**3.1 FACTS effects on conventional protection schemes**

The transmission lines are commonly protected with a distance protection relay. A key element for this protection is the equivalent impedance measured from the relay to the fault location, as shown on fig. 8. In non-compensated lines, the distance to the fault is lineally related to this impedance.

Fig. 8. Distance Relay

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

The TCSC is made of a series capacitor (*CTCSC*) shunted by a thyristor module in series with an inductor (*LTCSC*). An external fixed capacitor (*CFIXED*) provides additional series compensating. The structure shown in fig. 4 behaves as variable impedance fully dependable of the firing angle of the thyristors into the range from 180° to 90°. Normally the TCSC operates as a variable capacitor, firing the thyristor between 180° to 150°. The steady

*CTCSC LTCSC*

*X X*

( ) , ( ) 2 sin

 

*LTCSC CTCSC*

(4)

 

Fig. 6. TCSC

Where

Fig. 7. SSSC

state impedance of TCSC (*XTCSC*) is (4)

where is the firing angle of thyristor.

( ) ( ) ( )

*TCSC*

*X X <sup>X</sup>*

*X X LTCSC LTCSC X X LTCSC LTCSC* 

Before the fault occurs, the relay (R) measures voltage and current at node A and calculate the total impedance of line (ZLINE). When fault occurs at fault point (*FP*), the impedance measured by R is lower than ZLINE (*ZFP* < ZLINE) and proportional to distance between *FP* and node A.

In transmission lines compensated with series FACTS such impedance, -from measuring point of reference-, presents a nonlinear behavior. The impedance can abruptly change depending on the location of the fault in the line, after or before the FACTS controller. As mentioned above, protection relays for no compensated power lines centers its operation in a linear relationship between the distance to the fault and the equivalent impedance. For instance, the collateral effects of STATCOM on impedance had been presented in some detail (Kazemi et.al., 2005; Zhou et.al., 2005) showing that the shunt controller produces a modification in tripping characteristics for relay of protection. The impedance variation induced by the STATCOM affects the distance protection, meaning this that the fault is not precisely located in the line and the distant to the fault is wrongly determined. In relation with the UPFC, some studies indicate that this controller have significant effects on the grid at the point of common coupling, PCC, greater than those from shunt-connected controller (Khederzadeh, 2008). Similarly, series-connected FACTS controllers tends to reduce the total equivalent impedance a transmission line. As the conventional distance protection relies on the linear equivalent impedance-fault distance relationship, at fault occurrence such protection, -installed at in one end of the line-, faces two scenarios: a) scenario 1: the fault is located between the protection and the series FACTS, and b) scenario 2: the fault is not located between the protection and the series FACTS but after the controller. As example, Figure 9 shows the effect of the TCSC on the equivalent line impedance. It can be notice in Fig. 9 (b) that TCSC reduces the electrical line length, which means a reduction of the total equivalent impedance. In this case, a conventional distance protection can detect and locate a fault for the scenario 1 (a) but wrongly operates for scenario 2 (b).

Discrete Wavelet Transform Application to the Protection of Electrical

Fig. 11. a) Traveling waves in a faulted line; b) Laticce diagram

the wave encounters the FACTS when traveling from *FP* to *M1*.

It's important to analyze the effects caused by FACTS on traveling wave to determine if this latter can be used to detect and locate faults at FACTS environment. Considering a controller installed at the middle of the line, if fault occurs before the position of FACTS, as illustrated in fig. 12(a), the traveling wave can be analyzed at the same way that without controller, because it don´t encounter points of different impedance to *Z0* between *FP* and *M1*. In the other hand, if fault occurs after the position of controller, as shown in Fig. 12(b),

with the particularities of grids in a FACTS context.

electrical grids in the current context.

fault.

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 253

generation of protection installed should include algorithms with built-in techniques to deal

Artificial intelligence and digital signal processing techniques, DSP, have both provided a sort of tools to power systems engineers. In particular the combination of wavelets with artificial intelligence and estimation techniques is an attractive option for analyzing

In order to deal with the impedance nonlinear variation characteristic associated to the series FACTS compensation, various solutions have been proposed in the last decade. One of these proposals uses traveling waves to detect and locate faults in a transmission line (Shehab-Eldin&McLaren, 1988). As is known, after a fault in a transmission line two traveling waves are produced, this is shown if figure 11(a). The traveling wave is used to detect and locate the fault. The latter is achieved determining the time the wave needs to travel from the fault position *(FP)* to the measurement point (*M1*). Fig. 11(b), illustrates a lattice diagram of traveling waves. After the fault, the wave needs a time *t1* to travel from *FP* to *M1*. When the traveling wave reach a point at which impedance is different to characteristic impedance (*Z0*), then the wave is reflected, because of that, the wave is reflected when reach the node *A* and returns to *FP*. Once the wave reaches *FP* is reflected because the impedance at *FP* is different to *Z0* and travels again to node *A* in a time equals to *t2*. The fault is detected at time *t1* and time elapsed between *t1* and *t2* is useful to locate the fault position. This is possible because *t2-t1* has a linear relationship with distance to

