**4.1.1 Travelling waves and the TCSC**

Considering *x* point matches with FACTS location, then impedance at this point is given by contribution of *Z0* and impedance of TCSC. Fig. 14 illustrates the TCSC scheme under study and table 1 shows its parameters.

Fig. 14. TCSC controller


Table 1. Electric Parameters

Discrete Wavelet Transform Application to the Protection of Electrical

From fig. 16, the impedance seen at this point is given by (9)

1

*sC*

*TCSC*

*FIXED TCSC TCSC*

*TCSC TCSC TCSC FIXED <sup>v</sup> TCSC TCSC FIXED*

2

*TCSC TCSC TCSC FIXED <sup>v</sup>*

Once the wave reaches the SSSC, the impedance seen by wave is (11)

1

In this case, *LTCSC*= 8.8 mH, so the constant time of decrease is

*sC sL sC*

*<sup>v</sup>* is obtained by substituting (9) in (6)

1

0

decrease is done.

Fig. 17. SSSC Controller

0

**4.1.2 Travelling waves and the SSSC** 

17 pictures the SSSC equivalent circuit.

*v* is obtained substituting (11) in (6)

2

2 (1 )

*Z s L C sC*

3 2

0

<sup>1</sup> ( ) <sup>1</sup>

2 2

*sL C sL C*

*sL C L C s ZL C C s L C L C s ZC*

1

0 0

needed to reflect the wave. As the wave need 1.2 ms. to travel along the line, no significant

An SSSC can emulate a series-connected compensating reactance and is represented by a voltage source (*Vq*) in series with reactance of coupling transformer (*XL*) (Sen, 1998). The Fig.

( ) 1 2 ( )2 1

*TCSC TCSC FIXED TCSC TCSC TCSC FIXED FIXED*

<sup>1</sup> <sup>1</sup> <sup>2</sup> <sup>1</sup>

*TCSC*

*sL*

*TCSC*

2 2

*sC Zs Z*

*TCSC <sup>x</sup>*

1 1

*sC sL sL*

*TCSC FIXED TCSC TCSC <sup>v</sup> TCSC TCSC*

<sup>1</sup> <sup>1</sup> <sup>2</sup>

*sC sC sL C <sup>Z</sup>*

*FIXED TCSC*

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 257

1

*FIXED TCSC TCSC*

*sC sL sC*

*sC sC sL C*

*TCSC*

2

*TCSC TCSC TCSC FIXED*

<sup>0</sup> ( ) *Z s Z jX x L* (11)

0 2

*sL C sL C*

*TCSC FIXED TCSC TCSC*

*sL sL <sup>Z</sup>*

1

(9)

= 107.5 ms, and 430.1ms are

(10)

*sL*

When the travelling wave reaches the thyristor, this can be open or closed. If the thyristor is open at the moment when the wave reaches it, the array seen by wave is as shown in fig. 15.

Fig. 15. Traveling wave when Thyristor is open

From fig. 11, the impedance at FACTS location is given by (7)

$$Z\_x(\text{s}) = Z\_0 + \frac{1}{s\text{C}\_{T\text{CSC}}} + \frac{1}{s\text{C}\_{F\text{IXED}}} = Z\_0 + \frac{\text{C}\_{T\text{CSC}} + \text{C}\_{F\text{IXED}}}{s(\text{C}\_{T\text{CSC}})(\text{C}\_{F\text{IXED}})} \tag{7}$$

The coefficient of reflection seen at discontinuity is obtained by substituting (7) in (6)

$$\rho\_v = \frac{\frac{\mathbf{C}\_{\text{TSCC}} + \mathbf{C}\_{\text{FXED}}}{s\mathbf{C}\_{\text{TSCC}}\mathbf{C}\_{\text{FXED}}}}{2\mathbf{Z}\_0 + \frac{\mathbf{C}\_{\text{TSCC}} + \mathbf{C}\_{\text{FXED}}}{s\mathbf{C}\_{\text{TSCC}}\mathbf{C}\_{\text{FXED}}}} = \frac{1}{2\mathbf{Z}\_0 + \frac{1}{s\mathbf{C}\_{\text{SER}}}} = \frac{1}{s\mathbf{2}\mathbf{Z}\_0\mathbf{C}\_{\text{SER}} + 1} \tag{8}$$

where ( )( ) *C CC SERIE TCSC FIXED* .

