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4/19/12

WIND TURBINES, WIND

FARMS AND OPTIMAL

PLACEMENT FOR THE

WIND TURBINES WITHGENETIC ALGORITHM

İsmail KAYAHAN



4/19/12

Outline

• Introduction

• Modern Wind Power Systems –

Modern Wind Turbines – Wind Farms

• Wind Farm Placement

Optimization With G.A. – System Explanations

– Wind Power Calculations

– GA Optimization for Turbine



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Introduction

• Energy Demand

• The main factors of wind

power popularity – The need

– The potential

–

The technological capacity



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Modern Wind Turbines

• Main Components of Wind Turbine



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Wind Farms

• Wind Farm Technical Issues – Wind turbine spacing (both

downwind and crosswind)

– Wind turbine operatingcharacteristics

– The number of turbines and size

of the wind farm – Turbulence intensity

– Frequency distribution of the

wind direction (the wind rose)



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Operations and Controlof Wind Farms in a Grid• The requirements of grid

connection – The reactive power should be

regulated within a control band,at a maximum level of 10% of rated power

–

Wind turbine will generallyoperate in normal conditions(90– 105% voltage and 49–51Hz)

– Under the condition of a power



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Wind Farm Site of CaseStudies

• The wind farm is on theGökçeada Aydıncık.



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Wind Farm Site Technical Properties



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• Class of place is 4. Somemonths 5.



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Wind Turbine GridDistances



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Wind TurbineCharacteristics

• Enercon E-48 turbine will beused.

Rated Power 810kW

Rotor Diameter 48m

Swept Area 1810 m2

Cut-out wind Speed 20 m/s

Cut-in wind Speed 3 m/s

Number of Blades 3

Trust Factor 0.52Hub Height 50 m

Surface roughness (m) 0.005



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n ur ne owerand Power Coefficient

Curve



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Wind PowerCalculations

• Power

•

is the air density and equalsρto 1.225 kg/m3 at 16ºC,

• r is the radius of wind turbine

and 24 m.• U is wind speed which

changes with Weibull

Distribution.



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p o e ng(Efficiency Analysis of

One turbine)• Gausian Regresion with 5thorder is used for theregression.

5 10 15 20 25

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Y vs. X

fit 2

Goodness of fit:R-square: 0.9998Adjusted R-square:

0.9994RMSE: 0.004343



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Cp Regression

a1 0.1212 a4 4.088e+005 a3 -1.824

b1 6.194 b4 -170.1 b3 -0.2933

c1 1.507 c4 48.65 c3 6.583

a2 0.2187 a5 0.374

b2 8.884 b5 4.012

c2 3.81 c5 1.877



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Wake Effect Modelling

• Jensen deficit model

•

Where k is wake spreadingconstant and a is axialinduction factor.

•

The axial induction factor isrelated to the turbine trustcoefficient as



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x a n uc on ac orand Wake Spreading

Constant• Axial Induction Factora=0.1535

• Wake Spreading Constant



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Multiple Turbine DeficitFormulation

• Assuming multiple turbines inthe upstream of a turbine inconcern and ignoring the non-

linear near-wake region, thewake deficits are combinedby summing the squares of

the interacting deficits



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Statistics of WindSpeed

• Probability density functionf(V)

• Weibull shape parameter

•

Weibull scale parameter (m/s)



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Weibull Parametersand Pdf Graph

• From the reference k=1.94and c=9.81

• By the changing wind speedfrom 0 to 20 m2/s

0 2 4 6 8 10 12 14 16 18 200

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09



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Cost Calculations

• The total annual investmentcost of the wind farm relatesonly with the number of

installed wind turbines andcan be expressed as follows



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Genetic AlgorithmProperties

Creation Function Constraint DependentPopulation Type Bit String

Population Size 250

Fitness Scalling Rank

Selection Stochastic Uniform

Mutation Function Gausian

Crossover Scattered

Migration Function Forward

Migration Fraction 0.2

Migration Interval 20Change tolerance 1e-10

Stall Generation 500



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G.A. Flow Chart



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n ur nePlacement Cases (Max.

Power)

Layout No Cost($) Power (W) Number of Turbines

4 19.960.950,0 8.241.200,0 25

5 19.162.477,0 7.924.600,0 24

6 18.364.008,0 7.616.000,0 23



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n ur nePlacement Cases (Max.

