# Fault Studies and Distance Protection of Transmission Lines Connected to DFIG-Based Wind Farms
## 2 Fault Analysis of DFIG-Based Wind Farm and Its Verification
### Case Studies  
According to the real phase-to-phase fault case mentioned in Section 2.3.2, the trajectory of impedance measured by Equations (14) and (15) is shown in Figure 9. The red line and green line in Figure 9 are obtained based on the real resistance and inductance parameters of Line 1 and Line 2, respectively. Zone 1 is the polygon action areas of wind farm side instantaneous distance protection on Line 1, and 9.97 \(\Omega\) and 1.86 mH are setting values of resistance and inductance, respectively. Actually, the fault occurs on Line 2. Compared with Figure 8c, the measured impedance trajectory does not enter Zone 1 in Figure 9 and the wind farm side instantaneous distance protection on Line 1 will not maloperate. Thus, the reliability of distance protection on wind farm side transmission lines is guaranteed when using the time-domain distance protection method proposed in this paper. According to the real wind farm mentioned in Section 2.3.1, the corresponding wind farm model is established by Matlab/Simulink (R2014a, MathWorks, Natick, MA, USA, 2014). The topology of the wind farm is shown in Figure 4. The wind farm is equipped with 132 DFIGs with LVRT capability, and each main transformer connects 66 DFIGs. The parameters of a real DFIG and transmission lines are shown in Appendix B. The detailed model and control strategy of DFIG can be found in previous studies [14; 36]. This paper mainly researched the fault characteristics of DFIG-based wind farms connected to transmission lines and its influence on relay protection. The duration of the fault is relatively short, so the wind speed of the wind farm is considered as unchanged during the research process. For the convenience of research, all wind turbines are set to operate under the same conditions. Additionally, the impedance of the collector system is ignored. To compare the time-domain distance protection method with the traditional distance protection method based on the Fourier algorithm, the following three conditions are given as typical simulation examples: a phase A ground fault, a phase-A-to-phase-B fault, and a three-phase short circuit fault. The transition resistances are all zero. The fault points are all 11 km away from Bus 1 on Line 1. The wind speed is 11 m/s before the fault. The comparison of two kinds of distance protection methods used on the wind farm side transmission lines connected to DFIG-based wind farms are shown in Figure 10.  
Figure 9: The real phase-to-phase fault case’s trajectory of impedance measured with the time-domain method. In Figure 10, the red lines are the distance measured by Fourier algorithm and the blue lines are the distance measured by time-domain method. The faults occur at 0 s and the rotor speed before the fault is greater than the synchronous speed. Due to the existence of a rotor speed frequency AC component, the distance calculation results, which are obtained from the traditional distance protection method based on the Fourier algorithm, fluctuate considerably. The error of ground fault is smaller due to the domination of the zero-sequence current. The time-domain method proposed in this paper is not affected by the rotor speed frequency component, the distance calculation results converge to the real fault distance within a dozen milliseconds. To further verify the performance of the time-domain method, three fault points at 5, 10 and 15 km are selected on Line 1. The following four conditions are given as typical simulation examples: a phase A ground fault, a two-phase ground fault, a phase-to-phase short circuit fault and a three-phase short circuit fault. The transition resistances are all zero. The wind speed is 11 m/s before the fault and the corresponding rotor speed is greater than the synchronous speed. The data of 20-40 ms after faults are selected to calculate the errors of two methods' measurement results.