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  <front>
    <journal-meta><journal-id journal-id-type="publisher">WES</journal-id><journal-title-group>
    <journal-title>Wind Energy Science</journal-title>
    <abbrev-journal-title abbrev-type="publisher">WES</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Wind Energ. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">2366-7451</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/wes-6-203-2021</article-id><title-group><article-title>Redesign of an upwind rotor for a downwind configuration: design changes and cost evaluation</article-title><alt-title>Redesign of an upwind rotor for a downwind configuration: design changes and cost evaluation</alt-title>
      </title-group><?xmltex \runningtitle{Redesign of an upwind rotor for a downwind configuration: design changes and cost evaluation}?><?xmltex \runningauthor{G.~Wanke et~al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Wanke</surname><given-names>Gesine</given-names></name>
          <email>gesine.wanke@suzlon.com</email>
        <ext-link>https://orcid.org/0000-0002-8039-5449</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Bergami</surname><given-names>Leonardo</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Zahle</surname><given-names>Frederik</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Verelst</surname><given-names>David Robert</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3687-0636</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Blade Science Center, Suzlon, Vejle, Denmark</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>DTU Wind Energy, Technical University of Denmark, Roskilde, Denmark</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Gesine Wanke (gesine.wanke@suzlon.com)</corresp></author-notes><pub-date><day>2</day><month>February</month><year>2021</year></pub-date>
      
      <volume>6</volume>
      <issue>1</issue>
      <fpage>203</fpage><lpage>220</lpage>
      <history>
        <date date-type="received"><day>12</day><month>December</month><year>2019</year></date>
           <date date-type="accepted"><day>3</day><month>December</month><year>2020</year></date>
           <date date-type="rev-recd"><day>15</day><month>August</month><year>2020</year></date>
           <date date-type="rev-request"><day>2</day><month>April</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 Gesine Wanke et al.</copyright-statement>
        <copyright-year>2021</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021.html">This article is available from https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021.html</self-uri><self-uri xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021.pdf">The full text article is available as a PDF file from https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e113">Within this work, an existing model of a Suzlon S111 2.1 MW turbine is used
to estimate potential cost savings when the conventional upwind rotor concept
is changed into a downwind rotor concept. A design framework is used to get
realistic design updates for the upwind configuration, as well as two design
updates for the downwind configuration, including a pure material cost out of
the rotor blades and a new planform design. A full design load basis according
to the standard has been used to evaluate the impact of the redesigns on the
loads. A detailed cost model with load scaling is used to estimate the impact
of the design changes on the turbine costs and the cost of energy. It is shown
that generally lower blade mass of up to 5 <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> less than the upwind redesign can be achieved with the downwind
configurations. Compared
to an upwind baseline, the upwind redesign shows an estimated cost of energy
reduction of 2.3 <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>, and the downwind designs achieve a maximum
reduction of 1.3 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e149">Historically, the first wind turbines were dominantly downwind turbines, for which the rotor was placed behind the tower, as seen from the incoming wind. This
turbine configuration was considered safer than the alternative upwind
configuration with the rotor in front of the tower since the rotor blades
would bend away from the tower under turbine operation. Early research, mainly
by NASA and associated partners, compared the downwind rotor configuration with
the upwind configuration. <xref ref-type="bibr" rid="bib1.bibx8" id="text.1"/> showed that the wake behind the
tower caused significantly higher cyclic flapwise blade root loads in the
downwind configuration compared to the loads of the upwind rotor
configuration. However, neither for the flapwise mean blade root loads nor for
the edgewise blade root loads could differences between the two configurations be shown.</p>
      <p id="d1e155">Many residents living near early downwind wind turbines reported
high noise levels and especially the high unsteadiness, a “thumping” sound
being reported as a nuisance (<xref ref-type="bibr" rid="bib1.bibx20" id="altparen.2"/>). The rotor blades passing
through the tower wake caused high low-frequency noise and amplitude
modulation. Measurements in an anechoic wind tunnel by <xref ref-type="bibr" rid="bib1.bibx9" id="text.3"/>
demonstrated that downwind rotors on a lattice tower radiated more noise than
downwind rotors on a tubular tower due to the narrower and deeper tower
wake. Upwind rotor configurations, on the other hand, were found to be
significantly less noisy. Found to be overall advantageous, upwind rotor
configurations dominated industrial applications, as well as the focus of
research efforts during the 1990s and 2000s.</p>
      <p id="d1e164">Cost-driven industrial designs prefer larger rotor areas to capture more
energy. The rotor blades for modern-sized upwind wind turbines are designed
under a constraint of maximum blade tip deflection to avoid a collision of the
blades with the tower. Aiming to eliminate the tip deflection constraint for
modern-sized wind turbines under normal operation, the downwind configuration
is currently coming into research focus again.</p>
      <p id="d1e167">Advances in wind turbine noise mitigation techniques since the 1980s, as well
as airfoil design, could overcome the previously reported noise issues and bring them to an
acceptable level. <xref ref-type="bibr" rid="bib1.bibx23" id="text.4"/> successfully eliminated the tower shadow
effect on the fatigue loads by using<?pagebreak page204?> a fairing. While the fairing is a rather
costly device to implement, the study further showed the potential that fatigue
loads can be significantly reduced by a reduced flapwise stiffness,
alleviating loads by blade deformation.</p>
      <p id="d1e174"><xref ref-type="bibr" rid="bib1.bibx21" id="text.5"/> used an optimization framework to compare the levelized cost
of energy (COE) of land-based upwind and downwind turbines. The study included
turbines of different wind classes, rated power, and rotor diameter. Modest
cost savings could be achieved for the downwind configuration compared to the
upwind configuration for wind turbines of wind class III. Blade mass savings
had to offset the higher tower cost originating from the increased tower
bottom bending moment as the gravity overhanging moment of the rotor nacelle
assembly coincides with the moment from the thrust force.</p>
      <p id="d1e179">In a system-level design study for large rotors, <xref ref-type="bibr" rid="bib1.bibx31" id="text.6"/> showed
that coned downwind rotors significantly reduce peak blade loads during
operation but have a lower annual energy production (AEP) compared to a coned upwind
configuration of the same size. While the group predicts larger main bearing
peak loads for the downwind configuration related to blade length, mass, and
cone angle, they suggest that the increased tower loads observed by other
groups could be overcome by properly balancing the nacelle on the tower.</p>
      <p id="d1e185">A reduced edgewise damping for a downwind configuration compared to an upwind
configuration was identified by <xref ref-type="bibr" rid="bib1.bibx26" id="text.7"/>, leading to significantly
higher edgewise loads in the downwind configuration than in the upwind
configuration. In a following study on a 2.1 MW turbine, <xref ref-type="bibr" rid="bib1.bibx28" id="text.8"/>
showed that large downwind cone angles could reduce the edgewise damping
further as the out-of-plane contribution of the edgewise mode shapes is
decreased. A significantly reduced tower torsional stiffness, on the other
hand, e.g., a lattice tower configuration, would benefit the downwind
configuration.</p>
      <p id="d1e194">Aligning the blades with the loading direction of aerodynamic
forces, gravity, and centrifugal force is an opportunity for the downwind
configuration to significantly reduce flapwise bending loads, instead loading the
blade in axial tension. Such a load distribution is achieved by
adjusting the cone angle and blade prebend. These downwind rotors with
so-called “load alignment” have been suggested as an option to reduce blade
mass significantly, utilizing the large cone angles and downwind prebend from
<xref ref-type="bibr" rid="bib1.bibx18" id="text.9"/> for a 13.2 MW wind turbine. The study also indicated mass
