Comparative study of discretization method and Monte Carlo method for wind farm layout optimization under Weibull distribution

The wind farm layout optimization is an effective tool to alleviate the wake power losses caused by wind turbine interactions in a wind farm. It is widely recognized that for a real wind farm site with abundant wind resources, wind speed variation of the wind condition can be approximated by the Weibull distribution, which therefore needs to be incorporated into the power evaluation of a real wind farm design. Current researchers have employed the discretization method by dividing the wind speed region into bins to calculate the power output of wind turbines under Weibull distribution, which has two main drawbacks including: 1) complicated discretization process with large computational cost and 2) dependency of calculation accuracy on the discretization resolution. This paper aims to propose a new Monte Carlo method to evaluate the wind farm power output under Weibull distribution, and verify the effectiveness and efficiency of the new method by comparison to the widely used discretization method. Through reducing the wind speed discretizing interval, it is found that when the discretized wind speed interval is smaller than 0.1 m/s, the improvement of optimization results is negligible while the computational cost significantly increases for the discretization method. By testing different sample numbers, it is found that selecting 100000 samples for the Monte Carlo method calculation is able to achieve accurate results with less computational cost than the discretization method especially when large number of turbines is installed in the wind farm. In conclusion, the Monte Carlo method greatly facilitates the power evaluation of wind farm layout optimization under Weibull distribution, with a balance between the calculation accuracy and the computational cost.