POLItecnico
di MIlano
MULTI-DISCIPLINARY
CONSTRAINED OPTIMIZATION
OF WIND TURBINES
C.L. Bottasso, F. Campagnolo, A. Croce
Politecnico di Milano, Italy
EWEC 2010
Warsaw, Poland, April 20-23, 2010
Outline
Holistic Design of Wind Turbines
• Introduction and motivation
• Approach:
- Constrained multi-disciplinary optimization
- Simulation models
- Aerodynamic optimization
- Structural optimization
- Combined aero-structural optimization
• Applications and results
• Conclusions and outlook
POLITECNICO di MILANO
Poli-Wind Research Lab
Introduction and Motivation
Holistic Design of Wind Turbines
Focus 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.
POLITECNICO di MILANO
Poli-Wind Research Lab
Outline
Holistic Design of Wind Turbines
• Introduction and motivation
• Approach:
- Constrained multi-disciplinary optimization
- Simulation models
- Aerodynamic optimization
- Structural optimization
- Combined aero-structural optimization
• Applications and results
• Conclusions and outlook
POLITECNICO di MILANO
Poli-Wind Research Lab
Approach
Holistic Design of Wind Turbines
Aerodynamic parameters:
chord, twist, airfoils
Macro parameters:
rotor radius, max
chord, tapering, …
Partition of optimization parameters:
aerodynamic, structural, macro
(i.e. combined aero-structural)
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Structural parameters:
thickness of shell and
spar caps, width and
location of shear webs
Poli-Wind Research Lab
Holistic Design of Wind Turbines
Blade parameterization:
Chord and twist shape
functions deform a
baseline configuration
Constraints:
• Noise constraint (V tip):
regulation in region II1/2
• Torque-TSR stability
• Max chord
•…
Richer shape with fewer
dofs
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Poli-Wind Research Lab
Holistic Design of Wind Turbines
ANBA (Anisotropic Beam Analysis) cross
sectional model:
• Evaluation of cross sectional stiffness
(6 by 6 fully populated)
• Recovery of sectional stresses and strains
Compute sectional
stiffness of equivalent
beam model
Compute cross sectional
stresses and strains
• Rigid body
• Geometrically exact beam
• Revolute joint
• Flexible joint
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• Actuator
Poli-Wind Research Lab
Modeling:
• Extract reduced model from
multibody one
• Linearize reduced model
Synthesize controller:
• Compute LQR gains
Holistic Design of Wind Turbines
Analyses:
• DLCs (IEC61400: load
envelope, fatigue DELs)
• Eigenfrequencies
(Campbell diagram)
• Stability
Update process:
Update cross
sectional models
Compute beam
stiffness and
inertial properties
Update multibody
model
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Compute constraints:
• Max tip deflection
• Frequency placement
Analyses:
• Transfer loads from
multibody to cross sectional
models
• Recover sectional stresses
and strains
Compute cost function:
• Weight
Compute constraints:
• Stress/strains safety
margins
Poli-Wind Research Lab
Structural Blade Modeling
Holistic Design of Wind Turbines
Cross section types
Sectional structural dofs
Spanwise shape
functions
Location of structural dofs
and load computation
section
Load computation
section
Twisted shear webs
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Straight webs
Caps extend to
embrace full root circle
Poli-Wind Research Lab
Holistic Design of Wind Turbines
Parameter: radius, max chord, etc.
Example: tapering
Example: AEP over weight
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Example: spar cap thickness
Poli-Wind Research Lab
Outline
Holistic Design of Wind Turbines
• Introduction and motivation
• Approach:
- Constrained multi-disciplinary optimization
- Simulation models
- Aerodynamic optimization
- Structural optimization
- Combined aero-structural optimization
• Applications and results
• Conclusions and outlook
POLITECNICO di MILANO
Poli-Wind Research Lab
Optimization of a 3 MW Wind Turbine
Holistic Design of Wind Turbines
Parameter: blade tapering, constrained max chord
Long blade span (D=106.4m) and small
maximum chord (3.9m) is penalized by
excessive outboard chords
(lower flap frequency/increased tip deflections)
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di MILANO
Optimal solution:
intermediate
taper
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WT2, the Wind Turbine in a Wind Tunnel
Holistic Design of Wind Turbines
Aero-elastically scaled wind turbine model for:
• Testing and comparison of advanced control
laws and supporting technologies
• Testing of extreme operating conditions
Individual blade pitch
Civil-Aeronautical Wind Tunnel - Politecnico di Milano
Torque control
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Poli-Wind Research Lab
Design of an Aero-elastically Scaled
Composite Blade
Objective: size spars (width,
chordwise position & thickness)
for desired sectional stiffness
within mass budget
Cost function: sectional stiffness
error wrt target (scaled stiffness)
Constraints: lowest 3 frequencies
Holistic Design of Wind Turbines
Carbon fiber spars for
desired stiffness
Sectional optimization variables
(position, width, thickness)
Span-wise shape function interpolation
Chordwise Position
Width
Rohacell core with grooves
for the housing of carbon
fiber spars
Thickness
Thermo-retractable film
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ANBA (ANisotropic Beam Analysis) FEM
cross sectional model:
• Evaluation of cross sectional stiffness
(6 by 6 fully populated matrix)
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Design of an Aero-elastically Scaled
Composite Blade
Holistic Design of Wind Turbines
Solid line: scaled
reference values
Mass gap can be
corrected with weights
Dash-dotted line:
optimal sizing
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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
Poli-Wind Research Lab
Conclusions
Holistic Design of Wind Turbines
Presented 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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Poli-Wind Research Lab
Outlook
Real-life applications:
Holistic Design of Wind Turbines
• 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.)
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Poli-Wind Research Lab