savings compared to the conventional upwind rotor when the blade length is
increased to compensate for energy production losses.</p>
      <p id="d1e200"><xref ref-type="bibr" rid="bib1.bibx4" id="text.10"/> used an optimization framework to compare the cost
efficiency of an upwind configuration with a downwind configuration and a
downwind configuration with “load alignment”. The analysis for a
10 <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> turbine showed difficulties in reaching a more cost-efficient
design for the downwind configurations than the conventional upwind
configuration due to other component costs.</p>
      <p id="d1e213">Downwind configurations with a passive wind direction
alignment are often proposed. Such yaw systems could be cost efficient as they simplify the
turbine control and reduce operation and maintenance costs as they could
purely be used for cable unwinding. However, <xref ref-type="bibr" rid="bib1.bibx27" id="text.11"/> showed in an
example of a 2.1 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> turbine with a tilted rotor that such systems
align passively at high yaw angles for high wind speeds resulting in
significant power loss. The study concluded that tilt angle, cone angle, and
blade stiffness would need to be specifically designed for a free yawing
downwind configuration. This would expose additional constraints on a downwind
turbine design, while the benefit in terms of a cost-efficient turbine is
questioned.</p>
      <p id="d1e228">The cost-efficient design of wind turbines has been approached to an increasing extent by the use of optimization frameworks. Over the years, rotors designed for the maximum efficiency result in the most
cost-efficient turbine designs have been questioned. Optimizing a conventional 10 <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula>
upwind turbines for the lowest cost of energy, <xref ref-type="bibr" rid="bib1.bibx6" id="text.12"/>
showed that designing the rotor for minimum cost instead of maximum annual
energy production results in rotors with larger chord, higher
thickness, and lower AEP. Higher absolute thickness could utilize higher
stiffness with less material resulting in the lower cost compensating the AEP
loss from the less efficient, thicker airfoils.</p>
      <p id="d1e242">Lower rotor loads could potentially result in the possibility to increase the
rotor length and therefore increase the overall power capture. This could be a
more cost-efficient rotor than a traditional design approach also for upwind
turbines. <xref ref-type="bibr" rid="bib1.bibx5" id="text.13"/> tried, therefore, to design a low-induction rotor
for a 10 <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> wind turbine with an optimization framework in which the
blade shape was designed with the common aerodynamic parameters, such as
chord, twist, and airfoil thickness. Their work showed that maximum AEP
solutions might be achievable with low-induction rotors, but the minimum cost
solutions might be different from the maximum AEP solutions. It was seen to be
very dependent on the cost model if the higher AEP could pay for the increased
rotor diameter.</p>
      <p id="d1e256"><xref ref-type="bibr" rid="bib1.bibx17" id="text.14"/> investigated design trends by an optimization of power
capture based on 1D momentum theory. Their work indicated that the maximum
power capture is achievable by a larger rotor diameter and operation at a lower
power coefficient (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) than the maximum. For a conventional upwind turbine, this
is achieved by so-called thrust clipping or peak shaving. The peak shaving is
a control feature that reduces extreme flapwise loads and also increases
the minimum blade tip to tower clearance in the upwind configuration while
sacrificing AEP.</p>
      <p id="d1e272">This paper shows how rotor design trends for a downwind configuration differ
from design trends for an upwind rotor configuration due to differences in
design loads inherent to the configuration. Full design load bases (DLBs)<?pagebreak page205?> are
calculated to evaluate the impact of the rotor design trends on the turbine
loads, AEP, and estimated cost of energy. The work in this paper is based on
the specific example of the commercial S111 2.1 <inline-formula><mml:math id="M9" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> turbine. A
low-fidelity optimization tool is used to redesign the commercial rotor for an
upwind and a downwind configuration, generating the aerodynamic planform and
flap- and edgewise stiffness distribution. High-fidelity tools are used to
generate inputs for load calculations, the full load base analysis, mass, and
AEP calculations. An industrial grade cost-scaling model based on the load
calculations is used to estimate the impact of the designs on the cost of
energy.  Analyzing the impact of the redesigned rotor on load and cost allows us to discuss the potential of a downwind rotor configuration compared to an
upwind rotor configuration in greater detail. The discussion shows the impact
of the cost structure and other design choices like the tubular tower
influencing the potential of the downwind configuration in comparison to the
upwind configuration. The results show that a pure rotor redesign will hardly
achieve a lower cost of energy for the downwind configuration than for the
upwind configuration for the specific chosen example turbine.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d1e291">This work aims to compare design trends for an upwind configuration of an
existing turbine with a downwind configuration from a cost and mass
perspective. The chosen example turbine is the Suzlon S111 2.1 <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula>
turbine, a commercial upwind turbine. The turbine is designed for wind class
IIIA with glass fiber blades and a rotor diameter of 112 <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> on a
90 <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> tubular tower. The turbine is pitch-regulated with a variable
speed generator. The shaft is tilted, the rotor is coned, and the blades are
pre-bent. All three geometrical parameters increase the blade tip to tower
clearance in the upwind configuration.</p>
      <p id="d1e318">For this turbine, a new baseline rotor blade is defined, inspired by the
commercial blade, which is adapted to the framework. For the baseline rotor,
an upwind turbine configuration is generated, called S111uw. Additionally, a
downwind baseline turbine configuration is defined with the baseline rotor
called S111dw. The downwind configuration utilizes the same cone and tilt
angle, both increasing blade tip to tower distance. Since the blade prebend of
the rotor is towards the blade pressure side, the prebend decreases the blade
tip to tower distance in the downwind configuration. Three rotor redesigns are
made. For the upwind configuration, a blade planform and internal structural
redesign is made. The design is called S111uw PF. For the downwind
configuration, two scenarios are regarded. Firstly, a pure blade material
reduction is performed, called S111dw STR. This corresponds to a configuration
change from an existing upwind configuration into a downwind configuration while
keeping the blade molds but saving blade material. Secondly, a blade planform
and structure redesign in the same manner as for the upwind redesign is called
S111dw PF. Table <xref ref-type="table" rid="Ch1.T1"/> shows a summary of the design
configurations regarded, as well as the name indicators used throughout the study.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Table}?><label>Table 1</label><caption><p id="d1e326">Turbine configurations regarded in design and cost estimation.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Configuration</oasis:entry>
         <oasis:entry colname="col3">Planform</oasis:entry>
         <oasis:entry colname="col4">Structure</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">S111uw</oasis:entry>
         <oasis:entry colname="col2">Upwind</oasis:entry>
         <oasis:entry colname="col3">Baseline</oasis:entry>
         <oasis:entry colname="col4">Baseline</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">S111uw PF</oasis:entry>
         <oasis:entry colname="col2">Upwind</oasis:entry>
         <oasis:entry colname="col3">Optimized</oasis:entry>
         <oasis:entry colname="col4">Optimized</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw</oasis:entry>
         <oasis:entry colname="col2">Downwind</oasis:entry>
         <oasis:entry colname="col3">Baseline</oasis:entry>
         <oasis:entry colname="col4">Baseline</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw STR</oasis:entry>
         <oasis:entry colname="col2">Downwind</oasis:entry>
         <oasis:entry colname="col3">Baseline</oasis:entry>
         <oasis:entry colname="col4">Optimized</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw PF</oasis:entry>
         <oasis:entry colname="col2">Downwind</oasis:entry>
         <oasis:entry colname="col3">Optimized</oasis:entry>
         <oasis:entry colname="col4">Optimized</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e442">Flow chart of the work flow for design and cost estimation.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f01.png"/>

