Structural Optimization of Offshore Wind Turbines
Mario Torcinaro, Francesco Petrini, Stefania Arangio
Department of Structural and Geotechnical Engineering
Sapienza University of Rome
MotivationsEARTH&SPACE 2010
2 Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Motivations
1. Offshore wind farms are relatively new structural facilities located inchallenging environment, the preliminary design of the structural elements isusually very conservative. A refinement is needed.
2. An offshore wind farm is formed by a number of wind turbines (50-200elements) and, consequently, a small individual reduction of structuralmaterial amount can lead to significant saving of money if regarding thewhole farm.
3. A new support structure is proposed here, and the correct sizing of itsstructural parts is crucial in this phase.
EARTH&SPACE 2010
INTRODUCTION
System design approach for complex structural systems
optimization
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
z
y
x,x’
z’
y’
Waves
Mean wind
Current
P
(t)v P
(t)w P
(t)u P
Turbulent wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
z
y
x,x’
z’
y’
Waves
Mean wind
Current
P
(t)v P
(t)w P
(t)u P
Turbulent wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
d
Complex system
3 EARTH&SPACE 2010
Introduction Part I Part II
A “Complex System”
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
z
y
x,x’
z’
y’
Waves
Mean wind
Current
P
(t)v P
(t)w P
(t)u P
Turbulent wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
z
y
x,x’
z’
y’
Waves
Mean wind
Current
P
(t)v P
(t)w P
(t)u P
Turbulent wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
d
3 EARTH&SPACE 2010
Introduction Part I Part II
A “Complex System”
NonLinearities
Uncertainty
Interactions
Complex system
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
System Engineering
4 Structural Offshore Wind Turbines Optimization [email protected]
A System Engineering Approach
Since the structural behavior of offshore wind turbines is influenced by nonlinearities,uncertainties or interactions, they can be defined as complex structural system
“a set of interrelated components which interact one with another in an organized fashion toward a common purpose” (NASA,
1995)
Structure Structural system
“a device to channeling loads”
Decomposition
Structure
Actions
Performances
Structural System
A fundamental task concerns the Structural System and Structural Performancedecomposition
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Introduction Part I Part II
Bontempi F., Li H., Petrini F., Gkoumas K., (2008). Basis of Design of Offshore Wind Turbines by System Decomposition,Proceedings of the ASEM'08, Jeju , Korea, 26-28 May 2008.
System Engineering
5 Structural Offshore Wind Turbines Optimization [email protected]
Structural decomposition
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Introduction Part I Part II
Macro - LevelDetail - Level
Structure decomposition
Main structure
(carrying loads)
Secondary structure
Auxiliary structure
Rotor-nacelle assembly
Support structure
Energy production
Energy transfer
Operation
Maintenance
Emergency
Substructure
Tower
Rotor
Nacelle
Blades
Foundations
Meso - Level
Junctions
Junctions
Micro - Level
Bontempi F., Li H., Petrini F., Gkoumas K., (2008). Basis of Design of Offshore Wind Turbines by System Decomposition,Proceedings of the ASEM'08, Jeju , Korea, 26-28 May 2008.
Optimization in design process
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Introduction Part I Part II
Structural design and structural optimizationTopological
Optimization
Design Optimization
Structural check
Best design config?
Refine
NoSTOP
PBD
Pre sizing
Performance requirements
Advanced Model
Basic Models
Conceptual design
START
Yes
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
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Introduction Part I Part II
Structural design and structural optimizationTopological
Optimization
Design Optimization
PBD
No
Structural check
Best design config?
Refine
STOP
Pre sizing
Performance requirements
Advanced Model
Basic Models
Conceptual design
START
Refinement of the design configuration with the goal of
obtaining satisfaction performances in economical way
Shape optimization(Options definition)
Parameters optimization(Options refinement)
Feasible configuration selection(Option selection)
Yes
Optimization in design process
Present Work
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
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PART I, Case study structure:
Modeling and Optimization aspects
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Support Structures
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Introduction Part I Part II
Typologies of support structures
Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore windturbines. Report for MTC OTC Project
Water depth (m) Foundation type
0-10 Gravity based
0-30 Mono-pile
>20 Tripod/Jacket
>50 FloatingBontempi, F. (2010). Advanced topics for offshore wind turbines.
Earth&Space 2010 Conference
Strutted Quadruped
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Objective Funcrion
Analytics
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Introduction Part I Part II
Optimization problem formulation
Unconstrained Design spaceConstrains
Constrained Design space
We must find the minimum of a certain Objective Function f, depending on certain DesignVariables (DV) x1,…,xn subjected to a number of constrains and by bounding the values ofa certain number of state variables (SV)
nn11n LSV,,LSV,RXx,0)x(g,0)x(hbeing)x(fmin
Constrains Design variables State variablesObjective Functions
Von Misesstresses
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
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Introduction Part I Part II
First order Optimization methodOne introduces the following unconstrained objective function:
2 31 m
1i
m
1i
iwih
m
1i
ig
n
1i
ix
0
wPhPgPqxPq,Qf
fx
λ2
ii
iig
αg
ggP
λ is a large integer so that the function will be very large when the constraint isviolated and very small when it is not
Q is the dimensionless unconstrained objective function,
Px is the exterior penalty functions applied to the design variables,
Pg, Ph, and Pw are penalties applied to the constrained design and state variables,
f0 is the reference objective function value that is selected from the current group of design sets
q is the response surface parameter .
