Optimal Rotors for Distributed Wind Turbines

Curran Crawford∗ and Luke Stack†

University of Victoria, Victoria, BC, Canada

Small wind turbines deployed for distributed generation require careful design to max-imize their effectiveness, both economically and from an energy payback perspective. Therotors of these machines are critical to their performance, however systematic optimiza-tion taking into account the actual operating profile of the rotor and the application oflessons from larger scale machines are currently lacking. This paper begins with a recog-nition that distributed wind turbines must be sited in adequate wind resources to be aviable proposition. A design optimization procedure is presented next, taking into accountshape definition, structural and Low Frequency Noise (LFN) constraints, and specificallytargeting the design of a rotor for a specific Permanent Magnet Generator (PMG) withand without active speed control and associated Power Electronics (PE). Variations of theprocedure are applied to design optimal rotors for commercial 300 W, 600 W and 6 kWmachines. Experimental test results are also compared to performance predictions.

Nomenclature

c Chord lengthCP Power coefficientEann Annual energy yield

Nrot, Ω Rotor rotation speedRe Reynolds numbers Blade section position

S, Stip Blade lengthλ Tip speed ratioτ Torque

I. Introduction

Steadily increasing energy costs and a desire by individual consumers to defray these costs has motivated aresurgent interest in wind turbines at the kW scale. These small-scale machines are suitable for residential

and small commercial applications, either for off-grid sites or in conjunction with net-metering installations.While it is likely that MW scale machines will continue to provide the most cost-effective form of windpower, small-scale machines have a role to play when properly design, manufactured, sited and operatedreliably. The distributed generation provided by these small wind turbines will likely be supplemented byother residential-scale renewables such as Photovoltaic (PV) and thermal solar and micro Combined Heatand Power (CHP).

The siting of these small wind turbines is particularly critical. The logarithmic growth of the boundarylayer and turbulence created by surrounding buildings and other obstacles make it a challenge to yieldsignificant power. A Computational Fluid Dynamics (CFD) study1 of simple building arrays in West Londonhighlighted the minimal resource available if the turbines are placed at rooftop height (this assumes planningrestrictions limit tower height). The urban wind environment has also been examined in more detail forEaling, UK, where tower-mounted turbines were studied2 and found to have long payback periods owingto the low mean wind speed. Another study3 of building mounted machines indicates positive energy andfinancial payback is possible, provided the machines are well built and properly located. A UK-wide micro-wind study4 found that in suitable locations, micro-wind turbines could generate enough power to offsettheir carbon emissions within a few months or years. Unfortunately, large urban locations would be unlikelyto achieve these paybacks, and in all cases only the most durable, efficient and low maintenance turbineswould be effective. Other authors have studied building designs specifically tailored to augment flow pastmounted turbines.5

∗Assistant Professor, Member AIAA. University of Victoria, Department of Mechanical Engineering, PO Box 3055 STN CSC,Victoria, BC, Canada V8W 3P6. E-mail: curranc@uvic.ca†Undergraduate Researcher. University of Victoria, Department of Mechanical Engineering.

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47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-1546

Copyright © 2009 by Curran Crawford. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Many authors note that tower-mounted turbines will invariably be more effective than building-mountedmachines, leading to efforts to determine an optimal tower height.6 Most small-scale feasibility studies havebeen UK-centric, illustrating the need for further research into siting and wind resource of micro turbines.This is especially in the Canadian context with more rural dwellings away from built-up areas.7

The present work dealing with the design of rotors for these small machines therefore proceeds with arecognition of the challenges presented by the resource itself, but with sufficient evidence of utility in theproper locations. The wind turbine industry’s steady march towards ever larger machines has left only smallcompanies with limited resources to pursue kW scale machines. The lessons learnt at the large scale havenot yet percolated downwards to the smaller scale.8 Certification of small scale machines is also much lessrefined and only sought by a few manufactures. Even the standards9,10 themselves, relevant to these smallermachines, are quite recent. Apart from safety certification, methodical testing and verification of energy yieldis often not conducted, however recognition of the need for accurate consumer data is motivating efforts torigorously quantify performance.11

