Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 324203, 9 pages

http://dx.doi.org/10.1155/2015/324203

## Optimal Wind Turbines Micrositing in Onshore Wind Farms Using Fuzzy Genetic Algorithm

College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

Received 17 October 2014; Accepted 15 February 2015

Academic Editor: Victor Sreeram

Copyright © 2015 Jun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the fast growth in the number and size of installed wind farms (WFs) around the world, optimal wind turbines (WTs) micrositing has become a challenge from both technological and mathematical points of view. An appropriate layout of wind turbines is crucial to obtain adequate performance with respect to the development and operation of the wind power plant during its life span. This work presents a fuzzy genetic algorithm (FGA) for maximizing the economic profitability of the project. The algorithm considers a new WF model including several important factors to the design of the layout. The model consists of wake loss, terrain effect, and economic benefits, which can be calculated by locations of wind turbines. The results demonstrate that the algorithm performs better than genetic algorithm, in terms of maximum values of net annual value of wind power plants and computational burden.

#### 1. Introduction

Nowadays, wind energy plays a very important role in the field of renewable energy supply worldwide. According to Global Wind Energy Council (GWEC), the new global total wind power capacity was 318,105 MW by the end of 2013, representing more than 12.5 percent increase in cumulative market [1]. Wind power has become the most valuable and promising renewable energy option not only in developed but also in developing countries [2]. Wind energy technology develops rapidly and its cost is beginning to actually compete with existing fossil-fuel power production methods. But with the fast growth in the number and size of installed wind farms around the world, optimal wind turbines micrositing has become very important topic of study. The optimal turbines layout of a wind farm is a challenge from both mathematical and technological points of view. An appropriate position of wind turbines will directly influence the costs and the produced energy of a wind farm. The generated power from the turbines of a wind farm is often lower than expected, partly because the aerogenerators receive lower wind speeds and less energy captures if they are located behind the other one. This effect is called the wake effect [3].

So far, several works have appeared in which the optimization of a mathematical model of a wind farm has been addressed in order to undertake the optimal position of WTs [4–6]. In these studies, the optimized objective functions taking into account maximum energy production and minimum levelized cost of energy were used for determining the optimal locations of WTs. The problem was introduced by Mosetti et al. [7] which aimed to maximize the annual energy produced (AEP) and to minimize the installation costs by assuming a rather simplified cost model of the wind farm (based on economies of scale and the overlapping of wakes) to search for an optimal layout based on genetic algorithms (GAs). And the algorithm used a wake effect analysis similar to that of Katic et al. [8]. The following methods have considered Monte Carlo simulation with a simple model [6, 9], ant colony optimization (ACO) algorithm requiring large amount of calculation [10]. Geem and Hong [11] optimize the layout with the constraints of resources or budget bounds by an improved formulation method, but the cost and power functions are also experience function and cannot reflect the real WF model very well. Some other WT micrositing optimization methods, based on the Gaussian particle swarm optimization with local search strategy [12], binary particle swarm optimization [5], and greedy algorithm [13], have also been studied.

In the current study, we establish a new model for WF considering the main effective indicators simultaneously, including wake loss, terrain effect, hub height of the turbines, and economic benefit. Then we present an efficient methodology for the optimization of onshore WFs. In our approach, fuzzy control is implemented to adjust the crossover probability and mutation probability of the GA for determining the best sites of WTs in two different scenarios.

After this introduction, the paper is organized as follows. Section 2 presents a WF model including wake model, terrain effect model, energy production model, and economic model. Section 3 describes the approach to the problem and the proposed methodology. Test cases are provided in Section 4. At last, conclusions are discussed in Section 5.

#### 2. Wind Farm Modelling

##### 2.1. Wake Effect Model

The analytical model in this paper is similar to the wake decay model proposed by Jensen [14]. Depending on the wind farm geometry, the wind speed decay ratio produced in the airflow when the wind passes through the rotor of a wind turbine (see Figure 1) can be calculated by the expression:
where is the initial free stream velocity, is the velocity in the wake at a distance downstream of the upwind turbine,* D* is the diameter of the upwind turbine, and is the wake decay constant. is the axial induction factor or inflow factor that is related to the thrust coefficient, , according to
The expansion rate* k*, which is known as wake decay constant, is a value of 0.075 for onshore cases and 0.05 for offshore ones suggested in the literature [15] and is calculated as a function of surface roughness, given as
where is the hub height of the wind turbine and is surface roughness.