Abstract An accurate wake model is essential for the mathematical modeling of a wind farm (WF) and the optimal positioning of wind turbines (WTs). In order to effectively solve the WF layout optimization problem, this paper presents a newly-developed three-dimensional (3D) Gaussian wake model and applies it to the optimization of a WF layout. Firstly, the basic functions of the proposed model are deduced. Secondly, it is validated by wind tunnel measured data, and compared with the one-dimensional (1D) and the two-dimensional (2D) wake models. Then, the 3D Gaussian wake model is applied in the WF layout optimization problems with identical and multiple types of WTs. The optimization objective is to maximize the total output power of the WF with a set of constraints. The Mixed-Discrete Particle Swarm Optimization (MDPSO) algorithm is used to solve the uniform and nonuniform WF layout optimization problems. Test cases of various WF sizes, wind conditions, and different wake models are simulated and analyzed. The simulation results demonstrate that the 3D Gaussian wake model can effectively address the WF layout optimization problem and further illustrate that the nonuniform design is beneficial to increase the WF’s output power.

中文翻译：

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基于三维高斯尾流模型的风电场布局优化

摘要 准确的尾流模型对于风电场 (WF) 的数学建模和风力涡轮机 (WT) 的优化定位至关重要。为了有效解决WF布局优化问题，本文提出了一种新开发的三维（3D）高斯尾流模型并将其应用于WF布局的优化。首先，推导了所提出模型的基本功能。其次，通过风洞实测数据对其进行验证，并与一维（1D）和二维（2D）尾流模型进行对比。然后，将 3D 高斯尾流模型应用于具有相同和多种类型 WT 的 WF 布局优化问题。优化目标是在一组约束条件下最大化 WF 的总输出功率。混合离散粒子群优化 (MDPSO) 算法用于解决均匀和非均匀 WF 布局优化问题。对各种 WF 大小、风力条件和不同尾流模型的测试用例进行了模拟和分析。仿真结果表明，3D 高斯尾流模型可以有效解决 WF 布局优化问题，并进一步说明非均匀设计有利于提高 WF 的输出功率。