Unlike large wind turbines that can afford the complexities of active yaw and blade pitch control, smallwind turbines are extremely cost sensitive. Operational reliability is also paramount, motivating the mostrobust designs possible. Direct drive Permanent Magnet Generators (PMGs) are typically employed withPower Electronics (PE) as effective solutions at the small scale. The complexity of the power electronicssystem12 is dependent on the application, be it for battery charging or grid-tie. At the kW scale, the fullpower of the generator is typically passed through the PE; there is therefore the opportunity for speed controlby varying the torque of the generator with active PE control. One manufacturer has suggested utilizingthis control not only for power, but also load control to minimize blade fatigue.13 To maximize energy yield,reducing the cogging torque of the PMG is critical,14 to enable passive start-up at low wind speeds whenminimal aerodynamic torque is available.

Vertical Axis Wind Turbines (VAWTs) have received renewed attention for small machines,15,16 howeverthe current study deals with Horizontal Axis Wind Turbines (HAWTs) only. The omni-directional natureof VAWTs may afford them an advantage over HAWTs in highly turbulent conditions directly adjacent tobuildings, however without pitchable blades, the fundamental power capture ability of VAWTs is limitedin cleaner airflows. Both machine types have merit in pursuing, but are quite different in their analysesrequiring a choice to made for detailed study. The present study is restricted in scope to the optimal designof the HAWT blades themselves, defined by their aerodynamic shape, structural composition and controlstrategy (i.e. rotor torque control, passive pitching/twisting, etc.). Specific emphasis is given to properlymatching the blade design to the generator, to maximize energy yield. §II lays out the approach taken tooptimizing the rotor, followed by design study results in §III and final conclusions in §IV.

II. Design Approach

The ultimate goal of a “black-box” optimization tool is presently unattainable, owing to computationalcomplexity and the requirement for some interventions to guide the process. To tackle the problem of syn-thesizing an optimal rotor, a design study approach is used together with a stepwise numerical optimizationof the design. This section will describe the elements of the setup to be used for the rotor design studies,from the parameterization of the design through the various constraints and optimization procedures.

A. Blade Parameterisation and Analysis

The primary tool used for performance analysis is ExcelBEM,17 a hybrid Matlab–C–Excel program. It incor-porates steady-state and rigid-body dynamic aerodynamic analysis, including blade structural calculations.The aerodynamic calculations are a modified Blade Element Momentum (BEM) method incorporating cor-rections for coning and yawed flow, and including centrifugal stall delay and swept flow corrections to the2D airfoil lift/drag curves. Dynamic inflow and stall models are also included, as are tower wake models.The structural calculations include a tool to compute sectional properties of composite structural layups.

The shape of the blade is defined using Bezier curves, exploiting their convex-hull property to yieldsmooth chord and twist profiles. A parabolic tip chord profile is used to minimize tip noise. The airfoilthickness and chordwise pitch axis location are also controlled by Bezier curve profiles. These distributionsover the span are controlled by a set of Design Variables (DVs) defined fractionally with respect to the blade

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span Stip. Constraints are placed on the chord and twist to reflect geometric interface and manufacturingrealities. Stip is also an optional DV. A sample blade shape is shown in Fig. 1.

0 0.2 0.4 0.6-0.05

00.050.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.20.4

s (m)

c (m)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.802040

twist

(deg

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.802040

s (m)

thk, p

itchA

xis

thkpitchAxis

(a)

-0.5

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00.2

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(b)

Figure 1: Blade shape definition

The choices of airfoils are treated as parameters in the design studies. The Re ranges of small windturbines are typically well below the standard test ranges for large turbines18 and aircraft of 106, so onlya limited suitable dataset is available.19,20 Where possible, experimental data is used, and where it is not,XFoil21 is used for analysis just into stall. Standard flat-plate extensions are used to provide deep stallbehavior.

