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Renewable Energy 62 (2014) 506e515

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Multi-objective optimisation of horizontal axis wind turbine structureand energy production using aerofoil and blade properties as designvariables

Gunter Reinald Fischer a,*, Timoleon Kipouros b, Anthony Mark Savill b

aNordex Energy GmbH, 22419 Hamburg, GermanybCranfield University, Cranfield MK43 0AL, United Kingdom

a r t i c l e i n f o

Article history:Received 6 March 2013Accepted 12 August 2013Available online 7 September 2013

Keywords:Bernoulli beamHorizontal axis wind turbineMulti-objective optimisationParallel coordinatesTabu searchWind turbine blade design

* Corresponding author.E-mail address: gfischer@nordex-online.com (G.R.

0960-1481/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.renene.2013.08.009

a b s t r a c t

The design of wind turbine blades is a true multi-objective engineering task. The aerodynamic effec-tiveness of the turbine needs to be balanced with the system loads introduced by the rotor. Moreover theproblem is not dependent on a single geometric property, but besides other parameters on a combi-nation of aerofoil family and various blade functions. The aim of this paper is therefore to present a toolwhich can help designers to get a deeper insight into the complexity of the design space and to find ablade design which is likely to have a low cost of energy. For the research we use a Computational BladeOptimisation and Load Deflation Tool (CoBOLDT) to investigate the three extreme point designs obtainedfrom a multi-objective optimisation of turbine thrust, annual energy production as well as mass for ahorizontal axis wind turbine blade. The optimisation algorithm utilised is based on Multi-Objective TabuSearch which constitutes the core of CoBOLDT. The methodology is capable to parametrise the spanningaerofoils with two-dimensional Free Form Deformation and blade functions with two tangentiallyconnected cubic splines. After geometry generation we use a panel code to create aerofoil polars and astationary Blade Element Momentum code to evaluate turbine performance. Finally, the obtained loadsare fed into a structural layout module to estimate the mass and stiffness of the current blade by meansof a fully stressed design. For the presented test case we chose post optimisation analysis with parallelcoordinates to reveal geometrical features of the extreme point designs and to select a compromisedesign from the Pareto set. The research revealed that a blade with a feasible laminate layout can beobtained, that can increase the energy capture and lower steady state systems loads. The reduced aerofoilcamber and an increased L/D-ratio could be identified as the main drivers. This statement could not bemade with other tools of the research community before.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Regardless of the recent economic challenges, global wind tur-bine installation can record healthy growth figures year by year.Despite this encouraging development, competition betweencompanies in the sector is intensified and the profit margins areshrinking. The development of new, more reliable and efficientturbines is one way to answer this competitive pressure. Therefore,tools like the Computational Blade Optimisation and Load DeflationTool (CoBOLDT) can help to gain new insights into a highly con-strained and complex design space represented by wind turbinerotor blade development.

Fischer).

All rights reserved.

For the presented research paper three objective functions areminimize, that are proportional to the cost of energy (CoE) of awind turbine investment over its life time. This approach has beentaken because the direct calculation of CoE is partly ambitious andmany cost factors cannot be influenced by the turbine manufac-turer but are depended on the site where the wind turbine iserected. To evaluate all cost factors Fingersh et al. [1] proposed awind turbine scaling and cost model, in which statistical data ofthousands of turbines is used to derive empirical formulations forthe costs of the main wind turbine components. However, thephysics behind a certain turbine design is not reflected. We areapproaching the topic from a manufacturer perspective and focuson the reduction of wind turbine thrust and blade mass as proxy ofturbine capital cost and the improvement of Annual Energy Pro-duction (AEP). For this purpose we concentrate on the geometricalblade properties, namely the shape of the aerofoils and the blade

Nomenclature

AEP annual energy productionAoA angle of attackBEM blade element momentumCFD computational fluid dynamicsCl lift coefficientCoBOLDTComputational Blade Optimisation and Load

Deflation ToolCoE cost of energyDoF degrees of freedomEPD extreme point designFEM finite element methodGA genetic algorithmGFRP glass fibre reinforced plasticsHAWT horizontal axis wind turbineIEC international electrotechnical commissionMOTS Multi-Objective Tabu Search2D-FFD two-dimensional Free Form Deformation

Fig. 1. Workflow of CoBOLDT.