Power/Cost Ratio)

Ratio Ranking

Layout No Cost($) Power (W) Power/cost ratio Number of Turbines

7 7.984.336,0 3.756.400,0 0,402305798 10

8 7.186.010,0 3.380.730,0 0,402299767 9

9 6.387.694,0 3.005.100,0 0,402291593 8



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Energy Calculations of Wind Turbine

Wind Speed Probability T[h] P P/Pr Etotal (kWh)0-3 0,0652 571,152 0 0 0,00

3 0,0587 514,212 5 0,006173 2.571,06

4 0,0714 625,464 25 0,030864 15.636,60

5 0,0801 701,676 60 0,074074 42.100,56

6 0,0847 741,972 110 0,135802 81.616,92

7 0,0856 749,856 180 0,222222 134.974,08

8 0,0833 729,708 275 0,339506 200.669,70

9 0,0783 685,908 400 0,493827 274.363,20

10 0,0713 624,588 555 0,685185 346.646,34



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Different Approach ForEnergy Calculation

• The method just multiplyingthe power of one turbine withweibull distribution calculated

and the total hours in oneyear.



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Different Approach ForEnergy Calculation

• where t=8725 hours –

35 hours average formaintenance

• 1st approach result is

3.237.807 kWh



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nergy ro uc on n a Year for Wind Farm

CasesCases Number of

TurbineEnergyProduction (KWh)

Layout 4 25 71.904.470

Layout 5 24 69.142.135

Layout 6 23 66.449.600

Layout 7 10 32.774.590

Layout 8 9 29.496.869

Layout 9 8 26.219.497



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Capacity Factor

• The ratio of the ratio of theactual output of a power plantover a period of time and itsoutput if it had operated atfull rated capacity the entiretime.



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Capacity Factor

Cases EnergyProduction(KWh)

(kWh)

CapacityFactor

Layout 4 71.904.470 176.681.250 0,406973

Layout 5 69.142.135 169.614.000 0,407644

Layout 6 66.449.600 162.546.750 0,408803

Layout 7 32.774.590 70.672.500 0,463753Layout 8 29.496.869 63.605.250 0,463749Layout 9 26.219.497 56.538.000 0,46375



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Economic Analysis

• 3 main concept foroperational costs of a windfarm.

– Operations and Maintenance

• O&M cost in $ = 0.007/kWh * AEP

– Land Lease Costs

• LLC cost = $0.00108/kWh *AEP

– Levelized Replacement Cost

• LRC cost factor = 10.7 kW



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Operations Cost ForCase Studies

Operations

andMaintenance($ /year)

Land LeaseCost ($/year)

Levelized

Replacement Cost($/year)

Total($ /year)

Layout 7 229.422 35.397 40.193 305.012Layout 8 206.478 31.857 36.174 274.509

Layout 9 183.536 28.317 32.155 244.008Layout 4 503.331 77.657 88.181 669.169Layout 5 483.995 74.674 84.793 643.462Layout 6 465.147 71.766 81.491 618.404



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Costs For Next 20 Years

InvestmentCost ($)

OperationalCost ($)

Total Cost ($)

Layout 4 19.960.950,0

13.383.379 33.344.329

Layout 5 19.162.477,0

12.869.233 32.031.710

Layout 6 18.364.008,

0

12.368.079 30.732.087

Layout 7 7.984.336,0 6.100.243 14.084.579Layout 8 7.186.010,0 5.490.170 12.676.180Layout 9 6.387.694,0 4.880.162 11.267.856



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Profits After 20 Years

Total Cost($) AnnualRevenue ($) 20 YearRevenue($)

Profit After20 Years($)

Layout 4 33.344.329

5.033.313100.666.258

67.321.929

Layout 5 32.031.71

0

4.839.949 96.798.989 64.767.279

Layout 6 30.732.087

4.651.47293.029.44062.297.353

Layout 7 14.084.579

2.294.22145.884.42631.799.847

Layout 8 12.676.180 2.064.78141.295.61728.619.437

Layout 9 11.267.856

1.835.36536.707.297 25.439.441

1kWh=7c$



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Decision Making



4/19/12

Thanks ForLISTENING

QUESTIONS

Energy Sunum

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