      </fig>

      <p id="d1e451">The rotor design procedure uses a low-fidelity optimization tool to create a blade planform and stiffness distribution. The planform and stiffness distribution are afterwards matched within the HAWTOpt2 framework <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx30" id="paren.15"/> to create a full HAWC2 (<xref ref-type="bibr" rid="bib1.bibx19" id="altparen.16"/>) setup for aeroelastic load calculations. The higher-fidelity tools are not used for optimization but exclusively for an evaluation of the design resulting from optimization with the low-fidelity tool. For all designs, a full design load basis is calculated. The loads are used to calculate the failure index of the blades and to evaluate if the redesigns are acceptable. From the tower loads, the required tower material is calculated. Finally, the costs of all five designs are calculated with<?pagebreak page206?> a load and mass scaling cost model. This design procedure is conceptually outlined in Fig. <xref ref-type="fig" rid="Ch1.F1"/>.</p>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Baseline blade in BECAS</title>
      <p id="d1e469">The baseline blade is set up in BECAS (a 2D cross-sectional analysis tool;
<xref ref-type="bibr" rid="bib1.bibx2" id="altparen.17"/>) as it is implemented in the HAWTOpt2 framework. This
approach has several advantages. Firstly, through BECAS, it allows for having
reasonable structural blade properties which can be directly exported as
inputs for load simulations with HAWC2. Secondly, even though the HAWTOpt2
framework is not utilized for optimization, it allows us to parametrically modify
the planform and structural dimensions of the baseline blade. Within the
workflow of the framework, the structural properties are recalculated within
BECAS and can be exported for load calculations.</p>
      <p id="d1e475">The baseline blade is described according to the parameterization adopted in
HAWTOpt2 <xref ref-type="bibr" rid="bib1.bibx30" id="paren.18"/>. To set up the baseline blade in BECAS, the
planform geometry is directly loaded into the framework. From blade length,
relative thickness, chord, twist, and the airfoil geometry, the blade surface
is created as a 3D lofted surface. The chordwise position of the main structural
regions, namely trailing edge caps, spar caps, shell panels, trailing edge, and
leading edge are defined in 19 cross sections relative to the chord
length. For each region, the positioning and material stacking is applied from
blade lay-up plans.</p>
      <p id="d1e481">For the baseline blade structural properties, total mass, static mass moment,
and blade eigenfrequencies are compared to the commercial blade to assure the
baseline is reasonable and fairly close to the commercial blade. The same has
been done with turbine eigenfrequencies and damping, as well as the design-driving loads for blades, main bearing, and tower.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Design load basis and controller definition</title>
      <p id="d1e492">Full design load bases are simulated with HAWC2 (version 12.7) according to
the IEC standard 61400-1 Edition 3 (<xref ref-type="bibr" rid="bib1.bibx15" id="altparen.19"/>). The interpretation of
the design load basis by the Technical University of Denmark (DTU), described
by <xref ref-type="bibr" rid="bib1.bibx13" id="text.20"/>, is used. For the downwind configuration, the load
simulations are conducted with an inflow inclination angle of 0<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. The
combination of positive flow inclination angle and turbine tilt was seen to be
beneficial in downwind configurations by <xref ref-type="bibr" rid="bib1.bibx26" id="text.21"/>. It is therefore
assumed to be a more realistic scenario with relevant site conditions to
simulate wind fields without an inclination angle for downwind
configurations. The upwind configurations are subject to the inclination angle
of 8<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, as required by IEC standard for upwind configurations.</p>
      <p id="d1e522">The annual energy production (AEP) is calculated for all designs. It is
calculated from the normal operation load case with six turbulence seeds for
all configurations without inclination or yaw angle. The turbulence intensity
follows the class A IEC standard.</p>
      <p id="d1e525">For all load calculations, the controller setup from DTU
(<xref ref-type="bibr" rid="bib1.bibx12" id="altparen.22"/>) is used in this study with two additional features. The
controller is for pitch-regulated variable speed turbines with partial and
full load regions. Optimal <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> tracking is used in the partial load region
and a constant torque strategy in the full load region. The detailed
description of the controller can be found in <xref ref-type="bibr" rid="bib1.bibx12" id="text.23"/>, and the
source code is freely available online
(<uri>https://github.com/DTUWindEnergy/BasicDTUController</uri>, last access: 2 December 2019). The controller has been automatically tuned using
a pole placement routine implemented in HAWCStab2 (<xref ref-type="bibr" rid="bib1.bibx10" id="altparen.24"/>),
which is described in more detail by <xref ref-type="bibr" rid="bib1.bibx24" id="text.25"/>. Different events can
be initiated from the main controller, such as start-up and shutdown or
failure situations.</p>
      <p id="d1e555">Start-up and shutdown pitch speed in the implemented routines of the
DTU controller need different values for downwind configurations than
comparable upwind configurations. The moment due to both thrust force and the
gravity overhanging moment of the rotor nacelle assembly increases the
tower bottom bending moment. Start-up routines, especially at high wind
speeds, need to have a lower pitch speed in downwind configurations than the
comparable upwind configurations. Shutdown routines, especially during gusts,
have to be of faster pitch speed in the downwind configuration. Both
adjustments have to be made to unload the tower bottom as the moment due to
the thrust force is aligned with the overhanging rotor moment due to
gravity. A faster pitch decrease in gust situations reduces overshoot in the
thrust force due to the gust and therefore the tower base loads. During
start-up, a slower pitch increase avoids a thrust overshoot and related high
tower loads.</p>
      <p id="d1e559">For a control routine that reflects an industrial controller, three failure
scenarios are adapted. Firstly, the failure scenario of one blade getting
stuck at a current pitch angle, which means that the pitch angle of one blade is kept constant
at the current pitch angle at the time of failure. The deviation of the pitch
angle from the set point initiates a stop routine of the turbine. Secondly, the
pitch run away (design load case, dlc, 2.2p) is not included since the failure mode is prevented
by the type of pitch actuators used. Thirdly, for the scenario of a parked
turbine with high yaw errors, the wind field is interpreted as a wind direction
change of 360<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> over 570 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e579">To eliminate fault cases from the design-driving loads and to stay similar to
an industrial controller, two additional control features are implemented as
separate dynamic-link libraries manipulating the output or input from the controller to HAWC2
for practical reasons. The first addition is a thrust control aiming to reduce
fluctuations of the thrust. The second addition is a conditional stop routine
avoiding operations at high yaw errors and high wind speeds. The following
explains the two additions in more detail.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e584">Flow chart of the thrust control controller addition.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f02.png"/>

        </fig>

      <?pagebreak page207?><p id="d1e593">Figure <xref ref-type="fig" rid="Ch1.F2"/> shows the thrust control feature. The thrust
control uses the sum of the flapwise blade root moments to estimate the thrust
<inline-formula><mml:math id="M18" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>. On the one hand, the thrust signal is low-pass filtered, and, on the other hand,
a reference thrust <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is calculated as a moving average. A
PD controller is used to generate a collective pitch offset under a range
limitation. The pitch range is limited to avoid high loads from turbulence
(lower limit) and high power losses (upper limit). The filtered wind speed of
the nacelle anemometer is used for wind-speed-dependent gain scheduling to
guarantee a smooth transition between active and non-active thrust control.</p>
      <p id="d1e616">The conditional stopping routine triggers the turbine stop as soon as the
filtered wind speed and the filtered wind direction are above a certain
threshold. For practical reasons of implementation, the emergency stop is
triggered.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>STORM – optimization</title>
      <p id="d1e627">The redesign of the rotor blades is performed using the in-house code STORM
(Suzlon Turbine Optimization fRaMework). The code is aimed at fast conceptual
rotor design optimization studies and couples steady aerodynamic AEP
considerations with a simplified blade structural estimation. In the present
study, it minimizes the blade mass under AEP constraints. The code, written in
MATLAB, is organized as a nested optimization problem. The outer optimization
loop controls the blade geometrical planform and minimizes the blade mass
subject to linear constraints on the geometrical design variables, nonlinear
constraints on minimum AEP, and feasibility of all the inner optimization
problems (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>).</p>
      <p id="d1e632">In this study, the blade geometry design variables are limited to four spline
control points that set the thickness-over-chord (ToC) ratios in fixed points
along the blade span. The geometry at the blade root is fixed up to the point
of maximum chord for all configurations. For each iteration of the outer
optimization loop, six steps are taken; they are described in the following
sections and briefly consist of the following.
<list list-type="order"><list-item>
      <p id="d1e637">The blade ToC spline is defined from the control points (the four design variables).</p></list-item><list-item>
      <p id="d1e641">The blade geometrical planform is outlined in terms of chord, twist, and thickness distribution. An inner optimization returns the chord distribution that minimizes the squared difference from a target axial induction distribution.</p></list-item><list-item>
      <p id="d1e645">Steady operational loads and the power curve are retrieved from a standard steady blade element momentum (BEM) formulation. An inner optimization sets the pitch angle to maximize aerodynamic power, subject to limitation on maximum power, thrust, aerodynamic flapwise bending moment, and angle of attack (for stall considerations).</p></list-item><list-item>
      <p id="d1e649">The steady BEM loads are scaled to extreme loads to be used in the structural optimization.</p></list-item><list-item>
      <p id="d1e653">The blade structural properties are determined, solving a fast low-fidelity structural optimization problem. The blade structure is simplified to two symmetric glass fiber spar caps joined by an ellipse (Fig. <xref ref-type="fig" rid="Ch1.F4"/>). The inner optimization sets the thickness and width of the spar cap and the ellipse thicknesses to minimize the blade static mass moment, subject to constraints on maximum strain, maximum deflection, maximum linear buckling index, and design variable range.</p></list-item><list-item>
      <p id="d1e659">Finally, the outer loop optimization objective function is evaluated. The estimated blade mass is here taken as an objective function, and minimum AEP output is enforced as a nonlinear constraint.</p></list-item></list></p>
      <?pagebreak page208?><p id="d1e662">Figure <xref ref-type="fig" rid="Ch1.F3"/> shows a flow chart of the nested optimization routine
with the tool STORM. In the outer loop optimization, the pattern search uses the
ToC distribution as a variable (Sect. <xref ref-type="sec" rid="Ch1.S2.SS3.SSS1"/>). From those, the
aerodynamic planform is calculated, e.g., chord and twist distribution
(Sect. <xref ref-type="sec" rid="Ch1.S2.SS3.SSS2"/>). A BEM code is used to calculate the loads over
the operational range (Sect. <xref ref-type="sec" rid="Ch1.S2.SS3.SSS3"/>), and a scaling approach is
used to retrieve the extreme loads from the steady loads
(Sect. <xref ref-type="sec" rid="Ch1.S2.SS3.SSS4"/>). In an inner-gradient-based optimization with
analytical gradients, the girder thickness, girder width, and shell thickness
are found (Sect. <xref ref-type="sec" rid="Ch1.S2.SS3.SSS5"/>) with the minimum mass as the
optimization objective). It has been checked that the optimization algorithm
has converged to the given tolerances. This nested optimization approach
guarantees only that the optimum within each step of the loop is found. The
solution is not necessarily the global optimum. However, using the same
approach for both configurations allows us to investigate the design trends for
the two turbine configurations. The following subsections describe the single
blocks of Fig. <xref ref-type="fig" rid="Ch1.F3"/> in more detail.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e683">Flow chart of the optimization routine with STORM.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f03.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e694">Simplified model of the blade structure for each cross section, as applied in STORM. The section height <inline-formula><mml:math id="M20" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> and chord length <inline-formula><mml:math id="M21" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> are fixed with the blade geometry for each iteration. The structural optimization design variables are then for each section the spar caps thickness <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and width <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the ellipse thickness <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f04.png"/>

        </fig>

<sec id="Ch1.S2.SS3.SSS1">
  <label>2.3.1</label><title>Outer optimization loop</title>
      <p id="d1e757">The outer optimization problem (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>) is solved using the
MATLAB pattern search method (<xref ref-type="bibr" rid="bib1.bibx16" id="altparen.26"/>). The
algorithm is set up to perform a complete search and pooling around the
current point.