Fig. 9. Impedance of a transmission line after a three-phase fault at the end of line, a) without TCSC, b) with TCSC

The aforementioned nonlinear behavior is caused by the relationship ZLINE\_COMP = ZLINE-ZTCSC. In the fault scenario 1 ZLINE\_COMP = ZLINE; but in the fault scenario 2 ZLINE\_COMP = ZLINE-ZTCSC. Fig. 10 shows the nonlinear relation. The TCSC is situated at the middle of the line.

Fig. 10. Line impedance with TCSC after a fault.

As figure 10 shows, if the fault occurs before the TCSC location impedance has a linear relationship with distance to fault, however when fault occurs after the position of FACTS, then the impedance suffers a non linear change, evidenced by reduction of impedance, that cause a malfunction on distance relay.

#### **4. Procedure to detect and locate faults**

As shown in section 3, in compensated grid such the conventional distance protection schemes face conditions not taken into account in its original design, therefore the next

Fig. 9. Impedance of a transmission line after a three-phase fault at the end of line, a)

The aforementioned nonlinear behavior is caused by the relationship ZLINE\_COMP = ZLINE-ZTCSC. In the fault scenario 1 ZLINE\_COMP = ZLINE; but in the fault scenario 2 ZLINE\_COMP = ZLINE-ZTCSC. Fig. 10 shows the nonlinear relation. The TCSC is situated at the middle of the line.

As figure 10 shows, if the fault occurs before the TCSC location impedance has a linear relationship with distance to fault, however when fault occurs after the position of FACTS, then the impedance suffers a non linear change, evidenced by reduction of impedance, that

As shown in section 3, in compensated grid such the conventional distance protection schemes face conditions not taken into account in its original design, therefore the next

without TCSC, b) with TCSC

Fig. 10. Line impedance with TCSC after a fault.

cause a malfunction on distance relay.

**4. Procedure to detect and locate faults** 

generation of protection installed should include algorithms with built-in techniques to deal with the particularities of grids in a FACTS context.

Artificial intelligence and digital signal processing techniques, DSP, have both provided a sort of tools to power systems engineers. In particular the combination of wavelets with artificial intelligence and estimation techniques is an attractive option for analyzing electrical grids in the current context.

In order to deal with the impedance nonlinear variation characteristic associated to the series FACTS compensation, various solutions have been proposed in the last decade. One of these proposals uses traveling waves to detect and locate faults in a transmission line (Shehab-Eldin&McLaren, 1988). As is known, after a fault in a transmission line two traveling waves are produced, this is shown if figure 11(a). The traveling wave is used to detect and locate the fault. The latter is achieved determining the time the wave needs to travel from the fault position *(FP)* to the measurement point (*M1*). Fig. 11(b), illustrates a lattice diagram of traveling waves. After the fault, the wave needs a time *t1* to travel from *FP* to *M1*. When the traveling wave reach a point at which impedance is different to characteristic impedance (*Z0*), then the wave is reflected, because of that, the wave is reflected when reach the node *A* and returns to *FP*. Once the wave reaches *FP* is reflected because the impedance at *FP* is different to *Z0* and travels again to node *A* in a time equals to *t2*. The fault is detected at time *t1* and time elapsed between *t1* and *t2* is useful to locate the fault position. This is possible because *t2-t1* has a linear relationship with distance to fault.

Fig. 11. a) Traveling waves in a faulted line; b) Laticce diagram

It's important to analyze the effects caused by FACTS on traveling wave to determine if this latter can be used to detect and locate faults at FACTS environment. Considering a controller installed at the middle of the line, if fault occurs before the position of FACTS, as illustrated in fig. 12(a), the traveling wave can be analyzed at the same way that without controller, because it don´t encounter points of different impedance to *Z0* between *FP* and *M1*. In the other hand, if fault occurs after the position of controller, as shown in Fig. 12(b), the wave encounters the FACTS when traveling from *FP* to *M1*.

Discrete Wavelet Transform Application to the Protection of Electrical

Fig. 13. Voltage in any point along the line

**4.1.1 Travelling waves and the TCSC** 

and table 1 shows its parameters.