For each optimization iteration (j) a search direction vector d(j) is devised. The next iteration (j+1) is obtained from the following equation:
jj
j1j s dxx
1j1jk
jj rq,Q dxd
21j
jT1jj
1j
q,Q
q,Qq,Qq,Qr
x
xxx
where sj is the line search parameter, and
The key to the solution of the global minimization of Q relies on the sequential generation of the search directionsand on internal adjustments of the response surface parameter (q).
ANSYS Inc. (2008). ANSYS Theory reference
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Analytics
12 EARTH&SPACE 2010
Introduction Part I Part II
Optimization problem algorithm
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Algorithm
Modeling
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Introduction Part I Part II
Structural system
modeling
Structure
Actions
Interactions
Modeling levels
Systemic
Macro
Meso
Micro
Model level
Scale Detail level Type of Finite Elements
Systemic level
wind farmapproximate shape of the structural
componentsBEAM elements
Macro level
single turbineapproximate shape of the structural
components, correct geometrical ratios between the components
BEAM elements
Meso level
single turbinedetailed shape of the structural
componentsSHELL, BRICK elements
micro level
individual componentsdetailed shape of the connecting
partsSHELL, BRICK elements
Differentiation of the modeling levels
Bontempi F., Li H., Petrini F., Manenti S., (2008). Numerical modeling for the analysis and design of offshore wind turbines,Proceedings of ASEM'08, Jeju, Korea, 26-28 May 2008
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
1°1°
Macro
Global response
Meso Micro
Levels of modeling and results detail level
Jacket - Tower connection
Detailed global response and medium-detailed local response
Detailed local response and analysis of connections
ModelingIntroduction Part I Part II
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PART II, Case study structure:
Problem definition and results
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Design variables
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Introduction Part I Part II
Application
x1
x2
• Structure and piles 180 m• Structure height: 140 m• Immersed: 35 m• Over water level: 105 m
Local constraints:
• maximum Von Mises ideal stress equals
to 300MPa (strength criterion);
• maximum compression stress equals to
200MPa (local instability criterion);
• maximum ratio diameter/thickness
equals to 100 (local instability criterion);
Global constraints:
• Eulerian buckling multiplier greater that 5;
• maximum horizontal displacement
permitted 4 m.
• Objective Function: TOTAL VOLUME
Results
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Introduction Part I Part II
Macro-level model: Design variables trend
Diameters Thicknesses
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
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Introduction Part I Part II
Macro-level model: State variables trend
Compression stresses
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Von Mises stresses
Results
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Introduction Part I Part II
Macro-level model: Configuration evolution
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Results
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Introduction Part I Part II
Macro-level model: Objective function
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Results
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Introduction Part I Part II
Meso-level model
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Results
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Introduction Part I Part II
Meso-level model: Effective buckling modes detection
Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010
Macro-level model Meso-level model
Results
1° buckling mode load multipler = 9,08
1° buckling mode load multipler = 10,12
Optimal configuration
Optimal ConfigIntroduction Part I Part II
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VOLUME=116 [m3]
Diamet ers[m] Thicknesses[m] d/t
D1 2.25 T1 3.1E-02 72.5
D2 3.14 T2 4.2E-02 75.5
D3 4.03 T3 4.2E-02 96.9
D4 4.56 T4 4.2E-02 109.5
D5 5.09 T5 5.2E-02 97.5
D6 2.37 T6 3.3E-02 71.8
D7 5.09 T7 5.2E-02 97.5
D8 5.30 T8 5.4E-02 98.3
D9 5.05 T9 5.4E-02 93.7
D10 4.80 T10 5.4E-02 89.1
D11 4.55 T11 5.4E-02 84.5
D12 4.31 T12 4.4E-02 97.9
D13 3.84 T13 4.4E-02 87.3
D14 3.37 T14 4.4E-02 76.7
D15 2.91 T15 4.4E-02 66.0
D16 2.44 T16 3.8E-02 64.8
D17 1.52 T17 1.6E-02 95.9
D18 2.32 T18 2.3E-02 99.4
Monopile-Quadruped comparison
Quadruped: VOLUME = 116 [m3] Weight = 904 [t] D max = 5 [m]
Monopile: VOLUME = 234 [m3] Weight = 2377 [t] D max = 9 [m]
Optimal ConfigIntroduction Part I Part II
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Conclusions
1. The Design Optimization of Owts is a fundamental step in the design ofOffshore Wind Farms.
2. The Design Optimization of such a complex structural systems has beencarried out by assuming simplified models for the actions.
3. Multi level detail models are needed in order to capture the main physicalaspects.
4. A new support structure is proposed here, the optimization produced goodresults in terms of weight if compared with another feasible solution (amonopile support structure).