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

Enrique Reyes-Archundia, Edgar L. Moreno-Goytia, José Antonio Gutiérrez-Gnecchi and Francisco Rivas-Dávalos *Instituto Tecnológico de Morelia, Morelia, Michoacán, México* 

#### **1. Introduction**

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

Wang, L.; Dong, L.; Hao, Y. & Liao, X. (2009). Wind Power Prediction Using Wavelet

Yao, S.J.; Song, Y.H.; Zhang, L.Z. & Cheng, X.Y. (2000). Wavelet Transform and Neural

*Management*, Vol.41, No.18, (December 2000), pp. 1975-1988, ISSN 0196-8904 Yu, I.-K.; Kim, C.-I. & Song, Y.H. (2000). A Novel Short-Term Load Forecasting Technique

Zhang, H., Blackburn, T.R., Phung, B.T., & Liu, Z. (2004). Signal Processing of On-Line

Zhang, H., Blackburn, T.R., Phung, B.T., & Liu, Z. (2004). Application of Signal Processing

Zhen, R.; Qungu, H.; Lin, G. & Wenying, H. (2000). A New Method for Power Systems

2009

26-29, 2004

No.6, pp. 537–549, ISSN 1532-5008

Singapore, November 21-24, 2004

30/November 01, 2000

Transform and Chaotic Characteristics, *World Non-Grid-Connected Wind Power and Energy Conference (WNWEC)*, pp. 1-5, ISBN 978-1-4244-4702-2, September 24-26,

Networks for Short-Term Electrical Load Forecasting. *Energy Conversion and* 

Using Wavelet Transform Analysis. *Electric Machines and Power Systems*, Vol.28,

Partial Discharges Measurements in HV Power Cables, *Australasian Universities Power Engineering Conference*, ISBN 1-864-99775-3, Brisbane, Australia, September

Techniques to On-Line Partial Discharge Detection in Cables, *2004 International Conference on Power System Technology*, pp. 1780-1785, ISBN 0-7803-8610-8,

Frequency Tracking Based on Trapezoid Wavelet Transform, *International Conference on Advances in Power System Control, Operation and Management (APSCOM)*, Vol. 2, pp. 364–369, ISBN 0-85296-791-8, Hong Kong, October

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.

#### **2. 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)

$$\mathcal{C}\{scale\_{\prime}position\} = \bigcap\_{\rightarrow}^{\Rightarrow} f(t)\Psi(scale\_{\prime}position\_{\prime}t)dt\tag{1}$$

Discrete Wavelet Transform Application to the Protection of Electrical

2. Shorter regions where high-frequency information is needed.

Fig. 2. Shifting the wavelet signal

referred to discrete values.

Fig. 3. Discrete Wavelet Transform

(Misiti, 2001):

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 247

Due to the easiness to modify the scale-position parameters, the wavelet analysis enables

1. The use of long time intervals where more precise low-frequency information is needed

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

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 (*cA*n) and Details (*cD*n). 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.

3. To perform local analysis, that is, to analyze a localized area of a larger signal.

After filtering the signal is left down sampled but keeping complete information

where is the "mother" wavelet, is so named because it belongs a "family" of special wavelets to compare with *f(t)*. Examples of wavelets families are: Haar, Daubechies, Symlets, Mexican Hat, Meyer, Discrete Meyer. is selected to analyze a unknown portion of signal using convolution, i.e. the wavelet transform can detect if the analyzed signal is closely correlated with under a determined scale and position.

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.

Fig. 1. Scaling the wavelet signal

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)*.

Fig. 2. Shifting the wavelet signal

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

The Wavelet Transform (WT) is a tool highly precise for analyzing transient signal. The WT

*C scale position f t scale position t dt* , ( ) (, , ) 

wavelets to compare with *f(t)*. Examples of wavelets families are: Haar, Daubechies,

of signal using convolution, i.e. the wavelet transform can detect if the analyzed signal is

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.

In the other hand, the term "position" is referred to shifting the wavelet, this is delaying or

*)* is delayed

seconds of

*(t)*.

*(t-*

under a determined scale and position.

is the "mother" wavelet, is so named because it belongs a "family" of special

(1)

is selected to analyze a unknown portion

, both

is obtained from the convolution of the signal under analysis, *f* (*t*), with a wavelet

results in locating faults in power lines.

related to the coefficients *C* as shown in (1)

Symlets, Mexican Hat, Meyer, Discrete Meyer.

smaller scale factors are corresponding with high frequencies.

**2. Wavelet Transform** 

where

closely correlated with

Fig. 1. Scaling the wavelet signal

advancing the signal, as shown if fig 2.

Due to the easiness to modify the scale-position parameters, the wavelet analysis enables (Misiti, 2001):


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 (*cA*n) and Details (*cD*n). 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

Fig. 3. Discrete Wavelet Transform

*cA1* and *cD1* are obtained by (2) (Misiti et. al. 2001)

$$\begin{aligned} cA\_1(t) &= \sum\_k f(t)L\_d(k-2t) \\ cD\_1(t) &= \sum\_k f(t).H\_d(k-2t) \end{aligned} \tag{2}$$

Discrete Wavelet Transform Application to the Protection of Electrical

of the benefits of the FACTS controllers on the electric system:

2. Increased power transfer over long AC lines, 3. Damping of active power oscillations, and 4. Load flow control in meshed systems,

controllers are the SSSC and TCSC.

