## 3 Wind Turbine Generator Model
### Single WTG Aggregation Model  
When all the generators of a wind farm are aggregated to one generator, the wind farm is represented by a single WTG aggregation model. The single WTG aggregation model can be considered as a \"single wind turbine + single generator\" model, or a single WTG aggregation model for short. In a single WTG aggregation model, all wind turbines as well as generators are respectively aggregated to one wind turbine and one generator. Parameters of various units, such as the capacity, the active power, and the mechanical power of the wind turbines and the generators are aggregated as the parameters of the equivalent wind farm. The process of the aggregation is shown in Figure 6.  
In a single WTG aggregated model, there are two kinds of aggregation methods [41]. One aggregates wind turbines with equivalent incoming wind. When winds are different, the average wind speed of individual winds has been used as the equivalent wind. The other aggregates wind turbines along with generators with variable equivalent compensating capacitors to approximate the WTGs under different wind speed situations. The literature [42] has obtained the wind speed input of wind turbines according to the power coefficient curve and their coordinate positions, which is suitable for all wind farms, regardless of the number of wind turbines. Since all the WTGs are aggregated to a single WTG, the equivalent aggregation modeling of wind farms can be considered as part of the modeling of a WTG, where the WTG types are considered the main aspect, and the other working conditions are considered as secondary. The literature [43] has proposed an aggregated DFIG model based on a third-order quasi-sinusoidal model with simplifications of the transformer voltage and the grid-side converter. The literature [40] has taken the D-PMSG as an example, and established the single aggregation model by using the volume-weighted method. The performance comparison between the detailed model and multi-machine aggregation model is made to validate the practicability of the aggregating method. The literature [44] proposed an aggregated method of D-PMSG-based wind farms. It points out that the  
Figure 6: The aggregation of the “single wind turbine + single generator” model. D-PMSG wind turbine has three operating regions: the variable speed operating region, the constant speed, the variable power operating region, and the constant power and variable pitch-angle operating region, where \(\gamma_{1}\), \(\gamma_{2}\), and \(\gamma_{3}\) are used to represent the operating characteristics. The clustering index \(\gamma\) can be defined as follows:  
\[\gamma=(\gamma_{1},\gamma_{2},\gamma_{3}) \tag{13}\]  
where \(\gamma_{1}=\Omega_{r}/\Omega_{max}\), \(\gamma_{2}=(C_{p}/\lambda_{3})/(C_{p}/\lambda_{3})_{max}\), \(\gamma_{3}=\beta/\beta_{max}\); \(C_{p}\) is the utilization efficiency of wind energy; \(\lambda\) is the tip speed ratio of wind turbines; \(\Omega_{r}\) is the wind rotor speed; and \(\beta\) is the pitch angle. This aggregation method reflects all of the operating characteristics of D-PMSG wind turbines. The literature [39] takes the pitch-angle control actions of WTGs as the clustering principles, and uses the support vector machine to cluster WTGs. The aggregation contains initial speed, mechanical torque, electromagnetic torque, and the feature vector reflecting the pitch angle control action. The literature [45; 46] gives a type of wind farm model that portrays the capability of set-point tracking under intermittent wind conditions. The characteristics of this model in depicting the set-point operation under the automatic generation control are also proved by simulation. A single WTG aggregation model generally adopts the capacity-weighted average method to calculate the equivalent parameters. The aggregated parameters are expressed as:  
\[\delta_{i}=S_{i}/\sum\limits_{i=1}^{N}S_{i} \tag{14}\]  
\[\left\{