Analysis of HAWT Performance in Low Winf Site for 4 Domestic Turbines

Mr. Aaron P. Hillier, Student ID 1605238, University of Adelaide, Adelaide, Australia, 5000.

1

Suitability of a Horizontal Axis Wind Turbine (HAWT) to Generate Annual Household Energy Requirements in Littlehampton, S.A

Executive Summary

Members of Climate Action Network Australia have requested Hot Air Consultancies assess the potential of a Horizontal Axis

Wind Turbine (HAWT) system to generate the electrical energy necessary to completely power their home located at

Littlehampton in the Adelaide Hills, South Australia. This requires a minimum of 6695kWhr per year be extracted at this location

from the available wind power potential.

HAWT systems convert fluid mechanical energy present in winds perpendicular to their blades into kinetic energy, the kinetic

energy produced by the turbine blades is then converted into electrical energy by a generator. Despite disadvantages such as

directional dependency resulting in reduced performance in turbulent winds, HAWT systems are still the most efficient means of

harnessing the energy present in a clear wind stream.

Utilising annual wind speed data acquired from a Bureau of Meteorology weather station located 3.3km from Littlehampton at Mt. Barker, numerical and statistical methods were employed to estimate the available wind power potential and provide a preliminary

assessment as to the viability of an HAWT to deliver the required yearly energy. The annual energy produced by 4 domestic

HAWT designs from the available potential was then calculated numerically in order to model likely performance of a HAWT if

installed at this location.

Although installation of a HAWT represents one method of harnessing the clean, renewable energy present in the wind, Hot Air

consultancies does not recommend installation of a HAWT design as means to generate annual household electricity at

Littlehampton. Results indicate that the available wind power potential is insufficient for any HAWT suitable for domestic use to

realistically deliver the annual energy required. Winds at this location are characterised by a predominance of turbulence and lack

both the speed and duration necessary for a HAWT system to meet the requested target. These conditions are likely to result in

sub-optimal and uneconomic performance of any HAWT system operating at this location, regardless of output power rating.

1 Introduction

Wishing to reduce GHG emissions associated with annual household electricity consumption, Hot Air Consultancies

has been approached by members of the Climate Action Network Australia to advise on suitability of a horizontal axis wind turbine (HAWT) to provide their yearly household energy requirements. The property is located at

Littlehampton in the Adelaide Hills, in an area zoned as residential and governed by the Mt. Barker City Council

(Government of South Australia, 2013). Electricity meeting the requirement of an average 2 person household is to be

generated by the turbine.

The growing range of domestic scale wind turbines, defined as systems with rated power less than 100kW (Alternative

Technology Association, 2007), allows increased scope for extraction of clean, renewable power available in the wind and the associated environmental benefits. As availability of the wind resource is the single most important factor

governing HAWT power production, an assessment of wind power potential constitutes an essential prerequisite prior

to installation at any site (Sustainability Victoria, 2010). Although numerous design parameters govern efficiency and rated power output, sufficiency and consistency of winds at the site of operation are absolutely essential for optimum

or economic HAWT performance. A schematic detailing important features of an HAWT is depicted in figure 1 (right,

from: Scottish Government, 2014) alongside images of domestic scale HAWT installations (left, from: Renewable

Devices, 2010).

As small scale domestic wind power is relatively new compared to commercial operations, many local councils are yet

to establish planning guidelines for domestic wind turbines. Until formal regulation is widespread, installation of a domestic HAWT in a residential area will be subject to the jurisdiction, planning laws and sensitivity of the local

council governing the site (Sustainability Victoria, 2010) Further factors to be considered include issues of location

(proximity to owner and/or neighbours dwellings), environmental impacts (noise and effect on wildlife) and economic viability relating to financing, maintenance costs and payback times.