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M25" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:munder><mml:mtext>minimize</mml:mtext><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">h</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:mrow></mml:munder><mml:mspace width="1em" linebreak="nobreak"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>m</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">h</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>subject to</mml:mtext><mml:mspace linebreak="nobreak" width="1em"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>AEP</mml:mtext><mml:mfenced open="(" close=")"><mml:mi mathvariant="bold-italic">h</mml:mi></mml:mfenced><mml:mo>≥</mml:mo><mml:msup><mml:mtext>AEP</mml:mtext><mml:mtext>min</mml:mtext></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">δ</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">h</mml:mi></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">ε</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="1em"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E1"><mml:mtd><mml:mtext>1</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">η</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M26" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> is the mass of the blade depending on the variables of spar cap
width <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>, spar cap height
<inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>, the shell thickness
<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>, and the section height
<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">h</mml:mi><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> at each of the <inline-formula><mml:math id="M31" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> cross
sections. The constraints are a minimum AEP, a maximum blade deflection
<inline-formula><mml:math id="M32" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>, a maximum strain <inline-formula><mml:math id="M33" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, and a maximum buckling coefficient
<inline-formula><mml:math id="M34" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula>. A list of all formula symbols can also be found in
Table <xref ref-type="table" rid="App1.Ch1.S1.T5"/> in the Appendix.</p>
      <p id="d1e1167">The design variables are here the four thickness-over-chord (ToC) control
point ratios. Linear constraints on the design variables are enforced to
ensure that they are maintained within reasonable ranges and that monotonically
decreasing values are selected from root to tip. The objective function for this problem consists of minimizing the estimated blade mass, subject to
nonlinear constraints to reaching a minimum AEP output (as derived from the BEM
steady power curves) and ensuring feasibility in all the inner optimization
problems.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <label>2.3.2</label><title>Blade geometrical planform</title>
      <p id="d1e1178">Once the iteration ToC control points are fixed, the ToC distribution along
the blade span is outlined with a piecewise cubic Hermite interpolating
polynomial. A wind speed in the below-rated variable speed range is chosen,
and the target axial induction distribution for the blade at that wind speed
is fixed as an input. Similarly, the angles of attack at which the
airfoils are expected to operate at that wind speed point are also fixed.  The
target axial induction is kept according to the original commercial blade. It
has been assumed that this is a typical induction distribution resulting from
a commercial aerodynamic design process. It has been kept as the optimization
tool is not capable of reflecting the complexity of fully variable induction,
also regarding related concerns such as stability or stall margins.</p>
      <?pagebreak page209?><p id="d1e1181">With the given input set (ToC, target induction, target angle of attack) the blade
geometry is then retrieved in terms of chord, twist angle, and thickness for
each section along the blade span.  The chord is retrieved by solving a set of
independent minimization problems (Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>), one for each section
along the blade span. The optimization objective is to minimize the square
error between the target axial induction for that section, the current
induction, and function of chord, subject to a linear constraint on the minimum
and maximum chord.

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M35" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:munder><mml:mtext>minimize</mml:mtext><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:mrow></mml:munder><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mtext>ind</mml:mtext><mml:mrow><mml:mtext>target</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mtext>ind</mml:mtext><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>subject to</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:msup><mml:mi>c</mml:mi><mml:mtext>min</mml:mtext></mml:msup><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>c</mml:mi><mml:mtext>max</mml:mtext></mml:msup></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e1266">In the current iteration, the axial induction is retrieved from a steady BEM
formulation, following Ning's implementation (<xref ref-type="bibr" rid="bib1.bibx22" id="altparen.27"/>),
in which the BEM convergence is solved by minimizing a residual function of the
flow angle.  Once the chord is fixed, the twist angle is simply set as the
difference between the converged flow angle returned by the BEM and the input
angle of attack for that section (minus eventually a chosen constant reference
pitch angle).</p>
</sec>
<sec id="Ch1.S2.SS3.SSS3">
  <label>2.3.3</label><title>Steady loads and power curves</title>
      <p id="d1e1280">Given the blade geometrical definition like from the step above, the steady
power and loads curves are then determined running a standard steady BEM
formulation <xref ref-type="bibr" rid="bib1.bibx11" id="paren.28"/>, sweeping wind speeds between cut-in and
cut-out. From the steady power curve, the annual energy production (AEP) is
retrieved, accounting for the chosen wind speed distribution.</p>
      <p id="d1e1286">The operational pitch angle at each wind speed is retrieved from a simple
optimization loop, in which the objective is to maximize the aerodynamic power
output, subject to constraints on maximum power (the aerodynamic rated
power), maximum thrust force, maximum aerodynamic blade flapwise bending
moment, and minimum “stall distance” (Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/>). The latter is
defined as a minimum margin in degrees between the steady BEM angle of attack
and the point of maximum lift for the corresponding airfoil; the constrained stall
is only enforced for the outer 40 <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> of the blade span.

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M37" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:munder><mml:mtext>maximize</mml:mtext><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:munder><mml:mspace linebreak="nobreak" width="1em"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>P</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">β</mml:mi></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>subject to</mml:mtext><mml:mspace linebreak="nobreak" width="1em"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>P</mml:mi><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>P</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>T</mml:mi><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>M</mml:mi><mml:mtext>flap</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>M</mml:mi><mml:mtext>flap</mml:mtext><mml:mtext>max</mml:mtext></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd><mml:mtext>3</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="italic">α</mml:mi><mml:mo>&lt;</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msup><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>stall distance</mml:mtext></mml:msub></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math id="M38" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> is the pitch angle, <inline-formula><mml:math id="M39" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> is the aerodynamic power, <inline-formula><mml:math id="M40" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the
thrust force, and <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>flap</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the flapwise bending moment. The angle of
attack is <inline-formula><mml:math id="M42" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>stall distance</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the stall distance. In
the case of this study, the constraint of maximum thrust and maximum
aerodynamic flapwise bending moment are not active.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS4">
  <label>2.3.4</label><title>Loads scaling</title>
      <p id="d1e1477">The maximum aerodynamic steady flapwise bending moment is retrieved from the
step above and is scaled up to an extreme load using a ratio retrieved from
full DLB HAWC2 simulations of the baseline blade:

                  <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M44" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme baseline</mml:mtext></mml:msub><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>BEM</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>BEM baseline</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

            <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme baseline</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the extreme load distribution of the baseline rotor
extracted from full DLB simulations in HAWC2 for the baseline blade. The
distribution is fitted with a fourth-order polynomial to ensure that it can be
differentiated. Section forces are derived with the polynomial from the
bending moments. The <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>BEM baseline</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> moment is the corresponding maximum
steady BEM model retrieved for the same baseline blade.</p>
      <p id="d1e1538">In the case of the downwind configuration, a second flapwise design load case
for cut-out wind speed is considered as the minimum tower-blade clearance
arises in different loading conditions. The load distribution for the maximum
deflection towards the tower <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme deflection</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is thus scaled from the
baseline loads at cut-out wind speed as

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M48" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme deflection</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>=</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mtext>extreme baseline deflection</mml:mtext></mml:msub><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>BEM</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mtext>BEM baseline wsp out</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              For the downwind configuration, a decrease in the loading results into a
larger deflection towards the tower.</p>
      <p id="d1e1608">The edgewise loads remain unscaled as they are driven by the aerodynamic
torque, as well as the gravity load.</p>
      <p id="d1e1611">To verify the load scaling approach, it has been checked that the tower clearance
from dynamic HAWC2 simulations is captured reasonably well. Also the failure
indices for each blade section have been checked to assure that also locally
on the blade sections the approach captures the loads reasonably well. No
direct comparison between the scaled loads and the dynamic loads from HAWC2
has been done.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS5">
  <label>2.3.5</label><title>Blade structural design</title>
      <p id="d1e1622">The simplified blade structural model is based on the work of
<xref ref-type="bibr" rid="bib1.bibx3" id="text.29"/> and is also presented in the thesis work of
<xref ref-type="bibr" rid="bib1.bibx7" id="text.30"/> and <xref ref-type="bibr" rid="bib1.bibx1" id="text.31"/>. The blade
is described as a sequence of beam elements, each with a cross section
simplified to the elements shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/>. The main
load-carrying structure is simplified as a symmetric girder with two
glass reinforced plastic (GRP) spar caps connected by a GRP ellipse. The
major axis of the ellipse is taken equal to the section chord and the distance
between the spar caps taken equal to the section height, thus coupling the
structural problem to the aerodynamic planform definition. The structural
optimization problem has thus three design variables for each structural
section <inline-formula><mml:math id="M49" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> along the blade: the spar cap thickness <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and width <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
the ellipse thickness <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>e</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <?pagebreak page210?><p id="d1e1677">The load cases described in the previous section are applied to the finite
beam element model, and the structural optimization aims at minimizing the
blade static-mass moment, subject to constraints on the range of the design
variables, maximum strain levels on caps and ellipses, maximum tip deflection
for the deformed blade, and maximum buckling coefficient for a single spar
cap. The structural optimization problem can be stated as

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M53" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:munder><mml:mtext>minimize</mml:mtext><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:mrow></mml:munder><mml:mspace width="1em" linebreak="nobreak"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>m</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>subject to</mml:mtext><mml:mspace linebreak="nobreak" width="1em"/></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="italic">δ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold-italic">e</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">ε</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="1em"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mfenced><mml:mo>≤</mml:mo><mml:msup><mml:mi mathvariant="italic">η</mml:mi><mml:mtext>max</mml:mtext></mml:msup><mml:mo>,</mml:mo><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              with the tip deflection for the deformed blade <inline-formula><mml:math id="M54" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>, the strain levels on
caps and ellipses <inline-formula><mml:math id="M55" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, and the buckling coefficient <inline-formula><mml:math id="M56" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e1908">The buckling coefficient is added to the optimization problem compared to the
references. The buckling coefficient is calculated under the assumption of an
orthotropic plate under compression load. The compression load <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is
obtained from the bending moment, assuming that the internal flapwise bending
moment <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be distributed as two forces acting on one girder side as
compression forces and on the other girder side as tension forces.

