A mechanistic semi-empirical wake interaction model for wind farm layout optimization

Optimizing the turbine layout in a wind farm is crucial to minimize wake interactions between turbines, which can lead to a significant reduction in power generation. This work is motivated by the need to develop wake interaction models that can accurately capture the wake losses in an array of wind turbines, while remaining computationally tractable for layout optimization studies. Among existing wake interaction models, the SS (sum of squares) model has been reported to be the most accurate. However, the SS model is unsuitable for wind farm layout optimization using mathematical programming methods, as it leads to non-linear objective functions. Hence, previous work has relied on approximated power calculations for optimization studies. In this work, we propose a mechanistic linear model for wake interactions based on energy balance, with coefficients determined based on publicly available data from the Horns Rev wind farm. A series of numerical experiments was conducted to assess the performance of the wake interaction model. Results show that the proposed model is compatible with standard mathematical programming methods, and resulted in turbine layouts with higher energy production than those found using previous work.