## 3 Wind Turbine Generator Model
### Multi-WTG Aggregation Model
#### 3.3.1 Aggregation of Wind Turbines  
When wind conditions, land form, wake effect, and time delay for different wind turbines are respectively considered, wind turbines are firstly divided into several different regions, and then wind turbines in the same region are aggregated into one wind turbine. The simplified process of this aggregation is shown in Figure 7.  
Wind turbine aggregation is appropriate for the dynamic modeling of the wind farms when the differences in working conditions are large. The literature [52; 53] has pointed out that this model has some restrictions in the application of simulation because of its inherent structure changes. Due to the wake flow, the input speed of the downstream turbine is lower than that of the upstream turbine. The main factors of wake effect are the distances between wind turbines, the characteristics of thrust and power, and the turbulence intensity. The energy fluctuations could range from 2% to 30%. The wake effect is generally described by the Lissaman model and the Jensen model. The Jensen model simulates the wake effect in a flat area, and the Lissaman model simulates a non-uniform wind field. Sometimes, these two models are combined and used to deal with complex terrain. The literature [42] discusses three models of wake effect, where the wind shade, shear effect, and wind direction are considered. In [54; 55], the wake effect models of flat or complex terrain are introduced. Regardless of the wind speed attenuation, when the upstream turbines receive wind speed mutation, the downstream wind speed changes after a period. This situation is called the time delay effect. Compared with the time wake effect, the time delay effect introduces a lower impact on wind farms. The wind farm is divided into the \"flat terrain\" and the \"complex terrain\" situation, representing the regular area and irregular area, respectively, to illustrate the influence of the wake effect. (1) Flat terrain (regular area): Wind farms located offshore, or on non-obstructed flat ground can be considered as regularly on the main wind direction. WTGs are divided into the different clusters according to the types, the capacity, and the position relationship of the wind turbines. The minimum distance between turbines is three to five times the blade diameter within the same row, and five to nine times the blade diameter between rows [56]. The literature [57] has proposed a cluster division method according to the arrangement of wind turbines in wind farms, where wind farms are classified into the horizontal wind farm, vertical wind farm, and the mixed wind farm, as shown in Figure 8.  
(2) Complex terrain (irregular area): In practice, the spatial distribution location of WTGs results in different operating states of different turbines. Therefore, \"complex terrain\" is more in line with wind farms located in hill or mountain areas. The literature [58] has proposed a cluster method based on a constructed diffusion distance measure. First, the power output of each wind turbine is assumed to be a random process with Markovian characteristics; then, the overall process of all the turbines is represented by a Markov transition matrix that is constructed from real data by building a graph with Gaussian weights; finally, the spectral theory is applied to identify the number of clusters and map  
Figure 8: The different arrangement of wind turbines, (**a**) the horizontal wind farm; (**b**) the vertical–diagonal wind farm; (**c**) the vertical–longitudinal wind farm; and (**d**) the mixed wind farm. Figure 7: The aggregation process with the aggregation of different wind turbines. the original wind turbines to the appropriate cluster. Furthermore, this method has been developed to address the non-linearity and robustness issues in the K-means clustering process, which is a big success in cluster analysis. In [59], a method of probabilistic unit division is proposed.