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.

Copyright © 2016 by ASME
Topics: Wakes , Turbines , Wind , Wind farms
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Grahic Jump Location
Fig. 2

Wake cone membership detection

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Fig. 6

Proposed exclusion zone

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Fig. 5

Sector 3 upstream/downstream relationships

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Fig. 4

Wake cone generated by wind direction in Sector 3

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Fig. 7

Power loss curve and trapezoid approximation

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Fig. 8

Turbine power and thrust coefficient curves

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Fig. 9

Wind speed profiles

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Fig. 11

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



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