0
Research Papers: Design Automation

A Mixed Integer Linear Programing Formulation for Unrestricted Wind Farm Layout Optimization

[+] Author and Article Information
Ning Quan

Enterprise Systems Optimization Laboratory,
Department of Industrial and
Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: nquan3@illinois.edu

Harrison M. Kim

Enterprise Systems Optimization Laboratory,
Department of Industrial and
Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: hmkim@illinois.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 6, 2015; final manuscript received March 22, 2016; published online April 20, 2016. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 138(6), 061404 (Apr 20, 2016) (9 pages) Paper No: MD-15-1687; doi: 10.1115/1.4033239 History: Received October 06, 2015; Revised March 22, 2016

This paper presents a novel mixed integer linear programing (MILP) formulation for finding the optimal layout of a fixed number of identical turbines that maximizes wind farm power generation. Previous MILP formulations with power maximizing objectives discretize the feasible space by using a grid of possible turbine locations. The proposed MILP formulation takes a different approach by allowing unrestricted placement of turbines, but treats wake cone overlap as a binary outcome. The rationale behind the proposed formulation is that the expansion of the feasible space for turbine placement in the proposed formulation would offset the disadvantage of using a lower fidelity binary wake cone overlap model. For small wind farms, the proposed formulation was able to produce superior layouts compared to a grid-based MILP formulation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Wakes , Turbines , Wind , Wind farms
Your Session has timed out. Please sign back in to continue.