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515 507

functions, since they represent turbine parameters with highimpact on the chosen objective functions.

The paper is subdivided into six sections. After this introductionand the methodology and research outline in chapter two, theconstruction and functional details of the optimisation packageCoBOLDT are presented in chapter three. In chapter four a designcase using the Nordex Rotor Blade NR41 [2] as initial design isshown and the optimisation setup is stated. A detailed post opti-misation analysis of several points in the Pareto set will follow inchapter five which contains a parallel coordinates analysis to relategeometrical features to the considered performance metrics. Thisanalysis is supposed to help the designer to concentrate on onlythose parameters that are important for the design problem. Theconclusion in chapter six summarizes the findings and discussespossible future developments.

2. Methodology and research outline

In the field of wind turbine blade optimisation the choice of theoptimisation technique is particularly challenging since traditionalgradient-based algorithms are often unable to copewith numerical,mathematical or physical noise of the processed signals. In somecases the solution can be to evaluate and improve the gradientquality by curve approximation [3]. Another way to circumvent theproblem of establishing suitable gradients can be the use of meta-heuristic optimisation approaches. Especially Genetic Algorithmshave been in the focus of many recently published articles [4e8]. APaper from Benini and Toffolo [9] shows how a multi-objective GAcan solve the trade-off between structural requirements in the rootsection versus the aerodynamic requirements at the middle and tipsection of the blade. The design case uses a stall regulated windturbine with chord and twist parametrised with Bezier curves andthe tip speed and tip speed ratio as scalar parameters. The struc-tural mass is estimated with an I-beam for which the skin thicknessis calculated with glass fibre reinforced plastics (GFRP) and loadsfrom a steady Blade Element Momentum (BEM) simulation. Thisstructural model originally proposed by Fuglsang and Madsen [10]has also been used by other researchers in this field [11,12].

However in the current paper the core of the optimisationpackage CoBOLDT is based on the Multi-Objective Tabu Search(MOTS) as described by Jaeggi et al. [13]. It is a fast and efficientalgorithm with a powerful local searching scheme which has beenproven to successfully solve multi-dimensional aerodynamic

optimisation problems [14e18]. Since MOTS was designed to solvelarge problems it is able to run in a parallel computing environmenton a 64 bit Linux operating system. The memory management andthe selection of new parameters is the task of the master code,whereas the evaluation of each design will be performed by anumber of slaves. We prefer this type of optimisation over thementioned examples of GAs as the small modification from onedesign to the other in MOTS is perfectly suited for parameters withhigh impact on the optimisation objectives.

In terms of the aerodynamic performance evaluation of therotor three different methods with varying fidelity and associatedcomputational cost are most common. The slowest option isComputational Fluid Dynamics (CFD) which is therefore mainlyused to verify rotor performance after the optimisation [17] or toinvestigate wind turbine sub models like the blade tip [19]. Sec-ondly potential flow theory methods like in Abedi et al. [20] can beused but are also quite slow and usually require knowledge of thewind turbine wake. The third and most prevalent method is theBEM method, which is very fast a reasonably accurate [3,17,17] andis employed for this research. The automated structural layout witha Bernoulli beam model has been chosen due to its fast computa-tional speed opposed to the Finite Element Method (FEM) pre-sented by Jureczko et al. [7] or Chen et al. [21]. The model takesadvantage of the real laminate properties of the structure and canprovide a more realistic mass and stiffness prediction opposed tothe structural model of Benini and Toffolo [9] or Young andWu [11].The polar data needed for the BEM is created with Xfoil [22] likeshown in other publications in the field [6,23].

