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Part IV: Blade Geometry Optimization

Philippe Giguère

Graduate Research Assistant

Steady-State Aerodynamics Codes for HAWTsSelig, Tangler, and Giguère

August 2, 1999 NREL NWTC, Golden, CO

Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-Champaign

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Outline• Approaches to Optimization• Blade Geometry Optimization• Optimization Methods for HAWTs• PROPGA

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Approaches to Optimization• Iterative Approach

– Use direct or inverse design method

– Designer knowledge important

– Inverse design can lead directly to an optimum blade for maximum energy (variable-speed HAWTs)

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• Direct Optimization

– Many optimization techniques available– Nature of problem dictates the optimization method

Optimum DesignDesign Parametersand Constraints

OptimizationMethod

“Black Box”

AnalysisMethod

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•“Black Box” Warning!– An optimization method will take advantage of the weaknesses of the analysis tool(s) and problem

formulation– Optimization technique must be implemented with care– Know your analysis tool(s)

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Blade Geometry Optimization• Many Design Variables (continuous and discrete)

– Chord and twist distributions– Blade pitch– Airfoils– Turbine configuration and control systems

• Competing Objectives– Maximum energy– Minimum cost

• Airfoil data not always smooth (“noisy” problem)• Complex problem often with many local optima• Need a robust optimization technique

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Optimization Methods for HAWTs• Garrad Hassan (Jamieson and Brown, 1992)

– Simplex method for aerodynamic design– Optimize chord and twist for maximum energy

• University of Athens (Belessis et al., 1996)– Genetic algorithm for aerodynamic design with limited structural constraints– Parameterized airfoil data

• Risø (Fuglsang and Madsen, 1996)– Sequential linear programming with method of feasible directions for

aerodynamic design– Structural, fatigue, noise, and cost considerations

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PROPGA• Description

– Genetic-algorithm based optimization method – Optimize blade geometry given set of constraints

• Possible design variables– chord and twist distributions, blade pitch, rotor diameter, number of blades, etc.

• Typical constraints– Operating conditions, rated power, airfoil distribution, steady-blade loads, and all fixed

design variables

– Uses PROPID to evaluate the blade designs and achieve inverse design specifications

– Initially developed to optimize blades for max. energy

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• What are Genetic Algorithms (GAs)?– Robust search technique based on the principle of the survival of the fittest – Work with a coding of the parameters

• Simplified example: blade chord & pitch is 101001

– Search from sub-set (population) of possible solutions over a number of generations

– Use objective function information (selection)– Use probabilistic transition rules based on and genetic operations

• crossover: 111|1 & 000|0 gives 1110 & 0001• mutation: 1 to 0 or 0 to 1 (small probability)• etc.

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• PROPGA Flowchart

Step 2Formation of

Initial Population

Step 3Analysis of Each

Individual of Population

Step 4Creation of Mating PoolReproduction Operator

Step 5Crossover Operator

Step 6Mutation Operator

New PopulationOffsprings

Is this the lastgeneration?

Yes

No

Optimization ProcessComplete

Step 1Coding of theParameters

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• Blade Design Example (Maximize Energy Capture)– Evolution of the chord and twist distributions

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

N orm alized D istance A long B lade R adius (r/R )

0.0

0.1

0.2

Nor

mal

ized

cho

rd(c

/R)

2

1

1050

100

-10

0

10

20

30T

wis

t (de

g)

1

2

10

50100

G eneration 1

G eneration 2

G eneration 10

G eneration 50

G eneration 100

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– History of the energy production• Population of 100 blades over 100 generations

0 10 20 30 40 50 60 70 80 90 100

G enerations

0

5,000

10,000

15,000

20,000G

ross

Ann

ual E

nerg

y P

rodu

ctio

n(k

Wh/

year

)H istory of best b lade design

H istory of average b lade design

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• Blades Designed with PROPGA/PROPID– Tapered/twisted blade for the NREL Combined

Experiment Rotor – WindLite 8-kW wind turbine– Replacement blade for the Jacob’s 20-kW HAWT– Twist distribution of the replacement blade for the

US Windpower 100-kW turbines

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• New Features (Under Development)– Airfoil selection– Advanced GA operators– Structural modeling– Weight/cost modeling for main components

• Rotor, hub, drivetrain, and tower

– Minimize cost of energy– Multi-objectives (get tradeoff curves)– Paper at the ASME Wind Energy Symposium, Reno, NV, January 2000