.4. 70 5.D ESIGN ITERATION #3

The input of drive train efficiency (ηdt ) for different configurations are derived from Polinder et al. The values of η for each configuration at P 3MW is provided in dt r ated = Figure 5.1a. Although ηdt depends on the rotor rotational speed (Ω) and the machine rating (Pr ated ), in this use case, a cumulative value is taken and assumed to be independent of the Pr ated and Ω.

100% 900

800 98% 700 96% 600

94% 500

92% 400 Efficiency [-] Efficiency 300

90% [MWh] losses Energy 200 88% 100

86% 0 5 Gearbox Generator Converter Overall DFIG-3S PMSG-1S PMSG-DD DFIG-3S PMSG-1S PMSG-DD Gearbox Generator Converter

(a) ηdt for various configurations at (b) Drive train losses for various configurations P 3MW [72] at P 3MW [72] r ated = r ated = Figure 5.1: Drive train efficiency used in Use Case #3

5.3.2. MODEL UPDATE The gearbox, generator and converter models are updated with the WindPACT empirical formulas for mass and cost, as listed in Table 5.3. The efﬁciency of the components are taken from [72]. The units of Pr ated and Qr otor are in kW and kNm respectively. The costs are in USD, which is converted to EUR using the exchange rate of EUR/USD = 1.23 [50] for the integration of RNA to WINDOW. The XDSM of the updated RNA model is shown in Appendix A.3.

Discipline Conﬁguration Efﬁciency[72] Mass [kg][41] Cost [USD][41]

Gearbox PMSG-1S 96.8% 88.29 Q0.774 74.10 P × r otor × r ated DFIG-3S 93.7% 70.94 Q0.759 16.45 P 1.249 × r otor × r ated Generator PMSG-DD 96.8% 661.25 Q0.606 219.33 P × r otor × r ated PMSG-1S 97.9% 10.51 P 0.9223 54.73 P × r ated × r ated DFIG-3S 98.1% 6.47 P 0.9223 65.0 P × r ated × r ated Converter PMSG-DD, 97.1% 0.73 P 479.7 79 P × r ated + × r ated PMSG-1S DFIG-3S 99.0% 0.22 P 479.7 23.7 P × r ated + × r ated

Table 5.3: Empirical model of drive train 5.3.D EVELOPMENT 71

A 30% partial scale converter for DFIG is taken, as opposed to a full scale converter for PMSG, because the stator of DFIG is directly connected to the grid. The cost model of the generator and the converter for each configuration is assumed to be reflective of the cost associated with the grid compliance - harmonics filter and low voltage ride through capability.

Due to the empirical nature of the cost models, the design aspects of the drive train, such as the gear ratio of the gearbox, air gap diameter of the generator etc, are not captured, which makes this upscaling agnostic to the manufacturing, transportation and installation constraints. The effect of drive train efﬁciency and the generator type on the cut-in wind speed is ignored. The favorable effect of the unavailability of a turbine on the turbines in its wake - enhanced inﬂow wind condition and reduced fatigue loading - is also ignored.

The RNA cost is given by:

C C C C C (5.2) r na = r otor + gb + gen + conv 5 The RNA cost breakdown for different conﬁgurations at P 5 & 9.2MW are r ated = shown in Figure 5.2. The sensitivities of the drive train components cost and the overall RNA cost with respect to Rr otor at constant ζ are shown in Figure 5.3 and 5.4.

5.0

4.5

4.0

3.5

3.0 EUR] 6 2.5

2.0

Cost [10 Cost 1.5

1.0

0.5

0.0 PMSG-DD PMSG-1S DFIG-3S PMSG-DD PMSG-1S DFIG-3S Rated power = 5 MW Rated power = 9.2 MW

Rotor Gearbox Generator Converter

Figure 5.2: Breakdown of RNA cost for different drive train conﬁgurations

In Figure 5.3, it can be seen that both the gearbox and the generator costs for DFIG-3S are higher than that of PMSG-1S. The generator cost for PMSG-DD is signiﬁcantly higher than the others. DFIG-3S has an advantage in the converter cost, as seen in Figure 5.4a. Overall, the RNA cost of PMSG-DD is the highest and that of PMSG-1S is the lowest at all scales. 72 5.D ESIGN ITERATION #3

Prated Prated 6 6 10 10 "# "# # ! #! # ! #!

(a) Sensitivity analysis of gearbox cost (b) Sensitivity analysis of generator cost 5 Figure 5.3: Effect of scaling on the gearbox and generator cost

Prated Prated

6 6 10 10 "# "#

# ! #! # ! #!

(a) Sensitivity analysis of converter cost (b) Sensitivity analysis of RNA cost

Figure 5.4: Effect of scaling on the converter and overall RNA cost 5.4.V ALIDATION 73

5.4. VALIDATION Since the Blade, Hub and Cost sub-systems are kept intact in the RNA model, the focus of the validation of the updated RNA model is the Drive Train. Since the current RNA model is limited to the gearbox, generator and converter, the impact of the model de- ﬁciency with respect the RNA model used in the previous use cases is studied. In this regard, only the DFIG-3S conﬁguration is assessed, and the WindPACT empirical models for PMSG-1S and PMSG-DD are accepted at their face values.