Fig. 14. TCSC controller

Table 1. Electric Parameters

*<sup>x</sup>* represents wave traveling in negative direction and *V- e-*

in positive direction at *x* point (considering *x*=0 at node *A*), as shown in fig. 13.

If *Zx* (the impedance at *x* point) is different to *Z0*, there is a coefficient of reflection (

*<sup>x</sup> <sup>v</sup> x Z Z Z Z*

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

Parameter Value

Line voltage, infinite bus 400 kV Line length 360 km CTCSC 95 F LTCSC 8.77 mH Cfixed 98 F Z0 (considering a lossless line) 550

0 0

*V+e +*

by (6),

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 255

where is the attenuation constant , is phase constant and is a propagation constant.

*<sup>x</sup>* represents wave traveling

*<sup>v</sup>*) given

(6)

Fig. 12. Travelling waves generated after a fault at FACTS environment

The aim of subsections 4.1 and 4.2 is to show that traveling waves can be used to detect and locate faults when FACTS are installed. To demonstrate the neutrality of some seriesconnected FACTS on travelling waves, the TCSC and the SSSC are analyzed. Once the wave reaches the FACTS controller, two characteristics are evaluated: a) the effect of FACTS on magnitude of traveling wave, b) the harmonics due to FACTS.

The above are based on two hypotheses: a) the magnitude of traveling wave is not significantly affected when crossing FACTS because this latter doesn't contribute greatly to make different the impedance at location of controller to *Z0* and wave is not reflected at this point; b) the main harmonics of FACTS are the 3th , 5th and 7th (Daneshpooy&Gole, 2001; Sen, 1998 ), and discrete wavelet transform to analyze traveling wave can be adjusted to separate the harmonics from FACTS of signal due to fault, through proper selection of coefficient of detail.

#### **4.1 Effects on the magnitude of traveling waves**

To demonstrate that magnitude of traveling wave is not greatly affected when crossing the FACTS is necessary to analyze the coefficient of reflection (*v*) at the FACTS location. *v* indicates the energy of traveling wave that is reflected when reach the controller position. If impedance at FACTS location is different to *Z0* then the wave is reflected otherwise there is not reflection.

The voltage equation in any *x* point along the line for long lines is given by (Pourahmadi-Nakhli&Zafavi, 2011)

$$\upsilon\_{\chi} = \left(V\_-e^{-\gamma \chi} + V\_+e^{\gamma \chi}\right) \tag{5}$$

$$\chi^2 = \alpha + j\beta = \sqrt{(R + j\alpha L)(G + j\alpha C)}$$

where is the attenuation constant , is phase constant and is a propagation constant. *V+e +<sup>x</sup>* represents wave traveling in negative direction and *V- e- <sup>x</sup>* represents wave traveling in positive direction at *x* point (considering *x*=0 at node *A*), as shown in fig. 13.

Fig. 13. Voltage in any point along the line

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

Fig. 12. Travelling waves generated after a fault at FACTS environment

magnitude of traveling wave, b) the harmonics due to FACTS.

**4.1 Effects on the magnitude of traveling waves** 

FACTS is necessary to analyze the coefficient of reflection (

2 

detail.

not reflection.

Nakhli&Zafavi, 2011)

The aim of subsections 4.1 and 4.2 is to show that traveling waves can be used to detect and locate faults when FACTS are installed. To demonstrate the neutrality of some seriesconnected FACTS on travelling waves, the TCSC and the SSSC are analyzed. Once the wave reaches the FACTS controller, two characteristics are evaluated: a) the effect of FACTS on

The above are based on two hypotheses: a) the magnitude of traveling wave is not significantly affected when crossing FACTS because this latter doesn't contribute greatly to make different the impedance at location of controller to *Z0* and wave is not reflected at this point; b) the main harmonics of FACTS are the 3th , 5th and 7th (Daneshpooy&Gole, 2001; Sen, 1998 ), and discrete wavelet transform to analyze traveling wave can be adjusted to separate the harmonics from FACTS of signal due to fault, through proper selection of coefficient of

To demonstrate that magnitude of traveling wave is not greatly affected when crossing the

indicates the energy of traveling wave that is reflected when reach the controller position. If impedance at FACTS location is different to *Z0* then the wave is reflected otherwise there is

The voltage equation in any *x* point along the line for long lines is given by (Pourahmadi-

( ) *x x <sup>x</sup> v Ve Ve* 

*j R jLG jC* ( )( )

 

  (5)

  *v*) at the FACTS location.

*v* If *Zx* (the impedance at *x* point) is different to *Z0*, there is a coefficient of reflection (*<sup>v</sup>*) given by (6),

$$
\rho\_v = \frac{Z\_\chi - Z\_0}{Z\_\chi + Z\_0} \tag{6}
$$
