# High Voltage Ride through Strategy of Wind Farm Considering Generator Terminal Voltage Distribution
## 3 Reactive Power Output Characteristics of Wind Farm Transmission Systems  
### Reactive Power Output Characteristics of DFIG  
The topology of DFIG is shown in Figure 7 and the equivalent circuit of DFIG is shown in Figure 8. It can be seen that the power output from DFIG to the grid comes from the stator of DFIG and the grid-side inverter. In Figure 8, \(U_{\text{s}}\) and \(U_{\text{r}}\) are the voltage of rotor and stator, respectively; \(R_{\text{s}}\) and \(R_{\text{r}}\) are the equivalent resistance of rotor and stator, respectively; \(L_{\text{s}}\) and \(L_{\text{r}}\) are the equivalent inductance of rotor and stator, respectively; \(L_{\text{m}}\) is the mutual inductance between stator and rotor; \(\psi_{\text{s}}\) and \(\psi_{\text{r}}\) are the flux linkage of rotor and stator, respectively; \(\omega\) is the angular velocity; \(i_{\text{s}}\) and \(i_{\text{r}}\) are the current of rotor and stator, respectively.  
According to Figure 8, the voltage equation, the flux equation, and the power equation of DFIG are as follows:  
\[\left\{\begin{array}{l}\overset{\rightarrow}{U}_{\text{s}}=R_{\text{s}} \overset{\rightarrow}{i}s+\frac{\text{d}\overset{\rightarrow}{\phi}_{\text{r }}}{\text{d}t}+\text{j}\omega\overset{\rightarrow}{\psi}_{\text{s}}\\ \overset{\rightarrow}{U}_{\text{r}}=R_{\text{r}}\overset{\rightarrow}{i}r+ \frac{\text{d}\overset{\rightarrow}{\phi}_{\text{r}}}{\text{d}t}+\text{j} \omega\overset{\rightarrow}{\psi}_{\text{r}}\end{array}\right. \tag{7}\]  
\[\left\{\begin{array}{l}\overset{\rightarrow}{\psi}_{\text{s}}=L_{\text{s}} \overset{\rightarrow}{i}s+L_{\text{m}}\overset{\rightarrow}{i}r\\ \overset{\rightarrow}{\psi}_{\text{r}}=L_{\text{r}}\overset{\rightarrow}{i}r+ L_{\text{m}}\overset{\rightarrow}{i}s\end{array}\right. \tag{8}\]  
\[\left\{\begin{array}{l}P_{\text{s}}=\frac{3}{2}\text{Re}\left[\overset{ \rightarrow}{U}_{\text{dqs}}\overset{\rightarrow}{i}\overset{\rightarrow }{\text{d}\text{qs}}^{*}\right]\\ Q_{\text{s}}=\frac{3}{2}\text{Im}\left[\overset{\rightarrow}{U}_{\text{dqs}} \overset{\rightarrow}{i}\overset{\rightarrow}{\text{d}\text{qs}}^{*}\right] \end{array}\right. \tag{9}\]  
where \(U_{\text{dqs}}\) and \(i_{\text{dqs}}\) are the voltage and current of stator in the DQ coordinate system.  
Figure 8: The equivalent circuit of doubly-fed induction generators (DFIG).  
Figure 7: The topology of DFIG.  
Combining Equations (7)-(9), the range of the reactive power output, \(Q_{\rm s}\), from the stator of DFIG is:  
\[-\frac{3U_{\rm s}^{2}}{2\omega_{1}L_{\rm s}}-\sqrt{\left(\frac{3L_{\rm m}U_{\rm s }}{2L_{\rm s}}I_{\rm mmax}\right)^{2}-P_{\rm s}^{2}}\leq Q_{\rm s}\leq-\frac{3U _{\rm s}^{2}}{2\omega_{1}L_{\rm s}}+\sqrt{\left(\frac{3L_{\rm m}U_{\rm s}}{2L_{ \rm s}}I_{\rm mmax}\right)^{2}-P_{\rm s}^{2}} \tag{10}\]  
According to the stator and rotor power coupling of DFIG, and the maximum power limit of the grid-side converter (\(P_{\rm gmax}\)), the range of reactive power output, \(Q_{\rm g}\), for grid-side commutation is:  
\[-\sqrt{P_{\rm gmax}^{2}-s^{2}P_{\rm s}^{2}}\leq Q_{\rm g}\leq\sqrt{P_{\rm gmax }^{2}-s^{2}P_{\rm s}^{2}} \tag{11}\]  
Therefore, the maximum and minimum reactive power output of the DFIG can be obtained as:  
\[\left\{\begin{array}{l}Q_{\rm max}=-\frac{3U_{\rm s}^{2}}{2\omega_{1}L_{ \rm s}}+\sqrt{\left(\frac{3L_{\rm m}U_{\rm s}}{2L_{\rm s}}I_{\rm mmax}\right)^ {2}-P_{\rm s}^{2}}+\sqrt{P_{\rm gmax}^{2}-s^{2}P_{\rm s}^{2}}\\ Q_{\rm min}=-\frac{3U_{\rm s}^{2}}{2\omega_{1}L_{\rm s}}-\sqrt{\left(\frac{3L _{\rm m}U_{\rm s}}{2L_{\rm s}}I_{\rm mmax}\right)^{2}-P_{\rm s}^{2}}-\sqrt{P_{ \rm gmax}^{2}-s^{2}P_{\rm s}^{2}}\end{array}\right. \tag{12}\]  
According to Equation (12), the inductive reactive power output capability of DFIG is not as good as its capacitive reactive power output capability. Therefore, it is necessary to install a certain reactive power compensation device on the busbar to improve the HVRT capability of the wind farm.