Discrete Wavelet Transform Application to the Protection of Electrical Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment

The Wavelet Transform has been widely used to process signals in engineering and sciences areas. This acceptance is rooted on its proven capability to analyze fast transients signals which is difficult to perform with the FFT. In the area of electrical engineering, a number of publications have been presented about the analysis of phenomena in electrical grid at medium and high voltage levels. Some solutions have focused on the power quality (ChiaHungC Tse, 2006), short-term load forecasting (Chen, 2010) and protection of power systems (KashyapS Ning&Gao, 2009). However, there are few contributions in the open literature focusing in using WT for implementing relaying protection algorithms in power grids with presence of FACTS. The Thyristor Controlled Series Capacitor (TCSC), the Universal Power Flow Controller (UPFC), the Static Synchronous Series Compensator (SSSC), and the Statcom are some of the power controllers developed under the umbrella name of “Flexible AC Transmission Systems” (FACTS). These devices play a key role in nowadays electrical networks because they have the capability of improving the operation and control of power networks (power transfer, transient stability among others characteristics). Collateral to their many strong points, the FACTS controllers also have secondary effects on the grid that should be taken into account for engineering the next generation of protection schemes.


Introduction
The Wavelet Transform has been widely used to process signals in engineering and sciences areas. This acceptance is rooted on its proven capability to analyze fast transients signals which is difficult to perform with the FFT. In the area of electrical engineering, a number of publications have been presented about the analysis of phenomena in electrical grid at medium and high voltage levels. Some solutions have focused on the power quality (Chia-Hung&Chia-Hao, 2006;Tse, 2006), short-term load forecasting (Chen, 2010) and protection of power systems (Kashyap&Shenoy, 2003;Ning&Gao, 2009). However, there are few contributions in the open literature focusing in using WT for implementing relaying protection algorithms in power grids with presence of FACTS. The Thyristor Controlled Series Capacitor (TCSC), the Universal Power Flow Controller (UPFC), the Static Synchronous Series Compensator (SSSC), and the Statcom are some of the power controllers developed under the umbrella name of "Flexible AC Transmission Systems" (FACTS). These devices play a key role in nowadays electrical networks because they have the capability of improving the operation and control of power networks (power transfer, transient stability among others characteristics). Collateral to their many strong points, the FACTS controllers also have secondary effects on the grid that should be taken into account for engineering the next generation of protection schemes.
In power grids, -transmission lines included-, there are three-phase, two-phase and singlephase fault events. At fault occurrence of any type, a fast transient signal, named travelling wave-, is produced and propagates through the power lines. The travelling waves are helpful in determining the fault location in such line, faster than using other methods, if the appropriate tools are used.
This chapter presents the application of the Discrete Wavelet Transform (DWT) for extracting information from the travelling waves in transmission line and separate such waves from the signals associated to the TCSC and SSSC. This signal discrimination is useful to improve protections algorithms.
The chapter also presents a brief description of DWT in section 2 and includes a review of FACTS controllers in section 3. Section 4 presents the procedure to separate the effects of power electronic controller. Finally, sections 5 and 6 present the system under test and the results in locating faults in power lines.

Wavelet Transform
The Wavelet Transform (WT) is a tool highly precise for analyzing transient signal. The WT is obtained from the convolution of the signal under analysis, f (t), with a wavelet, both related to the coefficients C as shown in (1 where  is the "mother" wavelet, is so named because it belongs a "family" of special The WT produces a time-scale space. In the wavelet context, "scaling" means "stretching" or "compressing" a signal, as shown if fig. 1. In this way, scaling is related to frequency, meaning this that the smaller the scale factor, the more "compressed" the wavelet, i.e. smaller scale factors are corresponding with high frequencies. In the other hand, the term "position" is referred to shifting the wavelet, this is delaying or advancing the signal, as shown if fig 2. (t-) is delayed  seconds of (t).
www.intechopen.com Due to the easiness to modify the scale-position parameters, the wavelet analysis enables (Misiti, 2001): 1. The use of long time intervals where more precise low-frequency information is needed 2. Shorter regions where high-frequency information is needed. 3. To perform local analysis, that is, to analyze a localized area of a larger signal.
If a subset of scales and positions is taken under consideration instead a large number of coefficients then the analysis can be performed more efficiently. Scales and positions based on power of 2 (known as dyadic) are the common selection. The analysis performed under the aforementioned consideration is named Discrete Wavelet Transform (DWT), because is referred to discrete values.
In the DWT process, the input signal is filtered and sampled down. This processing keeps all valuable information complete but reduces the number of data needed. Two data sequences are obtained once the procedure is perform: Approximations (cAn) and Details (cDn). The former are the high-scale, low-frequency components of the signal and latter are the lowscale, high-frequency components. Both correspond to DTW coefficients, as shown in fig. 3. After filtering the signal is left down sampled but keeping complete information  (2) (Misiti et. al. 2001) where cA 1 , is the approximation coefficient of level 1, cD 1 is the detail coefficient of level 1. L d is the low-pass filter and H d is the high-pass filter. These filters are related to mother wavelet . In this process, signal f(t) is divided in two sequences, cD 1 contains highest frequency components (f s /4 to f s /2 range, where f s equals sampling frequency of f(t)) and cA 1 lower frequencies (lower than f s /4). At this stage, cD 1 extract elements of f(t) in f s /4 to f s /2 range that maintains correlation with .
As aforesaid, the initial decomposition of signal f(t) is the level 1 for Approximations (cA 1 ) and Details (cD 1 ). This cA 1 can in turn be divided in two sequences of Approximations and Details and then a new level of decomposition is obtained (cA 2 and cD 2 ). This procedure is repeated until the required level for the application is reached, as shown in fig. 4. Of course, cA 2 and cD 2 are obtained from cA 1 after to pass a filter and sampling down stage.
In this way, sequences cD 1 , cD 2 , … cD n relates f(t) to  at different scales, i.e. different frequency ranges.
(2) can be extended for higher levels cD and cA, as shown in (3)

