Research Papers

Objectives and Constraints for Wind Turbine Optimization

[+] Author and Article Information
S. Andrew Ning

National Wind Technology Center,
15013 Denver West Parkway,
Golden, CO 80401
e-mail: andrew.ning@nrel.gov

Rick Damiani, Patrick J. Moriarty

National Wind Technology Center,
15013 Denver West Parkway,
Golden, CO 80401

An Akima spline was chosen because of its robustness to outliers. If one of the chord variables differs significantly in magnitude from the others (which can happen during the course of an optimization), then oscillations are produced for many spline types. This may cause some sections to have negative chord values, which is nonphysical and will prevent the analysis from running properly. An Akima spline prevents these types of oscillations. A simple bound constraint on chord is sufficient to prevent intermediate designs with negative chord, as opposed to a nonlinear constraint on chord that would be required if using a cubic spline or Bezier curve.

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGYAND BUILDING ENERGY CONSERVATION. Manuscript received March 21, 2013; final manuscript received April 9, 2014; published online June 3, 2014. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 136(4), 041010 (Jun 03, 2014) (12 pages) Paper No: SOL-13-1092; doi: 10.1115/1.4027693 History: Received March 21, 2013; Revised April 09, 2014

Efficient extraction of wind energy is a complex, multidisciplinary process. This paper examines common objectives used in wind turbine optimization problems. The focus is not on the specific optimized designs, but rather on understanding when certain objectives and constraints are necessary, and what their limitations are. Maximizing annual energy production, or even using sequential aero/structural optimization, is shown to be significantly suboptimal compared to using integrated aero/structural metrics. Minimizing the ratio of turbine mass to annual energy production can be effective for fixed rotor diameter designs, as long as the tower mass is estimated carefully. For variable-diameter designs, the predicted optimal diameter may be misleading. This is because the mass of the tower is a large fraction of the total turbine mass, but the cost of the tower is a much smaller fraction of overall turbine costs. Minimizing the cost of energy is a much better metric, though high fidelity in the cost modeling is as important as high fidelity in the physics modeling. Furthermore, deterministic cost of energy minimization can be inadequate, given the stochastic nature of the wind and various uncertainties associated with physical processes and model choices. Optimization in the presence of uncertainty is necessary to create robust turbine designs.

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Fig. 1

Rotor blade chord distribution parameterization

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Fig. 2

Rotor blade twist distribution parameterization

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Fig. 3

Parameterization of spar cap thickness distribution

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Fig. 4

Maximum annual energy production for different designs. Each design was constrained to have a different blade mass. Point M1 is highlighted and corresponds to the maximum AEP solution, with the mass constrained such that mblade¯ = 1.

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Fig. 5

Flapwise loading for the baseline design and the maximum AEP solution with fixed mass (design M1). The root bending moment for the optimized design decreases, even without a root bending moment constraint.

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Fig. 6

Comparison between sequential aerodynamic and structural optimizations and an integrated aerodynamic and structural optimization. The percent change in mass is relative to the total turbine mass.

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Fig. 7

Chord and twist distributions for the three designs that were examined

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Fig. 8

Designs with minimum m/AEP as a function of rotor diameter. (a) Minimum m/AEP solutions are compared to minimum cost of energy solutions (both evaluated using COE). (b) Variation in m/AEP approximately predicts the correct optimal diameter.

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Fig. 9

Relative contributions to total mass and total cost of the baseline design. Cost contributions already include the fixed charge rate and tax rate. The tower contribution is of particular note.

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Fig. 10

Comparison of chord and twist distributions for minimum COE and minimum m/AEP design at D/D0 = 1.05

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Fig. 11

Designs with minimum mfixed/AEP as a function of rotor diameter. (a) Minimum mfixed/AEP solutions are compared to minimum cost of energy solutions (both evaluated using COE). (b) Variation in mfixed/AEP predicts wrong trend.

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Fig. 12

Cost of energy as a function of hub wind speed for a point design that was optimized at 10 m/s, as compared to a robust design that was optimized to minimize the expected value of the cost of energy across the wind speeds




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