The paper combines these theories and applies them in multi-disciplinary, multi-objective optimisation to an industrial scalewind turbine to achieve the afore mentioned research objective.Opposed to other design system presented in the literature asimultaneous relative parameterisation of aerofoils and the bladefunctions allows to exploit the effects of both design areas withoutbeing limited to one of them. The structural model at the same timeshould guarantee the structural feasibility, which is consideredanother novelty. The design strategy can hence give a more holisticindication of what kind of aerofoils properties are needed at whichspan wise position and how important the actual blade functionsare. However the tool cannot replace the designer as in the absenceof a loads base turbine cost model the selection of a compromisedesign is to some extend always subjective.

Table 1Target functions and hard constraints.

Target functions Hard constraints

TFAEP ¼ AEPini/AEP Steady chord reduction outboard of chordmax

TFMass ¼ mass/massini Steady absolute thickness reductionTFThrust ¼ thrust/thrustini Steady relative thickness reduction

Maximum chord < 4 mMaximum tip speed < 74 m/sNo exceedance of stall angle

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515508

3. Description of the CoBOLDT

The current optimisation package CoBOLDT features sevenmodules that provide the functionality for optimisation, parame-terisation, geometry generation, performance evaluation andstructural layout as presented in the flow chart in Fig. 1. Before theoptimisation process can be initialised the user needs to specify atleast two target functions that are minimised as well as for everyvariable the initial value, initial step size and minimum andmaximum ranges. After the optimisation process is invoked adesign vector is created and fed into the first parameterisationmodule.

Rather than an absolute parameterisation of blade functions weimplemented a relative parameterisation that depends on nor-malised initial blade functions. The advantage of the relativeparameterisation is that more complex features, like suddenchanges in the curvature at the hub or the tip of the blade, can becaptured with a lower number of design variables. The new func-tion is still similar to the initial blade function but simultaneously areduction of the design space dimensionality is achieved. Thedrawback, that not every blade can be reproduced with this tech-nique is compensated by the possibility to replace the initial designfor a restart run. For each function four variables are specifiedwhich control the shape of two tangentially connected cubicsplines. The first two specify the X and Y position of the splineconnection point whilst the remaining two define the slope at theconnection point (a1) and the end point at the tip (a2). The slope atthe root side is set to zero to prevent changes of the blade rootdiameter. If the spline curve has values below zero they are sub-tracted from the initial blade function or added if values are posi-tive. An example of the method and the effect on the bladegeometry is depicted in Fig. 2.

After several geometrical constraint checks (see Table 1) havesuccessfully been passed to secure transportation and turbine noiselevel, the perturbed blade functions are accepted and the aerofoilparameterisation routine starts. The spanning aerofoil family that isused to create the blade is normalised to a chord length of one andcomprises 8 profiles ranging from 100 percent relative thickness atthe circular root section to the thinnest aerofoil at the tip. Toreshape the aerofoils two-dimensional Free FormDeformation (2D-FFD) is used which is a method originating from computer graphicsthat has received a lot of attention in aerospace parameterisation[24e27].

Fig. 2. Spline parameteris

As opposed to aerofoil generationwith Bezier Splines [5,6,28,29]it has been integrated due to the relative nature of parameterisationand the capability to parametrise a design with a small number ofparameters whilst preserving the topology characteristics of thebaseline shape. The blade root and tip are not supposed to bechanged and therefore aerofoils at this location are excluded in thepresented approach. For every profile eight control points aredefined as shown in Fig. 3. The number of control points can beadjusted as appropriate to fit the parameterisation aim. The firstand the last control point on the suction and pressure side cannotbe distorted to maintain the leading and trailing edge positions andprevent a change of the chord length. The remaining control pointscan each be moved with two degrees of freedom along andperpendicular to the chord. To reduce the order of dimensionalitywe have chosen to use the same set of parameters for every aerofoilsince parameters for control point movement perpendicular to thechord are scaled with the relative thickness. Hence perturbations ofthick profiles are larger than those for thin profiles and smoothgeneration of the loft surface without the problem of long-wavedbuckling is ensured.

