# Optimization Of Wind Farm Layout

 Xinglong JuUniversity of Texas Southwestern Medical Center Jessica LeungThe University of Sydney

Wind energy is a vast potential source of renewable energy as wind supply is inexhaustible. Wind energy is generated using wind turbines. When the wind blows past a wind turbine, its blades capture the kinetic energy of the wind currents to spin an electric generator, which produces electricity.

For a given piece of land (wind farm), it is crucial to find the optimal positions of the wind turbines as the electricity power output of each turbine depends heavily on their locations and relative positioning with other turbines. Sub-optimal wind farm layout design often leads to lower net wind power yield and increased maintenance costs.

The process of determining the locations to maximized power production is called Wind Farm Layout Optimization (WFLO). While it may seem attractive to simply build a larger number of turbines in order to capture more kinetic energy from the wind current, densely packed turbines may lead to reduced energy production due to wake effects, an aerodynamic phenomenon that occurs between upwind and downwind turbines.

Figure 1: A wind farm layout optimization illustration

Modeling Wake effects

When the wind passes a wind turbine (denoted as Turbine 1), a part of the wind kinetic energy would be absorbed by Turbine 1 and transformed into electricity, leaving the wind velocity reduced in the downwind direction. The downwind turbine would produce less power than Turbine 1, and this phenomenon is called the wake effect.

WFLO aims to optimize the trade-off between energy generation and wake effects. Yet, a wind turbine can be affected by multiple wake effects generated by other turbines nearby in a wind farm. The resulting wake interference adds an extra layer of complexity to the optimization model. In Figure 2, we provide an illustration of the multiple wake effects. We display a single wind wake effect on the upper panel and multiple wake effects on the bottom. The x- and y-axis are the standardized distances from the turbine blade center along and perpendicular to the wind direction, respectively. The color represents the rate of reduction of wind velocity. From the right panel, we can see that the multiple wake effects affect the wind velocity significantly and therefore must be taken into account in the WFLO problem formulation.

A wide range of wake modeling approaches has been developed to capture the wake effects, for instance, the Ainslie model, the G. C. Larsen model (see [8][9]), and the Gaussian 3D model[2]. Yet, the Jensen model[1] remains the most popular analytical model due to its simplicity and accuracy.

Figure 2: Wind wake effect illustration: one wake effect and multiple wake effects

Solving WFLO with the advancement in Artificial Intelligence and Machine Learning

A myriad of optimization algorithms are used to solve the WFLO problem, and many of them are heuristic algorithms, such as Genetic [3], Particle Swarm Optimization [4], and Ant Colony [5]. With the recent development in artificial intelligence and machine learning, various powerful methods such as support vector machine [6] and deep learning [7], were used to guide the heuristic algorithm and developed into new optimization strategies with insights into the characteristic of the wind power distribution and computations of wind velocity.

Representation of wind farm layouts

The wind farm layout can be encoded as discrete or continuous variables. In a discrete representation, the farmland is divided into small grids as shown in Figure 3. The width of each grid is at least the diameter of the turbine blades such that two turbines are at least one diameter apart as long as wind turbines are placed in distinct grids.

Figure 3: Discretize the wind farm into grids

In a continuous setting, the wind farm layouts can be encoded using real-valued representations such as coordinates of turbines. Yet, the high precision often comes with computational cost. Given the same number of variables and the same inherent underlying problem complexity, the computational burden in continuous problems is typically greater than that of discrete problems in light of the larger variable-domain size of continuous variables [10].

Future Research

Designing wind farm layouts requires insights in managing the trade-offs between energy generation, operational costs, and capital investments. To gain insight in optimizing these trade-offs, the WFLO can be formulated as a multi-objective optimization problem. Given some of the constraints and complexities mentioned above, the best way to formulate and solve the WFLO problem remains largely an open question. It will be exciting to find a wind farm layout that achieves a global maximum power output in a continuous space with new strategies and algorithms, and we are looking forward to it.

References:

[1] Jensen, N.O., 1983. A note on wind generator interaction.
[2] Bastankhah, M. and Porté-Agel, F., 2014. A new analytical model for wind-turbine wakes. Renewable Energy, 70, pp.116-123. https://doi.org/10.1016/j.renene.2014.01.002
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[4] Chowdhury, S., Zhang, J., Messac, A. and Castillo, L., 2013. Optimizing the arrangement and the selection of turbines for wind farms subject to varying wind conditions. Renewable Energy, 52, pp.273-282. https://doi.org/10.1016/j.renene.2012.10.017
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[7] Ju, X., Liu, F., Wang, L. and Lee, W.J., 2019. Wind farm layout optimization based on support vector regression guided genetic algorithm with consideration of participation among landowners. Energy Conversion and Management, 196, pp.1267-1281. https://doi.org/10.1016/j.enconman.2019.06.082
[8] Thørgersen M, Sørensen T, Nielsen P (2005) WindPRO/PARK: introduction wind turbine wake modelling and wake generated turbulence. EMD International A/S, Aalborg
[9] Hou, P., Zhu, J., MA, K. et al. A review of offshore wind farm layout optimization and electrical system design methods. J. Mod. Power Syst. Clean Energy 7, 975–986 (2019). https://doi.org/10.1007/s40565-019-0550-5
[10] Rodrigues, S., Bauer, P. and Bosman, P.A., 2016. Multi-objective optimization of wind farm layouts–Complexity, constraint handling and scalability. Renewable and Sustainable Energy Reviews, 65, pp.587-609. https://doi.org/10.1016/j.rser.2016.07.021