Placement of wind turbines using genetic algorithms

doi:10.1016/j.renene.2004.05.007

Renewable Energy

Volume 30, Issue 2, February 2005, Pages 259-270

https://doi.org/10.1016/j.renene.2004.05.007 Get rights and content

Abstract

A genetic algorithm approach is employed to obtain optimal placement of wind turbines for maximum production capacity while limiting the number of turbines installed and the acreage of land occupied by each wind farm. Specifically, three cases are considered—(a) unidirectional uniform wind, (b) uniform wind with variable direction, and (c) non-uniform wind with variable direction. In Case (a), 600 individuals are initially distributed over 20 subpopulations and evolve over 3000 generations. Case (b) has 600 individuals spread over 20 subpopulations initially and evolves for 3000 generations. Case (c) starts with 600 individuals spread over 20 subpopulations and evolves for 2500 generations. In addition to optimal configurations, results include fitness, total power output, efficiency of power output and number of turbines for each configuration. Disagreement with the results of an earlier study is observed and a possible explanation is provided.

Introduction

Two main reasons for interest in wind as an energy source are diminishing fossil fuel resources and the effect use of fossil fuel sources has on the environment. Wind energy, a widely available derivative of solar energy that has been captured by the earth’s atmosphere, is receiving considerable attention as an emission-free, low cost alternative to traditional energy sources. Considerable development has taken place in the design of wind energy conversion systems. Modern wind turbines are highly sophisticated machines built on the aerodynamic principles developed in the aerospace industry. Advanced materials and electronics have been incorporated into wind turbines designed to deliver energy across a wide range of wind speeds.

As rule of thumb, 10 ha/MW can be taken as the land requirement of wind farms, including infrastructure [1]. The spacing of a cluster of machines in a wind farm depends on the terrain, the wind direction and speed, and the turbine size. According to Patel, the optimal spacing is found in rows 8–12 rotor diameters apart in the windward direction, and 1.5–3 rotor diameters apart in the crosswind direction [2]. Ammara et al. [3] contended that this intuitive spacing scheme resulted in sparse wind farms that were inefficiently using the wind energy potential of the site. A dense, staggered siting scheme was proposed that would yield production similar to the sparse scheme, but would use less land. While this approach successfully reduced the land mass required for a given amount of wind turbines, the method of placement was still intuitive.

Mosetti et al. proposed a position optimization scheme based on genetic algorithms [4]. In this research, algorithms were developed for wind farm performance evaluation and optimization. The investment cost and the total power extracted were the variables optimized. The wind and cost models chosen were incomplex for the purposes of demonstrating the effectiveness of the optimization algorithm. While the power and efficiency calculations of the optimally placed wind turbines compare favorably with a greater number of randomly placed turbines, the optimal configurations presented do not yield even the simplest empirical placement schemes. This study seeks to determine the effectiveness of the genetic algorithm optimization procedure in identifying optimum configurations.

Section snippets

Wake and cost modeling

As in the Mosetti study, a wake model similar to the Jensen analysis is used for simplification of the wind field calculations [4], [5], [6], [7]. This wake analysis is based on the assumption that momentum is conserved inside the wake. In the analysis of a single wake, the near field behind the wind turbine is neglected making it possible to model the resulting wake as a turbulent wake or a negative jet. At the turbine, the wake has a radius equal to the turbine radius, r_r. As the wake

Optimization

Genetic algorithms are probabilistic search algorithms combining the mechanics of natural selection and survival of the fittest. These algorithms are capable of efficiently finding an optimal solution for complex problems without necessitating reformulation for the evaluation of individual solution candidates. Unlike calculus-based methods, genetic algorithms are robust, global, and do not require the existence of derivatives for search. Enumerative schemes are lacking in robustness due to

Numerical procedure

A square grid divided into 100 possible turbine locations was used as the computational domain. The width of each cell, in the center of which a turbine would be placed, is equal to five rotor diameters, 5D, or 200 m, giving the domain dimensions of 50D×50D. Based on the dimensions of the computational domain, the maximum radius of the wake from a single turbine placed in the position (x, y)=(100 m, 100 m) (see Fig. 3 as a reference) is 189.9 m. The width of each cell, in the center of which a

Case (a)

The optimal solution for Case (a) can be derived heuristically. The domain under consideration for this study uses a wake model that increases in diameter only as a function of downstream distance. A simple optimization of one 10-cell column in the computational domain can therefore be projected across the entire domain in order to find the optimal solution for this simple wind scenario. This optimization produced an optimal configuration of three turbines in positions 1, 6 and 10 as shown in

Conclusions

The results of the present study demonstrate that genetic algorithms could accurately predict optimal wind farm configurations. In the simple case of uniform unidirectional wind, heuristic arguments verify the optimal configuration of the present study, which is at odds with that of Mosetti et al. It is possible that their work did not run enough individuals for sufficient number of generations to achieve convergence. Although the genetic algorithm is an effective global search method, it can

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A viscous three-dimensional differential/actuator-disk method for the aerodynamic analysis of wind farms
J Sol Energy Eng
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Technical notePlacement of wind turbines using genetic algorithms

Abstract

Introduction

Section snippets

Wake and cost modeling

Optimization

Numerical procedure

Case (a)

Conclusions

Energy Convers Manag

J Wind Eng Ind Aerodyn

Wind and Power Solar Systems

A viscous three-dimensional differential/actuator-disk method for the aerodynamic analysis of wind farms

J Sol Energy Eng

Technical note
Placement of wind turbines using genetic algorithms