RNA-DriveSE is used in reference to the RNA model from previous use cases, while RNA-WindPACT is used to refer to the RNA model for DFIG-3S conﬁguration used in this use case.

5.4.1. ERROR IDENTIFICATION The comparison of RNA-DriveSE (3-stage gearbox with DFIG generator) and RNA-WindPACT (DFIG-3S conﬁguration) for N5RT is shown in Table 5.4. 5

Parameters RNA-DriveSE RNA-WindPACT

Inputs Pr ated [kW] 5000 5000

Rr otor [m] 63 63

ηdt [-] 95% 91% Λ [-] 98% 98% 3 Outputs Cr otor [10 e] 905.66 888.65 3 Cgb [10 e] 555.5 555.5 3 Cgen [10 e] 263.2 263.2 3 Cconv [10 e] 320.0 96.0 3 Cr na [10 e] 3018.4 1803.4

Ur ated [m/s] 11.1 11.2 AEP [GWh] 1012 986 LCOE [ce/kWh] 7.92 7.10

Table 5.4: Validation of DFIG-3S model for N5RT

A very large difference is in Cr na and LCOE which is primarily due to the lack of comprehensiveness in RNA-WindPACT (missing main shaft, bearings and mainframe). The difference in mr otor and Cr otor is due to the difference in the input values of ηdt in RNA- WindPACT and RNA-DriveSE.

Since the underlying cost models in both RNA-DriveSE and RNA-WindPACT are the same, as discussed in Table 5.2, the costs of gearbox and generator are the same. The converter cost is considerably higher in RNA-DriveSE, which is because a full scale converter was used in the case of DFIG generator, while only a partial scale of 30% is used in RNA-WindPACT. 74 5.D ESIGN ITERATION #3

5.4.2. ERROR ANALYSIS The differences between RNA-DriveSE and RNA-WindPACT originate due to:

1. difference in the input values of ηdt 2. difference in the converter cost 3. lack of comprehensiveness in RNA-WindPACT due to missing main shaft, bearings and mainframe In this section, the propagation of these differences to the LCOE is studied. In this regard, the sensitivity analyses of the LCOE with respect to Rr otor at constant ζ from RNA-DriveSE and RNA-WindPACT are compared in Figure 5.5.

Prated Prated " ! "

]

kWh cEUR kWh cEUR 5 [ Δ

! ! ! !

(a) Comparison of DriveSE and WindPACT (b) Difference between DriveSE and WindPACT results results

Figure 5.5: Validating RNA-WindPACT against RNA-DriveSE

It can be seen that the difference in the values of LCOE from RNA-DriveSE (LCOEdr i vese ) and RNA-WindPACT (LCOEwpact ) follow a linear trend with respect to Rr otor . The effect of this error on the LCOE is represented by:

LCOE LCOE k R k (5.3) dr i vese ≈ wpact + 4 r otor + 5 ∂(LCOEwpact ) ∂(LCOEdr i vese ) k4 ⇒ ∂Rr otor ≈ ∂Rr otor − , where k 0. 4 >

The optimal Rr otor , as it would have been predicted by RNA-DriveSE, would be when ∂(LCOE ) ∂(LCOEdr i vese ) reaches zero. At that point, wpact is negative because k is greater ∂Rr otor ∂Rr otor 4 than 0, indicating that the LCOE is still decreasing. This implies that RNA-WindPACT will overestimate the optimum Rr otor as compared to RNA-DriveSE.

As discussed in Section 4.4.5.1, due to the assumption of zero wind shear, both RNA- DriveSE and RNA-WindPACT underestimate Rr otor . The former and latter errors have an opposing effect, however the extent to which they negate each other is not treated. 5.5.A NALYSIS 75

5.5. ANALYSIS The use case for the third research objective was framed in Section 5.1, which led to an update in the MDAO workﬂow, as discussed in Section 5.3. The updated model was validated in Section 5.4. This leads to the ﬁnal step of analyzing the third research objective.