Following the second parameterisation module the final blade isbuilt from the blade functions and the aerofoils in the geometrygeneration module of CoBOLDT. The resulting geometrical bladedescription list and the triangulated surface are the basis for thestatic BEM and the structural calculation respectively. In the laststage of this module, when all corrections of the aerofoil shape havebeen done to secure manufacturability of the whole blade (e.g.correction for minimal trailing edge thicknesses), equidistant sec-tions are considered to evaluate the aerodynamic performance.

For this purpose, Xfoil [22] was chosen, because an initialexploration confirmed its fast execution and accurate prediction ofaerodynamic coefficients for thin aerofoils. The calculation is

ation of blade chord.

Fig. 4. 360 degree lift coefficients at Re ¼ 3 Mio. for the NR41.

Fig. 3. 2D-FFD parameterisation of aerofoils.

Table 2CoBOLDT Parameters.

Parameter Initial value Initial step size Min range Max range

x-chord 0.5 0.005 0.1 0.9y-chord 0 0.002 �0.2 0.2a1-chord 0 0.002 �0.2 0.2a2-chord 0 0.005 �0.5 0.5

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515 509

limited to profiles thinner than 35% relative thickness. The codewas extended to include the sequential calculation of the aerofoilproperties from �10 to 20� angle of attack (AoA) at a fixed con-servative Reynolds number of 3 million. The decision to fix theReynolds number has been taken because at this point in time theinformation about the rotational speed, to calculate a Reynoldsnumber for a given blade, is not yet available. Each polar is thencalculated twice with one design case using the natural transitionand the other run being tripped at 1% chord on the pressure and thesuction side. The actual polar is established with a user-definedmixing ratio (currently 50:50) of the two cases to account for sur-face roughness due to dirt and surface imperfections from pro-duction. The mixing of polars in this case is preferred over the useof the parameter Ncrit in Xfoil as there is no information on how torelate turbulence magnitude to Ncrit values for long scale atmo-spheric turbulence. Within the Xfoil code an additional sectionwasappended which takes care of the extrapolation of the �10 to 20AoA polar to the full 360� polar needed by the BEM code. The al-gorithm is an industry standard approach and was adopted fromthe visual basic code Aerofoil Prep published by NREL [30]. Inprinciple it has 2 components, which are the 360� extrapolationdeveloped by Viterna and Janetzke [31] and Tangler and Kocurek

Fig. 5. Visualisation of a blade section in the structural model.

[32] and the 3D stall correction by Du and Selig [33] and Eggerset al. [34] for lift and drag coefficients. Several publications describethe successful application of this methodology [5,6,23]. For the360� extrapolation, the linear part of the lift curve needs to beconsidered that will serve as input for a trigonometric functionfitting for lift, drag and moment coefficient. The actual extrapola-tion uses the information of the thin plate theory [31] with theassociated limitations for thicker aerofoils. The 3D stall correctiondepends on the radial position, the chord length, the rotationalspeed and the wind velocity of each profile on the rotor which isestimated from the turbine operation at maximum tip speed. It canbe shown that the inboard profiles exhibit a stronger threedimensional behaviour than the profiles near the blade tip. This isdue to strong coriolis and centrifugal forces as well as a big varia-tion of dynamic pressure in this area [35], that effectively delay thestall and provide for higher lift and drag coefficients. An example ofthe resulting 360� lift coefficient (Cl) plots for five selected radialstations from 40 to 100 percent relative blade length (r/R) is shownin Fig. 4.