-0.25 -0.2 -0.15 -0.1 -0.05 0

-0.08

-0.06

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-0.02

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0.08

0.1

Figure 2: Blade section layup

The structural layups considered consist of a foam core and thermoplastic-fibreglass-carbon skins. Anexample section is shown in Fig. 2. The thickness of the skins may vary over the span, and also in chordwiseextent, as determined by a second set of DVs. The DVs are defined to reflect control over layers of materialplaced in the mold. For manufacturing simplicity, the layup is defined by 1 to 4 layers of material cut inrectangular strips. The width and length of the strips are varied to satisfy structural requirements.

B. Generator Matching

The generator and PE electrical designs are treated as given for the purposes of rotor optimization. Futurestudies may consider coupled electromechanical optimization. Two cases are considered in the present work:

• Passive PE: the generator is defined by a single mechanical torque/rotation speed characteristic andassociated electrical power. This configuration is typically used for battery charging applications withrelatively simple rectifying circuits.

• Active PE: the generator is defined by a 3D surface of electrical power, parameterized by mechanicaltorque and rotor speed. This approach uses PE to vary the load placed on the rotor by the generator,and hence can operate across a range of torques at a given rotor speed, with associated electrical lossesaccruing from the PE and generator operation at partial load. These more active PE are justified ongrid-tie or advanced battery applications, with attendant cost implications.

It should be appreciated that these characteristics are not only a function of the generator itself, but also ofthe coupled PE. Therefore, different characteristics may be required for say a 24 V or 48 V battery chargingdesign.

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In the case of a passive PE system, the steady-state calculations can algorithmically match aerodynamicand generator torque at each wind speed (both varying with rotor speed), to yield a steady operating point.Figure 3 illustrates this matching process and the steady operation points found for different wind speeds.Note that this is a badly matched example, with an underpowered generator, highlighting the need to

200 400 600 800 1000 1200 1400 1600 1800 20000

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50

Nrot (RPM)

τ (Nm

)

Generatoraero

Figure 3: Torque matching algorithm

specifically match rotor to generator over the wind speed range. The net power output is also determinedfrom the generator characteristic which defines a varying power output with generator speed to reflectinefficiencies in the PE and generator. This type of system must naturally stall the rotor in high winds, orincorporate a pitching or yawing mechanism to limit power. The latter is not considered here, as it tendsto be very noisy. Passive pitching mechanisms (Pitch to Stall (PTS)) are used for the smaller rotors in thecurrent study, operated by centrifugal forces.

For an active PE system, an optimal operating point is determined algorithmically by varying rotor speedat each wind speed to maximize electrical power output. For a small wind turbine in particular, this willyield a more optimal control target for the controller, by considering the varying Re effects. This is lostby simply specifying a λop value invariant with wind speed, as is commonly done. Once rated power isreached, a Variable Speed Stall (VSS) solution is obtained by determining the rotor speed required to stallthe rotor and limit power. The advantages of this configuration are avoidance of a pitching mechanism andmaximization of power output, at the expense of the PE and controller.

In both cases, an initial attempt was made with the optimizer to include the generator without addingextra DVs to the optimization formulation. The torque matching and optimal solution algorithms in Ex-celBEM were used to compute optimal rotor speeds at each design iterate. This approach proved impractical,as hundreds of complete BEM solutions were required at each step. Combined with finite differencing, thecomputational expense was overwhelming. An alternative approach was adopted later by adding extra DVscorresponding to 15–20 wind speeds, each DV controlling the corresponding rotor speed. This approach wasfound to be tractable.

C. Structural and Dynamic Constraints

Two design criteria were used in the current work.

• Simulated loading: ExcelBEM is used to compute loads at extreme storm and rated operational con-ditions. These load conditions are typically used in design studies.

• Simplified loading: The IEC 61400-2 specifies for certification purposes simplified root bending momentand tensile loading formula for a number of fatigue and limit load cases (e.g. maximum yaw rate,

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extreme storm). As these standards only provide root section loads, ExcelBEM is used to computeloads along the blade at the corresponding condition, and the loads are then scaled to match the rootsection loads of the IEC standards.

Material and load safety factors from the IEC 61400-2 standard are applied throughout. The stresses in theblade materials are checked for compressive and tensile failure, using a maximum fiber stress/strain theoryapproach. Buckling is not included at this point, assuming a good core-skin bond.