Because the capacitor opposes to abrupt changes in voltage, the wave tends to pass through the TCSC without a significant decrement. From (6), the voltage decreases with a constant time given by 0 2*Z CSERIE* 

If *CTCSC* = 98F, *CFIXED* = 95 F, and *Z0* = 550 , then = 53.1 ms. This array needs 212.2 ms to discharge; however, the traveling wave makes the travel in 1.2 ms, so the discontinuity due to TCSC represents only a decrement of 0.6% in magnitude of front of voltage wave.

If thyristor is closed at the moment when the wave reaches it, the array seen by wave is as shown in fig. 16.

Fig. 16. Traveling wave when Thyristor is closed

From fig. 16, the impedance seen at this point is given by (9)

$$Z\_x(s) = Z\_0 + \frac{1}{sC\_{F\text{IXED}}} + \frac{1}{\frac{sC\_{T\text{SCSC}}}{sC\_{T\text{SCSC}}} + sL\_{T\text{SCSC}}} \tag{9}$$

*<sup>v</sup>* is obtained by substituting (9) in (6)

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

When the travelling wave reaches the thyristor, this can be open or closed. If the thyristor is open at the moment when the wave reaches it, the array seen by wave is as shown in fig. 15.

Fig. 15. Traveling wave when Thyristor is open

where ( )( ) *C CC SERIE TCSC FIXED* .

front of voltage wave.

Fig. 16. Traveling wave when Thyristor is closed

time given by 0 2*Z CSERIE* 

shown in fig. 16.

From fig. 11, the impedance at FACTS location is given by (7)

*TCSC FIXED*

*C C*

0 0

*sC C sC*

If *CTCSC* = 98F, *CFIXED* = 95 F, and *Z0* = 550 , then

*C C Zs Z <sup>Z</sup>*

The coefficient of reflection seen at discontinuity is obtained by substituting (7) in (6)

<sup>0</sup> <sup>0</sup> <sup>0</sup>

*C C s ZC <sup>Z</sup> <sup>Z</sup> sC C sC*

Because the capacitor opposes to abrupt changes in voltage, the wave tends to pass through the TCSC without a significant decrement. From (6), the voltage decreases with a constant

If thyristor is closed at the moment when the wave reaches it, the array seen by wave is as

212.2 ms to discharge; however, the traveling wave makes the travel in 1.2 ms, so the discontinuity due to TCSC represents only a decrement of 0.6% in magnitude of

*TCSC FIXED SERIE <sup>v</sup> TCSC FIXED SERIE TCSC FIXED SERIE*

<sup>1</sup> 2 1 <sup>2</sup> <sup>2</sup>

1 1 ( ) ( )( ) *TCSC FIXED <sup>x</sup>*

*sC sC sC C*

*TCSC FIXED TCSC FIXED*

1

 (7)

1

(8)

= 53.1 ms. This array needs

2 0 2 0 2 2 2 0 1 1 1 1 1 <sup>1</sup> <sup>1</sup> <sup>2</sup> <sup>1</sup> <sup>1</sup> <sup>2</sup> <sup>1</sup> 1 2 (1 ) *TCSC TCSC FIXED TCSC TCSC TCSC FIXED TCSC TCSC <sup>v</sup> TCSC TCSC TCSC FIXED TCSC TCSC FIXED TCSC TCSC TCSC TCSC TCSC FIXED <sup>v</sup> TCSC TCSC FIXED sL sC sC sL sL sC sC sL C sL sL <sup>Z</sup> sC sC sL C <sup>Z</sup> sC sL sC sL C sL C Z s L C sC* 2 2 2 3 2 0 0 1 ( ) 1 2 ( )2 1 *TCSC TCSC TCSC FIXED TCSC TCSC TCSC FIXED <sup>v</sup> TCSC TCSC FIXED TCSC TCSC TCSC FIXED FIXED sL C sL C sL C L C s ZL C C s L C L C s ZC* (10)

In this case, *LTCSC*= 8.8 mH, so the constant time of decrease is = 107.5 ms, and 430.1ms are needed to reflect the wave. As the wave need 1.2 ms. to travel along the line, no significant decrease is done.

#### **4.1.2 Travelling waves and the SSSC**

An SSSC can emulate a series-connected compensating reactance and is represented by a voltage source (*Vq*) in series with reactance of coupling transformer (*XL*) (Sen, 1998). The Fig. 17 pictures the SSSC equivalent circuit.

