# High Voltage Ride through Strategy of Wind Farm Considering Generator Terminal Voltage Distribution
## 2 Voltage Distribution Characteristics under a Wind Power Transmission Fault
### Analysis of Generator Terminal Voltage Distribution in a Wind Farm  
The distribution of generators in a wind farm usually adopts a chain structure. Each busbar is normally with several collection lines, and each collection line is with multiple wind turbines. A typical large wind farm has more than one hundred wind turbines, and the number of wind turbines with each collection line is usually 10-12. Affected by geographical location, as the distance between each wind turbine ranges from hundreds of meters to thousands of meters, the distance between the beginning and end of the collection line is between thousands of meters and tens of kilometers. The topology of the typical wind farm studied in this article is shown in Figure 3.  
By randomly selecting two adjacent wind turbines, their equivalent circuit can be modeled, as shown in Figure 4. In Figure 4, \(U_{i}\) and \(U_{i-1}\) are the points connected to the main collection line; \(R_{\rm G}\), \(X_{\rm G}\), \(G_{\rm G}\), and \(B_{\rm G}\) are the equivalent resistance, reactance, conductance, and susceptance of the line from the wind turbine to transformer, respectively; \(R_{\rm L}\), \(X_{\rm L}\), \(G_{\rm L}\), and \(B_{\rm L}\) are the equivalent resistance, reactance, conductance, and susceptance of the collection line between two wind turbines, respectively; \(R_{\rm T}\), \(X_{\rm T}\), \(G_{\rm T}\), and \(B_{\rm T}\) are the equivalent resistance, reactance, conductance, and susceptance of the transformer, respectively; \(P_{i}\) and \(Q_{i}\) are the active and reactive power output of the left wind turbine, respectively; \(P_{i-1}\) and \(Q_{i-1}\) are the active and reactive power output of the right wind turbine, respectively. Figure 3: Topology of a wind farm. Assuming that the transformer equivalent circuit and the line equivalent circuit, between the left wind turbine to \(U_{i}\) point, and the right wind turbine to \(U_{i-1}\), are replaced by quantitative active and reactive losses, \(\Delta P\) and \(\Delta Q\), respectively, Figure 4 can be simplified as Figure 5. When wind turbines are operating in a non-constant power factor state, it can be calculated according to the voltage drop of the transmission line:  
\[\dot{U}_{i}=\left(U_{i-1}+\frac{(P_{i}+P_{i-1}-2\Delta P)R_{\text{L}}+(Q_{i}+Q _{i-1}-2\Delta Q)X_{\text{L}}}{U_{i-1}}\right)+\text{j}\frac{(P_{i}+P_{i-1}-2 \Delta P)X_{\text{L}}-(Q_{i}+Q_{i-1}-2\Delta Q)R_{\text{L}}}{U_{i-1}} \tag{4}\]  
In general, the power angle in the transmission line is small, so Equation (4) can be approximated as:  
\[U_{i}=U_{i-1}+\frac{(P_{i}+P_{i-1}-2\Delta P)R_{\text{L}}+(Q_{i}+Q_{i-1}-2 \Delta Q)X_{\text{L}}}{U_{i-1}} \tag{5}\]  
Based on the above analysis, we can calculate the voltage difference relationship between any two adjacent wind turbines on the collection line as:  
\[U_{k+1}-U_{k}=\frac{\left(\sum\limits_{i=1}^{m-k+1}P_{i}-m\Delta P\right)R_{ \text{L}}+\left(\sum\limits_{i=1}^{m-k+1}Q_{i}-m\Delta Q\right)X_{\text{L}}}{ U_{k}} \tag{6}\]  
where \(m\) is the number of wind turbines, from the selected wind turbines to the end of the collection line. It can be seen from Equation (6) that: First, the voltage of the wind farm depends on the voltage of the grid-connection point, and the deviation of the grid-connection point voltage will cause the deviation of the generator terminal voltage of all wind turbines in the wind farm. Second, the generator terminal voltage distribution in the wind farm is also related to the active and reactive power output of the wind turbines, and the output of the wind turbines will also cause fluctuations in the generator terminal voltage distribution of the wind farm. After the grid-connection point voltage is controlled within a reasonable range and the output of the wind turbines is stabilized, the generator terminal voltage distribution in the wind farm will also have a certain difference due to the power  
Figure 4: Equivalent circuit of adjacent wind turbines. Figure 5: Simplified equivalent circuit of adjacent wind turbines. flow distribution.