**5. System under study**

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

transmission line and reaches the protection relay, the value of *cD*, exceeds a threshold value (*cDTH*), because the transitory signal due to fault is situated within the range measured by

Once the wave reaches the *M1* position, it is reflected to *FP*, because the impedance at this point is different to *Z0*. Because the impedance of *FP* is different to *Z0*, the wave is reflected

*cD1*, then the system detects the Fault and the value of time of fault is stored (*tfd=t*).

Fig. 24. Signals monitored by *M1*, before and after a fault

again to *M1*, as shown in fig. 25.

Fig. 25. Path of traveling wave due to fault

To demonstrate the correct operation of procedure presented in section 4, an electrical grid was designed in PSCAD. To validate the detection process, several faults are simulated; ten different types of fault are considered.

To corroborate the location process, fault at every 60 km from *M1* are presented. Figure 26 shows the power grid used for the study cases.

Fig. 26. Electrical grid with series FACTS

*cD1* is used to detect and locate fault. The voltage data (*VA*, *VB* and *VC*) are taken from *M1*. These values are fed to MATLAB through an interface. MATLAB performs the tasks presented in subsection 4.3.

After the fault is located a signal of relay activation is sent from MATLAB to PSCAD and protection relay is activated. Protection relay is identified as *B1* in fig. 26 and is located at the same position of *M1*.

Electrical parameter of the transmission line are: line voltage: 400 kV; line length: 360 km.; Z0: 550 , others parameters to adjust TCSC were presented in table 1.

Figures 27 and 28 illustrate the SSSC and TCSC utilized in the case study.

Discrete Wavelet Transform Application to the Protection of Electrical

**6. Results** 

simulation:

1. AG (Phase A to Ground) 2. BG (Phase B to Ground) 3. CG (Phase C to Ground)

8. AB (Phase A to phase B) 9. AC (Phase A to phase B) 10. BC (Phase A to phase B)

4. ABG (Phases A and B to Ground) 5. ACG (Phases A and C to Ground) 6. BCG (Phases B and C to Ground) 7. ABCG (Three Phase Fault to Ground)

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

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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

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.

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

Fig. 27. SSSC configuration for the case study

Fig. 28. TCSC configuration for the case study
