کاربرد الگوریتم ژنتیک در بهینه سازی طرح باد مزرعه با ارتفاع هاب متفاوت توربین بادی

ABSTRACT Wind farm layout optimization using genetic algorithm with different hub height wind turbines

Serious environmental pollution is threatening humans’ health, which has raised a lot of public concerns. Fossil fuels as the main energy sources in current society are not sustainable and will be exhausted in the foreseeable future due to limited resources, rapid consumption, climate change, global warming, etc. [1]. In academia, a lot of researchers are investigating how to use renewable energy, such as solar energy, biomass, and wind energy, as substitutes of traditional energy resources.

Meanwhile, most countries are trying to use renewable energy to replace fossil fuels so as to keep a better environment. Regarding about wind energy, higher conversion rate, clean and safety are its major advantages compared to other types of renewable energy [1–6]. However, the large variation, uncertainty, and other non-predictable factors and issues impact the wind power estimation and the energy capture efficiency tremendously [1–6]. In US, the cumulative wind power installed capacity is only equal to about 3.3% of the nation’s electricity demand at the end of 2011 [7]. In order to increase power output and economic performance of a wind farm, wind speed estimation, wind turbine and gearbox design, and layout optimization are several focal research areas. Liu et al. [8] introduced a quantitative methodology of building an ARMA– GARCH-M model to improve the forecasted rate of wind speeds. Mohammadi and Mostafaeipour [9] demonstrated that Weibull distribution based on the standard deviation method and the power density method was able to estimate the mean wind power as an alternative method much better. Hall et al. [10] proposed variable ratio gearbox which was integrated into fixed speed wind turbine to adapt to the variable speeds in order to boost efficiency. Kenway and Martin [11] presented a multidisciplinary optimization framework for the design of wind turbine rotors to maximize the power output of a wind turbine by changing the blade geometry and structural sizes without any cost changes and non-compatibility with the rest part of turbine system. Ramos et al. [12] analyzed the factors that affected the wind farm energy output, and indicated that the location selection of a wind farm was very important. In Refs. [13–21], the researchers tried to optimize the layout of a wind farm by the intelligent algorithms with the objective of maximizing its power output or minimizing its cost per unit power.

In this paper, the authors mainly focus on wind farm layout optimization. Most previous research conducted on this topic made use of genetic algorithm (GA) to realize different research objectives. Mosetti et al. [13] first used GA to optimize the layout of a wind farm under three scenarios: constant wind speed and direction, constant wind speed and various wind directions, and various wind speeds and directions. Based on Mosetti et al.’s research, Grady et al. [14] employed more individuals (600) and generations (3000) in GA to achieve better layout for a wind farm.

Mittal [15] proposed the micro-sitting method with GA in order to find more accurate positions in a wind farm, and the cell size in his research was 1 m 1 m, which was different from 200 m 200 m cell size used in Refs. [13,14]. Compared to Grady et al.’s results, Mittal’s results indicated that the cost per unit power could be reduced in all three scenarios. In order to increase the wind farm power output, Acero et al. [16] investigated the possibility of applying wind turbines with two hub heights in a straight line, and the results demonstrated that using different hub height wind turbines might help generate more power output. Chen and McDonald [17] considered the landowners’ decision on wind turbines installation into wind farm layout optimization process. Regarding the tower cost, turbine machine cost and foundation cost, Mora et al. [18] proposed an evolution algorithm based on GA to design a wind farm layout with minimum investment and most efficient use of the wind resource. Later, Gonzalez et al. [19] extended the cost model developed in Ref. [18] to an integral cost model based on a life cycle cost approach. Besides GA, Mardis et al. [20] tried to use Monte Carlo algorithm to optimize layout of a wind farm under constant wind speed and direction. And under the same wind condition in Ref. [20], Chowdhury et al. [21] employed particle swarm optimization (PSO) algorithm to exhibit that the wind turbines with different diameters could improve the power output of a wind farm.

In this paper, the authors use GA in MATLAB to optimize the layout of a given wind farm with different hub height wind turbines in order to investigate the benefits of using wind turbines with different hub heights. Among all kinds of factors affecting wind farm layout design, the authors only consider the following factors based on the scope of this study: (1) number of turbines installed in a given wind farm, (2) hub heights of wind turbines, (3) wind directions and speeds, and (4) power output and cost per unit power of a given wind farm. As to the factors including local topography, wind farm soil conditions, the construction of roadways, nameplate capacity of a wind farm, and the local vegetation coverage [21], they are not taken into account within the scope of this study. The authors first conduct the layout optimization of a 500 m 500 m wind farm in three scenarios: (1) constant wind speed and direction, (2) constant wind speed and various wind directions, and (3) various wind speeds and directions. In each case, the power outputs of the optimal layouts using same hub height wind turbines and using different hub height wind turbines are compared, so that the effect of different hub height wind turbines on power output can be investigated. Different cost models are also taken into account in the analysis, and results show that different hub height wind turbines can also improve cost per unit power of the wind farm. At last, a large wind farm with commercial wind turbines is further analyzed to examine the benefits of using different hub height wind turbines in more realistic conditions.