![Page 1: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/1.jpg)
Anonymous MIT Students
![Page 2: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/2.jpg)
Introduction Problem Formulation Design Vector Analysis Methodology & Parameters Fidelity & Complexity Optimization Methods Single Objective Results Multi Objective Results Conclusions & Future Work
![Page 3: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/3.jpg)
Focus on renewable energy
Disciplines involved◦ Aerodynamics
◦ Control
◦ Structures
◦ Acoustics
◦ Electrical engineering
Interactions◦ Control (rotational speed affects aerodynamics)
◦ Structures (blade deflection affects aerodynamics)
Considered in this project
Renewable Energy Projection
Source: http://www.paulchefurka.ca/WEAP/WEAP.html
Considered in this project
![Page 4: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/4.jpg)
Objective Function
◦ Over a range of incoming wind speeds
Penalty Function
![Page 5: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/5.jpg)
Model reduction by Piecewise Cubic Hermite Interpolating Polynomials
Decision variable points
Assumed point
PCHIP Spline
![Page 6: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/6.jpg)
Decision variable points
k = 4
Weibull statisticsMean = 4.43 m/sStd. Dev. = 2.13 m/s
![Page 7: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/7.jpg)
N2 Diagram
Aero – Blade Element Momentum Theory
◦ Relaxed iteration root-finding
Expected Power – Simpson’s rule integration over Weibull distribution
Structure – Equivalent beam theory
Control – Line search convex optimization (fminbnd in MATLAB)
Inputs
x, param x, param x, param x, param x, param Output
Wrappercweibull,
kweibull
PE, Vblades,
Max(σmax(v0))
Max(σmax(v0)) Expected Power v0 ω, v0 ω, Ft/ΔR, Fa/ΔR
ω Control ω, v0
Q, P, Ft/ΔR,
Fa/ΔR
Q, P, Ft/ΔR,
Fa/ΔRAero
σmax(v0) Structure
Inter-module optimization
![Page 8: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/8.jpg)
Discretization Parameters (affect fidelity)
![Page 9: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/9.jpg)
Model order reduction◦ PCHIP
Analysis methodology low fidelity◦ Quick computation times
Validation◦ Structures code equates with analytical classical
beam theory for cantilevered beam
◦ Ran out of time to compare with Qprop / VABS high-fidelity codes
◦ Tell us if you know of a wind turbine design to benchmark against
![Page 10: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/10.jpg)
Design of Experiments (DOE)◦ Complex design space (initial idea)
◦ Main effects
◦ Space-filling starting points for Gradient-based methods
◦ Good results, short running times
Gradient-based methods◦ Continuous design variables with no discontinuities
◦ Constraints imposed by square term penalty method
◦ Implemented SQP with MATLAB’s ‘fmincon’
◦ Re-scaling Hessian
◦ Multi-start (non-convex objective function and feasible space)
◦ Good results, long running times
Heuristic methods◦ Multi-Objective Genetic Algorithm (MOGA)
◦ Poor results, long running times
![Page 11: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/11.jpg)
-Varying convergence rates-Varying solution values Non-convexity
![Page 12: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/12.jpg)
![Page 13: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/13.jpg)
![Page 14: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/14.jpg)
![Page 15: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/15.jpg)
Design Variables Values Comments
R 14.13
Qmax 20000
t 0.004
k 4
T(mid) 0.79 lower bound
T(tip) 0.78
F 0.25
C(root) 1.91 upper bound
C(mid) 0.79
C(tip) 0.24
beta 0.79
0.75
0.36162
![Page 16: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/16.jpg)
Sensitivity Analysis (2nd order central difference)◦ Decision variables that are tight on box bounds have directions of
improvement without violating feasibility (Qmax increase PE/Vblades increase, σmax decrease
◦ Decision variables that are free on box bounds have no directions of improvement that do not violate constraints (R increase σmax increase)
Connection to Lagrange multipliers
![Page 17: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/17.jpg)
Slope of Pareto Front◦ initially benefit from going to higher expected power
◦ later stages cost outweighs benefits of increasing expected power
◦ optimum somewhere in between
Utopia point – highest expected power for the lowest cost
SQP outperforms MOGA◦ Not enough running time
◦ Computational expense
Utopia point
Best result from SQP
![Page 18: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/18.jpg)
DOE is powerful and inexpensive
SQP works great for local optimization
Heuristic methods may be too expensive
![Page 19: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/19.jpg)
Higher resolution optimization◦ More decision variables for distributions
Higher fidelity analysis◦ Increase blade discretization
◦ Qprop
◦ VABS
Higher-powered optimization◦ DAKOTA implementation may be more powerful than the
Matlab Optimization Toolbox
Questions?
Also for validation
![Page 20: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/20.jpg)
Thickness of structural spar compensates for light structure◦ Adds leeway
t
tbox
Blade Cross-section
![Page 21: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/21.jpg)
![Page 22: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/22.jpg)
Best combination of factor levels
![Page 23: Anonymous MIT Students · ESD.77 Student Project, Wind Turbine Blade Design Optimization Author: Anonymous MIT Students Created Date: 10/22/2010 12:37:36 PM](https://reader036.vdocuments.us/reader036/viewer/2022062506/5fbe391e7609f0655448e8cc/html5/thumbnails/23.jpg)
MIT OpenCourseWarehttp://ocw.mit.edu
ESD.77 / 16.888 Multidisciplinary System Design Optimization
Spring 2010
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.