A number of dynamic issues are of concern for small wind turbine rotor design, including startup, freeyaw behavior, vibration modes (Campbell diagram) and performance in unsteady winds. Only startup isincluded in the optimization work presented here, by requiring enough steady-state aerodynamic torque τaero

to be available at the cut-in wind speed with the rotor at a standstill to overcome the generator coggingtorque τgen,cogging. Two methods were used in the optimization formulation:

• A simple constraint was added requiring τgen,cogging − τaero < 0 at a specified Vcut−in,spec, to besatisfied by adjusting existing shape and control DV.

• The same constraint was added requiring τgen,cogging − τaero < 0 at Vcut−in, but Vcut−in was added tothe list of DVs. This removed Vcut−in,spec as a parameter, better allowing the optimizer to focus onthe real objective of maximizing Eann and avoiding infeasible cogging torque constraints.

D. Design Procedure

Wind turbine design is non-trivial, even for large manufactures. A myriad of competing aerodynamic,structural, control and cost issues compete for governance of the design. Modern variable-speed, Pitchto Fine (PTF) machines are in fact relatively simple cases, as aerodynamic blade design can focus onperformance at an optimal λopt. Small wind turbines however, when attempting to passively match generatorand aerodynamic characteristics are more complicated, as no analytic formulation is available.22

In the realm of small wind turbine optimization, previous workers have looked at solidity and blade num-ber effects.23 Others have used stochastic algorithms, either differential evolution24 or genetic algorithms25

to determine optimal chord/twist distributions. The latter study trivially included airfoil choice, as a mixeddiscrete/continous algorithm was used. The former study, in addition to chord and twist distributions,included λopt and dynamic start-up time as a DV and constraint respectively.

The present study employs an Sequential Quadratic Programming (SQP) algorithm from Matlab as theoptimization tool. Finite differencing is used to compute gradients of objective and constraint functions; thestep size was carefully chosen to avoid roundoff or truncation errors. The SQP algorithm was used in concertwith parameter sensitivity studies. This approach efficiently and interactively explores the design space in astepwise fashion, avoiding the inefficiencies of stochastic algorithms. The steps followed are:

1. Pick airfoil set.

2. Optimize chord and twist for CP at a given λopt yielding an initial rotor, using both analytic equationsand numerical fitting of the chord and twist parameterizations using Matlab’s lsqnonlin functiona.

3. Optimize directly for Eann by simulating steady-state performance over the entire wind speed range,including any tip-speed or tower thrust constraints, generator torque matching or active control andpitching blades. The CP optimization yields a baseline design for this full optimization, aiding navi-gation of the design space.

4. Optimize blade structure to minimize mass.

5. Verify dynamic power output performance and Low Frequency Noise (LFN) signature.

For these small rotors, the structure is not as tightly coupled to overall performance, as aeroelastic effectsare limited for the stiff blades. This enables decoupling of the aerodynamic and structural design, althoughfuture efforts will simultaneously optimize blade shape and structure as the airfoil choice and loads areobviously connected to some degree.

Ideally the dynamic power curve would be simulated inside the optimization loop. This is not currentlypossible using the full BEM simulation, due to computation time constraints. An alternative simulation

aA subspace trust-region method based on the interior-reflective Newton method

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Table 1: Nominal rotor designs

Rating (W) Diameter (m) Generator/Control Orientation Airfoil family

300 1.3 passive/pitch upwind E387600 1.7 passive/pitch upwind E387

6000 5.5 active/no pitch downwind NACA 44XX

technique utilizing only the CP –λ curve of the rotor could be used with a 1D turbulent inflow to simulatedynamic performance in future work, as previously utilized for controller design.16 This approach may beexploited in the optimization loop, enabling direct optimization of a dynamic power curve. Unfortunately,this will still be an approximation as effects such as dynamic stall delay and 3D wind fields present in thefull BEM simulation are still ignored.