5.5.1. RNASCALING WITH DIFFERENT CONFIGURATIONS To study the effect of scaling of a turbine with different drive train conﬁgurations on the LCOE, N5RT is scaled at a constant value of power density (ζ). This is a different problem formulation as compared to the previous use case where ζ was variable. This is due to the limitations in the current cost model for different drive train conﬁgurations. As seen in Table 5.3, the cost model is only sensitive to Pr ated , which implies the model is based on data of turbines whose Rr otor and Pr ated are interdependent. Hence, the effect of independent variation in Pr ated and Rr otor on the cost is not captured using this model. In this regard, the scaling of Pr ated with Rr otor is given as:

µ ¶2 re f Rr otor P P (5.4) 5 r ated = r ated × re f Rr otor

With this scaling formulation, Ur ated stays constant, hence, δti p scales linearly with Rr otor , as given by:

d 2 y M (5.5) dx2 = EI M 2 δti p R ⇒ ∝ EI × r otor 3 Rr otor 2 δti p 4 Rr otor Rr otor ⇒ ∝ Rr otor × =

Hence, a value of τ 1 is sufficient for a feasible up-scaled design that meets the = tip deflection constraint, without a need for the iterative approach discussed in Equa- tion 4.18. Similar to Section 4.5.1, a brute force analysis of a square farm layout is done with Rr otor , turbine spacing (Dew ns ) and drive train configurations as design variables. = The domain of the design variables are listed in Table 5.5. The availability of the farm is assumed to be constant at Λ 98%, signifying that the reliability of the drive train con- = figuration is not captured in the brute force analysis.

Design Variable Domain

Conﬁguration {PMSG-DD, PMSG-1S, DFIG-3S }

Rr otor [m] {50.5, 53.0, 55.5, ..., 90.5}

Dew ns [m] {6D, 6.5D, 7D, ..., 13D} =

Table 5.5: Domain of the design variables for Use Case #3 76 5.D ESIGN ITERATION #3

The optimized LCOE - with respect to Dew ns - versus Rr otor for various drive train = conﬁgurations at Λ 0.98 is shown in Figure 5.6(L). The spacing between the turbines = (Dew ns ) at each point on the curve is shown in Figure 5.6(R). The dotted lines represent = the most optimal Pr ated and Rr otor for each conﬁguration. The optimal point for PMSG- 1S and PMSG-DD are the same.

Prated Prated

] kWh cEUR [

&)!#!* (&!$

5 &)!#" &)!#"

%)%'!# ) '# %)%'!# ) '#

Figure 5.6: Scaling of N5RT with different conﬁgurations at Λ 0.98 =

Prated Prated

6 10 !$

!#!" #" # " #"

(a) Effect of scaling on AEP (b) Effect of scaling on capital expenses

Figure 5.7: Effect of scaling on AEP and CAPEX

Figure 5.6 can be better analyzed by separating the capital cost and AEP analysis, as illustrated in Figure 5.7. The difference in the capital cost of each configuration is dictated by their RNA cost (Figure 5.4b). Although, there is a considerable difference in the RNA mass of these configurations, it only affects the support structure cost, which is only slightly sensitive to this variation and, hence, is not an influencing parameter in 5.5.A NALYSIS 77 this study.

In Figure 5.7, it can be seen that the capital expense of DFIG-3S is higher than that of PMSG-1S, while at the same time its AEP is slightly lower (due to higher gearbox losses), leading to a higher LCOE of DFIG-3S as compared to PMSG-1S.

PMSG-DD, on the other hand, has the highest capital cost, primarily due to the generator cost (Figure 5.3b), while there is no corresponding improvement in its AEP.PMSG- DD is the least favorable configuration - due to its highest LCOE - while PMSG-1S is the most favorable configuration, when reliability of these configurations is not taken into account.

A steeper increase in the LCOE of DFIG-3S at Pr ated greater than 8 MW is less clear from these ﬁgures; however, this could be due to the higher drive train losses becoming dominant at higher Pr ated .

The capital expense and AEP associated with DFIG-3S and PMSG-1S are approximately the same at lower rotor diameter (around 100m), as seen in Figure 5.7 as well as in 5 Figure 5.6 where their LCOE are almost the same. However, with the up-scaling, the RNA cost (and, thus, the capital expense) of DFIG-3S increases at a faster rate than PMSG-1S (Figure 5.4b), while the corresponding increase in AEP remains almost the same. This explains why the optimal rotor diameter of 116 m for DFIG-3S is lower than that of PMSG- 1S. The effect of model error, as discussed in Section 5.4, would also have an affect on this result.

The optimal LCOE for both PMSG-1S and PMSG-DD are seen at rotor diameter of 121 m and Pr ated of 4.6 MW. Due to the discrete nature of the brute force analysis, the difference smaller than the step size of 2.5 m in Rr otor is not captured.

Figure 5.8: Difference in wake loss in Use Case #2 and Use Case #3

With the upscaling of the turbine at constant ζ, the optimized spacing increases, as seen in Figure 5.6(R). This is an opposite trend as compared to the upscaling of the tur- 78 5.D ESIGN ITERATION #3

bine at constant Pr ated (Use Case #2 with variable ζ), as seen in the second use case in Figure 4.13. This is due to the faster rise in the wake loss in this case of constant ζ as compared to the case of constant Pr ated , as shown in Figure 5.8.

5.5.2. RELIABILITY STUDY OF DIFFERENT CONFIGURATIONS The analysis so far assumed a constant availability (Λ 0.98) of the wind farm for each = configuration. With this assumption, it is seen that the PMSG-1S is the most favorable option, while PMSG-DD is the least. However, the main advantage a PMSG-DD has over a PMSG-1S or DFIG-3S is its higher reliability due to a lack of gearbox. The reliability of a configuration has consequences on the availability of the farm and the associated O&M costs. In this section, this effect of reliability is studied using the LCOE versus Λ curve for the three configurations.