2 Methodology

2.1 Estimation of Available Wind Energy Potential and Implications for HAWT systems.

Wind speed data from the Bureau of Meteorology weather station I.D. 023733 located at Mt. Barker was utilised to

estimate available wind power potential and HAWT performance in Littlehampton. Data consisted of 730 time series


2

Fig. 1. Left: Installation options for Swift Wind Energy 1.5kW HAWT. Centre: Wind tunnel test speed-power curve for Swift

Wind Energy 1.5 kW HAWT. Right: Schematic diagram depicting elements of an HAWT

wind speed magnitudes, recorded twice daily from 1 minute-averaged 1 Hz anemometer measurements taken at a

reference height zr of 10m (Bureau of Meteorology, 2014). The data covers a period T of 1 year. This ensures that important seasonal variation of wind speeds and variances in available wind power potential is included in the

assessment (C.S.I.R.O., 2003). Although the sampling interval between data points is much greater than optimal,

record times of 09.00 and 15.00 provides some assurance that daily variations in wind speeds are still represented

within the data set. Approximately 3.3km distant from Littlehampton at an altitude zA of 360m, the distance and difference in altitude between the data site and property assessed is small in magnitude compared to length scales over

which boundary layers and pressure/temperature gradients driving winds operate. Mt. Barker data is therefore

assumed to be representative of conditions in Littlehampton. To determine as accurately as possible the energy output necessary to power an average household for a year, a government affiliated website was consulted (Energy Made

Easy, 2014). Annual energy usage data was available based upon postcode and number of inhabitants per household.

For a home in Littlehampton, 5250, electricity usage is estimated at approximately 6695kWhr per year.

Boundary layer dependency of wind speeds and air density on height and surface roughness was approximated using a

log law association in the case of wind speeds and an empirical relationship in the case of air density. As the intended

installation site is in a residential area within a mixed suburban/rural zone, a roughness length z0 of 0.3m was applied, representing either suburbs or wooded countryside. Data was analysed using spreadsheet software to determine

statistical parameters necessary to characterise the annual wind speed profile. These include the annual mean Um, root

mean cube Urmc, modal Umod and median Umed wind speeds, standard deviation u and turbulence intensity, T.I. As the wind speed data are at uneven time intervals, time weighting was applied when calculating Um and Urmc. An

expression to estimate the annual average wind power potential at any height z was derived using Urmc and the

boundary layer corrections listed above. Established formula were then applied relating power extracted from the wind

to HAWT dimensions, efficiency, installed height. Application of known theoretical limits and equating with the energy target specified enabled derivation of an absolute minimum blade radius R necessary if a HAWT is to output

6695kWhr per year at a given installed height. Results are provided in table 1 (left).

2.2 Modelled Performance Assessment of 4 Domestic HAWTs Using Probability Density Approximation.

Performance of 4 domestic HAWT designs with rated power between 1.5kW and 5kW was modelled using a

probability density approximation of the annual wind speed profile at Littlehampton. Manufacturer/distributor data sheets were consulted to obtain specifications essential for the evaluation including cut-in wind speed Ucut-in, cut-out

wind speed Ucut-out, blade radii and installed height. Where possible, design efficiency was estimated using empirical speed-power relationships, an example is depicted in figure 1 (centre, from: Renewable Devices, 2010). Calculation of statistical parameters characterising the wind speed data indicate that a Rayleigh probability density distribution

provides a reasonable fit to the data set, allowing estimation of annual wind speed duration below a given value.

Accounting for losses in power extracted due to wind speeds below Ucut-in, annual energy output was approximated for

each system and the capacity factor C.F. calculated as a measure of performance

This represents actual energy output by the HAWT as a percentage of maximum energy produced if operating at rated

power (optimum) for the year. No wind speed data greater than Ucut-out for any HAWT exist in the data set.