Flexible AC Transmission Systems (FACTS)
In this section, a brief description of series and shunt FACTS controllers is presented with emphasis on the TCSC and SSSC.
The FACTS controllers, once installed in the power grid, helps to improve the power transfer capability of long transmission lines and the system performance in general. Some of the benefits of the FACTS controllers on the electric system: 1. Series Controller. These controllers are series connected to a power line. These controllers have an impact on the power flow and voltage profile. Examples of these controllers are the SSSC and TCSC. 2. Shunt Controllers. These controllers are shunt connected and are designed to inject current into the system at the point of connection. An example of these controllers is the Static Synchronous Compensator (STATCOM). 3. Series-shunt controllers. These controllers are a combination of serial and shunt controllers. This combination is capable of injecting current and voltage. An example of these controllers is the Unified Power Flow Controller (UPFC). 4. Series-series controllers. These controllers can be a combination of separate series controllers in a multiline transmission system, or it can be a single controller in a single line. An example of such devices is the Interline Power Flow Controller (IPFC) The STATCOM, the TCSC and the SSCC are three of the FACTS controllers highlighted by their capacity to provide a wide range of solutions for both normal and abnormal conditions. Figures 5 to 7 illustrates the STATCOM, TCSC and SSSC structures and its network connection.

Fig. 5. STATCOM
The STATCOM is a voltage-source converter (VSC) based controller which maintains the bus voltage by injecting an ac current through a transformer. The TCSC is made of a series capacitor (C TCSC ) shunted by a thyristor module in series with an inductor (L TCSC ). An external fixed capacitor (C FIXED ) 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 state impedance of TCSC (X TCSC ) is (4) where  is the firing angle of thyristor. The SSSC injects a voltage in series with the transmission line in quadrature with the line current. The SSSC increases or decreases the voltage across the line, and thereby, for controlling the transmitted power.

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
Before the fault occurs, the relay (R) measures voltage and current at node A and calculate the total impedance of line (Z LINE ). When fault occurs at fault point (FP), the impedance measured by R is lower than Z LINE (Z FP < Z LINE ) 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).  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.

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 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 (M 1 ). Fig. 11(b), illustrates a lattice diagram of traveling waves. After the fault, the wave needs a time t 1 to travel from FP to M 1 . When the traveling wave reach a point at which impedance is different to characteristic impedance (Z 0 ), 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 Z 0 and travels again to node A in a time equals to t 2 . The fault is detected at time t 1 and time elapsed between t 1 and t 2 is useful to locate the fault position. This is possible because t 2 -t 1 has a linear relationship with distance to fault. 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 Z 0 between FP and M 1 . 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 M 1 . 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 Z 0 and wave is not reflected at this point; b) the main harmonics of FACTS are the 3 th , 5 th and 7 th (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.

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 Z 0 then the wave is reflected otherwise there is not reflection.
where  is the attenuation constant ,  is phase constant and  is a propagation constant.
V+e + x represents wave traveling in negative direction and Ve - x 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

Travelling waves and the TCSC
Considering x point matches with FACTS location, then impedance at this point is given by contribution of Z 0 and impedance of TCSC. Fig. 14 fig. 11, the impedance at FACTS location is given by (7) 00 11 () () ( ) The coefficient of reflection seen at discontinuity is obtained by substituting (7) in (6) Because the capacitor opposes to abrupt changes in voltage, the wave tends to pass through the TCSC without a significant decrement. From (6) 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 In this case, L TCSC = 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.