III. Design Study Results

Three rotors are presented in the present study, as shown in Table 1, representative of a program ofdevelopment of machines from 100 W–8 kW.b Each was designed at a different stage of optimization codedevelopment, starting with the 600 W rotor, followed by the 300 W rotor and the current 6000 W that isongoing development. Only the last was able to employ the full optimization procedure outlined in §D.

A. Airfoil Choice

The airfoils used for each rotor were primarily selected based on availability of experimental data at lowReynolds numbers for the requisite thicknesses. Although not optimal, these airfoils have adequate perfor-mance, and confidence in prediction was valued over chasing a slightly higher L/D with unproven real-worldbehavior. The larger 6 kW rotor employs a range of thickness (9%–20%), while the smaller rotors can usea 9% thickness throughout owing to more benign stuructral loads not requiring the added area moment ofinertia of a thicker section.

B. 600W Machine

As an initial project with a tight time line, generator data was not available at rotor design time. Therefore,optimization could only proceed to the second CP step, with numerical optimization applied directly tomaximizing CP operating on the shape DVs. Rotors were designed for a range of λopt, and it was foundthat λopt = 6 produced a reasonable blade shape (in terms of manufacturing requirements) and an adequateoperating profile. Structural design was carried out as outlined in §C for simulated loads.

The rotor was a retrofit to an existing machine, so there was some rough knowledge of the operatingprofile. Unfortunately, this amounted to rotor RPMs at cut-in and rated wind speeds, and the assumptionthat the pitching mechanism activated just after rated power. With this limited scheduling, the performanceof the rotor was simulated. Figure 4 shows the raw data points from over 280 hrs of field testing, superimposedon the power curve derived from the data according to the IEC 61400-12 standard and the prediction fromExcelBEM using the rough assumed operational profile. The prediction is only somewhat accurate at lowerwind speeds. It is clear that better knowledge of the generator characteristic is required. The pitchingmechanism is clearly not actuating in the same conditions in the simulation and real world test. Moreimportantly, the dynamic effects on the power curve are clearly visible. Although the IEC standard providesa method to compare different machines on an even footing, it is obvious that the optimization shouldconsider dynamic behavior to maximize performance that steady state predictions can only approximate.

C. 300W Machine

The 300 W rotor was designed for a well characterized generator/PE combination. Again, the full optimizerwas not available for directly tackling the Eann optimization problem directly. As noted in §B, the internal

bAs these rotors are being developed as part of a commercial project, units cannot be presented in some cases.

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V

Pele

c

Field data

IEC 61400−12

Prediction

Figure 4: Experimental power curve of 600 W rotor

torque-matching algorithm in ExcelBEM was too slow to include in the optimization process, although if thedesign process was repeated now, the reformulated torque matching in the optimization process itself couldbe employed.

Again, a range of rotors were numerically optimized for varying values of λopt with a CP objective. Post-processing was used to compute Eann for the optimal rotors by calculating the torque-matched solution.Figure 5 shows the optimal rotor performance. Note that the mechanical power available from the rotorvaries with wind speed, hence the different characteristics for each wind speed, overlapped on the generatorcharacteristic. The dots indicate the matched solution. Simulated structural design was carried out asoutlined in §C.

Figure 5: Optimal 300W blade torque-speed relationship without cogging constraint

After this initial rotor, the cogging torque constraint for the generator was added to the optimizationprocess. This produced a rotor with altered shape, and associated altered matched solutions. Note that theconstraint formulation used was for a 3 m/s cut-in. The rotor designed without cogging torque constraintwould not have started until 5 m/s due to its more slender profile and lower standstill torque.

The new rotor was fabricated and tested on Ampair’s VW Golf mounted test rig. Essentially the caris driven at uniform speed in quiescent conditions, and the wind speed, power, RPM, etc. are recorded atsteady state. Figure 7 displays the comparison of experimental and measured electrical power averaged over

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Figure 6: Optimal 300W blade torque-speed relationship with cogging constraint

a number of runs at each speed. The results indicate a reasonable degree of fidelity, considering the coupledgenerator-aerodynamic simulation.

