objectives and constraints for wind turbine optimizationobjectives and constraints for windturbine...

Objectives and Constraints for WindTurbine Optimization

S.Andrew Ning

National Renewable Energy Laboratory

January, 2013

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Overview

1. Introduction 2. Methodology (aerodynamics,

structures, cost, reference model, optimization)

3. Maximum Annual Energy Production (AEP)

4. Minimum m/AEP 5. Minimum Cost of Energy (COE) 6. Conclusions

NATIONAL RENEWABLE ENERGY LABORATORY 2

Introduction

WindTurbine Design

Optimization and Uncertainty Quantification

Aerodynamic Performance

Structural Design

Control Strategy

Site Selection

Farm Layout

Capital Costs

Maintenance Costs


WindTurbine Optimization


Objectives

• Max P/min Mb

• Max AEP • Min COE

Design Vars

• Blade shape • Rotor/nacelle • Turbine

Fidelity

• Analytic • Aeroelastic • 3D CFD

Optimization

• Gradient • Direct search • Multi-level

Methodology

Model Development

1. Capture fundamental trade-offs (physics-based) 2. Execute rapidly (simple physics) 3. Robust convergence (reliable gradients)


Aerodynamics

• Blade-element momentum theory

‣ hub and tip losses, high-induction factor correction, inclusion of drag

‣ 2-dimensional cubic splines for lift and drag coefficient (angle of attack, Reynolds number)

• Drivetrain losses incorporated in power curve • Region 2.5 when max rotation speed reached • Rayleigh distribution with 10 m/s mean wind

speed (Class I turbine) • Availability and array loss factors


�

Blade Element Momentum

⌦r(1 + a 0)

plane of rotation

U1(1 - a)W


a0)

a)1-U1(1-

⌦r(1 + a

�


plane of rotation

⌦r(1 +

U1(1 -W

a)a)

1 + a 0)0)


�


⌦r(1 + a 0)

plane of rotation

U1(1 - a)W



sin ¢ cos ¢f(¢) = - = 0

1 - a(¢) Ar(1 + a0(¢))



S.Andrew Ning, “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, to appear. CCBlade


Figure 1: Example of composites layup at a typical blade section. Principal material direction of laminas, shown in brown, is skewed with respect to the blade axis. This causes bend-twist coupling as evident at the blade tip.

igure 2: Example of spar-cap-type layup of composites at a blade section F

rn

t

LD�

S ply angle

principal materialdirection

Composite Sectional Analysis

Sector 3 Sector 1

AA BB

Sector 2

Laminas schedule at AA Laminas schedule at BB

PreComp NATIONAL RENEWABLE ENERGY LABORATORY 15

Beam Finite Element Analysis

1 Z 1

i (⌘)f00Kij = [EI](⌘)f 00 j (⌘)d⌘

L30 pBEAM


Panel Buckling

b

⇣ ⇡ ⌘2 Z

E(⌧ )⌧ 2

Ncr = 3.6 d⌧2b 1� ⌫(⌧ )


Fatigue (gravity-loads)


Cost Model

• Based on NREL Cost and Scaling Model • Replaced blade mass/cost estimate • Replaced tower mass estimate • New balance-of-station model


Reference Geometry

• NREL 5-MW reference design • Sandia National Laboratories

initial layup • Parameterized for optimization

purposes


Design Variables

Description Name # of Vars

chord distribution {c} 5

twist distribution {θ} 4

spar cap thickness distribution {t} 3

tip speed ratio in region 2 λ 1

rotor diameter D 1

machine rating rating 1


ultimate tensile strain

ultimate compressive strain

spar cap buckling

tip deflection at rated speed

blade natural frequency

fatigue at blade root due to gravity loads

fatigue at blade root due to gravity loads

maximum tip speed (imposed directly in analysis)

Constraints

minimize x

subject to

J(x)

(r

f rm✏

50

i

)/✏

ult < 1, i = 1, . . . , N

(r

f rm✏

50

i

)/✏

ult > -1, i = 1, . . . , N

(✏

50

j rf - ✏

cr

)/✏

ult > 0, j = 1, . . . ,M

6/6

0 < 1.1

!

