## 4 Wind Turbine Generator Transmission Aggregation Model  
For a large-scale wind farm, the transmission line and the transformers influence the precision of the aggregation model. Aspects of the WTG transmission system include the layout of wind farms, the size and type of conductors, and the delivery method. The aggregation of the WTG transmission model consists two parts, respectively, the circuit aggregation at the aggregation bus, and the transformer aggregation. (1) Circuit aggregation: The cable and overhead line are the main types of transmission lines, and are sometimes used together in large-scale wind farms. The cable is relatively unaffected by the environment changes, but the high charging capacitance of the cable may lead to single-phase to ground fault. Overhead lines have a negligible charging capacitor with low voltage and short length. The wire of the overhead line is exposed in the air and is strongly influenced by the environment. When facing severe weather conditions, such as for instance overhead transmission line icing, the safety and reliability are decreased. In a wind farm with hybrid lines, the cables are often constructed in the central region, while the overhead lines are constructed in scattered areas. The cable charging capacitance is 20 to 25 times that of the overhead line, so the susceptance in cables needs to be considered when calculating the equivalent circuit. There are three types of connection method that WTGs connect to an aggregation bus: the trunk type, the chain type, and the compound type. Three connection modes of WTGs, and the equivalent aggregation model of the WTG transmission line, are respectively shown in Figure 10.  
The aggregation of the trunk type in Figure 10a, \(Z_{\text{eq-tr}}\), can be expressed as:  
\[z_{\text{eq-tr}}=\sum_{i=1}^{n}P_{zi}^{2}Z_{i}/P_{zn}^{2} \tag{16}\]  
where \(P_{zi}\) is the total power of \(Z_{i}\). Figure 10: Connection types of wind turbines: (**a**) the trunk type; (**b**) the chain type; (**c**) the compound type; and (**d**) the aggregation of different connection types. Similarly, the aggregation of the chain type, \(Z_{\text{eq-ch}}\), and the compound type, \(Z_{\text{eq-co}}\), are respectively shown in Figure 10b,c, and can be respectively expressed as:  
\[z_{\text{eq-ch}}=\sum_{i=1}^{n}P_{zi}^{2}Z_{i}/\sum_{i=1}^{n}P_{zi}^{2} \tag{17}\]  
\[z_{\text{eq-co}}=(\sum_{i=1}^{n}n_{i}^{2}Z_{bi}+\sum_{i=1}^{n}\left(\sum_{j=1} ^{n}n_{j}\right)^{2}z_{ai})/\sum_{i=1}^{n}n_{i}^{2} \tag{18}\]  
Figure 11 shows the equivalent circuit of the aggregated WTG transmission system. As for the susceptance branch of the cable line, the voltage difference inside the wind farm can be ignored, and the equivalent susceptance equals the sum of all the susceptance of the branches, that is:  
\[B_{eq}=\sum_{i=1}^{m}B_{i} \tag{19}\]  
where \(B_{i}\) is the susceptance of the line connected with the \(i\)-th wind turbine. It should be noted that the line loss before and after the equivalence should be equal to each other. Moreover, the objective and working conditions should be considered in the aggregation simplification of WTG transmission topology. The literature [67] has considered the series or parallel relationship of the collector circuits, and proposed an equivalent model based on the parameter transformation. The power aggregation system is usually designed considering the maximum wind power output and the lowest installation and operation cost. The literature [68] has proposed an optimization model for the WTG transmission system of an offshore wind farm that can take different cable cross-sections into account. The literature [69] has also proposed a procedure to optimize the wind turbine location and the line connection topology, by using the genetic algorithm and the ant colony algorithm. The wake effect, the real cable parameters, and the wind speed series are considered when establishing an economical and efficient aggregation model for the offshore wind farm.