Fig. 17. SSSC Controller

Once the wave reaches the SSSC, the impedance seen by wave is (11)

$$Z\_x(\mathbf{s}) = Z\_0 + jX\_L \tag{11}$$

*v* is obtained substituting (11) in (6)

$$\rho\_v = \frac{jX\_L}{jX\_L + 2Z\_0} \tag{12}$$

Discrete Wavelet Transform Application to the Protection of Electrical

with and without FACTS are presented in fig. 19

TCSC

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 259

Because the fault is simulated after the position of controller, the voltage measurement in *M1*, contains harmonics induced by FACTS. To analyze the range of frequency at which fault signal and harmonics of FACTS are present, (3) is used to calculate *cDn* of voltage obtained from *M1*. Five coefficients of detail are considered because harmonics due to TCSC are present at range 156-312 Hz (see table 2). The results obtained when the fault is simulated

Fig. 19. Detail coefficients obtained in pre-fault and faulted conditions, with and with no

discriminated from the mix of signal from the line and fault occurrence.

analyzed with *cD4* and *cD5*, because have a range of 156 to 625 Hz.

As can be notice from 19(k) and 19(l), the TCSC effects due the harmonics are detected with *cD*5. On the other hand, from 19(c) and (d) the high-frequency traveling waves resulted from the fault are correctly detected with *cD*1, regardless of whether or not connected FACTS. Here therefore if lower levels of *cDn* are used then the harmonics due to TCSC can be

As a second example, the harmonics injected by the SSSC are also detected with the wavelet transform, because these, it is necessary to separate this signals from those resulted from the fault. In this example, a 6 pulses SSSC is used, so the main harmonic components are 3th, 5th and 7th, which are present at 180 to 420 Hz (Sen, 1998). From table 2, this signal can be

To show that harmonics due to SSSC can be discriminated from signals due to fault, a three phase to ground fault is simulated again at 300 km from *M1*, as illustrated in fig. 20. The

fault occurs at 0.3 s. Two cases are considered: a) without SSSC and b) with SSSC.

Due the transformer was selected to work as a coupling instrument, *XL* is enough small to give a *<sup>v</sup>* near to zero. So, the magnitude of incident wave is no significantly affected by SSSC. In the present case XL = *wL*= (2)(60)(0.1mH)= 0.0377 and *Z0* = 550 , then

$$\rho\_v = \frac{0.0377 \, j}{0.0377 \, j + 2(550)} \approx \frac{0.0377 \, j}{1100} \approx 0.0$$

Because of the value of *<sup>v</sup>*is zero and then there is not reflection of wave when reach the position of SSSC, so the magnitude of traveling wave is not affected.

In the case of both controllers, TCSC and SSSC, is evidenced that the magnitude of traveling waves are unaffected when passing through the FACTS controller and they are not an obstacle for the travelling waves to be a good option to detect and locate faults.

#### **4.2 FACTS harmonics effects on WT**

Although magnitude of traveling wave is no significantly affected by TCSC, a proper coefficient of detail in wavelet transform is needed to be selected. This is because the wavelet transform can detect the harmonics due to FACTS. This frequency can mix up with the traveling waves at some coefficients of details reason why is important to identify. For instance, the main harmonics of TCSC are 3th and 5th (Daneshpooy&Gole, 2001)

Table 2 shows the frequency ranges of the coefficients of details for the signals under analysis. The above considering a sampling frequency of 10 kHz. It can be seen that cD5, correspond to 156-312 Hz range, so main harmonics of TCSC are placed in that level.


Table 2. Range of frequency with coefficient of detail

As example to show the above, a three phase to ground fault is simulated at 300 km from *M1*, as illustrated in fig. 18. The fault occurs at 0.3 s. Two cases are considered: a) without FACTS and b) with FACTS.

Fig. 18. Three phase to ground fault at 300 km.

*<sup>L</sup> <sup>v</sup> L jX jX Z*

Due the transformer was selected to work as a coupling instrument, *XL* is enough small to

0.0377 2(550) 1100 *<sup>v</sup>*

In the case of both controllers, TCSC and SSSC, is evidenced that the magnitude of traveling waves are unaffected when passing through the FACTS controller and they are not an

Although magnitude of traveling wave is no significantly affected by TCSC, a proper coefficient of detail in wavelet transform is needed to be selected. This is because the wavelet transform can detect the harmonics due to FACTS. This frequency can mix up with the traveling waves at some coefficients of details reason why is important to identify. For

Table 2 shows the frequency ranges of the coefficients of details for the signals under analysis. The above considering a sampling frequency of 10 kHz. It can be seen that cD5,

As example to show the above, a three phase to ground fault is simulated at 300 km from *M1*, as illustrated in fig. 18. The fault occurs at 0.3 s. Two cases are considered: a) without

SSSC. In the present case XL = *wL*= (2)(60)(0.1mH)= 0.0377 and *Z0* = 550 , then

*j*

obstacle for the travelling waves to be a good option to detect and locate faults.

instance, the main harmonics of TCSC are 3th and 5th (Daneshpooy&Gole, 2001)

correspond to 156-312 Hz range, so main harmonics of TCSC are placed in that level.