In this regard, the optimal turbine (Rr otor , Pr ated and Dew ns ) for each conﬁguration = at Λ 0.98 is taken from Section 5.5.1, and is analyzed at varying Λ. The parameters for = these turbines are listed in Table 5.6. The LCOE versus Λ for the three conﬁgurations is 5 shown in Figure 5.9b.

Parameter PMSG-DD PMSG-1S DFIG-3S

Rr otor [m] 121 121 116

Pr ated [kW] 4611 4611 4238

Dew ns [m] 9.5D 9D 9D =

Table 5.6: Domain of the design variables for the brute force analysis

" $! " $! ] ] kWh kWh cEUR cEUR [ [

$ #% $ #%

(a) Λ 0.98 for PMSG-DD as reference (b) Λ 0.98 for DFIG-3S as reference = = Figure 5.9: Effect of reliability of different conﬁgurations on LCOE

From Figure 5.9a shows that if the reliability of PMSG-DD leads to Λ 0.98, then the = DFIG-3S should yield at least the availability of Λ 0.962 to be as competitive as the = former. On the other hand, if the reliability of DFIG-3S leads to Λ 0.98, then the PMSG- = DD should yield at least the availability of Λ 0.998 to be as competitive as the former, = 5.5.A NALYSIS 79 as depicted in Figure 5.9b.

The higher the reliability of geared conﬁgurations, the more difﬁcult is it for the PMSG-DD to be a more lucrative choice, because its availability approaches one.

Theoretically, the reliability of PMSG-DD is the highest whereas the reliability of DFIG- 3S is the lowest, primarily due to the failures in the gearbox, which usually leads to large downtime. The result of this use case depicts PMSG-1S as the clear winner among other drive train conﬁgurations because it has the lowest LCOE when equal availability is assumed for all the conﬁgurations while, theoretically, it has an additional advantage of higher reliability as compared to DFIG-3S. This observation is contrary to the industry trends where DFIG-3S is more prevalent. This anomaly could be because:

• lack of sufficient data points could lead to inaccuracy in the empirical cost models of PMSG-1S and PMSG-DD • the design constraints that have not been taken into consideration in this use case • the manufacturers have preference towards the configuration over which they have expertise in 5 • uncertainty in the reliability of different configurations and their effect on the availability of the wind farm

Although this analysis is agnostic to the design aspects of the drive train, and there are limitations in the cost model, the utility of this use case is in the presentation of an approach that enables the determination of the required reliability (availability) from PMSG-DD to yield a break-even LCOE with respect to the geared conﬁgurations.

6 CONCLUDING REMARKS

The objective of this chapter is to elucidate the research ﬁndings of this report and identify the directions for future research. This chapter is divided into three parts:

1. Conclusion - to accrete the technical implication of all the use cases 2. Retrospection - to list the tasks that could have been done differently 3. Future research - to discuss the scope of pertinent future research

6.1. CONCLUSION The design of the wind turbines for an offshore wind farm is a tug-of-war between the energy yield and the incurred costs. A gain in the former comes with a compromise on the latter, suggesting that there exists an optimal solution that minimizes the levelized cost of energy. This optimal solution can be deciphered by capturing the inter-disciplinary dynamics among various disciplines that constitute an offshore wind farm. This report presented an approach to perform the multi-disciplinary optimization of rotor nacelle assemblies for offshore wind farms by comprehensively representing their components using the models that are physically precise and computationally fast.

An offshore wind farm has myriad disciplines and several stakeholders. A single model that serves all the purposes does not exist. Agility is an important aspect of systems engineering (SE) that allows every stakeholder to analyze the wind farm for their specific use case. In this regard, to accomplish the primary objective of this report, three different research objectives were set that contributed to the agile development process. Each research objective targeted a different aspect of RNA: blade design, power density and drive train configuration. Due to the different input-output connections necessary to analyze these aspects, the Multi-Disciplinary Analysis and Optimization (MDAO) workflow and the RNA model had to be tailored to suit each one of them.

The objective of the ﬁrst use case was to develop insight into the beneﬁts of SE by studying the effect of system scope on the rotor design. The dissemination of knowledge

81 82 6.C ONCLUDING REMARKS

on the utility of the tool in painting a bigger picture of an offshore wind farm among the wind energy researchers was intended. The key conclusions drawn from this use case are:

• Siloed application or the optimization of blade design in a limited system scope leads to sub-optimal design at the wind farm level because they fail to capture all the inter-disciplinary inﬂuences. • A gradual increase in the scope of the system that is being optimized does not necessarily lead to a monotonic improvement in the design at the wind farm level. This is evident when a smaller system scope of Blade yields a better design than a larger system scope of RNA. This is because thrust is a dominant factor both at the Blade level as well as the Farm level, while torque is a dominant factor at the RNA level. • The LCOE of the wind farm is minimum when the system scope for the blade design is at the wind farm level, where all the necessary inter-disciplinary couplings are captured. • Rapport among all the disciplines of the wind farm using a SE framework helps in identifying latent inter-disciplinary dynamics. An agile framework that enables simple integration of niche models can help the wind energy researchers in capturing such dynamics in their models.

