Multi-objective mathematical model for optimal wind turbine placement in wind farm under uncertainty

The main objective of this research is to introduce three energy risk management models grounded in optimization techniques for the strategic placement of wind turbines, considering wake effects and uncertainties in wind speed and direction. For this purpose, wind speed and direction data are gathered, and Monte Carlo simulation is employed to model the uncertainties. Subsequently, the risk management models undergo optimization using Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Pareto envelope-based selection algorithm II (PESA-II), and Multi-Objective Particle Swarm Optimization (MOPSO) algorithms. Findings reveal that the wind farm's maximum power output reaches approximately 5.8 megawatts across all three algorithms and optimal turbine placements. A risk assessment was conducted using a tenth percentile criterion, revealing a significant production risk within the study area, with production falling below 1.8 megawatts in 90 % of cases. Regarding the performance evaluation of the algorithms across all three models, superior performance in terms of solution proximity to the ideal solution is exhibited by PESA-II, while enhanced diversity and solution spread compared to the other algorithms are demonstrated by NSGA-II.