Level of Coefficient of Detail Range of frequency cD1 (level 1) 2500 Hz to 5 kHz cD2 (level 2) 1250 Hz to 2500 Hz cD3 (level 3) 625 Hz to 1250 Hz cD4 (level 4) 312.5 Hz to 625 Hz cD5 (level 5) 156 Hz to 312 Hz

position of SSSC, so the magnitude of traveling wave is not affected.

Table 2. Range of frequency with coefficient of detail

Fig. 18. Three phase to ground fault at 300 km.

FACTS and b) with FACTS.

**4.2 FACTS harmonics effects on WT** 

give a 

Because of the value of

<sup>0</sup> 2

*<sup>v</sup>* near to zero. So, the magnitude of incident wave is no significantly affected by

0.0377 0.0377 <sup>0</sup>

*j j*

*<sup>v</sup>*is zero and then there is not reflection of wave when reach the

(12)

Because the fault is simulated after the position of controller, the voltage measurement in *M1*, contains harmonics induced by FACTS. To analyze the range of frequency at which fault signal and harmonics of FACTS are present, (3) is used to calculate *cDn* of voltage obtained from *M1*. Five coefficients of detail are considered because harmonics due to TCSC are present at range 156-312 Hz (see table 2). The results obtained when the fault is simulated with and without FACTS are presented in fig. 19

Fig. 19. Detail coefficients obtained in pre-fault and faulted conditions, with and with no TCSC

As can be notice from 19(k) and 19(l), the TCSC effects due the harmonics are detected with *cD*5. On the other hand, from 19(c) and (d) the high-frequency traveling waves resulted from the fault are correctly detected with *cD*1, regardless of whether or not connected FACTS. Here therefore if lower levels of *cDn* are used then the harmonics due to TCSC can be discriminated from the mix of signal from the line and fault occurrence.

As a second example, the harmonics injected by the SSSC are also detected with the wavelet transform, because these, it is necessary to separate this signals from those resulted from the fault. In this example, a 6 pulses SSSC is used, so the main harmonic components are 3th, 5th and 7th, which are present at 180 to 420 Hz (Sen, 1998). From table 2, this signal can be analyzed with *cD4* and *cD5*, because have a range of 156 to 625 Hz.

To show that harmonics due to SSSC can be discriminated from signals due to fault, a three phase to ground fault is simulated again at 300 km from *M1*, as illustrated in fig. 20. The fault occurs at 0.3 s. Two cases are considered: a) without SSSC and b) with SSSC.

Discrete Wavelet Transform Application to the Protection of Electrical

Fig. 22. Procedure to extract the Coefficients of Details

Fig. 23. Procedure to detect and locate fault

signals from M1.

detect and locate the fault.

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 261

position (*FP*) to measurement point (*M1*); b) Based on subsection 4.2, harmonics due to

Wavelet toolbox from MATLAB is the tool used to calculate detail coefficients and the distance to the fault location. Figure 22 shows the procedure to extract *cD1* obtained of

When the voltage signal from *M1* is decomposed in *cA1* and *cD1*, *cD1* is used to determinate the instant at which the fault occurs, because of the correspondence with high frequency signals. Figure 23 shows the procedure for analyzing the signals obtained in PSCAD, to

Protection relay located at *M1* is continuously monitoring the instant value of voltages *VA, VB* and *VC*, in this way, *cD1* is being monitored. If fault is not present, then the only signal monitored by *M1* is the fundamental signal of 60 Hz, as shown in fig. 24 (a). In this case, *cD1* has insignificant values, because there are not signals of frequency determined by this coefficient (2.5 to 5 kHz). Considering a fault occurs in 0.3 seconds at 240 km away from *M1*, as illustrated in fig. 24 (b), the transient signal generated by the fault travels across the

FACTS don't affect the measurement of traveling wave at *M1*, when *cD1* is selected.

Fig. 20. Three phase to ground fault at 300 km.