6 The objective of the second use case was to study the effect of the rotor radius and its rated power - or the power density in general - 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 turbine/farm developers was intended. The key conclusions drawn from this use case are:

• As the rotor diameter increases, the energy yield of the turbine increases, but at the same time the capital cost - RNA, support structure and cable - also increases. The disciplines outside the RNA respond non-linearly to the changes in the RNA design variables. This SE framework enabled capturing such inter-disciplinary dynamics to find an optimal rotor size. • The position of the substation has a large influence on the cable topology and the spacing between the turbines. • As expected, a turbine with lower power density is optimal for a site with lower wind resource. • The optimal machine rating was in the range of 3.5 MW which is contrary to the current market trend. This could be because larger turbines in terms of machine rating can be lucrative when it leads to lower number of turbines (in a farm with fixed capacity) which translates to lower operation and maintenance cost. In this use case, the number of turbines was held fixed. The utility of the tool could be enhanced by taking variable number of turbines. • For a wind turbine manufacturer, upscaling of a turbine may not be an easy task because they might not have a suitable manufacturing facility for such turbines. The utility of this tool lies in demonstrating that better design could be possible which deserves further deliberation. 6.1.C ONCLUSION 83

The objective of the third use case was to compare various RNA drive train configurations and the effect of their reliability on the LCOE of the wind farm. The three different drive train configurations to be studied were Doubly Fed Induction Generator with 3- stage gearbox (DFIG-3S), Permanent Magnet Synchronous Generator with 1-stage gearbox (PMSG-1S) and Permanent Magnet Synchronous Generator with direct-drive (PMSG- DD). 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 was intended. The key conclusions drawn from this use case are:

• 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. However, the empirical nature of the models used in this use case inhibited the study of influencing design parameters, such as gearbox ratio, generator air-gap radius etc. • The analysis led PMSG-1S to be the most favorable configuration. However, due to a lack of sufficient data points for such configurations, its empirical cost model may be inaccurate. • The higher the reliability of geared configurations, the more difficult is it for the PMSG-DD to be a more lucrative choice, because its expected availability approaches one. • A physical model of the drive train components would give a better indication of the cost, efficiency and design constraints and hold more utility to the wind tur- 6 bine manufacturers.

The cost models for different components - blades, drive train, support structure, cable etc - have high implication on the result because they are the limiting factors in the second and the third use cases. The determination of a precise cost model is difﬁcult because they are volatile in nature. In this regard, a sensitivity analysis of the model with respect to the price coefﬁcients would have been reinforcing.

Finally, in the grand scheme, this project sought to meet the key requirements of a SE framework: comprehensiveness, physical precision, low computational cost and agility.A comprehensive physical model of RNA enabled the study of its interaction with the wind farm by capturing the necessary inter-disciplinary dynamics. The low ﬁdelity models facilitated the study of various use cases at an acceptable accuracy and computational cost. The agile framework brought three diverse aspects of RNA design - rotor blades, power density and drive train conﬁgurations - to fruition. 84 6.C ONCLUDING REMARKS

6.2. RETROSPECTION With the lessons learnt during the course of this project, in retrospect, it is realized that there are several tasks that could have been done differently. These are:

• A partial scale converter should have been used in Use Case #1 and #2. • The assumption of zero wind shear in the RNA scaling exercise in the second and third use cases was inadvertent, and could have been avoided. • A combined analysis of Use Case #1 and Use Case #3 using the physical models for different drive train conﬁgurations would have generated more insights than the current Use Case #3.

6.3. RECOMMENDATION The open-source nature of the developed software seeks to aid future research in the systems engineering of offshore wind farms by supporting scalability and user-friendliness. In this regard, this framework has opened a new horizon in the multi-disciplinary study of offshore wind farms. There are myriad ways to bolster the RNA model and further the study of its coupling with the offshore wind farm:

• An unsteady aerodynamics model coupled with a high-fidelity structural dynamics model of the blade would paint a detailed picture of the loading on the blade 6 and enable its control system design. Although, this may impose some computational issues at the wind farm level, OpenMDAO support for surrogate modelling could be harnessed to circumvent such problems. • Active Wake Control of the turbines combined with a wake deflection model (FLORIS) can be coupled to study the variation in the yaw misalignment of the first row of the turbines on the overall energy yield of the farm and the fatigue loading on the turbines in their wake. • In practise and in literature, a wind farm is generally assumed to comprise of a distinct wind turbine design. The current framework can be improved to support multiple wind turbine designs - rotor diameter, power rating, hub height etc - although this would also require a 3D wake model to capture the speed deficit in the wake of the turbines at differing hub heights. EPILOGUE

The objective of this chapter is to develop insights into our lives using systems engineering. In this regard, the target milestone is a low ﬁdelity model of our lives. The dissemination of knowledge on the utility of the tool in self-assessment of our lives is intended.

