# Ensuring Stable Operation of Wind Farms Connected to Distribution Networks
## 4 Results
If the voltage at the PLL unit is below 20% \(U_{\text{nom}}\), the reactive current injection function is temporarily blocked, and if the duration of the voltage dip exceeds the set value of the LVRT characteristic, the wind turbine is switched off. These restrictions on the operation of the wind turbine inverter are due to the following:  
* The value of the capacitance of the capacitor used in the DC link between the rectifier and the inverter;
* The power supply to the control circuits of the inverter controller from the DC link;
* The generation of erroneous signals in the PLL unit when the voltage at its input is below 20% \(U_{\text{nom}}\). Let us determine the parameters of the capacitance of the capacitor in the DC link of the wind turbine, which are necessary for the implementation of two main functions:  
* Smoothing the ripples related to the operation of the rectifier;
* Eliminating the overvoltage caused by switching off the inverter power switches and by the variable schedule of the wind generator operation. To ensure the stable operation of the wind turbine in the case of voltage dips in the distribution network, we determine the minimum requirements for the parameters of the capacitor in the DC link. Let us determine this, subject to the value of reactive current injection maintained by the wind turbine inverter during a standard disturbance with a voltage dip of up to 20% \(U_{\text{nom}}\) within 0.2 s.  
The capacitance of the DC link capacitor can be determined knowing the amount of energy accumulated in the capacitor before the onset of a standard disturbance, considering the law of conservation of energy. The energy stored in the capacitor is calculated by Formula (1):  
\[W=\frac{C_{\text{cap}}\times U_{\text{d}}^{2}}{2}=U_{\text{res}}\times I_{ \text{r}}\times\Delta t, \tag{1}\]  
where \(C_{\text{cap}}\) is the capacitance of the DC link capacitor; \(U_{\text{d}}\) is the voltage of the DC link (\(U_{\text{lin}}/0.87\)--with a six-pulse inverting circuit; \(U_{\text{lin}}=690\) V); \(U_{\text{res}}\) is the residual voltage at the inverter output, taken to be equal to 20 % \(U_{\text{nom}}=0.2\times 690=138\) V; \(I_{\text{r}}\) is the reactive current injection, taken to be equal to \(I_{\text{rated}}=I_{\text{r}}=\frac{\text{Srated}}{\sqrt{3}\,U_{\text{lin}}}= \frac{2778}{\sqrt{3}\times 690}=2.324\) A; and \(\Delta t\) is the duration of the voltage dip, assumed to be 0.2 s.  
The required capacitance of the capacitor is calculated by Expression (2):  
\[C_{\text{cap}}=2\times\frac{U_{\text{res}}\times I_{\text{r}}\ \times\Delta t}{U_{\text{d}}^{2}}=2 \times\frac{138\times 2324\times 0.2}{\left(690/0.87\right)^{2}}=0.204\text{ F} \tag{2}\]  
The capacitance of the inverter capacitor is selected according to the criterion of smoothing ripples and is 0.03 F, i.e., seven times less than the calculated value. This does not allow the injection of a reactive current in the event of a voltage dip with a duration of 0.2 s, which leads to the shutdown of the wind turbine by the protection unit due to a decline in the voltage in the DC link below the permissible value [57; 58]. To maintain the voltage in the DC link during a voltage dip, it is necessary to additionally install a capacitance of 0.17 F in the form of a supercapacitor [59]. Given the specific feature of the supercapacitor (low voltage on the plates is 2.7 V), it is required to additionally install a DC-DC converter to increase the voltage to 800 V in order to connect the wind turbine inverter to the DC link, as shown in Figure 10.  
Let us calculate the capacitance of the supercapacitor in terms of the law of conservation of energy and the required value of additional capacitance (0.17 F):  
\[W=\frac{C_{\text{add,cap}}\times U_{\text{d}}^{2}}{2}=\frac{C_{\text{supercap}} \times U_{\text{d supercap}}^{2}}{2}. \tag{3}\]  
\[C_{ \begin{subarray}{c}\text{super}\\ \text{cap}\end{subarray}