Optimization of wind turbine layout position in a wind farm using a newly-developed two-dimensional wake model

The development and validation of a 2D analytical wind turbine wake model based on Jensen's wake model using Gaussian function is presented in this paper. The velocity deficit predicted by the newly-developed Jensen-Gaussian wake model is compared with wind tunnel experimental measured data in literatures and results show that, the velocity deficit predicted by the model fits well with the measured data at different downwind distances of X = 2.5D, X = 5D, X = 7.5D and X = 10D. Considering the turbulence inside the turbine wake, a new turbulence model is developed and based on this, the Jensen-Gaussian wake model was improved and validated. The 2D Jensen-Gaussian wake model is then applied in the wind turbine layout optimizing process within a wind farm based on the multiple populations genetic algorithm (MPGA). The performance of this newly 2D model in the optimization process is validated and compared with the results presented in some typical studies on the turbine layout optimization. The comparison is performed for 'constant wind speed of 12 m/s with variable wind directions'. Using the 2D Jensen-Gaussian wake model instead of Jensen's wake model in the MPGA turbine layout optimization program, both the total power generation and wind farm efficiency decreased. The wind farm efficiency drop to 77.83%, 78.47% and 81.84% from 96.83%, 96.34% and 96.23% for 38, 39 and 40 wind turbines, respectively which is in accordance with the literatures on the power losses caused by wake effect in large wind farm. The development and application of the 2D Jensen-Gaussian wake model means more theory significance and practical values in wind energy utilization.