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 (X L ) (Sen, 1998  v is obtained substituting (11) in (6) www.intechopen.com Due the transformer was selected to work as a coupling instrument, X L is enough small to give a  v near to zero. So, the magnitude of incident wave is no significantly affected by SSSC. In the present case X L = wL= (2) (60) 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.

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 3 th and 5 th (Daneshpooy&Gole, 2001) 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 3 th , 5 th and 7 th , which are present at 180 to 420 Hz (Sen, 1998). From table 2, this signal can be analyzed with cD 4 and cD 5 , 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 M 1 , as illustrated in fig. 20. The fault occurs at 0.3 s. Two cases are considered: a) without SSSC and b) with SSSC. Fig. 20. Three phase to ground fault at 300 km.
As expected, the harmonics due to controller are present with cD 4 and cD 5 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)).

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 www.intechopen.com position (FP) to measurement point (M 1 ); b) Based on subsection 4.2, harmonics due to FACTS don't affect the measurement of traveling wave at M 1 , when cD 1 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 cD 1 obtained of signals from M 1 .

Fig. 22. Procedure to extract the Coefficients of Details
When the voltage signal from M 1 is decomposed in cA 1 and cD 1 , cD 1 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. Protection relay located at M 1 is continuously monitoring the instant value of voltages V A , V B and V C , in this way, cD 1 is being monitored. If fault is not present, then the only signal monitored by M 1 is the fundamental signal of 60 Hz, as shown in fig. 24 (a). In this case, cD 1 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 M 1 , as illustrated in fig. 24 (b), the transient signal generated by the fault travels across the transmission line and reaches the protection relay, the value of cD, exceeds a threshold value (cD TH ), because the transitory signal due to fault is situated within the range measured by cD 1 , then the system detects the Fault and the value of time of fault is stored (t fd =t).

Fig. 24. Signals monitored by M 1 , before and after a fault
Once the wave reaches the M 1 position, it is reflected to FP, because the impedance at this point is different to Z 0 . Because the impedance of FP is different to Z 0 , the wave is reflected again to M 1 , as shown in fig. 25.

System under study
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 M 1 are presented. Figure 26 shows the power grid used for the study cases. 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 M 1 .

Results
As presented in section 4, traveling waves were no significantly affected by presence of FACTS if cD 1 is selected. Following the procedure showed in section 4, cD 1A , cD 1B , cD 1C , were employed to detect and locate faults. Ten different types of fault were considered to simulation:  Figure 29 shows cD 1 obtained for a fault of type ABCG at 240 km from M 1 and t = 0.3 s. As can be notice, cD 1A , cD 1B , and cD 1C appear at 0.3008 s. In this way the fault event can be detected with any cD 1 . The magnitude differences among cD 1A , cD 1B , and cD 1C is endorsed to the inception angle of fault, i.e. the value of V A (tx), V B (tx) or V C (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 M 1 . This is the reason for the delay of time in which cD 1 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 www.intechopen.com at 0.3 s and is located at 240 km. These is obtained using (13) 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 M 1 Fig. 30. System used to simulate 6 different locations of faults.
Once the simulation is initiated, voltages values of V A , V B and V C are fed to MATLAB. This latter, develop the algorithm of subsection 4.3 and the result is shown in fig. 31 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 AG  BG  CG  ABG BCG ACG ABCG  AB  BC  AC   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  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. The relationship of the time elapsed between first and second traveling waves (t elap =t fl -t fd ), 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 t elap 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 t elap , the distance to fault is easily obtained with (13). 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 cD 1 , obtained before and after a fault occurs in t=0.3 s at 240 km from M 1 The use of the wavelet transform to analyze the behaviour of the complex systems from various fields started to be widely recognized and applied successfully during the last few decades. In this book some advances in wavelet theory and their applications in engineering, physics and technology are presented. The applications were carefully selected and grouped in five main sections -Signal Processing, Electrical Systems, Fault Diagnosis and Monitoring, Image Processing and Applications in Engineering. One of the key features of this book is that the wavelet concepts have been described from a point of view that is familiar to researchers from various branches of science and engineering. The content of the book is accessible to a large number of readers.

How to reference
In order to correctly reference this scholarly work, feel free to copy and paste the following: Enrique Reyes-Archundia, Edgar L. Moreno-Goytia, Jose Antonio Gutierrez-Gnecchi and Francisco Rivas-Davalos (2012). Discrete Wavelet Transform Application to the Protection of Electrical Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment, Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology, Dr. Dumitru Baleanu (Ed.), ISBN: 978-953-51-0494-0, InTech, Available from: http://www.intechopen.com/books/advances-in-wavelet-theory-and-theirapplications-in-engineering-physics-and-technology/discrete-wavelet-transform-application-to-the-protectionof-electrical-power-system-a-solution-appro