USECASE The use case underlying this objective is to perform a multi-disciplinary optimization of our lives. Our lives comprise of vivid disciplines, where each discipline is coupled in a complex way with every other discipline. The idea of this exercise is to granularise our lives into important disciplines and identify their ﬁxed parameters (parameters beyond our control), degrees of freedom (parameters that we can control) and input-output connections.

LITERATURE SURVEY No literature on systems engineering of life was found.

DEVELOPMENT The XDSM of a low-ﬁdelity empirical model of our lives is shown in Figure 6.1. The presence of connections in the lower triangle of the matrix denotes the implicit relationship between different disciplines.

Freedom, Freedom, Freedom, Freedom, Culture, Tlife ? Culture Culture Culture Human nature

Tself , Tsociety, Tself , Tjob, Driver Tjob, Ambition Tff , Love ? Passion Altruism Tff , Tsociety,

Self Wisdom Wisdom Wisdom ?

Experience, Money, Job Money Money, Value ? Gratiﬁcation

Experience, Friends & Emotion, Joy, Inspiration ? Family Inspiration

Experience, Society ? Gratiﬁcation

Constraint Constraint value

Objective Objective function value function

Figure 6.1: XDSM of an individual’s life

85 86 6.C ONCLUDING REMARKS

VALIDATION The premises of this empirical model are discussed in the next section. However, the objective of this use case is not to draw conclusions but to equip the readers with a systems engineering approach towards life.

ANALYSIS An individual’s life, in a simple form, can be granularised into four disciplines - Self, Job, Friends & Family and Society. All these disciplines are shaped largely by the Freedom and Culture of the society we live in. Depending on the society where we live, it is nor- mally beyond our control to change such factors; hence, it is taken as a ﬁxed parameter.

Self represents an individual’s relationship with self, which is marked by the time spent on learning and reﬂecting, during which we contemplate on ourselves and our relationship with other disciplines, and turn our Experience into Wisdom.

Our Ambition and Wisdom determine the output we derive from our Job. A job with insufﬁcient Gratiﬁcation or Money feeds back to Self and creates an urge for a job change.

Friends & Family are responsible for the Emotional support and the Joy we experi- 6 ence in our lives. Depending upon the Nature of our friends and family, which is beyond our control to change, we can control our love or hatred towards them. The Inspiration we draw from them not only helps us in assessing ourselves but also in ﬁnding a suitable profession.

Our relationship with society is governed by the Culture and our sense of Altruism. The Culture of our society affects our Job and Friends & Family in a way beyond our control. But the effect of our relationship with the Society on our Job and Friends & Family is relatively less straight-forward.

The primary Constraint in our life is Time. The most esoteric aspect of an individual’s life is the Objective function. Epicurus, an ancient Greek philosopher, suggested a fulfilling life is where we have Freedom to do things that we like, where we share Joy with our Friends & Family and where we spend enough time on reflecting on Self. This can be mathematically written as: ³ ´ F MAX Freedom T Joy ob j = × sel f × However, every individual is the "master of his fate, and the captain of his soul" (William Ernest Henley). In this regard, the objective function is individual-specific and depends on his or her preferences and priorities. What is the objective function of your life? A APPENDIX

A.1. CHAPTER 3 This details of DriveSE components, their underlying models and IO connections, are elucidated in this appendix.

HUB The rotor radius (Rr otor ), number of blades (B), shaft tilt angle (Ψ), blade root diameter or the root chord (c(Rhub)), mass of each blade (mbl ade ) and the ﬂapwise moment at the blade root (M f l ap (Rhub)) are used to calculated the mass of the hub (mhub), pitch system (mpi tch) and the spinner (mspinner ). The overall rotor mass (mr otor ), rotor torque (Qr otor ) and rotor thrust (Tr otor ) are used to calculate the aerodynamic load at the hub centre (Fhub~ , M~hub).

The hub is modelled as a thin walled, ductile cylinder made of cast iron with circular holes for the blade root and the low speed shaft ﬂange. The dimensions of this cylinder - radius, height, thickness - are scaled empirically with Rr otor and c(Rhub), and the volume is determined using geometrical calculations. The mass of the pitch system depends on the mbl ade and M f l ap (Rhub), while the mass of the spinner is empirically scaled with Rr otor .

