Introduce a linear discrete model to optimization of wind farm layout using mixed integer programming considering of sound constraint

Optimization of the arrangement of turbines with the aim of producing the maximum power in a wind farm is inherently part of continuous and nonlinear problems. In the present study, for the linearization of the Wake constraint and the connection between turbine power and single Wake and discrete models. Also, the criterion of placing a turbine in another turbine has been applied indirectly and linearly. The proposed mathematical model compares to continuous nonlinear mathematical models, while maintaining the advantage of achieving exact optimum, has a lower runtime and higher stability. Comparison of the results of the present study with the results of previous studies suggests that metaheuristics algorithms may not be obtained in absolute optimal answer. In addition to the power output, environmental issues can also affect the arrangement of turbines. As an example, the maximum noise level is applied in the present model. In order to calculate the intensity of sound, Euclidean distance based on the spread of the hemisphere and the effects of atmospheric absorption has been used. According to the results, it can be said that under the conditions under consideration, the noise level can cause a significant reduction in the output power of the wind farm. Therefore, in selecting the field, attention should be paid to the distance to residential areas. In addition, the effect of cell count on the accuracy of the results was investigated. The results show that there is no clear relationship between optimal power and number of cells.