1

/(3⌦

rated

) > 1.1

0

root-gravity

/S

f < 1

0

root-gravity

/S

f > -1

V

tip < V

tip

max

ultimate tensile strength ultimate compressive strength spar cap buckling tip deflection at rated blade natural frequency fatigue at blade root (gravity loads) fatigue at blade root (gravity loads) maximum tip speed

cset(x) < 0


Maximum Annual Energy Production

Why a single-discipline objective?

1. No structural model 2. No cost model 3. Organizational structure 4. Computational limitations


Maximize AEP at Fixed Mass

maximize AEP (x)

with respect to x = {{c}, {✓}, �}subject to cset < 0

mblade = mc


AEP First

maximize AEP (x)

with respect to x = {{c}, {✓}, A}subject to V

tip < V

tip

max


i

aero

< i

aero0

S

plan

< S

plan0

maximize AEP (x)

with respect to x = {{c}, {✓}, }subject to V

tip

< V

tip

max

AEP First

maximize AEP (x)

with respect to

subject to

x = {{c}, {✓}, A}V

tip < V

tip

max

i

aero < i

aero0

✓

iaero ⌘

Z M

b

t dr

◆

S

plan < S

plan0

(

root < (

root0


minimize m(x)

with respect to x = {t}subject to c

set

(x) < 0

maximize AEP (x)

with respect to x = {{c}, {✓}, }subject to V

tip

< V

tip

max

i

aero

< i

aero0

S

plan

< S

plan0

J

root

< J

root0

AEP First

maximize AEP (x)

with respect to x = {{c}, {✓},A}subject to V

tip < V

tip

max

i

aero < i

aero0

S

plan < S

plan0

(

root < (

root0

minimize m(x)

with respect to x = {t}subject to c

set

(x) < 0


mass 1st min COE

Comparison Between Methods

AEP mass COE

0

0.5

% c

hang

e

-0.5

-1

-1.5 AEP 1st


Mass First minimize

with respect to

subject to

maximize

with respect to

subject to

minimize

with respect to

subject to

m(x)

x = {{c}, {t}}

cset(x) < 0

AEP (x)

x = {{✓}, �}V

tip < V

tip

max

m(x)

x = {{c}, {t}}

cset(x) < 0


min COE


AEP mass COE

-1

-0.5

0

0.5

% c

hang

e

-1.5 AEP 1st mass 1st


Minimize COE

minimize COE(x)

with respect to x = {{c}, {✓}, {t},�}subject to cset(x) < 0



AEP mass COE

-1

-0.5

0

0.5

% c

hang

e

-1.5 AEP first mass first min COE


Conclusions

1. Similar aerodynamic performance can be achieved with feasible designs with very different masses.

2. Sequential aero/structural optimization is significantly inferior to metrics that combine aerodynamic and structural performance.


Minimum Turbine Mass / AEP

Cost of Energy FCR (TCC + BOS) + O&M mturbine

COE = ⇡ AEP AEP


Vary Rotor Diameter

minimize COE(x; D) or m(x; D)/AEP (x; D)

with respect to x = {{c}, {✓}, {t}, �}

subject to cset(x) < 0


Tower Contributions to Mass/Cost mass cost

53%33%

14% 17%

24%

9%

38%

12%

rotor nacelle tower rotor nacelle tower bos o&m


Fixed Mass m

fixed = mblades + m

other


Fixed Mass


Conclusions

1. m/AEP can work well at a fixed diameter but is often misleading for variable diameter optimization

2. Problem must be constructed carefully to prevent over-incentivizing the optimizer to reduce tower mass


Minimum Cost of Energy

Robust Optimization

Wind Power Class Wind Speed (50m) 3 6.4

4 7.0

5 7.5

6 8.0

7 11.9


Robust Optimization

minimize < COE(x; V hub) >

where V hub ⇠ U(6.4, 11.9) with respect to x = {{c}, {✓}, {t},�, D, rating}subject to cset(x) < 0


Robust Design

Vhub


Conclusions

1. Optimization under uncertainty is important given the stochastic nature of the problem

2. Fidelity of the cost model can dramatically affect results


Conclusions

Conclusions

1. Sequential (or single-discipline) optimization is significantly inferior as compared to integrated metrics

2. m/AEP can be a useful metric at a fixed diameter if tower mass is handled carefully

3. High-fidelity cost modeling and inclusion of uncertainty are important considerations


Acknowledgements

• Rick Damiani

• Pat Moriarty

• Katherine Dykes

• George Scott


ThankYou

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