**6. Results**

264 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Fig. 27. SSSC configuration for the case study

Fig. 28. TCSC configuration for the case study

As presented in section 4, traveling waves were no significantly affected by presence of FACTS if *cD1* is selected. Following the procedure showed in section 4, *cD1A*, *cD1B*, *cD1C*, were employed to detect and locate faults. Ten different types of fault were considered to simulation:


Figure 29 shows *cD1* obtained for a fault of type *ABCG* at 240 km from *M1* and *t* = 0.3 s. As can be notice, *cD1A*, *cD1B*, and *cD1C* appear at 0.3008 s. In this way the fault event can be detected with any *cD1*. The magnitude differences among *cD1A*, *cD1B*, and *cD1C* is endorsed to the inception angle of fault, i.e. the value of *VA(tx), VB(tx)* or *VC(tx)* (*tx* represents de instant value when fault occurs) at the moment of fault is incepted. It is important to see that wave requires 0.0008 s to travel from *FP* to *M1*. This is the reason for the delay of time in which *cD1* appears and fault is detected. This delay time is considered in detecting time and locating distance.

Fig. 29. *cD1* from the three phase fault at *t*= 0.3 s.

The time elapsed between first and second traveling wave is used by the algorithm to locate the fault. The algorithm developed to detect the fault gives as a result that fault is detected

Discrete Wavelet Transform Application to the Protection of Electrical

Distance (km) to M1

efficiently the distance to fault.

Fig. 32. Voltage of phase A, before and after to AB fault

located.

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 267

TYPE OF FAULT

60 60 60 60 60 60 60 60 60 60 60 120 120 120 120 120 120 120 120 120 120 120 180 180 180 180 180 180 180 180 180 180 180 240 240 240 240 240 240 240 240 240 240 240 300 300 300 300 300 300 300 300 292.5 300 300 360 360 360 360 360 360 360 360 360 360 360

Table 4. Distance to the fault for four types of faults in transmission line with SSSC

Tables 3 and 4, show that the algorithm closely determines de distance to the fault. For instance, table 3, illustrates that for faults simulated at 60 km from *M1*, the distance at which the fault occurs is correctly identified for all types of faults. This is true for cases when TCSC or SSSC is installed at the middle of the line. The distance to fault is well calculated for 60, 120, 180, 240 and 360 km. The only cases in which the algorithm presents deviations are with AB fault type; these have been linked to those faults with a small inception angle (less than 5 degrees). Fig. 32 shows that transient signal (enclosed in red) generated by fault of type AB at 0.3 s is small, in this condition, it's difficult to calculate

When the fault is simulated at different time, for example 0.31 s, the fault is correctly detected and located. Fig. 33, shows the screen displayed by MATLAB, after the fault is

AG BG CG ABG BCG ACG ABCG AB BC AC

at 0.3 s and is located at 240 km. These is obtained using (13), in this case, time elapsed between the first and second traveling waves is *tfl-tfd* = 1.6 ms, so

$$FL = \frac{\upsilon(t\_{fl} - t\_{fd})}{2} = \frac{300000km/s(0.0016\,\text{s})}{2} = 240km$$

To further test the performance of the developed algorithms, the capability for determining the distance to the fault is also evaluated for different distances. Fig. 30 illustrates that transmission line is divided in 60 km segments. In this way, 6 different positions of fault can be analyzed. As example, the fault is simulated in 0.3 s, at 60 km from *M1*

Fig. 30. System used to simulate 6 different locations of faults.

Once the simulation is initiated, voltages values of *VA, VB* and *VC* are fed to MATLAB. This latter, develop the algorithm of subsection 4.3 and the result is shown in fig. 31.

Fig. 31. Result obtained from MATLAB when fault is detected and located

As a resume, the results for 6 different distances to *M1* are shown in tables 3 and 4 for a grid with one FACTS.


Table 3. Distance to the fault for four types of faults in transmission line with TCSC

at 0.3 s and is located at 240 km. These is obtained using (13), in this case, time elapsed

2 2

be analyzed. As example, the fault is simulated in 0.3 s, at 60 km from *M1*

Fig. 30. System used to simulate 6 different locations of faults.

( ) 300000 / (0.0016 ) <sup>240</sup>

*fl fd vt t km s s FL km*

To further test the performance of the developed algorithms, the capability for determining the distance to the fault is also evaluated for different distances. Fig. 30 illustrates that transmission line is divided in 60 km segments. In this way, 6 different positions of fault can

Once the simulation is initiated, voltages values of *VA, VB* and *VC* are fed to MATLAB. This

As a resume, the results for 6 different distances to *M1* are shown in tables 3 and 4 for a grid

TYPE OF FAULT

60 60 60 60 60 60 60 60 60 60 60 120 120 120 120 120 120 120 120 120 120 120 180 180 180 180 180 180 180 180 180 180 180 240 240 240 240 240 240 240 240 240 240 240 300 300 300 300 300 300 300 300 292.5 300 300 360 360 360 360 360 360 360 360 360 360 360

Table 3. Distance to the fault for four types of faults in transmission line with TCSC

AG BG CG ABG BCG ACG ABCG AB BC AC

latter, develop the algorithm of subsection 4.3 and the result is shown in fig. 31.