In the next module the actual evaluation of the turbine perfor-mance is conducted using the static BEM theory [36] whereas themethod of calculating the axial and rotational induction factors hasbeen adopted from Hansen [37]. The sequence of calculation andmore details of the setup can be found in Fischer et al. [17]. Theresults of the aerodynamic module are the value of the annualenergy production along with the rotor thrust at rated power.Moreover, section moments at discrete radii in flapwise andedgewise directions are derived and prepared for use in the lastmodule of CoBOLDT that calculates the mass and the stiffness of thecurrent blade design.

The mentioned mass and the stiffness estimation module arecompletely automated. In addition to the section moments asexternal loads it needs the blade contour at discrete radial stations

x-thick 0.5 0.005 0.1 0.9y-thick 0 0.002 �0.2 0.2a1-thick 0 0.002 �0.2 0.2a2-thick 0 0.005 �0.5 0.53-X 0 0.002 �0.1 0.13-Y 0 0.002 �0.1 0.14-X 0 0.002 �0.1 0.14-Y 0 0.002 �0.1 0.15-X 0 0.002 �0.1 0.15-Y 0 0.002 �0.1 0.16-X 0 0.002 �0.1 0.16-Y 0 0.002 �0.1 0.1

Fig. 6. Optimisation history.

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515510

as well as an initial internal structure definition and initial laminatelayout of the load carrying structure. The initial laminate layoutcontains the information which zones should be automaticallysized (e.g. main girder and aft girder see Fig. 5) and which shouldstay untouched. To get the internal loads the blade is modelled as aBernoulli beamwith the actual laminate layout and blade geometryserving as input to calculate the beam stiffnesses in flap andedgewise directions corresponding to Librescu and Song [38]. Thestrains are evaluated on the blade skin at discrete radii andcircumference positions out of the external loads and stiffnesses inflapwise and edgewise directions [38]. In the next step, for eachdiscrete position of the skin the calculated strains are divided by apreviously defined allowed design strain. The strain ratio is used for

Fig. 7. Objective fu

the internal structural sizing, which will add (strain ratio > 1) orremove layers (strain ratio < 1) in the sizing zone until the ratio isequal to one and therefore a minimum weight is obtained. Theinitial layout data are then updatedwith new thicknesses to reach afaster convergence next time the structural sizing module is star-ted. The blade mass as the final target function is then providedback to the global optimisation routine. In the current version ofCoBOLDT no parameters from the structural layout (e.g. the posi-tion or width of the girders) are defined as parameters for theglobal optimisation, however the option is considered for a futurerelease of CoBOLDT.

4. Design case NR41 with CoBOLDT

The design case chosen to demonstrate the optimisation capa-bilities of CoBOLDT is based on a generic blade (NR41) for an 82 mdiameter wind turbine. The blade manually designed for thespecifications of a 1.5 MW pitch controlled wind turbine and hasbeen described in a paper by Fischer et al. [13]. The initial aerofoilseries as been designed by Claas-Hinrik Rohardt at the DeutschesZentrums fr Luft- und Raumfahrt in Braunschweig and is para-metrised with 8 variables, namely 3-X, 3-Y, 4-X, 4-Y, 5-X, 5-Y, 6-Xand 6-Y (see Fig. 3). The parameters are similar for each bladesection to keep aerofoils compatibility. The functions for chord andthe absolute thickness will be altered using four parameters foreach. Table 2 explains the parameterisation setup of the mastercode according to Figs. 2 and 3 in more detail.

The steady reduction of chord as well as of the absolute andrelative thickness is required by the utilized BEM code to distributethe spanning profile correctly. The geometrical requirement of themaximum chord being below 4 m stems from the road trans-portation for onshore blades underneath bridges, whereas the lasttwo constraints are needed to guarantee a certain noise emission innormal operation. During optimisation the blade design is checkedto satisfy all the hard constraints. The target functions are AEP at anIEC Class 3 wind sitewith a probability of wind following a Rayleigh

nction space.