0%

1%

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8%

3 5 7 9 11 13 15

% e

rror

in e

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Figure 7: Comparison of predicted performance and car testing for 300W machine, normalized by nominalpower

D. 6000W Machine

The 6000 W, as the latest rotor to be designed, benefits from the full optimization procedure set out in §D.Unlike the smaller rotors, active speed control is used without a pitching mechanism to optimize and limitpower. The full optimization procedure targeting Eann can therefore be used to take into account the varyingoperational efficiency of the generator across the operational range. The results presented in this paper usean assumed generator characteristic, as dynamometer results were not yet available. The maximum chordwas limited to 0.3 m for manufacturing and overall packaging reasons.

1. Analytic Results

As an initial comparison, the simple analytic equations and shape-fitting routines for CP were applied for arange of λopt. The results are given in Table 2, both for the baseline shapes and altered profiles that simplycapped the chord to 0.3 m. Using the 3D generator map, optimal operational profiles were then computed

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Table 2: Annual energy yield for CP optimized rotors

Eann (kWh)λopt No chord cap 0.3 m chord cap

3 17329 159394 17652 169245 17559 170386 17354 169907 17118 168678 16772 16646

Table 3: Annual energy yield for Eann optimized rotors

Cogging torque constraint (Nm) Eann (kWh) Startup speed (m/s)

0.0 17177 -2.5 17003 2.695.0 16645 3.61

using the routines in ExcelBEM. The optimum is apparently in the range of 5–6, and arbitrarily limitingthe chord has impact on performance.

2. Numerical Optimization

Next, three rotors were designed using the full optimization routine on Eann. Three cogging constraints wereimposed, using the constraint formulation adding a DV for Vcut−in (see §B). The results are tabulated inTable 3.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

s (m)

c (

m)

0 0.5 1 1.5 2 2.5 3−20

0

20

40

twis

t (d

eg

)

0 Nm

2.5 Nm

5 Nm

λ = 6

Figure 8: 6 kW blade profiles

The various blade shapes and operational profiles of these rotors and the λopt = 6 rotor with no chordconstraint rotor are also compared in Figs. 8 and 9. A number of observations can be made from theseresults:

• The complete optimization process does yield rotors with superior performance relative to the simplechord cap of a CP optimized blade.

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0 5 10 15 20 250

0.5

1

U (m/s)

CP

0 5 10 15 20 250

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U (m/s)

Thru

st (N

)

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Ω (

RP

M)

8

0 Nm

2.5 Nm

5 Nm

λ = 6

Figure 9: 6 kW operating curves

• The variations in shape between the various rotors are predominantly in the chord profiles, with someadjustment of twist to maintain optimal angles of attack.

• Increasing the cogging torque constraint leads to higher solidity rotors, with attendant structural andweight repercussions.

• The operational CP values below rated power are marginally different between rotors. The rotationspeeds above rated are more differentiated (lower with higher solidity), leading to increased torquelevels required of the generator and increased thrust on the tower.

Furthermore, it was found that the optimal blade designs do not change for different mean wind speeds. Onlythe operational profiles are altered. Further investigation is required to ascertain the effect of the Weibullshape factor on the results.c

Figure 10 presents the 3D surface generator characteristic used in the optimization. The open circlesindicate the data used to generate the surface.d The operational curves are plotted over the generatorsurface, illustrating the differing optimal operation points with blade design. The maximum torque pointsrequired are also visible. The structure for this blade was then designed with the IEC prescribed loading.

3. Acoustics

The 6000 W rotor is a downwind design. Downwind rotors are self-aligning, eliminating the need for a yawvane. A drawback, in addition to the potential for up-winding in some dynamic cases, is that the blades passthrough the tower wake. The LFN created by these varying loads may be studied by a module in ExcelBEMthat implements a low-frequency compact acoustic noise model26 into the BEM method, with propagationto an observer location.17 The pressure signal is then transformed via Fast Fourier Transform (FFT) toprovide a spectral Sound Pressure Level (SPL), and the overall noise level computed by binning. Windowingand ensemble averaging is used to properly conduct the FFT analysis.

