POLI di MI tecnicolanotecnicolanotecnicolano MULTI-DISCIPLINARY CONSTRAINED OPTIMIZATION OF WIND TURBINES C.L. Bottasso, F. Campagnolo, A. Croce Politecnico

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CONSTRAINED OPTIMIZATION OF WIND

TURBINES

C.L. Bottasso, F. Campagnolo, A. CrocePolitecnico di Milano, Italy

EWEC 2010 Warsaw, Poland, April 20-23, 2010

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POLITECNICO di MILANO Poli-Wind Research Lab


OutlineOutline

• Introduction and motivation

• Approach:

- Constrained multi-disciplinary optimization

- Simulation models

- Aerodynamic optimization

- Structural optimization

- Combined aero-structural optimization

• Applications and results

• Conclusions and outlook

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Introduction and MotivationIntroduction and MotivationFocus of present work: integrated multi-disciplinary (holistic)

constrained design of wind turbines, i.e. optimal coupled sizing of:• Aerodynamic shape • Structural members (loads, aero-servo-elasticity and controls)

Constraints: ensure a viable design by enforcing all necessary design requirements

Applications:• Sizing of a new machine• Improvement of a tentative configuration• Trade-off studies (e.g. performance-cost)• Modifications to exiting models

Previous work: Duineveld, Wind Turbine Blade Workshop 2008; Fuglsang &

Madsen, JWEIA 1999; Fuglsang, EWEC 2008; etc.

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OutlineOutline


• Approach:


- Simulation models






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Optimizer • Local/global solvers (SQP, GA)• Functional approximators

ApproachApproach

1. Aerodynamic Optimization

2. Structural Optimization

3. Combined Aero-Structural Optimization

Cp-Lambda aero-servo-elastic multibody simulator

ANBA cross sectional analyzer

Parameters

Cost function & constraints

Aerodynamic parameters: chord, twist, airfoils

Structural parameters: thickness of shell and spar caps, width and location of shear webs

Macro parameters: rotor radius, max chord, tapering, …

Partition of optimization parameters: aerodynamic, structural, macro (i.e. combined aero-structural)

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Aerodynamic Optimization

1. Compute Cp-TSR curves

2. Compute AEP

3. Compute constraints

4. Converged blade design?

5. Update rotor model

Constraints: • Noise constraint (V tip):

regulation in region II1/2• Torque-TSR stability• Max chord• …

Blade parameterization: Chord and twist shape functions deform a baseline configuration

Richer shape with fewer dofs

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Cp-Lambda (Code for Performance, Loads, Aero-elasticity by Multi-Body Dynamic Analysis):• Global aero-servo-elastic FEM model

• Rigid body

• Geometrically exact beam

• Revolute joint

• Flexible joint

• Actuator

ANBA (Anisotropic Beam Analysis) cross sectional model:• Evaluation of cross sectional stiffness

(6 by 6 fully populated) • Recovery of sectional stresses and

strains

Compute cross sectional stresses and

strains

Compute sectional stiffness of equivalent

beam model

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Structural Optimization

1. Control synthesis

2. Cp-Lambda

multibody analysis

3. ANBA cross

sectional analysis

4. Converged blade

design?

5. Update models

Analyses: • Transfer loads from

multibody to cross sectional models

• Recover sectional stresses and strains

Compute cost function: • Weight

Compute constraints: • Stress/strains safety

margins

Analyses: • DLCs (IEC61400:

load envelope, fatigue DELs)

• Eigenfrequencies (Campbell diagram)

• Stability

Compute constraints: • Max tip deflection• Frequency

placement

Modeling:• Extract reduced model

from multibody one• Linearize reduced model

Synthesize controller: • Compute LQR gains

Update process:

Update cross sectional models

Compute beam stiffness and

inertial properties

Update multibody model

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Structural Blade ModelingStructural Blade Modeling

Maximum chord line

Straight websCaps extend to

embrace full root circle

Cross section types

Sectional structural dofs

Twisted shear webs

Location of structural dofs and load computation section

Load computation section

Spanwise shape functions

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Combined Aero-Structural Optimization

1. Family of optimal

aerodynamic designs

2.Associated family

of structurally optimal designs

3.Define combined

cost

4.Compute optimum

Parameter: radius, max chord, etc.Example: tapering

Example: spar cap thicknessExample: AEP over weight

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OutlineOutline


• Approach:


- Simulation models






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Parameter: blade tapering, constrained max chord

Optimization of a 3 MW Wind Turbine

Optimization of a 3 MW Wind Turbine

1. Aerodynamic Optimization

2. Structural Optimization3. Combined Aero-Structural Optimization

Long blade span (D=106.4m) and small maximum chord (3.9m) is penalized by excessive outboard chords(lower flap frequency/increased tip deflections)Optimal solution: intermediate taper

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WT2, the Wind Turbine in a Wind Tunnel

WT2, the Wind Turbine in a Wind Tunnel

Civil-Aeronautical Wind Tunnel - Politecnico di MilanoIndividual blade

pitch

Torque control

Aero-elastically scaled wind turbine model for:

• Testing and comparison of advanced control laws and supporting technologies

• Testing of extreme operating conditions

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Structuraloptimization

Design of an Aero-elastically Scaled Composite Blade

WidthChordwise Position

Thickness

Sectional optimization variables (position, width, thickness)Span-wise shape function interpolation

Optimization

Cross sectional analysis

Equivalent beam model

ANBA (ANisotropic Beam Analysis) FEM cross sectional model:• Evaluation of cross sectional

stiffness (6 by 6 fully populated matrix)

Objective: size spars (width, chordwise position & thickness) for desired sectional stiffness within mass budgetCost function: sectional stiffness error wrt target (scaled stiffness)Constraints: lowest 3 frequencies

Rohacell core with grooves for the housing of carbon fiber spars

Thermo-retractable film

Carbon fiber spars for desired stiffness

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Design of an Aero-elastically Scaled Composite Blade

Filippo Campagnolo

Modes Reference [Hz]Optimization

procedure [Hz]

1st Flap-wise

23.2 23.1

2nd Flap-wise

59.4 59.1

1st Edge-wise

33.1 33.1

Mass gap can be corrected with weights

Solid line: scaled reference values

Dash-dotted line: optimal sizing

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ConclusionsConclusionsPresented holistic optimization procedures for wind turbines:

• Refined models: aero-servo-elastic multibody + FEM cross sectional analysis can account for complex effects and couplings from the very inception of the design process (no a-posteriori fixes)

• Fully automated: no manual intervention, including self-tuning model-based controller that adjusts to changes in the design

• Fast design loop: can perform a full design in 1-2 days on standard desktop computing hardware

• General and expandable: can readily add constraints to include further design requirements

• Ready-to-use multibody aero-servo-elastic model of final design: available for further analyses/verifications, evaluation of loads for design of sub-components, etc.

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OutlookOutlook

Real-life applications:

• Completed design of 45m blade (to be manufactured end 2010)

• Design of 16.5m blade under development

Software enhancements:

• Improved speed: parallelization of analyses (DLCs, Campbell, FEM cross sectional analyses, etc.)

• Improved coupling between aerodynamic and structural optimizations

• Automated generation of CAD model (mould manufacture, FEM analysis)

• Automated generation of 3D FEM model for detailed verification (stress & strains, buckling, max tip deflection, fatigue, etc.)

Documents

POLI di MI tecnicolanotecnicolanotecnicolano MULTI-DISCIPLINARY CONSTRAINED OPTIMIZATION OF WIND TURBINES C.L. Bottasso, F. Campagnolo, A. Croce Politecnico