3. Results and Recommendations

3.1 Discussion

It is clearly evident that the wind profile for Littlehampton is characterised by low speeds. Annual mean wind speed in the area Um is 3.38ms

-1, the mode Umod and median Umed speeds are 2.0ms

-1 and 3.05ms

-1 respectively. The latter result

are significant, indicating that for 27.4% of the year (2400 hr) wind speeds are below 2.0 ms-1

at this location, for 50%

Capacity Factor =

( ) x 100%


3

of the year they are below 3.05ms-1

. The mean annual wind speed is also below the limit of 5ms-1 suggested for

practical operation of a HAWT (Sustainability Victoria, 2010). Although wind speeds of significant size do exist

(12ms-1

and 15.5ms-1

at 60hr and 48hr per year respectively), annual duration is minor compared to the high frequency

of lower values. A turbulence intensity of 0.74 indicates dominance of the fluctuating component of wind over wind

speeds of consistent duration and magnitude necessary for optimum HAWT performance. This may suggest that the area surrounding Littlehampton lies in a region of turbulent flow separation, a not unexpected result given the rapid

urban expansion evidenced in Mt. Barker. Average wind speeds in urban areas are significantly lower and more

turbulent than rural due to increased surface roughness (Alternative Technology Association, 2007)

When installed at heights up to 20m, results for estimated absolute minimum blade radius R lie at the upper limit or

outside the range of most HAWT turbines suited for domestic suburban use (typically less than 2.0m) or within areas of low annual mean wind speeds (Sustainability Victoria, 2007). This is significant as under South Australian

development regulations council approval is not needed for installation of domestic HAWTs up to 10m (Energy Matters, 2014). An installation up to 20m may be passed depending on the individual case, however realistic values

for theoretical minimum R are not reached until installed heights greater than 33m and would be unlikely to obtain approval. It is important to remember that additional losses in extracted power arising from wind speeds below cut-in

wind speed Ucut-in are not factored in to the approximation.

Results modelling the performance of domestic HAWTs at Littlehampton confirm that the area most likely lacks wind speeds of sufficient size and duration for efficient performance. The Eco Whisper 325 turbine delivering the

greatest annual energy, based on an installation height of 20m, only manages to generate 50% of the required target. Designs not requiring planning permission achieve less than 32%, the Swift Wind Energy system only yields 304.8

kWhr per year. Although a significant amount of energy is produced by the 5kW and 3kW designs due to greater rated

power, associated performance is severely compromised. Capacity factors for all systems are below 10%, indicating

both highly inefficient and uneconomic production, regardless of power rating. Losses in power extracted due to speeds below Ucut-in depend on wind speed durations at the site and speedpower curves of a given HAWT. As the relative percentage of power lost is greatest at wind speeds less than Um, the effect on performance at low wind speed

sites is more significant (Grauers, 1996). At Littlehampton the wind speed of greatest duration Umod is less than Um, resulting in a predominance of wind speeds below the mean and the significant reduction in capacity factor observed.

3.2 Recommendations

Given the results for wind power potential in the vicinity of Littlehampton and likely performance of an HAWT if employed as the method of power extraction, Hot Air Consultancies does not recommend installation of a HAWT

system, domestic or otherwise, intended to output sufficient annual power to grid-off a residential household of 2

adults in this area. Although there is potential for a limited amount of electricity generation, a predominance of low wind speeds and turbulence, coupled with inconsistency in wind speed duration and magnitude, will severely limit

operational efficiency, performance and economic viability.

4 Conclusion

Whilst HAWT systems may offer a perceived advantage in terms of efficiency, matching design to operational

environment is of much greater importance. Performance of a wind turbine is governed by the suitability of the design to the wind profile at the intended location. The area surrounding Littlehampton is characterised by low wind speeds

and turbulence. Turbulent winds can cause problems for HAWT operation, resulting in irregular performance,

increased wear and tear and reduced economic viability. An additional essential consideration is the requirement of directional stability if optimum performance and the potential greater efficiencies offered by HAWT systems are to be

harnessed. Directional stability cannot be easily maintained in such conditions, especially problematic for domestic

HAWTs with passive yawing.