Fig. 8. Full dataset in parallel coordinates [42].

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515 511

distribution (mean wind 7.5 m/s), the blade mass and the thrust ofthe rotor. The maximum root bending is not considered since itheavily correlates with the blade mass. A summary of the optimi-sation objective functions is shown in Table 1. The run is performedon a 32-core Linux cluster with one slave initialised on every2.4 GHz core. After 78,773 evaluated blade designs and 2717 opti-misation iterations the run was manually stopped. The optimisa-tion took 84 h of wall clock time.

5. Post optimisation analysis of design case NR41

The optimisation strategies (see Ref. [13]) over the number ofoptimisation iterations are presented in Fig. 6. It shows that 23

Fig. 9. Extreme point designs in

intensification moves (green cross) were carried out which lead tothe exploration of five regions with fast optimisation progress andhence low number of unsuccessful iterations (red cross). The othertwo available search strategies, namely diversification and step sizereduction, were not performed at all. This is mainly due to tworeasons that the optimisation process was not finished by the timeit wasmanually stopped. The optimiser was still able to find enoughPareto solution and the unsuccessful iteration counter (red cross)never reached the threshold necessary to perform a diversificationor step size reduction move. The obtained Pareto surface accordingto the objectives in Table 1 is shown in Fig. 7 and proves the effi-ciency of MOTS to explore complex and fragmented objectivefunction spaces. Especially the relation of AEP and thrust is worth

parallel coordinates [42].

Table

3Ex

trem

epointan

dco

mpromisedesignparam

eters.

x-ch

ord

y-ch

ord

a1-chord

a2-chord

x-thick

y-thick

a1-thick

a2-thick

3-X

3-Y

4-X

4-Y

5-X

5-Y

6-X

6-Y

TFAEP

TFMass

TFTh

rust

AEP

0.26

50�0

.002

0.08

800.04

000.60

00�0

.002

0.00

80�0

.110

�0.006

�0.048

�0.004

�0.056

0.00

60�0

.008

�0.054

�0.052

0.99

191.00

280.97

77Mass

0.37

50�0

.008

�0.038

0.11

000.60

000.00

00�0

.008

�0.095

�0.006

�0.026

0.01

00�0

.046

0.00

60�0

.014

�0.032

�0.040

0.99

780.99

090.96

32Th

rust

0.33

50�0

.006

�0.038

0.11

500.60

50�0

.002

�0.010

�0.085

�0.006

�0.028

0.01

00�0

.048

0.00

20�0

.014

�0.030

�0.048

0.99

780.99

630.95

73Com

p0.25

50�0

.002

�0.094

0.04

500.60

50�0

.002

0.01

00�0

.100

�0.004

�0.048

�0.004

�0.056

0.00

00�0

.010

�0.054

�0.050

0.99

270.99

930.96

41

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515512

mentioning in that context, as the projection reveals a discontinuityin the concave area of the projected Pareto front, which couldhardly be explored by gradient-based optimisers. The samediscontinuity can also be found in the AEP and mass related Paretoset projection, even though the front exhibits a rather convexbehaviour.

The extreme point design for each objective function has beeninvestigated further to link the geometrical properties of the designdefined by the parameters to the physics that lead to improvedperformance. A powerful tool in the post optimisation analysis isthe application of parallel coordinates in the design space as pub-lished by Kipouros et al. [39] and Inselberg [40,41]. The completedataset with 516 Pareto points is used as the basis for the analysis. Itwas segmented into three clusters using the Euclidean distance as ametric in the parameter space as visualised in Fig. 8. The methodbuilds the hierarchy starting from the individual blades by mergingclusters that are geometrically similar, until the required number ofclusters is obtained. The AEP discontinuity mentioned in the pre-vious section is clearly visible and is formed mainly by the red andthe blue cluster. To find the blade designs with the biggestimprovement for each of the three target functions, namely theextreme point designs (EPDs), we use the slider to highlight a smallcluster (up to approx. 5) of very similar extreme point design inFig. 9. The AEP EPDs are marked in dark green as well the mass andthrust EPDs in orange and blue respectively. Table 3 underneathshows the designs with the lowest value for each objectivefunction.