GEARBOX The gearbox transforms the high torque, low speed rotation of the main shaft to the low torque, high speed rotation of the generator shaft. There are two major types of gearbox stages available for a wind turbine drive train [47]:

• Parallel - comprises of an input gear shaft and an output pinion shaft. The stage ratio is limited by the interface between the gear and the pinion • Planetary or Epicylic - comprises of multiple planet gears supported by a planet carrier that serves as the input, and a sun pinion that acts as the output. It yields a

87 88 A.A PPENDIX

higher stage ratio per unit mass as compared to the parallel gearbox, and is capable A of carrying higher torque, since it has a higher number of contact points.

The mass of the gearbox (mgb) and its dimensions - length (Lgb) and radius (Rgb) - are functions of the rotor radius (Rr otor ), rotor torque (Qr otor ), overall gearbox ratio (rgb) and number of planets in each stage of the gearbox (Np ). The mass of each gearbox stage - comprising of a sun, a ring and the planets for the planetary stage and a gear i and a pinion for the parallel stage - depends on Qr otor , Np , stage speed ratio (rgb) and the intensity of tooth load (Ktooth)[76]. The gearbox is designed for the torque that is 1.5 times the rated Qr otor . To account for the effect of non-torque loads on the gearbox in 3-point suspension system, the mass of the ﬁrst stage of the gearbox is multiplied by 1.25 [49]. As Qr otor and Np are the known inputs and Ktooth is empirically determined, i an optimization problem is framed with rgb as the design variables and the objective Q3 i to minimize the overall gearbox mass subject to the constraint of ( i 1 rgb) rgb. The = = model results in a linear relationship between Mgb and Qr otor , as shown in Figure 3.11. Lgb and Rgb are empirically scaled with Rr otor . The detailed information regarding the pinion diameter, sun diameter or tooth width are unavailable.

LOWSPEEDSHAFT The inputs to the LSS model are: rotor radius (Rr otor ), rated power (Pr ated ), rotor mass (mr otor ), gearbox mass (mgb), gearbox length (Lgb), overhang length (Loverhang ), shaft tilt angle (Ψ) and the force (Fhub~ ) and moment (M~hub) at the hub centre. The outputs of up the model are: mass of the LSS (ml ss ), upwind main bearing (mmb) and downwind main down bearing (mmb ); and the dimensions of the main shaft - length (Ll ss ), upwind radius up down (Rl ss ) and downwind radius (Rl ss ).

The shaft is modelled as a hollow taper made of steel with the ratio of the inner and the outer diameter as 0.1. This is done to allow the transfer of power and signals to the blade pitch system. The design of the LSS includes the mass of the shrink disc (mshr ink ) 1 2 and the gearbox carrier bearing (mcar r ier ) , which are scaled empirically with Pr ated . 3 The ﬂange length (L f l ange ) and the distance of the upwind main bearing from the hub centre (Lhub_mb) are scaled empirically with Rr otor .

The force and moment at the critical points - interfaces with the main bearings and the gearbox - depend on M~hub, Fhub~ , mr otor , mgb, mshr ink , mcar r ier , L f l ange , Lhub_mb, Lgb, Ll ss and Ψ (Figure 3.9). All these parameters except Ll ss are either known inputs or empirically derived. A longer LSS leads to reduced radial loads at the downwind main bearing and the gearbox, but its maximum value is limited by Loverhang and the deﬂec- tions at the critical points. With an initial guess of Ll ss , the loads are calculated by the force and moment balancing, and the von Mises stresses at the critical points are deter-

1Shrink disc is a coupling device that connects the main shaft to the low speed side of the gearbox, enabling torque transmission using the frictional force between its inner and outer ring [77]. 2A carrier is a rotating mount for the planets in a planetary gearbox. They are supported by cylindrical roller bearings, which is referred here as carrier bearing. [78] 3A flange forms the connection between the hub and the main shaft. A.1.C HAPTER 3 89 mined using the system stiffness properties. Then the distortion energy failure theory up down A with a peak load safety factor of 2.5 is applied to determine Rl ss and Rl ss . The size and the mass of the upwind and downwind (if present) main bearings are then scaled empirically [79] with the LSS outer diameters at their corresponding locations. Thereafter, the deflections at the critical points are checked, and if the limits are not satisfied, the aforementioned steps are repeated with an updated values of Ll ss . Upon convergence, up down up down this process yields Ll ss , Rl ss , Rl ss , ml ss , mmb and mmb . A factor of 3.92 is multi- up down plied to mmb and mmb to account for the mass of housing. The bearing type is a fixed parameter, and can be chosen as one of the following:

• Compact-aligning toroidal roller bearing • Spherical roller bearing • Single-row tapered roller bearings • Double-row tapered roller bearings • Cylindrical roller bearing • Single-row deep-groove radial ball bearings

HIGHSPEEDSHAFT The length (Lhss ), radius (Rhss ) and the mass (mhss ) of the HSS are determined using the following inputs: rotor radius (Rr otor ), rotor rated torque (Qr otor ), LSS upwind ra- up dius (Rl ss ) and gearbox ratio (rgb). The mass (mhss ) is empirically scaled with the HSS Qr otor side torque ( ), which is then multiplied by 1.5 to include the brakes, wheras Lhss is rgb scaled empirically with Rr otor . Like the gearbox, the HSS is also designed for the torque that is 1.5 times the rated Qr otor .