                  <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M59" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>N</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mi>h</mml:mi></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi>a</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

            The buckling coefficient <inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula> is then obtained via

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M61" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="italic">η</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">6</mml:mn><mml:msub><mml:mi>M</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi>Q</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>a</mml:mi><mml:mrow><mml:msup><mml:mi>t</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E8"><mml:mtd><mml:mtext>8</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>G</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msqrt><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="italic">ν</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:msqrt><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              with the elastic modulus <inline-formula><mml:math id="M62" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, the Poisson ration <inline-formula><mml:math id="M63" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula>, and the shear modulus
<inline-formula><mml:math id="M64" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e2143">The optimization is solved with the Interior Point Optimizer, Ipopt
(<xref ref-type="bibr" rid="bib1.bibx25" id="altparen.32"/>), and analytical gradients are given
for the objective and the constraint functions, thus speeding up the
process considerably (<xref ref-type="bibr" rid="bib1.bibx3" id="altparen.33"/>). The solution returns a
reliable estimate of the overall blade mass (and hence blade cost), which is
here taken as the objective for the outer optimization loop.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Design evaluation</title>
      <p id="d1e2161">The optimized planform (chord, twist, and thickness distribution) and
the changes in the structural geometry (spar cap width, thickness of the spar,
and trailing edge caps) are applied in HAWTOpt2 according to the planform
calculated by STORM. All thickness distributions are fitted by hand at five control points, and a spline fit is applied in between the control points. The
HAWC2 inputs are extracted from HAWTOpt2, and a DLB is calculated for each
redesign. From the DLB, the maximum load at each blade cross section is
extracted. The failure index is calculated with BECAS for each
cross section. The design is accepted if the failure index <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>i</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is
<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>. The failure index calculated by BECAS is not used in the design
process.</p>
      <p id="d1e2196">The DLB calculation is further used to calculate the tower wall thickness <inline-formula><mml:math id="M67" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula>
for a tubular tower of the given outer wall diameter <inline-formula><mml:math id="M68" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>. The tower is divided
into 50 cross sections, and the outer diameter, as well as the load
distribution, is varied linearly between tower top and tower bottom.  Within
a for loop, the wall thickness is increased until the stress
<inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mtext>steel</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> reaches the allowed stress of the tower steel
material.

                <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M70" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mtext>steel</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>M</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>SF</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where the bending moment <inline-formula><mml:math id="M71" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> is the bending moment of the cross section, SF
is the safety factor for steel material, and <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the section modulus
calculated as

                <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M73" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>W</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">32</mml:mn></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mrow><mml:mi>D</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>w</mml:mi></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow><mml:mi>D</mml:mi></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          The iteration is done twice: once for the extreme loads and the according
stress limit for steel and once for the lifetime equivalent load from the
fatigue calculation and the fatigue stress limit for steel. From the two
resulting wall thicknesses, the maximum thickness is picked for each
cross section. Constant masses for the tower interior are added and kept the
same as for the baseline. The new tower mass distribution, as well as the
stiffness redistribution, does not enter the DLB calculations.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Cost estimation</title>
      <p id="d1e2331">The cost model used for the cost evaluation consists of costs that scale with
the mass, such as tower and blade costs. For other components, the costs scale
with a design-driving load or measure called cost driver (CD). The cost driver
is scaled with a factor <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>CD to mass</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> to the component mass
<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mtext>Cost</mml:mtext><mml:mtext>component</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. A second factor <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>mass to cost</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is defined to
scale component masses to component costs.

                <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M77" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mtext>Cost</mml:mtext><mml:mtext>component</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>mass to cost</mml:mtext></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>CD to mass</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mtext>CD</mml:mtext></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e2396">Other cost components, e.g., logistics or operation and maintenance costs, are scaled directly with the factor <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>CD to mass</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from a cost driver to the cost. Table <xref ref-type="table" rid="Ch1.T2"/> shows the cost drivers for the components entering the applied cost model. All component costs sum up to the capital expenditures (CAPEX). The operation
and maintenance costs form the operational expenditures (OPEX). The OPEX costs
are calculated with a net present value for a turbine lifetime of
20 years. The COE is calculated from the CAPEX, the OPEX, and the AEP of a
20 year lifetime.

                <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M79" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>COE</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>CAPEX</mml:mtext><mml:mo>+</mml:mo><mml:mtext>OPEX</mml:mtext></mml:mrow><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mtext>AEP</mml:mtext></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

          The component costs and total turbine costs (CAPEX <inline-formula><mml:math id="M80" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> OPEX) of the baseline have
been compared to the commercial turbine to assure a reasonable cost scaling
and cost distribution within the present study.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Table}?><label>Table 2</label><caption><p id="d1e2448">Cost drivers (CDs) for turbine cost and mass split by main cost components.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col2" align="center">Turbine component and cost design driver </oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Nacelle</oasis:entry>
         <oasis:entry colname="col2"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Gear box incl. cooling<inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal torque</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Pitch bearing</oasis:entry>
         <oasis:entry colname="col2">Maximum static flapwise moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Main bearing</oasis:entry>
         <oasis:entry colname="col2">Rotor static mass moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Main frame</oasis:entry>
         <oasis:entry colname="col2">Extreme tilt moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Hub</oasis:entry>
         <oasis:entry colname="col2">Extreme flapwise moment, blade static mass moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Main shaft</oasis:entry>
         <oasis:entry colname="col2">Rotor own weight moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Gear rim</oasis:entry>
         <oasis:entry colname="col2">Extreme yaw moment, tower top diameter</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Yaw drives</oasis:entry>
         <oasis:entry colname="col2">Extreme yaw moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Pitch drives</oasis:entry>
         <oasis:entry colname="col2">Maximum pitch moment, maximum pitch rate</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Converter<inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Nacelle nose cone cover<inline-formula><mml:math id="M84" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Power cables<inline-formula><mml:math id="M85" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power, tower height</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Lift<inline-formula><mml:math id="M86" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Tower height</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Electrical</oasis:entry>
         <oasis:entry colname="col2"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Generator<inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Bottom panel<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Top panel<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Hub panel</oasis:entry>
         <oasis:entry colname="col2">Maximum pitch moment, maximum pitch rate</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Transformer<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Blades</oasis:entry>
         <oasis:entry colname="col2">Mass 70 <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> (30 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> constant labor cost)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Tower</oasis:entry>
         <oasis:entry colname="col2">Nass</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Civil (foundation)</oasis:entry>
         <oasis:entry colname="col2">Extreme tower bottom bending moment</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col2" align="center">Cost component and cost design driver </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Logistics</oasis:entry>
         <oasis:entry colname="col2">Nacelle mass, blade length<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula>, tower height<inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Electrical balance of plant</oasis:entry>
         <oasis:entry colname="col2"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Yard<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Blade length squared</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Electrical lines<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Nominal power, average length of lines</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Installation (main crane)</oasis:entry>
         <oasis:entry colname="col2">Nacelle mass times tower height</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Operation and maintenance (OPEX)<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">AEP</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e2451"><inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Indicates costs that are not scaled within the study due to CD.</p></table-wrap-foot></table-wrap>

</sec>
</sec>
<?pagebreak page211?><sec id="Ch1.S3">
  <label>3</label><title>Results</title>
      <p id="d1e2890">The following section presents the resulting design configurations regarding
the planforms and resulting blade masses. Further, the design-driving loads
and the resulting changes in turbine costs and COE are presented. All results
are shown relative to the S111uw design configuration as the data are
confidential.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2895">Comparison of planforms for different designs. Thickness over chord ratio and  the range of the thickness constraints, chord and twist are normalized with the maximum chord.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f05.png"/>