The wind resource assessment provided dictates that the area is unsuitable for installation of a HAWT design, opportunity does exist for some wind power generation at the Littlehampton property if desired. In this case the results

presented here mandate a turbine design more suited to the prevailing conditions, such as a vertical axis wind turbine

(VAWT). Although annual energy delivered by a VAWT design would certainly be less than the 6695 kWhr expected, enhanced performance in turbulent conditions and a design better suited to suburban domestic wind power generation

has potential to result in an economically attractive and environmentally conscious means of limiting GHG emissions

associated with electricity consumption. Hot Air Consultancies would certainly be able to provide advice on VAWT systems or a preliminary assessment of VAWT performance if requested.


4

Table 1. Left: Estimated theoretical minimum blade radius R (m) of a HAWT design required to deliver 6995kWhr annual

energy when installed at a height z(m) at Littlehampton, S.A. Right: Performance evaluation of 4 domestic HAWT systems using a Rayleigh wind speed probability distribution of annual wind speed durations in Littlehampton, S.A.

Installed Height, Z

(m)

Absolute Minimum

Blade Radius, R

(m)

HAWT

& Rated

Power

(kW)

Installed Height

z, (m)

Blade

Radius R,

(m)

Energy Output per year

E (kWhr)

Capacity factor at site, C.F.

(%)

10 3.10

Swift

Wind

Energy

1.5 kW

8 (or 5m +

wall/roof)

1.0 304.8 2.32

20 2.37

Aeolos H

2kW

9 (mast) 12

(guyed)

2.0 1414.4 8.1

30 2.06

Aeolos H

3kW

9 (mast) 12

(guyed)

2.5 2134.8 8.1

40 1.88 EcoWhispe

r 325

5 kW 19.6 1.63 3344.7 7.64

References Alternative Technology Association (2007) Viability of Domestic Wind Turbines for Urban Melbourne, Sustainability Victoria, Melbourne: Vic.

Australian Wind and Solar (n.d.) Aeolos-H 2Kw Grid-Off Technical Brochure, Australian Wind and Solar, Melbourne: Vic. Last retrieved Aug 13, 2014 from: http://www.australianwindandsolar.com/profile/Aeolos-H%202kw%20Brochure.pdf Australian Wind and Solar (n.d.) Aeolos-H 3Kw Grid-Off Technical Brochure, Australian Wind and Solar, Melbourne: Vic. Last retrieved Aug 13, 2014 from: http://www.australianwindandsolar.com/profile/Aeolos-H%203kw%20(Grid-off)%20Brochure.pdf Baldocchi, D. (2004) Lecture 19: Wind and Turbulence, Part 4- Surface Boundary Layer Theory and Principles, ESPM 129 - Biometeorology, Wind and Turbulence, Part 4.

Bureau of Meteorology (2014) Mount Barker, South Australia. September 2014 Daily Weather Observations, [Online]. Last retrieved Aug 27, 2014, from: http://www.bom.gov.au/climate/dwo/IDCJDW5039.latest.shtml Coppin, P.A., Ayotte, K.A., & Steggel, N. (2013) Wind Resource Assessment Australia, Wind Energy Research Unit, C.S.I.R.O. Land and Water, Canberra: A.C.T. Energy Matters (2014) Backyard Wind Turbines? In Adelaide You Can For Now, [Online]. Last retrieved Aug 28, 2014, from: http://www.energymatters.com.au/index.php?main_page=news_article&article_id=3413

Energy Made Easy (2014) Understand and Compare Your Energy Usage, [Online]. Last retrieved Aug 12, 2014, from: http://www.energymadeeasy.gov.au/bill-benchmark ENHAR Sustainable Energy Solutions (2010) Victorian Consumer Guide to Small Wind Turbine Generation, Sustainability Victoria, Melbourne, Vic. Government of South Australia (2013) Mount Barker Council Development Plan, Department of Planning, Transport and Infrastructure,