Static Synchronous Compensator (STATCOM).

these controllers is the Unified Power Flow Controller (UPFC).

1. Fast voltage regulation,

network connection.

Fig. 5. STATCOM

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 249

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

The FACTS controllers are commonly divided in 4 groups (Hingorani&Gyugyi, 2000):

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

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

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

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

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

The STATCOM is a voltage-source converter (VSC) based controller which maintains the

bus voltage by injecting an ac current through a transformer.

line. An example of such devices is the Interline Power Flow Controller (IPFC)

where *cA1*, is the approximation coefficient of level 1, *cD1* is the detail coefficient of level 1. *Ld* is the low-pass filter and *Hd* is the high-pass filter. These filters are related to mother wavelet . In this process, signal *f(t)* is divided in two sequences, *cD1* contains highest frequency components (*fs*/4 to *fs*/2 range, where *fs* equals sampling frequency of *f(t)*) and *cA1* lower frequencies (lower than *fs*/4). At this stage, *cD1* extract elements of *f(t)* in *fs*/4 to *fs*/2 range that maintains correlation with .

As aforesaid, the initial decomposition of signal *f(t)* is the level 1 for Approximations (*cA1*) and Details (*cD1*). This *cA1* can in turn be divided in two sequences of Approximations and Details and then a new level of decomposition is obtained (*cA2* and *cD2*). This procedure is repeated until the required level for the application is reached, as shown in fig. 4.

Fig. 4. Wavelet decomposition tree.

Of course, *cA2* and *cD2* are obtained from *cA1* after to pass a filter and sampling down stage. In this way, sequences *cD1*, *cD2,* … *cDn* 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)

$$\begin{aligned} cA\_{n+1}(t) &= \sum\_{k} cA\_{n}(t)L\_{d}(k-2t) \\ cD\_{n+1}(t) &= \sum\_{k} cA\_{n}.H\_{d}(k-2t) \end{aligned} \tag{3}$$

#### **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. Fast voltage regulation,

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

( ) ( ). ( 2 )

*cA t f t L k t*

*cD t f t H k t*

where *cA1*, is the approximation coefficient of level 1, *cD1* is the detail coefficient of level 1. *Ld* is the low-pass filter and *Hd* is the high-pass filter. These filters are related to mother

frequency components (*fs*/4 to *fs*/2 range, where *fs* equals sampling frequency of *f(t)*) and *cA1* lower frequencies (lower than *fs*/4). At this stage, *cD1* extract elements of *f(t)* in *fs*/4 to

As aforesaid, the initial decomposition of signal *f(t)* is the level 1 for Approximations (*cA1*) and Details (*cD1*). This *cA1* can in turn be divided in two sequences of Approximations and Details and then a new level of decomposition is obtained (*cA2* and *cD2*). This procedure is

Of course, *cA2* and *cD2* are obtained from *cA1* after to pass a filter and sampling down stage.

( ) ( ). ( 2 )

() . ( 2)

frequency ranges. (2) can be extended for higher levels *cD* and *cA*, as shown in (3)

*n nd k n n d k*

*cA t cA t L k t*

*cD t cA H k t*

In this section, a brief description of series and shunt FACTS controllers is presented with

1

1

at different scales, i.e. different

(3)

*k*

*k*

.

repeated until the required level for the application is reached, as shown in fig. 4.

*d*

*d*

. In this process, signal *f(t)* is divided in two sequences, *cD1* contains highest

(2)

( ) ( ). ( 2 )

1

1

*cA1* and *cD1* are obtained by (2) (Misiti et. al. 2001)

*fs*/2 range that maintains correlation with

Fig. 4. Wavelet decomposition tree.

emphasis on the TCSC and SSSC.

In this way, sequences *cD1*, *cD2,* … *cDn* relates *f(t)* to

**3. Flexible AC Transmission Systems (FACTS)** 

wavelet


The FACTS controllers are commonly divided in 4 groups (Hingorani&Gyugyi, 2000):


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.

Discrete Wavelet Transform Application to the Protection of Electrical

**3.1 FACTS effects on conventional protection schemes** 

controlling the transmitted power.

related to this impedance.

Fig. 8. Distance Relay

and node A.

Power System: A Solution Approach for Detecting and Locating Faults in FACTS Environment 251

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

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

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*

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).

Fig. 6. TCSC

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

$$X\_{\rm TCSC}(a) = \frac{X\_{\rm CTSCSC} X\_{\rm LTSCSC}(a)}{X\_{\rm LTSCC}(a) - X\_{\rm CTSCC}}\tag{4}$$

Where

$$X\_{LT\text{SCSC}}(\alpha) = X\_{LT\text{SCSC}} \frac{\pi}{\pi - 2\alpha - \sin \alpha}, \\ X\_{LT\text{SCSC}} < X\_{LT\text{SCSC}}(\alpha) \le \infty$$

where is the firing angle of thyristor.

Fig. 7. SSSC

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.
