Wind Farm Layout Optimization Problem Using Joint Probability Distribution of CVaR Analysis

This study proposes the optimal layout of an offshore wind farm (WF) allocation for a number (N) of wind turbines (WTs) in a 2 km × 2 km fixed area. The paper aims to maximize expected WF power output and efficiency, considering the joint probability distribution of wind speed and direction. In fact, the effects of both stochastic variables (wind speed and direction) are considered to find optimal WF layout. Unlike most previous studies, using the coordinate model (CM) allows the WTs to be located on any available spot in the WF but not only at the center of the grids. Thus, by applying joint probability distribution to the WF expected power output, a new multi-variant conditional value-at-risk model is being presented to find the best possible layout under the worst-case scenarios for both wind speeds and directions. Indeed, the presented optimization model obtains the optimal WF locations, while it guarantees the robustness of the WF layout with certain confidence level (1-α). Finally, a case study with actual manufacturer data for the same WTs with realistic wind profile data are performed under the scope of this research to show the robustness of presented model.