Adelaide: S.A. Grauers, A. (1996) Efficiency of three wind energy generator systems, IEEE Transactions on Energy Conversion, Vol. 11, No. 3. Pp.650-657 Renewable Devices Ltd. (2010) Swift Wind Energy System: Technical and Planning Pack, Renewable Devices Ltd., Edinburgh: Scotland. Last Retrived Aug 18, 2014, from:http://renewabledevices.com/wp-content/2012/04/SD0037-07-part-1-of-2-Technical-and-Planning-Pack.pdf Renewable Energy Solutions Australia Holdings Ltd. (2011) Eco Whisper Turbine 325: Technical Specifications, [Online]. Last retrieved Aug

28, 2014, from: http://www.resau.com.au/attachments/EWT_325_tech_brochure_260214.pdf Scottish Government (2014) Planning for Micro Renewables Annex to PAN 4: Renewable Energy Technologies, [Online]. Last Retrieved Aug 29, 2014, from: http://www.scotland.gov.uk/Publications/2006/10/03093936/2 Smulders, P.T. (2004) Rotors for Wind Power, Wind Energy Group, Faculty of Physics, University of Technology, Eindhoven: Holland.


5

Appendix A1: Data Acquisition and Potential Annual Wind Energy Calculations.

A1.1 Wind Speed Data

Source: Bureau of Meteorology (BOM) weather station I.D. 023733 (Bureau of Meteorology, 2014).

Location: Mount Barker, South Australia. Latitude: 35.07 S, Longitude 138.85 E

Altitude above mean sea level: ZA = 359m

Data type: Wind speed magnitudes in kmhr-1

at 09.00 and 15.00 daily from 01 July 2013 to

31 July 2014, averaged at 1 minute intervals from 1Hz time series data over 10

minutes prior to 09.00 and 15.00.

Wind speed sampling height: zr = 10 m.

Sample period: T = = 8760 hr.

Sampling interval: ti = 6hr for i even, ti = 18hr for i odd.

No. of data Ui: N = 730

A1.2 Assessment Site and Approximate Annual Energy Consumption Required

Location: Littlehampton SA, 5250. Latitude: 35.05 S, Longitude: 138.85 E Altitude above mean sea level: 345m ZA 402m

Altitude relative to data site: -14.0m < zA < +43.0m

Distance from data site: Approximately 3.3 km.

Zoning: Residential (Government of South Australia, 2014).

Required annual energy: To meet average annual consumption of 2 adults at the location assessed,

Ereq 6695 kWhr (Australian Government, 2014).

A1.3 Boundary Layer Approximations

A1.3.1 Approximation of Wind Speeds at Height Z > Zr

Assuming steady state, incompressible flows with no pressure or temperature gradients, and a high Reynolds number

Re dominated flow regime with wind speeds within the surface boundary layer outside the region of flow separation, the effect of friction on wind speeds at a height z > zr can be approximated by a log law wind speed profile:

( ) ( ) (

)

( )

where zr is the height of wind speed data measurement and z0 is the surface roughness length. As the measurement and

assessment locations are suburban areas located in the Adelaide Hills, the roughness length is set as

z0 = 0.3m

For the BOM wind speed data

zr = 10m


6

The relationship for wind speed versus height then becomes

( ) ( ) (

)

(

)

U(z) = 0.285 x U(zr) (

)

where z is height above ground surface. As the distance between the data and assessment sites is small compared to

length scales over which the boundary layer exists, the wind speed data and roughness length can be considered

representative of both locations.

A1.3.2 Effect of Altitude on Air Density

To model the effect of altitude zA on air density an empirical relationship is applied

(zA) = 1.226 (1.194 x 10-4

)zA

zA 360m

1.183 kgm-3

As the range of potential altitude differences between the data acquisition and assessment sites is small

-14.0m < zA < +43.0m

air density is assumed to be constant at 1.183 kgm-3 for both locations and over the range of HAWT heights used for calculations in the following analysis.

Although the boundary layer assumptions applied above cannot be verified as valid over the entire period T represented by the data, the atmospheric flow regime is expected to be characterised by high Re, approximations based

on these assumptions should suffice for the accuracy required by this assessment.

