# Key Issues on the Design of an Offshore Wind Farm Layout and Its Equivalent Model
## 4 Optimization of Wind Turbine Layout  
From both engineering and economic perspectives, wind farm layout is a key aspect of wind farm design. Using various wake models, numerous investigations have developed various wind-turbine layout optimization methods. In those studies, the optimal locations of wind turbines were designed by using various objective functions that take the maximum wind generation into account. Generally, wind farm optimization problem is defined using four basic elements, which are data, problem variables, the objective function, and constraints. Those data comprise wind data, turbine data, wake effect data (such as the decay factor), wind farm data (such as water depth and foundation costs), cable data, and substation data. With regard to wind-speed data, several studies [26] have used the same wind scenarios: (a) Single wind direction with a 12 m\(\cdot\)s\({}^{-1}\) wind speed, (b) single wind speed of 12 m\(\cdot\)s\({}^{-1}\) and variable wind directions ranged between 0\({}^{\circ}\) to 360\({}^{\circ}\), and (c) a wind direction that is equally likely to be in ten ranges of 36\({}^{\circ}\) and with a variable wind speed of 8 m\(\cdot\)s\({}^{-1}\), 12 m\(\cdot\)s\({}^{-1}\) and 17 m\(\cdot\)s\({}^{-1}\). Other wind scenarios about wind conditions involve (a) a single wind direction with a constant wind speed, (b) measurements made at a real wind farm, (c) single and multiple wind directions with a fixed wind speed, or (d) wind conditions that are generated using a Weibull distribution function. A set of constraints determines the feasible ranges of problem variables. The numerous important constraints in the wind farm layout problem include minimum distance between turbines and the area limits of the wind farm area. For safety, the minimum distance among wind turbines in a wind farm is generally limited to four rotor diameters. Numerous investigations have utilized the Annual Energy Production (AEP) as the objective function. As the basic elements of the optimization problem have been defined, its mathematical programming definition can be provided and the solution obtained using various methods. Such a problem is a nonlinear mathematical programming problem with linear and non-linear inequality constraints. Several works have compared different technique about the optimization [27; 28]. In the early stage, genetic algorithms have been frequently utilized to solve the optimal wind farm layout problem [29]. However, many other algorithms have recently been proposed for the purpose [30; 31; 32; 33; 34]; they include the binary artificial algae algorithm (AAA), the bionic method, the ant colony algorithm, the minimum spanning tree algorithm, particle swarm optimization, Gaussian particle swarm optimization with a local search strategy, the turbine distribution algorithm, the extended pattern search method, the neural network algorithm, the evolutionary strategy algorithm, and quality threshold clustering. For instance, the study in reference [30] applied different binary algorithms with various transfer functions of AAA to solve the problem of wind turbine locations; the result demonstrates that the proposed algorithm obtains an effective placement of wind turbines with a larger number of grids. However, those optimization problems only considered the optimal layout of wind turbines; the internal cable connections and the collector system were not considered. The placement of wind turbines could also refer to other optimization algorithms that have been applied to other energy-related areas, such as the distribution system expansion planning [35] and the allocation of storage devices and renewable generators [36]. In reference [35], the planning of the electrical power distribution systems was investigated by considering the variation and uncertainty from renewable energy sources, and a two-stage stochastic programming model was used; additionally, different techniques about the optimization were also compared.