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). The mass of the generator (mgen) is scaled empirically with the machine rating (Pr ated ), whereas the dimensions - length (Lgen) and radius (Rgen) - are scaled with rotor radius (Rr otor ).

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. In some turbines, the transformer is located in the nacelle, while in others it could be on the ground. In DriveSE model, the option for an uptower transformer can be switched on or off. The transformer mass (mts f ) and the converter mass (mconv ) are scaled with the machine rating (Pr ated ), whereas the transformer’s length (Lts f ) is assumed to be the same as that of the generator (Lgen). The converter mass is approximately 30% of that of the generator.

MAINFRAME

The inputs to this discipline are: rated power (Pr ated ), rotor radius (Rr otor ), force (Fhub~ ) and moment (M~hub) at the hub centre, mass of the rotor (mr otor ), LSS (ml ss ), main up down bearings (mmb, mmb ), gearbox (mgb), HSS (mhss ), generator (mgen) and transformer 90 A.A PPENDIX

A (mts f ), and the length of LSS (Ll ss ), gearbox (Lgb), HSS (Lhss ), generator (Lgen) and transformer (Lts f ). The outputs of this discipline are: bedplate length (Lbed ), mass of the bedplate (mbed ), platform (mpl at ), HVAC components (mhvac ) and the nacelle cover (mcover ). The distance of the upwind main bearing from the hub centre (Lhub_mb) is determined empirically with Rr otor .

Bedplate is the support piece that bears the non-torque loads from the main bearings, torque arms of the gearbox, mechanical brakes and the generator platform. The upwind section of the bedplate bears majority of the aerodynamic and gravity load, and is modelled as two parallel cast iron I beams. The downwind section bears minor loads from the mechanical brakes and the generator platform, and are modelled as two parallel steel I beams. The forces acting upon the front bedplate depend on Fhub~ , mr otor , ml ss , mmb, msb and mgb; while the moment about the root additionally depends on M~hub, Lhub_mb, Ll ss and Lgb. On the other hand, the forces acting upon the rear bedplate depend on mgb, mhss , mgen and mts f ; and their moment arms depend on Lgb, Lhss , Lgen and Lts f . With an initial guess of the rear and front bedplate dimensions (length, width and thickness), the deflection and the stress experienced by the respective I-beams are calculated using the Euler-Bernoulli beam theory. A multiplier of 8 is used to scale the calculated stress to fit the industry data. The front and rear dimensions are varied un- Lbed til the deflection is lower than the 1500 and the stress is lower than the corresponding material UTS (cast iron for the upwind section and steel for the downwind section). The dimensions thus determined are used to calculate mbed . mpl at is assumed to be 12.5% of mbed , while mhvac and mcover are empirically scaled with Pr ated and Lbed respectively.

YAWDRIVE Yaw drive is used to align the rotor to the wind direction, to ensure maximum aerodynamic efﬁciency and fatigue life of the blades. The yaw system comprises of several yaw motors and a friction plate bearing. The mass of the friction plate is empirically derived from the diameter of the tower top (Dtower ) and the rotor radius (Rr otor ). The number of yaw motors and their weights are determined based on knowledge based engineering. The mass of the yaw drive (myaw ) is equal to the sum of the masses of the friction plate and the motors. A.2.C HAPTER 4 91

A.2. CHAPTER 4 A

B, Ψ, λ, θ, U , ηdt, ∞ cref (r), ref ref ref ref δ , Rrotor, γ, βref (r), B, Ψ, rgb, Np m , $ tip i i UTS Ucut in, − Ucut out, Airfoils−

Prated, Rrotor, Prated, rotor RNA Prated R τ Rrotor

Rhub, c(Rhub), Loverhang, Paero(U), Dtower, σflap(r), Blade mblade Ct(U) mblade, Trotor, σedge(r), δtip Qrotor, Mflap(Rhub)

mrna Hub & Nacelle mi

Crna Cost

Constraint Constraint value

Figure A.1: XDSM of the RNA model for Use Case #2

A.3. CHAPTER 5

B, Ψ, λ, θ, U , ηdt, ∞ cref (r), ref ref ref ref δ , R , γ, βref (r), B,Ψ m , $ tip rotor i i UTS Ucut in, − Ucut out, Airfoils,− τ

Prated Prated Prated Prated Prated RNA 2 ∝ 2 ∝ 2 ∝ 2 ∝ 2 ∝ Rrotor Rrotor Rrotor Rrotor Rrotor

Rhub, c(Rhub), Paero(U), mblade, Trotor, σflap(r), Blade mblade Ct(U) Qrotor, σedge(r), δtip Mflap(Rhub)

mrotor Hub mhub

mgb, mgen, Drive Train mconv

Crna Cost

Constraint Constraint value

Figure A.2: XDSM of the RNA model for Use Case #3

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