A1.4 Wind Speed Data Analysis

A1.4.1 Estimation of Site Annual Energy Potential

Using Microsoft Excel software the wind speed data Ui are converted to ms-1

, grouped into bins for 0.0ms-1

Ui < 0.5ms

-1 and 0.5ms

-1 Ui < 16.5ms-1 at 1ms-1 intervals and analysed yielding the following profile for wind speeds

over the sample period T = 8760 hr:

Maximum wind speed: Umax = 15.556 ms-1

Minimum wind speed: Umin = 0.0 ms-1

Modal wind speed class & frequency: Umod = 1.5 ms-1

U < 2.5 ms-1 ,

f = 27.4% = 2400 hr

Median wind speed: Umed = 3.05 ms

-1

Time weighted mean wind speed: Um =

3.38 ms-1

Time weighted root mean cubed wind speed: Urmc =

4.90 ms-1

Wind speed data standard deviation: U = 2.497 ms-1


7

The instantaneous wind speeds Ui are comprised of both a mean Um and fluctuating component Ui, the relative magnitudes of each can be assessed from the turbulence intensity T.I.

T.I. =

0.739

Applying the assumptions indicated in A1.3 above, the average annual wind power potential

at the site at height

z can be estimated using

( )

( )

Applying the relationship for wind speeds at height z > zr developed in A1.3 above

Ui, z = 0.285 x (

)

hence U(z)rmc = ( (

))

= [ ( )] x

( )

= [ (

)] U(zr)rmc

( ) = [ (

)]

yielding

( )

( ) ( ) (1x10-3)x(4.90)3 x [ (

)] kWm

-2

( )

[ (

)] kWm

-2

For a HAWT of swept area A and overall efficiency installed at height z, electrical power extracted from the available potential at the site can be estimated as

Wex,rmc(z) = [ (

)] kW

Wex,rmc(z) = CP x G x B x [ (

)] kW

where R is the HAWT blade radius, CP the power coefficient and G, B the generator and gearbox efficiencies respectively. Thus the annual energy produced by the HAWT at height z can be estimated as

E(z) 8760 x Wex,rmc(z) kWhr

E(z) CP x G x B x [ (

)] kWhr

Assuming maximum generator and gearbox efficiencies of G = 0.8 and B = 0.9 and equating with the required annual energy E = 6695 kWhr yields an approximation between the dimensions and coefficient of power for a HAWT

installed at height z if the annual energy target is to be met.


8

R

[ (

)]

The unattainable maximum theoretical value for conversion of wind power to mechanical energy (and hence ideal

value of CP in a perfectly efficient turbine) is the Betz limit of 59.3%. Effects such as wake rotation, drag effects and

finite number of turbine blades limit the maximum value of CP to the range 0.3 CP 0.5 for HAWT designs (Smulders, 1991).

Applying the upper limit of CP = 0.5 therefore provides an initial estimate of the absolute minimum dimensions of a

HAWT realistically able to deliver the required annual energy at the site when installed at height z

R [ (

)]

if no additional loss due to wind speeds below Ucut-in, or above Ucut-out or transmission losses occur. Results for a range

of heights are presented in table A1.1. Table A1.1 Installed height and estimated absolute minimum blade radius of a HAWT required to deliver 6695 kWhr annual

energy at Littlehampton, South Australia. Estimates based on wind speed data from Mt. Barker BOM, station ID 023733.

Installed Height Z

(m) 10 20 30 40

Estimated Minimum

Radius R (m) 3.10 2.37 2.06 1.88

A1.4.2 Assessment of Annual Energy Availability Using a Wind Speed Probability Density Approximation

Annual energy delivered by a specific HAWT system can be estimated using the design parameters of the chosen HAWT and probability distribution of wind speeds at a given location.

Probability of a given wind speed U in the interval a U b can be estimated using

( ) ( )

where f(U) is the probability density function (pdf) for the wind speed distribution at the site.

Calculation of the wind speed data set parameters

Skewness SkU =

( )

= 1.34

Kurtosis KrU =

( )

= 6.45

indicate that the wind speed distribution is Gaussian skewed with modal wind speed less than mean wind speed (SkU >

1.0) and the modal peak close to the mean with rapid decline (KrU > 3.0) (Baldocchi, n.d.).

