Layout Optimization of Onshore HAWTs in Wind Farms

Abstract

Wind energy has been recognized as one of the fastest-growing energy sources globally. With the growing development and installation of wind farms, more research is needed to study and optimize wind turbines to reduce deficiencies created by the upfront wind turbines. The power loss due to wake effects can reach up to 40% of the upstream wind turbines. Wind farm design and optimization is a complex multidisciplinary topic that requires a lot of expertise. Several computational fluid dynamics (CFD) methods have been used for Wind Farm Layout Optimization (WFLO), using complete or total modeling of the rotor and the wake. However, selecting good wind farm locations is difficult and time-consuming. It is influenced by various factors such as wind energy potential, wind turbine site, distance to the electrical grid, distance from populated areas, and land usage. In this study the Genetic Algorithm (GA) is parametrized and employed to increase the expected power generation in a wind form. The algorithm is an optimization technique based on evolution and natural selection theories. The GA-developed method was capable to predict the optimal locations of wind turbines in a wind farm and identify the most suitable layout to maximize the power production and minimize the cost. The mathematical model has been built based on the wind wake model of wake losses based on the conservation laws of momentum and mass with assuming a linear expansion downstream. The GA optimization model considers five phases: initial population, fitness function, selection, crossover, and mutation. It is worth mentioning that, our own MATLAB code has been developed from scratch. The developed model has been validated against trusted results from the literature. After that, numerical experiments are conducted and four case studies are presented using our model. These case studies are created to study the impacts of four parameters; population size, cost model, hub height, and surface roughness and target four aspects: the objective function, fitness, average power, and wind turbine distribution. The population sizes of 500, 1000, 1500, and 2000 are considered and it is found that 1500 is the optimal population size for the present model. However, when the number of generations increases beyond 55 generations, the population sizes 1500 and 2000 have very close fitness values, which means increasing the population by more than 1500 has no effect on the output. Additionally, the findings of this study show that Mosettie's cost model leads to having a minimum objective function and optimal wind farm layout in comparison to Chen's cost model. Furthermore, the taller the turbine, the more wind it receives, thus more average power produced. Also, it was found that the objective function value decreases with increasing the smoothness of the wind farm terrain.