      </fig>

<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Design configurations</title>
      <p id="d1e2911">Figure <xref ref-type="fig" rid="Ch1.F5"/> shows the planforms resulting from the design
workflow. All values are normalized with the maximum chord. The figure shows
that the chord and the twist distribution change only slightly, while larger
differences can be observed for the thickness over chord distribution, which
is likely primarily due to the induction distribution being kept fixed during
the optimization, while the larger changes in thickness are due to the direct
coupling between AEP constraint, blade structural constraints, and blade
mass. For the S111uw PF and S111dw PF, the thickness over chord ratio
increases from the 70 <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> span and inboard compared to the baseline
(S111uw). The S111dw PF has a slightly lower thickness than the S111uw PF
design in this area up to the tip. From 40 <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> span and inboard to the
displayed region, the S111dw PF design shows a larger thickness over chord
ratio than the S111uw PF design. In the outer 8 <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> of the blade span,
the PF redesigns show a greater thickness than the<?pagebreak page212?> baseline blade. The latter
is an artifact of the combination of the spline type chosen and the fixed
airfoil thickness at the blade tip. For none of the redesigns is the constraint
on thickness over chord active.</p>
      <p id="d1e2940">While the S111uw PF design is constrained in blade deflection, in none of the
downwind designs is the blade deflection constraint active. All the resulting
redesigns are generally utilizing the maximum strain of the material over a
larger blade span than the S111uw and S111dw design configurations. All
downwind redesigns are fully strain constrained in the spar caps. However, the
tower clearance for the S111dw PF design is only marginal. In the structural
module of the optimization, the buckling constraint is active along the full
blade span. The downwind configurations generally show greater shell thickness
than the upwind configuration.</p>
      <p id="d1e2943">Generally, the difference in active design constraints between the S111uw PF
and S111dw PF design are that the S111uw PF design is strain constrained only
in a small part of the mid-span section, and the tip deflection constraint is
active. The S111dw PF design, on the other hand, is fully strain constrained over
the full blade span, and the tip deflection constraint is not active.</p>
      <p id="d1e2946">For all redesigns of the rotor blade, significant mass savings of at least 12 <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> could be achieved. The lowest blade mass savings are achieved
by the upwind configuration. For the S111uw PF, 12.5 <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> of blade mass
could be saved. For the S111dw STR, 14.5 <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> mass savings is achieved,
and 17.1 <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> blade mass reduction was observed for S111dw
PF. Table <xref ref-type="table" rid="Ch1.T4"/> summarizes the blade masses for
all design configurations, together with other data collected.</p>
      <p id="d1e2984">The planform redesigns utilize greater stiffness with less material by using
thicker airfoils in the inboard part, resulting in an overall reduction in
mass. In the outboard part, thinner, more efficient airfoils compensate for a
production loss of the inboard part of the blade. This effect is amplified as
a small AEP penalty was allowed in the design procedure. From the S111dw STR,
it can be seen that the downwind configuration benefits from lower flapwise
loads and a release of the tower clearance constraint resulting in a reduced
blade mass. A greater shell thickness is required to carry the higher edgewise
loads in the downwind configurations. Comparing the S111dw PF design to the
S111uw PF design, a further effect of the edgewise load increase can be
seen. To carry the increased edgewise loads, there are two options. The first
one is to increase the shell thickness like for the S111dw STR design. The
second option is to increase the stiffness by using airfoils with higher
relative thickness. The solution found in the optimization routine for the
S111dw PF is a combination<?pagebreak page213?> of both, showing slightly thicker airfoils on the
inboard part for the S111dw PF than for the S111uw PF. Another solution to
carrying the increased edgewise loads is an increased chord, but since the
variation in chord is limited due to a fixed induction and tip speed ratio,
this design freedom is not utilized. The lower flapwise loads in the S111uw PF
design allow us, on the other hand, to compensate for a power loss with slightly
thinner airfoils in the outboard part. The chord distribution is hardly
changing as the AEP is constrained to not deviate from the baseline AEP. As
this results in a similar lift level along the blade for all designs and the
induction distribution is frozen, the chord length does not change. The twist
is simply adjusting the given operational point of the airfoils at the given
spanwise position.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Table}?><label>Table 3</label><caption><p id="d1e2990">Turbine loads for mass and cost drivers. Blade root moment (BRM), tower bottom bending moment (TBM), and tower top moment (TTM).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Load sensor</oasis:entry>
         <oasis:entry namest="col2" nameend="col5" align="center"><inline-formula><mml:math id="M105" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> normalized load relative to </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center">S111uw configuration in percent </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">S111uw</oasis:entry>
         <oasis:entry colname="col3">S111dw</oasis:entry>
         <oasis:entry colname="col4">S111dw</oasis:entry>
         <oasis:entry colname="col5">S111dw</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">PF</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">STR</oasis:entry>
         <oasis:entry colname="col5">PF</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Max. mean flapwise BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M106" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>3</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M107" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M108" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>38</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M109" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>35</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme flapwise BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M110" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M111" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>17</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M112" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>19</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M113" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>18</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme edgewise BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M114" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>12</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M117" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme torsion BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M118" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>18</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M120" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>18</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M121" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme TTM yaw</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M123" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M124" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>9</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M125" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme TTM tilt</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M126" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>9</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">27</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Extreme TBM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M130" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>4</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Longitudinal</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fatigue flapwise BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M134" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fatigue edgewise BRM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M138" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>11</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M141" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>10</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fatigue TTM tilt</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M142" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fatigue TBM</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M146" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M147" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M148" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M149" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Longitudinal</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Cost driving loads from full DLB calculation</title>
      <p id="d1e3608">The following section shows the loads driving either the cost components in
Table <xref ref-type="table" rid="Ch1.T2"/> or the designed tower and blade mass. For
all regarded designs, the minimum tower clearance is guaranteed. The operation
at high wind speeds and high turbulence level (DLC 1.3) is design driving for
the minimum tip to tower distance in the downwind configuration as the
outboard part of the blade is subject to negative lift forces. High pitch
angles at high wind speeds cause the negative lift force, and the blade tip
bends towards the tower. For the upwind configuration, the operation at the
thrust peak at high turbulence (DLC 1.3) is design driving for the minimum tip
to tower distance. For all loads entering the cost model either directly or
via the mass calculations DLC 1.3, the operation at extreme turbulence remains
design driving. The only exception is the extreme blade root torsion moment
in which load cases of operation during wind direction change, operation at
extreme yaw errors, or yaw errors during parked situations with a locked rotor
(DLC 1.4, DLC 2.2y, or DLC 7.1) are design
driving. Table <xref ref-type="table" rid="Ch1.T3"/> shows the loads influencing the cost
estimation of the designs relative to the S111uw configuration. It can be
seen that the S111uw PF design clearly benefits from the reduced blade mass
on the edgewise extreme and fatigue blade root bending moment, as well as on
the tower bottom bending moment. The only disadvantage is an increase in the
tower top yaw moment.</p>
      <p id="d1e3615">The table also shows that the downwind designs generally benefit on the
flapwise mean, flapwise extreme blade root moment, and the related tower
top yaw moment. This is mainly due to the alignment of the rotor cone and the
rotor forces (“load alignment”). The tower top tilt moment is increased in
the downwind designs compared to the upwind designs. Here, the influence of
the tower shadow, as well as the alignment of the rotor overhanging gravity
moment with the moment due to thrust force, is observed. Due to the latter,
an increase in the extreme tower bottom bending moment is also seen compared to the
S111uw design. The gravity-related loads, e.g., tower top tilt moment and
longitudinal tower bottom bending moment are reduced for each configuration by
the reduction of mass due to the redesign (e.g., S111uw vs. S111uw PF and
S111dw vs. S111dw PF). With the reduced flapwise stiffness of the S111dw PF
design, the tower shadow effect is overcome. As a result, the fatigue load of the
S111dw PF is reduced to the level of the S111uw. A relative reduction of the
flapwise stiffness compared to the edgewise stiffness increases the edgewise
damping. Therefore, a load decrease for edgewise extreme and fatigue loads of
the S111dw STR and S111dw PF compared to the S111dw is observed.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Turbine mass, cost and COE estimate</title>
      <p id="d1e3626">This section shows the estimated costs resulting from the load and mass
difference of the design configurations. Figure <xref ref-type="fig" rid="Ch1.F6"/> shows the
summary of the main cost components of the turbine with an indication of the
cost that is not affected by the design process (constant cost). The costs sum
up to the total CAPEX. All results are normalized by the CAPEX of the S111uw
design. It can be seen that the nacelle is the main cost component, followed
by the blades, the tower, and the costs for electrical equipment.  The figure
shows that more than a third of the CAPEX is not affected by the chosen
redesigns. In the CAPEX distribution of the nacelle, major cost differences
are associated with the pitch bearing, the mainframe, and the pitch drives. The
blade costs reduce significantly with the redesign of the blades, for which the S111dw PF shows the lowest blade costs associated with the lowest blade