Fig. 31. Result obtained from MATLAB when fault is detected and located

with one FACTS.

Distance (km) to M1

between the first and second traveling waves is *tfl-tfd* = 1.6 ms, so


Table 4. Distance to the fault for four types of faults in transmission line with SSSC

Tables 3 and 4, show that the algorithm closely determines de distance to the fault. For instance, table 3, illustrates that for faults simulated at 60 km from *M1*, the distance at which the fault occurs is correctly identified for all types of faults. This is true for cases when TCSC or SSSC is installed at the middle of the line. The distance to fault is well calculated for 60, 120, 180, 240 and 360 km. The only cases in which the algorithm presents deviations are with AB fault type; these have been linked to those faults with a small inception angle (less than 5 degrees). Fig. 32 shows that transient signal (enclosed in red) generated by fault of type AB at 0.3 s is small, in this condition, it's difficult to calculate efficiently the distance to fault.

Fig. 32. Voltage of phase A, before and after to AB fault

When the fault is simulated at different time, for example 0.31 s, the fault is correctly detected and located. Fig. 33, shows the screen displayed by MATLAB, after the fault is located.

Discrete Wavelet Transform Application to the Protection of Electrical

Fig. 35. Protection tripping

**7. References** 

compromise coordination with others protection relays.

*Delivery, Vol. 21, No. 3*, pp. 1106-111, July 2006

*Delivery of Electrical Energy in the 21st Century*, pp. 1-6

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 269

As can be seen in fig. 35, before t=0.3 s, the current signals are only the fundamental of 60 Hz. At t=0.3008 s, the algorithm detects the fault event (the wave needs 0.0008 s to reach the *M1* position). The second traveling wave appear at t= 0.3012, at this moment the fault is located. After successful detection and locating of the fault event the protection is activated. The time given to activating relay is sufficiently small (15 ms after detection of fault) to don't

Chen Y, et. al. (2010), "Short-Term Load Forecasting: Similar Day-Based Wavelet Neural

Chia-Hung L. & Chia-Hao W. (2006), "Adaptive Wavelet Networks for Power-Quality

Daneshpooy A.&Gole A.M. (2001), "Frequency Response of the Thyristor Controlled Series Capacitor", *IEEE Transactions on Power Delivery, Vol. 16, No. 1*, pp. 53-58, Jan 2001 Hingorani N. & Gyugyi L. (2000), *Understanding FACTS*, IEEE PRESS, New York USA, 2000 Kashyap K.H. & Shenoy U.J. (2003), "Classification Of Power System Faults Using Wavelet

*International Symposium on Circuits and Systems,* May 2003, pp 423-426 Kazemi A., Jamali S. & Shateri H. (2005), "Effects of STATCOM on Distance Relay". In *Proc. 2005, IEEE Transmission and Distribution Conference and Exposition*, pp. 1-6 Khederzadeh M. (2008), "UPFC Operating Characteristics Impact on Transmission Line

Networks", *IEEE Transactions on Power Systems, Vol. 25, No. 1*, pp. 322-330*,* Feb. 2010

Detection and Discrimination in a Power System", *IEEE Transactions on Power* 

Transforms And Probabilistic Neural Networks", *Proceedings of the 2003* 

Distance Protection"*,* In *Proc. 2008, IEEE-PES General Meeting - Conversion and* 

Fig. 33. Screen displayed after *AB* fault, in 0.31 s at 300 km from *M1*

The relationship of the time elapsed between first and second traveling waves (*telap=tfl-tfd*), has a linear relationship with the distance of fault, this is illustrated in fig 34. This is true when FACTS are or not connected. As this way, the method to calculate de distance to fault using *telap* is a better choice compared with distance to fault obtained by measurement of impedance used in conventional schemes. The relationship between distance to fault and impedance are non linear when FACTS is connected (see fig. 10), while using *telap*, the distance to fault is easily obtained with (13).

Fig. 34. Relationship between time of traveling waves and distance to fault.

As mentioned earlier, after the detection and location of fault, MATLAB display a screen that includes time of detection and location of fault. After that, MATLAB send an activation signal to protection relay. Fig. 35 shows the line current signals and *cD1*, obtained before and after a fault occurs in t=0.3 s at 240 km from *M1*

Fig. 35. Protection tripping

As can be seen in fig. 35, before t=0.3 s, the current signals are only the fundamental of 60 Hz. At t=0.3008 s, the algorithm detects the fault event (the wave needs 0.0008 s to reach the *M1* position). The second traveling wave appear at t= 0.3012, at this moment the fault is located. After successful detection and locating of the fault event the protection is activated. The time given to activating relay is sufficiently small (15 ms after detection of fault) to don't compromise coordination with others protection relays.