Combined with calculation of the Weibull parameters

k = [

]

= (T.I.)-1.086

= (0.739)-1.086

k 1.4

c = 3.38 x (0.568 + 0.433/1.4)-1/1.4

3.7


9

indicates that a Rayleigh pdf (k =2, c=2Um/ 3.81) should provide a reasonable estimate of wind speed probabilities at the site.

The Rayleigh probability of a wind speed within the interval a U b is given by

prob(a U b) = C(b) C(a)

C(U) = [

(

) ]

Annual duration of wind speeds within the interval a U b can then be estimated using

t (a U b) = prob(a U b) x 8760

hr

where c is the number of wind speed intervals applied to the data set. At this location, under the assumptions listed in

A1.3, for a HAWT design of swept area A and efficiency the power extracted from wind within the interval a U b is approximately

Wex,j (0.5) x (1.183) x x A x [

]

x (1x10-3

) kW

and total annual energy availability can be calculated using

E Wex,j kWhr

Four HAWT turbines suitable for domestic power generation (Sustainability Victoria, 2007) were selected to estimate

performance at the site. The turbines selected range in rated power between 1.5kW Wrated 5kW, with installed heights of approximately 8m z 20m and dimensions 1m R 2.5m. As indicated previously, turbines with an installed height of z 10m require no council planning permission for use at the given location. Turbine specifications have been sourced from manufacturer/distributor data sheets (Aussie Wind and Solar, n.d.;

Renewable Energy Solutions Australia Holdings Ltd., n.d.; Renewable Devices Ltd., 2010) and efficiencies

approximated using

=

Where possible, values for Urated were sourced from manufacturer performance evaluation speed-power curves

available in the data sheets, in one instance (Eco Whisper 325) only theoretical data was available.

Losses in annual energy production due to wind speeds below Ucut-in and above Urated and Ucut-out were accounted for

in the annual energy calculation by applying conditions upon the interval energy contributions

Ej = 0.0 kWhr if Uj < Ucut-in

Ej = tj Wex, j kWhr if Ucut-in Uj Urated

Ej = tj Wrated kWhr if Urated Uj

in the Excel calculations. No wind speeds in the data set were above Ucut-out for any of the HAWT systems considered.

At installed heights of z 10m wind speed data at zr = 10m were used in the calculations, for the single case of an installed height of z 20m (Eco Whisper 325) wind speed data were calculated using the relationship provided in A1.3. Results are presented in table A1.2 and an example Excel calculation in table A1.3.


10

Table A1.2 Total annual energy estimation for 4 HAWT systems at the assessment site using a Rayleigh wind speed probability

distribution based on site wind speed data.

HAWT

& rated

power (kW)

Installed Height

(m)

Blade Radius

(m)

Swept Area

(m2)

Cut-in Wind Speed (ms-1)

Rated Wind Speed

(ms-1)

Cut-out Wind Speed

(ms-1)

Estimated design

efficiency

(-)

Estimated Energy per year

(kWhr)

Capacity

factor at site

(%)

Swift Wind

Energy

1.5 kW

8 (or 5m + wall/roof)

1.0 3.14 3.4 14 22.0 0.28 304.8 2.32

Aeolos H

2kW

9 (mast) 12 (guyed)

2.0 12.57 3.0 9.5 25.0 0.3 1414.4 8.1

Aeolos H

3kW

9 (mast) 12 (guyed)

2.5 19.63 3.0 9.5 25.0 0.29 2134.8 8.1

EcoWhisper

325

5 kW 19.6 1.63 8.30 2.5 14 25.0 0.36 3344.66 7.64

Table A1.3 Example spreadsheet calculation of site annual energy availability using a Rayleigh wind speed probability

distribution. Turbine type: Aeolos 2 kW installed at z =10m

Documents

Analysis of HAWT Performance in Low Winf Site for 4 Domestic Turbines