The comparison in Fig. 9 reveals that:

1. Mass and thrust EPD exhibit a high correlation of parameters,except for x-chord, y-chord, y-thick and 6-y

2. The biggest difference between mass and thrust EPD occurs fory-thick, which translates to a bigger absolute thickness of thebending beam for the design with lower mass

3. Parameters y-thick of all EPDs only differ by one step size. Thispoints to a poor choice of the initial step size for this variable.

4. Huge difference for most parameters between AEP EPD and themass and thrust EPDs

5. Bigger chord (y-chord) is associated with a high axial inductionfactor and therefore a high AEP

In terms of the design driving variables for the profile param-eterisation, 3-y, 4-x, 5-y and 6-x can be identified as most influ-ential. Since all parametrised aerofoils are changed with the sameparameters, a closer look to one of the spanning aerofoils revealsthe design trend for the whole aerofoil family. Fig. 10 shows thatfrom the initial aerofoil designs all EPDs show a considerablereduction in aerofoil camber with the associated lower down-stream flow angle. Again, AEP as opposed to mass and thrust canbe identified with some unique properties. Firstly, the AEP EPDexhibits the lowest camber of all aerofoils. Secondly, the pressure

Fig. 10. Aerofoil design trend.

Fig. 11. Lift and drag coefficients (r/R ¼ 70%).

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515 513

recovery region at the suction side shows a comparably flat shape,which proved in a subsequent CFD calculation (not included in thepaper) to reduce the tendency for stall at high angles of attack(AoA).

To calculate the polars the blade is cut at specified radial sec-tions and therefore the relative thickness can change. In Fig. 11 theaerodynamic coefficients that correspond to profiles at (r/R ¼ 70%)are considered, which translate to a relative thicknesses of 18.6%(Initial), 20.9% (AEP), 22.3% (Mass) and 20.8% (Thrust). It is obviousthat the thin 18.6% profile exhibits very low drag at low AoA. Be-sides this advantage the other designs e although they are muchthicker e can show a 10% better L/D-ratio in the design range of 6e8� AoA. Fig. 12, which shows the L/D distribution at partial loadingwith a wind velocity of 7.5 m/s is underlining the superiority of thenew profile designs. Fig. 13 depicts the AoA distribution at fivedistinct operational wind speeds for the compromise design. For 7e8 m/s the turbine is still at partial loading with constant tip speedratio and variable tip speed. The local AoA’s are below the value atwhich maximum L/D is obtained (thick red curve) and well belowthe local stall angles (thick black curve). At 9 m/s the maximum tipspeed of 74 m/s is reached, the turbine increases the countermoment at the generator to increase power output further and thelocal angle of attack rises. At 10 m/s the turbine is just before ratedpower and here the local AoA coincides with the curve for thehighest L/D. At 11 m/s the rated power of 1500 kW is fed into thegrid and the turbine is in pitching mode to regulate the poweroutput the this value.

Fig. 12. L/D distribu

The comparison in terms of the objective functions can befound in Table 3. The increase in L/D for the profile family trans-lates to a higher AEP value of the AEP EPD (þ0.8%) and the massand thrust EPDs (þ0.2%). Additionally, the thrust of the thrust EPDand mass EPD is considerably reduced by 4.3% and 3.7%. The dif-ference in blade mass between initial and mass EPD is found tobe 0.9%.

