Multi-objective genetic algorithm based innovative wind farm layout optimization method
Introduction
With the concern of running out of current mainstream energy sources such as oil and gas, the utilization of sustainable energy has become more and more important in various aspects, including capital investment, scientific research, and consumers’ choices. Wind energy, as one of sustainable and clean energy sources, is attracting more and more attention from industry and academia. In US, the Department of Energy expects that 20% electricity would be from wind energy by 2030 [1]. However, the cumulative wind power installed capacity by 2011 is only equal to almost 3.3% of the nation’s electricity demand in US [2]. The major obstacles affecting the development of wind energy are low conversion efficiency, non-predictability and uncertainty [3]. Quality of gearbox, shape of wind blades, locations of wind farms, and many other factors affecting the conversion efficiency have been studied. For instance, a model-based design methodology was presented to study the performance gain of integrating a variable-ratio gearbox into a fixed-speed stall-regulated wind turbine system [4]. It was demonstrated that the power output of a wind turbine could be improved by changing the blade geometry and structural sizes while maintaining a fixed cost and compatibility with the remainder of turbine system [5]. A factorial analysis was conducted to show that location could have significant impact on the power output of a wind farm [6]. A wind generator maximum power point tracking system was created to improve the energy conversion rate [7]. A flexible joint probability density function of wind speed and direction was introduced in order to improve the accuracy of the wind energy analysis [8]. Uncertainty analysis was employed [9] to assess the wind resource of a wind turbine. Weibull and Rayleigh distribution [10] and mixture of two Weibull distributions [11] were also used to evaluate the wind energy. Liu et al. [12] proposed a quantitative method to effectively obtain a reliable interval estimation of wind speed and an accurate forecasted operation probability and expected power output of the wind turbine. Mohammadi and Mostafaeipour [13] found out a specific location that has sufficient wind for small wind turbines but not large wind turbines, which further improves the importance of location selection for wind farm development.
In addition, a lot of researches have been conducted related to the wind farm layout optimization. The major approaches in layout optimization can be divided into three major categories: grid based approach, array based approach and unrestricted layout approach. Grid based approach is to divide a wind farm into a set of equal-sized cells and lay out wind turbines in these cells, while unrestricted layout approach allows any positions in a wind farm can be reached.
Grady et al. [14] applied GA to lay out wind turbines in a 2 km × 2 km farm and the results showed that more generations and individuals could generate better results. Furthermore, Mittal [15] reduced the grid cell size to 1 m × 1 m in order to find more available positions, which makes it close to unrestricted layout approach. It clearly showed that 1 m × 1 m cell size played an important role in decreasing the cost per unit power. The ownership of the land has been considered in the layout optimization process, which showed landlord’s decision was superior in the optimization process [16]. Mora et al. [17] developed an evolutive algorithm to optimize the profits given an investment of a wind farm. Based on Mora’s results, Gonzalez et al. [18] improved the evolutive algorithm and optimization process based on a global wind farm cost model using the initial investment and the present value of the yearly net cash flow through the entire wind farm life span. Different hub height wind turbines were first introduced into a one dimensional wind farm layout optimization [19]. Case studies with one dimensional wind farms and simple wind conditions were conducted to further investigate the benefit of using different hub height wind turbines in a wind farm [20]. It was also proved that wind turbines with different hub heights could increase power output and decrease cost per unit power of a two dimensional wind farm [21]. Through research on an array layout wind farm, it was demonstrated that the wake model proposed by Jensen had the most accurate prediction compared to the others [22]. Mikkelsen et al. [23] showed that decreasing the loading on the foremost turbine could increase power generation of specific turbines in a row.
Besides using GA as optimization tool, some other optimization methods have been used for layout optimization of a wind farm. For instance, Monte Carlo simulation method was used to optimize the layout of a wind farm [24]. Ant colony algorithm was also used to optimize the layout of a wind farm with simplified wind conditions [25]. Choudhury et al. applied particle swarm optimization method to optimize the layout of a wind farm with different diameter wind turbines [26]. Shakoor et al. optimized a wind farm layout using definite point selection and genetic algorithm [27]. The results showed that power output of the wind farm was increased by using different dimensions while keeping the same area. Complex terrain condition for wind farm layout optimization problem has also been investigated by using lazy greedy algorithm [28]. Sequential convex programming algorithm was applied into the wind farm layout optimization by Park and Law [29]. An applicable hybrid (quadratic assignment problem-genetic algorithm) evolutionary method was also developed and applied to optimizing the layout of a more realistic wind farm [30].
In this paper, the authors focus on creating a multi-objective genetic algorithm based innovative wind farm layout optimization method. The following factors are taken into account: (1) real wind conditions; (2) commercial wind turbines parameters; (3) type and hub height selections of each wind turbine; (4) number of wind turbines needed in a given wind farm; and (5) regular and irregular shape wind farms. In the rest part of this paper, the authors first introduce the optimization method in Section 2, and describe three other models used in the optimization method in Section 3. Four case studies are conducted and the results are discussed in Section 4, while summary and future research areas are given in the last section.
Section snippets
Innovative optimization method
Among all the intelligent algorithms that have been used in wind farm layout optimization, genetic algorithm is the most popular optimization method used in previous researches. The main reason is that the chromosomal string of GA is a binary string. For the grid based approach, “0” and “1” are able to represent if there is a wind turbine in the cell or not. Furthermore, “0” and “1” can represent the decision of landowner [16], and can also be utilized to stand for the wind turbines hub
Other models used in the wind farm layout optimization
In the wind farm layout optimization procedure, cost model, wind condition model, wake model, and turbine parameters are also very important.
Case studies
Four case studies are conducted using the innovative optimization method. The first case study is based on a regular rectangle wind farm with a given size of 2800 m × 900 m, while the other three are focusing on irregular shape by changing one side of rectangle to an arbitrary curve. In order to compare the results among all four case studies, the total areas of regular and irregular shapes are kept same. An improved optimization procedure is introduced in the third case study. While the first
Conclusion
In this paper, the authors introduce an innovative wind farm layout optimization method based on the multi-objective genetic algorithm. Different from traditional GA, the authors use GA with the mixed discrete real integer string to represent the wind turbines positions, types and the hub heights simultaneously. This innovative optimization method can be used to optimize layouts of both irregular shape and regular shape wind farms, and it can also optimize the combination of different wind
Acknowledgments
This work is supported by Frank H. Dotterweich College of Engineering at Texas A&M University-Kingsville. The authors are also thankful to HP Catalyst Initiative for providing computational equipment for this project.
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