The more standard sources of noise (e.g. trailing edge (TE) laminar and turbulent noise, inflow noise,etc.) can be investigated with other codes, for example NREL’s semi-empirical code.27 Only the LFNcomponent is addressed in the current study, as the other conventional sources are well addressed by properairfoil selection,28 rather than overall blade configuration.

cA shape factor of k = 2.2 was used for the current study.dReal data will be generated by running the generator at varying torque and speeds on a dynamometer.

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(a) Complete generator map (b) Zoomed to operational area

Figure 10: Generator characteristic map

The offset of the hub downwind from the tower and the fixed coning angle of the rotor were determinedfrom a design study based on LFN and structural loads. Figure 11 shows the variation in SPL with coningangle for 4 observer locations at rated conditions. Figure 12 shows the variation in SPL with hub distancefrom the tower for a fixed coning angle for 4 observer locations at rated conditions. Note that sound is adirectional quantity (e.g. blade advancing or retreating from observer, etc.)

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L

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30m DOWN WIND

30m UP WIND

30m TO LEFT

30m TO RIGHT

Figure 11: SPL variation with cone angle at 11 m/s (constant 0.376 m tower to hub distance)

Figure 13 shows the root flapwise bending moment variation with coning angle. These results include thecentrifugal load relief from the structure. Based on these results, a coning angle of 7was deemed acceptable,with a tower offset of 0.38 m. This will limit overhang loads on the tower head, take advantage of bendingmoment relief, and capture some of the SPL reductions available from moving the blades away from thetower.

Swept blades, as installed on the Sweep Twist Adaptive Rotor (STAR)29 and Southwest’s Skystreammachines, offer bend-twist coupling to in principal alleviate loads. They may also ameliorate LFN, as thepressure variation occurs at different times along the blade as each section sweeps through the tower wake,thereby reducing the pressure/loading spike that causes LFN. Within the confines of the BEM method,the aerodynamics of swept blades may only be approximated. The chordwise pitch axis location may bevaried in ExcelBEM to define swept blades, however this will simply alter the temporal relation of assumedindependent blade elements, without simulating tip vortex or spanwise flow effects. More advanced codesbased on lifting line theory are under development by the author to address enable studies in this direction.

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0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650S

PL

[dB

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Distance from tower centre to hub (m)

30m DOWN WIND

30m UP WIND

30m TO LEFT

30m TO RIGHT

Figure 12: SPL variation with distance from tower at 11 m/s (constant 7cone angle)

0

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M_y_

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045678910

Figure 13: Root flapwise bending moment variation with coning angle (deg)

IV. Conclusions and Future Work

Design of small wind turbine rotors demand consideration of both generator characteristics and thevariation in performance with low Reynolds numbers. Both of these characteristics make optimization ofthese small machines a challenging exercise. The present work has demonstrated an approach of incrementaloptimization, and demonstrated the superiority of the approach relative to simple CP optimization at anarbitrary λopt. Ongoing development of this family of rotors will continue to refine the optimization process.Direction inclusion of structural optimization and performance in stochastic inflow (including yaw errors) inthe process are the next key steps to advance the efficacy of these small machines.

Acknowledgments

The authors wish to express their appreciation for funding of this work by Ampair, NSERC and the UVicEngineering Design Office.

References

1Heath, M. A. and Walshe, J. D., “Estimating the Potential Yield of Small Building-Mounted Wind Turbines,” WindEnergy, Jan. 2007, In Press.

2“Ealing Urban Wind Study,” Tech. rep., Centre for Sustainable Energy, Bristol, UK, July 2003.3Dutton, A. G., Halliday, J. A., and Blanch, M. J., “The Feasbility of Building-Mounted/Integrated Wind Turbines

(BUWTs): Achieving Their Potential for Carbon Emission Reductions,” Tech. rep., Energy Research Unit CCLRC, 2005.

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4Phillips, R., Blackmore, P., Anderson, J., Clift, M., Aguilo-Rullan, A., and Pester, S., “Micro-Wind: An Assessment ofthe Likely Effectiveness of Domestic Wind Generation in Urban Environments,” Tech. Rep. 233645a, BRE Trust, Nov. 2007.

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