mass. The tower and foundation costs are for the downwind configurations
generally higher than for the upwind configurations as the associated extreme
loads and also the tower top fatigue loads are significantly higher. The costs
of the electrical components reflect the change in hub panel costs as these
scale with the extreme blade root torsion. Only small differences in the
logistics costs are observed due to the change in nacelle mass. The balance of
the plant is achieved for the same estimated costs, while the installation
reflects the changes in total main frame mass, driven by the extreme tilt
moment. Overall, the total CAPEX costs of the turbine vary only marginally
between all the redesigns. The OPEX costs, on the other hand, are lower for
all the downwind designs since the OPEX costs scale with the lower AEP. As a
result, the combined turbine costs of the redesigned downwind configurations
(S111dw STR and S111dw PF) are lower than for the S111uw PF design.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Table}?><label>Table 4</label><caption><p id="d1e3634">Blade mass, tower mass, CAPEX, AEP, and COE differences for the regarded turbine configurations relative to the S111uw design.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M150" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> blade mass (%)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M151" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> tower mass (%)</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M152" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> AEP (%)</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M153" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> COE (%)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">S111uw PF</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M154" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>12.5</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M155" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>3.9</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M156" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.33</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M157" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.3</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw</oasis:entry>
         <oasis:entry colname="col2">0.0</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">17.8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M159" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.0</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw STR</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M161" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>14.5</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6.8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M163" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.32</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M164" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S111dw PF</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M165" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>17.1</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6.6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M167" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.37</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M168" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.3</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e3871">Table <xref ref-type="table" rid="Ch1.T4"/> summarizes the achieved blade and tower mass, as well as the AEP and the estimated COE differences, compared to the S111uw design.
With a COE reduction of <inline-formula><mml:math id="M169" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.3 <inline-formula><mml:math id="M170" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>, the S111uw PF shows the lowest COE, as the CAPEX is low, while the AEP is high. A pure configuration change from S111uw to S111dw is most expensive in terms of COE due to the high CAPEX mainly caused by high tower and foundation loads. A structural redesign of the blades for the downwind configuration achieves significant COE savings of <inline-formula><mml:math id="M171" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.2 <inline-formula><mml:math id="M172" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> due to reduced rotor mass.<?pagebreak page214?> A planform optimization of the downwind configuration reduces the COE <inline-formula><mml:math id="M173" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.3 <inline-formula><mml:math id="M174" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> below the S111uw baseline turbine. Overall, the S111uw PF still has the lowest COE since the rotor mass is only 5 <inline-formula><mml:math id="M175" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> above the S111dw PF, while the tower is 10 <inline-formula><mml:math id="M176" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> lighter and the AEP is 2 <inline-formula><mml:math id="M177" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> higher.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e3949">Turbine CAPEX cost split by main cost components normalized by the sum of the S111uw configuration with an indication of constant costs not affected by the redesign process.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://wes.copernicus.org/articles/6/203/2021/wes-6-203-2021-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Summary</title>
      <p id="d1e3967">Within this study, the COE reduction potential for the Suzlon S111
2.1 <inline-formula><mml:math id="M178" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> turbine has been estimated for changing the original upwind
configuration into a downwind configuration. A design framework including a
low-fidelity in-house optimization tool has been used to redesign rotors for
upwind and downwind configurations. A full design load basis has been
simulated for every design configuration. The design configurations have been
evaluated by a COE estimation.</p>
      <p id="d1e3978">New planforms were optimized for upwind and downwind configurations for
minimum blade mass under the constraint of a minimum AEP. The new planforms
were shown to have higher thickness over chord ratios inboard, utilizing
higher stiffness with less material. This design trend agrees well with
findings by <xref ref-type="bibr" rid="bib1.bibx6" id="text.34"/> and <xref ref-type="bibr" rid="bib1.bibx30" id="text.35"/>.</p>
      <p id="d1e3987">The downwind designs were generally subject to lower flapwise blade root
moments than the comparable upwind designs due to the coning direction, as
also proposed by, for example, <xref ref-type="bibr" rid="bib1.bibx14" id="text.36"/> and
<xref ref-type="bibr" rid="bib1.bibx4" id="text.37"/>. As a result, lower blade mass could be achieved for
downwind configurations than for upwind configurations. The S111dw PF design
showed, for example, 4.6 <inline-formula><mml:math id="M179" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> lower blade mass than the S111uw PF
design.</p>
      <p id="d1e4004">The load saving on the blade in the downwind configuration is offset by an
increase in the tower bottom bending moment as the gravity overhanging moment
of the rotor nacelle assembly is aligned with the thrust force, as also shown
by <xref ref-type="bibr" rid="bib1.bibx21" id="text.38"/>. As a result, around 10.5 <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> higher tower masses
were seen in the direct comparison of the S111uw PF design and the S111dw PF
design.</p>
      <p id="d1e4019">The downwind configurations are subject to a lower AEP production due to the
coning direction. This effect has also been observed by, for example,
<xref ref-type="bibr" rid="bib1.bibx31" id="text.39"/> and <xref ref-type="bibr" rid="bib1.bibx21" id="text.40"/>. In the direct comparison, the AEP of
the S111dw PF is 2.04 <inline-formula><mml:math id="M181" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> lower than the AEP of the comparable S111uw
PF.</p>
      <p id="d1e4036">Lower rotor and nacelle costs can be achieved by the downwind
designs. However, the downwind designs also<?pagebreak page215?> come with higher tower and
foundation costs. Overall, the downwind configurations of comparable rotor
size achieve a lower total turbine cost than the upwind design
configuration. The difference in cost is due to the lower OPEX cost and does
heavily depend on the cost model. Overall, the lower turbine cost does not
compensate for the loss in AEP. The lowest COE level is achieved by the S111uw
PF design configuration which achieves a significant mass and load reduction
for a small sacrifice in AEP compared to the baseline.</p>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion and future work</title>
      <p id="d1e4048">This study has shown, for the example of the Suzlon S111 2.1 <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula>
turbine, that a downwind rotor configuration could be achieved with lower
total turbine costs than the comparable upwind configuration. Due to a lower
AEP of the downwind configurations, the upwind configuration, on the other
hand, showed overall the lowest COE. A downwind configuration would,
therefore, be the configuration to choose on a cost-driven turbine market,
while for COE-driven markets, the upwind configuration would be chosen.</p>
      <p id="d1e4059">These results depend on the very baseline-specific cost model. Scaling the
OPEX with the AEP has been the only cost driver for the OPEX which results in
the lower turbine costs for the downwind configuration. It could be expected
that the higher fatigue load of the downwind configuration would increase the
material wear, but this does not enter the OPEX model.</p>
      <p id="d1e4062">It should also be highlighted that the costs are effected by the chosen
optimization approach, namely a mass minimization under AEP constraint. This
does not give the true optimal solution in the sense of cost of
energy. However, it does show the influence of the observed design trends on
the turbine cost and the cost of energy.</p>
      <p id="d1e4065">The cost model generally depends on the loads simulated. This comes with
uncertainty due to the seed number, the seeds themselves, and the
assumptions of the wind field inclination angle. In the case of the downwind
configuration, additionally, the dynamic effect of the tower shadow is not
captured correctly within the HAWC2 simulations. Within HAWC2 the tower shadow
model for downwind configurations is a pure deficit model and the increased
vorticity behind the tower is not reflected. It can be expected that
especially flapwise blade root and tilt-related fatigue loads are
underpredicted. Further research would need to be done to quantify the impact
of this effect.</p>
      <p id="d1e4069">Generally, fatigue loads should be part of the design process in future
work. In the chosen approach, fatigue loads are not regarded in the design
process and hardly reflected in the cost model. This might be a valid
assumption in the<?pagebreak page216?> upwind configurations, but for downwind configurations, this
approach needs to be proven. Due to the tower shadow effect, as well as a
possible decrease in edgewise damping, it might be possible that rotors of
downwind configurations are driven by edgewise fatigue loads rather than
flapwise extreme loads.</p>
      <p id="d1e4072">Prescribing the induction distribution in the optimization is a major
restriction of the chosen design approach. The resulting chord and twist
distributions are therefore very similar. The induction should be a design
variable in future work as unloading the tip might allow for increases in
rotor diameter and therefore AEP increase. The latter does not just hold for
the downwind configuration but also for the upwind configuration.</p>
      <p id="d1e4075">Prescribing the induction distribution did, however, have the advantage that
the load scaling approach was possible. Scaling loads from the BEM code loads
to the extreme loads has decreased computation time significantly. A drawback
of the load scaling approach is that a change in aerodynamic damping is not
reflected. For the downwind configuration, the flapwise stiffness could be
significantly reduced, while the edgewise stiffness had to be increased; the
edgewise whirl modes can, therefore, be expected to increase in damping due to
the frequency placement of the edgewise frequency compared to the second yaw
frequency. An increase in damping decreases the blade extreme loads. The
effect of the loads has been observed in the downwind designs, but there is no
feedback within the optimization reflecting the change in damping. In future
work, the framework would need to be enhanced with either time consuming load
calculations or with a set of transfer functions that can transfer a wind
field to extreme loads from a linearized turbine model. Such a linearized
turbine model could be extracted, for example, from HawcStab2, which uses these
models for eigenvalue analysis. In this case, a representative wind field
could be used that represents extreme loads from a simulation set with a much
larger seed number and with known uncertainty. This would decrease the
computational time drastically while achieving reasonable results.</p>
      <p id="d1e4078">As designed for fast conceptual rotor design studies, the chosen design