References

Pineda, I. , Azau, S. , Moccia, J. , and Wilkes, J. , 2014, “ Wind in Power, 2013 European Statistics,” The European Wind Energy Association, Last accessed Jan. 8, 2015, http://www.ewea.org/fileadmin/files/library/publications/statistics/EWEA_Annual_Statistics_2013.pdf
Wiser, R. , and Bolinger, M. , 2012, “ 2012 Wind Technologies Market Report,” United States Department of Energy, Last accessed Jan. 8, 2015, https://www1.eere.energy.gov/wind/pdfs/2012_wind_technologies_market_report.pdf
González, J. S. , Payán, M. B. , Santos, J. M. R. , and González-Longatt, F. , 2014, “ A Review and Recent Developments in the Optimal Wind-Turbine Micro-Siting Problem,” Renewable Sustainable Energy Rev., 30, pp. 133–144. [CrossRef]
Herbert-Acero, J. F. , Probst, O. , Réthoré, P.-E. , Larsen, G. C. , and Castillo-Villar, K. K. , 2014, “ A Review of Methodological Approaches for the Design and Optimization of Wind Farms,” Energies, 7(11), pp. 6930–7016. [CrossRef]
Zhang, P. Y. , Romero, D. A. , Beck, J. C. , and Amon, C. H. , 2014, “ Solving Wind Farm Layout Optimization With Mixed Integer Programs and Constraint Programming,” EURO J. Comput. Optim., 2(3), pp. 195–219. [CrossRef]
Turner, S. D. O. , Romero, D. A. , Zhang, P. Y. , Amon, C. H. , and Chan, T. C. Y. , 2014, “ A New Mathematical Programming Approach to Optimize Wind Farm Layouts,” Renewable Energy, 63, pp. 674–680. [CrossRef]
Bertsimas, D. , and Weismantel, R. , 2005, Optimization Over Integers, Dynamic Ideas, Belmont, MA.
Mosetti, G. , Poloni, C. , and Diviacco, B. , 1994, “ Optimization of Wind Turbine Positioning in Large Windfarms by Means of a Genetic Algorithm,” J. Wind Eng. Ind. Aerodyn., 51(1), pp. 105–116. [CrossRef]
Grady, S. A. , Hussaini, M. Y. , and Abdullah, M. M. , 2005, “ Placement of Wind Turbines Using Genetic Algorithms,” Renewable Energy, 30(2), pp. 259–270. [CrossRef]
Salcedo-Sanz, S. , Gallo-Marazuela, D. , Pastor-Sánchez, A. , Carro-Calvo, L. , Portilla-Figueras, A. , and Prieto, L. , 2013, “ Evolutionary Computation Approaches for Real Offshore Wind Farm Layout: A Case Study in Northern Europe,” Expert Syst. Appl., 40(16), pp. 6292–6297. [CrossRef]
Chen, L. , and MacDonald, E. , 2012, “ Considering Landowner Participation in Wind Farm Layout Optimization,” ASME J. Mech. Des., 134(8), p. 084506. [CrossRef]
Chen, K. , Song, M. X. , He, Z. Y. , and Zhang, X. , 2013, “ Wind Turbine Positioning Optimization of Wind Farm Using Greedy Algorithm,” J. Renewable Sustainable Energy, 5, p. 023128. [CrossRef]
Dobrić, G. , and Durisić, Z. , 2014, “ Double-Stage Genetic Algorithm for Wind Farm Layout Optimization on Complex Terrains,” J. Renewable Sustainable Energy, 6, p. 033127. [CrossRef]
Song, M. , Chen, K. , Zhang, X. , and Wang, J. , 2015, “ The Lazy Greedy Algorithm for Power Optimization of Wind Turbine Positioning on Complex Terrain,” Energy, 80, pp. 567–574. [CrossRef]
Kwong, W. Y. , Zhang, P. Y. , Romero, D. , Moran, J. , Morgenroth, M. , and Amon, C. , 2014, “ Multi-Objective Wind Farm Layout Optimization Considering Energy Generation and Noise Propagation With NSGA-II,” ASME J. Mech. Des., 136(9), p. 091010. [CrossRef]
Crespo, A. , Hernández, J. , and Frandsen, S. , 1999, “ Survey of Modelling Methods for Wind Turbine Wakes and Wind Farms,” Wind Energy, 2(1), pp. 1–24. [CrossRef]
Frandsen, S. , Barthelmie, R. , Pryor, S. , Rathmann, O. , Larsen, S. , Højstrup, J. , and Thøgersen, M. , 2006, “ Analytical Modeling of Wind Speed Deficit in Large Offshore Wind Farms,” Wind Energy, 9(1–2), pp. 39–53. [CrossRef]
Lackner, M. A. , and Elkinton, C. N. , 2007, “ An Analytical Framework for Offshore Wind Farm Layout Optimization,” Wind Eng., 31(1), pp. 17–31. [CrossRef]
Kusiak, A. , and Song, Z. , 2010, “ Design of Wind Farm Layout for Maximum Wind Energy Capture,” Renewable Energy, 35(3), pp. 685–694. [CrossRef]
Lu, S. , and Kim, H. M. , 2014, “ Wind Farm Layout Design Optimization Through Multi-Scenario Decomposition With Complementarity Constraints,” Eng. Optim., 46(12), pp. 1669–1693. [CrossRef]
Du Pont, B. L. , and Cagan, J. , 2012, “ An Extended Pattern Search Approach to Wind Farm Layout Optimization,” ASME J. Mech. Des., 134(8), p. 081002. [CrossRef]
Eroğlu, Y. , and Seçkiner, S. U. , 2012, “ Design of Wind Farm Layout Using Ant Colony Algorithm,” Renewable Energy, 44, pp. 53–62. [CrossRef]
Chowdhury, S. , Zhang, J. , Messac, A. , and Castillo, L. , 2013, “ Optimizing the Arrangement and the Selection of Turbines for Wind Farms Subject to Varying Wind Conditions,” Renewable Energy, 52, pp. 273–282. [CrossRef]
Réthoré, P.-E. , Fuglsang, P. , Larsen, G. C. , Buhl, T. , Larsen, T. J. , and Madsen, H. A. , 2014, “ TOPFARM: Multi-Fidelity Optimization of Wind Farms,” Wind Energy, 17(12), pp. 1797–1816. [CrossRef]
Wagner, M. , Day, J. , and Neumann, F. , 2013, “ A Fast and Effective Local Search Algorithm for Optimizing the Placement of Wind Turbines,” Renewable Energy, 51, pp. 64–70. [CrossRef]
Park, J. , and Law, K. H. , 2015, “ Layout Optimization for Maximizing Wind Farm Power Production Using Sequential Convex Programming,” Appl. Energy, 151, pp. 320–334. [CrossRef]
Long, H. , and Zhang, Z. , 2015, “ A Two-Echelon Wind Farm Layout Planning Model,” IEEE Trans. Sustainable Energy, 6(3), pp. 863–871. [CrossRef]
Pérez, B. , Mínguez, R. , and Guanche, R. , 2013, “ Offshore Wind Farm Layout Optimization Using Mathematical Programming Techniques,” Renewable Energy, 53, pp. 389–399. [CrossRef]
Jonkman, J. , Butterfield, S. , Musial, W. , and Scott, G. , 2009, “ Definition of a 5-MW Reference Wind Turbine for Offshore System Development,” National Renewable Energy Laboratory, Technical Report No. NREL/TP-500-38060.

Figures

Grahic Jump Location
Fig. 2

Wake cone membership detection

Grahic Jump Location
Fig. 4

Wake cone generated by wind direction in Sector 3

Grahic Jump Location
Fig. 5

Sector 3 upstream/downstream relationships

Grahic Jump Location
Fig. 6

Proposed exclusion zone

Grahic Jump Location
Fig. 7

Power loss curve and trapezoid approximation

Grahic Jump Location
Fig. 8

Turbine power and thrust coefficient curves

Grahic Jump Location
Fig. 9

Wind speed profiles

Grahic Jump Location
Fig. 11

Wake cones generated along the 270 deg direction in the square wind farm

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In