The paper “Wind farm power density optimization according to the area size using a novel genetic algorithm” by Kirchner-Bossi and Porte-Agel presents an in-depth study on optimizing power density (PD) in wind farms, emphasizing the sensitivity of PD to the available area size. The authors introduce a novel self-adaptive genetic algorithm (PDGA) to optimize both PD and turbine layouts, adapting to varying area sizes and solution diversities.​Semantic Scholar+2Infoscience+2MDPI+2

Introduction to Power Density (PD) in Wind Farms:

Power Density (PD) is defined as the amount of power generated per unit area of a wind farm. Optimizing PD is crucial for maximizing energy output and ensuring efficient use of land or sea space allocated for wind energy projects. Higher PD implies more efficient energy production within a confined area, which is particularly important in regions where space is limited or land use is a concern.​

Genetic Algorithms (GAs) in Optimization:

Genetic Algorithms (GAs) are computational search and optimization techniques inspired by the process of natural selection. They are particularly effective in solving complex optimization problems with large search spaces, such as determining the optimal layout of wind turbines to maximize PD. In the context of wind farm design, GAs iteratively evolve turbine layouts by selecting, combining, and mutating candidate solutions to find the most efficient configuration.​

Novel Self-Adaptive Genetic Algorithm (PDGA):

The authors developed a novel self-adaptive genetic algorithm, termed PDGA, to optimize PD and turbine layouts. This algorithm self-adapts to the PD and solution diversity, enhancing its effectiveness in finding optimal configurations. PDGA uses the levelized cost of energy (LCOE) as the cost function, incorporating the EPFL analytical wake model to derive power output. This integration allows for a more accurate assessment of turbine interactions and their impact on overall energy production.

Sensitivity of PD to Area Size:

The study reveals that PD is sensitive to the size of the available area. As the area increases, the optimal number of turbines and their arrangement change, affecting the overall PD. This sensitivity underscores the importance of considering area size in wind farm design to maximize efficiency.​

Key Findings:

1. LCOE Reduction: For the baseline area size, PDGA achieved a 2.25% reduction in LCOE, which is 2.6 times more than optimizing with constant PD. This demonstrates the algorithm’s effectiveness in reducing costs associated with energy production.
2. Area-Specific Optimization: PDGA-driven solutions provided 11% and 6% LCOE reductions against the default layout for the smallest (6.4 km²) and largest (386 km²) scaled wind farm areas, respectively. This highlights the algorithm’s adaptability to different area sizes and its capability to optimize PD accordingly.
3. Convex Fronts for Area vs. LCOE/PD: The optimized solutions depict convex fronts for area vs. LCOE or vs. PD. This characteristic allows for determining the required area or turbine number given a target LCOE, facilitating more informed decision-making in wind farm planning.
4. Linear Relationship Between LCOE and PD: Unlike default layouts, optimized ones reveal a linear relationship between LCOE and PD. This insight suggests that as PD increases, LCOE decreases proportionally, providing a clear target for optimization efforts.
5. Optimal Turbine Spacing: The mean turbine spacing tends to 8-9 rotor diameters (D) for very large areas. This finding aligns with industry standards and provides a benchmark for future wind farm designs.​
6. PD vs. Atmospheric Limits: The economics-optimized PDs are below the estimated PD available in the atmosphere. This indicates that there is room for increasing PD without surpassing atmospheric limitations, suggesting potential for further optimization.​

Implications for Wind Farm Design:

• Optimizing Turbine Layout: The findings highlight the necessity of optimizing turbine layouts to achieve higher PD. By utilizing advanced algorithms like the PDGA, designers can determine the optimal number and placement of turbines, leading to more efficient wind farm designs.​
• Area-Specific Design Strategies: Understanding the sensitivity of PD to area size enables the development of tailored design strategies for different site conditions. For instance, in smaller areas, maximizing PD might involve different turbine configurations compared to larger areas. This approach ensures that wind farms are designed to be both efficient and cost-effective, considering the specific characteristics of each site.​

Limitations and Future Work:

The study acknowledges certain limitations, including the use of a simplified offshore wind climatology, a specific wind turbine model, and the LCOE specifications applied. Future research could expand on these findings by incorporating diverse climatological data, different turbine models, and varying economic parameters to validate and generalize the applicability of the PDGA.​

In summary, the paper emphasizes the importance of optimizing power density in wind farms through advanced genetic algorithms, considering the sensitivity of PD to the available area size. These insights are crucial for designing efficient and effective wind energy projects.

Original paper:

Kirchner-Bossi, N., & Porté-Agel, F. (2023). Wind farm power density optimization according to the area size using a novel genetic algorithm. Renewable Energy, 214, 763-777. https://doi.org/10.1016/j.renene.2023.07.027