If the normalised variance (absolute variance over the mean) ofthe design variables in the Pareto set is considered (see Fig. 14) therelative impact of parameters on the design problem can bedetermined. In this case the normalised variation is used to allowfor comparison of parameters with different ranges. From the barchart it is obvious that the variance of x-chord, a1-chord, a1-thickand 3-x accounts for a major proportion of the total variability.Nevertheless, y-thick which was found to have a big influence onmass, has a very low normalised variance. The reason for thisproblem is the big initial step size. Only 3 distinct values are presentin the Pareto range for the parameter (see Fig. 8) and the optimiserhad no chance to reduce its step size due to the cancellation of theoptimisation run prior to the first step size reduction. At this pointanother approach to step size reduction with MOTS should besuggested.

1. After a predefined number of optimisation iterations, when agood approximation of the Pareto set is available, determinemaximum and minimum values (Pareto range) of eachparameter in the Pareto set.

tion at 7.5 m/s.

Fig. 13. AoA distribution for 7e11 m/s for the compromise design.

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515514

2. Reduce or increase the step size to fit a predefined number ofdesigns in the Pareto range.

3. After the application of this method the normalised variation ofeach parameter really reflects its relative importance (as thevariance is not skewed by different step sizes) and parameterswith low importance might be used to reduce the dimension-ality of the optimisation problem.

The described analysis of the design driving parameters andtheir influencemight be a goodway to pro-actively design blades tocomply with the rules found. However in a commercial context thequestion of choosing a good compromise design is of high impor-tance. For this purpose it is sensible to pick the design with thelowest cost of energy e as a composite target e after the multi-objective optimisation. The total cost analysis considers thechanges of component cost due to the different load level as well asthe income from the energy produced. Since the actual cost modelis confidential it cannot be disclosed with this paper. However fromTable 3 it can be noted that the compromise design inherits most ofits features from AEP EPD.

Fig. 14. Normalised variance of the Pareto Set.

6. Conclusions

This paper describes the effect of changes in blade and aerofoilgeometry on turbine performance for a horizontal axis wind tur-bine blade using the Computational Blade Optimisation and LoadDeflation Tool. The design case that is presented is based on anindustrial scale wind turbine with a rotor diameter of 82 m and arated power of 1.5 MW. The three target functions that areconsidered are maximisation of the annual energy production,minimisation of the blade mass as well as minimization of the rotorthrust. They have been chosen since there are turbine properties inthe control of the turbine designer with a high impact on cost ofenergy. In terms of the parameterisation 16 variables have beenused to alter the blade geometry relative to the datum design. Eightparameters are defined to change the blade chord and the bladeabsolute thickness (4 parameters each) whereas 8 parameters serveas input for the aerofoil parameterisation.

Post optimisation analysis reveals that for the compromisedesign all objectives could be improved. The geometrical designdrivers that lead to the improvements could be studied with a se-lection of three extreme point designs chosen from the associatedclusters in a parallel coordinate analysis. It was found that:

1. AEP extreme point design is very different from the extremepoint designs of mass and thrust

2. Reduction in camber of the aerofoils lead to an enhancedL/D-ratio in the design range

3. Reduction in blade chord resulted in a lower blade thrust4. Increased relative profile thickness allowed for the reduction of

blade mass5. Close before rated power the compromise design showed an

AoA distribution that allows to operate the aerofoils at the localmaximum L/D-ratio

Finally it has been shown that the normalised variation of pa-rameters in the Pareto set (to find themost energetic parameters) isskewed due to the initial step size value of parameters prior to thefirst step size reduction. Tomitigate this effect a novel approach hasbeen suggested which scales the parameters to a set Pareto rangeafter a certain number of optimisation steps.

To further improve the CoBOLDT optimisation package theimplementation of a multi-dimensional surrogate model and the

G.R. Fischer et al. / Renewable Energy 62 (2014) 506e515 515

development of a restart model based on relative parameterisationis envisaged. Also the stationary BEM solver is due to be replacedwith a transient solver to account for aero-elastic effects duringturbine operation.

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