approach with STORM is limited in finding truly optimal solutions in the sense
of the lowest cost of energy. The reasons are, on the one hand, the simplified
structural model. On the other hand, the aerodynamic planform is limited by
the assumption of a prescribed target induction, thus, allowing hardly any
freedom of chord variations.  Further, fixing the rotor diameter limits the
investigations of the cost of energy for the different designs as it is fixed
to one point of investigation. With the chosen approach and the AEP constraint,
it is only possible to find the lowest blade mass for a certain targeted AEP
at a specific blade length. With these limitations the resulting designs are
not truly optimal in the sense of the lowest cost of energy. However, the chosen
approach does allow for the comparison of design trends between the upwind and
the downwind configurations.</p>
      <p id="d1e4081">The COE estimation and therefore success criteria of the downwind concept do
also depend on the cost share between the different components. Since in the
chosen example turbine the rotor and the tower are similar in the CAPEX share,
it is difficult in the downwind configuration to offset the increased tower
cost with savings on the rotor. If the baseline had a comparably more
expensive rotor and a cheaper tower, the downwind configuration would be more
competitive. Possible scenarios could be lower steel prices or higher blade
material prices.</p>
      <p id="d1e4084">Another possibility to increase the competitiveness of the downwind
configuration would be a change in the tower configuration, such as a wired
tower for which wires are a cheap measure to take the bending
loads. Alternatively, a low-labor-cost market could give the options of low
tower costs with lattice or hybrid-lattice towers which generate bending
stiffness from the increased footprint of the tower rather than large tower
wall thicknesses for a tubular tower. These options could make the downwind
configuration competitive as the cost share of the tower decreases. However,
the cost model with the chosen baseline is not able to reflect such
significant design changes.</p>
      <p id="d1e4088">Compensating the AEP loss in the downwind configuration with a larger rotor
area could be an option to decrease the COE. Nevertheless, this does also
increase the turbine cost not just due to an increased rotor diameter and
therefore rotor mass but also to mass-related loads such as tilt loads and tower
base loads. The rotor diameter has not been part of the rotor design as the
cost model is very specific and does not reflect large differences from the
baseline. Especially for components such as generator or gearbox which are not
available in any possible configuration but are bought as “off-the-shelf”
components, the linear cost scaling is insufficient. A rotor diameter increase
of 4 <inline-formula><mml:math id="M183" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> has been investigated, indicating the potential to decrease
the COE for the downwind configurations further with an increase in rotor
diameter. With the investigated increase of 4 <inline-formula><mml:math id="M184" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>, the cost of energy
could only be reduced to <inline-formula><mml:math id="M185" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.4 <inline-formula><mml:math id="M186" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> compared to the baseline cost. The
increase in AEP was offset by the higher costs associated with increased rotor
and tower mass, as well as increasing nacelle costs. Generally, future
investigations should be performed more thoroughly that include the rotor diameter in
the optimization. However, it is not expected that the conclusions for the
example turbine will change significantly as margins for loads and tower
clearance are low.</p>
      <p id="d1e4122">Future work should also consider a redesign of the nacelle for the better
balancing of the rotor mass on the tower for the downwind configuration, as
suggested by <xref ref-type="bibr" rid="bib1.bibx31" id="text.41"/>. However, it should be kept in mind that the
upwind configuration will always be beneficial in terms of tower bottom
bending moment. Masses that can not be relocated for balancing such as rotor,
hub, pitch, and yaw-system-related masses account for around 50 <inline-formula><mml:math id="M187" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> of
the mass of the rotor nacelle assembly. Extending the lengthwise dimensions of
the remaining components to relocate the center of gravity might<?pagebreak page217?> be more
expensive than the higher tower costs of downwind configurations.</p>
      <p id="d1e4136">It should not be forgotten in the discussion of the cost efficiency of
downwind configurations that simple control features such as peak shaving, as
suggested by <xref ref-type="bibr" rid="bib1.bibx17" id="text.42"/>, might benefit the upwind configuration in
the same manner as the configuration change: the tower clearance is increased, and
the flapwise blade root moment is decreased with a penalty on AEP. Since the
tower bottom load does not in this case increase, as in the case of the
downwind configuration, such an upwind configuration might outperform a
downwind configuration in terms of COE.</p>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e4150">Overall, the study shows that a downwind configuration of the chosen example
2.1 <inline-formula><mml:math id="M188" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> turbine would need to be pushed to much larger rotor sizes than
investigated. Further, low-cost measures would need to be chosen to carry the
increased tower loads if the downwind configuration should become competitive
in terms of COE with the comparable upwind configuration.</p>
      <p id="d1e4161">The optimization framework would need to be extended to be able to capture the
design changes regarding the rotor, but also different tower configurations
need to be included. To be able to evaluate such changes, a more comprehensive
cost model is required to do a fair comparison of the designs.</p>
      <p id="d1e4164">It can be concluded from the study that it will be difficult to design a
downwind configuration in the 2 <inline-formula><mml:math id="M189" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MW</mml:mi></mml:mrow></mml:math></inline-formula> range which can show significant
economic benefits unless the design targets a different market than the upwind
configuration or more drastic changes are made than just a rotor redesign and
a structural redesign of the tower.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<?pagebreak page218?><app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>List of symbols</title>
      <p id="d1e4187">The following Table <xref ref-type="table" rid="App1.Ch1.S1.T5"/> states the symbols used in the equations.</p>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.S1.T5"><?xmltex \currentcnt{A1}?><?xmltex \def\figurename{Table}?><label>Table A1</label><caption><p id="d1e4195">List of symbols used in the equations.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Greek symbol</oasis:entry>
         <oasis:entry colname="col2">Definition</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M190" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Angle of attack</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M191" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Pitch angle</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M192" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Material strain</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M193" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Blade deflection</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M194" display="inline"><mml:mi mathvariant="italic">η</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Buckling coefficient</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M195" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Poisson ratio</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mtext>steel</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Steel material stress</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M197" display="inline"><mml:mi mathvariant="bold-italic">ψ</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Cross-section strain and curvature vector</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Latin symbol</oasis:entry>
         <oasis:entry colname="col2">Definition</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M198" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Spar cap width</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CD</oasis:entry>
         <oasis:entry colname="col2">Cost driver</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M199" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Outer tower diameter</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M200" display="inline"><mml:mi>e</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Shell thickness</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M201" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Elastic (Young's) modulus</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M202" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Cost-scaling factor</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M203" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Shear modulus</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M204" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Section height</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">ind</oasis:entry>
         <oasis:entry colname="col2">Induction</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M205" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Mass</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M206" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Local mending moment</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M207" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Number of cross sections</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Buckling load</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SF</oasis:entry>
         <oasis:entry colname="col2">Safety factor</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M209" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Spar cap thickness</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M210" display="inline"><mml:mi mathvariant="bold-italic">u</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Displacement vector</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M211" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Tower wall thickness</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Section modulus</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\clearpage}?>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e4602">The data are not publicly accessible since the research is based on a commercial turbine and the data are not available
for disclosure by Suzlon.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e4608">GW created the baseline model and implemented the downwind design case in the optimization framework. LB developed and set up the optimization framework. FZ set up the HAWTOpt2 framework for the baseline and design case evaluation. All authors revised the models and results. With revisions of all coauthors, GW and LB prepared Sect. 2.3, and GW prepared the remaining paper. DRV supported the setup of the models and revised the models, results, and the final paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e4614">This project is an industrial PhD project funded by the Innovation Fund Denmark and Suzlons Blade Science Center. Gesine Wanke is employed at Suzlons Blade Science Center.</p>
  </notes><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e4620">This research has been supported by the Danish innovation fund (grant no. 5189-00180B).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4626">This paper was edited by Raimund Rolfes and reviewed by Andrew Ning and Pietro Bortolotti.</p>
  </notes><ref-list>
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  </ref-list></back>
    <!--<article-title-html>Redesign of an upwind rotor for a downwind configuration: design changes and cost evaluation</article-title-html>
<abstract-html><p>Within this work, an existing model of a Suzlon S111 2.1&thinsp;MW turbine is used
to estimate potential cost savings when the conventional upwind rotor concept
is changed into a downwind rotor concept. A design framework is used to get
realistic design updates for the upwind configuration, as well as two design
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the rotor blades and a new planform design. A full design load basis according
to the standard has been used to evaluate the impact of the redesigns on the
loads. A detailed cost model with load scaling is used to estimate the impact
of the design changes on the turbine costs and the cost of energy. It is shown
that generally lower blade mass of up to 5&thinsp;% less than the upwind redesign can be achieved with the downwind
configurations. Compared
to an upwind baseline, the upwind redesign shows an estimated cost of energy
reduction of 2.3&thinsp;%, and the downwind designs achieve a maximum
reduction of 1.3&thinsp;%.</p></abstract-html>
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