4 - Structural Optimization of Offshore Wind Turbines - Petrini

Structural Optimization of Offshore Wind Turbines

Mario Torcinaro, Francesco Petrini, Stefania Arangio

[email protected]

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.

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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


P

H

h

vw(z’)

Vcur(z’)

d

Complex system

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Introduction Part I Part II

A “Complex System”


z

y

x,x’

z’

y’

Waves

Mean wind

Current

P

(t)v P

(t)w P

(t)u P


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


P

H

h

vw(z’)

Vcur(z’)

d

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A “Complex System”

NonLinearities

Uncertainty

Interactions

Complex system


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

EARTH&SPACE 2010


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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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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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


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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


EARTH&SPACE 2010

PART I, Case study structure:

Modeling and Optimization aspects


Support Structures

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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


Objective Funcrion

Analytics

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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


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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


Analytics

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Optimization problem algorithm


Algorithm

Modeling

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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


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

14 EARTH&SPACE 2010 Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010

EARTH&SPACE 2010

PART II, Case study structure:

Problem definition and results


Design variables

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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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Macro-level model: Design variables trend

Diameters Thicknesses


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Macro-level model: State variables trend

Compression stresses


Von Mises stresses

Results

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Macro-level model: Configuration evolution


Results

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Macro-level model: Objective function


Results

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Meso-level model


Results

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Meso-level model: Effective buckling modes detection


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


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


EARTH&SPACE 2010

24 Structural Offshore Wind Turbines Optimization [email protected]&SPACE 2010

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).

4 - Structural Optimization of Offshore Wind Turbines - Petrini

Design

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