As expected, the harmonics due to controller are present with *cD*4 and *cD5* as shown in figs. 21(i) to 21 (l). As the same of TCSC case, cD1 can be used to detect the fault signal, with or without the SSSC installed (fig. 21(c) and 21(d)).

Fig. 21. Coefficients of Detail obtained before and after a fault, with and with no SSSC

As figures 19 and 21 illustrates, the harmonics produced by the FACTS (TCSC and SSSC) are present in levels *cD*4 and *cD*5. If only lower coefficients of details are considered, then there is no difference between waveforms of voltage/current signals of the faulted line with or without the presence of a FACTS controller. Here therefore *cD1* is a good option for detecting, locating and classifying faults

#### **4.3 Algorithm to detect and locate faults**

The algorithm presented in this subsection is based on utilizing traveling waves as mentioned at the beginning of section 4, by means of getting DWT: a) Based on subsection 4.1, the magnitude of traveling wave it's not affected when FACTS lies in its path from fault position (*FP*) to measurement point (*M1*); b) Based on subsection 4.2, harmonics due to FACTS don't affect the measurement of traveling wave at *M1*, when *cD1* is selected.

Wavelet toolbox from MATLAB is the tool used to calculate detail coefficients and the distance to the fault location. Figure 22 shows the procedure to extract *cD1* obtained of signals from M1.

Fig. 22. Procedure to extract the Coefficients of Details

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

As expected, the harmonics due to controller are present with *cD*4 and *cD5* as shown in figs. 21(i) to 21 (l). As the same of TCSC case, cD1 can be used to detect the fault signal, with or

Fig. 21. Coefficients of Detail obtained before and after a fault, with and with no SSSC

As figures 19 and 21 illustrates, the harmonics produced by the FACTS (TCSC and SSSC) are present in levels *cD*4 and *cD*5. If only lower coefficients of details are considered, then there is no difference between waveforms of voltage/current signals of the faulted line with or without the presence of a FACTS controller. Here therefore *cD1* is a good option for

The algorithm presented in this subsection is based on utilizing traveling waves as mentioned at the beginning of section 4, by means of getting DWT: a) Based on subsection 4.1, the magnitude of traveling wave it's not affected when FACTS lies in its path from fault

Fig. 20. Three phase to ground fault at 300 km.

without the SSSC installed (fig. 21(c) and 21(d)).

detecting, locating and classifying faults

**4.3 Algorithm to detect and locate faults** 

When the voltage signal from *M1* is decomposed in *cA1* and *cD1*, *cD1* is used to determinate the instant at which the fault occurs, because of the correspondence with high frequency signals. Figure 23 shows the procedure for analyzing the signals obtained in PSCAD, to detect and locate the fault.

Fig. 23. Procedure to detect and locate fault

Protection relay located at *M1* is continuously monitoring the instant value of voltages *VA, VB* and *VC*, in this way, *cD1* is being monitored. If fault is not present, then the only signal monitored by *M1* is the fundamental signal of 60 Hz, as shown in fig. 24 (a). In this case, *cD1* has insignificant values, because there are not signals of frequency determined by this coefficient (2.5 to 5 kHz). Considering a fault occurs in 0.3 seconds at 240 km away from *M1*, as illustrated in fig. 24 (b), the transient signal generated by the fault travels across the

Discrete Wavelet Transform Application to the Protection of Electrical

uses (13) to locate the distance (*FL*) at which the fault occurs.

time of first traveling detection (s)

different types of fault are considered.

Fig. 26. Electrical grid with series FACTS

presented in subsection 4.3.

same position of *M1*.

shows the power grid used for the study cases.

**5. System under study** 

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 263

When the traveling wave reaches *M1*, in a second time, this generates a new peak in *cD1* that

where *v*=300,000 (km/s) speed of light, *tfl* = time of second traveling (s) detection and *tfd* =

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

To corroborate the location process, fault at every 60 km from *M1* are presented. Figure 26

*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

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

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.

( ) 2 *fl fd vt t*

*FL* (13)

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 *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

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

Fig. 25. Path of traveling wave due to fault

When the traveling wave reaches *M1*, in a second time, this generates a new peak in *cD1* that uses (13) to locate the distance (*FL*) at which the fault occurs.

$$FL = \frac{v(\mathbf{t}\_{fl} - \mathbf{t}\_{fl})}{2} \tag{13}$$

where *v*=300,000 (km/s) speed of light, *tfl* = time of second traveling (s) detection and *tfd* = time of first traveling detection (s)
